River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Dynamics of Civil Structures, Volume 2 Shamim Pakzad Caicedo Juan Proceedings of the 34th IMAC, A Conference and Exposition on Structural Dynamics 2016 River Publishers
Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Kristin B. Zimmerman, Ph.D. Society for Experimental Mechanics, Inc., Bethel, CT, USA
River Publishers Shamim Pakzad • Caicedo Juan Editors Dynamics of Civil Structures, Volume 2 Proceedings of the 34th IMAC, A Conference and Exposition on Structural Dynamics 2016
Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN ‘978-87-7004-926-9 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2016 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 Dynamics of Civil Structures represents one of ten volumes of technical papers presented at the 34th IMAC, A Conference and Exposition on Structural Dynamics, organized by the Society for Experimental Mechanics, and held in Orlando, Florida, in January 25–28, 2016. The full proceedings also include volumes on Nonlinear Dynamics; Model Validation and Uncertainty Quantification; Dynamics of Coupled Structures; Sensors and Instrumentation; Special Topics in Structural Dynamics; Structural Health Monitoring, Damage Detection & Mechatronics; Rotating Machinery, Hybrid Test Methods, Vibro-Acoustics & Laser Vibrometry; Shock & Vibration, Aircraft/Aerospace, Energy Harvesting, Acoustics & Optics; and Topics in Modal Analysis & Testing. Each collection presents early findings from analytical, experimental, and computational investigations on an important area within structural dynamics. Dynamics of Civil Structures is one of these areas which cover topics of interest of several disciplines in engineering and science. The Dynamics of Civil Structures Technical Division serves as a primary focal point within the SEM umbrella for technical activities devoted to civil structures analysis, testing, monitoring, and assessment. This volume covers a variety of topics including damage identification, human-structure interaction, hybrid testing, vibration control, model updating, modal analysis of in-service structures, sensing and measurements of structural systems, and bridge dynamics. Papers cover testing and analysis of all kinds of civil engineering structures such as buildings, bridges, stadiums, dams, and others. The organizers would like to thank the authors, presenters, session organizers, and session chairs for their participation in this track. Bethlehem, PA Shamim Pakzad Columbia, SC Caicedo Juan v
Contents 1 Damage Assessment of Steel Structures Using Multi-Autoregressive Model ..................................... 1 Chin-Hsiung Loh and Chun-Kai Chan 2 Damage Detection with Symplectic Geometry Spectrum Analysis in Changing Environment ................. 9 Dong-Sheng Li and Xiao-Hai Li 3 Compressive Sensing Strategies for Multiple Damage Detection and Localization.............................. 17 S. Golnaz Shahidi, Nur Sila Gulgec, and Shamim N. Pakzad 4 Structural Damage Detection Through Vibrational Feature Analysis with Missing Data ...................... 23 Matthew Horner and Shamim N. Pakzad 5 Structural Assessment of a School Building in Sankhu, Nepal Damaged Due to Torsional Response During the 2015 Gorkha Earthquake ..................................................................... 31 Supratik Bose, Amin Nozari, Mohammad Ebrahim Mohammadi, Andreas Stavridis, Moaveni Babak, Richard Wood, Dan Gillins, and Andre Barbosa 6 Damage Detection Optimization Using Wavelet Multiresolution Analysis and Genetic Algorithm............ 43 S.A. Ravanfar, H. Abdul Razak, Z. Ismail, and S.J.S. Hakim 7 A Novel Acoustoelastic-Based Technique for Stress Measurement in Structural Components................. 49 Mohammad I. Albakri and Pablo A. Tarazaga 8 A Machine Learning Framework for Automated Functionality Monitoring of Movable Bridges ............. 57 Masoud Malekzadeh and F. Necati Catbas 9 Non-Model-Based Damage Identification of Plates Using Curvature Mode Shapes ............................. 65 Y.F. Xu and W.D. Zhu 10 Ambient Vibration Testing of Two Highly Irregular Tall Buildings in Shanghai ................................ 87 Xiang Li, Carlos E. Ventura, Yu Feng, Yuxin Pan, Yavuz Kaya, Haibei Xiong, Fengliang Zhang, Jixing Cao, and Minghui Zhou 11 Development of an Acoustic Sensing Based SHM Technique for Wind Turbine Blades ........................ 95 Rukiye Canturk and Murat Inalpolat 12 Damage Location by Maximum Entropy Method on a Civil Structure ........................................... 105 Pastor Villalpando, Viviana Meruane, Rubén Boroschek, and Marcos Orchard 13 Making Structural Condition Diagnostics Robust to Environmental Variability ................................ 117 Harry Edwards, Kyle Neal, Jack Reilly, Kendra Van Buren, and François Hemez 14 Experimental Dynamic Characterization of Operating Wind Turbines with Anisotropic Rotor .............. 131 Dmitri Tcherniak and Matthew S. Allen 15 Exploring Environmental and Operational Variations in SHM Data Using Heteroscedastic Gaussian Processes ...................................................................................................... 145 N. Dervilis, H.Shi, K. Worden, and E.J. Cross vii
