Chemometric and methods for real time monitoring and modeling using acoustic sensors Applications in the pulp and paper industry

Anders Björk

Doctorial Thesis School of Chemical Science and Engineering Department of Division of

Stockholm 2007

Akademisk avhandling som med tillstånd av Kungliga Tekniska Högskolan i Stockholm framlägges till offentlig granskning för avläggande av teknologie doktorsexamen, fredag den 1 Juni, 2007, kl 13.00 i sal K1, Teknikringen 56, KTH, Stockholm. Avhandlingen försvaras på engelska.

Chemometric and signal processing methods for real time monitoring and modeling using acoustic sensors. Applications in the pulp and paper industry PhD Thesis © Anders Björk, 2007 ISBN 978-91-7178-679-1 TRITA-CHE-Report 2007:33 ISSN 1654-1081

Royal Institute of Technology School of Chemical Science and Engineering Department of Chemistry Division of Analytical Chemistry SE-100 44 Stockholm Sweden

NOTE: This on-line version has some figures removed due to that some material is unpublished (and is aimed to be published) and others are removed for copyright reason for publishing on-line, compared to the printed version.

A paper copy can be obtained from the author on request on these figures. By email to [email protected] or [email protected] write "Thesis Figures" in the subject.

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Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry Anders Björk, Royal Institute of Technology, School of Chemical Science and Engineering, Department of Chemistry, Division of Analytical Chemistry. Written in English. © Anders Björk, 2007 In the production of paper, the quality of the pulp is an important factor both for the productivity and for the final quality. Reliable real-time measurements of pulp quality are therefore needed. One way is to use acoustic or vibration sensors that give information-rich signals and place the sensors at suitable locations in a pulp production line. However, these sensors are not selective for the pulp properties of interest. Therefore, advanced signal processing and multivariate calibration are essential tools. The current work has been focused on the development of calibration routes for extraction of information from acoustic sensors and on signal processing algorithms for enhancing the information-selectivity for a specific pulp property or class of properties. Multivariate analysis methods like Principal Components Analysis (PCA), Partial (PLS) and Orthogonal Signal Correction (OSC) have been used for visualization and calibration. Signal processing methods like Fast Fourier Transform (FFT), Fast Transform (FWT) and Continuous Wavelet Transform (CWT) have been used in the development of novel signal processing algorithms for extraction of information from vibration- acoustic sensors.

It is shown that use of OSC combined with PLS for prediction of Canadian Standard Freeness (CSF) using FFT-spectra produced from vibration on a Thermo Mechanical Pulping (TMP) process gives lower prediction errors and a more parsimonious model than PLS alone. The combination of FFT and PLS was also used for monitoring of beating of kraft pulp and for screen monitoring. When using regular FFT-spectra on process acoustic data the obtained information tend to overlap. To circumvent this two new signal processing methods were developed: Wavelet Transform Multi Resolution Spectra (WT-MRS) and Continuous Wavelet Transform Fibre Length Extraction (CWT-FLE). Applying WT-MRS gave PLS-models that were more parsimonious with lower prediction error for CSF than using regular FFT-Spectra. For a Medium Consistency (MC) pulp stream WT-MRS gave predictions errors comparable to the reference methods for CSF and Brightness. The CWT-FLE method was validated against a commercial fibre length analyzer and good agreement was obtained. The CWT-FLE-curves could therefore be used instead of other fibre distribution curves for process control. Further, the CWT-FLE curves were used for PLS modelling of tensile strength and optical parameters with good results. In addition to the mentioned results a comprehensive overview of technologies used with acoustic sensors and related applications has been performed.

Keywords: Acoustic, Vibration, Multivariate, Chemometrics, PLS, OSC, PCA, FFT, , WT-MRS, CWT-FLE, Pulp Quality, CSF, Brightness, Tensile Strength properties, Optical Properties, Measurement Technology, On-line, Non-invasive, Process Control, Process Analysis, Process Analytical Technology, PAT.

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Kemometriska metoder och signalbehandling för realtids- monitorering och modellering baserad på signaler från akustiska sensorer. Tillämpningar i massa- och pappersindustrin. Anders Björk, Kungl. Tekniska Högskolan, Skolan för kemivetenskaperna., Institution Kemi, Avdelningen för Analytisk kemi. Skriven på Engelska. © Anders Björk, 2007

Vid framställning av pappersprodukter är kvaliteten på massan en viktig faktor för produktiviteten och kvalitén på slutresultatet. Det är därför viktigt att ha tillgång till tillförlitliga mätningar av massakvalitet i realtid. En möjlighet är att använda akustik- eller vibrationssensorer i lämpliga positioner vid enhetsoperationer i massaprocessen. Selektiviteten hos dessa mätningar är emellertid relativt låg i synnerhet om mätningarna är passiva. Därför krävs avancerad signalbehandling och multivariat kalibrering. Det nu presenterade arbetet har varit fokuserat på kalibreringsmetoder för extraktion av information ur akustiska mätningar samt på algoritmer för signalbehandling som kan ge förbättrad informationsselektivitet. Multivariata metoder som Principal Component Analysis (PCA), Partial Least Squares (PLS) and Orthogonal Signal Correction (OSC) har använts för visualisering och kalibrering. Signalbehandlingsmetoderna Fast Fourier Transform (FFT), Fast Wavelet Transform (FWT) och Continuous Wavelet Transform (CWT) har använts i utvecklingen av nydanande metoder för signalbehandling anpassade till att extrahera information ur signaler från vibrations/akustiska sensorer. En kombination av OSC och PLS applicerade på FFT-spektra från raffineringen i en Termo Mechnaical Pulping (TMP) process ger lägre prediktionsfel för Canadian Standard Freeness (CSF) än enbart PLS. Kombinationen av FFT och PLS har vidare använts för monitorering av malning av sulfatmassa och monitorering av silning. Ordinära FFT-spektra av t.ex. vibrationssignaler är delvis överlappande. För att komma runt detta har två signalbehandlingsmetoder utvecklats, Wavelet Transform Multi Resolution Spectra (WT-MRS) baserat på kombinationen av FWT och FFT samt Continuous Wavelet Transform Fibre Length Extraction (CWT-FLE) baserat på CWT. Tillämpning av WT-MRS gav enklare PLS-modeller med lägre prediktionsfel för CSF jämfört med att använda normala FFT-spektra. I en annan tillämpning på en massaström med relativt hög koncentration (Medium Consistency, MC) kunde prediktioner för CSF samt ljushet erhållas med prediktionsfel jämförbart med referensmetodernas fel. Metoden CWT-FLE validerades mot en kommersiell fiberlängdsmätare med god överensstämmelse. CWT-FLE-kurvorna skulle därför kunna användas i stället för andra fiberdistributionskurvor för processtyrning. Vidare användes CWT-FLE kurvor för PLS modellering av dragstyrka samt optiska egenskaper med goda resultat. Utöver de nämnda resultaten har en omfattande litteratursammanställning gjorts över området och relaterade applikationer.

Nyckelord: Akustik, Vibrationer, Multivariat, Kemometri, PLS, OSC, PCA, FFT, Wavelets, WT-MRS, CWT- FLE, Massakvalitet, CSF, Ljushet, Dragstyrkeegenskaper, Optiska egenskaper, Mätteknik, On- line, Icke berörande mätning, Processtyrning, Processanalys, Processanalytisk Teknologi, PAT.

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Populärvetenskaplig sammanfattning

Detta arbete behandlar hur man genom att lyssna på rör i pappersmassafabriker kan få reda på vilken kvalitet det är på massan. Metoderna för att få värdefull information ifrån ljudet bygger på två huvudprinciper. I den första försöker man att få så god information som möjlig genom att använda transformer, dvs avbildningar från en form till en annan. De transformer som har används i avhandlingen heter Fourier transform samt Wavelets (Krusningar). De visar på olika sätt hur ofta liknande vågor uppträder i tiden och ofta återkommande de är, deras frekvens. Ett försök till att förklara hur dessa två metoder har använts i arbetet: Förenklat kan man säga att det fungerar som en oljemålning av ett landskap. Detta är en avbildning med möjligheter där man kan välja att framhäva och undertrycka aspekter av ett landskap mer eller mindre. Den andra metoden bygger på att använda informationen från ett antal landskapsbilder tillsammans med en egenskap förekommande i landskap t.ex. hur stor yta som består av vattendrag. Detta för att bygga en matematisk modell från en landskapsbild som visar hur stor vattenytan är. Detta för att man ska kunna ta en ny landskapsbild och direkt få ett värde på vattenytans storlek. Det matematiska verktyg som används för att göra dessa modeller heter Partial Least Squares, PLS. Den bygger på att man bara försöker anpassa de delar av landskapsbilderna som är relevanta för vattenytans storlek och inte använda all information som är tillgänglig. Vi kallar detta att kalibrera modellen, sedan testar man hur bra och användbar modellen är i ett moment som kallas validering.

I denna avhandling har utveckling av metoder för att använda ljudmätningar på rör med strömmande pappersmassa utförts genom att: Hitta en beskrivning av massakvaliteten genom en avbildning av det insamlade ljuden eller i kombination med data på massakvalitet bygga modeller som kopplar samman ljudavbildningarna och kvalitet. Metoden ska därefter kunna tillämpas för att producera en avbildningen av ljudet vid ett tillfälle och sedan använda avbildningen själv eller i kombination med modellen för att få ett värde på massakvaliteten i produktionsögonblicket (just nu dvs i realtid).

Allt detta kan sammanfattas med att gammalt uttryck inom massaindustri “Massan Ho blir” dvs man trodde massakvaliteten blir lite hursomhelst, något som kanske var sant för 40-50 år sedan. Men knappast med dagens kunskapsläget och instrumenteringsnivå. Genom detta arbete kan tilläggas "Men låter Ho olika beroende på hur Ho blitt till!". Man kan nu förstå av vad några “tonerna” och de små “stroferna” innebär även om mycket arbete återstår.

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List of symbols

Here symbols used within chemometrics and multivariate are explained, in addition to descriptions given in the text. All other symbols are described when they first appear in the text.

Name Description Dimensions and other information lv No. of latent A scalar for the number of principal components or variables partial least squares components. Context dependent. X Data matrix m rows and n columns. The convention in chemometrics is that rows are objects and columns are variables. T Scores matrix m rows and lv columns. P Loadings matrix n rows and lv columns. E Residuals matrix m rows and n columns, same dimension as X (Using PCA, PCR or PLS) Y Data matrix m rows and p columns. U Y-Scores m rows and lv columns. (PLS) Q Y-Loadings p rows and lv columns. (PLS) F Residuals matrices m rows and k columns, same dimension as Y. (Using PLS or PCR) G Residual matrix 1 row and lv columns (for inner relation in PLS) m, n, k Indices and p A, B, C X-Loadings in m rows and lv columns, lv rows and n columns resp. lv NPLS rows and k columns.

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Abbreviations

ADC Analogue to Digital Converter AE Acoustic Emission BP Band Pass Filter CSF Canadian Standard Freeness CWT Continuous Wavelet Transform DAC Digital to Analogue Converter or Direct Acoustometry (Context dependent) DCS Distributed Control System FFT Fast Fourier Transform FWT Fast Wavelet Transform or Forward Wavelet Transform HP High Pass Filter LP Low Pass Filter lv Latent Variables (Number) same as PC LWC Light Weight Coated MC Medium Consistency MPCA Multiway Principal Component Analysis MRA Multi Resolution Analysis MRS Multi Resolution Spectra NIPALS Non-linear Iterative Partial Alternating Least Squares NN Neural Net N-PLS Multilinear Partial Least Squares Regression PARAFAC Parallell PC Principal Component or Partial Least Squares Component (Context dependent) PCA Principal Component Analysis PLS(R) Partial Least Squares sometimes with a clarifying R for Regression. Also called Projection to Latent Structures RMSEP Root Square Error of Prediction RRm Reject Ratio by Mass RRv Reject Ratio by Volume SR Schopper Riegler Number SVD Singular Value Decomposition TMP Thermo Mechanical Pulp WRV Water Retention Value WT Wavelet Transform

x List of papers

Papers included in their order of appearance in the summary of papers

I. Applied Real-Time Acoustic Chemometrics for Measurements of Canadian Standard Freeness A Björk, L-G Danielsson and A Gannå Paperi ja Puu - Paper and Timber 87 (2005), 452-457 II. Pulp Quality And Performance Indicators For Pressure Screens Based On Process Acoustic Measurements A Björk and L-G Danielsson, Manuscript. III. Spectra of wavelet scale coefficients from process Acoustic Measurements as input for PLS modelling of pulp quality A Björk and L-G Danielsson Journal of Chemometrics. 16 (2002), 521-528 IV. Predicting Pulp Quality from Process Acoustic Measurements on a Medium Concistency Pulp Stream A Björk and L-G Danielsson JPAC, Journal of Process Analytical Chemistry. 10-1(2006), 1-5 V. Extraction of Distribution Curves from Process Acoustic Measurements on a TMP- Process A Björk and L-G Danielsson, Pulp and Paper Canada 105 No.11 (2004), T260-T264 VI. Modeling of Pulp Quality Parameters from Distribution Curves Extracted from Process Acoustic Measurements on a Thermo Mechanical Pulp (TMP) Process A Björk and L-G Danielsson Chemometrics and Intelligent Laboratory Systems 85(1)(2006), 63-69

An early version of paper I was presented as poster on International Mechanical Pulping Conference 2001. Early versions of paper II & III were presented as oral presentations at Control System 2002 Conference. Paper IV was presented as an oral presentation at the 7th Scandinavian Symposium on Chemometrics 2001. An early version of paper V was presented as a poster at the International Mechanical Pulping Conference 2003. Paper VI was presented as a poster at the 8th Scandinavian Symposium on Chemometrics 2003.

Additional material included in the section ”Summary of Papers” is based on an oral presentation at the 9th Chemometrics in Analytical Chemistry Conference, 2004 and on a poster at the 9th Scandinavian Symposium on Chemometrics, 2005.

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List of Papers

Other papers where the author has made contributions but that are not included in the thesis

MALDI- and PALDI-tof-ms analysis of low molecular weight polystyrenes and polyethyleneglycols, A Woldegiorgis, P Löwenhielm, A Björk and J Roeraade Rapid. Commun. Mass. Spectrom. 18 (2004), 2904-2912

Improved Method for Peak Picking in MALDI-TOF/MS M Kempka, J Sjödahl, A Björk and J Roeraade Rapid. Commun. Mass Spectrom. 18 (2004), 1208–1212

The author has also contributed to discussions and implementation of multivariate fault detection with Rasmus Olsson at the department of Automatic Control at Lund Institute of Technology, Lund University. This work was a part of Rasmus Olsson’s PhD thesis presented in June 2005.

xii Table of contents

THESIS SCOPE AND OUTLINE...... 1 PULP AND PAPER ...... 3

MECHANICAL PULPING ...... 3 PAPER MAKING ...... 6 Stock preparation and beating ...... 6 PULP CHARACTERIZATION ...... 7 Pulp and sample handling ...... 7 Concentration...... 8 Sheet testing...... 8 Strength testing ...... 8 Optical measurements...... 9 Pulp slurry measurements ...... 9 Chemical characterization ...... 11 VIBRATIONS, SOUND AND PIPES...... 13

WHAT IS ACOUSTICS, SOUND AND VIBRATIONS ...... 13 ONE DEGREE OF FREEDOM SYSTEM E.G. AN ACCELEROMETER ...... 14 THE FIBRE-STEAM SYSTEM, BEAM THEORY, BEATING AND THE DOPPLER EFFECT ...... 16 Beam theory applied to fibres ...... 16 The beating effect ...... 18 The Doppler-effect ...... 18 The pipe/fluid interface ...... 20 The influence of flow patterns ...... 20 Summarizing the steam-fibre system...... 20 MEASUREMENT SYSTEM DESIGN ...... 23

VIBRATION SENSORS ...... 25 Some different designs frequently used for vibration sensors...... 26 Related sensor technologies ...... 26 ANALOGUE SIGNAL CONDITIONING ...... 27 Amplifiers ...... 27 Filters...... 27 ANALOGUE TO DIGITAL CONVERSION...... 29 HANDLING AND COLLECTION OF DATA ...... 30 DIGITAL SIGNAL PROCESSING ...... 33

PURPOSE OF DSP IN THE CONTEXT OF ACOUSTIC CHEMOMETRICS...... 34 POWER SPECTRA USING FAST FOURIER TRANSFORM ...... 34 WAVELETS ...... 36 Continuous Wavelet Transform ...... 36 Fast Wavelet Transform ...... 38 ANGLE MEASUREMENT TECHNIQUE...... 41 SPECTRAL IMAGES OR CUBES ...... 41 MODELING ...... 43

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Table of Contents

MULTIVARIATE ANALYSIS AND CHEMOMETRIC METHODS ...45

SCALING AND TRANSFORMATIONS OF DATA MATRICES ...... 45 PRINCIPAL COMPONENT ANALYSIS, PCA ...... 46 CLASSIC UNIVARIATE METHODS AND METHODS WITH FEW VARIABLES...... 48 PRINCIPAL COMPONENT REGRESSION, PCR ...... 48 PARTIAL LEAST SQUARES, PLS ...... 49 ORTHOGONAL SIGNAL CORRECTION, OSC ...... 51 METHODS RELATED TO PLS AND OSC ...... 52 WAVELETS IN CHEMOMETRICS ...... 53 UNCERTAINTY IN MEASUREMENTS ...... 53 VALIDATION ...... 54 Partitioning of data sets for generating uncertainty values ...... 54 Sample leverage ...... 55 ...... 55 Physical, chemical, process and system knowledge in validation ...... 56 MULTIVARIATE MODELLING IN PRACTICE...... 57 EXPERIMENTAL DESIGN ...... 62 INDUSTRIAL APPLICATION AND IMPLEMENTATION ISSUES65

DEVELOPMENT OF THE MEASUREMENT SYSTEM USED ...... 65 EXPERIMENTAL DESIGN IN THE MILL ENVIRONMENT ...... 65 HANDLING OF IN A MILL...... 65 ENVIRONMENTAL CONSIDERATION IN SYSTEM DESIGN ...... 66 PREVIOUS WORK IN THE FIELD OF ACOUSTIC CHEMOMETRICS AND RELATED TECHNOLOGIES...... 67

PASSIVE ACOUSTICS WITH AND WITHOUT THE USE OF CONSTRICTIONS ...... 68 ACOUSTIC EMISSION AND ACTIVE ULTRASONICS...... 69 PULP AND PAPER APPLICATIONS AND LOW ...... 71 SUMMARY OF ARTICLES - FROM ADAPTED CHEMOMETRICS TO NEW SIGNAL PROCESSING SCHEMES FOR BETTER INPUT TO STANDARD MVA TOOLS...... 73

ADAPTED CHEMOMETRICS FOR ACOUSTIC SIGNALS, PAPER I AND BEATING OF KRAFT PULPS IN PILOT SCALE ...... 73 Thermo mechanical pulp refiner ...... 73 Main findings in Thermo mechanical pulp refiner...... 75 Beating of Kraft pulps in pilot scale (Additional unpublished results) ...... 76 Main findings in Beating of Kraft pulps in pilot scale ...... 80 CONNECTING QUALITY VALUES, SCREEN AND ACOUSTIC SENSORS FOR OBTAINING BETTER UNDERSTANDING OF A SCREEN SYSTEM, PAPER II ...... 80 Main findings in connecting quality values, screen efficiency and acoustic sensors for obtaining better understanding of a screen system ...... 82 ABSTRACT FEATURE EXTRACTION WITH IMPROVED INTERPRETABILITY, PAPER III AND IV...... 82 Main findings in Abstract feature extraction with improved interpretability. 88 FEATURE EXTRACTION RESULTING IN PHYSICAL INTERPRETATION, PAPER V AND VI..88 Main findings in Feature extraction resulting in physical interpretation ...... 95 xiv Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry.

