Evaluation of damage detection techniques for steel structures using electromechanical impedance method

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method

structures using electromechanical impedance

Evaluation of damage detection techniques for steel

Academic year 2019-2020

Master of Science in Electromechanical Engineering

Master's dissertation submitted in order to obtain the academic degree of

Counsellor: Mojtaba Khayatazad

Supervisors: Prof. dr. ir. Wim De Waele, Prof. dr. ir. Mia Loccufier

Student number: 01504984

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method

structures using electromechanical impedance

Evaluation of damage detection techniques for steel

Academic year 2019-2020

Master of Science in Electromechanical Engineering

Master's dissertation submitted in order to obtain the academic degree of

Counsellor: Mojtaba Khayatazad

Supervisors: Prof. dr. ir. Wim De Waele, Prof. dr. ir. Mia Loccufier

Student number: 01504984

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Preface

I would like to thank my supervisors, Prof. dr. ir. Wim De Waele for the guidance and the detailed feedback throughout the whole year, and Prof. dr. ir. Mia Loccufier for the help regarding the data acquisition. Both have also been helpful in deciding the new goals for this dissertation when the Covid-19 pandemic begun.

I would also like to thank Mojtaba Khayatazad for the weekly meetings and the guidance for the numerical simulation.

Lastly, I want to thank my parents for their support during all these years, and my brother for giving tips on courses and providing help for my job search. Also my partner, Eline, earns a spot for always making me laugh.

Wouter Wittevrongel, 31st _{of May 2020}

The author gives permission to make this master dissertation available for consultation and to copy parts of this master dissertation for personal use. In all cases of other use, the copyright terms have to be respected, in particular with regard to the obligation to state explicitly the source when quoting results from this master dissertation.

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Covid-19 Preamble

On the 18th _{of March 2020, a lockdown went into effect in Belgium to contain the spread of}

Covid-19. As a consequence, students were not allowed to enter university buildings. At that time, experiments on large steel girders were being prepared. It was planned to gather and discuss data gained from these experiments. It was quickly clear that the experiments could not be done during the semester, thus a new goal for this dissertation had to be decided. In a previous master dissertation on the electromechanical impedance method [1], a lot of data had been captured from a lab scale steel plate. Not all experimental results had been thoroughly post-processed and discussed; thus there was still room for further discussion due to the large amount of data available. Together with the supervisors it was decided to do an extensive discussion on the available data from the steel plate. The literature study that was already done, was still very relevant for the discussion of the data. The main difficulty was determining which data file corresponded to what exact experiment, however the author of the previous dissertation had been very helpful in providing us additional information, making the discussion in this book possible.

This preamble was written in consultation between the student and the supervisor and ap-proved by both.

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Evaluation of damage detection techniques for steel structures

using electromechanical impedance method

Wouter Wittevrongel

Supervisors: Prof. dr. ir. Wim De Waele, Prof. dr. ir. Mia Loccufier Counsellors: Ir. Kevin Dekemele, Mojtaba Khayatazad

Master’s dissertation submitted in order to obtain the academic degree of Master of Science in Electromechanical Engineering

Department of Electromechanical, Systems and Metal Engineering Chair: Prof. dr. ir. Luc Dupr´e

Faculty of Engineering and Architecture Academic year 2019-2020

Abstract

In this dissertation different damage detection techniques for steel structures using the elec-tromechanical impedance (EMI) method are evaluated. The EMI method uses piezoelectric elements as a basis for the monitoring technique, which can be used in a structural health monitoring (SHM) system. In order to evaluate the capability of the EMI method for larger structures, a large steel girder with welded attachments was designed, inspired by an overhead crane girder. A fatigue crack was supposed to be introduced using a four-point bending test rig. Using a finite element simulation, the direction of the crack and the necessary loads were approximated. Due to the Covid-19 measures, the test was not performed. Instead, previ-ously collected data from a small steel plate was used to perform an evaluation of the damage detection capabilities of the EMI method. Two types of experiments are discussed, one with an added mass on the plate at different locations and the other with two cuts progressively introduced. Different damage metrics (RMSD, MAPD and CCD) and the frequency shift are examined for their ability to detect, quantify and localize an added mass or damage. From the added mass experiment it is concluded that on a lab scale, detection is easily possible, while localization is not. It is also found that lower frequencies result in higher damage met-rics. From the damage experiment, it is clear that every new damage is easily detected using relative damage metrics, while localization could not be evaluated due to a large inconsistency from one of the transducers. Quantification of damage was also not possible, and the effect of frequency on the magnitude of damage metrics could only be confirmed for RMSD. The use of frequency shift was found to be difficult.

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Evaluation of damage detection techniques for steel

structures using electromechanical impedance

method

Wouter Wittevrongel

Supervisors: Wim De Waele, Mia Loccufier

Abstract— The electromechanical impedance (EMI) method uses piezoelectric elements as a basis for the mon-itoring technique, which can be used in a structural health monitoring (SHM) system. In order to evaluate the capa-bility of the EMI method for larger structures, a large steel girder with welded attachments was designed, and an ex-periment methodology was defined. Due to the Covid-19 measures, the test was not performed. Instead, previously collected data from a small steel plate was used to perform an evaluation of the damage detection capabilities of the EMI method. Different damage metrics (RMSD, MAPD and CCD) and the frequency shift were examined for their ability to detect, quantify and localize an added mass or damage. From the added mass experiment it is concluded that on a lab scale, detection is easily possible, while local-ization is not. It is also found that lower frequencies result in higher damage metrics. From the damage experiment, it is clear that every new damage is easily detected using rel-ative damage metrics, while localization could not be evalu-ated due to a large inconsistency from one of the transduc-ers. Quantification of damage was also not possible, and the effect of frequency on the magnitude of damage metrics could only be confirmed for RMSD. The use of frequency shift was found to be difficult.

Keywords— Electromechanical impedance (EMI), piezo-electric transducer, damage detection, damage metric

I. INTRODUCTION

Large steel or concrete structures, from transport in-frastructure for example, require regular inspection to as-sess their integrity and lifetime. This is done by periodi-cally using nondestructive evaluation (NDE) techniques, to detect and characterize flaws in order to determine whether they require further remedial action. Common

NDE techniques require an operator, mostly very close to the specific region that is inspected, which may be diffi-cult and time consuming for large structures [1]. A struc-tural health monitoring (SHM) system aims to continu-ously monitor the structure and notify an operator if dam-age is detected, which enables condition-based mainte-nance [2]. Such monitoring technique can be based on piezoelectric elements (PZT’s) that are permanently at-tached to the structure. A PZT induces a voltage when it is deformed, and vice versa, so it can sense vibrations as well as apply them, i.e. a transducer. The electromechan-ical impedance (EMI) method uses this effect to detect changes in the mechanical impedance of the structure, by measuring the electrical impedance of the PZT. A damage will then be reflected in a change of electrical impedance [3]. The goals of this dissertation are to evaluate the capa-bility of the EMI method for larger steel structures, and to examine the ability for damage detection, quantification and localization of an added mass or damage on lab scale.

II. ELECTROMECHANICAL IMPEDANCE METHOD

The EMI method is based on a relation between the mechanical impedance of the structure – the resistance against motion for an applied harmonic force – and the electrical impedance measured at the PZT. Often the in-verse of the electrical impedance is used, the admittance, which consists of a real and an imaginary part, respec-tively the conductance and the susceptance. It has been proven that the electrical admittance is influenced by the mechanical impedance of the structure [4]. A change in mechanical impedance because of a crack can then be de-tected from the signature of the electrical admittance.