viii Contents 16 Ambient Vibration Testing of a Super Tall Building in Shanghai.................................................. 155 Yuxin Pan, Carlos E. Ventura, Yu Feng, Xiang Li, Yavuz Kaya, Haibei Xiong, Fengliang Zhang, Jixing Cao, and Minghui Zhou 17 Inelastic Base Shear Reconstruction from Sparse Acceleration Measurements of Buildings................... 163 Boya Yin and Henri Gavin 18 Vibration Testing for Bridge Load Rating............................................................................ 175 Mohamad Alipour, Devin K. Harris, and Osman E. Ozbulut 19 Finite Element Model Updating of French Creek Bridge........................................................... 185 Xiang Li, Yavuz Kaya, and Carlos Ventura 20 Damage Detection of a Bridge Model After Simulated Ground Motion .......................................... 195 C. Rainieri, D. Gargaro, G. Fabbrocino, L. Di Sarno, and A. Prota 21 Bridge Assessment Using Weigh-in-Motion and Acoustic Emission Methods ....................................................................................................... 205 L. Dieng, C. Girardeau, L. Gaillet, Y. Falaise, A. Žnidaricˇ, and M. Ralbovsky 22 Model-Based Estimation of Hydrodynamic Forces on the Bergsoysund Bridge ................................. 217 Øyvind Wiig Petersen, Ole Øiseth, Torodd S. Nord, and Eliz-Mari Lourens 23 Operational Modal Analysis and Model Updating of Riveted Steel Bridge....................................... 229 Gunnstein T. Frøseth, Anders Rönnquist, and Ole Øiseth 24 Full-Scale Measurements on the Hardanger Bridge During Strong Winds ...................................... 237 Aksel Fenerci and Ole Øiseth 25 Finite Element Model Updating of Portage Creek Bridge .......................................................... 247 Yu Feng, Yavuz Kaya, and Carlos Ventura 26 Seismic Behavior of Partially Prestressed Concrete Structures .................................................... 255 Milad Hafezolghorani Esfahani, Farzad Hejazi, Keyhan Karimzadeh, and Tan Kok Siang 27 Estimating Effective Viscous Damping and Restoring Force in Reinforced Concrete Buildings ............... 265 P. Hesam, A. Irfanoglu, and T.J. Hacker 28 Design of Metamaterials for Seismic Isolation ....................................................................... 275 P.-R. Wagner, V.K. Dertimanis, E.N. Chatzi, and I.A. Antoniadis 29 Genetic Algorithm use for Internally Resonating Lattice Optimization: Case of a Beam-Like Metastructure................................................................................... 289 Osama Abdeljaber, Onur Avci, and Daniel J. Inman 30 Vibration Transmission Through Non-Structural Partitions Between Building Floor Levels.................. 297 P.J. Fanning and A. Devin 31 Hybrid Time/Frequency Domain Identification of Real Base-Isolated Structure................................ 303 Patrick Brewick, Wael M. Elhaddad, Erik A. Johnson, Thomas Abrahamsson, Eiji Sato, and Tomohiro Sasaki 32 The Use of OMA for the Validation of the Design of the Allianz Tower in Milan................................ 313 Elena Mola, Franco Mola, Georgios Stefopoulos, Carlo Segato, and Chiara Pozzuoli 33 Transfer Length Probabilistic Model Updating in High Performance Concrete................................. 325 Albert R. Ortiz, Ramin Madarshahian, Juan M. Caicedo, and Dimitris Rizos 34 Multi-Shaker Modal Testing and Modal Identification of Hollow-Core Floor System.......................... 331 Atheer F. Hameed and Aleksandar Pavic
Chapter 1 Damage Assessment of Steel Structures Using Multi-Autoregressive Model Chin-Hsiung Loh and Chun-Kai Chan Abstract For application in operational modal analysis considering simultaneously the temporal and spatial response data of multi-channel measurements, the multivariate-autoregressive (MV-AR) model was used. The parameters of MV-AR model are estimated by using the least squares method via the implementation of the QR factorization as an essential numerical tool and are used to extract the structural damage sensitive features. These parameters are used to develop the Vectors of autoregressive model and Mahalanobis distance, and then to identify the damage features and damage locations. Verification of the proposed method using a series of white noise response data of a steel structure is demonstrated. This method is thus very effective for damage detection in case of ambient vibrations dealing with output-only modal analysis. In addition, comparisons and discussions on the proposed method with other methods, such as stochastic subspace identification and wavelet-based energy index, are also presented. Keywords Damage detection • Multi-autoregressive model • Damage sensitive feature • SSI-COV • Wavelet-based energy index 1.1 Introduction Structural system identification and damage detection have received more and more attention in the field of civil engineering. Through monitoring data on structures a quantity of information can be obtained. A well known classification for damage identification methods can be defined