CONCLUSIONS ...... 97 FUTURE OUTLOOK ...... 99 ACKNOWLEDGEMENTS ...... 101

INDIVIDUALS ...... 101 ORGANISATIONS ...... 102 FOUNDATIONS AND GRANT CONTRIBUTORS ...... 102 REFERENCES ...... 103

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Thesis Scope and outline

Thesis scope

The overall scope of this thesis is to use measurements of vibrations on process pipes for determining properties of the flowing fluid inside a pipe. The field is called Acoustic Chemometrics, AC, or simply Acoustometry. The focus of the thesis is on modelling, calibration and signal processing. However, the signal processing area is so broad that some further limitations must be made. Methods used by the author will be presented against the background of other author’s work in AC and in general signal processing.

Concepts and knowledge from the following scientific areas are used Multivariate data analysis, also called Chemometrics Vibration measurement technology Digital signal processing Analytical chemistry Vibration and sound theory Fluid dynamics

Also needed is sufficient knowledge on The nature of the process the acoustic measurements are performed on The reference methods for the properties of interest Sampling and sample handling

However using this as the boundaries for a thesis would make it impossible to be complete in a reasonable volume, due to the many areas of science that are needed to get an overall understanding of the field. Narrowing the scope is a necessity to make a readable thesis.

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Thesis Scope and outline

Thesis Outline

In order to give a background to the applications focused on the pulp and paper industry information about processes, measurements and industrial practices is given in the first chapter "Pulp and paper". The chapter "Sound, vibrations and pipes" gives a brief introduction to the fundamentals and models of vibration system dynamics. This is followed by a chapter on "Measurement system setup". Thereafter follows the major chapter on "Digital Signal Processing, DSP", "Modelling" and "Multivariate analysis, MVA and chemometric methods". In the chapter "Industrial application and implementation issues" the conditions and restrictions to be considered when making experiments in a process industry is discussed. Techniques similar or related to those employed in this thesis are discussed in the chapter of the theory called "Previous work in the field of acoustic chemometrics and related technologies". The author’s own work is presented and discussed in the chapter "Summary of articles - From adapted chemometrics to new signal processing schemes for better input to standard MVA tools". The "Conclusions" chapter summarizes the main findings and contributions in this thesis and in "Future outlooks" the use and applicability of the methods will be discussed in a five years perspective.

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Pulp and paper

Knowledge and timber shouldnʹt be much used till they are seasoned. Oliver Wendell Holmes (1809 ‐ 1894), The Autocrat of the Breakfast‐Table, 1858

Pulp and paper represents one of the largest industrial branches in Sweden and in many other countries. The mills use capital demanding equipment and any step towards higher productivity is therefore of great interest. There are two pulping methods, mechanical pulping and chemical pulping. The two processes yield fibre material with different properties that is more or less suitable in different paper types and grades. There also exist combinations of the two principal chemical and mechanical treatments. In chemical pulping there are two main processes the so called Sulphite process and the Kraft process. The Kraft process is the predominant chemical pulping process in the Nordic countries. The work presented in this thesis is focused on methods to measure pulp properties more efficiently. This could in the long run give better control of the pulping processes. A minor part of the thesis work is related to monitoring of beating of Kraft pulp a step in the stock preparation before the paper machine. For further information on pulp processes see the book on wood chemistry by Sjöström [1] and the book on pulp technology by Brännwall et al. [2]. After pulping follows the process of making paper of the pulp or pulps. Figure 1 shows an overview of the major processes from wood logs to paper products. For more information about paper technology consult the book by Fellers and Norman [3].

Mechanical Pulping In mechanical pulping there are also two major processes grinding and refining [4, 5]. The character of mechanical pulps has been discussed by Höglund [6], Sundholm [7] and McDonald & Miles [8]. In grinding, fibres or fibre-chunks are removed from a barked wood log by grinding it against a rotating "stone". The grinding process is the older of the two processes and has been partly replaced by Thermo Mechanical Pulping, TMP. Since no measurements have been done by the author after grinders, no further details regarding this process will be discussed.

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Pulp and paper

Figure 1 From wood to paper products. A simplified overview of process steps

Figure 2 Schematic overview of the TMP-process from chips to high grade mechanical pulp. Placement of vibration sensor is indicated by a filled ring, with V1 to V5. In refining processes wood chips are usually preheated. They are fed into a refiner (a disk mill) in which chips are successively worked to separate free fibres or smaller chunks of fibres (shives). In Figure 2 a typical TMP process is outlined. White water is re-circulated process water containing dissolved components and fine material.

4 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

A TMP system includes at least the following units/unit operations: Chip washer, chip dewatering, metering screw, preheating step, plug screw or rotary valve, feeding screws, refiner, blow-line, steam separation of some kind, latency chest and screening room. Additionally an advanced control system is needed to keep the system under control.

The steps before the refiner are crucial for its stability. A varying production or water content may cause the refiner load to shift too fast, which activates the load guards that prevent a plate clash (touching of the two plates, doing the actual defibration work). One of the refiner plates has at its inner part structures similar to a centrifugal pump impeller. Further out on both plates there are breaker bars and finally the finer refiner segments. All along the radius of the refiner plate the wood chips are reduced in size more and more and finally most of the fibres get completely separated. Additionally during this process fine material is formed and the fibre surfaces become more irregular. Since the wood chips contain water the defibration process also produces steam. This that the pressure will vary along the radius of a refiner plate. When leaving the plate gap of the refiner the fibres are transported via a blow-line to some type of steam separator.

The steam separation can be done by use of scrubbers, steam cyclones or by a fibre accelerator (separating fibres by an additional centrifugal force). The steam is then recovered in heat exchangers and the fibres are diluted and relaxed in a latency chest. The word latency comes from the fact that fibres partially "freeze" in shape after the rough treatment in a refiner and the lowered temperature after the refiner gap. To overcome this pulp (the fibres) is relaxed in a latency chest at 3-5 % fibre concentration and at a temperature of 80- 90 ºC for 10-20 min. After or on the latency chest some automatic pulp quality sensors may be placed. The pulp quality values obtained are used for control of process settings in the refiner. The most commonly used quality parameter is Freeness (Canadian Standard Freeness, CSF) [9] a value of the drainage resistance for pulp. The CSF-method is described in depth in the section Pulp slurry measurements, later in this chapter.

The next step is normally screening, to remove shives and/or coarse or less mechanically treated fibres [10]. The normal control strategy in screening is to keep feed concentration constant and to remove a fraction of the feed flow as a reject stream. The feed flow to the screen may be regulated in such a way that the latency chest level determines the set point for the feed flow. Note that normally no quality information is used in the screen control although feed forward of

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Pulp and paper information from automatic pulp quality sensor would be possible. The fibres rejected in the screens are normally treated in a reject refining step before being recycled to the screen. The final pulp is dewatered to enable efficient storage or bleaching before use in paper making.

The measurements and control of TMP systems has been discussed in a book by Leiviskä [11] and in a book by Sundholm [4] among others. Advanced control strategies for TMP-systems recently presented can be found in Lidén [12] and in Strand et al. [13]. A paper worth mentioning is Hills "Process understanding profits from sensor and control developments" [14] where he discusses the refining process from a systems engineering perspective. In a personal communication he stated that "The average operator thinks of pulp quality in terms of hours. Mainly because we have not had measurements faster than that.".

Paper making The major part in the paper making process is the removal of free water from the stock by (wet end) and then removal of bound water by pressing and drying. This will not be treated further here, see Fellers and Norman [3] for more information. Before the de-watering steps there is the stock preparation were components are added, refining and mixing is done to achieve good run-ability of the paper machine. The process-steps in a normal paper making process are outlined in Figure 3.

Figure 3 Principal process scheme for a paper machine system Stock preparation and beating In stock preparation different pulps, additives, performance chemicals and broke (re-circulated re-slushed paper) are mixed and diluted. The process flow in stock preparation for an LWC paper machine for e.g. magazine paper is outlined in Figure 4. Positions where vibration sensors have been tested are marked with circles V6-7. One step in the stock preparation before mixing, is beating of the pulp. This is done to enhance the flexibility and bonding ability of the pulp [15]. The control of this step is not as straightforward as it can seem because pulp have varying beat- ability. That is, the pulps require different energy input to reach a certain quality level. Even if

6 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry pulp is manufactured under constant process conditions, the beat-ability may vary due to variation in raw material quality. One control strategy is to measure the freeness (CSF) or Shopper Riegler number (SR) and keep this constant by manipulating the specific energy input (kwh/ton). The CSF and SR are two numbers describing drainage resistance of pulp, for further information see the section Pulp slurry measurements on page 9.

Pulp characterization Pulp characterization has been done since the first papermaker started production of paper. The at that time was probably based on stirring with a hand in the pulp slurry and feeling the fibres between fingers. In this way they could control the stock concentration and the overall quality of the raw material.

Figure 4 Principal process scheme for stock preparation for LWC-paper machine. Note that sensors V6-7 were tested in a pilot plant and not at an industrial site. Pulp sampling and sample handling Pulp sampling presents a lot of difficulties, due to the properties of fibre/water or fibre/steam (and water) suspensions. For instance, to withdraw a sample a pressure drop is needed, due to the viscous and elastic properties of the pulp. This pressure drop varies with how much the sampling valve is opened. An additional force may be needed to withdraw a sample from a main stream. The magnitude of the force needed may also be dependent on the pulp quality. Although the pressure in main streams is often kept reasonably constant, there is always a variation in pressure. These facts indicate that fractionation will probably occur in sampling-valves at least to some extent. This can lead to differences in fibre length distribution between the main stream and the

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Pulp and paper withdrawn pulp sample. The problem mentioned can occur both in fibre/water and fibre/steam systems. When samples are taken, they should preferably be marked with date and time, position and person who made the sampling. This makes it possible to identify "error-makers". This is of course not always so easy to conform to due to various practicalities. If there will be a long time between the sampling and the laboratory analysis, more than some hours, the samples must be refrigerated (analysis done within 24 hours) or else preferably deep frozen. Often a sample size reduction is performed when packaging pulp for freezing. In such cases it is important to mix the sample carefully before the sample reduction step. Storage of frozen pulp samples have neglectable effect on the pulp properties for mechanical pulps according to Levlin and Söderhjelm [16].

Concentration One of the most critical measures in characterisation of pulp is the consistency. This is due to the fact that many test methods require a certain content of fibres in water. The pulp slurry should also be stirred to ensure that a sub sample will have the same concentration as the primary sample. However, the sample must not be stirred so much that it will affect pulp properties.

Sheet testing Since paper is made by letting fibres and other components form a sheet, it is of interest to imitate the sheet formation in a paper machine. However, today's paper machines are much faster then when the manual sheet testing methods were invented. The main difference between sheets formed manually and in the paper machine is in the orientation of fibres. In a paper machine sheet the fibres are oriented, while the direction of fibres is more random in a laboratory made sheet. There are two main classes of measurements made on sheets strengths and optical properties.

Strength testing Two common testing methods for strength are tensile and tear testing. In the tensile testing a paper strip is clamped and stretched until it breaks. This can be regarded as a method for testing the E-module of the paper. In tear testing a paper strip is clamped, then the paper is cut to induce a rip/crack, a weight is lifted to a certain position and finally released to tear the paper. The work needed to tear the paper is the tear strength of the paper. It is common to normalize measurements by the specific surface weight of the sheet to obtain tensile index, tensile stiffness index and tear index. This minimizes the effect of errors introduced in the concentration measurements in the sheet making step.

8 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Optical measurements Commonly used optical measurements on pulp sheets are brightness, Y-value and the corresponding light absorption and light scattering coefficients. These measurements are performed using a diffuse reflectance spectrometer. For brightness 457 nm wavelength is used and for Y-value a weighted function of different wavelengths corresponding to the sensitivity of the eye is used.

Pulp slurry measurements There are a number of slurry measurements that can be made on pulps. These measurements can give low-cost information on how a certain pulp will act when sheets are made. Therefore these measurements are of great importance for continuous quality control in pulp mills and for the stock preparation before a paper machine. Papermakers want e.g. to know how a pulp will dewater on the paper machine. Therefore laboratory methods were developed to mimic this. Two of those methods are Canadian Standard Freeness, CSF, [9] and Shopper Rielger, SR. These measure drainage resistance and drainability respectively [17]. Note that a small value for CSF corresponds to high value for SR. A schematic outline of the events using CSF-apparatus for the CSF determination is shown in Figure 5. The first step (from left to right) is filling with pulp slurry and closing the release valve. In the second step the release valve has been opened and water has entered through the mesh and started to fill the cone. In the third step, the cone is filled up to the level of the side discharge and white water is discharged both ways. In step four the CSF-apparatus is now empty except for a small fibre cake on the mesh. The measuring cylinder can be read and this value is compensated for deviations from the optimal measurement temperature and concentration according to standard tables. The value obtained is drainage resistance, CSF, in the unit millilitres.

Figure 5 An outline of the events using CSF-apparatus for CSF determination.

9

Pulp and paper

Another estimate of how much water that is withheld in a pulp/paper sheet, after dewatering and pressing a sheet is the Water Retention Value, WRV. A slurry container is prepared according to the standard with a certain volume and fibre concentration. Then the container is centrifuged and the free water is removed from the fibres. The pulp fibres are then weighed, dried in an oven and weighed again. The ratio between the weights of dry and the wet fibres is calculated.

A slurry measurement that gives to a great extent the same information as strength measurements is fibre length distribution. This measure has been in use for a long time for measuring mechanical pulp quality. One of the first machines made for measuring fibre length distributions was the Bauer-McNett fractionator [18, 19]. It is a stepwise screening device where the different fractions are retained in slots. It is operated as follows: dilution of samples to the right fibre concentration, collection, drying and weighing of each fraction. All these steps make the use of Bauer-McNett fractionator rather labour- and time-consuming. The time required for each sample limits the sample throughput. These drawbacks make the fractionation method unsuitable for on-line implementation. The needs for on-line fibre distributions lead to the first generation of optical instruments. These instruments are based on one or a few light paths and detection of the reflection of plane polarized light or the extinction of non-polarized light when a fibre passes the detector. The fibre length calculations are based on the duration of the changed light intensity and the flow rate of the pulp suspension through the cuvette. The FS100 and PQM developed by Kajanni and Sunds Defibrator respectively are instruments based on this technology [18, 20]. On-line versions of the first generation optical fibre length distribution measurement systems have been in use since the 1980-ies. Motivated by the need for higher productivity in the paper production and improved paper quality there was a call for more detailed information about fibre shape and a call for more rapid measurements. This lead to a second generation of instruments based on image analysis [18, 20]. All image analysis systems are composed of a light source, one or a few cameras, a frame grabber card with or without specialized image analysis program and a computer for supplementary calculations and presentation of data. With image analysis based systems like FibreMaster, FibreLab and PQM-inline it is possible to determine length, width, coarseness and even fibre flexibility. Both laboratory and process adapted instruments are available of the brands mentioned.

10 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Chemical characterization For a general overview of wood chemistry see the book by Sjöström [1]. There are a number of both classical and more modern methods for determining the chemical composition of pulps [1, 17].

11

Vibrations, sound and pipes

Every cell pulsates, absorbs, reflects and interacts with the acoustic oscillations of the medium. From Man’s Cosmic Game by Guiliana Conforto [http://www.lightwithin.com/SomaEnergetics/Quotes.htm]

In this section, a brief overview of the underlying theory of vibrations and acoustic engineering will be presented. The theory will be presented in the context of using vibration measurements as a means for physical and chemical characterization of fluids. The one-degree of freedom system is introduced at this stage for later use as a model for accelerometers. Some of the models are presented to serve as hypotheses for describing the fibre-steam system in particular. An empirical approach using multivariate analysis for connecting vibration measurements and fluid properties is recommended. For a deeper understanding of the field consult the following books on sound and wave theory, vibrations, solid and structural dynamics and vibration engineering [21-24].

What is acoustics, sound and vibrations Acoustics is "The science of sound waves including production and propagation properties.". Sound is considered "The periodical mechanical vibrations and waves in gases, liquids and solid elastic media. Specifically the sensation felt when the eardrum is acted upon by air vibrations within a limited frequency , i.e. 20 Hz to 20 kHz. Sound of frequency below 20 Hz is called infrasound and above 20 kHz ultrasound.". Vibration is defined as "A repetitive periodic change in displacement with respect to some reference point.". [25]

In this thesis, the words Acoustic and Vibration will be used in the same context, since the acoustic waves of the fluids create the vibrations measurable on pipes. There are two major wave types, longitudinal and transverse. However, combinations of them exist, like bending waves. Longitudinal waves have a particle displacement acting parallel to the direction of wave propagation. Transverse waves have particle displacement perpendicular to wave propagation. An example of a transverse wave is shaking a rope up and down. In this case the particle displacement will be up and down while the wave propagation is away from the source of the motion. In gases and fluids, only longitudinal waves exist while in solid materials both longitudinal and transverse waves can exist. This means that bending waves do not exist in gases and fluids. However, they may be important for the transfer of sound from a solid material

13

Vibrations, sound and pipes to gas or liquid. When measuring on a pipe with a fluid moving at varying speed the Doppler effect may cause shifts in the measured frequencies.

One degree of freedom system e.g. an accelerometer The so-called one degree of freedom system is schematically shown in Figure 6. In this system, a mass m1 is connected to a mass m2, where m2 is much larger than m1. This can be described by different models in a system dynamics sense. The choice of model depends on the action of the connection points between the masses, for instance Hooke's law may be applicable.

