Application of Laser Vibrometry to Assess Defects in Ship Hull's

sensors

Article Application of Laser Vibrometry to Assess Defects in Ship Hull’s Welded Joints’ Technical Condition

Adam Szelezi ´nski 1,*, Adam Muc 2 , Lech Murawski 1 , Marcin Kluczyk 3 and Tomasz Muchowski 2

1 Department of Maritime Engineering, Gdynia Maritime University, 81-225 Gdynia, Poland; [email protected] 2 Department of Electrical Engineering, Gdynia Maritime University, 81-225 Gdynia, Poland; [email protected] (A.M.); [email protected] (T.M.) 3 Mechanical-Electrical Department, Polish Naval Academy of the Heroes of Westerplatte, 81-103 Gdynia, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-516-513-666

Abstract: The paper presents the measurement process and test results for six thin-walled plates with different dynamic characteristics caused by different defects of welded joints. The tests were carried out using non-destructive testing (NDT). The authors made an attempt to determine the validity of the use and degree of effectiveness of the tests based on laser vibrometry in detecting defects in welded joints. The tests of welded plates were carried out using displacement laser sensors and piezoelectric accelerometers, while the source of vibration extortion was a modal hammer. In the adopted measurement methodology, the application of accelerometers was to obtain the reference data, which allowed for comparison with the measurement data obtained from the laser vibrometer. The analysis of the obtained measurement data, in the ﬁelds of time and frequency, made it possible to verify the correctness of the data obtained by means of laser vibrometry and to

determine the requirements which are necessary for the correct performance of NDT tests and in the future structural health monitoring (SHM) system of welded joints with the use of a laser vibrometer.

Citation: Szeleziński,A.; Muc, A.; The mathematical model developed in the MSC software Pastran-Nastran was also used in the work. Murawski, L.; Kluczyk, M.; The model was developed for the purpose of mutual verification of the measurement and calculation Muchowski, T. Application of Laser tests. At the present stage of work, it can be stated that the results obtained by laser vibrometry Vibrometry to Assess Defects in Ship methods should be treated as a supplement to the research conducted with traditional piezoelectric Hull’s Welded Joints’ Technical accelerometers. In certain situations, they can be used as an alternative to accelerometers, due to the Condition. Sensors 2021, 21, 895. fact that laser sensors do not require direct contact with the examined object. Where the object under https://doi.org/10.3390/s21030895 test may be in a strong electromagnetic field, optical sensors are better suited than contact sensors.

Received: 8 January 2021 Keywords: structural health monitoring; non-destructive testing; optical vibrometry Accepted: 25 January 2021 Published: 29 January 2021

Publisher’s Note: MDPI stays neutral 1. Introduction with regard to jurisdictional claims in published maps and institutional affil- The main causes of defects in welded joints are deviations from the correct welding iations. technology, improper selection and mispreparation of basic and additional materials for welding [1–4]. Other important factors influencing the quality of welds include non- technological structural solutions of joints, non-observance of the welding technology, insufficient qualifications and irresponsibility of welders and malfunctioning of welding equipment [5,6]. Knowledge of the reasons for the occurrence of inconsistency allows for Copyright: © 2021 by the authors. easier and more precise interpretation of the quality of the tested joints, assessment of the Licensee MDPI, Basel, Switzerland. This article is an open access article impact of such inconsistency on the operational properties of joints and taking action to distributed under the terms and eliminate defects in the process of manufacturing welded structures [6,7]. Welding defects conditions of the Creative Commons due to the mechanism of their occurrence are divided into technological defects, which are Attribution (CC BY) license (https:// directly related to the manufacturing method and arise during an incorrectly performed creativecommons.org/licenses/by/ technological operation (e.g., lack of re-melting, sticking) and operational defects caused 4.0/). by the working conditions of the element (e.g., fatigue cracks). Regardless of the reasons

Sensors 2021, 21, 895. https://doi.org/10.3390/s21030895 https://www.mdpi.com/journal/sensors Sensors 2021, 21, 895 2 of 18

for the defect in the weld, failure to detect it in the production process or release for use can lead to serious consequences [2]. Both the safety of the structure and human life may be at risk. The purpose of using non-destructive testing (NTD) is to determine the type, size and location of inconsistencies (defects in the welded joint) in order to determine their acceptance or the necessity of removing them from the tested item [1,8,9]. Inspection activities to ensure the quality of welded joints are carried out both during the production process and during operation (structure monitoring). Failure to carry out in-service non- destructive testing of technical facilities such as aircraft, ships, lifting equipment or bridges, or to carry it out in accordance with the test procedures, may lead to serious catastrophes and accidents. NDT testing techniques are well researched and give results with usually sufficient reliability [10–14]. However, they have a fundamental disadvantage—they are carried out periodically. In the periods between the tests, the reliability of the structure is un- known. Especially in case of critical events such as a strong storm or collision, it is important to know the possibility of further exploitation of the object. This information must include the degree of potential disaster risk together with the parameters of exploitation with particular emphasis on the time of safe use of the object [13–16]. To this end, research on new techniques known as structural health monitoring (SHM) is being developed [1,5,17–20]. SHM systems use a number of advanced sensors, such as fiber Bragg grating (FBG) sensors [21–24]. There are also works connected with the application of laser vibrometers in SHM application [8,25–31], but authors have not found any information about the use of such sensors onboard ships. A wide range of different measurement techniques and methods are used in marine NDT and SHM techniques. What is more, proper optimization and processing of the obtained measurement signals are extremely important [32]. It is also necessary to “teach” the automatic fault recognition system, both in NDT and SHM examinations [33]. Especially ship structures require precise recognition of their characteristics [34] due to untypical marine constructions [35] and the strong interference of measurement signals by the sea environment. Numerous researchers have conducted trials with various measurement methods, ranging from: electromagnetic sensors [36], ultrasonic-guided waves [37], vibrothermography [38] and fibreoptic techniques (mostly FBG sensors) [39,40]. The aim of this article is to check whether SHM systems based on accelerometers— relatively simple and cheap sensors—can be useful. The authors are interested in the development of SHM systems in shipbuilding [28,41]. Typical dynamic characteristics can be determined for each object [21,42,43]. The distribution of resonance frequencies for the tested and undamaged elements should be constant during the operation of the object. The frequency and amplitude of vibrations in resonance are directly influenced by the mechanical characteristics of the tested object: mass, stiffness, damping factor [44]. A change in one or more of the above elements results in a change in the element’s response to extortion. The difference between the resonance characteristics of the tested object and the resonance characteristics of the reference object may inform us about the occurrence of a fault in the tested object. The authors see the need to implement a fast and reliable method of assessing the correctness of welded joints in a ship’s hull elements, which can be carried out automatically during the ship’s operation [9,45]. The authors attempted to adapt laser vibrometry for this purpose.