four levels: (Level-1) Determination or detection that damage is present in the structure, (Level-2) Determination of the geometric location of the damage, (Level-3) Quantification of the severity of the damage, (Level-4) Prediction of the remaining service life of the structure. Generally, detection is performed by pattern recognition methods or Novelty detection [16], and the key issue for inverse methods is the damage location identification. Once the damage is located, it may be parameterized with a limited set of parameters and quantification. One of the efficiently and accurately monitoring techniques to all types of structural systems is the vibration-based damage detection. It is based on the principal that damage in a structure will alter the dynamic response of that structure and the selection of damage-sensitive features such as natural frequencies [12], displacement mode shapes [5], wavelet analysis of dynamic signals [7] will be concerned. In the viewpoint of global monitoring, system identification techniques extract natural frequencies, damping ratios, and mode shapes of a structure using acceleration data [3, 8]. But these dynamic features are not sensitive to damage. Fundamentally, feature extraction can also be based on fitting some model, either physics-based [Moaveni et al., 2008] or data-driven [13], to the measured system response data. Time-series analysis based on the use of autoregressive (AR) models have been extensively used in the SHM process as a feature extraction technique and also applied to damage detection [10, 11]. The algorithm is based on the premise that structural damage will change the vibration response of the structure. In this study, damage identification on the seismic response of two steel structures is examined. By using the response data of the two structures from white noise excitation between a series of earthquake excitations back to back from the shaking table tests, the multivariate signal processing techniques are used to extract the dynamic features directly from response measurements. The state of damage severity as well as the damage location through the developed novel damage detection algorithms is proposed. C.-H. Loh ( ) • C.-K. Chan Department of Civil Engineering, National Taiwan University, Taipei 10617, Taiwan e-mail: lohc0220@ccms.ntu.edu.tw; r98521205@ntu.edu.tw © The Society for Experimental Mechanics, Inc. 2016 S. Pakzad, C. Juan (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29751-4_1 1
2 C.-H. Loh and C.-K. Chan 1.2 Structural Model and Instrumentation The major research objective of this study is to examine the applicability of the proposed damage features to detect the structural damage and to identify the damage location using the output-only measurement. The structural models used for this study are two 3-story (Specimen 1 and Specimen 2) with 350 cm in height steel structures and the floor area is 1.5 m 1.1m, respectively. The two steel structures are constructed with the same member size except Specimen 2 in which one column in the first floor (i.e. column at the north-west corner designed with smaller web thickness). Therefore, specimen 1 is a symmetric structure while specimen 2 is an anti-symmetric structure. The total weight of each structure is 2.94 t (include additional 0.5 t on each floor). Three different types of instrumentation were installed to collect the vibration response of the structure: accelerometer, LVDT and NDI optical tracker. The distribution of accelerometer and the LVDT is shown in Fig. 1.1. The two specimens are tested on NCREE shaking table. The spectrum compatible acceleration record (from Ch-Chi earthquake station TCU071) is used as the desired base excitation of the shaking table. The base excitation is arranged back to back with different input intensity level. In between the earthquake excitation white noise excitation (with peak acceleration of 50 gal) was also applied to serve as the reference state of the structure before and after each earthquake excitation, as shown in Table 1.1. In these experiments all the response measurement is with 200 Hz sampling frequency. 1.3 Methods on Damage Identification Two methods on structural damage identification were applied by using output-only measurement of structure: the multivariate autoregressive model (parametric MV-AR model) and the time-frequency analysis of response signal. Fig. 1.1 (a) Photo of the two structures on shaking table. (b) Instrumentation of accelerometer Table 1.1 Test protocol for the two steel structures CASE WN1 WN2 EQ1 WN3 EQ2 WN4 EQ3 WN5 EQ4 WN6 EQ5 PGA(gal) 50 50 95 50 269 50 400 50 572 50 674 CASE WN7 EQ6 WN8 EQ7 WN9 EQ8 WN10 EQ9 WN11 EQ10 WN12 PGA(gal) 50 858 50 994 50 1090 50 1329 50 1440 50