Figure 6 Example of a one degree of freedom mechanical system

By use of Newton's second law equations can be set up for a mass m connected to a second large mass by a viscous damping medium with damping constant dv and a spring with the spring constantκ . Some simplifications yield equations (1)-(3). For more details see pages 99-101 in [21] alternatively [22]. The normalized amplification factor can be written as follows: 1 φ = 2 (1) 2 2 2 ⎛ω ⎞ ()1− ()ω − ω0 + 4()δ ω0 ⎜ ⎟ ⎝ ω0 ⎠

Where κ ω0 = Angular frequency (resonance frequency) (2) m

d v δ = Damping constant (3) 2m

14 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

κ Spring constant

d v The viscous damping constant m The added mass ω Angular frequency acting on the system

5 Using equations (1-3) with κ = 1.55⋅10 N/m, d v = 100 kg/s and m = 50 and 1000 kg over a frequency range 1-1000 Hz gives the solid and dashed lines respectively in Figure 7. The graph shows how the system reacts when acted on by a wave with a certain frequency. For instance for a wave with frequency well below the resonance frequency, the system does not amplify the amplitude of the wave (sensitivity 0 dB). The linear region for a system is where the sensitivity is within ±10% of the baseline sensitivity, in Figure 7 from 0 Hz and up to the upper limit indicated by the arrow and vertical line. Whereas for an incoming wave with frequency near or at the resonance frequency (above the linear region) the system heavily amplifies the wave by several decades (sensitivities 19 dB and 12 dB respectively). Note that a higher mass implies a lower resonance frequency but also a higher sensitivity at resonance.

Figure 7 The sensitivity response for two systems with different masses. The solid and dashed lines represent masses, m1, in the one-degree system of 50 kg and 2000 kg respectively.

15

Vibrations, sound and pipes

The fibre-steam system, beam theory, beating and the Doppler effect A brief overview of phenomena likely to occur in fibre-steam-pipe system will be presented. The model concepts are admittedly oversimplified. However some important conclusions can still be drawn.

Beam theory applied to fibres Beam theory can be used as a tool to describe the frequency of single flexing fibres although it is an approximate description. This since all necessary parameters are not accurately known and in the real system there are millions of fibres in motion simultaneously and not only one fibre at the time. Beams are structures with lengths much greater than their widths and depths, typically the length is 20-1000 times the width and depth. The vibration of beams is described by a classical work of Euler [26].

Figure 8 Two beams with free ends and hinged ends, showing first and second nodes. For a beam with two hinged ends the frequency can be calculated by

πK E 2 f m = m (4) 8L2 ρ m =1,2,3,K For a beam with both ends free πK E 2 2 2 2 n = 4,5,6 f m = 2 []3.011 ,5 ,7 ,K,()2n +1 K (5) 8L ρ

Note that in equation (5), for the first three nodes specific numbers apply, 3.0112 for the first node, 52 for the second node, 72 for the third node and thereafter for the n-th node given by (2n- 1) 2. Equation (4) describes a beam that can not move in the ends and equation (5) describes a beam with fully movable ends. Equations (4)-(5) both include L, the length of the beam, K, the momentum of inertia, E, the elasticity modulus also called Young's modulus and ρ, the density of the material. These equations hold for beams with equal material properties in all directions.

16 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

The momentum of inertia can be written for a tube with outer diameter a and inner diameter b as follows: ()a 2 + b2 K = (6) 2 For a square rod with height h the momentum of inertia can be written as follows: h K = (7) 12 The equations (4)-(7) are commonly applied for metallic materials of typical construction dimensions. Applying this set of equations on fibre materials with much smaller dimensions must be considered as a very rough approximation. The fibre width for Norwegian spruce is in the region of 30 μm with wall thickness around 3-6 μm and a corresponding length of 3 mm. However, the ratio between width and length is comparable for fibres and construction beams. 80 mm 30 μm The ratio for a small construction beam is = 0.02 and for a fibre = 0.01. 4m 3mm The real case is even more complex. Temperature and moisture dependence of the Torsional- module was presented in early works of Höglund et al., [27, 28]. If the material properties are assumed to be the same in all directions for simplicity and if the torsion-module is dependent on temperature and moisture then the same applies for the E-module. To simplify even further moisture content and temperature effects are not considered here. Acquiring accurate single fibre values for Young's modulus is difficult. Using Young's modulus values from wood testing or sheet testing on pulps serves as an acceptable approximation. 12.5 GPa What would the ratio E in (4) or (5) for wood be? = 2.1⋅107 Nm/kg using values of ρ 600 kg/m3 E and ρ obtained from [29]. Note also that the inertial moment, K, is much smaller for a fibre than for a regular beam, since the fibre diameter is 30 micrometers while a regular beam typically has a diameter of 5 centimetres or more. Calculations on fibres give rather high frequencies for the short fibres and relative low for the longer fibres. Figure 9 shows calculated Eigen- frequencies for fibres with 30 micrometer width, 3 micrometer wall thickness and lengths from 0.001 mm to 7 mm. Equation 4 and 6 were used for different fibre lengths and the first node. Values of Young's modulus and density of woods given above were used. Even lower frequencies than those indicated in Figure 9 should be expected since the fibres are commonly found in the form of clusters in the blow-line.

17

Vibrations, sound and pipes

Using beam-theory on wood-fibres with lengths 0.001-7 mm 10 10 10 10

9 8 10 10

8 10 6 10 7 10 Frequency [Hz] Frequency [Hz] 4 10 6 10 Possible overlay of beating wave 2 5 10 10 0 5 10 0 0.2 0.4 Fibre length [mm] Fibre length [mm]

Figure 9 Using beam-theory as an illustration of the Eigen-frequencies of fibres with different lengths. To the right the full graph and to the left a zoom of the shorter fibre fragments. In the left graph the resulting frequency has been extrapolated for fibre lengths of 7-10 mm, indicated by a dashed-line. Also indicated are the frequencies that could cause a beating wave overlaying frequencies from longer fibres.

The beating effect When two waves are near each other in space and close in frequency a beating wave is formed. The beating wave has a frequency equal to the frequency difference between the two original waves, fbeating= f2 - f1. The frequencies of the two separate interfering waves (f1 and f2 ) are generally much greater than the frequency of the beating wave. By inspection of Figure 9 it is apparent that if beating would occur for the shorter fibres the resulting wave might coincide with the Eigen frequencies of the longest fibres.

The Doppler-effect The Doppler Effect is a shift in the frequency of a wave due to the speed of the source in relation to the receiver.

18 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Figure 10 The Doppler effect.

In the different quantities used in Equation (8) for the example listening on a pipe with an accelerometer the steel-steam and steam-fibre interfaces are neglected. The frequency shift due to the Doppler effect is obtained by: ⎛ v ± v ⎞ ⎜ O ⎟ f = f0 ⎜ ⎟ (8) ⎝ v ± v S ⎠

Where f is the frequency perceived by observer, f0 is the actual frequency of the wave, vO the relative speed of the observer, vS the speed of the source and v the speed of the wave in the medium. Note that vO is zero for the types of sensors presented here, i.e. stationary sensors. When having a sensor measuring on a pipe with moving fluid there will be a spread in frequency, the range will be:

⎛ v ⎞ ⎛ v ⎞ f ⎜ ⎟ to f ⎜ ⎟ 0 ⎜ ⎟ 0 ⎜ ⎟ (9) ⎝ v + v S ⎠ ⎝ v − v S ⎠ The sound speed ( v ) is affected by the ambient temperature as follows:

T v = v0 (10) T0

Where v0 is the specified ground state speed at T0 and T is the actual temperature. Equation (10) is a version of Eq. 4-51 in [21] where 273 K has been replaced by T0 . Reasonable values for the systems examined where fibres are transported in steam [30] are

v0 = 404, m/s, T0 = 373 K and T = 413 K. Inserted in (10) this gives v = 425.9 m/s. Note the approximation that the fluid is composed of steam only. The actual fluid is composed of steam, fibres, and probably small amounts of liquid water.

19

Vibrations, sound and pipes

The pipe/fluid interface At the pipe wall, we have losses due to different acoustic impedance for steam and steel. The pipe system itself also exhibits characteristics influencing the signal measured by an accelerometer.

The influence of flow patterns From fluid dynamics, for a homogenous one-phase system two types of flow patterns are found laminar (streamline) flow and turbulent flow (vortices). However, this description is too simple for two- and three phase systems, e.g. gas-solid, gas-fluid, gas-fluid-solids systems. For a thorough description of different flow patterns for these types of systems the reader is referred to [31], see Figure 11.

Removed in the on-line version.

Figure 11 Different flow patterns.

Different flow patterns will influence the measured vibration spectra. Plug or slug flow will probably give a strong stochastic low frequency component. Annular flow will give less low frequency components and more mid frequency components. Mist flow will probably give much less low frequency components and more mid and high frequency components.

Summarizing the steam-fibre system In conclusion, the coupling of the E-Modula and the sound speed to temperature is presented. Additionally the E-Modula depends on the degree of moisture in the fibres. Moreover, the frequency dependence on fibre dimensions in the beam theory and that of the perceived frequency dependence on the flow speed were discussed. By inspection of Figure 9, it is apparent that if beating would occur for the shorter fibres the resulting wave might coincide with those caused by the longest fibres. However, in reality the fibres are mostly in clusters in a refiner blow- line. These clusters are either porous and have Eigen frequencies similar to separate fibres or compact having lower Eigen frequencies than single fibres. This needs to be modelled for a more

20 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry accurate representation of the problem. Damping is also found between fibres in steam in the blow-line case and in water slurries. Since the measurements are done on the outside of a pipe, some additional damping may be expected as well. Add to this that fibres have distributions in width, wall thickness and length. These distributions are somewhat broad which makes this system quite complex to model in a mechanistic fashion. Finally, how the fibres and fibre lumps are dispersed (the flow patterns) in the steam affects the overall signal measured. A well-dispersed system with a flow pattern similar to mist flow would give rather stationary signal strength while a slug flow like pattern would give greater variations in signal strength.

All these factors make the interpretation of the vibration or acoustic measurements even more challenging. Therefore, a convenient way is an empirical approach based on helpful signal processing and multivariate analysis.

21

Measurement system design

Measure what is measurable, and make measurable what is not so. Galilei, Galileo (1564 ‐ 1642), Quoted in H. Weyl ʺMathematics and the Laws of Natureʺ in I. Gordon and S. Sorkin (eds.) The Armchair Science Reader, New York: Simon and Schuster, 1959.

The measurement system for acquiring vibration/acoustic signals (for acoustic chemometrics) is important and one of the determining factors for how accurate predictions we can make. There are similarities with systems used in structural mechanics and vibration control, the objectives are, however, notably different. In structural studies a set of tools for reducing vibration and sound is used. A linear system approach is applied using superposition. For that reason the measurements should be linear and the absolute values or the power of the measured vibration [21] are used. Figure 12 shows a schematic overview of a measurement system for performing vibration analysis or acoustic chemometrics. Many of the components are the same for vibration analysis and acoustic chemometrics. One difference is that in acoustic chemometrics it is often useful to record higher frequencies than in regular vibration analysis.

Figure 12 Schematic overview of a measurement system for vibration analysis or acoustic chemometrics.

In acoustic chemometrics non-linear signals are partly handled since we linearize around a stationary point by centering or standardization. For instance, we collect spectra under various conditions. On each frequency the average power value is subtracted and usually the result is divided by the . This means that all variables have average zero and a standard deviation of one. Hence, relative signal strength or power difference is of importance rather than the absolute value. This means that we can make use of sensors in a different way than in regular vibration analysis. For instance, as a rule of thumb in vibration engineering one should not measure vibrations with a frequency greater than one third of the resonance frequency of the accelerometer [21]. This stems from the demand on linear measurement response, which is

23

Measurement system design required for the use of linear vibration theory. The linear range of measurement for an accelerometer is the frequencies where the sensitivity is within +/-10 % from 1, see Figure 13. In an acoustic chemometrics setting there are no reasons why we should not use frequencies above or below the resonance frequency for a sensor. However due to the extreme attenuation around the resonance frequency, f r the use of frequencies near resonance should be avoided, see Figure 13. If the object we measure on has an important part of its signal content around the sensors resonance frequency, it is probably wise to change the sensor Further if the object has a resonance frequency near the sensors resonance frequency, this situation would be even worse.

Figure 13 The normalized amplification factors for two accelerometers based on an ideal model for an accelerometer.

Acoustic measurement setups can be both active and passive as illustrated in Figure 14. The active type uses one or several sources like an ultrasonic transmitter, a loud speaker or a piezo electric shaker (indicated in Figure 14 by a loud speaker symbol). The receiving sensor can be an accelerometer, an acoustic emission sensor, an ultrasonic sensor, an optical vibration sensor or a dynamic pressure sensor, indicated in Figure 14 as a microphone. Note that the active attenuation sound sensing and probably also the active echo sound sensing could be used in audible frequencies by using a loud speaker as a source sending out frequencies below 20 kHz. Not indicated in Figure 14 for the two active cases, is that a flowing fluid will always generate some sound. This might to some extent interfere with the measurements. One way to avoid this is to use both passive and active modes during measurement. The common way in industry is to use

24 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry active sensors to measure the sound speed in the fluid. The acoustic chemometric pathway on the other hand uses not only one value but the complete frequency spectra from a sensor. These spectra can be made from data from passive sensors and active sensors.

Figure 14 Different sensor setups that could be used for acoustic chemometrics.

Figure 15 presents an idea about how to increase the amount of sound generated, by introducing a constriction in the flow. This idea was proposed by Hope in 1987 [32].

Figure 15 Passive forced sound sensing using a constriction. Vibration sensors A number of different designs for vibration sensors exists. They have different characteristics in many aspects like sensitivity, number of axis for measurement directions, maximum allowed chock level, electric design, temperature toughness and complexity/cost. For instance, if the surface temperature where an accelerometer is to be affixed exceeds 150 ºC it is not possible to use accelerometers with internal amplifying electronics. For accelerometers the weight of the seismic mass determines the frequency response of the sensor, in particular the resonance frequency. However in use, the resonance frequency obtained for a sensor is a function of its seismic mass and the stiffness of the bounding to the surface.

25

Measurement system design

Some different designs frequently used for vibration sensors In compression accelerometers the seismic mass is placed above the piezoelectric element, causing a varying compressive force on the element. Shear accelerometers are designed with the seismic mass placed around the piezoelectric element. When the mass vibrates this causes a shear force on the measurement element [33-34]. There are also designs based on optical detection of acceleration using a laser as light source and a photo-detector for the actual detection. One could think of two different setups using a laser based system; I) sending and receiving the light pulses through the air and II) using fibre optic cables to lead the light to and from a measurement point. At least for the first setup there are complete instruments [35] and for the second there are components [36] to buy but the interface at the actual measurement-point must probably be tailor made. For the variant measuring through air the advantages are that no load is placed on the structure. A disadvantage may be that something could block the light path. An advantage for the variant with fibre optics light path is that the electronics can be placed outside environments that do not permit normal electronic equipment.

Related sensor technologies There are a few technologies related to vibration sensors, e.g. for measurement of higher frequencies or for measurement of sound and pressure. The most common sensors are microphones [37, 38]. These usually have membranes that are thin and flexible. The materials range from polymeric films to super-thin metal sheets. For media other than air or certain gases dynamic pressure sensors [39] may be suitable. Piezoelectric elements are used in those. They are commonly available for applications with wide pressure and temperature ranges. One application where they are used is in monitoring of engines [39]. Active ultrasonic transducers are composed of a transmitting and a receiving part. A measurement setup thus includes a signal generator, a pre-amplifier, possibly a decoupling amplifier/filter and a post amplifier/filter, to acquire the correct signal level with a limited bandwidth. The transmitting signal can be setup as short pulses, pure frequency, frequency sweep or coded sequences. Combinations may also exist. When using frequency sweep or coded sequences decoupling of the transmitted signal is likely to be more efficient with digitized data. For a review on active ultrasonics see Hauptmann, et al. [40]. For an overview of the use of active ultrasonics or acoustic emission, in chemical plants consult the book by Asher [39]. For a review of acoustic emission in see Boyd & Varley [41]. The acoustic emission sensors are passive receiving devices. They may be designed as normal accelerometers. Piezoelectric crystals are mainly used as detecting elements. However, a high-pass filter is often needed to remove the sensors resonance frequency, which without this filtering would overpower the higher frequencies of interest.

26 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Analogue signal conditioning Most sensors require some type of signal conditioning before a useful signal can be acquired and further processed. In fact, the benefit of having a good analogue signal conditioning can not easily or in some cases never be replaced by later digital signal conditioning [42, 43].

Amplifiers Amplifiers do not only improve the signal strength, often they also supply sensor with suitable power supply. Many piezo electrical sensors have internal amplifying electronics that need suitable feeding. Some types of microphones require a polarisation over the microphone membrane (a potential difference) in order to work. Many sensors do not deliver a suitable raw signal for use in an analogue to digital signal conversion step or a pre-filtering step. In a pre- filtering step we may need a certain mean signal level in order to retain the signal quality and after filtering the signal level may have dropped and additional amplification is needed. Achieving a good signal conversion in an Analogue to Digital Converter, ADC, may also require a certain signal level compared to the resolution in the ADC to get an adequate signal representation. Transferring too weak signals through long cables, might lead to corruption by external disturbances/noise. Moreover sensors that have high impedance may cause a cable to pick-up additional noise especially when using long cables.

Filters Signals are by default corrupted by some types of noise or other disturbances. This means that removing or signals at specific frequencies is sometimes needed. Most commonly needed is an anti-alias filter removing all frequencies above half the sampling frequency used in the ADC. This is in accordance with the so called Nyquist-Shannon sampling theorem [44-46]. In Table 1 different filter types are presented including their function. In Figure 16 their modes of work are outlined. For some applications and sensor types band-pass filters are important when a signal has a strong low frequency content and a high frequency content that is of no interest. When using for instance an acoustic emission sensor it may pickup certain low- frequency components and signals at higher frequencies may be of low relevance. Another objective would be to filter-out harmonics of the electrical net frequency and simultaneously do anti-alias filtering.

27

Measurement system design

Table 1 Filters, function and their common use. Filter type Function Common use Low Pass, Removes high frequency Anti-alias effect filters before ADC. To restrict bandwidth in LP components. measurement system to get a low noise level. High pass, Removes low frequency To remove electrical net frequency and low order harmonics. HP components Band pass, Removes both low and A combination of low and high pass filters. BP high frequency content To focus on a specific frequency region, i.e. when using in a signal. ultrasonic high frequency sensors. Band stop, Removes a region of For blocking signals at the resonance frequency of a sensor or at BS frequencies from a other disturbing frequencies. signal.

Lowpass Highpass

1 1

0.5 0.5 Amplification

0 0 0 0.5 1 0 0.5 1 Bandpass Bandstop

1

0.5 Amplification

0 0 0.5 1 0 0.5 1 Normalized Frequency Normalized Frequency

Figure 16 The amplitude response for ideal filters

In some applications a disturbance or a natural signal component can be so strong that it saturates the system so that frequencies of interest are rendered impossible to use. Here a band stop filter comes handy blocking a specific region of frequencies.