2. Materials and Methods Laser vibrometry allows carrying out measurements using a laser beam [26,27,31,46]. It enables measurements of vibrations in a non-contact and non-invasive way. This means that the tests do not affect the examined object in any way. The main principle of the laser vibrometer is that the frequency of vibrations of the tested surface can be measured by analyzing the reﬂected laser beam. The physical phenomena used in the measurements are Sensors 2021, 21, x FOR PEER REVIEW 3 of 19

that the tests do not affect the examined object in any way. The main principle of the laser Sensors 2021, 21, 895 vibrometer is that the frequency of vibrations of the tested surface can be measured3 of by 18 analyzing the reflected laser beam. The physical phenomena used in the measurements are interference and the Doppler effect. Laser vibrometry allows detection of high-fre- interferencequency vibrations and the with Doppler high accuracy. effect. Laser As measurements vibrometry allows are made detection optically, of high-frequency laser vibrom- vibrationsetry is resistant with highto external accuracy. interference As measurements in the form are of made a strong optically, electromagnetic laser vibrometry field. The is resistantmain limitation to external in the interference application in of the vibration form of parameters a strong electromagnetic measurements field. with Thethe use main of limitationlaser devices in the is the application influence of of vibration significant parameters air pollution measurements on the accuracy with of the the use measure- of laser devicesments (in is theextreme influence cases, of significantit is not possible air pollution to perform on the measurements accuracy of the at measurements all). The second (in extremeimportant cases, limitation it is not ispossible the need to to perform place th measurementse vibrometer on at all).a stable The secondand non-vibrating important limitationsurface to isavoid the need measurement to place the errors. vibrometer on a stable and non-vibrating surface to avoid measurementVibration errors. tests with the use of laser vibrometry are often carried out by using the DopplerVibration effect tests[8]. The with laser the beam use offocused laser vibrometryon the tested are surface often will carried be shifted out by if usingthe tested the Dopplersurface moves effect [ 8at]. a The certain laser speed. beam focused By knowing on the the tested distribution surface will of the be shifted vibration if the velocity, tested surfacethe vibration moves frequency at a certain can speed. be calculated. By knowing The theuse distributionof interferometry of the (e.g., vibration Michelson velocity, in- theterferometer) vibration frequencyallows detecting can be the calculated. Doppler Thefrequency use of interferometryshift, which correlates (e.g., Michelson with the interferometer)speed and frequency allows of detecting vibrations the [47]. Doppler In prac frequencytice, in the shift, beam which splitter, correlates a laser withbeam the re- speedflected and from frequency the examined of vibrations object is [applied47]. In practice,to the control in the beam. beam This splitter, creates a lasera changing beam reflectedpattern of from interference the examined on the object detector, is applied which to will the vary control depending beam. This on the creates vibration a changing of the patternexamined of interferenceobject. The data on the of detector, vibration which parameters will vary are depending recovered onusing the vibrationthe interference of the examinedpattern by object. measuring The datathe distance of vibration between parameters the interference are recovered strips using or by the measuring interference the patternlight intensity. by measuring Figure the 1 shows distance a betweendiagram theof the interference Doppler stripslaser vibrometer or by measuring measurement the light intensity.system. Figure1 shows a diagram of the Doppler laser vibrometer measurement system.

FigureFigure 1.1. DiagramDiagram ofof thethe DopplerDoppler laser laser vibrometer vibrometer measurement measurement system, system, where where M M is ais mirror,a mirror, BS BS is a beamis a beam splitter, splitter, BC is BC aBragg is a Bragg cell andcell Oand is theO is object the object under under investigation. investigation.

TheThe operationoperation of of the the measuring measuring system system shown shown in Figurein Figure1 is as1 is follows. as follows. The monochro-The mono- maticchromatic light light emitted emitted by the by laser the laser is separated is separated into twointo partstwo parts by the by first the beamfirst beam splitter. splitter. The testThe beamtest beam hits thehits object the object after passingafter passing through through the second the second beam splitter.beam splitter. The control The control beam passesbeam passes through through the Bragg the Bragg cell. The cell. object The object reflects reflects the test the beam test beam and itand passes it passes through through the thirdthe third beam beam splitter, splitter, where where it is superimposedit is superimpos oned the on controlthe control beam beam and and then then it goes it goes to the to detector,the detector, where where an interference an interference pattern pattern is created is created in accordance in accordance with with the movementthe movement of the of object.the object. The The total total intensity intensity falling falling on the on detectorthe detector is expressed is expresse byd Equation by Equation (1): (1): 2𝜋𝑟 𝑟 p 2π(r − r ) I =𝐼=I + 𝐼 I +𝐼22II𝐼𝐼coscos[ 1 2 ] (1)(1) 1 2 1 2 λ𝜆 where I1 is the intensity of the control beam, I2 is the intensity of the test beam, r1 is the where I1 is the intensity of the control beam, I2 is the intensity of the test beam, r1 is the optical length of the control beam path, r2 is the optical length of the test beam path and λ optical length of the control beam path, r is the optical length of the test beam path and is the wavelength of the laser beam. The result2 of the above equation is interference, which λ is the wavelength of the laser beam. The result of the above equation is interference, describes the change in intensity created by the difference in the distance of the test and which describes the change in intensity created by the difference in the distance of the test the control beam path. The task of the Bragg cell is to modify the interference pattern and the control beam path. The task of the Bragg cell is to modify the interference pattern depending on the direction of the object’s movement (without the Bragg cell, the pattern would be identical for both directions of movement), whereas if the information about the direction of movement is insignificant in the context of the conducted study, the use of the Bragg cell is optional. Sensors 2021, 21, x FOR PEER REVIEW 4 of 19

depending on the direction of the object’s movement (without the Bragg cell, the pattern Sensors 2021, 21, 895 4 of 18 would be identical for both directions of movement), whereas if the information about the direction of movement is insignificant in the context of the conducted study, the use of the Bragg cell is optional. DespiteDespite thethe muchmuch greatergreater sensitivitysensitivity andand frequencyfrequency rangerange ofof detecteddetected vibrations,vibrations, DopplerDoppler laserlaser vibrometry vibrometry is is used used much much less less frequently frequently in SHM in SHM and NDTand NDT than passivethan passive laser vibrometry.laser vibrometry. The reason The reason is the greateris the greater complexity complexity of the systemof the system construction, construction, which meanswhich highermeans costshigher of thecosts system of the itself, system but itself, also of but the also measurements. of the measurements. Passive laser Passive vibrometry laser has vi- abrometry much simpler has a operatingmuch simpler principle operating than interferometerprinciple than laserinterferometer vibrometry. laser The vibrometry. measuring deviceThe measuring consists device of two consists parts—a of laser two andparts—a a detector. laser and The a detector. laser beam The is laser directed beam at is the di- vibratingrected at objectthe vibrating and the object reflection and goesthe reflection to the detector. goes to A the change detector. in intensity A change in the in reflectedintensity beamin the from reflected a vibrating beam objectfrom a is vibrating detected. Duringobject is vibration, detected. the During object vibration, changes its the position. object Whenchanges the its object position. is further When the away object from is furt theher measuring away from device the measuring (position 2),device the distance(position traveled2), the distance by the lasertraveled beam by is the greater, laser beam which is means greater, that which the intensitymeans that of the reflectedintensity beamof the isreflected lower. beam The situation is lower. is The reversed situation if the is reversed object is if in the a closerobject positionis in a closer (position position 1) to(posi- the measuringtion 1) to the device. measuring The principle device. The of operation principle is of illustrated operation inis Figureillustrated2. in Figure 2.

