Structural Health Monitoring, Volume 5

River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Structural Health Monitoring, Volume 5 Alfred Wicks Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014 River Publishers

Conference Proceedings of the Society for Experimental Mechanics Series Series Editor TomProulx Society for Experimental Mechanics, Inc., Bethel, CT, USA

River Publishers Alfred Wicks Editor Structural Health Monitoring, Volume 5 Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014

Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-7004-893-4 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2014 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Preface Structural Health Monitoring, Volume 5represents one of the eight volumes of technical papers presented at the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014 organized by the Society for Experimental Mechanics, and held in Orlando, Florida, February 3–6, 2014. The full proceedings also include volumes on Dynamics of Coupled Structures; Nonlinear Dynamics; Model Validation and Uncertainty Quantification; Dynamics of Civil Structures; Special Topics in Structural Dynamics; Topics in Modal Analysis I; and Topics in Modal Analysis II. Each collection presents early findings from experimental and computational investigations on an important area within structural dynamics. Structural Health Monitoring is one of these areas. Topics in this volume include: Structural health monitoring Damage detection Energy harvesting The organizers would like to thank the authors, presenters, session organizers, and session chairs for their participation in this track. Blacksburg, VA, USA Alfred Wicks v

Contents 1 Assessment and Localization of Active Discontinuities Using Energy Distribution Between Intrinsic Modes .......................................................................................................... 1 Reza Mohammadi Ghazi and Oral Buyukozturk 2 Wave Analyses in Structural Waveguides Using a Boundary Element Approach....................................................................................................... 11 Stefan Bischoff and Lothar Gaul 3 Spectral Element Based Optimization Scheme for Damage Identification........................................ 19 M.I. Albakri and P.A. Tarazaga 4 Nonlinear Dynamic Behavior of Cantilever Piezoelectric Energy Harvesters: Numerical and Experimental Investigation........................................................................................ 29 P.S. Varoto and A.T. Mineto 5 Nonlinear Dynamics of a Hybrid Piezo-Electromagnetic Vibrating Energy Harvester ......................... 41 S. Mahmoudi, N. Kacem, and N. Bouhaddi 6 Numerical Modeling of Steel-Framed Floors for Energy Harvesting Applications .............................. 49 Joshua A. Schultz, Christopher H. Raebel, and Aaron Huberty 7 Identification of Tie-Rods Tensile Axial Force in Civil Structures ................................................. 59 S. Manzoni, M. Scaccabarozzi, and M. Vanali 8 A New Measure of Shape Difference .................................................................................. 71 Shawn Richardson, Jason Tyler, Patrick McHargue, and Mark Richardson 9 Non-destructive Examination of Multiphase Material Distribution in Uranium Hexafluoride Cylinders Using Steady-State Laser Doppler Vibrometery......................................................... 81 David Goodman, Kelly Rowland, Sheriden Smith, Karen Miller, and Eric Flynn 10 Damage Detection Using Large-Scale Covariance Matrix.......................................................... 89 Luciana Balsamo, Raimondo Betti, and Homayoon Beigi 11 Load Identification of Offshore Platform for Fatigue Life Estimation ........................................... 99 Nevena Perišic´, Poul Henning Kirkegaard, and Ulf T. Tygesen 12 Monitoring Proximity Tunneling Effects Using Blind Source Separation Technique............................ 111 Soroush Mokhtari, Nader Mehdawi, Si-Hyun Park, Amr M. Sallam, Manoj Chopra, Lakshmi N. Reddi, and Hae-Bum Yun 13 Endowing Structures with a Nociceptive Sense Enabled by a Graphene-Oxide Sensing Skin.................. 117 Alan Kuntz, Cole Brubaker, Stephanie Amos, Nathan Sharp, Wei Gao, Gautam Gupta, Aditya Mohite, Charles Farrar, and David Mascarenas 14 Modal Strain Energy Based Damage Detection Using Multi-Objective Optimization .......................... 125 Young-Jin Cha and Oral Buyukozturk vii