28 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

In Figure 17 the amplitude response of a low pass filter is seen. In describing filters the term cut- off frequency is used, commonly defined as the stage where the signal is dampened 3 dB. A second term often used is roll-off, meaning damping as a function of frequency. Roll-off is often given as dB/octave, the slope of the damping, where an octave is 10n – 10n+1 Hz (n is a positive integer). The third term often used is centre frequency that is used for band-pass filters. The centre frequency is the frequency equal to the midpoint between cut-off for the low frequency damping part and cut-off for the high frequency damping part.

Figure 17 Amplitude response of a low pass filter.

Analogue to digital conversion The number of bits in an Analogue to Digital Converter, ADC, sets the number of possible finite steps in the conversion of an analogue signal to a digital signal. The dynamic range of the ADC is set by the nominal converter range and the possible levels of amplification before the converter on an ADC-card. The sampling rate naturally sets an upper limit for the highest frequency that can be recognized in a sampled sequence. This is half the sampling rate/frequency, the so called Nyquist frequency. One should aim at using a sampling rate at least two times as fast as the highest frequency component of interest in a signal.

29

Measurement system design

Most ADC-cards are equipped with pre-amplifiers and the noise level in the pre-amplifiers may set the actual resolution of the complete ADC-card. In many ADC setups multiplexers are applied. That is, different channels are fed to the same converter in a sequential way. The maximum sampling rate is therefore determined by the settling time of the multiplexer. If a sampling rate higher than the corresponding multiplexer settling frequency is used there will inevitably be cross talk between the channels. High quality data acquisition cards today have all the above features implemented and the technology improves continuously. In 1996 a 16 bit ADC-card was expensive and not at all standard. Today there are 24 bit ADC-cards available with higher sampling rates and at lower cost than the 16-bit card in 1996. However, the importance of all components in a measurement chain such as sensors, connectors, cables and additional analogue signal conditioning should not be neglected.

Handling and collection of data The handling of acoustic data may become rather complex and require a lot of computing power, especially when saving both raw data and Fourier Transform spectra. In order to have the opportunity to extract time-synchronized data from process databases proper time synchroni- zation has to be performed manually or by means of a Network Time Protocol server [47]. Further, it is an advantage to store settings for signal conditioning. The software available for vibration analysis is not generally adapted to the needs of data transferability in an acoustic chemometric setting. The best solution is to have tailor-made software. The software could in principle be programmed in a number of programming languages and development environments like C [48], C++ [49], Java [50] or LabVIEW (G) [43]. All of these programming languages have advantages and disadvantages. Properties of interest may be documentation issues, learning threshold/time and the availability of functions and libraries for hardware and certain software functionality.

LabVIEW from National Instruments was chosen for the following reasons: Relatively low learning threshold. Good support for different types of hardware. Graphic programming language yielding instant documentation. Good library of signal processing tools. High flexibility when making routines for exporting data in various formats.

Due to system limitations in the early measurement system data processing was done after storing of data. All post processing like FFT was done using MATLAB and Signal Processing Toolbox.

30 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

For writing data in to the data file format, MAT (specified by The Mathworks) [51] an implementation in a public domain VI (Function/sub-function in LabVIEW) was used. In later versions of the measurement system, version two and three, FFT was performed in real- time using LabVIEW but still results were saved in MAT-file format. More details about the design and programming of the measurement system used in this thesis work can be found in [52].

31

Digital Signal Processing

A technique succeeds in mathematical physics, not by a clever trick, or a happy accident, but because it expresses some aspect of a physical truth. O.G. Sutton

The purpose of Digital Signal Processing, DSP, is to process a signal so that it becomes fit for a certain purpose. For instance in mobile phones the speech signals needs to be compressed in terms of bits to be sent and received. Another example is the JPEG2000 standard where wavelets are used to compress images to reduce file sizes. In the context of this thesis one of the objectives with DSP is to get a representation e.g. in frequencies, that can be used with a calibration to get a value for a certain property. Another objective for the use of DSP-methods is to increase the selectivity of information regarding a property to make further modelling less complicated and to provide improved predictions. In addition methods that could be used to extract direct information about the composition of a fluid are of interest. In brief, the objective of digital signal processing in the thesis context is data compression and extraction of relevant features related to pulp quality from the vibration signals. Different DSP methods use different templates and are therefore more or less efficient in extracting information in a given situation. The fundamental assumption in is that any signal can be approximated by a sum of sine waves. Signal decomposition by wavelets is done by summing contributions of short, limited, non-periodic waves that are stretched according to scale (frequency region). These two methods are therefore complimentary. Wavelets may be a good choice when the signal content is non-stationary (varies with time). The Fourier transform works best when the signal content is fairly stationary (does not vary with time). However, if one of these methods is the best choice in a given situation or a combination is more appropriate is a tricky question. The choice must be easy to implement and also take the following use of the data into account. Some good books on these and other DSP methods are [53-57].

33

Digital Signal Processing

Purpose of DSP in the context of Acoustic Chemometrics The purpose of digital signal processing in the context of acoustic chemometrics is to obtain a more useful representation of the acoustic signal. Demands on the representation are that it retains information about a specific analyte or property and suppresses noise and other disturbances. The signal processing chain starts with a . An example is given in Figure 18 showing an amplified and filtered signal from an accelerometer placed on a refiner blow-line. This signal was measured during approximately 0.5 seconds at a sampling rate of 80 kSamples/second. We collected 40 000 samples at each sampling occurrence. In the figure only the 32768 points (215) in the middle of these 40 000 points are shown. Also shown in Figure 18 is the division of points into blocks and a zoom in on one of the blocks.

Figure 18 Plot of a time-series of a vibration signal collected on the blow-line of a refiner Power spectra using Fast Fourier Transform In 1948 Bartlett proposed a method for averaging spectra (periodograms) after calculating spectra block-wise for data and thereby improved the results [58]. Another improvement for calculating spectra was dividing the time series into blocks and applying a weighting window making FT and then finally averaging the frequency representations. This was introduced by Welch [59] using overlaps between the separate blocks of the time-series. The weighting windows were there to reduce the Gibb's effect. This ringing effect is caused by discontinuities when using Fourier transforms to describe a time series.

34 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

A summary of different weighting windows e.g. the Hamming Bartlett and Blackman was presented by Harris [60]. In this article a number of different windows developed during the 1970's are presented, each having both advantages and disadvantages. The developments by J. W. Cooley and J. W. Tukey in the early sixties [61] lead to an algorithm for Fast Fourier Transform, FFT. It was later found that Gauss had worked out the foundation upon which FFT is based already in the 19th century. At the same time similar algorithms were developed in England. In an article about the development of FFT-like algorithms [62] the authors conclude that Cooley and Tukey made a significant contribution after all. The FFT is an efficient algorithm for calculation of the discrete Fourier transform. The algorithm exists in many variants the most common one is called radix-2. For this variant the time series length must be evenly dividable by two. However, there are algorithms available that are capable of handling also other lengths efficiently.

In the book by Hayes [53] a section was devoted to spectrum estimation. This chapter treats algorithms for power spectra from the simplest, to averaged, overlapped and using windows. There are also methods based on eigenvector decomposition (of the signal matrix) before an FFT step. Further, parametric spectral estimation methods based on Auto Regressive (AR), (MA) and Auto Regressive Moving Average (ARMA) models are discussed.

Figure 19 shows the improvements in algorithms for producing spectra. a) FFT performed on a single time-series block (2048 points), b) The same as a but applying Hanning window before FFT, c) Average of FFTs on time-series blocks each with length 2048 point and a total time- series length 32768 points, d) The same as c but Hanning window before FFT. e) The same as c but Hanning window and overlap of 50% on the time-serie blocks. Note that some improvement can be seen from a to b and a large improvement from a-b to c-e due to the averaging effect. There is also a small improvement from c to d using windowing and only minor improvement using overlap of the time-series blocks d-e.

35

Digital Signal Processing

a b 20 20

0 0

−20 −20

−40 −40

−60 −60

Power Spectral Density (dB) 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 c d e 20 20 20

0 0 0

−20 −20 −20

−40 −40 −40

−60 −60 −60

Power Spectral Density (dB) 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 Normalized Frequency Normalized Frequency Normalized Frequency

Figure 19 The results of different spectral calculation algorithms and settings. Spectra made on the time-series shown in Figure 18. Wavelets Wavelets functions are essentially small localized waves. They depend on a base function called the mother wavelet and the scale they are used at. The first known wavelet was created by Haar around 1909 [63]. There is now a vast literature on wavelets. Some good books are Mallat’s oriented towards signal processing [54], an introductory book by Bergh et al. [64] and finally Strang and Nguyen's book on signal processing using some matrix notation [57]. Other good introductory texts and tutorials about wavelets present various applications that may be useful e.g. Alsberg, Woodward & Kell [65], Trygg [66], Unser & Aldroubi [67], Graps [63], Polikar [68], Walczak & Massart [69] and Jetter et al. [70].

Continuous Wavelet Transform The basis for the wavelet theory is the Continuous Wavelet Transform, CWT. A brief introduction can be found in the book by Bergh, Ekstedt and Lindberg [71]. CWT has higher flexibility than the Discrete Wavelet Transform, DWT in it's normal formulation. A more elementary difference between discrete and continuous transforms is that information at each scale is successively peeled of the signal (f) before it is analyzed at the next scale in the discrete version.

36 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

The algorithms for performing CWT on sampled data is often based on first performing an FFT on the signal and then applying a wavelet and scale depending windowing function. This can be formulated as follows [71]

∞ ⎛ t − b ⎞ −1/ 2 (11) W ψ f ()a,b = f ()t ψ ⎜ ⎟a dt ∫−∞ ⎝ a ⎠

Here W ψ is the wavelet transform operator and ψ the mother wavelet. The mother wavelet is parameterized with parameters a and b and the variable t. The scales (dilations) are given by a continuous set of values for the parameter a and the positions (translations along the times axis) are given by a continuous set of values for parameter b. The function of the a parameter is to stretch or to compress the mother wavelet to enable extraction of different frequency components of f. Using this notation we write the mother wavelet at scale a as

−1/ 2 ⎛ − t ⎞ ψ a ()t =a ψ ⎜ ⎟ (12) ⎝ a ⎠ Equation (11) can be seen as a convolution and with the notation given by Eq. (12) we can write Wf ()a, b :=W f ()a,b = f ∗ψ ()b ψ a (13) Fourier transform with respect to variable b gives ℑWf a,β = fˆ β ψˆ β ( ) ()a () (14)

The Fourier transform operator is denoted as ℑ . We now have one part of the expression on the ˆ right side of Eq. (14) that is the Fourier transform of the times series, f (β ). The other part is the Fourier transformed mother wavelet at a certain scale (a) and the “frequency”-translation (shifting) (β). These two parts can be calculated separately which means that we only need to calculate the Fourier part once for each time-series and then weigh this by all the “windows” ψˆ ()β given by the a part. To obtain the CWT of f we need to use inverse Fourier transform of scale normalized Eq. (14) on each scale defined by the set a and b. If we collect and order the results within each scale a by the b a landscape figure can be obtained. In Figure 20 a signal called Devils Staircase is shown (left) and the corresponding CWT on the right. The y-axis on the right is the scale number. The coarsest scale is at the top and the finest scale at the bottom. The intensity in the graph is the magnitude of the CWT.

37

Digital Signal Processing

Devil Staircase Signal CWT

2 0.5

0.4 4

0.3 6 log2(s) 0.2 8 0.1

10 0 1000 2000 3000 4000 0 1000 2000 3000 4000 Time step Time step Figure 20 The Devils Staircase raw-signal and the result of Continuous Wavelet Transform, CWT applied to the signal. Fast Wavelet Transform Fast Wavelet Transform, FWT, and Fast Fourier Transform, FFT, are complementary to each other. The difference between FFT and FWT is that the FFT divides the signal-time series in a finite number of equal sized frequency bins. The Fast Wavelet Transform gives a representation of the signal localization in time while divided in scales with band-delimited frequencies. The scales themselves are the frequency bands of the signal and the information within a scale gives information about a signals location in time. If mild conditions apply for the signals f(t) it is possible to write the Fourier and Wavelet transforms as follows [55]: Fourier Transform 1 ∞ f (t) = f (t) eiω⋅ eiωt dω (15) 2π ∫ −∞

Wavelet Transform

∞ f (t) = ∑ f (t)ψ j,k ψ j,k ()t (16) j,k =−∞

j / 2 j Where ψ j,k ()t =2 ψ (t)(2 t − k) all are translations and dilations of the function ψ . Here j is the scale index and k the translation index. The inner product in eq. (15) and (16) produces

iωt the coefficients representing the original signal in the new bases, e for the FFT and ψ j,k (t) for the DWT .

38 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

One way of using Wavelet Transform is in so-called multi resolution analysis, MRA. One variant of this method is to keep DWT coefficients, the f (t)ψ j,k part for a specific scale, set all the other scale coefficients to zero and then apply inverse DWT.

Yet another use for the DWT coefficients at each scale is to calculate the scale wise, thereby we get a wavelet power spectrum [72] in analogy with what can be acquired by use of FFT.

Wavelet decomposition can be implemented by digital filter banks. This was discovered by Mallat [207] and is called Fast Wavelet Transform. Recursively arranged filters are combined with down sampling until the coarsest scale has been reached. This discovery made the use of wavelets more computationally efficient and therefore more attractive as an analysis tool. The coarsest scale describes the overall signal for the complete time-series using one coefficient. The concept, decomposition and scales are shown in Figure 21. In the Measurement section analogue filters were discussed but the same functionality can be implemented in digital filters.

Figure 21 The concept of decomposition step-wise in scales.

Since the wavelets are scale dependent, their shape vary with scale. In Figure 22 the concepts of location and scale are shown for the Daubechies number 10 wavelet.

39

Digital Signal Processing

Daubechies 10 at various scales and locations

(7,101)

(7,77)

(7,51)

(6,42)

(6,34)

(6,26)

(6,12)

(4,11)

(4, 7)

(4, 3)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Figure 22 Concept of scale and, location (4,3) means scale 4 and location 3 respectively (6,28) scale 6 and location 28.

The most well known wavelets are the orthogonal Haar and Daubechies. The wavelet Haar is both symmetrical and orthogonal, it is actually the same as Daubechies 2. The higher Daubechies wavelets are orthogonal but not symmetrical. The Symmlet wavevlets are nearly symmetrical and orthogonal. This is shown in Figure 23. However, the orthogonality constraints on wavelets can sometimes be less efficient. For analysis of transient behaviour in time-series the Haar wavelet may be a good choice. However, if one whishes to analyse a smooth curve with symmetric peaks a Symmlet wavelet would be a more reasonable choice. If the signal of interest has characteristics in between these extremes the Daubechies wavelets may be suitable. In a chemometric context the choice is not obvious since characteristics that seem appealing when inspecting by eye may not be optimal when using Partial Least Squares, PLS, in a later stage. Testing different wavelets for the specific purpose is recommended.

40 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Haar Daubechies 4 0.2 0.2

0.1 0.1 0 0 −0.1 −0.1 −0.2

−0.2 −0.3 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 Daubechies 10 Symmlet 10 0.2 0.2

0.1 0.1

0 0

−0.1 −0.1

−0.2 −0.2 0.2 0.4 0.6 0.8 1 0.2 0.4 0.6 0.8 1 Figure 23 Graphs of the common Haar, Daubechies and Symmlet wavelets.

Angle Measurement Technique The Angle Measurement Technique, AMT was created by Andrle to characterize geomorphic lines [73]. In chemometrics Esbensen et al. introduced AMT for more general use [74]. The technique gives the measures MDy, MDx, Sdy and Angle as functions of scale. The implementation requires interpolation and is therefore computational time-consuming. Recently the technique has been used in multivariate image analysis by Kvaal et al. [75] and by Huang & Esbensen [76, 77]. Application in image analysis was improved by a new sampling scheme by Mortensen et al. [78].

Spectral images or cubes By combining different transforms on data sets or different sets of related data we can create two or higher dimensional representations of signals. Another alternative would be applying two- or three-dimensional wavelets on two or three dimensional data [79]. The corresponding wavelet power spectra could then be combined into different surfaces or cubes respectively. The development and prospects of higher order data and calibration methods was discussed by Geladi [80] and by Booksh and Kowalski [81].

41

Digital Signal Processing

These higher dimensional representations may for instance be a surface of the product spectra of two different properties or two measurement methods for a physical sample and therefore yields a 3D data cube for a set of samples. A case that would yield a cube for each physical sample is an image where each pixel contains a spectrum e.g. NIR imaging and therefore yields a 4D data hyper-cube for a set of samples. In the thesis scope one could consider two sensors on the same pipe for instance and the surface formed by multiplying the two frequency spectra. The method WT-MRS could also be considered as a one dimensional to a two dimensional representation.

42

Modeling

Nature uses as little as possible of anything. Kepler, Johannes (1571‐1630)

Modelling is an inherent part of our lives, without it the cognitive load would simply be overwhelming. We use models for different purposes e.g. improving the signal to noise ratio from our senses when extracting certain features and in the decision-making processes. Some of the models are unconscious for us and we do not intervene in the use and updating of them. In a technical system like a Fourier transform Near Infra Red-spectrometer we seldom look for how the actual implementation is performed and often we have no need for acquiring that knowledge. When developing practical modelling systems we have to go down to the basics of the implementation or at least to the building blocks of such an implementation. This can e.g. mean to improve the signal adaptively at an early stage rather than to fix the resulting problem in a later step with greater effort. In humans there also exist adaptive systems like the effect when having a conversation at a cocktail party and you suddenly hear your name, then automatically your hearing is sharpened to catch just that voice again. Chemometrics was originally statistical methods for chemical systems [82]. Chemometrics has evolved to cover analysis of other types of data e.g. physical measurements. Svante Wold stated (translated from Swedish) ”It was not long ago that every analytical chemist knew that the best information was obtained from one single signal (variable), that was measured with the highest precision. Chemometrics learn us instead that it is usually better to measure many non-selective signals and then combining them in a multivariate model that is optimal for the question of interest." [83].

When talking about models in a chemometric setting often only the active part of a model is discussed and considered to be "The Model". In reality we always truncate information which we consider just noise. Further, the noise is often so complex that we can not create an appropriate noise model. However, we use the information from the noise space to track when data are outside the normal noise pattern since using a model with these data could yield unreliable results.

43

Multivariate analysis and chemometric methods

To isolate mathematics from the practical demands of the sciences is to invite the sterility of a cow shut away from the bulls. Chebyshev in G. Simmons, Calculus Gems, New York: Mcgraw Hill, Inc., 1992, page 198.