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Damage detection is done by comparing two conduc-tances and in order to quantify the amount of change, damage metrics are used. The most widely used metrics are root mean square deviation (RMSD), mean absolute percentage deviation (MAPD) and correlation coefficient deviation (CCD) [5]. There are many effects that should be considered for implementation; the frequency range, size of the structure and external temperatures and loads are some important ones [6] [7] [8] [9].

III. TEST SETUP

A. Large girder test specimen

To evaluate the effect of large structures, it was decided to perform experiments on a larger specimen, a steel I-beam with welded attachments, which will be cyclically loaded in four-point bending to promote crack initiation and growth. Inspiration came from steel crane girders and a study on fatigue behaviour of girders [10]. The cho-sen beam is an S235 IPE-270 profile, 1200 mm long, 270 mm high and 135 mm wide. Two small stiffeners of 10 mm thick are to be welded on one side of the web, just outside the constant bending region between the two load points. Using a finite element simulation in ABAQUS, it is found that for a total load of 100 kN, there is a princi-pal stress concentration of 55 MPa at the bottom corner of the stiffener. It is expected that a crack will initiate at that location, due to a deliberate incomplete weld at one of the stiffeners. The simulation also shows the direction of the principal stresses, which gives an indication of the crack growth direction, approximately 65◦ _{with the length}

di-rection upwards into the web and downwards towards the flange, similar to the crack shown in Figure 1 [10].

Fig. 1: Example of an inclined crack starting at a stiffener ter-mination [10]

For the location of the PZT’s, an array around the ex-pected crack path is chosen, with an extra PZT on the other side of the stiffener and on the bottom flange.

The goals of the test are to; evaluate the effect of the low frequency (6 - 8 Hz) cyclic loading on the measurement; determine sensitivity to crack initiation and growth; and determine sensing range.

B. Small plate test specimen

Instead of the test described in the last section, there is a discussion on previously collected data from a small steel plate. The plate has dimensions 305 × 200 × 6 mm and is instrumented with two PZT’s, model DuraAct P-876.A12. Three experiments are discussed, one with an added mass (a magnet) at four different locations, one with two cuts at different locations that are progressively introduced (first damage 1 10 – 20 – 30 mm, then damage 2) and a repeata-bility experiment spanning several days. The specimen and locations for the experiments are shown on Figure 2, the magnet locations are indicated in red. The specimen was suspended in frame using rubber bands.

Fig. 2: Small steel specimen

C. Data acquisition

The data had been already collected [3], using a DAQ device instead of an impedance analyzer. The acquisition is based on a proposal from Baptista and Filho [11]. It is based on the frequency response function, the input sig-nal (excitation, a chirp sigsig-nal) and the output sigsig-nal at the PZT. Using MATLAB the admittance is calculated.

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IV. EXPERIMENTAL STUDY ON THE EFFECT OF ADDED MASS AND DAMAGE

A. Repeatability

A zoom of one peak of the conductance signatures is shown in Figure 3, showing data recorded at several days. In the first two days, there are large shifts, but from mea-surement 4 to 10a, the signatures seem to stabilize and show more random variations instead of large shifts. For example, with signature 9 as baseline, following three measurements result in an RMSD of 1.66, 2.12 and 2.53 %, calculated over the frequency range [20, 180] kHz. For MAPD this results in 1.07, 1.35 and 1.53 % and for CCD in 0.0003, 0.0003 and 0.0006. The shifts cannot be ex-plained, but as the other experiments are done in quick succession, this shift is neglected and the mentioned val-ues can be used as an order of magnitude for repeatability.

Fig. 3: Conductances spanning several days

B. Baseline

PZT A and B are symmetrically attached, so it can be expected that their conductance signatures would be sim-ilar. This is confirmed, however there are small differ-ences in magnitude over the entire frequency range. This is confirmed by the damage metrics: RMSD=14.67 %, MAPD=7.34 % and CC=0.9712. This means that the sig-natures should always come from the same PZT.

C. Added mass

Figure 4 shows the RMSD values for each added mass location for both PZT’s; the other metrics show very sim-ilar results. The frequency interval [20, 180] kHz of the

conductances is used. For every location the added mass is easily detected, the values are an order of magnitude higher than the repeatability values. It is true that the lo-cation closest to the PZT results in the highest value (ex-cept for MAPD of PZT B), but the other locations show that the value is not proportional to the proximity of the added mass. Also localization by comparing values be-tween PZT’s is not possible.

Fig. 4: RMSD values of added mass experiment

The frequency interval can be split into sub-frequency intervals of size 10 kHz, see Figure 5, which shows that higher frequency intervals result in lower RMSD values and in less difference between locations. Some intervals also result in lower values, in between higher value in-tervals. The first four intervals have the same discussion as for the full frequency interval. For PZT B, the discus-sion is not the same as for the full frequency interval, see Figure 6. The lower frequency intervals do not show the highest RMSD value for the magnet closest to the PZT. It is concluded that an added mass can be detected, but not localized and that lower frequencies are more sensitive. This also holds for MAPD and CCD.

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Using frequency shift it is found that small intervals (e.g. 1 kHz) should be used to gain more information. A filter based on CC can be used to eliminate peaks that split or disappear, so that only steady shifts remain. After averaging the absolute shifts over all remaining intervals, the discussion is then similar as for RMSD, but due to difficulties with filtering this method is less ideal.

Fig. 6: RMSD for all locations and intervals for PZT B

D. Damage

The signature of PZT B showed a very large vertical shift from damage case 2-20 and on. The cause is un-known, one possibility is that the bonding layer was dam-aged due to the cutting operation. The values of PZT B can thus not be used to evaluate localization. This can be seen on Figure 7 where the RMSD for PZT B for case 1-20 jumps to 80 %. The RMSD for each PZT for all damage cases is given in Figure 7, using the entire fre-quency range [20, 160] kHz and ’no damage’ condition as reference. For PZT A, the first damage is easily detected, but it is clear that increasing the size of the cut does not increase RMSD, but a new cut does increase the values, all case 2 values are higher than those of case 1. The same holds for MAPD and CCD.

Fig. 7: RMSD values of damage case 1 & 2 (all sizes)

Another approach is using relative RMSD, where the conductance of the previous damage case is used as ref-erence. Results in Figure 8 show that each new damage is easily detected by PZT A with relative RMSD values higher than 24 %, 10 times the repeatability value. Case 1 has a downward trend for increasing damage, but this is not true for case 2. Introducing damage case 2 results in a jump in value. The values for PZT B again indicate the large deviation for case 1-20. Again the same discussion holds for relative MAPD and CCD.

Fig. 8: Relative RMSD values of damage case 1 & 2 (all sizes)

The results when using sub-frequency intervals of size 10 kHz are shown in Figure 9 and Figure 10, the higher frequency intervals again show lower RMSD values, but the effect is not that strong. The RMSD using baseline as reference again shows no trends, but detection of the first damage is easily achieved. With relative RMSD, each damage size is easily detected, but no trends can be found. This is the same for MAPD and CCD, but for MAPD and CCD the higher frequency intervals do not show lower values.

Fig. 9: RMSD values of all damage sizes for each interval

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men-Fig. 10: Relative RMSD values of all damage sizes for each interval

tioned for repeatability, RMSD is second best in this as-pect.

The frequency shift was very hard to use due to the large changes in conductance signatures, peaks often split or new peaks originated.