viii Contents 15 Development of Vibration Damper for Energy Harvesting......................................................... 135 Nobuyuki Okubo, Taiju Kunisaki, and Takeshi Toi 16 Structural Damage Detection Using Soft Computing Method ..................................................... 143 S.J.S. Hakim, H. Abdul Razak, S.A. Ravanfar, and M. Mohammadhassani 17 Multiple Crack Detection in Structures Using Residual Operational Deflection Shape......................... 153 Erfan Asnaashari and Jyoti K. Sinha 18 Numerical Enhancement of NMT for Predicting Fatigue Failure.................................................. 159 Timothy A. Doughty, Matthew R. Dally, and Mikah R. Bacon 19 Subspace-Based Damage Detection on Steel Frame Structure Under Changing Excitation.................... 167 M. Döhler and F. Hille 20 Real-Time Structural Damage Identification of Time-Varying Systems .......................................... 175 Jiann-Shiun Lew 21 Wavelet Transformation for Damage Identification in Wind Turbine Blades ........................................................................................................... 187 M.D. Ulriksen, J.F. Skov, P.H. Kirkegaard, and L. Damkilde 22 Vision Device Applied to Damage Identification in Civil Engineer Structures................................................................................................................. 195 Giorgio Busca, Alfredo Cigada, and Emanuele Zappa 23 Damage Detection and Quantification Using Thin Film of ITO Nanocomposites................................ 207 Breno Ebinuma Takiuti, Vicente Lopes Júnior, Michael J. Brennan, Elen Poliani S. Arlindo, and Marcelo Ornaghi Orlandi 24 The Use of Orbitals and Full Spectra to Identify Misalignment ................................................... 215 Michael Monte, Florian Verbelen, and Bram Vervisch 25 Damage Detection Based on Wavelet Packet Transform and Information Entropy ............................. 223 S.A. Ravanfar, H. Abdul Razak, Z. Ismail, and S.J.S. Hakim 26 Identification of Localized Damage in Structures Using Highly Incomplete Modal Information.............. 231 Eric M. Hernandez 27 Damage Detection Using Derringer’s Function based Weighted Model Updating Method..................... 241 Shankar Sehgal and Harmesh Kumar 28 Energy Harvesting in a Coupled System Using Nonlinear Impact................................................. 255 K. Vijayan, M.I. Friswell, H.H. Khodaparast, and S. Adhikari 29 Spatiotemporal Sensing for Pipeline Leak Detection Using Thermal Video...................................... 263 Ganesh Sundaresan, Seung-Yeon Kim, Jong-Jae Lee, Ki-Tae Park, and Hae-Bum Yun 30 Vibration-Based Continuous Monitoring of Tensile Loads in Cables and Rods: System Development and Application.......................................................................................... 271 C. Rainieri, D. Gargaro, L. Cieri, and G. Fabbrocino 31 Non-Model-Based Crack Identification Using Measured Mode Shapes........................................... 279 Y.F. Xu, W.D. Zhu, J. Liu, and Y.M. Shao

Chapter1 Assessment and Localization of Active Discontinuities Using Energy Distribution Between Intrinsic Modes Reza Mohammadi Ghazi and Oral Buyukozturk Abstract A method for localization and severity assessment of structural damages is proposed. The algorithm works based on nonlinear behavior of certain type of damages such as breathing cracks which are called active discontinuities in this paper. Generally, nonlinear features are more sensitive to such damages although their extraction is sometimes controversial. A major controversy is the imposition of spurious modes on the expansion of the signal which needs to be addressed for an effective application and robustness of the method. The energy content of Intrinsic Mode Functions (IMFs), which are the resultants of Empirical Mode Decomposition (EMD), and also the shape of energy distribution between these modes before and after damage, are used for localization and severity assessment of the damages. By using EMD, we preserve the nonlinear aspects of the signal while avoiding imposition of spurious harmonics on its expansion without any assumption of stationarity. The developed algorithms are used to localize and assess the damage in a steel cantilever beam. The results show that the method can be used effectively for detecting active structural discontinuities due to damage. Keywords Structural health monitoring • Active discontinuity • Nonlinearity • Normalized Cumulative Marginal Hilbert Spectrum • Energy transfer 1.1 Introduction Structural Health Monitoring (SHM) can play a significant role in improving the safety of structures as well as extending their life time. Greater complexity, aging, higher operational loads, and severe environmental effects result in more attention to this field. However, after more than 30 years of research, SHM has not been vastly applied in real world structures. Nonunique solutions of inverse problems, complexity, and variety of systems in the real world are the most important reasons that slow down the progress of SHM from research level to application. For instance, several methods have been proposed to detect breathing cracks such as mode shape curvature [1], model updating [2], energy method [3], and nonlinearities [4– 7]. All of the aforementioned methods were shown to be effective in a specific problem; however, this does not guarantee their generality. Methods which use numerical models suffer from difficulties of providing a precise model to monitor a system. Most other methodologies are not generalizable since they have been tested on a very specific structure. Moreover, the approach of these papers, typically, is proposing a metric, called a damage index (DI), and then verifying its sensitivity to a certain type of damage. Applicability of the methods with the mentioned approach is possible only after answering the following questions: Is the proposed DI sensitive to the same type of damage, but in different structures? Is the physics behind the DI the best possible representative of damage in the system? If not, how can we improve the method for application in R.M. Ghazi Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Bldg 5-336, Cambridge, MA 02139, USA e-mail: rezamg@mit.edu O. Buyukozturk ( ) Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Bldg 1-281, Cambridge, MA 02139, USA e-mail: obuyuk@mit.edu A. Wicks (ed.), Structural Health Monitoring, Volume 5: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04570-2__1, © The Society for Experimental Mechanics, Inc. 2014 1