FigureFigure 2.2. DiagramDiagram principleprinciple ofof thethe operationoperation ofof aa passivepassive laserlaser vibrometer.vibrometer. The change in beam intensity is due to the effect of the law of inverted squares, which The change in beam intensity is due to the effect of the law of inverted squares, which explains that the intensity of a light source is inversely proportional to the distance traveled. explains that the intensity of a light source is inversely proportional to the distance trav- The law of inverted squares might be represented by Equation (2): eled. The law of inverted squares might be represented by Equation (2): 1 1 I =𝐼= (2)(2) d2𝑑 wherewhere II isis thethe intensityintensity ofof lightlight andand dd isis thethe distancedistance traveled.traveled. InIn orderorder to carry out out the the measurement measurement with with a apassive passive laser laser vibrometer vibrometer correctly, correctly, it itis isnecessary necessary to toset set it properly it properly in inrelation relation to tothe the examined examined object. object. The The distance distance and and angle angle be- betweentween the the measuring measuring device device and and the the object object is is important. important. An An incorrect distance oror angleangle makesmakes itit impossibleimpossible toto correctly measuremeasure thethe reflectedreflected laserlaser beambeam onon thethe detector’sdetector’s surface, whichwhich maymay leadlead toto aa misrepresentationmisrepresentation ifif thethe beambeam onlyonly partiallypartially reflectsreflects onon thethe detector’sdetector’s surfacesurface (only(only inin certaincertain positionspositions ofof thethe objectobject duringduring itsits vibration).vibration). ForFor thisthis reason,reason, thethe specificationspecification ofof devices devices for for measuring measuring vibrations vibrations by passiveby passive laser laser vibrometry vibrometry often includesoften in- thecludes information the information with details with ofdetails the correct of the settingcorrect ofsetting the measuring of the measuring devices. devices. InIn orderorder toto determinedetermine thethe usefulnessusefulness ofof thethe proposedproposed measurementmeasurement methodsmethods inin thethe analysisanalysis ofof the the technical technical condition condition of plates’of plates’ welded welded joints joints of thin-walled of thin-walled structures, structures, 6 plates 6 ofplates the sameof the dimensions,same dimensions, i.e., 500 i.e.,× 500500 × 500× 4 × mm, 4 mm, made made of of the the same same material, material, i.e., i.e., DH36DH36 steel,steel, werewere tested.tested. TheThe weldswelds werewere mademade byby thethe samesame welderwelder andand thethe platesplates werewere plasmaplasma cut.cut. WeldingWelding waswas carriedcarried outout withwith TIGTIG method,method, wherewhere thethe edgesedges werewere chamferedchamfered beforebefore weldingwelding andand welding welding was was carried carried out out in positionin position 1 G 1 with G with 1 bead 1 bead joint. joint. In most In cases,most jointscases, withjoints welds with welds unsuitable unsuitable for further for further use were use were selected. selected. The jointsThe joints were were evaluated evaluated using using the radiographic method in an external accredited laboratory according to standard 17636-1 and EN 5817. Due to the fact that, in international standards, there are just criteria of acceptance or rejection of welded joints to describe the degree of damage, two RTG/NDT inspectors were asked to determine it. Therefore, the percentage values of damage given Sensors 2021, 21, x FOR PEER REVIEW 5 of 19

the radiographic method in an external accredited laboratory according to standard 17636-1 and EN 5817. Due to the fact that, in international standards, there are just criteria Sensors 2021, 21, 895 5 of 18 of acceptance or rejection of welded joints to describe the degree of damage, two RTG/NDT inspectors were asked to determine it. Therefore, the percentage values of damage given below are subjective but based on many years of RTG/NDT inspectors’ work experience. Thebelow following are subjective types of damage but based to onthe manywelds years were ofdetected RTG/NDT (the inspectors’estimation of work experience. the strength of Thethe welded following joint types in relation of damage to the to parent the welds material were detectedis given in (the brackets): estimation of the strength • P1 plate (100%)—plateof the welded without joint in welded relation joints to the (reference); parent material is given in brackets): • P2 plate (70%)—no• P1 plate full (100%)—platemelting; without welded joints (reference); • P3 plate (95%)—a• P2 platefew spherical (70%)—no blisters; full melting; according to the guidelines of classification societies, the• combinationP3 plate (95%)—a is considered few spherical good; blisters; according to the guidelines of classification • P4 plate (85%)—nosocieties, full melting; the combination is considered good; • P5 plate (80%)—no• P4 plate full (85%)—nomelting; full melting; • P6 plate (55%)—no• P5 plate full (80%)—nomelting, edge full gluing, melting; longitudinal bladder. Before starting• P6the plate measurement (55%)—no tests, full melting, a mathematical edge gluing, model longitudinal of a plate bladder.without a weld was made in orderBefore to startingdetermine the its measurement basic natural tests, frequencies. a mathematical This made model it possible of a plate without a to precisely defineweld the was conditions made in and order experimental to determine research its basic program. natural frequencies.The MSC software This made it possible Patran-Nastranto environment precisely define was used the conditions for this purpose. and experimental The plate and research the mounting program. were The MSC software modeled usingPatran-Nastran 3D solid hexagonal environment elements was with used eight for thisnodes purpose. per element The plate (Hex and 8). the A mounting were model with 407586modeled finite usingelements 3D solid and 1572795 hexagonal degrees elements of freedom with eight was nodes obtained. per element The size (Hex 8). A model of the model waswith the 407586 same as finite the real elements object, and i.e., 1572795 500 × 500 degrees × 4. The of modal freedom analysis was obtained. allowed The size of the determining themodel forms was of the the system’s same as own the real vibrations. object, i.e.,From 500 the× research500 × 4. point The modal of view, analysis allowed only the first fourdetermining forms shown the forms in Figure of the 3 system’sare relevant. own The vibrations. next forms From of the natural research vibra- point of view, only tion have valuesthe above first four180 Hz. forms These shown forms in Figure are hardly3 are relevant. enforceable The in next the forms real situations; of natural vibration have additionally, theyvalues have above small 180 amplitudes Hz. These which forms are are usually hardly enforceableunable to damage in the real the situations; object. additionally, they have small amplitudes which are usually unable to damage the object.