V. CONCLUSION

This dissertation aimed to evaluate the electromechan-ical impedance method using piezoelectric elements on large steel structures. A large steel girder test specimen was designed for a destructive fatigue test. From this test, the capability of the PZT’s for damage detection, quan-tification and localization could be evaluated. This test could not be performed due to Covid-19 measures. Thus, the goal of this dissertation was shifted to a discussion of the capability of PZT’s using data acquired from a small steel plate. The most important findings from this discus-sion are that using damage metrics; the detection of an added mass or of damage is easily possible; the quantifi-cation of damage is not possible; localisation of an added mass is not possible on lab scale; for an added mass higher frequencies result in lower damage metrics, for damage this effect is only confirmed for RMSD and slightly for MAPD. Future work can be done by investigating the fol-lowing: the effect of the vibration on mode on sensing range or area; the PZT interface technique; the repeata-bility over large periods of time; the use of structural me-chanical impedance.

REFERENCES

[1] Theodore Hopwood, Christopher Goff, Jared Fairchild, and Sud-hir Palle, “Nondestructive evaluation of steel bridges: Methods and applications,” 2016.

[2] Charles R Farrar and Keith Worden, “An introduction to struc-tural health monitoring,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sci-ences, vol. 365, no. 1851, pp. 303–315, 2007.

[3] Jonathan Deschodt, “Electromechanical impedance method for damage detection in steel structures using piezoelectric ele-ments,” 2019.

[4] Gyuhae Park, Hoon Sohn, Charles R. Farrar, and Daniel J. In-man, “Overview of piezoelectric impedance-based health mon-itoring and path forward,” Shock and Vibration Digest, vol. 35, no. 6, pp. 451–463, 2003.

[5] K. K.H. Tseng and A. S.K. Naidu, “Non-parametric damage detection and characterization using smart piezoceramic mate-rial,” Smart Materials and Structures, vol. 11, no. 3, pp. 317– 329, 2002.

[6] Chee-Kiong Soh, Yaowen Yang, and Suresh Bhalla, Smart Ma-terials in Structural Health Monitoring, Control and Biomechan-ics, Springer, Berlin, Heidelberg, 2012.

[7] Fabricio Guimar˜aes Baptista and Jozue Vieira Filho, “Optimal frequency range selection for PZT transducers in impedance-based SHM systems,” IEEE Sensors Journal, vol. 10, no. 8, pp. 1297–1303, 2010.

[8] Fabricio Guimar˜ae Baptista and Jozue Vieira Filho, “Trans-ducer loading effect on the performance of PZT-based SHM sys-tems,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 57, no. 4, pp. 933–941, 2010.

[9] Fabricio G Baptista, Jozue Vieira Filho, and Daniel J Inman, “Sizing PZT Transducers in Impedance-Based Structural Health Monitoring,” IEEE Sensors Journal, vol. 11, no. 6, pp. 1405– 1414, 2011.

[10] John W. Fisher, Pedro A. Albrecht, Ben T. Yen, David J. Klinger-man, and Bernard M. McNamee, Fatigue Strength of Steel Beams with Welded Stiffeners and Attachments, National Cooperative Highway Research Program Report, 1974.

[11] Fabricio Guimar˜aes Baptista and Jozue Vieira Filho, “A new impedance measurement system for PZT-based structural health monitoring,” IEEE Transactions on Instrumentation and Mea-surement, vol. 58, no. 10, pp. 3602–3608, 2009.

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List of Figures

1.1 Age distribution of metallic railway bridges [2] . . . 1

1.2 Before and after picture of the Ponte Morandi [4] . . . 2

2.1 1-D model for PZT attached to a structure [13] . . . 8

2.2 Conductance signatures of healthy and damaged states at constant temperature [1] . . . 9

2.3 Detailed view of one shifting peak for increasing crack size [14] . . . 10

2.4 Sensitivity of a PZT for ∆=0.05 [17]. . . 12

2.5 Sensitivity of the transducer and RMSD for (a) specimen 1, (b) specimen 2, (c) specimen 3, and (d) specimen 4, for a damage at distance of 100 mm from the transducer [17]. . . 13

2.6 Electrical impedance of PZT as a function of the ratio Zs Zt for (a) 1kHz, (b) 10kHz and (c) 50kHz [18] . . . 14

2.7 RMSD values obtained using (a) the real part, (b) the imaginary part of Zel [18] 15 2.8 CCDM values obtained using (a) the real part, (b) the imaginary part of Zel[18] 16 2.9 (a) RMSD and (b) CCDM values for the same specimen with different damages [18] . . . 16

2.10 The four specimens with different PZT arrangements [19] . . . 17

2.11 (a) RMSD and (b) CCDM values for beam and plate [19] . . . 18

2.12 (a) CCDM and (b) RMSD values for the three plates [19] . . . 18

2.13 Vibration modes for PZT interface on a circular plate with corresponding ex-cited regions . . . 20

2.14 Effect of temperature for a small aluminium beam [23] . . . 20

2.15 Aluminium specimen with sequentially drilled holes [20] . . . 22

2.16 RMSD for PZT 1 [20] . . . 22

2.17 RMSD for PZT 2 [20] . . . 22

2.18 Second specimen with location of loosened bolts [20] . . . 24

2.19 RMSD versus damage distance (a) PZT1 (b) PZT2 [20] . . . 25

2.20 MAPD versus damage distance (a) PZT1 (b) PZT2 [20] . . . 25

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List of Figures

2.22 MAPD versus hole diameter [20] . . . 25

2.23 Covariance versus hole diameter [20] . . . 26

2.24 Cross Correlation versus hole diameter [20] . . . 26

3.1 Picture of a large overhead crane [27] . . . 29

3.2 Cross sectional dimensions of an IPE 270 profile . . . 30

3.3 An example of an inclined crack starting at stiffener termination [29] . . . . 30

3.4 Percentage of total amount of cycles for certain crack growth [29] . . . 30

3.5 Location of the stiffeners . . . 31

3.6 Dimensions of the stiffener . . . 31

3.7 Vectors illustrating magnitude and direction of the maximum principal stress (MPa) . . . 32

3.8 Contour plot of maximum principal stresses indicating the stress concentration at the stiffener (MPa) . . . 33

3.9 Location of PZT’s on the test girder . . . 34

3.10 The previous test specimen [1] . . . 36

3.11 Test setup showing the boundary conditions [1] . . . 37

3.12 Locations of the magnet . . . 37

3.13 Location of damage case 1 and 2 on the plate . . . 38

3.14 Scheme of data acquisition [30] . . . 39

3.15 The auxiliary circuit [30] . . . 39

3.16 Different methods for calculation of FRF . . . 40

4.1 The conductance baselines of PZT A and B . . . 42

4.2 Zoom of the conductance baselines of PZT A and B . . . 42

4.3 The susceptance baselines of PZT A and B . . . 43

4.4 Conductances spanning several days . . . 44

4.5 RMSD values of magnet experiment using frequency range [20,180] kHz . . . 45

4.6 MAPD values of magnet experiment using frequency range [20,180] kHz . . . 45

4.7 COV values of magnet experiment using frequency range [20,180] kHz . . . . 46

4.8 CCD values of magnet experiment using frequency range [20,180] kHz . . . . 47

4.9 RMSD for all locations and sub-intervals for PZT A . . . 48

4.10 RMSD for all locations and sub-intervals for PZT B . . . 49

4.11 RMSD for all locations and smaller intervals of 5 kHz for PZT A . . . 49

4.12 Conductance of baseline, location 2 and 4 for PZT A . . . 50

4.13 RMSD for PZT A and B for all locations . . . 51

4.14 MAPD for all locations and sub-intervals for PZT A . . . 52

4.15 MAPD for all locations and sub-intervals for PZT B . . . 52

4.16 MAPD for PZT A and B for all locations . . . 53

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List of Figures

4.18 CCD for all locations and sub-intervals for PZT B . . . 54

4.19 CCD for PZT A and B for location 1 . . . 55

4.20 Shifted conductance of PZT A for location 4 for interval [30,40] kHz . . . 56

4.21 Shifted conductance of PZT A for location 4 for interval [34,35] kHz . . . 57

4.22 The conductances for case 1 of PZT B . . . 59

4.23 RMSD values of damage case 1 & 2 (all sizes) for both transducers . . . 60

4.24 Relative RMSD of damage case 1 & 2 (all sizes) for both transducers . . . 60

4.25 MAPD values of damage case 1 & 2 (all sizes) for both transducers . . . 61

4.26 Relative MAPD values of damage case 1 & 2 (all sizes) for both transducers . 62 4.27 CCD values of damage case 1 & 2 (all sizes) for both transducers . . . 63