1 Damage Assessment of Steel Structures Using Multi-Autoregressive Model 3 1.3.1 Damage Detection Using Migration of Autoregressive Model Coefficients Consider the multiple measurement in the experiments, a multivariate autoregressive model (MV-AR model) was used. First, a vector autoregressive model with d sensors can be expressed as follows [4, 14]: fy.t/gCŒ˛1 fy.t 1/gCŒ˛2 fy.t 2/gC ˛p fy.t p/gDfe.t/g (1.1) Or fy.t/gd 1 DŒA d dpf .t/gdp 1 Cf e.t/gd 1 Where ŒA d dp D Œ˛1 Œ˛2 Œ˛i Œ˛p (1.2) is the model parameter matrix and p is the order of the AR model, Œ˛i d d is the matrix of autoregressive parameters relating the output fy(t i)g tofy(t)g, i D1:p. And f .t/gdp 1 D 8 ˆ ˆ< ˆ ˆ: fy.t 1/gd 1 fy.t 2/gd 1 : : : fy.t p/gd 1 9 > >= > >; (1.3) is the regressor for the output vector fy(t)g, fy(t i)gd 1 (i 1:p) is the output vector with delay time i Ts, T is the sampling period (s), and fe(t)gd 1 is the residual vector of all output channels, which is considered as the error of the model. If (N dpCd) consecutive output vectors of the responses fromfy(k)g to fy(kCN–1)g are taken into account, the model parameters can obviously be estimated with the least squares method by minimizing a norm of error sequences. The data matrix is first constructed from N successive sample: ŒK N .dpCd/ D 2 6 6 6 6 4 f .t/g T dp 1 f y.t/g T d 1 f .t C1/g T dp 1 f y.t C1/g T d 1 : : : : : : f .t CN 1/g T dp 1 f y.t CN 1/g T d 1 3 7 7 7 7 5 (1.4) The QR factorization of the data matrix [K]N (dpCd) D[Q]N N [R]N (dpCd) can be computed by the Householder method or Givens rotation. It gives [Q]N N which is an orthogonal matrix (QQT DI) and [R] N (dpCd) is an upper triangular matrix. Through detail derivation, the model parameters matrix [A]d dp can be calculated. Once the model parameters are estimated, the state matrix of the system can be established in the form of autoregressive parameters [2]: Œˆ dp dp D 2 6 6 6 6 6 6 4 Œ˛1 d d Œ˛2 d d Œ˛i d d ˛p d d I 0 0 0 0 I 0 0 : : : : : : : : : : : : : : : 0 0 0 I 0 3 7 7 7 7 7 7 5 (1.5) The identified model parameters can also be used for damage detection. It is assumed the matrix coefficients for obtained MV-AR models, in particular diagonal elements in matrix [˛1] and [˛2] are used to extract the damage features in sensor location j at different events of the system. By applying MVAR model to the ambient vibration data the system natural frequencies of specimen 1 and specimen 2 can be identified, as shown in Fig. 1.2. It is observed that for the symmetric structure (Specimen 1) the lowest five modes can be identified while for the torsion-coupling structure (Specimen 2) nine modes can be identified. Besides, the identified modal frequencies of the two structures did not change with respect to different test even though the structure was subjected to severe earthquake excitation.
4 C.-H. Loh and C.-K. Chan Fig. 1.2 Comparison on the identified dominant frequencies from two test specimen; (a) Specimen 1, (b) Specimen 2 Since the coefficients for recent time lags of AR model are most informative about different modes of vibration [14], therefore, the damage feature is defined as ŒDFi 2 M D " 1 ii;1 1 ii;2 2 ii;1 2 ii;2 k ii;1 k ii;2 Mii;1 Mii;2 # (1.6) The reason for selecting the previous two step of AR model coefficients is because that other coefficient in the parameter matrix contains mixed information about sensor locations so that they do not capture vibration changes at a single location, where ‘m’ is the m-th dataset collected from sensor node ‘i’ and a total of Mdata set is collected from a particular test case. Each column vector in ŒDFm 2 M represents the two coefficients identified from a specific time window data using MV-AR model. Data fromŒDFm 2 M matrix can be plotted into a Cartesian coordinate system with k ii,1 and k ii,2 as two perpendicular coordinates. The distribution of each coefficient pair represents the variation of the identified coefficients from a specific sensing node with dataset from ‘k-th’ time window of the specific test. Combine all the distribution of each coefficient pair from a specific test data indicated the uncertainty of the subsystem system near the sensing node. This approach can be applied to all the recorded sensing nodes and extended to all the test cases. Based on the calculated damage feature matrix, ŒDFi 2 M , a covariance matrix can be defined: ŒCi 2 2 DŒDFi ŒDFi T (1.7) Through eigen-value analysis on the covariance matrix ŒCi 2 2 , two eigen-vectors and the corresponding eigen-values can be calculated. As a result, the error ellipse by considering two eigen-values as major and minor axes and two eigen-vectors as the orientation of the ellipse is developed to get a clearer result for observation. One can observe the migration of the ellipse error among all the test cases to see the change of feature. If the migration of ellipse calculated from each test case becomes diverse, it indicated the structural properties near the sensing node are changed from event to event. Through such an observation one can detect the damage location. Based on the white noise test data the damage feature matrix of each sensing node for each test case can be constructed using MV-AR coefficients. From which the error ellipse at each sensing node for all test cases can be generated. Significant migration of error ellipse at any particular sensing node through all the test cases indicated the dynamic characteristics of local structure near that sensing node were changed. From the observation of the migration of error ellipse of