2 R.M. Ghazi and O. Buyukozturk real structures? Is comparing the values of DIs sufficient for characterization of a structure as intact or damaged? A damage detection algorithm is not applicable unless all these questions are answered. We address the first three questions in this study by proposing several DIs based on nonlinearities due to damage. Other questions will be addressed in future studies. The proposed algorithm in this paper is suitable for detection of a certain type of damage called an active discontinuity. As defined in [8], active discontinuities, such as breathing cracks, are regarded as additional degrees of freedom whose effects on response of the system are above the noise floor. Obviously, activation of a discontinuity depends on the input energy and characteristics of excitation, meaning that the effect of discontinuity on the response of the system may not be discernible from noise under a specific excitation and hence, not activated. Note that even if the discontinuity is activated, it may or may not be detectable using a certain DI depending on its sensitivity to damage and/or how the damage affects the system response. For example, fundamental frequencies of a beam are not changed more than 2 % in presence of a breathing crack with the depth of around 20 % of the beam’s cross section [4], so it turns out to be quite difficult to detect small breathing cracks using a DI based on fundamental frequencies. The problem can be ameliorated by capturing nonlinear effects of damage since nonlinear features of structural response are generally more sensitive to damage [4–7]. On the other hand, a DI should not demonstrate a very high sensitivity to changes in a signal since the results of the algorithm are highly affected by noise and hence, not reliable. Several methods have been proposed based on different types of nonlinearities such as [4–7]. Most of the mentioned DIs suffer from one of these two shortcomings: (1) there is no solid physical interpretation behind the damage index such as those which aim to capture changes in the geometry of signal, (2) subjectiveness which makes it very difficult to use the DIs in complex structures and large sensor networks. In this paper we try to capture nonlinear effects using an energy-based method. The algorithm not only is sufficiently sensitive to active discontinuities, but also has a concrete physical interpretation behind each DI related to the concept of energy transfer between vibrating modes. There are two requirements essential for retaining the validity of the method; the first is preservation of nonlinearities and the second, prevention of energy leakage of any kind in signal processing. By the use of Empirical Mode Decomposition (EMD) [9], all nonlinearities are preserved in the expansion of a signal in terms of its Intrinsic Mode Functions (IMFs). In addition, there is no leakage of energy due to imposing spurious harmonics on such an expansion, and hence, both requirements are satisfied. The efficacy of the algorithm has been experimentally verified on different structures. The results show that the method can effectively detect active discontinuities due to damage in all cases. In this paper, we present the results only on one simple case which is a cantilever beam consists of three elements. 1.2 Active Discontinuities and Energy Transfer Between Vibrating Modes As defined in [8], an “Active Discontinuity” is a type of damage which can affect response of the system such that its effect is discernible from the sensor noise floor. Activation of a discontinuity mostly depends on the severity of damage as well as characteristics of the excitation. It implies that a discontinuity which is activated under a certain excitation may not be activated, and therefore detectable, under a different excitation. Such damage, if activated, generates new modes of vibration or amplify some existing ones. In other words, the damage results in transfer of energy between existing modes or from them to newly generated ones. Based on experiments, this phenomenon showed more sensitivity to damage compared to frequency shift while there is no controversy on the definition of frequency in this concept. In fact, the behavior of active discontinuities is nonlinear and the generated modes by their activation are mostly of high frequency. These high frequency modes change the energy content of other existing ones although they do not affect the dominant response of the system unless the damage is very severe. That is the reason that the energy based method with consideration of nonlinearities is more preferable than other methods which try to capture any kind of change only in frequency response of a system assuming linearity. However, there is a requirement which needs to be satisfied in order to make use of the strengths of the energy method. The requirement is to prevent leakage of energy in any form. Immediately, one can conclude that this condition cannot be always completely satisfied in the Fourier domain, especially in presence of noise, because of spurious harmonics which are imposed on the expansion of the signal. Note that the argument is about the accuracy of method and does not mean to totally disregard Fourier transformation for energy methods. In this paper, we use EMD as the signal processing tool to expand a signal into a set of nonlinear IMFs without any spurious modes and hence, prevent energy leakage. It is also noteworthy that by the “energy of a signal” we mean the norm of the signal or mode function. The norm is the actual energy only if the signal is displacement time history. Two assumptions are required for development of the algorithm in the simplest form. First, that the input energy and frequency content of excitations are consistent before and after damage. This implies that the algorithm has not been developed for damage detection using arbitrary excitations. There is always a baseline required, but the baseline is calculated using the structure itself without any theoretical assumptions. Secondly, the presence of damage is the only difference between the intact and damaged structure. This assumption is equivalent to consistency of environmental effects.

1 Assessment and Localization of Active Discontinuities Using Energy Distribution Between Intrinsic Modes 3 0 1 2 3 4 5 6 7 8 9 101112131415 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 IMF no. Normalized energy intact damaged 0 100 200 300 400 500 600 10-4 10-3 10-2 10-1 100 Frequency (Hz) Normalized energy intact damaged a b Fig. 1.1 Different energy distribution curves for same sensor data, (a)MHS, (b) energy distribution between IMFs 0 100 200 300 400 500 600 700 800 900 1000 0 2 4 6 8 10 12 14 16 18 Frequency (Hz) Cumulative MHS test#1 test#2 Fig. 1.2 Cumulative MHS for an empirical data of two tests on an intact structure (same sensor) 1.2.1 Normalized Cumulative Marginal Hilbert Spectrum (NCMHS) With energy methods, we need to express the distribution of energy with respect to a physical quantity. If this quantity is frequency in the sense of Fourier transformation, the distribution is called Power Spectral Density (PSD). Same concept can be defined using EMD and Hilbert Huang Transformation (HHT) and the distribution is called Marginal Hilbert Spectrum (MHS) in this domain. Energy distribution can also be expressed with respect to each IMF as defined in [8]. The latter is useful only if the IMFs are monocomponent. It is less accurate compared to the MHS but computationally more efficient. Figure 1.1 shows different energy distributions for empirical data. Working with the non-smooth functions shown in Fig. 1.1 is not mathematically preferable. Smoothing can be regarded as solution for this problem, but the true physics may be lost. Instead of modifying the curves by smoothing, we propose a more elegant way of solving the non-smoothness problem which is using the cumulative energy distributions rather than the distribution itself. The cumulative function is strictly increasing, smooth, and therefore easy to use, and preserves all physics without imposing any approximation on the problem. In Fig. 1.2 the cumulative MHS for two tests’ data from same sensor on the same structure vibrating under similar excitations are shown. It should be noted that smoothness is used for functions and not sampled data. If we assume that the MHS can be represented as a continuous function, meaning that all frequencies in a specific range have some contribution, then its cumulative summation will be smooth. Although the cumulative distributions are smooth and monotonically increasing, they still need modification before comparison. As shown in Fig. 1.2, there is a considerable deviation between two curves although they obtained from the