4.28 Relative CCD values of damage case 1 & 2 (all sizes) for both transducers . . 63

4.29 RMSD values of damage case 1 & 2 for PZT A for each sub-interval . . . 64

4.30 Relative RMSD values of damage case 1 & 2 for PZT A for each sub-interval 65 4.31 MAPD values of damage case 1 & 2 for PZT A for each sub-interval . . . 66

4.32 Relative MAPD values of damage case 1 & 2 for PZT A for each sub-interval 66 4.33 CCD values of damage case 1 & 2 for PZT A for each sub-interval . . . 67

4.34 Relative CCD values of damage case 1 & 2 for PZT A for each sub-interval . 68 4.35 Frequency shift of the intervals of size 1 kHz after filtering for all damage case 1 sizes for PZT A . . . 69

4.36 Conductances of baseline, case 1-10 and case 1-20 in a frequency interval [64, 68.5] kHz . . . 70

4.37 Conductances of baseline, case 1-10, case 1-20 and case 1-30 in a frequency interval [65, 68.5] kHz . . . 70

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List of Tables

2.1 Properties of the used PZT for calculation of η [17] . . . 12

4.1 Frequency shifts (Hz) of each location for PZT A and B in a selection of frequency intervals . . . 58

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Nomenclature

Abbreviations

AC Alternating Current

CC(D) Cross Correlation (Deviation) COV Covariance

DAQ Data Acquisition

DFT Discrete Fourier Transform EFS Effective Frequency Shift EMI Electromechanical Impedance ET Eddy current Testing

FRF Frequency Response Function

MAPD Mean Absolute Percentage Deviation MT Magnetic particle Testing

NDE Non-Destructive Evaluation NDT Non-Destructive Testing PT Penetrant Testing

PZT Lead zirconate titanate; piezoelectric transducer RMSD Root Mean Square Deviation

RT Radiographic Testing

SHM Structural Health Monitoring UT Ultrasonic Testing

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Nomenclature

Symbols ¯

Complex dielectric constant [F/m] ¯

Y Young’s modulus [N/m2_]

η Sensitivity [%]

ω Angular frequency [rad/s] ρ Mass density [kg/m3_] σ Standard deviation a Geometry constant of PZT [m] B Susceptance [S] C Damping [N s/m] C0 Static capacitance [F ]

d Piezoelectric coupling constant [m/V ] E Electric field [V /m]

F Harmonic force [N ]

Fs Sampling frequency [Samples/s]

G Conductance [S]

H Frequency response function I Current [A]

j Imaginary unit K Stiffness [N/m]

k Wave number [rad/m] M Mass [kg]

N Number of samples

n Number of frequency intervals [_−−] R Resistance [Ω]

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Nomenclature Rs Sensing resistor [Ω] s Compliance [m2_{/N ]} V Voltage [V ] v Velocity [m/s] X Reactance [Ω] x Input signal Y Admittance [S = Ω−1] y Output signal

Zs Mechanical impedance of the structure[N s/m]

Zt Mechanical impedance of transducer [N s/m]

Zel Electrical impedance [Ω]

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Chapter 1

Introduction

1.1 Setting the scene

In 2004, a survey was conducted from European railway companies which showed the very old age of railway bridges. A total of 220 000 bridges were included, of which 21% or 47 000 were metallic. The age distribution can be seen in Figure 1.1. 28% is over 100 years old and another 40% is between 50 and 100 years old. Note that this survey was taken in 2004, which means the distribution would be even worse now. As the design life of bridges is generally around 75 years or 100 years, this emphasizes a significant challenge of ageing infrastructure. The question arises whether these old bridges can still be used and if so, whether there are measures which should be taken. This means there is an issue of both safety and cost.

10% 22% 40% 28% < 20 years 20-50 years 50-100 years > 100 years

Figure 1.1: Age distribution of metallic railway bridges [2]

The companies were also asked which research topic is a priority according to them. Assess-ment and inspection/monitoring came out on top [2].

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Chapter 1. Introduction

Not only steel infrastructure has to deal with this challenge, also concrete infrastructure. On August 14, 2018 the Ponte Morandi in Italy collapsed, costing the lives of 43 people, see Figure 1.2. It had been in use for 51 years before it collapsed, getting little maintenance during its life. The official investigation of the failure is still ongoing, yet it can be said that structural health monitoring could have prevented this event. After collapse, an investigation of the prestressed concrete stay cables showed that they were corroded. In [3] they tested the hypothesis that due to corrosion and fatigue, the load capacity of the bridge was reduced, leading to failure as there was also no redundancy in the amount of stay cables. The authors predicted failure to occur in 2014 or 2016, according to different methods.

Figure 1.2: Before and after picture of the Ponte Morandi [4]

This example indicates the need for better lifetime assessments of structures. Structural health monitoring is a technique that could make structural evaluation cheaper and most importantly safer.

1.2 Structural Health Monitoring

During the lifetime of a steel bridge (or an other steel structure), it is subjected to loading, environmental conditions and service practices (postponed maintenance, chemicals for deic-ing) which result in deterioration of the steel. Whether this deterioration requires action is generally determined by periodically evaluating the bridge using nondestructive evaluation (NDE). The goal of NDE is to detect and characterize flaws in materials in order to deter-mine whether they constitute a defect, which requires action. Common NDE methods for steel bridges are penetrant testing (PT), magnetic particle testing (MT), eddy current test-ing (ET), radiographic testtest-ing (RT) and ultrasonic testtest-ing (UT). A limited overview of the procedures and their limitations is given [5] and discussed here.

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Penetrant Testing (PT)

The test surface first has to be thoroughly cleaned. A colored penetrant is sprayed over the surface, which can penetrate in surface flaws due to capillary action. After some time, the penetrant is wiped off and a developer is sprayed on the test surface. The (white) developer will interact with the penetrant to draw out the flaws which make them visible due to the color contrast. This method is simple, cheap and can be used to confirm visual testing. It is quite slow, especially if a lot of areas have to be evaluated. Only surface flaws can be detected, and the surface has to be quite smooth for good results.

Magnetic Particle Testing (MT)

This method needs more equipment; magnets or powered yokes are needed to apply a magnetic field. Powders or inks are also needed. Due to a flaw there will be some magnetic flux leakage, which attracts the powders or inks, resulting in a visible indication. The method is also relatively simple and faster than PT. It can only reliably be used for surface flaws, and thick layers of paint might give problems, so they should be removed. The orientation of the flaw is very important for detection, the crack should ’cut’ the flux lines.