all sensing nodes one can identify the damage location. Consider the test case of specimen 2 the migration of AR-coefficient ellipse error from each sensing node is calculated. The ellipse error index calculated from the top floor and the first floor was shown in Fig. 1.2. The three identified fundamental modes of specimen 2 is also shown in this figure. To detect the damage location of the specimen 2, the migration of elliptic error index in cooperated with the identified mode shapes of specimen 2 are used. The following observation were pointed out: 1. Location of sensing node with significant migration of elliptic error index shows good correlation with the large nodal modal response of the identified torsion mode (i.e. AX11 node and AY6 node). Besides, location of sensing node with
1 Damage Assessment of Steel Structures Using Multi-Autoregressive Model 5 significant migration of elliptic error of AX11 node is also caused by first and second transverse modes while the elliptic error of AY6 node is cause by second transverse mode and the torsion mode. Besides, small migration error index was observed from AX12 node and AY5 node. These results indicated the floor rotation center is at the location of North-West column (Large migration of the elliptic error index can be observed at the two corner of the roof floor). 2. Large migration of elliptic error index can also be observed from AX7 node and AX8 node of the first floor. This effect is due to the translational and torsion modes of columns at the first floor (also shown in Fig. 1.3). Other nodes, such as AX9, AX10, AX 12, AY1, AY2, AY3, AY4 and AY5, the migration of error elliptic index is very small. Based on these two analysis, it can be confirmed that the location of stiffness reduction is located in the first floor of north-west column. Fig. 1.3 Plot the migration of AR-coefficient elliptic error from sensing nodes on top floor and the first floor. Besides, the identified three fundamental modes of specimen 2 is also shown
6 C.-H. Loh and C.-K. Chan 1.3.2 Enhanced Time-Frequency Analysis for Damage Location Identification Based on WPT, the absolute acceleration response data can be decomposed into several components that each component corresponds to a central frequency. Thus, one can generate a time-frequency matrix W(t, f ) by the decomposed components f i j(t), and the value of each element in the matrix is calculated by the absolute value of the Hilbert transform of the value itself. Since the time-frequency representation W(t, f ) may be greatly affected due to the presence of noise and may cause poor resolution. An SVD-based technique is proposed [6] to enhance the spectrogram of the signal. W.t; f / DŒU ŒS ŒV T (1.8) To reduce the noise effect, Savitzky-Golay smooth filter is employed on the singular vectors (SVs) [U] and[V]. The SavitzkyGolay filter is a low-pass filter which has the advantage of no shift effect in the time series after filtering [1]. With pre-assigned polynomial P and degree k, the SVs, the smoothed SVs, [U0] and [V’], can be obtained. Then the enhanced time-frequency representation is represented as; W’ .t; f / DŒU’ ŒS ŒV’ T (1.9) If a structure is in a damage state, the response of the damage state will be different from the healthy state. As a result, a damage index is proposed based on WPT and Hilbert transform of the recorded response is proposed. First, the WPT is applied to each of the recorded response data, i.e. xk i (t), where i and k indicate the sensor location and the test event. First, the Hilbert amplitude of the reconstructed data set is calculated: Ak i .t/ D q xk i .t/ 2 C Qxk i .t/ 2 (1.10) where Qxk i .t/ represents the Hilbert transform of x k i (t). Second, define the total energy time history of the Hilbert amplitude of i-th sensor and k-thevent as IDEk i D Z Ek i .t/dt where E k i .t/ D 1 2 Ak i .t/ 2 (1.11) Therefore, the cross energy matrix ink-thevent is defined as: ŒM k D 2 6 6 6 6 6 6 4 qIDEk 1IDEk 1 qIDEk 1IDEk 2 qIDEk 1IDEk N qIDEk 2IDEk 1 qIDEk 2IDEk 2 qIDEk 2IDEk N : : : : : : : : : : : : qIDEk NIDEk 1 qIDEk NIDEk 2 qIDEk NIDEk N 3 7 7 7 7 7 7 5 (1.12) By comparing the cross energy matrix of different state of a structure, the damaged location will have larger difference than the others. The damage matrix is defined as: ŒD k D ŒM ref ŒM k ŒM ref (1.13) where ref represents the referenced event. The larger value in the damage matrix indicates larger difference at the sensor location. Based on the enhanced WPT-based Hilbert amplitude spectrum the damage index matrix was calculated using data from specimen 1 and 2. It is observed that a relative larger index value was calculated between WN3 and WN2 in the first floor, while in the second and third floors much less index value are observed. This larger index value in the first story can be explained as the influence of earthquake loading. For specimen 1 larger index value will concentrate in the first floor and then propagate to the second floor due to the impact of larger earthquake excitation. The off-diagonal index value is relative small as compare to the diagonal element as shown in Fig. 1.4a. On the contrary, for specimen 2 the damage index propagated to the upper floor and to the off-diagonal terms of index matrix. This phenomenon becomes significant starting