4 R.M. Ghazi and O. Buyukozturk 0 100 200 300 400 500 600 700 800 900 1000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Frequency (Hz) NCMHS Intact #1 intact # 2 Damaged Fig. 1.3 NCMHS of empirical data consists of two tests on an intact structure and one test on the same structure with damage (same sensor) intact structure. The reason is that the total input energies of the tests are different. As a result, comparing these two curves may lead us to a totally wrong deduction which is classifying an intact structure as damaged. Of course, it depends on the comparison methodology; for instance, if we focus only on the pattern of the distribution, they may be consistent. On the other hand, if we measure some other quantity such as the area under the curves the result of the algorithm will be wrong. In order to solve this problem we use the first basic assumption which is the consistency of spectrum and input energy of excitations in all tests. The consistency means that the difference between input energy does not affect the response of the structure; therefore, the effect of this difference can be neglected. As a result, we disregard the difference between input energy and normalize the cumulative function with respect to total input energy. The result is the Normalized Cumulative Marginal Hilbert Spectrum (NCMHS), examples of which are shown in Fig. 1.3. In this figure, the NCMHS for a set of empirical sensor data consisting of two tests on an intact structure and one for the same structure with damage are illustrated. In contrast to cumulative curves, the difference between Normalized Cumulative curves of the intact structure is not significant while the deviation between the damaged and intact structures is quite obvious. This procedure is generalizable to any other energy distribution such as the PSD to obtain the Normalized Cumulative PSD (NCPSD) or to energy distribution between IMFs as well, provided the assumption is satisfied. 1.3 Damage Indices In previous section, it was shown that the NCMHS can be regarded as a reliable signature for the intact state of a structure under excitations with consistent spectra and input energies. In addition, it was shown that the NCMHS for the certain type of damages, active discontinuities, deviates from that signature due to the change in the pattern of energy distribution. Some, out of many, possible ways of quantifying this deviation are presented in this paper. We also do not restrict ourselves to use only the normalized cumulative curves since some quantities, such as the mean frequency, make sense only if the original curves are used. The first DI is defined as DI1 D X i jAi j ABL (1.1) where Ai is each portion of the area between NCMHS of the structure we are testing and the baseline NCMHS (Fig. 1.4); ABL is the area under the baseline NCMHS. In this study, we defined the baseline using median of tests on intact structure, using only the sensor data and without any theoretical assumption. The median is chosen because of its robustness with

1 Assessment and Localization of Active Discontinuities Using Energy Distribution Between Intrinsic Modes 5 Fig. 1.4 Parameters for comparing NCMHS respect to outliers. The numerator in Eq. (1.1) is the absolute value of the whole area between two curves and its physical interpretation is the total energy transfers between different modes. The denominator is only for normalization which provides a dimensionless DI in the range of zero to one. Similarly, another measure of energy transfer can be defined as DI2 D ˇ ˇ ˇ ˇ ˇ X i Ai ˇ ˇ ˇ ˇ ˇ ABL (1.2) In this DI, some of the Ais are cancelled out if one curve oscillates around the other. Indices for comparing these curves are not restricted to Eqs. (1.1) and (1.2). Other possible methods are the ones which are used for comparing cumulative probability distributions. Of course, some of them cannot be interpreted physically even if they work well. For instance, Kolmogorov–Smirnov distance can be used and it shows a good sensitivity to damage; however, it has no solid physical interpretation. As it mentioned before, some DIs should be defined using the original MHS. Again, based on the assumption for consistency of input energy, we can normalize the MHS to make a more meaningful comparison. Using normalized MHS one can define DI3 D F FBL (1.3) where the F is the mean frequency of MHS, FBL is the mean frequency of baseline MHS. This DI can be interpreted as a measure of change of fundamental modes (frequencies), but not in Fourier domain. It tells us where the accumulation of energy is. 1.4 Severity Assessment After localization of damage, the same concept of energy transfer between modes can be used for severity assessment of the active discontinuity. Stiffness reduction and generation of nonlinear high frequency vibrating modes are two main effects of such damages on the behavior of structure. The first effect dominates when the damage severity is low. In this case, the rigidity of the structure around the damage is high enough such that it prevents the generation of higher modes; therefore, the fundamental frequencies shift due to the energy transfers into low frequency modes. If the severity is high, the later effect dominates and the energy of high frequency modes will be increased. Capturing this phenomenon is easier if the distribution of energy between IMFs is used rather than the MHS. In fact, the high resolution discretization of frequency bands in the MHS hides these tiny effects. As shown in Fig. 1.5, the cumulative

