Energy Conversion and Management 49 (2008) 3654–3665 Contents lists available at ScienceDirect Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman Multiple faults diagnosis for sensors in air handling unit using Fisher discriminant analysis Zhimin Du *, Xinqiao Jin School of Mechanical Engineering, Shanghai Jiao Tong University, 800, Dongchuan Road, Shanghai 200240, China article info abstract Article history: This paper presents a data-driven method based on principal component analysis and Fisher discriminant Received 26 November 2007 analysis to detect and diagnose multiple faults including fixed bias, drifting bias, complete failure of sen- Accepted 29 June 2008 sors, air damper stuck and water valve stuck occurred in the air handling units. Multi-level strategies are Available online 15 August 2008 developed to improve the diagnosis efficiency. Firstly, system-level PCA model I based on energy balance is used to detect the abnormity in view of system. Then the local-level PCA model A and B based on supply Keywords: air temperature and outdoor air flow rate control loops are used to further detect the occurrence of faults Multiple faults and pre-diagnose them into various locations. As a linear dimensionality reduction technique, moreover, Principal component analysis Fisher discriminant analysis is presented to diagnose the fault source after pre-diagnosis. With Fisher Fisher discriminant analysis Air handling unit transformation, all of the data classes including normal and faulty operation can be re-arrayed in a Detection and diagnosis transformed data space and as a result separated. Comparing the Mahalanobis distances (MDs) of all the candidates, the least one can be identified as the fault source. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction fault detection and diagnosis methods or strategies that can be summarized into two classes. One is the model-based method, To satisfy the increasing demand of indoor air quality (IAQ) and and the other is the data-driven method. energy conservation, the optimal control strategies of air handling The model-based method is most widely used and developed. unit (AHU) become more and more complex. In the system com- Stylianou and Nikanour [14] used a first-order model to detect posing of AHU and affiliated facilities, the measurements of the faults of temperature sensors by comparing the actual temperature temperature, pressure and flow rate sensors not only indicate the decay with the model output using the hypothesis testing. Wang operation condition, but also play essential role in the different and Wang [15] developed a model-based sensor fault diagnosing feedback control loops. Without the accuracy of the sensor strategy, which took all the commonly used temperature and flow measurements, the controllers may be misled and give incorrect rate sensors in chilling plant into account at the same time. The actions. Consequently, performance degradation, damage to com- model-based method is efficient to detect the complete failure of ponent, waste in energy consumption and decrease of IAQ may sensors through monitoring and analyzing the change of operation happen. As for a long-term used system, actually, one or more sen- condition after the abrupt change of sensor measurement happen. sor faults including complete failure, fixed bias, drifting bias and As to the fixed and drifting bias of sensors, however, it is insensi- precision degradation may occur inevitably. The complete failure tive because the occurrence of these kinds of faults may result in of the sensors may lead to the faulty or dangerous actions of the not the abrupt hard fault but the slow degradation of the operation controller, decrease the life of the facility or even damage them. condition and control efficiency. The fixed or drifting bias may decrease the control efficiency of The data-driven approaches, typically as some statistic methods the controller that result in the invalidation of the advanced opti- [16–19], were presented in HVAC systems recently. With the pro- mal strategies. Therefore, it is necessary to develop suitable meth- cess data collected from both normal and abnormal conditions, the ods to detect and diagnose the sensor faults occurred in the AHU correlation among variables can be analysed. Accordingly, the system. Recently, the study of sensor fault detection and diagnosis intrinsic relationship among those variables can be obtained. Actu- (FDD) are more active in deed. ally, it is the reflection of the corresponding physical models that Based on Annex25 [1] and Annex34 [2], Many studies [3–13], are usually difficult to build for HVAC systems. Obviously, the concerning various faults of facilities and sensors in heating, venti- data-driven method highly relies on the quantity and quality of lation and air conditioning (HVAC) systems, developed kinds of the data obtained. Fortunately, with the popularity of building automatic (BA) and energy management and control systems * Corresponding author. Tel./fax: +86 21 