1 Damage Assessment of Steel Structures Using Multi-Autoregressive Model 7 Fig. 1.4 Damage index matrix between test cases WN2 and WN3, WN2 and WN4, WN2 and WN5, WN2 and WN6, WN2 and WN7 of specimen 2 from the test case of WN6/WN2. It demonstrated that after the earthquake excitation of Run-03 (Earthquake excitation with PGAD95 gal), the response of the first floor is different from the original response (reference case) for both test cases. The calculated damage matrix between WN6 test case (after EQ 4 earthquake excitation) and WN2 test case for specimen 2 is not just concentrated on the first floor, but also distributed to other floors including the off-diagonal term of damage matrix, as shown in Fig. 1.4b. This indicated that for specimen 2 the stronger base excitation which may induce the torsion-coupling effect that may cause the distribution of damage index more diverse. From the damage detection point of view, the migration of AR coefficients elliptic error index and the wavelet-based energy damage index were proposed. The wavelet-based energy damage index can detect the abnormal condition of structural response with respect to the reference state. Through the comparison on wavelet-based energy damage index from different state, the abnormal condition can be identified. Through the observation of migration of AR coefficient elliptic error on a series of test, the damage location can be identified. Both damage detection methods need reference state (undamaged test case) as a base case for comparison. 1.4 Conclusions In this research signal processing techniques and damage evaluation methods were proposed and applied to the ambient vibration response measurements (white noise excitation) of two steel structures after a series of seismic base excitation. Both modal-based and signal-based system identification and feature extraction techniques were studied to examine the damage severity of the two steel structures from output-only measurement. The system identification using both parametric MV-AR model and non-parametric SOBI method are used. Through MV-AR model the mode shapes and system natural frequencies can be identified. This method can provide a more clear stability diagram to estimate the dynamic characteristics of the structure. The SOBI method provided a fast computation on the estimation of modal contribution function (or source function) for structure with well-separated modes. The modal contributions for each test case were also identified using SOBI. The signal-based damage identification methods, which included the proposed wavelet-based energy index and the migration of AR coefficients elliptic error, can provide feature for detecting damage location. To quantify the damage local deformation measurement from dense optical tractor was used to quantify the damage of the test structure. From the data analyses the following conclusions are drawn: 1. In this study the MU-AR algorithm provided a straight forward method through selecting a suitable model order in advance to construct the stability diagram from which the system modal parameters can be identified. Besides, use SOBI it is assumed that the sources have different autocorrelation function and are mutually uncorrelated. For the analysis of
8 C.-H. Loh and C.-K. Chan building structural system this assumption is acceptable. The identified sources are the modal response functions which can be used to estimate modal contribution. 2. Based on the identified modal frequencies and mode shapes from the white noise test data after each earthquake input excitation, the identified modal frequencies from each test case almost no change at all even for input PGAD1300 gal. Different from the reinforced concrete structure, almost no severe stiffness degradation and stiffness deterioration were observed from the test of these two structures. 3. Combine the enhanced time-frequency analysis on response measurement (WPT-based signal analysis) and the waveletbased damage index matrix; the damage severity can be identified. A further study of damage location identification using the migration of AR-coefficient elliptic error, damage location can be identified. 4. The optical tracker provided good ability for recording the local behavior of a structure. Analysis through PCA technique, physical local feature could be extracted. PCA could be used to reduce the noise effect as well as the rigid body motion; therefore, the precise time history of member displacement could be extracted which can be used to estimate the stress distribution of the element. This approach can only be applied where the light target of optical tracker were installed. Acknowledgements The authors wish to express their thanks to National Center for Research on Earthquake Engineering, NARL, for developing the two test specimens and conduct the shaking table tests. The support from Ministry of Science & Technology (Taiwan) under grant No. MOST 103-2625-M-002-006 is acknowledged. References 