6 R.M. Ghazi and O. Buyukozturk 0 1 2 3 4 5 6 7 8 9 10111213141516 0 0.2 0.4 0.6 0.8 1 IMF no. Normalized cumulative energy major damage intact minor damage Fig. 1.5 Comparison of normalized cumulative distribution of energy between IMFs Table 1.1 Different damage scenarios Damage scenario Description 1 Minor damage at node #2 2 Major damage at node #2 3 Minor damage at node #3 4 Major damage at node #3 energy distribution in the case of major damage lays above the intact case. The reason for the high slope of the curve near the high frequency IMFs in the damaged case is the accumulation of energy in these modes. For the minor damage, on contrary, the slope of the curve is high near the low frequency IMFs and hence, it is below the baseline. 1.5 Experimental Setup In this study, we try to capture some nonlinear phenomena which are very difficult to simulate numerically. Therefore, experimental tests have been chosen as a more rigorous way of verification of the algorithm. The algorithm has been verified for different structure and the one which is presented in here is a cantilever beam consisting of three elements bolted together as shown in Fig. 1.6. The bolts are completely tightened in the intact structure such that the end plates of the elements are clamped. A triaxial accelerometer also is attached in the vicinity of each connection. Free vibration is chosen as the excitation in order to reduce the complications of dealing with different excitations and focus only on the efficacy of the algorithm. The structure was tested under four damage scenarios which are listed in Table 1.1. In the case of minor damage, two bolts removed in one side of the connection while two other bolts were completely tightened. For the major damage, all four bolts were slightly loosened such that the structure did not lose stability. The sampling rate was chosen to be 3 kHz in order to capture the higher modes as precisely as possible. 1.6 Results The sensor data in z direction (Fig. 1.6), perpendicular to the discontinuities, was analyzed. To assess the sensitivity of the algorithm to data length, two signal lengths were investigated: 5 s of data, and 2 s of data for comparison. In this paper, only the results of the later one are shown because there is no considerable difference between them. Moreover, multiple tests were conducted for each damage scenario, but, because the results are similar, for the sake of brevity only one of them is illustrated.

1 Assessment and Localization of Active Discontinuities Using Energy Distribution Between Intrinsic Modes 7 Fig. 1.6 Experimental setup; (a) cantilever beam consists of three elements; (b) accelerometer attached near a connection 0 1 2 3 4 5 6 7 8 9 10111213141516 0 0.2 0.4 0.6 0.8 1 IMF no. Cumulative normalized energy intact damaged 0 1 2 3 4 5 6 7 8 9 10111213141516 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 IMF no. Cumulative normalized energy intact damaged a b Fig. 1.7 NCMHS for the sensor at node #3; (a) minor damage; (b) major damage The NCMHS for all tests and both minor and major cases are shown in Fig. 1.7. As expected, the curves are above the intact case in the case of major damage due to transfer of energy to high frequency modes and vice versa for minor damages. The damage index in all cases, which is shown in Fig. 1.8, has the highest value for the sensor at the node adjacent to the damage. It should be noted that for minor damage, the two end plates of elements in the connection where the damage presents are completely clamped in one side and there is no visible gap. However, the algorithm can effectively detect and also assess the severity of damage by considering nonlinearities in a very simple way. 1.7 Conclusions In this study, an algorithm for localization and assessment of certain type of damages named active discontinuities was proposed. Breathing cracks and loosened bolts in a connection are examples of this type of damage. Activation of such discontinuities results in the generation of new vibrating modes which are nonlinear and mostly have high frequency content.

8 R.M. Ghazi and O. Buyukozturk 1 2 3 4 1 1.5 2 2.5 Node No. DI1 minor damage major damage 1 2 3 4 1 1.5 2 2.5 3 3.5 4 Node No. DI1 minor damage major damage Fig. 1.8 DI1 for (a) damages at node #2 and (b) damages at node #3 Assuming the same excitations for both intact and damaged structures, the distribution of input energy between the modes of vibration is changed due to damage. In other words, active discontinuities result in energy exchange between existing modes and newly generated modes due to damage. In order to capture this effect, several conditions should be satisfied. First, the spectrum and input energy of the excitation for both intact and damaged structures should be consistent. Second, any leakage of energy should be prevented for the method to be reliable. By using EMD for the decomposition of a signal, nonlinearities are preserved and all requirements for the second aforementioned condition is satisfied. To capture the nonlinearities after decomposition, we use the distribution of energy between different modes of vibration which can be expressed in different ways. MHS and distribution of energy between IMFs are examples of such distributions. Two modifications are accomplished on the energy distribution to make it easier to analyze them. The modifications are, first using cumulative energy distribution and the second, normalization with respect to total input energy. These modifications give us well-behaved monotonically increasing curves, named the NCMHS if the MHS is used as the original distribution, which can be regarded as a signature for the system by preserving all physics. Among several methods of comparing the normalized cumulative curves, we used the area between NCMHSs for the damaged structure and the baseline. This index, in contrast to other pure mathematical indices, has a solid physical interpretation which is the total transferred energy between modes. Stiffness reduction and generation of nonlinear high frequency modes are two important effects of active discontinuities. These effects, which manifest themselves in the shape of the energy distribution, can be used for severity assessment of the damage. The energy distribution between IMFs, because of low resolution, magnifies the accumulation of energy in certain frequency band and hence, more appropriate for severity assessment. In the case of major damage, the energy is transferred to high frequency modes and the corresponding curve lays above the baseline. The opposite is true for the minor damages. The efficacy of the algorithm is experimentally verified by testing a cantilever beam consisting of three elements which are bolted together under four damage scenarios. The results show that the algorithm can effectively detect and localize active discontinuities and also assess their severity even in the case of minor damages. The algorithm provides quantitative damage indices by capturing nonlinearities in a simple and effective manner. Acknowledgments The authors acknowledge the support provided by Royal Dutch Shell through the MIT Energy Initiative, and thank chief scientists Dr. Dirk Smit and Dr. Sergio Kapusta, project manager Dr. Yile Li, and Shell-MIT liaison Dr. Jonathan Kane for their oversight of this work. Thanks are also due to Dr. Michael Feng and his team from Draper Laboratory for their collaboration in the development of the laboratory structural model and sensor systems. Sincere appreciation is given to Justin Chen for his help in collecting experimental data and editing the paper. References 1. Pandey AK, Biswas M, Samman MM (1991) Damage detection from changes in curvature mode shapes. J Sound Vib 145(2):321–332 2. Lam HF, Katafygiotis LS, Mickleborough NC (2004) Application of a statistical model updating approach on phase I of the IASC-ASCE structural health monitoring benchmark study. J Eng Mech 130(1):34–48