Multivariate statistics is now a well-established field with ongoing research in many areas, from algorithms to issues when applying chemometrics in real-time applications. Further, the use of these methods has spread from laboratories to process control rooms over the years. The words chemometrics and multivariate analysis will be used interchangeably throughout this thesis. The term chemometrics was coined by Svante Wold and Bruce Kowalski [82]. For an overview of multivariate analysis the following books; [84-87] and tutorials [88-90] may be useful.

In chemometrics, variables are commonly subdivided into X where often measurements, process data, experimental plans etc go and Y where reference measurements, economical or environmental figures or class (indicated by -1, 0 or 1) can be included. This division has its reason in the use of regression-tools for modelling where x is the independent variable and y is the dependent variable in a univariate regression setting.

Scaling and transformations of data matrices One reason for applying scaling and transformations on data before modelling is to set different variables/frequencies on an equal footing. Another reason is that reference measurements may have a non-linear behaviour that we wish to linearize. The pre-treatment of data before multivariate modelling is sometimes crucial for obtaining high quality models. In the acoustic setting, the dynamic range is large, hence, in order to get the variables on a suitable scale, logarithms are normally applied. One could also use auto-scaling on the data directly. The latter option may be a bit risky if there is an outlier at some frequency. Centering means substracting the average of a variable. This results in a linearization around a stationary point. Auto scaling means first centrering and then dividing by the standard deviation of the variable. Thus, resulting in a variable with mean zero and a standard deviation of one. This is graphically presented in Figure 24 for two variables where x has average -2 and standard deviation 0.5 and y average 3 and standard deviation 5.

45

Multivariate analysis and chemometric methods Original data Mean centering 15 10 10 5 5 0 0 −5 −5 −10 −3 −2 −1 −1 −0.5 0 0.5 1

Scaling by standard dev. Auto scaling

2 2

0 0

−2 −2 −6 −4 −2 −2 −1 0 1 2

Figure 24 The effect of centering and scaling on two variables

If a certain variable a has relatively small standard deviation compared to the others in the same block of data X or Y auto scaling may be problematic. By weighting up a possibly less significant variable compared to the other variables, noise may be amplified [85]. It is especially important to keep an eye on this when using PLS2 with several Y-variables. If the ratio between the standard deviation for a variable in a dataset and the standard deviation for that particular measurement method is low, then it is likely that merely noise is modelled. A variable with this character may control modelling to a great extent, therefore down-weighing of such Y-variables might be sensible.

Principal Component Analysis, PCA Principal Component Analysis, PCA is the workhorse in multivariate analysis. It can be said to be a development of the . Least square fit was invented by Gauss in 1795, but his work was not published until 1808. Meanwhile, Legendre published the procedure for least square fit in 1805. In least squares fit the distance between the curve and the dependent variable, y, is minimized. In 1901 Pearson introduced what could be regarded as PCA for two variables [91]. In Figure 25 it is shown what distances that are minimized in Orthogonal least squares (PCA-like) and Ordinary least squares.

46 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Note that for orthogonal least squares the distances between the data points and the regression line perpendicular to the regression line is minimized while for Ordinary least squares the distance parallel to the y-axis between the data points and regression line is minimised [92]. Orthogonal Ordinary 60 60

50 50

40 40

30 30

20 20

10 10 0 2 4 6 8 0 2 4 6 8

Figure 25 The difference between Orthogonal least squares and ordinary least squares There is a large basis of literature from many fields about the use of PCA [90, 93]. The major computational methods for PCA are Singular Value Decomposition, SVD [94] and Non-linear Iterative Partial Alternating Least Squares, NIPALS, [95, 96]. One advantage with the NIPALS algorithm is that it can easily be modified to handle . According to Nelson et al. [97] up to 20 % of the data may be missing using a modified version of the NIPALS algorithm and the replacement of missing data still works. However, if the missing data is non-randomly distributed to a high degree, it might be problematic. There are also a large number of rules and performance indicators for guiding the choice of a suitable number of principal components for different purposes [93, 98, 99]. The purpose of using PCA is usually to enable an overview of data by lowering its dimensionality by a change of coordinates. In Figure 26 the matrices involved when using PCA are shown.

Figure 26 Overview of matrices involved when applying PCA

47

Multivariate analysis and chemometric methods

In equation form

T X = TP + E (17) Where T contains the new coordinates called Scores and P the coefficients transferring old coordinates into new. P is called the Loadings matrix. E is the residual matrix, lv is the number of principal components, m is the number of variables (or frequencies) and n is the number of objects/observations.

Classic univariate methods and methods with few variables In regular (the least squares fit), we have independent X and dependent Y. In univariate Classical or Ordinary Least squares, CLS or OLS respectively, the squared distance between the Y-value predicted by the model , Yˆ , and the Y-value from data, Y , is minimized. By using this criterion it is assumed that X is error free and only Y have errors. The regression coefficient can be calculated as follows [100].:

T −1 T b = ()X X X Y (18) The optimal fit can be written:

Yˆ = Y = Xb (19) When X is extended to be a data-matrix containing several variables applying equation (18) is called Multi , MLR. This works well as long as the X-variables are not co-linear. Then problems with inversion of the (XT X) part in (18) will inevitably occur.

Principal Component Regression, PCR To overcome the shortcomings of Multi Linear Regression in the case of having co-linear X- variables, one possibility is to use the scores, T from a PCA-model. Modifying equation 3 by replacing X by T gives.

T −1 T b PCR = ()T T T Y + ε (20) Replacing X by T in equation (19) gives: ˆ T Y = Y = T b PCR (21) The combination of first applying PCA on X and then regress Y on the scores is called Principal Component Regression, PCR [101]. When PCR is used, the PCA components are ordered according to the explained variance of X. Thereafter, MLRs are performed on scores, T from PC1, PC 1 & 2, PC 1-3 etc and Y. The combination that yields the highest explained variance of Y with a reasonable number of PCs is then chosen.

48 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Note that the order of the principal components comes from X only. This might be undesirable if the main variation of X does not coincide with the variation in Y. One approach is to reorder the principal components according to the portion of the Y variance that each component explains. The combination of the reordered scores that explains the highest degree of Y variance should be selected for the model. Note that PCR possibly could be beneficial compared to PLS if Y has a high noise level compared to X. The reason is that PCR determines scores from X only and not from the covariance of X and Y as in PLS. Worth mentioning is that PCA is often used as a compression method before using Neural Nets, NN [102, 103]. The combination of PCA and NN could be seen as non-linear PCR.

Partial Least Squares, PLS In modelling a system we often want a model describing X and Y simultaneously, not X and Y separately. Partial Least Squares also called Projection to Latent Structures is a method towards this direction. The PLS (PLSR) algorithms used in this thesis is defined by the work of S. Wold, H. Wold and H. Martens [82, 104]. The abbreviation PLSR, Partial Least Squares Regression is advocated by Martens to distinguish this method from the original PLS now sometimes called PLS path modelling developed by H. Wold. Variants of PLS used mainly in social sciences and have recently been described by Tenenhaus et al. [105]. Only the PLS-versions commonly used in a chemometric context will be treated henceforth in this thesis.

In PLS the aim is to find a space yielding the highest covariance between X and Y. When building models this is accomplished by using two sets of score vectors T and U and a linear relationship between them. In Figure 27 the different vectors and matrices used in PLS are shown with an exception for the inner relation between the scores T and U.

49

Multivariate analysis and chemometric methods

Figure 27 Schematic overview of matrices involved when using PLS

In form of equations T X = TP + E (22)

T Y = UQ + F (23)

U= bT + G (24) Where U and Q are scores and loadings respectively, corresponding to the Y-variables. b in equation (24) is the slope in the inner relation modelling the connection between T and U, the X- and Y-scores. E, F, G are the model error matrices, ideally containing only noise, lv is the number of PLS-components and p is the number Y-variables.

Note that there are PLS-extensions with non-linear relations replacing (24). Replacements could be polynomials [106, 107], splines [108] or small neural nets [84]. A more straightforward way was proposed by Berglund and Wold. By expanding the X-matrix with squared or cubic terms, non-linearities could be handled. In this way normal diagnostic plots could be used [109]. They later proposed a serial PLS variant [110]. Serial here means to first calculate a model partly describing Y and then model the residual Y with another model structure.

50 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

It was shown that it could be advantageous to first model the linear part, then in the next step model the non-linear part by squaring the residual X-matrix. There are also extensions with an additional “outer” relation, replacing Y = Yˆ in Equation (19) and adding an equation

Y = f (Yˆ)where f may be a polynomial [111] or a small neural net [112].

k k Feature 1 C 1 1 1 lv 1 m NPLS 1 lv B Object _X 1 lv _Y 1

n n A 1 m 1 p n Variable Var.

Figure 28 Schematic overview of some of the matrices involved when using NPLS.

Bro extended the PLS2 algorithm into a n-way formulation dealing with X and Y matrices with more dimensions than 2 [113]. Bro et al. further improved the NPLS algorithm to give more reasonable predictions for new independent data [114]. In Figure 28, some of the matrices involved when using an NPLS model are shown. Note that Y can be a column vector, matrix or a tensor (Y), in the figure indicated by the dashed lines. The factors A, B, C describe the X-part, but there exist a similar set of factors for the Y-part (not shown) and there also exists an inner relation similar to (24). Note that Y must have the same number of objects but the other directions can be different from the corresponding directions of X.

Orthogonal Signal Correction, OSC In Orthogonal Signal Correction, the main idea is to remove information not correlated with Y from X. This is done by constraining the deflation of non-relevant information from X so that only information orthogonal to Y should be removed. The first paper on Orthogonal Signal Correction was presented by Wold et al. [115] for use on NIR-spectra. An application to calibration transfer for NIR was published by Sjöblom et al. [116].

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Multivariate analysis and chemometric methods

Methods related to PLS and OSC Direct Orthogonalization, DO, was developed by Andersson [117]. Westerhuis et al. claimed that the prediction errors were not improved by using DO, but the interpretability was enhanced [118]. They also remarked that loosening the orthogonality constraint against Y might improve the method. External Parameter Orthogonalisation Partial Least Squares, EPO-PLS [119], is also similar to OSC. However, external measurements are used remove the associated spectral variance, this is exemplified by using temperature measurements to remove spectral variance caused by temperature effects. Generalized Least Squares, GLS is a method using prior knowledge about interferents and their spectra to remove this information prior to modelling by PLSR or other methods [120]. Extended Multiplicative Scatter Correction, EMSC, is a further development of MSC [121] which removes the slope and intercept of a spectrum (scattering effects will often affect these parameters). EMSC has been shown to remove scattering effects in Near Infrared Transmission spectroscopy while not removing the chemical information [122]. According to Martens and Naes [84] the scattering effects are handled as a first-order approximation in bi-linear methods, like PCR and PLS. FactNet™ or Factor Network Analysis, FNA, was introduced by Strand [123, 124] for statistical modelling of pulp and paper data. A number of applications has been reported mainly in conjunction with mechanical pulp production or development [125, 126]. Exactly how the FNA- model is estimated, is not well described in the literature. However, it appears to be a principal component analysis of the composite [X Y] matrix. The factors (c.f. scores in PCA/PLS) can then be used in either "filter " (similar to predictions from PCA-model with lv number of PCs) or "input/output mode" which means regressing Y against the common factors.

Total Least Squares, TLS, is well described in the book by Wantufel & Vanderwalle [127]. This method seems to solve the same problem as the input/output version of FNA. To the author's knowledge this has not been commented elsewhere. It should be noted that TLS has now evolved to a large number of algorithms for handling specially structured data. Further, TLS has evolved to handle data with different distributions and for applications in control theory, signal processing and other scientific areas [127, 128].

What is the relation between PLS and TLS/FNA? They both model one subspace for both X and Y. One could argue that PLS models a common subspace for X and Y.

52 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

However, PLS does not use the same objective function as FNA or TLS. The PLS maximizes co- variance between X and Y while TLS/FNA maximizes the data reconstruction of X and Y using the selected subspace of the composite [X Y].

A further development of PLS is Orthogonal Projections to Latent Structures O-PLS [129] and O2-PLS [130]. These methods can be considered to be implementations of PLS with an integrated OSC-filter [131].

Wavelets in chemometrics The use of wavelets in chemometric applications has increased a lot lately. The book by Chau et al. [132] has many examples from the analytical chemistry area. There are also a number of applications used for modelling process industry plants. Specifically, there are an increasing number of applications of wavelets in the pulp and paper area. The works that follow are sorted according to application and purpose of using wavelets. The first area to look at is wavelets used for removing background or noise in spectroscopic or chromatographic data e. g. for background removal [133, 134], compression [66, 135], de-noising [136], fault detection [137] or feature extraction [70, 138-145]. Wavelets used on process data and process models is another large area [146-152]. In the pulp and paper area wavelets have been used in connection with the application of NIR [135, 137] as mentioned above and for analysis and improved control of paper machines [153]. Another application is the analysis of paper formation using wavelets [154].

Instead of looking at the applications and the purpose where wavelets are used, works can be arranged after how data fusion is performed. How the data are merged in steps like feature extraction, feature selection, feature weighting and top-level weighting. For more information on this subject, consult Liu & Brown [155].

Uncertainty in measurements In order to properly calibrate for a specific property of any kind, knowledge of the measurement error is a necessity. Knowing the approximate error of the reference methods (including sampling uncertainty), gives us a hint of the prediction error that a calibration model can ideally yield. This can be used as a reasonable first target for a project using these techniques. Information on the origin of the major contributions to the uncertainty in a method gives us the opportunity to improve those inferior steps.

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However, in reality there are often few steps that can be changed. On the other hand, the standard procedures may require certain steps to be performed in defined ways. Further, to have knowledge of the possible errors in the signal from the sensor/s on which the calibration and prediction is based is useful. Thereby it might be possible to minimize these errors and provide predictions that are more trustworthy.

Validation In validation of models there are different approaches, statistical and physical/chemical. The statistical way is to use values of goodness of fit or confidence limits on model parameters. The physical/chemical way of validation is to verify the model parameter’s agreement with pre- existing knowledge of the system. The essence of model validation is to determine if a model give results that are accurate enough for the intended purpose.

Partitioning of data sets for generating uncertainty values The first, best and most optimal procedure would be to have two or more independent data sets. Using one set for building a model and one set for testing the model. However, it may be costly or even impossible to acquire an additional data set. The second best is cross validation, CV, [98, 156, 157]. CV is to keep out a certain portion of a data set, calculate a new model, apply the model on the kept out part of the data set and repeat this until all portions of data have been kept out. Thereafter, goodness of fit values for the cross-validated models and the within model variation are calculated. The data kept out are usually sample/s or alternatively certain combinations of variables and sample/s taken out one at a time, as proposed for PCA by Wold [98]. Note that there are two ways of validating multivariate models. One is to recalculate the models completely for each round in the cross validation and the other is to do it component- wise for each round. The simplest validation is internal validation where the validation is made on the same data as the model is built on. In Figure 29 a schematic overview of the different validation procedures is shown.

54 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Figure 29 Different ways of model validation in a regression setting. Sample leverage A useful metrics for how strongly a sample affects a PCA or PLS model compared to other samples is the leverage. However, it is not a validation figure in itself, but combined with the sample residuals, it can be very useful. It is defined as follows [86]:

NoPC 2 1 tia hi = + ∑ T (25) n a=1 ta ta Where

hi sample leverage n total number of samples in the model

tia scores value for sample i and PC number a

T ta score vector for PC a, ta is the transpose of ta As seen from the equation the leverage is a measure of how far a sample is from the centre of the model.

Goodness of fit Goodness of fit expresses how well the model describes data. It is natural to inspect how well X and Y are described by the model, in terms of percentage explained variance. A name for the X- part is R2X or Explained variance of X. For the Y-part a similar metric can also be calculated. In addition, for validation data R2X and R2Y can also be calculated whether test set or cross validation is used. R2Y calculated for cross-validated models is often called Q2.

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Multivariate analysis and chemometric methods

These metrics work well even if we have multivariate Y and not only one single Y-variable. Often we also look at how well a model predicts a single y property, the Root Mean Square Error of Prediction or Calibration, RMSEP or RMSEC respectively, shows the error in the same unit as the property measured [86].

2 ∑()yRef − yEstimated RMSEC = (26) (n −1)

yRef value obtained by the reference measurement on a sample

yEstimated value obtained by using the model and X-data for a sample

n total number of samples in the model

Note that we can compare RMSEP/C with the of the reference method (including all stages from sampling to analysis) and see this standard error as a lower bound for the model prediction error (RMSEP/C). Another commonly used acronym is RMSECV where CV stands for cross validation. RMSEP is also used when talking about predictions during cross validation.

When calculating RMSEP on a completely external validation set YEstimated is replaced by YPredicted. Commonly used is also Pearson product moment correlation, r2 that equals one if the prediction and the reference values are identical and equals zero when they are completely un-correlated [158]. Note that RMSEP/C and r2 do not directly incorporate any errors in the reference values. To consider errors in both predicted and reference values we have to use something like regression, orthogonal least squares, orthogonal distance regression or similar [92].

Physical, chemical, process and system knowledge in validation Here we use data or knowledge from sources other, than those used directly in building the models. Such complementary information or pre-knowledge can support or undermine the model. Some techniques have scales that are well known and we can therefore based on our knowledge of the sample/s, confirm or reject a calibration model. This is the case e.g. in Near Infra Red, NIR, or . In NIR bands/position on the wavelength scale exist for different functional groups. Therefore, with knowledge about the analytes, a comparison of the loadings or regression coefficients and bands can be made. In mass spectroscopy, the peaks correspond to the chemical compounds or fragments of them. With knowledge of the analytes we can compare the masses for complete compounds and possible compound fragment with the mass spectra.

56 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

When using passive acoustics we do not have the Golden standard we would wish. Here we have to rely on relative changes between samples. Sometimes it is possible to obtain a semi-physical interpretation of passive acoustic data. If one have several installations on close to identical process-lines the spectra acquired are often very similar. This could be seen as within site validation of the measurements.

Multivariate modelling in practice When modelling, it is always good to start by a first look at the raw data. However, we have to keep down the number information bits, by using clever graphs or by aggregating data in a bright way. This is needed since according to Miller we can only handle seven plus or minus two information bits simultaneously [159]. There are a number of ways to compress data. The best choice depends on the starting structure. For time-series, it is natural to use Fourier transform or for compression. Wavelets may also be useful to minimize the number of points in the time series. Since many measurements are related to concentration or other properties in a non-linear way it is reasonable to apply univariate transforms like logarithms or square root on those variables.