Eddy Current Testing (ET)

For ET no consumable materials are needed. A battery powered device is used together with wires and probes. An alternating current flows through the probe, inducing alternating currents (eddy currents) in the test piece. (Near-) surface flaws influence the eddy currents which can be detected by the device. Operators have to be skilled in using the device and selecting the right probes and in assessing the indications of the device. It is faster than PT and MT and test data can be stored.

Radiographic Testing (RT)

This method mainly requires a radiation source and films. The radiation goes through the test structure while on the other side the film captures the radiation, producing a ’shadow image’. The equipment usage is difficult, also due to the radiation, from which the operator should be protected. The film also has to be developed afterwards to see the actual image. Sub-surface volumetric flaws can be detected, while planar flaws have to be aligned correctly w.r.t. the radiation source. It is the most expensive NDE method yet it can give critical information about flaw severity.

Ultrasonic Testing (UT)

This method is good at detecting subsurface volumetric or planar flaws. It requires a portable detector consisting of a pulser and receiver, signal control, screen,... The pulser induces

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mechanical vibrations of high frequency through the steel, which bounce back at the other end or due to a flaw, creating an ’echo’. The surface has to be cleaned and coatings removed, increasing the inspection duration. Operators should be skilled in assessing the echos.

The general disadvantages of these methods are that they require an operator, mostly very close to the specific region that is inspected, which may be difficult for bridges. They have a long duration and they are relatively expensive due to the previous two points. Another disadvantage of using periodic non-destructive techniques for inspection is that it is possible that they were not required, which is an unnecessary financial cost.

Structural Health Monitoring uses permanent sensors to continuously monitor the structure, sending data to external computers where storage and analysis can be done. Farrar C. and Worden K. [6] give an excellent description of what Structural Health Monitoring (SHM) is: ”The process of implementing a damage identification strategy . . . This process involves the observation of a structure or mechanical system over time using periodically spaced measure-ments, the extraction of damage-sensitive features from these measurements and the statistical analysis of these features to determine the current state of system health.”

SHM tries to eliminate the need of operators for inspection while reducing the response time to a flaw. This process can replace scheduled inspection using NDE with as-needed inspection/ maintenance, potentially reducing cost by eliminating unnecessary inspection. The safety of the user of the infrastructure could also be increased due to the frequent measurements which makes a faster response time possible. After an unusual event, say an earthquake or a heavy storm, the structural health can be immediately assessed. The system health is better up-to-date. Of course the typical NDE methods can still be used together with SHM, in the situation where SHM can not give detailed enough information about the flaws, where NDE could give the answer. In fact, SHM uses a non-destructive technique, but it is one that enables permanent sensors and on-line monitoring without an operator on site. [7]

Piezoelectric elements can be used as the basis for the monitoring technique in SHM. Very often this element is a ceramic, lead zirconate titanate, which is why the elements are often called PZT’s. Since they are small and lightweight, they can be permanently installed on the structure. This makes fast on-demand evaluation possible as well as very frequent scheduled measurements. The essence of the working principle of a PZT can be briefly explained as follows. A piezoelectric element links electricity and deformation. When such an element is deformed, a charge is induced over the element, so a voltage can be measured when connected in a circuit. The opposite is also possible: applying a voltage to the element, it will deform. Since it works in both ways, it can act to sense vibrations and also to apply vibrations to a structure.

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technique. An excitation voltage (a sinusoidal wave of different frequencies) is sent to the PZT, and the actual vibration response is measured as a voltage signal. After some calculations the electrical impedance signature of the PZT is found, which is influenced by the mechanical impedance of the structure. Damage will influence this mechanical impedance and thus also the electrical impedance. For further explanation, see chapter 2. This technique using PZT’s has proven its potential in different types of applications. In 2012, Annamdas and Yang [8] have used PZT’s to monitor the support structure of an excavation. Since no actual damage was present in the structure, variations in load were captured. They found that PZT’s were able to detect the increasing load on the upper strut that is expected when the excavation goes deeper. A comparison was made with strain gauges which showed a similar trend. Soh et al [9] have shown that PZT’s are able to detect cracks in reinforced concrete beams. The beam was of considerable size, over 10 m long, 250 mm high and 100 mm thick and was heavily loaded. After cracks appeared close to the PZT’s, their signatures had changed and this change was measured with a statistical metric. A high metric corresponded with cracks being close. Huynh and Kim [10] have shown that force loss in steel cables could be detected using PZT’s at the anchorage of the cable. A loss of force corresponded to a change in contact conditions at the anchorage, which changed the impedance signature of the PZT. Also here the amount of change was quantified using statistical metrics.

More in depth information about piezoelectric elements can be found in [7] and [1].

1.3 Goals of the dissertation

Ghent University, more specifically the department of Electromechanical, Systems and Metal Engineering, wants to gain knowledge and experience with SHM using piezoelectric elements. Therefore research is being conducted on that subject, along with Master’s dissertations. A first dissertation was written by Zwaenepoel [11]. A lab scale aluminium plate was instru-mented with round PZT’s (buzzers) and the effect of damage on the plate and of temperature was evaluated. A following dissertation by Deschodt [1] used more sensitive PZT’s and has implemented a new data acquisition system. Again the effect of temperature and damage on a small steel plate were discussed.

An important question is whether the results from these works can be extended to full scale metal structures. To that end, an important goal of this dissertation is to test the electrome-chanical impedance method for a larger structure. This can be done by experimenting on a larger steel structure and introducing a fatigue crack, representing a more realistic scenario.

Another goal is to examine the capability of the EMI-method for damage quantification, for damage localisation and for tracking damage propagation.

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As mentioned in the preamble, experiments on a large girder could not go through. Instead the focus lies on the second goal of examining the capability of the EMI-method.

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Chapter 2

Electromechanical Impedance

Method: a literature review

The electromechanical impedance (EMI) method is a non-destructive testing (NDT) method that can be applied in structural health monitoring. It received a lot of attention in recent research, but it has not reached commercial applications yet because of existing challenges, i.e. the selection of frequency range, the correct interpretation and possibilities of the metrics and the exclusion of effects other than damage [12]. This chapter will explain the working principle of the EMI-method, its use for structural health assessment, external influences,...

2.1 Working Principle

2.1.1 Basic concepts

Before the working principle is explained, some concepts have to be defined.

First of all, the mechanical impedance, which reflects the resistance of a structure against motion for an applied harmonic force.

Zs(ω) =

F (ω)

v(ω) (2.1)

With Zs(ω) the mechanical impedance, F (ω) a harmonic force, v(ω) the resulting velocity

and ω the angular frequency. The mechanical impedance of a structure is determined by its mass, stiffness and damping.

Equivalently, the electrical impedance reflects the resistance against a current for an applied voltage.

Zel(ω) =

V (ω)

I(ω) (2.2)

With Zel(ω) the electrical impedance, V (ω) an alternating voltage, I(ω) an alternating current

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Chapter 2. Electromechanical Impedance Method: a literature review

Note that the electrical impedance and admittance are complex numbers

Zel= R + jX (2.3)

Y = G + jB (2.4)

R is the resistance, X the reactance, both in ohms [Ω]. G is the conductance and B is the susceptance, both measured in siemens [S].

2.1.2 Electromechanical coupling

As the name implies, the EMI method uses a link between electricity and mechanics which is made by a piezoelectric element, further noted as a PZT or a transducer. By attaching the PZT to the structure, a coupling can be created between the mechanical impedance of the structure and the electrical impedance of the PZT. Different models for this coupling exist, with a basic one being a one-dimensional model introduced by Liang et al, described in [13], see Figure 2.1.