1 Assessment and Localization of Active Discontinuities Using Energy Distribution Between Intrinsic Modes 9 3. Cornwell P, Doebling SW, Farrar CR (1999) Application of the strain energy damage detection method to plate-like structures. J Sound Vib 224(2):359–374 4. Peng ZK, Lang AQ, Billings SA (2007) Crack detection using nonlinear output frequency response functions. J Sound Vib 301:777–788 5. Nochols JM, Todd MD, Seaver M, Virgin LN (2003) Use of chaotic excitation and attractor property analysis in structural health monitoring. Phys Rev 67:016209 6. Nichols JM, Trickey ST, Todd MD, Virgin LN (2003) Structural health monitoring through chaotic interrogation. Meccanica 38:239–250 7. Yin SH, Epureanu B (2006) Structural health monitoring based on sensitivity vector fields and attractor morphing. Philos Trans A Math Phys Eng Sci 364:2515–2538 8. Mohammadi Ghazi R, Long J, Buyukozturk O (2013) Structural damage detection based on energy transfer between intrinsic modes. In: Proceedings of ASME 2013 conference on smart material, adaptive structures and intelligent systems (SMASIS), September 2013, No. 3022 9. Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen N, Tung CC, Liu HH (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc A Math Phys Eng Sci 454:903–995

Chapter2 Wave Analyses in Structural Waveguides Using a Boundary Element Approach Stefan Bischoff and Lothar Gaul Abstract Wave-based SHM concepts are widely used for an efficient evaluation of the state of a structure. In order to localize defects in waveguides, an exact knowledge of the propagation properties of ultrasonic waves is required. Within this work, a boundary element formulation for modeling 3D waveguides is presented by which wave numbers as well as mode shapes of wave modes can be analyzed. In a BE modeling process, a segment of the periodic waveguide is considered. The collocation method, in which the boundary integral equation is solved at discretized nodes, is used to set up the corresponding system matrices. Applying a periodicity condition, the solution of the resulting eigenvalue problem provides both propagating and non-propagating modes of the waveguide. The model is verified by comparing the numerical results with theoretical considerations. Additionally, a SHM application is demonstrated in order to characterize defects. The numerical accuracy of the simulation results are validated by an energy balance criteria. Keywords Boundary elements • Periodic structural waveguide • Structural health monitoring • Crack detection 2.1 Introduction In civil engineering, multi-wire strands are frequently used as stay cables of cable-stayed bridges, or overhead transmission lines. Generally, these structures are exposed to the ambient environmental conditions, and thus subjected to wind-induced vibrations, corrosion etc. As sight inspection techniques are limited to the detection of surface flaws, automated monitoring schemes such as vibration-based methods are developed in order to detect failure in multi-wire strands [5]. This work focuses on active wave-based approaches for damage localization and characterization. Considering elongated structures such as pipes, railroad rails and multi-wire strands ultrasonic waves are preferably used as they may travel over long distances with little decay and therefore allow for long range inspections. An example for power cables of overhead transmission lines is depicted in Fig. 2.1. Ultrasonic waves are excited in the monitored multi-wire strand and are partially reflected and transmitted at discontinuities. Reflections are measured by a sensor and damage detection algorithms evaluate whether a defect exists. The work is structured as follows. First, a theoretical description of guided waves in waveguides is presented. As the use of analytical models is restricted to relatively simple geometries, a more general approach based on Boundary Element (BE) formulations is applied. A brief theoretical background of the classical BE method is given, and subsequently extended to the Waveguide BE method by modeling a waveguide segment with a periodicity condition. In the forth section, the method is applied to waveguides with circular and Z-shaped cross-section. Several numerical results, e.g. circular wavenumbers, showing convergence of the numerical results to the analytical solution, are presented. Section 2.5 illustrates a Structural Health Monitoring (SHM) application of ultrasonic guided waves in order to characterize defects in waveguides. Herein, the Waveguide BE method is used in combination with the classical BE method to predict scattering phenomena induced by surface opening defects of various depths. Based on measured reflection coefficients, the inverse problem of defect classification is possible. Conclusions complete this article. S. Bischoff ( ) • L. Gaul Institute of Applied and Experimental Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70550, Stuttgart, Germany e-mail: bischoff@iam.uni-stuttgart.de; gaul@iam.uni-stuttgart.de A. Wicks (ed.), Structural Health Monitoring, Volume 5: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04570-2__2, © The Society for Experimental Mechanics, Inc. 2014 11