Validation of the data-flow is an important issue to secure high quality throughout a work. Selecting data from a sensor to visualize in each step of data treatment, compression or feature extraction might be worthwhile in large projects. A sensor could in this case be an NIR- spectrometer that is validated to give consistent spectral output. A variant of sensor could be a custom-built instrument based on a physical sensor for vibration or pressure. This means that we need to validate each step from the sensor to the spectral output. In commercial instruments e.g. an NIR-spectrometer this is performed by the producer. This step is also crucial when moving from off-line use of models to on-line use of models, especially when using custom-built instruments.. It is easy to discard incomplete data in the modelling process but while running on- line there is a risk that a fraction of data is incomplete or faulty. Therefore validating the data flow and data conversions is important to ensure the quality of data fed into the models. Thereby, improving the reliability of the used models.

After raw data inspection, it is common to make a proper centering and scaling. For a graphical overview of the effects of centering and scaling see Figure 24. Centering means that we make the modelling around a stationary point, usually the mean value of data. Scaling may be needed to bring different variables/properties on the same scale or to make groups of properties or variables of equal importance. For two-way data tables centering and scaling is usually done in the

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Multivariate analysis and chemometric methods object/sample direction. A common scaling is to divide each variable by its standard deviation and thereby give all variables standard deviation one. The combination of mean centering and scaling by division by the standard deviation is usually called auto scaling or z-standardization. However, before centering and scaling in the object direction, these operations might be needed in a similar way in the variable direction. This can reduce variations caused by disturbances not related to the property we wish to model. For instance, the shape of a spectrum might be of interest and not the magnitude at each frequency. Scaling in the variable direction can be done by constant sum normalization or Standard Normal Variate, SNV transformation (auto scaling in the variable mode/direction) [160]. In three-way tensors/data tables, scaling is often done in other directions/modes than the sample/object mode.

The next step is to use PCA or if data has a dimensionality larger than 2, use unfolding versions, MPCA [161] alternatively Multiway PCA [162] or true multi-way methods such as PARAFAC [163] or TUCKER3 [164]. The aim is to get a lower order representation of the multivariate data, facilitating inspection. For simplicity, we only deal with two-way data and PCA here. Using standard software the variance explained for both X and Y is presented for the samples used in model building. Similarly, the explained for samples predicted from a model using cross validation or test set validation are given. These figures are usually presented as a function of the number of principal components. The within model total explained variance typically gets higher and higher, while the validation total explained variance usually reaches one or several maxima. If the within model and the validation explained variance differs largely it is an indication that some variables or objects deviate from the rest. This means that the magnitude of the coefficient for the object or variable differs significantly from the main pattern. A large difference between within model and the validation explained variance could also be an indication of over fitting. The next to inspect is an x-y plot of scores with PC1 versus PC2, looking for groupings and outlying samples. The latter may be supported by the use of Hotellings T2 confidence intervals identifying samples lying outside or near the limit. However, this should be used with caution, since a 95 % confidence limit means that one in twenty samples are by default outside the limit. A score plot is shown in Figure 30.

58 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Figure 30 An example of a score plot PC2 vs. PC1

It is often motivated to look at the first 2 or 3 PCs, since they often contain the major part of the variance in the data. If the purpose is to use the model for multivariate process control or regression, we might consider inspecting all significant components found by cross validation. Here it is often a good idea to look at the corresponding loadings to see what variables influence the scores for a particular sample or group of samples. In addition, looking for variables that deviate from the main pattern in the loading plot is recommended. Possibly, those variables that are strongly deviating can be removed and could thereby improve the model quality. Additionally those variables that are clustered at origin in an x-y loading plot can possibly be removed. However, caution should be taken so variables explained by higher PCs are not removed, if the objective is not to obtain the simplest model possible. The next graph to look at is the sample residual versus the model leverage. Here the samples lying above the diagonal from lower right to upper left is considered. They should be at a higher risk of being outliers the closer to the upper right corner they are. By medium risk samples we mean samples that might affect the model while the evidence for being an outlier is low. A high information sample means that the model explains the sample well and it is of great importance for the model. This is shown in Figure 31. If a confirmed outlier is not removed from modelling, we risk that the estimated model will not be representative for the data set and likely not representative for similar future data sets. When building a model with extreme values (outliers) present these will influence the model weights to a great extent.

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Multivariate analysis and chemometric methods

Figure 31 Residual vs. Leverage plot

When the outliers found have been removed and a new PCA-model has been made this can be used for finding outliers in the new sample set. At this stage, we have probably found a few possible outliers. If the PCA-model is to be used the outliers should be removed. If the data should be used in a calibration the following way may be used: If the outliers can be judged as purely X or Y outliers it is wise to remove them from further modelling. If it is likely that these samples exhibit the same pattern in both X and Y it is wise to further investigate these possible outliers before removing them. This can be done by iteratively removing them in different regression models. Keeping a sample if the model does not improve when it is removed and rejecting a sample permanently if the model improves significantly.

We now have data arranged in two blocks X and Y for regression analysis, with PLS or PCR. Usually we use PLS because it produces simpler models measured as the number of principal components. In the modelling phase it is common to use leave-one-out cross validation. That is, leave one sample out of the sample set in the modelling. Using the model to predict the sample excluded and calculate its goodness of fit. This procedure is repeated for all samples in the sample set. Cross validation is a substitute for having a separate set of samples for validation. In many applications, the cost of reference analysis is very high. Therefore, it is hard to justify the additional costs for extra samples.

60 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

There are several more important graphs and figures to look at. Since we most often calibrate for some property the predicted versus reference graph gives a fast impression of how good the property is modelled. In this type of graph it is common that predictions from a model built on all samples along with predictions using cross-validation are presented together. This gives a first view of possible over- and under-fitting. If the predictions using a model built on all samples and predictions using cross validated models differ a lot then caution should be taken. Some outlying samples may be present even if they seem to be predicted correctly. Possibly, there could be variables with irrelevant information. It could even be so that X-data are not informative enough in explaining Y-data. This missing information or unmeasured data are sometimes named Lurking variables [123]. One other thing that might be present is a non-linearity between X and Y. Inspecting the scores t vs. u component-wise is a way to identify this type of non-linearity. This is shown in Figure 32. Note that no outliers are shown in this figure. Outlying samples can be identified in this type of plot if they do not follow the general pattern or if a sample is an outlier by extrapolation. The latter is when a sample lies close to the same line but separated from the rest of the samples. Further, if X contains information that does not overlap with Y there will be a larger spread around the linear relation between t and u..

Figure 32 Example of t vs. u graph, with one linear inner relation and one quadratic inner relation.

Another graph to look at is the scores plot for instance tPC1 vs. tPC2 for an overview of samples, to identify outliers and groups of samples in a similar way as mentioned for PCA c.f. Figure 30.

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Multivariate analysis and chemometric methods

The next graph that is useful to inspect is a leverage vs. residual variance graph, this is available both for the X- and Y-part of the data. In this graph, we can see which samples are of importance for the model and samples that are poorly modelled. If a sample is both important and poorly modelled it is likely that it has features that are different from the rest of the population. The inspection is done in the same fashion as for PCA, see Figure 31. Thereafter graphs showing the degree of variance modelled for the two data parts X and Y should be inspected. Commonly the explained variance for samples used for modelling and explained variance for samples used for validation are shown in such graphs. If the within and validation explained variance differ significantly it indicates that the model has deficiencies. Such differences can be caused by lurking variables, variables with low information content or a non modelled non-linear relationship between the different X-variables or between X and Y. One example is scattering effects in spectroscopic data having a systematic variation not related to Y. Based on one or several of these graphs iterative re-modelling is often needed. Attempts where suspected outliers are moved in or out of the data set is often required to find a reliable and stable model. It is important not to exclude important information-rich samples while excluding erroneous ones to achieve high quality models that are valid for explaining future samples. When the resources are available, it is usually very good to have a second data set for the final evaluation of a model. However, resources are often limited so cross-validation is often the only viable way to test a model.

Experimental design The word experimental design has a wide meaning. Here the statistical plans and the use of plans is discussed. For instance, we might want to optimize a quality parameter by changing Feed (A), Energy input (B) and Water Feed (C) in a mill. Very commonly, we could vary A first and keep B and C constant. Then vary B and C and keep respectively A & C and A & B constant. This optimization strategy is called one variable at a time. The advantage is that it is simple and easy to understand for everyone. However, the disadvantage is that we do not find the global optimum, only some local optimum. An additional disadvantage or advantage depending on the purpose is that combinations that are impossible to run in a process will not be found by this optimization approach. To overcome these disadvantages the use of statistical designs for trials is advantageous. Here we can also look at co variation between variables. A disadvantage is that the number of experiments can become numerous, using this approach. Another purpose is to use a statistical design for trials as a clever "selector" of different process conditions when calibrating a sensor.

62 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

In Figure 33 a full factorial design in three variables and two levels (to the left) and a , CCD, are shown. The two level design can be used to evaluate main effects A, B, C and combinations AB, BC, AC and ABC but no square effects of A, B or C. For evaluation of square effects of A, B or C a CCD-design or similar designs must be used.

Figure 33 A full factorial design (to the left) and central composite design (to the right) for three variables. Additional trial points in the CC design are unfilled or gray, centre point is in gray and so called star points unfilled. The designs mentioned are suitable when the number of variables is low and the costs for experiments are bearable. D-optimal designs provide a way to reduce the number of experiments. These designs work essentially by space filling the experimental domain. When using D-optimal designs, you often specify the equation you wish to use for your model. An advantage is that they can be used to rescue factorial designs that fail in the middle of a trial. This is done by putting in the model structure and the additional process constraints that have arisen during the trial. Thereafter the algorithm is supplied with the finished trial points and finally new adapted trial points are calculated.

A good introduction to experimental design and optimization can be found in a tutorial by Lundstedt et al. [165] and the books by Box, Hunter and Hunter [166] and by Esbensen [86]. In this work experimental design has been used where it was practical. It has been used to systematically vary process parameters for obtaining high information quality spectra/acoustic data and pulp samples spanning large ranges in different properties.

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Industrial application and implementation issues

It isnʹt that they canʹt see the solution. It is that they canʹt see the problem. Chesterton, G. K. (1874 – 1936) in ʺThe Point of a Pin in The Scandal of Father Brown.ʺ

A very brief overview of the background and development of the measurement system used for collecting data used in this thesis work will be presented. Further, issues concerning performing trials in a process industry environment will be discussed. In addition the modifications made on the equipment originally intended for use in a laboratory environment will be described.

Development of the measurement system used We built our first measurement system in 1997. Since then a number of modifications have been made. The largest change is in the data storage capacity. We have moved from 4 GB to 500 GB and the present price tag for the storage capacity is only half the initial one. Another improvement is that we now have the option to compute spectra in real-time, which was not possible with a first generation Pentium computer. Also, the improved processing capacity has made it possible to acquire data at higher rates and with better robustness. For more through overview of the measurement system used from see [52] (In Swedish).

Experimental design in the mill environment For proper use and successful experimental design in an industrial environment pre-trials are necessary to find hard and semi hard system limitations and non practical operating regions. Hard system limitations are those set by law and those introduced for safety reasons. Semi-hard limitations are set for control reasons during normal operation and for hindering operators from running the process in less stable regions. Pre-trials also have a training effect on plant operators and plant supervisors. It is easy to forget all the time and effort that is necessarily put into planning before presenting the idea of a trial, for mill managers and operators. The motivation gap [167] between an engineer in planning and those involved in the performance in a later step may be enormous. The unknown might be frightening and create insecurity. In such cases tiny amounts of additional information can do wonders.

Handling of experiments in a mill Additional constraints may cause an experimental plan or design to be non-applicable, when it is to be used. It is a good idea to think of possible pitfalls and to prepare a strategy for changes. It is always better to sacrifice a trial point in the beginning of a trial series and make changes that

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Industrial application and implementation issues could facilitate completion of the trial in a controlled way, then causing problem in the middle or end of a trial. Running a trial with factors that were supposed to be controlled but turned out to be uncontrollable due to process constraints is a waste of time. It is wise to always collect additional data in the normal production state. This may help out if something fails during the course of the trials. However, special care should be taken in the analysis step when using such data. Another more feasible option would be to use experimental design software that supports D-optimal designs. In such software the model equation of interest, the limits for the different variables and results for already run trial points are added. After adding the additional constraints needed to handle problematic settings new trial points can be found. This will take advantage of already run trial points and all new trial points will be optimal.

Environmental consideration in system design In designing a measurement system there are considerations in the physical design that needs special attention. Securing that electric currents are not affecting people or machinery is essential as is securing that electric fields do not affect the measured signals. Humans are affected by such low currents as 1 mA and 50-150 mA may be lethal [168]. Physical shielding of the conductors in the cables is important. In an industrial environment placement of cables and selection of materials for the cables is essential so that the insulating properties are not degraded by heat or by contact with oils or other chemicals. Most available hardware for high quality measurement of vibration is intended for laboratory use or for use during short periods in an industrial setting. Hence, we need additional containment of measurement equipment to ensure that it will not come in contact with water. The same applies to cable connectors that may need an additional sealing protecting it from humidity. We also need to protect the equipment from being altered by mistake by unauthorized personnel. Different parts of the electrical system in a process industry may have potential differences that are nearly constant or even worse, floating in correlation with the load on the electrical system. For instance if two power outlets exist that give 220.4 V and 220.9 V respectively we have a potential difference of 0.5 V between the outlets. Therefore one must connect all units in the measurement chain to one connection point on one phase in the electrical system. From this point leads are connected as needed to equipment placed for instance in proximity of a process unit.

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Previous work in the field of Acoustic Chemometrics and related technologies

The ideal engineer is a composite ... He is not a scientist, he is not a mathematician, he is not a sociologist or a writer; but he may use the knowledge and techniques of any or all of these disciplines in solving engineering problems. N. W. Dougherty, 1955

In this chapter, work that is closely connected to techniques used or developed in this thesis will be presented. Due to the many fields touched upon in this work including vibration, acoustic and ultrasonic techniques, it is impossible to give a complete overview of all related techniques and applications. Figure 34 shows an overview of related acoustic sensor technology. The starting point will be “Passive acoustics with and without the use of constrictions” followed by “Acoustic emission and active ultrasonics”. The final part is dedicated to "Pulp and paper applications and low frequency spectroscopy”. There is some degree of overlap between these areas but they are there to provide a background to the current work.

Figure 34 Overview of related methods and the main contributors.

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Previous work in the field of Acoustic Chemometrics and related technologies

Passive acoustics with and without the use of constrictions In 1989 Björn Hope patented an acoustic method using specialized valves or constrictions for monitoring oil production [32]. The samples were composed of crude oil, sand and water in fluids from an oil well [169]. Another application monitoring of the content of de-icing fluid in water at Gardemoen Air Port outside Oslo [170], is described on the company Sensortekknikks’ home page. The company markets the product under the name FPS (Fluid Purity System). An application quite close to Hope's oil application acoustic monitoring of two phase flow through nozzles in refineries was proposed by Cody et al. [171]. They used the invention to improve operation stability and to improve product yield. Belchamber & Collins applied for a patent [172] for acquiring audible sound from (ball) mills during grinding. The signal was processed to obtain the particle size distribution of the material. At Telemark College University a large amount of work based mostly on Hope’s basic idea was performed from 1994 and onward. The first paper by Esbensen et al. deals with monitoring of pneumatic transport of particulate materials. They discuss sensor positioning and different data transforms as well as variable selection. The frequency region they use is from zero to almost 50 kHz [173]. Halstensen and Esbensen presented the idea to use additional particle segregation making coarse and fine particles come out of the particle transport system at different times. They made several acoustic measurements with a certain interval between recordings for one batch of particles, using such a system. In this way they got time-resolved spectra that could be used, in two-way and three-way PLS, to predict the particle size distributions [174]. Huang et al. used a similar technique without any additional constriction to measure the degree of powder breakage when transporting alumina powder using pneumatics [175]. In this paper they tried FFT, AMT and Wavelets for making representations of the vibration signal before powder fraction size modelling using PLS. However, they came to the conclusion that FFT was superior. In a second comprehensive paper by Esbensen et al. the use of constrictions to create additional turbulence is discussed and shown to facilitate extraction of features of the fluid. They present results for three different systems, trace levels of oil in water, jet-fuel-glycol mixtures and paper- pulp constituents in water. The problems with a complex system are illustrated by the latter, where a minor part of the spectral variation is modelled for prediction of the constituent named "S". They also discuss sensor positioning and the use of vibration measurements for predicting flow rates for complex mixtures [173]. Eggen, Halstensen and Esbensen patented a method for measuring viscosity of polymers using a constriction and recording acoustic emission [176]. In Halstensen's PhD thesis further applications and projects that he has been involved in are listed [177].

68 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

By using acoustic chemometrics Esbensen et al. showed the feasibility of EMF (transverse ElectroMagnetic Field)-induced pipeline friction reduction [178]. Halstensen et al. showed the feasibility to use acoustic monitoring for an industrial granulation process [179]. Among other things they tested a new type of high temperature microphone. Mortensen and Frank patented a method for determining the particle size of a biotechnical compound using passive sensors in the frequency range 10-50 kHz [180]. Bruwer et al. developed a soft-sensor based on vibration measurements for snack food texture [181]. Interestingly, they built PCA-models on spectra for each trial point, which they used for removing outlying spectra, before calculating an average for the trial point. Very good results were obtained for two textural parameters. An introductory book chapter was written by Westad, Esbensen and Hope presenting the outline of using passive audible and low frequency ultrasonic acoustic chemometrics [182].

At the Swedish Environmental Institute, IVL, Hope's method was used to measure the concentration of different oils in a cold rolling mill emulsion [183]. A cross-validated explained variance of 98 % was achieved for three oils in the emulsion examined.

Acoustic emission and active ultrasonics Belchamber et al. used acoustic-emission to study hydration of silica gel to obtain information about amount of material present, water content and particle size. They used and found four different AE-signals during the reaction [184]. power spectra was applied when different phase transitions were studied in some chemical model processes by Wentzell and Wade [185].

Most likely the first acoustic chemometric article was “Acoustic Emission: Is Industry Listening?” written by Wade in Chemometrics and Intelligent Laboratory Systems 1990 [186]. The author outlines many issues that are still important when setting up and using acoustic chemometric systems. Wade states “Chemometric techniques and acoustic data are ideally suited to each other.” and continues “…Without chemometric techniques interpretation of such data would be nearly impossible. Moreover, the problems posed by acoustic data analysis are suggesting new chemometric tools. This is hardly surprising when one realizes the number of ways a stochastic series of individual waveforms may be interpreted.”. This was further promoted in a similar way for the analytical chemistry community by Wade et al. [187].

Wentzell, et al. showed that it is feasible to follow a catalysed decomposition of hydrogen peroxide to water and oxygen using acoustic emission [188]. Crowther et al studied acoustic

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Previous work in the field of Acoustic Chemometrics and related technologies emission from an electrolysis cell by use of a broadband transducer (audible to 800 kHz) [189]. The characteristics of the different signals and different data extraction techniques like pulse counting, DC level and frequency are discussed. They remarked that good control of the bubble formation is essential for the measurement reproducibility. Brock et al. published a paper on an extensive software toolbox for acquiring and analysing chemical acoustic emission data [190].