FigureFigure 3. 3.From From the the left: left: first, first, second, second, third third and and fourth fourth forms forms of of natural natural vibration vibration of of the the analyzed analyzed plate. plate. Even higher forms of natural vibration, starting with the sixth one, are difficult to Even higherforce forms with of frequencies natural vibration, exceeding star 300ting Hz. with Difficulties the sixth with one, extortion are difficult of higher to forms result force with frequenciesfrom more exceeding nodal vibration 300 Hz. Difficul lines. Therefore,ties with extortion the number of higher of local forms amplitudes result of vibrations is from more nodalhigher. vibration In order lines. to Therefore, force such complexthe number forms of local of vibration, amplitudes it would of vibrations be necessary to apply at is higher. In orderleast to aforce few such forces complex and moments forms of remaining vibration, in it thewould relevant be necessary phase relationships. to apply In further analyses, only the first two forms of natural vibration will be considered. This decision was at least a few forces and moments remaining in the relevant phase relationships. In further supported by preliminary analyses of the measurement tests. These were carried out using analyses, only the first two forms of natural vibration will be considered. This decision a laser vibrometer. The analysis of the measurements showed that the first two forms of was supported by preliminary analyses of the measurement tests. These were carried out the object’s own vibration are clearly observable. using a laser vibrometer. The analysis of the measurements showed that the first two The adopted measurement methodology assumed simultaneous measurement of vi- forms of the object’s own vibration are clearly observable. bration parameters of the plates, which were enforced by a modal hammer. The assumption is to use accelerometers only in order to verify the correctness of the values obtained during the measurements with the use of a laser vibrometer. Such an approach is to serve the subsequent easy examination of repetitive elements which could be tested in the technological sequence without the necessity of installing accelerometers [29]. The laser vibrometer allowing non-contact measurement is perfectly suited for such an application [48]. Sensors 2021, 21, x FOR PEER REVIEW 6 of 19 Sensors 2021, 21, x FOR PEER REVIEW 6 of 19

The adopted measurement methodology assumed simultaneous measurement of vi- The adopted measurement methodology assumed simultaneous measurement of vibration parameters of the plates, which were enforced by a modal hammer. The assump- bration parameters of the plates, which were enforced by a modal hammer. The assumption is to use accelerometers only in order to verify the correctness of the values obtained tion is to use accelerometers only in order to verify the correctness of the values obtained during the measurements with the use of a laser vibrometer. Such an approach is to serve during the measurements with the use of a laser vibrometer. Such an approach is to serve the subsequent easy examination of repetitive elements which could be tested in the tech- Sensors 2021, 21, 895 the subsequent easy examination of repetitive elements which could be tested in the tech-6 of 18 nological sequence without the necessity of installing accelerometers [29]. The laser vi- nological sequence without the necessity of installing accelerometers [29]. The laser vibrometer allowing non-contact measurement is perfectly suited for such an application brometer allowing non-contact measurement is perfectly suited for such an application [48]. [48]. ParticularParticular attention attention was was paid paid to to the the way way in in which which the the plates plates were were mounted mounted in orderin order to Particular attention was paid to the way in which the plates were mounted in order ensureto ensure the the greatest greatest possible possible repeatability repeatability of theof the tests tests an an example example of aof plate a plate mounted mounted on on a to ensure the greatest possible repeatability of the tests an example of a plate mounted on testa test bench bench is shownis shown in in Figure Figure4. 4. a test bench is shown in Figure 4.

FigureFigure 4.4.P1 P1 plateplate (without(without weldedwelded joints)joints) mountedmounted onon a a test test bench. bench. Figure 4. P1 plate (without welded joints) mounted on a test bench. TheThe measurementsmeasurements were carried carried out out according according to to the the scheme scheme shown shown in Figure in Figure 5. En-5. The measurements were carried out according to the scheme shown in Figure 5. En- Enforcementforcement with with a modal a modal hammer hammer was was applied applied in inthe the marked marked place. place. The The hammer hammer was was op- forcement with a modal hammer was applied in the marked place. The hammer was op- operatederated manually, manually, so soit can it can be concluded be concluded that thatthe place the place of application of application of the offorced the forcedimpact erated manually, so it can be concluded that the place of application of the forced impact impactpulse was pulse not was fixed not both ﬁxed in bothterms in of terms location of locationand the value and the of valuethe extortion. of the extortion. This simulates This pulse was not fixed both in terms of location and the value of the extortion. This simulates simulatesthe actual the working actual conditions working conditions of the planne of thed structure planned structuremonitoring monitoring system. The system. recording The the actual working conditions of the planned structure monitoring system. The recording recordingof the signals of the was signals repeated was ten repeated times for ten each times plate. for each The plate.aim was The to aim check was both to check the repeat- both of the signals was repeated ten times for each plate. The aim was to check both the repeat- theability repeatability of the measurement of the measurement results and results the possibility and the possibility of testing of their testing errors their and errors spreads. and abilityspreads. of the measurement results and the possibility of testing their errors and spreads.

ACC1 LD ACC1 LD HI HI Weld Weld ACC3 ACC3 M M ACC2 ACC2

Figure 5. The arrangement of sensors during the second series of tests. ACC1–3—accelerometers, FigureFigureHI—place 5. 5.TheThe ofarrangement impact arrangement with of a ofsensorsmodal sensors hammer,during during the M—mountings, the seco secondnd series series ofLD—vibrometer tests. of tests. ACC1–3—accelerometers, ACC1–3—accelerometers, laser spot. HI—place of impact with a modal hammer, M—mountings, LD—vibrometer laser spot. HI—place of impact with a modal hammer, M—mountings, LD—vibrometer laser spot. The signals from the modal hammer and accelerometers were recorded using a B&K The signals from the modal hammer and accelerometers were recorded using a B&K measuringThe signals system from consisting the modal of hammera B&K 3050 and-A-60 accelerometers cassette, 4514 were B recorded accelerometers using a and B&K a measuring system consisting of a B&K 3050-A-60 cassette, 4514 B accelerometers and a measuringB&K 2270 type system modal consisting hammer. of aThe B&K apparatus 3050-A-60 wa cassette,s configured 4514 in B such accelerometers a way that andit was a B&K 2270 type modal hammer. The apparatus was configured in such a way that it was B&Kpossible 2270 to type automatically modal hammer. detect Thesensor apparatus overloads was and conﬁgured double impacts in such of a waythe modal that it ham- was possible to automatically detect sensor overloads and double impacts of the modal ham- possiblemer. Accelerometers to automatically mounted detect sensoron one overloads of the tested and plates double are impacts shown of in the Figure modal 6. hammer. mer.Accelerometers Accelerometers mounted mounted on oneon one of the of the tested tested plates plates are shownare shown in Figure in Figure6. 6.

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ACC1 ACC1

ACC3 ACC3

ACC2 ACC2 Figure 6. Picture of the tested plate on a measuring station with the accelerometers installed. FigureFigure 6. 6.Picture Picture of the of testedthe tested plate on plate a measuring on a measuring station with station the accelerometers with the accelerometers installed. installed. Simultaneously to the measurements of amplitudes of vibration accelerations, the measurementsSimultaneously of to amplitudes the measurements of plate of amplitudesdisplacements of vibration after the accelerations, impact with the a modal ham- Simultaneously to the measurements of amplitudes of vibration accelerations, the measurementsmer were performed. of amplitudes The of plate registration displacements of plat aftere theposition impact withchanges a modal was hammer carried out with the measurements of amplitudes of plate displacements after the impact with a modal ham- wereuse performed.of an optoNCDT The registration triangulation of plate position laser sensor changes type was ILD2300-10. carried out with In the order use of to eliminate pos- anmer optoNCDT were performed. triangulation The laser registration sensor type ILD2300-10.of plate position In order changes to eliminate was possible carried out with the sible vibrations of the measuring element that could negatively affect the obtained results, vibrationsuse of an ofoptoNCDT the measuring triangulation element that laser could sensor negatively typeaffect ILD2300-10. the obtained In order results, to eliminate pos- the laser sensor was mounted on a special bracket, using a metal-rubber shock absorber thesible laser vibrations sensor was of mounted the measuring on a special element bracket, that using could a metal-rubber negatively shock affect absorber the obtained results, (Figure(Figure7). The7). The sensor sensor was located was located 35 mm from 35 mm the tested from plates. the tested plates. the laser sensor was mounted on a special bracket, using a metal-rubber shock absorber (Figure 7). The sensor was located 35 mm from the tested plates.