1. Biydreaux-Bartels, G.F., Parks, T.W.: Time-varying filtering and signal estimation using Wigner distribution synthesis techniques. IEEE Trans. Acoust. Speech Signal Process. ASSP-34(3), 442–451 (1996) 2. Bjorck, A.: Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics, Philadelphia (1996) 3. Ceravolo, R.: Use of instantaneous estimators for the evaluation of structural damping. J. Sound Vib. 274(1–2), 385–401 (2004) 4. Chatfield, C.: The Analysis of Time Series. Chapman & Hall, London (1989) 5. Doebling, S.W., Farrar, C.R., Prime, M.B., Shevitz, D.W.: Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review. Research Report, LA-13070-MS, ESA-EA, Los Alamos National Laboratory, Los Alamos, NM (1996) 6. Hassanpour, H.: Improved SVD-based technique for enhancing time–frequency representation of signals. In: IEEE International Symposium on Circuits and Systems (ISCAS), pp. 1819–1822, New Orleans, LA (2007) 7. Kim, H., Melhelm, H.: Damage detection of structures by wavelet analysis. Eng. Struct. 26, 347–362 (2004) 8. Loh, C.H., Mao, C.H., Huang, J.R., Pan, T.C.: System identification of degrading hysteresis of reinforced concrete frames. Earthq. Eng. Struct. Dyn. 40, 623–640 (2011) 9. Mosavi, A.A., Dickey, D., Seracino, R., Rizkalla, S.: Identifying damage locations under ambient vibrations utilizing vector autoregressive models and Mahalanobis distances. Mech. Syst. Signal Process. 26(1), 254–267 (2012) 10. Nair, K.K., et al.: Time series-based damage detection and localization algorithm with application to the ASCE benchmark structure. J. Sound Vib. 291(2), 349–368 (2006) 11. Naira, K.K., Kiremidjian, A.S.: Damage diagnosis algorithms for wireless structural health monitoring. Stanford University, Technical report (2007) 12. Salawu, O.S.: Detection of structural damage through changes in frequency: a review. Eng. Struct. 19, 718–723 (1997) 13. Sohn, H., et al.: Reference-free damage classification based on cluster analysis. Comput. Aided Civ. Infrastruct. Eng. 23(5), 324–338 (2008) 14. Vu, V.H., Thomas, M., Lakis, A.A., Marcouiller, L.: Operational modal analysis of non-stationary mechanics systems by short-time autoregressive (STAR) modeling. In: Proceedings of the 3rd International Conference on Integrity, Reliability and Failure (2009) 15. Vu, V.H., Thomas, M., Lakis, A.A., Marcouiller, L.: Operational modal analysis by updating autoregressive model. Mech. Syst. Signal Process. 25(3), 1028–1044 (2011) 16. Worden, K., Manson, G., Fieller, N.R.J.: Damage detection using outlier analysis. J. Sound Vib. 229, 647–667 (2000)
Chapter 2 Damage Detection with Symplectic Geometry Spectrum Analysis in Changing Environment Dong-Sheng Li and Xiao-Hai Li Abstract Time-varying environmental and operational conditions such as temperature and external loading may often mask subtle structural changes caused by damage and have to be removed for successful structural damage identification. In the paper, a symplectic geometry spectrum analysis method is employed to decompose a time series into the sum of a small number of independent and interpretable components, in which one can determine which components are caused by external influences. The symplectic geometry spectrum analysis method is performed in four steps: embedding, symplectic QR decomposition, grouping and diagonal averaging. One excellent advantage of the method is that it can deal with nonlinear time series which is inherently rooted in structural damage due to crack opening and closing. Numerical simulation shows that the method is promising to detect structural damage in the presence of environmental and operational variations. Keywords Structural health monitoring • Environment variable • Damage identification • Symplectic geometry spectrum analysis 2.1 Introduction Nowadays, Damage identification method based on vibration characteristics in structural health monitoring has been widely researched and applied [1, 2]. The main idea is that the structure characteristics will change after structure damage, thus through the analysis of the real-time on-line monitoring data (acceleration, velocity, etc.) of a structure, one can infer if damage is present or not to the structure. While, in fact, varying environmental and operational conditions also have a great influence on structure characteristics [3] and may mask changes in the system’s vibration signal caused by damage, so that one may make a wrong judgment to the structure damage. For instance, temperature affects the Young’s modulus of many materials, thus the stiffness distribution of a structure is changed with temperature. Moreover, thermal expansion and contraction render joint connections and boundary conditions of a structure varied [4]. Therefore, how to separate environmental effect in the structural damage identification has drew more and more attention to researchers and practitioners. Damage identification algorithms can only be feasible and possible to be applied to the actual structure when the environmental factors are taken into account. Many structure damage identification algorithms have been proposed considering the effects of environmental