12 S. Bischoff and L. Gaul sender/ receiver defect incident wave reflected wave a b Fig. 2.1 (a) Scheme of SHM concept for overhead transmission lines. Piezoelectric transducers (b) attached at surface wires are used as actuators and sensors being able to generate and measure guided ultrasonic waves in power cables 2.2 Wave Propagation in Waveguides with Circular Cross-Section Guided waves appear in elongated structures where internal disturbances are totally reflected at the lateral boundary. As a result, standing waves are formed in the cross-section propagating in axial x3-direction. In the following, the analytical solution describing wave propagation in cylindrical wires is presented briefly—for further information see e.g. [1, 9]. The governing partial differential equation for a homogeneous isotropic elastic domain is the Lamé Navier equation of the displacement field u. Neglecting body forces, the wave equation can be expressed as . C /r.r u/ C r2uD Ru (2.1) with the Lamé constants, and , and the density . Application of the Helmholtz theorem connected with the potential technique leads Eq. (2.1) into two uncoupled wave equations for the scalar and vector potential functions, ˆandH, r2ˆD 1 c2 1 @2ˆ @t2 and r2H D 1 c2 2 @2H @t2 (2.2) with the extensional and shear wave velocities, c1 and c2, for an infinite media. The solution of these wave equations can be found by applying the technique of separation of variables, arriving at the following general complex form for the displacement fieldu u.x; t/ DOu.x1;x2/e j.kx3 !t/ (2.3) with the circular wavenumber k and the angular frequency!. The characteristic mode shapes are described by displacement fields, Ou.x1;x2/. For waveguides with circular cross-section, three types of waves may propagate: longitudinal, flexural and torsional waves [1]. Using common nomenclature, these waves are abbreviated as L(0,m), F(n,m) andT(0,m) with order n and sequential numberingm. Solving the characteristic equations for each mode type is complex. As the use of analytical models is also restricted to relatively simple geometries, such as waveguides with circular cross-section, various numerical techniques have been developed in order to analyze waveguides with arbitrary cross-sections. Mace et al. [12] introduced a wave-based approach for analyzing guided waves in arbitrarily shaped waveguides. Based on Floquet’s principle only a Finite Element (FE) discretized waveguide segment is considered using periodic boundary conditions. In the following, an alternative approach, namely the Waveguide BE method, is introduced for modeling 3D waveguides of arbitrary cross-section. The method requires a BE discretization of a waveguide segment and a periodicity condition that allows harmonic wave motion in direction of propagation. Instead of discretizing the waveguide segment with Finite Elements, the BE method can be employed effectively as the boundary data are of primary interest. Furthermore, the problem dimension is reduced by one and as the method is based on fundamental solutions which analytically fulfil the field equations [7], high accuracy is obtained. Unfortunately, the BE method usually leads to fully populated system matrices, in contrast to sparse matrices which are often associated with FE approaches. Below, the Waveguide BE method for 3D elastodynamics is outlined and thereafter applied to various different periodic waveguides with different cross-sections.

2 Wave Analyses in Structural Waveguides Using a Boundary Element Approach 13 2.3 Waveguide Boundary Element Method At the beginning, a theoretical background of the BE method in the elastodynamics is given. By applying the collocation technique, a system of linear algebraic equations is obtained. Taking into account the given constraints, the system of equations is transferred into an eigenvalue problem, whereas the solutions are obtained in terms of circular wavenumbers and mode shapes. 2.3.1 Elastodynamic Boundary Element Formulation The process of deriving the boundary integral equation (BIE) for the unknown field quantities is well known from the standard BE literature (see e.g. [3, 6]) and is therefore only briefly outlined here. The elastodynamic BIE of a boundary model may be derived from Cauchy’s equation of motion through a weighted residual statement [7] as follows cij. /uj. / C Z Tij.x; /uj.x/d D Z Uij.x; / tj .x/d ; 2 ; (2.4) whereR denotes a Cauchy principal value (CPV) integral andcij is the free term coefficient at 2 . The physical quantities introduced in Eq. (2.4) are the displacement and traction components, uj and tj, on the boundary . Uij and Tij are the displacement and traction fundamental solutions at the field point x when a unit load is applied at the load point in i direction. The numerical implementation of Eq. (2.4) requires a discretization of the boundary into finite boundary elements .e/, see Fig. 2.2a. By means of shape functions ˆn and nodal values, Mun j and Mt n j , the field quantities, uj and tj, are approximated as follows u.e/ j DX n ˆnMun j and t .e/ j DX n ˆnMtn j : (2.5) Applying the collocation technique to Eq. (2.4), one gets a system of algebraic equations in matrix form HMuDGMt ; (2.6) where the matrices H and G contain the boundary integral terms of the traction and displacement fundamental solutions, while the displacement and traction vectors on the boundary are given by Muand Mt, respectively. In these formulations, the numerical integration of the regular integrals over the boundary elements is performed by Gaussian quadrature. The weak singularities are solved by regularising the transformation to polar coordinates [11], while strongly singular integrals are carried out by means of traction-free rigid body motion used for elastostatic singular integration in combination with regular Gaussian quadrature [7]. 2.3.2 Boundary Element Analysis of Periodic Structures A periodic waveguide segment is shown in Fig. 2.2b. The structural models required for the BE formulation are created with the aid of a universal preprocessor, such as HyperMesh of Altair Computing Inc. Thereby, the segment of the periodic structure is meshed with an equal number of nodes on their left and right cross-section. According to Sect. 2.3.1, the dynamics of the waveguide segment is given as HuDGt. Partitioning of degrees of freedom with respect to the external surface, E, as well as the left and right cross-section, L and R, lead to 2 4 HLL HLE HLR HEL HEE HER HRL HRE HRR 3 5 2 4 uL uE uR 3 5D 2 4 GLL GLE GLR GEL GEE GER GRL GRE GRR 3 5 2 4 tL tE tR 3 5 : (2.7)