34206774. (EMCS), the operation data including measurements and control E-mail addresses: [email protected] (Z. Du), [email protected] (X. Jin). signals can be collected or obtained easily. Wang and Xiao [16] 0196-8904/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2008.06.032 Z. Du, X. Jin / Energy Conversion and Management 49 (2008) 3654–3665 3655 Nomenclature x measure vector HVAC heating, ventilation and air conditioning L loading matrix FDD fault detection and diagnosis P model projection matrix G data class Greek symbols Sw within-class scatter matrix Qa threshold for SPE Sb between-class scatter matrix u Fisher optimal discriminant direction k eigen value l mean vector l eigen vector y discriminant function Subscripts and superscripts T temperature (°C) ^ modelled part of a vector M flow rate (kg/s) un-modelled part of a vector h relative humidity (%) – mean of samples CX control variable k number of the classes RX related variable in a control loop set set point C control signal sup supply air PCA principal component analysis fre outdoor air SPE square prediction error rtn return air FDA Fisher discriminant analysis w water MD Mahalanobis distance ws supply water AHU air handling unit wr return water IAQ indoor air quality presented principal component analysis (PCA) to detect single sen- x ¼ ^x þ x~ ð1Þ sor fault occurred in the air handing unit. Subsequently, PCA-based where strategies were applied in the variable air volume (VAV) [17,20] T and centrifugal chilling system [18,21]. Actually, as a statistic ^x ¼ PL ð2Þ method, PCA-based strategy can quickly discover the abnormity is the modelled part that represents the projection on the principal occurred in the system after learning the normal condition. How- component subspace showing the normal conditions, while ever, its isolation ability is unsatisfied although contribution plot ee [16], joint angle analysis [20] and knowledge-based analysis [22] ~x ¼ P LT ð3Þ have been incorporated. Also as a statistic method, Fisher discrim- is the un-modelled part on the residual subspace indicating the inant analysis (FDA) is widely used in pattern classification origi- abnormities or faults. With this decomposition, the measurement nally [23]. It is a linear dimensionality reduction technique that space can be divided into two orthogonal subspaces: principal com- can optimize the separation among different data classes. Because ponent subspace and residual subspace. The former refers to the of this characteristic, it can be used to isolate different fault classes condition that normal data variation occurs, while the latter refers so as to diagnose the fault source. As a promising diagnosis meth- to the condition that abnormal variation or noise may occur. Under od, however, FDA still has not been used in the HVAC field at pres- normal operation conditions, most of the projection of x is on prin- ent. Moreover, the multiple faults issue, which was seldom cipal component subspace, while the projection on the residual sub- concerned in the past studies, needs to be paid more attention space is very little. When a fault occurs, however, the projection on since the occurrence of several faults is always inevitable in the residual subspace can be greatly increased. system after a long-term operation. Normal and faulty operation can be distinguished using the Therefore, FDA incorporated with multi-level strategies is pre- squared prediction error (SPE). If Eq. (4) is satisfied, it means nor- sented in this paper to diagnose the multiple faults in AHU after mal operation. On the contrary, it indicates faulty operation or they are detected using PCA method. Firstly, Multi-PCA models abnormity. including system-level and local-level are used to detect whether 2 there is any abnormity in view of different levels. Multiple detect- SPEðxÞ¼k~xk 6 Q a ð4Þ ing models can not only confirm the occurrence of faults but also where Qa denotes a confidence limit or threshold for the SPE. pre-diagnose them into related locations. In addition, FDA is devel- oped to diagnose the corresponding fault source in different local 2.2. Geometric interpretation of Fisher discriminant analysis control loops. With a series of Fisher transformation, FDA can sep- arate different fault classes optimally through maximizing the Fisher discriminant analysis [29,30] is a linear dimensionality scatter between classes while minimizing the scatter within clas- reduction technique, optimal in terms of maximizing the separa- ses. Then the faulty sensor can be isolated through comparing tion among different classes. Through a series of linear transforma- the Mahalanobis distance (MD) for all of the candidates. tion, FDA technique can maximize the scatter between the classes and minimize the scatter within the classes. Consequently, various 2. Fault diagnostics methodology classes can be re-arrayed and separated in the transformed data space. This property of FDA can be used to isolate the fault source. 2.1. Overview of principal component analysis 2.2.1.