FigureFigure 7. Laser7. Laser displacement displacement sensor sensor on the test on bench. the test bench. Figure 7. Laser displacement sensor on the test bench. TheThe laser laser sensor sensor used used for the for non-contact the non-contact displacement displacement measurement measurement works on the works on the principle of triangulation which was already described (Figures2 and8). This direct method of principle of triangulation which was already described (Figures 2 and 8). This direct the displacementThe laser measurement sensor used does for not the cause non-contact an integration displacement error and is therefore measurement preferable works on the method of the displacement measurement does not cause an integration error and is there- toprinciple the displacement of triangulation determination which based on was accelerometric already accelerationdescribed measurements. (Figures 2 and 8). This direct foreThe preferable applied laser to sensorthe displacement is characterized determin by high resistanceation based to external on accelerometric interferences, acceleration method of the displacement measurement does not cause an integration error and is there- asmeasurements. well as the built-in electronics which determine the position of the object with a sampling frequencyfore preferable up to 49.02 to kHz. the Atdisplacement the output of the determin sensor, aation discrete based voltage on signal accelerometric is obtained. acceleration Themeasurements. basic data of the sensor ILD2300-10 are shown in Table1.

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FigureFigure 8. 8. MeasurementMeasurement principle principle using using a laser a laser displacement displacement sensor sensor [49]. [ 49].

TableThe 1. ILD2300-10applied laser sensor sensor data. is characterized by high resistance to external interferences, as well as the built-in electronics which determine the position of the object with a sam- Type ILD 2300-10 pling frequency up to 49.02 kHz. At the output of the sensor, a discrete voltage signal is Measurement range [mm] 10 (start of measurement 30, end of measurement 40) obtained. TheResolution basic data at 20of kHzthe [sensµm]or ILD2300-10 are shown in Table 0.151. 1 mW laser diode with a light output wavelength of Light source Table 1. ILD2300-10 sensor data. 670 nm Power supply [V] 24 Marker size at the beginning of the measuringType rangeILD 2300-10 75 × 85 [µm] 10 (start of measurement 30, end of measure- MarkerMeasurement size at the end of range the measuring [mm] range [µm] 110 × 160 ment 40) Resolution at 20 kHz [µm] 0.15 There was the assumption that the distance1 mW of laser the sourcediode with of light a light in the output laser wave- vibrometer Light source will not exceed the measuring range of the sensor (Tablelength1). Theof 670 other nm assumption was that the anglePower between supply the [V] sensor and object will be ﬁxed. It 24 was also assumed that the temperature of operation will be in the range of 0–50 ◦C and the sensor will not operate in Marker size at the beginning of the measur- a very dusty or hazy environment. 75 × 85 ing range [µm] An example of the plate vibration displacement recorded with a laser sensor after the Marker size at the end of the measuring impact with a modal hammer is shown in Figure9. The obtained110 × 160 time waveforms were range [µm] then analyzed in the Matlab software. The main purpose of the analyses was to determine the course of natural vibration frequency changes during the measurement signal damping. There was the assumption that the distance of the source of light in the laser vibrom- Sensors 2021, 21, x FOR PEER REVIEWSigniﬁcant changes in dynamic characteristics may indicate non-linearity—damage of9 of the 19 eter will not exceed the measuring range of the sensor (Table 1). The other assumption wastested that object. the angle between the sensor and object will be fixed. It was also assumed that the temperature of operation will be in the range of 0–50 °C and the sensor will not operate in a very dusty or hazy environment. An example of the plate vibration displacement recorded with a laser sensor after the impact with a modal hammer is shown in Figure 9. The obtained time waveforms were then analyzed in the Matlab software. The main purpose of the analyses was to determine the course of natural vibration frequency changes during the measurement signal damping. Significant changes in dynamic characteristics may indicate non-linearity—damage of the tested object.

FigureFigure 9.9. TimeTime coursecourse ofof thethe P2P2 plateplate displacementdisplacement afterafter impactimpact withwith aa modalmodal hammer.hammer.

3. Results and Discussion The analyses of the recorded vibration signals were carried out in three stages. In the first stage, the analyses of plate displacement signals recorded using a laser vibrometer were performed. The signals were firstly analyzed in a time domain. A new method of damping decrement description was proposed. First of all, as a starting point, a begging of a positive slope greater than the background noise was set for all time domain signals recorded with the laser sensor. Then, the envelopes for positive values were created (Figure 10).

Figure 10. Time course of the P1 plate displacements with the envelope of positive values determined.

To calculate a damping decrement, a well-known equation was used, but we changed the values of specific amplitudes to values of the envelope at specific time points.

𝐴 Λ =𝑙𝑛 (3) 𝐴

where Λ is the time logarithmic damping decrement, 𝐴 is the value of the displacement time series envelope at the first moment of plate response and 𝐴 is the value of the displacement time series envelope after 1 s of the plate’s first response. Such method of damping ratio calculation should be easier to implement in an SHM system installed onboard a ship due to the fact that the system will not have to find values of specific amplitudes. Calculated envelopes for all plates being investigated are presented in Figures 11–13.

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Figure 9. Time course of the P2 plate displacement after impact with a modal hammer.

3. Results and Discussion The analyses of the recorded vibration signalssignals werewere carriedcarried outout inin threethree stages.stages. InIn thethe first stage,stage, thethe analyses analyses of of plate plate displacement displaceme signalsnt signals recorded recorded using using a laser a laser vibrometer vibrometer were performed.were performed. The signals The signals were firstly were analyzedfirstly analyzed in a time in domain. a time domain. A new method A new of method damping of decrementdamping decrement description description was proposed. was Firstproposed. of all, asFirst a starting of all, as point, a starting a begging point, of a begging positive slopeof a positive greater slope than greater the background than the background noise was set noise for allwas time set for domain all time signals domain recorded signals with rec- theorded laser with sensor. the laser Then, sensor. the envelopes Then, the envelopes for positive for values positive were values created were (Figure created 10 (Figure). 10).

Figure 10. Time coursecourse ofof the the P1 P1 plate plate displacements displacements with with the the envelope envelope of positiveof positive values values determined. determined. To calculate a damping decrement, a well-known equation was used, but we changed the valuesTo calculate of speciﬁc a damping amplitudes decrement, to values a well-k of thenown envelope equation at speciﬁc was used, time but points. we changed the values of specific amplitudes to values of the envelope at specific time points. A0 Λt = ln 𝐴 (3) Λ =𝑙𝑛A1 (3) 𝐴 where Λt is the time logarithmic damping decrement, A0 is the value of the displacement time where Λ is the time logarithmic damping decrement, 𝐴 is the value of the displacement series envelope at the first moment of plate response and A1 is the value of the displacement time series envelope at the first moment of plate response and 𝐴 is the value of the displace- time series envelope after 1 s of the plate’s first response. Such method of damping ratio ment time series envelope after 1 s of the plate’s first response. Such method of damping ratio calculation should be easier to implement in an SHM system installed onboard a ship due calculation should be easier to implement in an SHM system installed onboard a ship due to Sensors 2021, 21, x FOR PEER REVIEWto the fact that the system will not have to find values of specific amplitudes. Calculated10 of 19 the fact that the system will not have to find values of specific amplitudes. Calculated enve- envelopes for all plates being investigated are presented in Figures 11–13. lopes for all plates being investigated are presented in Figures 11–13.