Figure 2.1: 1-D model for PZT attached to a structure [13]

This model represents the PZT as an axial bar attached to the structure consisting of a mass M , a stiffness K and a damping C. When an alternating voltage is applied to the PZT, the following relation can be found for the electrical admittance Y (ω):

Y (ω) = jωa ¯T 33− Zs(ω) Zs(ω) + Zt(ω) d2 31Y¯11E ! (2.5)

With j = √_{−1, a a geometry constant, ¯}T

33 the complex dielectric constant of the PZT at

zero stress, d31 the piezoelectric coupling constant, ¯Y11E the Young’s modulus at zero electric

field, Zs(ω) and Zt(ω) the mechanical impedance of respectively the structure and the PZT

(actuator).

From Equation 2.5 it can be seen that the electrical admittance of the PZT Y (ω) is a function of the mechanical impedance of the structure Zs(ω). This forms the basis of the EMI-method.

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If all parameters in this equation can be assumed constant, a change in structural impedance, for example by damage, is directly reflected in the PZT’s electrical admittance.

2.2 Practical implementation and issues

2.2.1 Damage detection and evaluation

For damage detection, an admittance signature has to be compared with a ’healthy’ signature or a ’baseline’. By plotting these signatures a visual way of damage detection is possible. An example is given in Figure 2.2 [1]. This figure shows the conductance signatures of a small steel plate for the initial reference condition and for the condition with cuts introduced. Signatures change in shape and peaks shift, which indicate a change in structural properties. However for damage detection, all other effects on the signature have to be excluded, i.e. temperature, loading, boundary conditions, ... These are discussed later.

Figure 2.2: Conductance signatures of healthy and damaged states at constant temperature [1]

Soh and Lim [14] have experimented on an aluminum beam and observed a shift in peak frequency for a growing crack. The crack grew due to cyclic loading and measuring the electrical impedance happened in identical (free) conditions. Figure 2.3 shows the peak shift to lower values for a growing crack.

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Figure 2.3: Detailed view of one shifting peak for increasing crack size [14]

Damage metrics have been defined to put a number on the amount of change between two sig-natures. Most used metrics are root mean square deviation (RMSD), mean absolute percent-age deviation (MAPD), correlation coefficient (CC) and covariance (Cov), see Equation 2.6 to Equation 2.10. It should be noted that the factor 100 in the formula for RMSD is not always used, if used, RMSD is normally represented as a percentage. In these equations Z1 i

represents the real or imaginary part of the electrical impedance, i.e. conductance or suscep-tance, in state ’1’ for frequency interval i and Z0

i is the conductance or susceptance in state

’0’ or the baseline for frequency interval i. n is the amount of frequency intervals, σ0 and

σ1 represent the standard deviation of the baseline and the evaluated signature, respectively.

The bar sign represents an average.

RM SD(%) = 100· v u u u u t Pn i=1 h Z1 i − Zi0 i2 Pn i=1 h Z0 i i2 (2.6) M AP D(%) = 100 n n X i=1 Z1 i − Zi0 Z0 i (2.7) CC = 1 nσ0σ1 n X i=1 " (Z1 i − ¯Z1)(Zi0− ¯Z0) # (2.8) CCD or CCDM = 1− CC (2.9) Cov = 1 n n X i=1 " (Z_i1_{− ¯}Z1_)(Z0 i − ¯Z0) # (2.10)

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The metrics or indices given above are called non-parametric statistical damage indices as they do not take into account structural parameters of the structure. It is only a comparison of two signatures [15]. A comprehensive discussion on damage metrics is given in section 2.3.

2.2.2 Frequency range

The frequency ranges used are in the order of tens to hundreds of kHz, because the wavelength of the resulting stress wave in the structure has to be smaller than the defect size which should be detected. Typical ranges reported in literature are between 30 and 500 kHz. A subrange is evaluated, depending on the density of major peaks in the signature. This means a large frequency range is first viewed, then a smaller range is selected based on this result, i.e. trial-and-error [13] [15]. This is of course not ideal. Different researchers have investigated the issue of selecting the optimal frequency range. Peairs [16] has investigated whether the resonance frequencies of the PZT are related to sensitive frequency ranges. The conclusion is however that at time of writing it is not possible to select optimal frequency ranges prior to attachment of the PZT, because of varying results. Baptista and Filho [17] are the only researchers (that were found at this time) that theoretically investigated the frequency range selection. They introduced the concept of sensitivity to a certain damage ∆ (a change in mechanical impedance Zs), which is calculated using:

η = 100||Zel,d| − Zel| |Zel|

(2.11)

With Zel according to Equation 2.12:

Zel= 1 jωC0 jZt s₁₁ d31l 2 " 1 2tan kl 2 −_sin(kl)1 + Zs j2Zt # (2.12) with

meaning parallel connection. Zel,dis the electrical impedance of the PZT after damage:

Zel,d= 1 jωC0 jZt s₁₁ d31l 2 " 1 2tan kl 2 −_sin(kl)1 + (1 + ∆) Zs j2Zt # (2.13)

With C0 the static capacitance of the PZT, ω the angular frequency, s11 compliance at

constant electric field, d31 the piezoelectric coupling constant, l the length of the side of the

square PZT and k is the wave number, calculated according to

k = ω√s11ρT (2.14)

With ρT the mass density of the piezoceramic. It should be noted that Equation 2.12 differs

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a certain ∆, a ratio Zs

Zt and the parameters of the PZT, η can be calculated, see Figure 2.4

and Table 2.1 for the used values. It can be seen that in general the sensitivity decreases for higher frequencies, and for higher mechanical impedances of the structure (ZS in the figure) for a given sensor (ZT in the figure). There are also local maxima and minima which can be calculated using the derivative of the sensitivity η. While the magnitude of the sensitivity changes for different amounts of damage ∆, the frequencies at which they occur stay almost constant. This implies that frequency selection is important, as for some frequencies the sensitivity is around 0!

Figure 2.4: Sensitivity of a PZT for ∆=0.05 [17].

Table 2.1: Properties of the used PZT for calculation of η [17]

Symbol Value Unit s11 16.1· 10−12 m2/N

d31 −320 · 10−12 m/V

ρT 7800 kg/m3

C0 35 nF

l 20 mm

The authors have experimented on three aluminium beams of constant length 500 mm and thickness 2 mm, but of increasing widths 30, 60 and 120 mm and on one plate of 500_×300×2

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mm. The specimens one to four have increasing mechanical impedance. A PZT was attached at the same location for all specimens and damage was simulated using a small nut. RMSD was calculated for each frequency (RMSDn) to evaluate the effect. This means removing the

sums in Equation 2.6 (and also the factor 100). The results are shown in figure Figure 2.5. Highest values of RMSD are in the region of high theoretical sensitivity and vice versa [17].

Figure 2.5: Sensitivity of the transducer and RMSD for (a) specimen 1, (b) specimen 2, (c) specimen 3, and (d) specimen 4, for a damage at distance of 100 mm from the transducer [17].