As mentioned above Belchamber and Collins were some of the first to show the benefits of using acoustic emission for analytical chemistry. They were pioneers in the modern use of ultrasonics for monitoring of chemical processes working in the process analytical group at British Petroleum, BP. A part of the group later founded the Process Analysis and Automation, PAA Ltd. They market complete measurement and evaluation systems based on ultrasonic or acoustic emission sensors. Additionally, as mentioned above they patented a method for determining particle size.

Using PAA equipment work has been performed at the University of Hull by Flåten & Walmsley. In their first work they used Savitsky-Golay smoothing of spectra from an acoustic signal (from a Root Mean Square-Direct Current (RMS-DC)-converter) before analysis by PCA. The recordings were made on a fluidised bed. They achieved a more distinct time trail and the smoothing before PCA made it easier to detect an agglomeration event [191]. Flåten & Walmsley also developed a tool for handling acoustic data called "Caterpillar" that uses a moving window PCA [192]. They build models on data t(-n) to t(-k) and use the model on the prediction-window t(-k+1) to t(0), where t(0) is the present time and where k is less than n (n, k are finite sample steps).They then determine the prediction error when using the PCA model on the prediction window. This allows for detection of changing processing conditions while the model adapts to new conditions. The method seems robust against added noise and trends in the acoustic signals.

Mylvaganam et al. used impedance measurements from ultrasonic transducers for gas density measurements in combination with chemometrics to circumvent the dual effect of temperature and density on the sensors [193]. In a later work Mylvaganam et al. used both active and passive sound sensors to monitor flow of solids in silos. They used multivariate data analysis as a data fusion method [194]. Whitaker et al. used acoustic emission measurements for following physical properties of powder material during high shear granulation [195]. They reported that the technique was able to

70 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry monitor changes in particle size, flow and compression properties. Models connecting the acoustic spectra with the different properties were built using PLS2. Cross validation was used due to a small number of runs. They evaluated three different ultrasonic sensors from Physical Acoustics, Cambridge, UK with resonance frequencies 30, 70 and 150 kHz. The signal conditioning for the ultrasonic sensors came from PAA Ltd. It was concluded that spectra from the 30 kHz sensor yielded the lowest prediction errors.

Pulp and paper applications and low frequency spectroscopy In an early and rather comprehensive work by Reiner & Jackson, they used an active ultrasonic sensor setup for characterization of ground wood pulp [196]. Dumount et al. used acoustic emissions from a pulp refiner to classify which wood specie that was used [197]. Using this data set Yang & Dumont tried a Hebbian net, a type of neural net as feature extraction method [198]. Eriksen measured both vibration and pressure on refiner-plates inside refiners. He used commercial accelerometers and pressure sensors as well as tailor made fibre optic sensors [199]. Backlund measured shear forces and temperatures inside refiners and related this to the fiber development [200]. Hartler and Strand measured vibration on the outside of a refiner stator using accelerometers. They found that the variation in vibration along the refiner-plate radius changes during a plate- life [201, 202]. Strand and Mokvist showed that at a certain point along the plate radius vibrations increase while the motor load decreases. Here fibre cutting occurred thereby lowering the long fibre fraction [203]. It is notable that the spectrum of vibrations [199, 201, 202] measured on refiners differ strongly from the author's spectrum of vibrations measured on the blow-line from a refiner.

Backa, Liljenberg, Åbom and Thegel at ABB developed and patented an application of active low-frequency spectroscopy. They proposed the use of a low-frequency sound source, like a loud speaker or electric shaker (preferably below 20 kHz). The sound interacts with a composite of gases, liquids and solids. The sound resulting after the is recorded by use of microphones, dynamic pressure sensors or accelerometers and a spectrum or the phase is calculated. This spectrum is used to predict particle size, concentration/content or other properties of the suspension. Possible applications in pharmaceutical process lines and refiner lines in pulp production are outlined. Different types of signal sources are also proposed, even amplitude modulated signals. In the description they discuss different measurement cases, the effect of different source signal types and the evaluation. However they came to the conclusion:

71

Previous work in the field of Acoustic Chemometrics and related technologies

"The above examples are only given as oversimplified examples to increase the understanding of the possibilities of a system with controllable active sources. In real cases the situations are far more complicated and multivariate statistical analysis or neural networks are for instance used to evaluate the measured acoustic spectra" [204]. At the same time Backa et al. also applied for a patent for refiner control based on the same technonology [205]. They point out in both applications that influences by disturbances are lowered by using an active source compared to passively measuring on the process fluid. They also claim that they do not need to recalibrate for different production sites as opposed to passive acoustics [205]. ABB later followed up and patented the use of similar technology for determining the velocity of a fluid [206]. The application seems to require less statistical treatment of the measured signal. Another difference is that the sound resulting from the fluid in interaction with the sound source is measured both up and down stream from the source. ABB also applied the technology for monitoring and control of pharmaceutical, chemical and food processes, where biological processes are active. That is micro-organisms or bio-molecules are produced in the process. The state of these processes is detected by monitoring the viscosity, aggregate size, contents of dispersion of proteins, crystalline particles or fat droplets. Here they used the technology described in [204] and they also used ultrasonic transducers for measuring e.g. fat dispersions. A new sensor approach is also introduced by using a plurality of polymeric tubes with piezoelectric wires as sensing device. They also used hydrophones as sensors. Another additional component compared to previous systems is a silencer in the flow-path of the fluid to reduce pulsations. This system also seems to need chemometric evaluation.

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Summary of articles - From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

In this chapter, a summary of the main findings in the articles and also some additional unpublished results will be presented. The work can be arranged naturally into four areas. These areas show the shift in the main focus of the thesis from using standard chemometric tools to signal processing methods for best utilization of the information in the acoustic measurements in the applications studied. The division into areas could have been made from application or measurement points of view but the main theme is the development of generic tools for acoustic chemometrics.

Adapted chemometrics for acoustic signals, Paper I and Beating of Kraft pulps in pilot scale (Additional unpublished results) In this section we deal with articles where standard chemometric tools are used in conjunction with standard Fast Fourier Transform for prediction of properties of interest in pulp applications. The first application is in TMP refining systems, paper I, with data from two refiners. These data come from May-July 1997 and December 1998. The second application is on monitoring of beating of kraft pulps in a pilot plant. The first preliminary trial was performed in November 2003 and followed by a more comprehensive trial in April 2004.

Thermo mechanical pulp refiner From article I, the average spectra from three trials performed in 1997-1998 are shown in Figure 1a. Note the similarity in spectral shape between trials 1 and 3. In a later step these trials are modelled together. In Figure 35b all spectra from the third trial are shown. Two apparent outliers are visible, one spectrum differs by exhibiting generally greater amplitude and the other spectrum by having generally lower amplitude. These two trial points should be kept out of modelling since they are clearly not representative for the trial.

73 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

Removed in the on-line version. Fig 3 in Paper I

Figure 35 a) Average spectra for trial 1-3, b) All trial point spectra from trial 3

In article I separate modelling of the different trials are discussed. Here some important results are highlighted. In Figure 36 the results from modelling Canadian Standard Freeness, CSF based on data from trial 1 and 3 are shown. CSF is a measure of the drainage resistance of a pulp. In Figure 36a the cross-validated results are shown for an optimal PLS model, using 6 PLS- components. In Figure 36b corresponding results are shown using a combination of 2 plus 2 OSC- and PLS-components. The prediction error is 58 ml for the PLS model and 39 ml for the OSC-PLS model.

Removed in the on-line version. Fig 6 in Paper I

Figure 36 Predicted vs. Reference CSF for a) PLS-model, b) OSC-PLS-model. CSF is given in the unit ml. From Paper I. In other reports where OSC-PLS has been used the total number of components has usually been the same as with PLS alone. Here the model complexity in terms of the number of components is reduced by two. We believe the two data sets contain different features

74 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry corresponding to CSF but also include features not related to CSF, among those are differences between the different trials. The two data sets come from different seasons and also different refiners. Note that CSF measurements cover a large range and the pulp characteristics most certainly change non-linearly in this range. This may be an additional reason for the good result using OSC-PLS.

Removed in the on-line version. Fig 7 in Paper I

Figure 37 Prediction of CSF every second for three process conditions (180 s for each condition). From Paper I. Using data from the first trial, models were built and used for prediction of CSF every second. Three models were used for prediction using the same number of PLS-components. The predictions for each second for three process conditions A, B and C are shown in Figure 37. Trial points A, B and C respectively were omitted during the model building phase. In Figure 37 we have added a gray-line using a Savitsky-Golay smoothing, for removing short-time variations (spikes). Clearly there are more pronounced spikes for conditions A and B. An explanation to this may be that the process is normally operated at the C level. The CSF prediction every second could be used in control of the refiner. Before use in a controller the prediction should be subjected to some filtering.

Main findings in Thermo mechanical pulp refiner The combination of OSC and PLS for modelling of FFT-spectra from the refiner blow-line gives lower prediction error and overall more parsimonious models, then using only PLS. Data from two different trials were combined for this test. Prediction of CSF every second was achieved for three different process conditions (runtimes 180 s each). However, filtering would be needed if this signal should be used in a controller.

75 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

Beating of Kraft pulps in pilot scale (Additional unpublished results) In December 2003 and April 2004 we attempted monitoring of beating of Kraft pulps in a pilot plant at the Swedish pulp and paper research institute, STFI. The major difference between this system and the TMP-system is that here we have fibres in water and not fibres in steam. Another difference is that in Kraft pulping wood is treated with high temperature alkali to remove the lignin while in TMP wood chips are divided and defibrated by the use of mechanical energy. In these trials we used additional hardware compared to that described in Paper I, see Appendix 1, Systems 2 and 3. For evaluation MATLAB 6.5 and Unscrambler 8 and 9 were used. Two questions were of importance: Do the measured vibration signals depend on the pulp quality rather than only on the energy input in the mill? Can we predict some selected pulp properties with use of PLS models?

We made one small trial in December 2003, where pulp was beaten in one stage at six diffent energy levels. All beaten pulp was collected in a storage tank and thereafter beaten at three levels. During trials signals from vibration sensors before and after the mill were logged and treated to yield power spectra. Vibration data were collected at 80 kHz sampling rate therefore yielding power spectra with a frequency range of 0-40 kHz. Some frequencies at the lower and upper ends were not used in the analysis, because they were disturbances from net frequencies or they had low information content. We also collected various process variables by a second data acquisition system and also in the Distributed Control System, DCS, in the pilot plant. After making preliminary examination of data by use of PCA, it was concluded that one index summarizing the degree of beating seemed to be a good idea.

76 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Figure 38 Dataflow in a hierarchical PCA based model In Figure 38 the data and parameter flow from these models are shown. The index is composed by the summed difference between auto scaled score values from PCA models from sensors before and after the mill.

The index was visually fitted to net energy input by adjusting the scale for the net energy. When fitting only data belonging to the first beating step was used. This is shown in the first part of Figure 39 by comparing the dashed line with the solid line.

77 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

Figure 39 Comparison between index and energy input. The energy used in the actual stage is indicated by the dashed line and the index by the solid line. The dash-dotted line indicates the actual energy input plus 14 % of the energy in previous stage.

The next step is to compare the same lines in the second beating stage. Not surprising the lines deviate. A new line was made where 14% of the average energy in the first stage was added to the actual value in the second stage in every time point. This to get a good agreement with the new dash-dotted line and the index is obtained. This illustrates that the model value, V does not only reflect the energy input but the actual state of the pulp.

In a second more comprehensive trial pulp was beaten using different, flow/consistency, refiner plates and conductivity. Here seven beating curves with varying energy input were produced with all conditions constant within a curve. For one curve pulps were collected in a tank and re-beaten in a second stage yielding an additional beating curve. Vibration data was collected with a sampling rate of 200 kHz, yielding power spectra with a frequency range 0-100 kHz. Frequencies at the lower end and the upper third/quarter part of the spectra were not used in the later analysis, due to their level of disturbances or low information content. In this work it was decided to model all quality data together in a PLS2 model. Data from both sensors (after and before mill) were used in the major modelling. Due to using a too high amplification of one accelerometer signal in two beating curves, the intercept and the slope of the spectra had to be removed. This was done by taking the second derivates of the power spectra. For this we used the Savitsky & Golay method. Characteristics of two reference methods made the scaling of

78 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry quality(Y)-data in the PLS2-model important. The parameter Britt Dynamic Drainage Jar, BDDJ, seems to have high measurement noise and the parameter Shopper Riegler, SR, is non-linear in its character. In addition Water Retention Value, WRV, was measured on the complete slurry (WRV whole pulp) and where the fines fraction was removed before analysis (WRV fibre fraction). For the validation of the PLS2 model cross validation was applied keeping a complete beating curve out of modelling. This was repeated until all beating curves had been held out and tested. The results from the modelling are shown in Table 2. In model M1 all beating curves were used except for one single point in one beating curve that was withheld. M2 is where one beating curve was kept out in addition to that in M1 (including the bad point in M1). M3 is the same as M2 except for the property BDDJ was down-weighted. M4 is separate models for each property, otherwise same as M3. For all models, spectral regions with low information content were kept out.

Table 2 Resulting models from the second trial at STFI. Correlation (r2) and prediction error (RMSEP/C) are shown both for calibration (cal) and cross validated beating curves (val). r2- RMSEP- r2- RMSEC- No. val. val. cal. cal. PC M1-SR 0.74 3.591 0.92 2.057 3 M1-WRV whole pulp 0.81 0.060 0.95 0.031 3 M1-WRV fiber fraction 0.80 0.041 0.95 0.024 3 M1-Fine fraction BDDJ 0.72 1.011 0.86 0.747 3 M2-SR 0.81 3.044 0.96 1.434 4 M2-WRV whole pulp 0.86 0.052 0.97 0.023 4 M2-WRV fiber fraction 0.81 0.040 0.95 0.022 4 M2-Fine fraction BDDJ 0.72 1.011 0.88 0.695 4 M3-SR 0.83 2.950 0.97 1.363 4 M3-WRV whole pulp 0.86 0.052 0.97 0.026 4 M3-WRV fiber fraction 0.81 0.040 0.95 0.023 4 M3-Fine fraction BDDJ 0.70 1.045 0.85 0.770 4 M4:1-SR 0.83 2.892 0.98 0.997 5 M4:2-WRV whole pulp 0.85 0.054 0.97 0.026 3 M4:3-WRV fiber fraction 0.75 0.044 0.96 0.020 3 M4:4-Fine fraction BDDJ 0.81 0.886 0.96 0.387 5

In the M4 models where one pulp quality parameter at a time was modelled using PLS1, slightly better result were obtained, when using one PLS2-model. For the BDDJ property the improvement using PLS1 is the greatest compared to the others. It is expected that it would gain from concurrent modelling with other properties. It is our opinion that these parameters describe similar variation in pulp quality. Therefore, not much is gained by modelling them separately. Additionally, making the vibration measurement chain more robust e.g. by automatic fine-tuning of the amplification of the accelerometer signals would improve the results.

79 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

Main findings in Beating of Kraft pulps in pilot scale The vibration based quality indicator does not only show the energy input in the refiner, it also reflects the beating history of the pulp. Predictions of important pulp quality parameters such as SR, WRV for the fine fraction, WRV for the complete pulp and Britt Jar Dynamic Drainage can be made with acceptable uncertainty.

Connecting quality values, screen efficiency and acoustic sensors for obtaining better understanding of a screen system, Paper II A unique combination of engineering numbers for evaluation of screens and data from acoustic sensors is explored. It should be seen as a preliminary conceptual assessment of what can be done in this application with acoustic sensors and multivariate analysis. The screen engineering numbers used here was delta CSF, fine fraction yield, long fibre fraction yield and passage ratio. These were calculated from a combination of process data and laboratory values. Fibre length distributions measured with Kajaani FS100 were used to calculate these numbers but were also analysed by PCA. PLS-model were built for composite measurements of pulp quality (CSF, Long fibre and fines content) and the screen engineering numbers were analysed in the same way. The main objective here was not to predict quality values or screen numbers but to show that we could use them to get an indication of the total status in a screening system based on acoustic measurements.

Removed in the on-line version. Figure 2 in Paper II

Figure 40 Scores and loadings from a PCA model of quality parameters. From Paper II.

80 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Removed in the on-line version. Figure 8 in Paper II

Figure 41 Scores and loadings from a PCA model for screen efficiency numbers. From Paper II. In Figure 41a the scores for every trial point is seen and in Figure 41b the corresponding loadings are shown. In the loadings we can se that the passage ratio could be used to control the delta CSF since loadings are at almost same the level in PC2.

Removed in the on-line version. Figure 11 in Paper II

Figure 42 X-scores and X-loadings from a PLS model using data from both accelerometers and screen efficiency numbers. From Paper II.

The scores shown in Figure 42a are more ordered compared to Figure 41a. This is due to the simultaneous modelling of both acoustic data and screen efficiency numbers. A comparison of Figure 42b and Figure 41b shows that the weights for delta CSF and passage ratio is now shifted towards the negative side of PC2 otherwise the pattern from Figure 41b is retained.

81 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

Main findings in connecting quality values, screen efficiency and acoustic sensors for obtaining better understanding of a screen system Acoustic measurements and quality measures predicted from acoustic data could be used to monitor the conditions in a screen. In addition concentration can also be predicted using the acoustic sensors. This work should be seen as a feasibility study of some of the possibilities this technique may offer.

Abstract feature extraction with improved interpretability, Paper III and IV One of the drawbacks of ordinary FFT and standard multivariate calibration is the low interpretability. Here a step towards better interpretability is taken by the use of a combination of Wavelet Transform and Fourier Transform.

The new algorithm Wavelet Transform Multi Resolution Spectra, WT-MRS, is built on first performing wavelet transform of a time series and then performing Fourier transform on coefficients from each wavelet scale. This gives features that are more accessible than by using regular FFT-spectra. However, there is a drawback with the coarse wavelet scales where there are few coefficients compared to FFT-points. Here zero-padding (adding zeros to a time-series to get even numbers of two elements) has to be applied to enable the use of the same number of FFT- points. On the other hand on finer scales we have more coefficients than the number of FFT- points, here blocks with the length of the FFT-points are made, the FFT is done on each block and then averaged. A schematic drawing of WT-MRS is shown in Figure 43.

82 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Removed in on-line version. Figure 3 in Paper III

Figure 43 Schematic overview of WT-MRS. Slightly modified from Paper III.