Figure 11. Envelope course of the P1–P6 ﬁrstfirst seriesseries ofof measurements.measurements.

Figure 12. Envelope course of the P1–P6 s series of measurements.

Figure 13. Envelope course of the P1–P6 third series of measurements.

By analyzing the envelopes’ curves presented in Figures 11–13, it can be observed that the time of decay of vibrations resulting from the impulse impact differs for individual plates. Data collected in this step of analysis were used with Equation (3) to calculate the damping decrement. Results are presented in Table 2.

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Sensors 2021, 21, 895 10 of 18 Figure 11. Envelope course of the P1–P6 first series of measurements. Figure 11. Envelope course of the P1–P6 first series of measurements.

FigureFigure 12.12. Envelope course course of of the the P1–P6 P1–P6 s sseries series of of measurements. measurements. Figure 12. Envelope course of the P1–P6 s series of measurements.

Figure 13. Envelope course of the P1–P6 third series of measurements. Figure 13. EnvelopeEnvelope course course of of the the P1–P6 P1–P6 third third series series of ofmeasurements. measurements. By analyzing the envelopes’ curves presented in Figures 11–13, it can be observed that Bythe analyzingtime of decay the envelopes’of vibrations curves resulting presen presented fromted the in impulse Figures 1111–13,impact–13, it differs cancan bebe for observedobserved individ- that thethatualtime plates.the time of Data decay of decay collected of vibrationsof vibrations in this step resulting resulting of analysis from from were the the impulse impulseused with impactimpact Equation differs differs (3) for to for calculateindivid- individual plates.ualthe plates.damping Data Data collected decrement. collected in thisinResults this step step are of presentedof analysis analysiswere in were Table used used 2. with with Equation Equation (3)(3) toto calculate the dampingthe damping decrement. decrement. Results Results are are presented presented in in Table Table2. 2.

Table 2. Damping decrement values calculated with Equation (3).

Plate Number Envelope Value at t = 0 s Envelope Value at t = 1 s Damping Decrement 0.108 0.026 1.434 P1 0.133 0.031 1.442 0.125 0.028 1.442 0.127 0.036 1.267 P2 0.117 0.035 1.191 0.119 0.032 1.313 0.131 0.047 1.013 P3 0.167 0.058 1.058 0.118 0.045 0.966 0.167 0.064 0.958 P4 0.141 0.062 0.825 0.150 0.065 0.845 0.069 0.019 1.303 P5 0.062 0.015 1.389 0.067 0.018 1.314 0.122 0.039 1.150 P6 0.115 0.045 0.942 0.117 0.043 1.003 Sensors 2021, 21, x FOR PEER REVIEW 11 of 19

Table 2. Damping decrement values calculated with Equation (3).

Envelope Value at Envelope Value at Plate Number Damping Decrement t = 0 s t = 1 s 0.108 0.026 1.434 P1 0.133 0.031 1.442 0.125 0.028 1.442 0.127 0.036 1.267 P2 0.117 0.035 1.191 0.119 0.032 1.313 0.131 0.047 1.013 P3 0.167 0.058 1.058 0.118 0.045 0.966 0.167 0.064 0.958 P4 0.141 0.062 0.825 0.150 0.065 0.845 0.069 0.019 1.303 P5 0.062 0.015 1.389 0.067 0.018 1.314 0.122 0.039 1.150 Sensors 2021, 21, 895 P6 0.115 0.045 0.942 11 of 18 0.117 0.043 1.003

Analysis of data presented in Figures 11–13 and in Table 2 allow stating that the proposed method of dampingAnalysis decrement of data presenteddetermination in Figures provides 11– results13 and which in Table are2 differentallow stating that the for different technicalproposed conditions method ofof dampingwelded joints decrement in the determination analyzed plates. provides It might results be used which are different in an SHM systemfor differentinstalled technical onboard conditionsa ship to detect of welded changes joints in inwelded the analyzed joints’ technical plates. It might be used condition. If thein damping an SHM decrement system installed value of onboard a hull in a shipgood to condition detect changes in the place in welded where joints’ technical a laser vibrometercondition. will be installed If the damping is known, decrement continuous value tracking of a hull of in its good value condition changes in will the place where a laser vibrometer will be installed is known, continuous tracking of its value changes will allow detecting abnormalities in the hull structure. allow detecting abnormalities in the hull structure. During the next step, signals were analyzed with the use of the FFT algorithm. The During the next step, signals were analyzed with the use of the FFT algorithm. The recorded signals turned out to be of such good quality that it was unnecessary to subject recorded signals turned out to be of such good quality that it was unnecessary to subject them to filtration or other forms of post-processing. All the recorded waveforms were an- them to ﬁltration or other forms of post-processing. All the recorded waveforms were alyzed (10 for each of the plates—3 of them are presented in the paper), obtaining very analyzed (10 for each of the plates—3 of them are presented in the paper), obtaining very high repeatability in the frequency domain in relation to individual plates. In the further high repeatability in the frequency domain in relation to individual plates. In the further part of the work, three waveforms for each of the plates are presented—Figures 14–19. part of the work, three waveforms for each of the plates are presented—Figures 14–19.

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Figure 14. Vibration displacement spectra of P1 plate, signals recorded by a laser vibrometer. FigureFigure 14. 14.VibrationVibration displacement displacement spectra spectra of P1 of P1plate, plate, signals signals recorded recorded by bya laser a laser vibrometer. vibrometer.

FigureFigure 15. 15.VibrationVibration displacement displacement spectra spectra of P2 of P2plate, plate, signals signals recorded recorded by bya laser a laser vibrometer. vibrometer. Figure 15. Vibration displacement spectra of P2 plate, signals recorded by a laser vibrometer.

Figure 16. Vibration displacement spectra of P3 plate, signals recorded by a laser vibrometer. Figure 16. Vibration displacement spectra of P3 plate, signals recorded by a laser vibrometer.

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Figure 14. Vibration displacement spectra of P1 plate, signals recorded by a laser vibrometer.

Sensors 2021, 21, 895 Figure 15. Vibration displacement spectra of P2 plate, signals recorded by a laser vibrometer. 12 of 18

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FigureFigure 16. 16. VibrationVibration displacement displacement spectra spectra of P3 of P3plate, plate, signals signals recorded recorded by a by laser a laser vibrometer. vibrometer.

Figure 17. Vibration displacement spectra of P4 plate, signals recorded by a laser vibrometer. Figure 17. 17. VibrationVibration displacement displacement spectra spectra of ofP4 P4 plate, plate, signals signals recorded recorded by a by laser a laser vibrometer. vibrometer.