2.2.3 PZT loading effect

In the previous section, it has been shortly stated that sensitivity decreases for larger struc-tures i.e. increasing mechanical impedances of the strucstruc-tures. The same authors called this phenomenon the loading effect [18]. The PZT loading effect is the impact of the mechanical impedance of the monitored structure on the sensitivity of the PZT to a change in that me-chanical impedance. In this paper, a different 1-D model than in Figure 2.1 is derived and used, which results in Equation 2.12 for electrical impedance of the PZT Zel. Two limits for

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Zel can be calculated, for very small structures and very large structures respectively:

Zel,min= lim Zs→0 Zel= 1 jωC0 jZt s₁₁ d31l 2 " 1 2tan kl 2 − _sin(kl)1 # (2.15) Zel,max = lim Zs→∞ Zel= 1 jωC0 (2.16)

This means that for large structures Zelwill reach its limit, which is not anymore a function

of Zs. This of course means that a change in mechanical impedance of the structure can no

longer be reflected in the electrical impedance of the PZT. If all necessary PZT properties are known, Zel (Equation 2.12) can be drawn for a fixed frequency, as a function of Z_Zs_t,

see Figure 2.6. The loading effect is illustrated on Figure 2.6 (b), the same change in Zs

corresponds to a small change in Zel for high ratios Z_Zs_t (large structures). This figure also

indicates that for a higher frequency, the upper limit of Zel is reached more quickly. In other

words, the PZT loading effect is achieved for lower ratios of Zs

Zt.

Figure 2.6: Electrical impedance of PZT as a function of the ratio Zs

Zt for (a) 1kHz, (b) 10kHz and

(c) 50kHz [18]

This was also experimentally evaluated using aluminum beams and plates of different sizes and applying the same mass (simulating damage). A square PZT with a length of 20 mm

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was attached on each specimen, 10 mm from the edge. The beams had fixed length and thickness of respectively 500 mm and 2 mm with varying widths of 30, 60, 120 and 240 mm, the corresponding ratios Zs

Zt are respectively 7.8, 15.6, 31.2 and 62.3. The plates had fixed

length and width of respectively 500 mm and 300 mm, but varying thicknesses of 2 and 16 mm corresponding to ratios Zs

Zt of 77.9 and 623.3. The mechanical impedances were calculated

according to Equation 2.17.

Zs= A

r ρ

s (2.17)

With A the cross sectional area orthogonal to the propagating wave (the vibration), ρ the density and s the compliance. The damage metrics were calculated for a frequency range of 15 kHz to 40 kHz which was experimentally determined to give higher values of damage metric (i.e. trial-and-error). The results for RMSD and CCDM are given on Figure 2.7 and Figure 2.8. It should be noted that a different definition of RMSD was used. For a given damage, both damage metrics decrease as Zs increases, although there are some exceptions;

there is a clear trend. An important note here however, is that the same mass was applied on all specimens (a steel nut of diameter 4 mm and thickness 2 mm). As the specimens become larger and heavier, it could be said that the amount of ’damage’ decreases.

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Figure 2.8: CCDM values obtained using (a) the real part, (b) the imaginary part of Zel [18]

Another way the effect is experimentally confirmed, is by increasing the mass (simulated damage) added to a single specimen (the plate of 16 mm thickness). The mass went from a small steel screw-nut of 4 mm diameter and 2 mm thickness to a lead block of 2.9 kg. Even though difference in added mass was very big, RMSD and CCDM showed similar results, see Figure 2.9. This shows that the PZT is loaded, i.e. the upper limit of Zel is reached.

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2.2.4 Sizing PZT

In subsection 2.2.3 the influence of Zs is discussed, i.e. for a given PZT, the effect of the

specimen size. The discussion can also be held the other way around, by comparing different PZT sizes and configurations. In Figure 2.6 it can also be noted that the electrical impedance Zel has a certain range of ratio Z_Zs_t where it has a steep slope. This is the sensitive region,

so for a given structure with impedance Zs, the PZT with mechanical impedance Zt should

be chosen accordingly. As this sensitive region also changes with frequency, the optimal Ztis

dependent on frequency as well.

In [19] the authors tested the effect of PZT size, parallel arrangement and PZT loading. The four specimens are: a beam with a small PZT, three plates with respectively a small PZT, a large PZT and a parallel arrangement of small PZT’s, see Figure 2.10. Damage is simulated by adding a small nut (0.89 g) on the beam with a mass load of 1.25%. This same nut is used for the plates as ’small damage’ and also a larger nut (9.26 g) is used as ’big damage’ with a mass load of 1.67 %. The mass load on the beam (1.25%) is a bit lower than the mass load on the plate with the larger nut (1.67 %). Damage metrics were calculated using the conductance in a frequency range of 15 to 40 kHz.

Figure 2.10: The four specimens with different PZT arrangements [19]

First, the PZT loading effect can be observed again by comparing results from the beam and the plate with one small PZT, see Figure 2.11. In all cases the beam shows the highest values of damage index. The plate has lower values because its ratio Zs

Zt is higher and outside the

most sensitive region of the PZT, even though the mass load of the big damage on the plate is higher than the mass load of the beam. Also the difference between small and big damage is limited, even though the mass difference is considerable. For example, the small damage at distance 400 mm gives an RMSD _{≈ 2700 while the big damage at the same distance only} gives RMSD _{≈ 2900. This is also because the PZT is loaded.}

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Figure 2.11: (a) RMSD and (b) CCDM values for beam and plate [19]

The three plates are then compared, see Figure 2.12. First the ’big damage’ case is analyzed. CCDM shows larger values for the big damage case of the large PZT and the parallel connec-tion, compared to the small PZT. This is due to the lower ratio of Zs

Zt, as could be expected.

However, this does not hold for the small damage case, instead the opposite happens when the distance is 50 mm. Another observation is that the difference between small and big damage is larger for the large PZT and the parallel connection compared to the small PZT. RMSD for the large PZT shows very low values compared to the other configurations, due to the larger static capacitance C0 of the PZT, which decreases the electrical impedance.

The parallel connection also has a higher static capacitance than the small PZT, but not as high as the large PZT. The difference between small and big damage is larger for the parallel connection compared to the small PZT, but the values compared to the healthy state are lower [19]. There is no simple conclusion to take. The RMSD for the small PZT showed very good results, despite the higher ratio Zs

Zt.

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2.2.5 Sensing range

A very important characteristic of the PZT is the sensing range. Actually, following subsec-tion 2.2.3 and subsecsubsec-tion 2.2.4, this is not a characteristic of only the PZT, but of the entire PZT-structure system. Yet, it can still be useful to compare some different experimentally determined sensing ranges.

The results of [20] will be discussed in section 2.3. Their first specimen was an aluminium plate of length 1250 mm, width of 100 mm and thickness 3 mm, weighing approximately 1 kg. The PZT with outer diameter 14 mm (which is the size of the electrode) could easily detect damage, a 5 mm drilled hole, at a distance of 950 mm, which was the maximum distance. This means that the actual sensing range is at least 950 mm. The ratio of sensing radius to outer radius of PZT is in this case 135.

Bhalla et al [21] have tested the sensing region on a larger specimen, coming a little closer to large real applications. A steel I-beam 100 mm high, 55 mm wide and 730 mm long weighing approx. 6 kg was instrumented with one square PZT of size 12 mm on the bottom flange at mid span. They found that damage in the web could not be detected by the PZT on the flange. Damage in the flange could be detected at a distance 132 mm but not at 198 mm, the ratio of sensing radius to outer radius of PZT is thus limited to 11 in this case.

Park et al [13] state that the sensing radius is between 0.4 m and 2 m for composite structures and simple metal beams respectively. The size of the PZT and the case studies used for this conclusion are unfortunately not mentioned. The sensing range depends on material properties, geometry, the used frequency range and the PZT material.

Huynh et al [22] have done research into the sensing region of a PZT interface using finite elements simulation. Interesting about this research is that the shape of the sensing region is not simply a circle. A certain frequency peak will correspond to a certain vibration mode of the interface which will excite a smaller region, see Figure 2.13. Damage in the unexcited region will be harder to detect.

2.2.6 Temperature effect

Admittance signatures are also influenced by temperature. This can lead to false positive er-rors, i.e. detecting damage while the change is temperature is due to temperature. Generally, it is reported that an increase in temperature shifts the conductance signature to the left and decreases the amplitude of the peaks. The slope of the susceptance signature increases for increasing temperature [1] [23].