14 S. Bischoff and L. Gaul s s+1 s-1 us L ts L u s+1 L t s+1 L us R ts R h ΓL ΓR ΓE a b Fig. 2.2 (a) Boundary element waveguide model as well as (b) integrated segment s of a cylindrical waveguide with displacement and traction fields on the left and right cross-section, L and R Elimination of displacements uE by the boundary condition of vanishing tractions, tE D0at E, yields the dynamic stiffness relation D uL uR D tL tR ; (2.8) which allows for coupling with neighboring waveguide segments at the interfaces, L and R. Depending on the total number of external degrees of freedom, the order of the dynamic stiffness matrixDmay reduce drastically. Considering periodic continuation of the waveguide segments, continuity of displacements and equilibrium of tractions at the cross-sections between neighboring segments, s ands C1, yields, us C1 L Dus R ; t s C1 L D t s R : (2.9) Combining Eqs. (2.8) and (2.9) one obtains the so called transfermatrix T relating the displacements and tractions in the cross-sections of subsequent segments T us L ts L D us C1 L t s C1 L (2.10) where the single partitions of the transfermatrix are given as T D D 1 LRDLL D 1 LR DRL CDRRD 1 LRDLL DRRD 1 LR : (2.11) Assuming harmonic wave propagation the displacements and tractions of neighboring cross-sections can be linked by a complex phase shift , defined as Dejkh with the lengthh, us C1 L D u s L ; t s C1 L D t s L : (2.12) Inserting Eq. (2.12) into Eq. (2.10) results in a eigenvalue problem T us L ts L D us L ts L : (2.13) Using eigenvalues and eigenvectors, the guided wave propagation characteristics such as wavenumbers k and mode shapes for displacement and traction fields, Ou and Ot, respectively, can be derived. On the basis of wavenumbers, guided waves can be classified as propagating and non-propagating modes. The logarithm of a complex eigenvalue Dj j ej with 2Œ ; / is generally defined as Ln. / Dln.j j/ Cj. C2 m/ ; mD0;1;2;3;::: : (2.14) In order to ensure precise results and unique solutions, the wave analysis is restricted to modes whose wavenumbers, k D j h Ln , fulfill the condition h real fkg < h : (2.15)

2 Wave Analyses in Structural Waveguides Using a Boundary Element Approach 15 In general, the Waveguide BE solutions are obtained in a stable manner, and thus do not require the root searching algorithms used in analytical formulations. 2.4 Numerical Results In this section, the performance of the Waveguide BE method for various periodic waveguides with different cross-sections and with respect to the mesh density is analyzed. Boundary models are built with HyperMesh, simulations are performed using MATLAB. 2.4.1 Waveguide with Circular Cross-Section First, the Waveguide BE method is applied for uniform rods with circular cross-section. As aluminium is well known for its high electrical conductivity and is therefore frequently used in power cables, the analysis is conducted for aluminium [EN AW-6082 T6] wires of radius r D2mm. A waveguide segment of length h D 0:5mm is truncated from the cylindrical structure and meshed using quadratic boundary elements. Each segment is exactly one element long. The accuracy of the Waveguide BE solution depends on both the discretization of the waveguide cross-section and the order of the used interpolation function. Figure 2.3 shows the relative wavenumber error of all propagating wave modes at a frequency of 200kHz, calculated for different discretizations. The benefit of improved accuracy must be carefully weighted against the increased computational effort due to the higher number of elements. As the relative wavenumber error for BE meshes with 726DOF’s is below1%, the waveguide crosssection is discretized in the further course with32quadratic elements (entire waveguide segment is meshed with80quadratic elements) avoiding high computational effort for determining the system matrices. Additional outcomes of the Waveguide BE method are displacement and traction fields. The in-plane displacement fields for the basic wave modes are shown in Fig. 2.4. In agreement with theory, the longitudinal mode L(0,1) is axially symmetric, whereas the torsional wave T(0,1) contains only rotational components. Also note that the flexural wave F(1,1) is arbitrarily oriented and occurs in pairs of equal wavenumbers due to the cross-sectional symmetry. In the same way, higher order modes can be analyzed. For a specific frequency, the Waveguide BE method allows for an efficient determination of wave modes. While an analytical determination of the propagating modes is possible for waveguides with circular cross-section, the Waveguide BE results also obtain nonpropagating modes, which are especially important when analyzing guided wave interaction at defects in SHM applications. L(0,1) T(0,1) F(1,1) Relative error of wave number DOFs of wave guide BE model 2166 DOF 1014 DOF 726 DOF 294 DOF 294 DOF 726 DOF 1014 DOF2166 DOF 10−5 10−4 10−3 10−2 10−1 Fig. 2.3 Relative error between analytically derived and numerically calculated wavenumbers for various discretizations

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