FigureFigure 18. 18. VibrationVibration displacement displacement spectra spectra of P5 of P5plate, plate, signals signals recorded recorded by a by laser a laser vibrometer. vibrometer. Figure 18. Vibration displacement spectra of P5 plate, signals recorded by a laser vibrometer.

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Figure 17. Vibration displacement spectra of P4 plate, signals recorded by a laser vibrometer.

Sensors 2021, 21, 895 13 of 18 Figure 18. Vibration displacement spectra of P5 plate, signals recorded by a laser vibrometer.

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FigureFigure 19. Vibration 19. Vibration displacement displacement spectra spectra of P6 of plate, P6 plate, signals signals recorded recorded by laser by laser vibrometer. vibrometer. Figures 14–19 show the values of vibration amplitudes of P1–P6 plates obtained during Figures 14–19 show the values of vibration amplitudes of P1–P6 plates obtained dur- the measurements with a laser vibrometer. It was observed that the frequency values of the ing the measurements with a laser vibrometer. It was observed that the frequency values analyzed forms of the plate’s own vibrations vary depending on the technical condition of of the analyzed forms of the plate’s own vibrations vary depending on the technical con- the plate. Average frequency values from the three measurements are collected in Table3. dition of the plate. Average frequency values from the three measurements are collected in Table 3. Table 3. Frequency of the first and second forms of natural vibration obtained during the simulation and measurement of displacements. Table 3. Frequency of the first and second forms of natural vibration obtained during the simulation and measurement of displacements.Simulation P1 Plate P2 Plate P3 Plate P4 Plate P5 Plate P6 Plate Mode Simulation P1 Plate P2 Plate P3 Plate P4 Pl[Hz]ate P5 Plate P6 Plate Mode I 22.2 21.95[Hz] 26.08 17.59 25.84 25.36 22.74 I 22.2 II21.95 50.45 26.08 51.03 17.59 35.84 25.84 39.27 25.36 39.48 22.74 37.57 36.29 II 50.45 51.03 35.84 39.27 39.48 37.57 36.29 The results obtained by means of the simulation are characterized by an error of less The resultsthan obtained 2% (P1 by plate) means compared of the simulation to the results are characterized obtained when by an measuring error of less a plate without a than 2% (P1 plate)welded compared joint. During to the results the numerical obtained simulation, when measuring attempts a plate were without also made a to model the welded joint. Duringweld with the defectsnumerical correctly. simulation, Local stiffnessattempts changes were also caused made by to defects model and the the weld itself weld with defectsare suchcorrectly. a complex Local issuestiffness that changes the analysis caused becomes by defects extremely and the complex, weld itself which disqualifies are such a complexthis methodissue that as the a validation analysis be supportcomes extremely when measuring complex, repeatable which disqualifies weldments. In case of this method asimplementation a validation support of this when method, measuring it will be repeatable necessary weldments. to thoroughly In case examine of the form of implementationnatural of this vibrations method, ofit severalwill be elementsnecessary which to thoroughly are certain examine of the correctness the form ofof welds. On this natural vibrationsbasis, of itseveral is possible elements to determine which are limit certain values, of the in whichcorrectness the frequencies of welds. On of the individual this basis, it is possibleforms must to determine be included. limit The values, diagnostic in which method the frequencies will base of on the comparing individ- the spectra of ual forms mustthe be testedincluded. object The with diagnostic historical method spectra will of base the sameon comparing object (in the the spectra case of of an SHM system the tested objectinstalled with historical onboard spectra a ship) of or th spectrae same ofobject other (in objects the case produced of an SHM as a system series (in the case of installed onboarda damage a ship) detectionor spectra system of other on objects the production produced line).as a series The analysis(in the case ofthe of a presented data damage detection(Table system3, Figures on the 14 production–19) shows li unequivocallyne). The analysis that of thethe occurrencepresented data of a properly executed (Table 3, Figuresweld 14–19) (P3 plate)showschanges unequivocally the values that ofthe the occurrence frequency of of a occurrenceproperly executed of the first two forms weld (P3 plate)of changes natural the vibration values comparedof the frequency with a of plate occurrence without of a weld.the first This two is forms particularly of noticeable natural vibrationin thecompared case of with the firsta plate form without of natural a weld. vibration, This is particularly where the P3noticeable plate achieves in values at the case of the leastfirst form 30% lowerof natural than vibration, those of other where plates. the P3 The plate comparison achieves values of the values at least obtained in the 30% lower thancase those of P2,of other P3 and plates. P5 plates, The comp whosearison welds of the are values characterized obtained by in the the same case type of defect (no re-melting), with the remaining ones also allows concluding that the type of defects of P2, P3 and P5 plates, whose welds are characterized by the same type of defect (no re- occurring in the weld has such a significant influence on changes in the local stiffness of melting), with the remaining ones also allows concluding that the type of defects occur- the material that it is observable in changes in the frequency of the first form of natural ring in the weld has such a significant influence on changes in the local stiffness of the vibration (especially the first form). material that it is observable in changes in the frequency of the first form of natural vibration (especially the first form). A very important issue is also the high repeatability of the obtained frequency values of both forms of natural vibrations for all the tested plates. The lack of repeatability of the accompanying amplitudes results from the adopted measurement methodology, where the extortion with a modal hammer was carried out manually, with different extortion forces. In the case of automation of the process, it will probably also be possible to obtain the repeatability of values of amplitudes of vibration displacements.

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A very important issue is also the high repeatability of the obtained frequency values of both forms of natural vibrations for all the tested plates. The lack of repeatability of the Sensors 2021, 21, x FOR PEER REVIEW accompanying amplitudes results from the adopted measurement methodology,15 of 19 where Sensors 2021, 21, x FOR PEER REVIEW 15 of 19 the extortion with a modal hammer was carried out manually, with different extortion forces. In the case of automation of the process, it will probably also be possible to obtain the repeatability of values of amplitudes of vibration displacements. The assumption of the measurements was to use two different measuring methods The assumptionThe of assumption the measurements of the measurements was to use two was different to use two measuring different methods measuring methods at at the same time, which was to enable verification of the correctness of the measurements at the same time,the which same time, was to which enable was verifica to enabletion of verification the correctness of the of correctness the measurements of the measurements carried out using a laser vibrometer. Piezoelectric accelerometers were attached to the ob- carried out usingcarried a laser out vibrometer. using a laser Piezoelect vibrometer.ric Piezoelectricaccelerometers accelerometers were attached were to attachedthe ob- to the object ject tested using bases equipped with neodymium magnets. In order to eliminate possible ject tested usingtested bases using equipped bases with equipped neodymiu withm neodymium magnets. In magnets.order to eliminate In order possible to eliminate possible errors that may occur during the analysis of vibration displacement recordings in the errors that mayerrors occur that during may occurthe analysis during of the vibration analysis displacement of vibration displacementrecordings in recordingsthe in the Matlab environment, the analysis of vibration acceleration parameters was additionally Matlab environment,Matlab environment,the analysis of the vibratio analysisn acceleration of vibration parameters acceleration was parameters additionally was additionally carried out with the use of the dedicated Pulse Reflex software from B&K. During these carried out withcarried the use out of with the thededicated use of the Pulse dedicated Reflex software Pulse Reflex from software B&K. During from B&K.these During these verification analyses, the resolution in the frequency domain was limited to 0.25 Hz. verification analyses,verification the resolution analyses, in the th resolutione frequency in domain the frequency was limited domain to 0.25 was Hz. limited to 0.25 Hz. Figures 20 and 21 show the vibration acceleration spectra of the first two forms of natural Figures 20 andFigures 21 show 20 theand vibration 21 show acceleration the vibration spectra acceleration of the spectrafirst two of forms the first of natural two forms of natural vibration of P1 and P4 plates. The full frequency repeatability of their occurrence is visible. vibration of P1vibration and P4 plates. of P1 andThe P4full plates. frequency The fullrepeatability frequency of repeatability their occurrence of their is visible. occurrence is visible.