An example of this effect is shown in Figure 2.14 which shows the conductance signatures of an aluminium beam of dimensions 500× 38 × 3 mm for a temperature of 25◦_{C and 45}◦_C.

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Figure 2.13: Vibration modes for PZT interface on a circular plate with corresponding excited regions

A possible way around this effect is by shifting the signal with a value depending on the measured temperature during the impedance measurement. This requires that the frequency shift per degree Celsius should be known, which also varies depending on the frequency range. This is important, since the method then loses its efficiency if a wide frequency interval is viewed. This method is called the effective frequency shift (EFS) [1] [23]. EFS has been developed by Koo et al [24]. It works by maximizing CC between two signatures, the baseline and the measured signature. The measured signature is shifted along the frequency axis so that CC is maximum. This method subtracts the mean value of the signature so that shifts in amplitude may also be compensated. It has been experimentally confirmed that damage detection is possible using EFS.

2.2.7 External force effect

According to Lim and Soh [25], when a beam is axially loaded, the natural frequencies in-duced by transverse modes of vibration increase (rightward shift) for tension and decrease for compression. The natural frequencies induced by the extensional modes stay constant.

Annamdas et al [26] have experimented on three beams of increasing dimensions using small

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loads to induce bending stresses in the beams. The PZT’s were bonded to the bottom at mid span, so they are loaded in tension. They observed that conductance signatures shift upwards and that this shift is higher for higher loads, as well as higher for higher frequencies. Besides the upward shift, there are also rightward shifts, splitting peaks or origination of new peaks in the conductances. Similar things happen for the susceptance signatures, but the shifts are more clear, making them more suited to identify a load. Another observation is that the shift is higher for smaller, less stiff specimens.

2.3 Damage metrics: a critial appraisal

In this section the capabilities of the damage metrics are more comprehensively studied. The damage metrics were defined in subsection 2.2.1, some experiments that have been given in earlier sections will be further discussed here with a focus on the damage metrics.

It is clear from earlier discussed experimental results that if damage is introduced or a mass is added, the conductance signature changes and this is detectable by a damage metric. However the further capabilities of the damage metrics are not yet confirmed. The question arises whether they can be useful for the quantification of damage, the localization of damage and the propagation of damage.

Recall Figure 2.7 which shows RMSD values using the conductance and the susceptance of several beams and plates with the same added mass, a steel nut of 4 mm diameter and 2 mm thickness. The four beams had constant length and thickness, resp. 500 mm and 2 mm, and varying widths of 30, 60, 120 and 240 mm. The two plates had a length of 500 mm, a width of 300 mm and thickness of 2 and 16 mm. The results of the conductance show that a weight closer to the PZT does not consistently correspond to a higher RMSD, only the beam of width 240 mm seems to show a consistent trend. When using the susceptance there are no consistent trends. Figure 2.8 shows the CCDM values for the same experiment. Again it is not possible to conclude that a weight at a closer location corresponds to a higher damage index. In Figure 2.9 results for RMSD and CCDM were also shown for a ’big damage’ which is a large lead block weighing 2.9 kg. The CCDM values do uniformly increase when distance decreases, but the values for a distance of 30, 20 and 10 cm are quite close.

In subsection 2.2.4 some results are discussed with respect to the size of the PZT. The same graphs can be used to compare damage metrics, Figure 2.11 and Figure 2.12. For the beam RMSD is high for both distances, and higher when the weight is closer to the PZT. The CCDM is high when the weight is close, and very clearly lower when the weight is further. The plate with small damage (small weight) has almost the same RMSD for both distances, the CCDM values are more distinct. The plate with big damage (larger weight) has more distinctive RMSD and CCDM values as the differences for the distances are larger. Figure 2.12 shows

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that for every PZT size, RMSD and CCDM increase when the weight increases. In most but not all cases, a higher metric is observed for a lower distance. The cases where this is not true, are all using the small weight.

Tseng and Naidu [20] have done experiments to determine the capability of RMSD, MAPD, Cov and CC. In a first experiment on an aluminium strip of 1250_{× 100 × 3 mm, holes had} been sequentially drilled, see Figure 2.15. Results for RMSD of conductance in two different frequency ranges are given in Figure 2.16 and Figure 2.17.

Figure 2.15: Aluminium specimen with sequentially drilled holes [20]

Figure 2.16: RMSD for PZT 1 [20] Figure 2.17: RMSD for PZT 2 [20]

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the first hole even at distance of 950 mm, but only increases uniformly for the first three new holes. Following holes result in varying RMSD values, although the authors have drawn an increasing trend line. For example when the hole at 750 mm is drilled, the RMSD w.r.t. no damage decreases compared to the previous state. In the higher frequency range, the increasing trend for RMSD w.r.t. no damage is stronger and more uniform, although from a distance of 450 mm and closer the values stop increasing and vary around 16%. Note that the values for RMSD are a lot smaller compared to the lower frequency interval. The RMSD w.r.t. previous state shows increasing trend lines, but the increase is not uniformly at all for both frequency ranges. The authors do not mention how the trend line was determined, but it seems that the first element (≈ 0) was considered. This has a large effect on the trend line, making its result doubtful. However, the RMSD w.r.t. previous state is consistently between 25 and 40 % or between 7 and 10 %, indicating a new hole is easily detected. Because the increase for closer damage is not consistent, it can not be said that damage closer to the PZT corresponds to higher RMSD w.r.t. previous state.

For PZT2, Figure 2.17, the damage started close and new holes were further away. In both frequency ranges the first hole is easily detected. RMSD w.r.t. no damage shows an increas-ing trend, stronger for the high frequency range, but again the first element was probably considered in the calculation of the trend line. In the higher frequency interval the trend starts of strong and similar to PZT1, values stop increasing and start fluctuating around 18%. RMSD w.r.t. previous state shows a slight decreasing trend, but also here the decrease is not consistent. Again this is a useful result, each new hole is easily detected using the RMSD w.r.t. previous state.

When comparing both PZT’s, some localization seems to be possible. The first hole, 50 mm from PZT2 and 950 mm from PZT1, resulted in an RMSD of about 53% and 40%, respectively, in the low frequency range. For the high frequency range RMSD resulted in about 13% and 9%. However when the last hole was drilled, the RMSD w.r.t. no damage indicates the difference between the original plate (0 holes) and the plate completely filled with holes (19 holes) which is a symmetrical state. This RMSD was higher for PZT2 in both frequency ranges. This again means that higher RMSD does not necessarily mean that damage is closer to that PZT.

The authors claim that using the RMSD w.r.t. the previous state, it can be determined if the damage moves away from the PZT or towards it. An increasing trend would mean damage moving towards the PZT and vice versa. However as already mentioned, the trend lines drawn are doubtful and the trends are not uniform.

Similar results hold for MAPD, except that the values are a bit lower.

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compared to RMSD and MAPD. The trends of Cov and CC using their previous states for PZT1 and PZT2 were not as distinct. They are thus deemed worse in revealing the increasing extent of damage and its direction.

The second experiment reported in [20] also used an aluminium strip of the same size. Holes were drilled with a spacing of 25 mm and bolts were put through them. They then simulated damage at one location by unscrewing a bolt, Figure 2.18. It is seen in results on Figure 2.19 and Figure 2.20 that both RMSD and MAPD are higher if damage is closer to the PZT, but MAPD has again lower values. The results are consistent with only one exception being the configuration with hole 30 and hole 32.