Figure 44 shows from top to bottom the original time-series and Multi Resolution Analysis, MRA, for selected wavelet scales (left) and power-spectra on the original time-series and Multi Resolution Spectra, MRS for selected scales (right). It can be seen that different features are extracted at different scales. Performing FFT and WT-MRS on raw data from Trial 3 in Paper 1 combined with PLS calibration gives an opportunity to compare two methods alongside. Here N- PLS was also tested to enable us to arrange data into a three dimensional data cube (tensor). This is natural since we have the trial points, wavelet scales and the frequencies at each scale. Although the frequency scales are not the same for the different wavelet scales it seemed appropriate. For comparison to FFT we folded the spectra to a surface. Different wavelets and vanishing moments were also tested. Best results were obtained using Symmlet 10.

83 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

Removed in the on-line version. Figure 5 in Paper III

Figure 44 Treating data using Multi Resolution Analysis, MRA / Multi Resolution Spectra, MRS. From Paper III.

84 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Removed in the on-line version. Fig 7 in Paper III

Figure 45 Comparison of FFT and WT-MRS for a) Regular PLS and b) N-PLS. Grey indicates calibration data and black validation data. From paper III.

In Figure 45 it can be seen that the prediction error, RMSEP for the first PCs, is strongly reduced for WT-MRS compared to only FFT, this applies for both a) 2d PLS models and b) 3d PLS models. Worth mentioning is the lower RMSEP for a WT-MRS model using one component compared to the FFT-only model using 5 (in a) respectively 3 (in b) components. Examining the explained variance for Y, Yfitted, it can be seen that WT-MRS, symm10 captures more variance for the first PC than only FFT. Additionally, the captured variance for calibration (grey) and captured variance for validation (black) is more similar for symm10 than only FFT. Finally looking at explained variance for X for both PLS-versions we find that models using only FFT seem to over fit rather fast. Symm10 data on the other hand fits nicely and stops with a small but confidence giving gap in height between calibration (grey) and validation (black) within model explained variance and cross validated explained variance. One advantage using WT-MRS on vibration data from a TMP blow-line is that features related to CSF is better extracted. The features seem more accessible in the PLS-modelling and hence gives both lower prediction error and a more parsimonious model.

85 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

With these promising results we decided to use the technique on a quite different system. Measurements were performed on the outside of the process pipe containing Medium Consistency pulp. This system is a very thick fibre–in-water system, 7-12 % fibres, and has a consistency similar to a pudding. In the pipe the flow pattern is likely laminar/streamline, at the most very mildly turbulent. This in addition to the vibrations damping of fibres in this thick slurry makes the frequency content decay rather fast. With this in mind, we tried to use the WT- MRS algorithm. In this setup of the WT-MRS we analyzed longer time-series, here 131072 points (the middle part of 200 k points series) instead of 32786 point previously (the middle part of 40 k points series). Therefore we used 17 wavelet scales instead of 15 scales in the previous work. Here we also used 64 points in the FFT step while we used only 32 points in the previous paper. The reason for this is that we anticipated extracting enhanced information with twice as many FFT-points.

Removed in on-line version. Figure3 in Paper IV

Figure 46 WT-MRS of measurement on Medium Consistency, MC stream. From Paper IV.

In Figure 46 the natural logarithm of WT-MRS for the trial is shown. It is possible to see a lot of fine structure in the data, but also the decay in signal strength at the higher dyads -10 to -16. In addition an increase in signal strength can be seen from dyad -1 to -8 in the figure. The corresponding regular power spectra do not provide the easily accessible features that the WT- MRS gives. The next step is modelling of selected pulp properties, here CSF and Brightness. Before PLS-modelling, the natural logarithm treated WT-MRS, CSF and Brightness data were auto scaled. Since dyad 0, -1 and -16 seemed to contain little information it was appropriate to keep these scales out from further modelling. Full cross validation was performed and 6 and 4

86 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

PLS-components respectively were selected for the final model. For CSF an RMSEP of 3.2 ml and for Brightness an RMSEP of 0.4 % ISO was obtained. Both values are similar to the reference method error. Using the final models and scrutinizing their regression coefficients it is possible to see which parts of the WT-MRS that show a relationship to CSF or Brightness.

Removed in the on-line version. Fig 7 in Paper IV

Figure 47 Regression coefficients from models for CSF and Brightness. From Paper IV.

In Figure 47 the regression coefficients for the models for CSF and Brightness can be seen. We can see indications that more information is utilised in the lower dyads (-2 to -6) for CSF than for Brightness and that more information is used in higher dyads (-13 to -15) for Brightness than for CSF. This seems to coincide with what the different properties measure in physical terms. CSF measures how fast and how compact or dense a fibre sheet is formed. This is to some degree depending on how flexible the fibres are. Brightness is composed by light scattering and light absorption. The long fibre fraction (should be represented at the low frequency/scale) should contribute less than the short fibre fraction to both light scattering and absorption due to its lower surface area. It seems like intermediate scales (-7 to -10) contribute rather equal to both properties.

87 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

Main findings in Abstract feature extraction with improved interpretability. A new algorithm WT-MRS was developed for better extraction of information about CSF from vibration data recorded on the blow-line after a TMP-refiner. The combination of WT-MRS and PLS calibration gives more parsimonious models and lower prediction error than FFT and PLS. The combination of WT-MRS and PLS calibration seems to minimize the risk for model over fitting compared to FFT and PLS.

The applicability of WT-MRS to vibration data from a medium consistency pulp stream for prediction of CSF and Brightness has been shown. We have also discussed the magnitude of regression coefficients for both properties and their physical relevance.

This indicates that the algorithm developed helps separating features and facilitates validation of the PLS models in a semi-physical sense.

Feature extraction resulting in physical interpretation, Paper V and VI Here we show a method based on continuous wavelet transform to extract curves that resemble fibre length curves. This gives possibilities to enhanced interpretation in terms of pulp characteristics. In the next step, we used this technique as a base for modelling of optical and strength properties by using PLS2 models.

The starting point for this work was when I tried continuous wavelets on acoustic data and discovered that curves similar to fibre length distributions were obtained. Thereafter the work was started on formalizing an algorithm and optimization of some meta parameters. No direct calibration to the fibre length curves are required. Fortunately, pulp samples were saved and stored deep frozen, so they could be tested for different properties. A comparison between two length distribution methods can not be done directly. Curves from one method have to be scaled to fit the other method and data may have to be binned for the comparison. We have tried to make the evaluation as independent as it can possibly be done. In Figure 14 a schematic overview of the algorithm Continuous Wavelet Transform – Fibre Length Extraction, CWT-FLE is shown.

88 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Step by step the algorithm is as follows 1) Windowing of the time-series in suitable block-length (4096 points) 2) FFT performed on a block. 3) Building a weighting window associated with the Continuous Wavelet base function and changing with the different wavelet scales. 4) Weighting the FFT with weighting function from step three. 5) Performing Inverse FFT to get the time-series in its original domain. 6) Collecting all scales from the CWT-scales, from step 2-5. 7) Taking the average over the “time” direction, then normalizing the obtained length distribution, to sum one. All blocks mentioned in step one are calculated in the same way and averaged after this. Additionally the results for all time-series belonging to a trial point are averaged and a within trial point standard deviation is calculated. For further details, see paper V. In Figure 49 all obtained CWT-FLE are shown.

89 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

Removed in the on-line version. Fig 1 in Paper IV

Figure 48 CWT-FLE Algorithm outline. From Paper IV.

90 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Removed in the on-line version. Fig 1 in Paper V

Figure 49 CWT-FLE for all trial points. Slightly modified from Paper V.

Here only the results and some comments on the direct comparison between FiberMaster (Reference method) and CWT-FLE in terms of relative standard deviation, slope, intercept and correlation are shown. These figures are presented in Table 3. Note that as the fibre length increases the relative standard deviation of FiberMaster increases much faster than for the CWT- FLE. This is pronounced in the 3-4.5 mm and > 4.5 mm fibre class. In the regression and correlation table it can be seen that the absolute value of the slope is above 0.6 for all classes expect the last. This may be caused by the large error of the reference method. At this stage, unfortunately, there is no explanation why the slope becomes negative for the 0.5-1.5 mm class. However, since it seems rather linear it would be fairly simple to correct for this. Note also that the intercepts are fairly small for all fractions except the first one. This could possibly be explained by the fact that FiberMaster has a threshold rule for when a signal is a fibre. Such rule is not possible to include in the CWT-FLE algorithm, or at least it would be very hard to implement.

91 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

Table 3 Statistical number in the comparison between FiberMaster and CWT- FLE. From Paper V. FiberMaster CWT-FLE Length Fraction Slope Intercept r Rel. Std. Rel. Std.

[%] [%] 0-0.5 mm 1.09 0.12 0.78 5.2 3.5 0.5-1.5 mm -0.78 0.32 -0.74 2.8 2.1 1.5-3.0 mm 0.82 -0.01 0.74 6.4 1.1 3.0-4.5 mm 0.61 0.03 0.69 12.1 1.5 4.5- mm 0.25 0.00 0.48 25.4 1.9

A natural step is to use the obtained length curves to model pulp strength and optical properties by multivariate calibration. PLS2 models were used for modelling tensile strength and optical parameters simultaneously yielding two PLS2-models. For comparison, PLS1-models were built separately for each parameter for the tensile parameters and the optical parameters. These models gave equal results obtained by the two PLS2-models. In addition to these models we also tried to model tear strength parameters using CWT-FLE or FiberMaster length curves but without success.

In Figure 50 we show the result of PLS1 and PLS2 models made for tensile parameters both based on CWT-FLE and FiberMaster data. Note that we have expressed them relatively to the reference methods. The levels of uncertainty in the models are on a level that can be expected, for this type of data.

In Figure 51 the corresponding data for optical measurements are shown. Here the prediction errors are somewhat higher then for the tensile parameters. The difference between CWT-FLE data and FiberMaster can partly be explained by that CWT- FLE data was collected 1998 while the laboratory analysis of strength and optical parameters and FiberMaster was made in 2003. Another difference is the physical state of the fibers in the blow- line and in the preparation and the testing in the laboratory. The fibers in the blow-line are in steam while those in the FiberMaster are in water. For the optical and strength testing fibres are prepared in water and then dried.

92 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Removed in the on-line version. Fig 3 in Paper IV

Figure 50 Strength parameters modelled using CWT-FLE and PLS1 & PLS2 models. From Paper VI.

93 Summary of articles -From Adapted Chemometrics to New Signal Processing Schemes for Better Input to Standard MVA Tools

Removed in the on-line version. Fig 5 in Paper IV

Figure 51 Optical parameters modelled using CWT-FLE and PLS1 & PLS2 models. From Paper VI.

94 Anders Björk, Chemometric and signal processing methods for real time monitoring and modelling using acoustic sensors. Applications in the pulp and paper industry

Main findings in Feature extraction resulting in physical interpretation A method/algorithm has been developed for extracting fibre length distributions from acoustic/vibration data measured on a TMP-blow-line. Use of the method on acoustic data has been validated against a commercial instrument, FiberMaster. The results can be considered very good in view of that the CWT-FLE method/algorithm is not fully optimized. This is exemplified by the relative standard deviation for the method being lower than for the reference method; this is pronounced for the two longest fibre fractions. It is additionally shown that prediction of tensile and optical properties can be done by using a PLS2 model in combination with CWT-FLE curves. These results are comparable to those obtained based on using FiberMaster curves instead of CWT-FLE. There were also attempts to model tear strengths both by use of CWT-FLE treated acoustics and FiberMaster data, however, with no success.

95

Conclusions

The work presented in this thesis has resulted in a number of generic tools and algorithms for optimal use of vibration-acoustic measurements for measuring different fluid properties. These tools and algorithms have been applied on acoustic data from various pulp applications with good results. The work performed has also resulted in a comprehensive overview of the technologies needed in an acoustic chemometric measurement system.

It is shown that the use of a fully cross-validated combination of OSC and PLS can give a more parsimonious model in terms of total number of principal components than PLS alone, when using vibration spectra from a refiner blow-line. This might work well also for other acoustic chemometrics applications. The application of OSC seems more promising here than in conjunction with NIR.

Regarding better signal representations two methods that have different use and applicability have been built. They have different objectives. The first method, WT-MRS, extracts as much information from a time series as possible. This results in a non-smooth and feature rich representation with rather low interpretability. The gains in lower prediction error seem, however, promising and on-line implementation would be of interest. The second method, CWT-FLE, is a method for extraction of distribution curves. The results are smooth and interpretable against some reference distribution. Note that this is only tested for fibre length distributions but it is almost certainly extendable to other distribution curves. The validation against reference fibre-length-distributions show encouraging results. Using the CWT-FLE for prediction of strength and optical properties of pulps are viable.

The combination of engineering numbers for screens and acoustic measurements show a possibility for real-time optimization of screening processes.

In the patents on low frequency acoustic spectroscopy an increased sensitivity towards disturbances is mentioned for passive acoustic measurements. These are now at least partly possible to eliminate by the method that facilitates improved feature extraction. It can be concluded that the signal processing developments give new tools that further facilitates the use of acoustic sensors.

97

Conclusions

In terms of applications there is now better scientific background and support. It is possible to measure Canadian Standard Freeness on-line with a sampling rate of 1 sample/second with a PC- based system. Furthermore, it is shown that fibre-length curves could be extracted from acoustic measurements.

In addition to the modelling and signal processing developments related to TMP production a new application on Kraft pulp has been tested with promising results.

With this thesis as a background it can be clearly stated that on-line applications of acoustics in the pulp and paper industry can be successfully implemented if the techniques and procedures discussed herein are used. This could make it possible to use a more proactive control of pulp quality.

98

Future outlook

Some areas certainly need more attention before passive vibration based sensors can be considered standard industrial instrumentation. What’s needed is robustness, cost efficiency and low maintenance. Further, not to underestimate is the current lack of knowledge of the real dynamics in the processes. It is not uncommon that a new sensor technology support new in- depth knowledge about the real dynamics of the processes. This iterative knowledge gathering and technology development sets the demands for the future process control and economic gains thereof.

Pinpointing the areas needed to be improved before this technology breaks through? The complete measurement chain must be made robust against overload. That is e.g. making the system saturated for some time. Further the proper shielding and cabling for long-time stability in an industrial environment is essential. Synchronization of data is very important, doing this automatically would save resources. First saving data from the acoustic system and process data in one database. Secondly connecting switches on sampling valves and feeding this value into the database. Thirdly having a proper residence-time model on-line also feed into the database. Fourthly using residence-times and sampling times to produce a very tightly synchronized data set for calibration. The need for low- cost calibration of these systems preferably without doing many reference analyses would give this technique a boost. Automatic updating calibration models should be something worthwhile putting efforts into, this especially when this sensor technique is used in a closed loop control of process.

Finally, to couple the output from the different methods developed in this thesis with model predictive control, fussy logic control or online simplex optimization of process parameters would be interesting. This should give a boost value of end use of these methods. Likely it would be as a first step to use a normal PID-controller for some property that needs stabilization by control. In addition the method for real-time measurement could enable the use of chemicals for fine-tuning the quality of pulp.

99

Acknowledgements

What we need to do is learn to work in the system, by which I mean that everybody, every team, every platform, every division, every component is there not for individual competitive profit or recognition, but for contribution to the system as a whole on a win‐win basis. W. Edwards Deming (1900 ‐ 1993)

Many individuals have contributed in different ways to this thesis. Some contributions and contributors have been crucial enabling the work in the way it was practically performed.

Individuals Lars-Göran Danielson you are greatly acknowledged for all your efforts in transferring general chemical, statistics and multivariate analysis knowledge. For your ability and drive for new technology, in improving my writing skills and for the good friendship. It has really been a privilege and honour to work for and with you.

My mother Gunhild, father Kjell and my brother Paul is acknowledged for their endless support. A thought is also sent to my no longer present grand parents for all wisdom, knowledge and support they gave.

Rasmus Olsson is thanked for a good and refreshing cooperation on batch modelling. The work contributed to deeper understanding of the mathematics, matrix rearrangements and data structures in batch data modelling for me.

Anders Gannå is especially acknowledged for good overall support, discussion about performing mill trials and good friendship. Anders Åhlund is acknowledged for advocating for a third test at the Ortviken Mill. Joar Lidén is thanked for good support during mill trials. U. Nordlund and R. Persson for arranging with help for installing and repairing equipment and for arranging production shutdowns needed. H. Gavell, H. Persson, B. Svensson, K.-E. Rosenholm, and all others from the ES department helping out at the Ortviken mill. L. Torstensson and his staff at the laboratory at Ortviken mill are acknowledged.

Bertil Roos, Börje Svensson, Anna Tubek-Lindblom and others in planning and running the experiments in the pilot-plant. Ulla-Britt Mohlin and Thorulf Pettersson for inviting me do work at STFI-Packforsk.

101

Acknowledgements

Andreas Woldegiorgis and Martin Kempka for good, nice and refreshing works on different aspects of modeling of MALDI-TOF spectra. Fredrik Aldaeus and Axel Weyler for enlightening questions and thoughts during their master thesis's. Erik Furusjö and Veronica Profir for letting me try acoustic measurements during your crystallization trials in the laboratory.

Graduate students and seniors researcher within CPDC for good discussions at courses and workshops. All the NICE people on the courses in the Nordic countries special thanks to Geir- Rune Flaten and Lari Vähäsalo for your good company and discussions. H. Bärring, E. Furusjö, Y. Liu and M. Åberg for good cooperation during CPDC and NICE courses.

Ola Berntsson for the good times sharing room with you, good help with computers including SETI@home and good company at all breaks. Catharina Silverbrant-Lindh for good cooperation during preparation and lecturing at the courses, nice and friendly company at all breaks. Kiki Price for good friendship and your strong sense for right and wrong. Richard Olsson, Marcus Persson, Atte Kumpulainen and John Sjöberg for your friendship, relaxing dinners and pinball play. Martin Edlund and Karl Bruze is thanked for good friendship and fascinating discussions.

The klot-pepole and Tessla and kikki for many good brakes from science thanks too you all.

Finally all present or previous people at the division analytical chemistry at the school of chemical sciences at the Royal Institute of Technology are acknowledged.

Organisations Centre for Chemical Process Design and Control, CPDC for financial support and for arranging high quality courses and meetings. SCA Graphic Sundsvall, Ortviken paper mill for allowing use of data and for opportunity to make additional trials at the mill. STFI for the interest and resource put in for testing the technique for monitoring of kraft pulp. IVL for allowing me to take additional leave for finishing this thesis.

Foundations and grant contributors Bo Rydins stiftelse for scientific research and Helge Ax:sons stiftelse are acknowledged for the contribution in making pulp testing of large number of pulp samples possible. Klasons stiftelse is acknowledged for making the travel to IPST in Atlanta and the participation at conference the IFPAC04 possible. Roos stiftelse is acknowledge for founds making the presentation at International Mechanical Pulping conference in Quebec possible. Preems Miljö stiftelse is acknowledged for funding the purchase of the first measurement systems.

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