Figure 20. VibrationFigureFigure 20. acceleration 20. Vibration Vibration acceleration spectra acceleration corresponding spectra spectra corresponding corresponding to 10 excitations to to10 for 10excitations excitations the ﬁrst twofor for the forms the first first of two natural two forms forms vibration of of of P1 plate (ACC3).naturalnatural vibration vibration of ofP1 P1 plate plate (ACC3). (ACC3).

Figure 21. Vibration acceleration spectra corresponding to 10 excitations for the ﬁrst two forms of natural vibration of P4 FigureFigure 21. 21. Vibration Vibration acceleration acceleration spectra spectra corresponding corresponding to to10 10excitations excitations for for the the first first two two forms forms of of plate (ACC3).naturalnatural vibration vibration of ofP4 P4 plate plate (ACC3). (ACC3).

FigureFigure 22 22 shows shows the the vibration vibration acceleration acceleration spectra spectra of ofall all the the tested tested plates plates with with a limita limit of of100 100 Hz. Hz. The The values values of ofthe the frequencies frequencies of ofthe the first first two two forms forms of ofnatural natural vibration vibration are are collectedcollected in inTable Table 4. 4.

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Figure 22 shows the vibration acceleration spectra of all the tested plates with a limit Sensors 2021, 21, x FOR PEER REVIEW 16 of 19 of 100 Hz. The values of the frequencies of the ﬁrst two forms of natural vibration are collected in Table4.

FigureFigure 22. 22.ComparisonComparison of the of thevibration vibration acceleration acceleration spectra spectra of all of allthe the tested tested plates plates (ACC3). (ACC3).

Table 4. Frequency of the first and second form of natural vibration obtained during the analysis Table 4. Frequency of the first and second form of natural vibration obtained during the analysis of of acceleration parameters of the tested plates. acceleration parameters of the tested plates. P1 P2 P3 P4 P5 P6 Mode P1 P2 P3 P4 P5 P6 Mode [Hz] I 22.00 26.00 17.50 25.75 [Hz] 25.50 22.75 II 51.00I 22.0035.75 39.25 26.00 39.25 17.50 37.50 25.75 36.25 25.50 22.75 II 51.00 35.75 39.25 39.25 37.50 36.25 The obtained frequency values of the vibration acceleration amplitudes recorded with the use of accelerometersThe obtained confirm frequency the co valuesrrectness of the of vibrationthe measurements acceleration of vibration amplitudes recorded displacementswith recorded the use with of accelerometersa laser vibromet confirmer. Moreover, the correctness the commercial of the software measurements used of vibration during the verificationdisplacements indicates recorded that no with erro ars laser were vibrometer. made both Moreover, during the the simulation commercial and software used in the first stageduring of the the research. verification The obtained indicates frequency that no errors values were are made burdened both with during a small, the simulation and negligible error.in the first stage of the research. The obtained frequency values are burdened with a small, negligible error. 4. Conclusions 4. Conclusions In the literature available to the authors, no descriptions of the use of laser vibrometry in diagnostics ofIn welded the literature joints availableonboard toships the authors,were found. no descriptions The combination of the useof meas- of laser vibrometry urements of displacementin diagnostics of ofwelded welded elements joints onboard stimulated ships by werea force found. pulse The with combination the analy- of measure- sis of frequencyments changes of displacement of the first two of welded forms elementsof natural stimulated vibration offers by a force promising pulse withre- the analysis sults. Further,of the frequency new proposed changes method of the firstof a twodamping forms decrement of natural vibrationcalculation offers provides promising results. very promisingFurther, results. the After new additional proposed veri methodfication of atests damping on other decrement objects, methods calculation can provides very be implementedpromising as a tool results. for quick After weld additional diagnostics, verification also during tests the onoperation other objects, of the ob- methods can be implemented as a tool for quick weld diagnostics, also during the operation of the object. ject. This applies especially to small welded elements. The most important conclusions This applies especially to small welded elements. The most important conclusions might might be considered as those shown below: be considered as those shown below: 1. Both methods based on damping decrement calculation or displacement spectra 1. Both methods based on damping decrement calculation or displacement spectra analysis require knowledge of parameters describing the object with a known, good analysis require knowledge of parameters describing the object with a known, good technical condition. Therefore, these are qualitative diagnostics methods that enable technical condition. Therefore, these are qualitative diagnostics methods that enable the detection of damage without indicating its specific cause. According to this, we the detection of damage without indicating its specific cause. According to this, we mean that a new ship (or its element) should be tested with the proposed method mean that a new ship (or its element) should be tested with the proposed method before exploitation in order to obtain reference spectra of critical hull points. before exploitation in order to obtain reference spectra of critical hull points. 2. It should be noted that the methods have the character of non-contact measurements and therefore they can also be used on production lines, where the entire diagnostic process can be automated. 3. During the measurements, a modal hammer was used as the source of the impact signal, so it must be concluded that similar good results will be obtained in the case

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2. It should be noted that the methods have the character of non-contact measurements and therefore they can also be used on production lines, where the entire diagnostic process can be automated. 3. During the measurements, a modal hammer was used as the source of the impact signal, so it must be concluded that similar good results will be obtained in the case of impulse extortions implemented in other ways (e.g., stochastic environmental extortion). 4. Undoubtedly, before starting to test a series of products, it will be necessary to know the form of the object’s own vibrations. For this purpose, it will be necessary to test several specimens of a known technical condition. 5. It will be advisable here to use two independent methods of determining dynamic parameters (one of them may be a numerical analysis based on the ﬁnite element method (FEM)). Obtaining the frequency value of the ﬁrst two forms of the object’s own vibrations with welds without defects will allow for testing the remaining ones using only a laser displacement sensor. 6. In the low-frequency range, direct measurement of displacement amplitudes (laser sensors) shows an advantage over the measurement of acceleration amplitudes (accelerometers). This is mainly due to the fact that there is no need to double integrate the acceleration waveforms.

Author Contributions: Methodology, project administration—A.S., supervision, resources, analysis, conceptualization, simulation studies, software, writing review and editing—A.M., supervision, writing review and editing, conceptualization, project administration, analysis—L.M., resources, simulation studies, writing review and editing—M.K., writing review and editing—T.M. All authors have read and agreed to the published version of the manuscript. Funding: The project is financed within the program of the Ministry of Science and Higher Education called “Regionalna Inicjatywa Doskonało´sci” in the years 2019–2022, project number 006/RID/2018/19, sum of financing PLN 11870000. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data sharing not applicable. Conflicts of Interest: The authors declare no conflict of interest.

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