factors, According to the necessity to measure environmental variables or not, they can be divided into two categories. One category is to first measure the environmental parameters, and then to establish the relationship between environmental parameters and damage feature. While, in reality, measuring environmental variables have many shortcomings and limitations [4]. Totally different with the first category, the other one does not need to directly measure the environmental parameters. It separates the external influences from the measured signals with complex algorithms. Compared with the former category, this one detects structure damage based on the structure response signals, and therefore is becoming a promising approach. Liang et al. [5] put forward a damage identification method based on the combination of the structure continuous displacement curvature, and the linear combination of the structure displacement curvature of adjacent three-node under static force is used as the damage feature. The new damage feature is not sensitive to the changes of environment temperature and is verified in identifying and locating damage with a simulated example of a simply supported beam. Moreover, the concept of cointegration in econometrics is introduced into the structural damage identification to eliminate the influence of ambient temperature [6] and frequency cointegration is proposed as a simple online damage feature, which is based on the theory that changes of the structural frequency caused by environmental factors is different from real structural damage for linear systems. To eliminate D.-S. Li ( ) •X.-H. Li Dalian University of Technology, School of Civil Engineering, Linggong Road 2, Dalian 116023, China e-mail: dsli@dlut.edu.cn © The Society for Experimental Mechanics, Inc. 2016 S. Pakzad, C. Juan (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29751-4_2 9
10 D.-S. Li and X.-H. Li these environmental and operational influences, data normalization methods such as the factor analysis [7], statistical means [8], co-integration, outlier analysis and principal component analysis [9] and recent state-space reconstruction [10] may be employed. In fact, such non-stationary changes in the structural state requires a corresponding time-varying structural model based on the consistent load–effect relationship. In this paper, a symplectic geometry spectrum analysis method is introduced as a time series analysis method. It can decompose the structural response signals into the sum of a small number of independent and interpretable components. Certain component may reflect the effects of changing environmental and operational changes and can thus be eliminated. This paper first introduce the theoretical basis and implementation process of the symplectic geometry spectrum analysis method, then a computer-simulated example is used to demonstrate the effectiveness of the method in structural damage identification considering temperature effect. 2.2 Theoretical Basis and Procedure of the SGSA The SGSA is based on symplectic QR decomposition. Its implementation procedure is similar to the principal component analysis method and can be summarized as following four steps: embedding, symplectic QR decomposition, grouping and diagonal averaging [11]. 2.2.1 Embedding This step can also be named as phase space reconstruction, let the original time series signal as x1; x2; ; xn, and X D 2 6 6 6 4 x1 x1C x1C.d 1/ x2 x2C x2C.d 1/ : : : : : : : : : xm xmC xmC.d 1/ 3 7 7 7 5 d is called embedding dimension, is delay time. In this step, choosing a proper embedding dimension d is the most important factor. 2.2.2 Orthogonal Symplectic QR Decomposition This step is the core of SGSA. First, a Hamilton matrix M is constructed. Let A DXTX; MD AT 0 0 A ; N DM2, then according to the definition above one knows that matrix M and N are all Hamilton matrix, construct an orthogonal symplectic matrix Q, making QTNQD H R 0 HT (2.1) According to the introduction in Sect. 2.2, the upper triangular matrix H in Eq. (2.1) can be calculated through the transformation of N by the two kinds of orthogonal symplectic matrix. Decomposing matrix H by QR decomposition to get its eigenvalues 1; 2; d. According to the properties of the Hamilton matrix, i D p i .i D1; d/ is the eigenvalues of matrix A, Qi .i D1; d/ is the eigenvector of A corresponding to the eigenvalues i. Let Si DQT i XT; Y D Yi .i D1; d/, then the restructured matrix is, Y DYi and the original phase space reconstruction matrix can be represented as X DX1 CX2 Xd.
2 Damage Detection with Symplectic Geometry Spectrum Analysis in Changing Environment 11 2.2.3 Components Grouping After orthogonal symplectic QR decomposition, one obtains X1; X2 Xd, totallyd components. Although these components are not totally independent with each other, some of them do have the same periods. Therefore, d components are grouped intop independent components as follows, X DX1 CX2 Xp (2.2) 2.2.4 Diagonal Averaging Xi .i D1; p/ in Eq. (2.2) is transformed into a time series with the length n by this step, the procedure of this step is as follows: let .Xi/m d with the elementsyij, 1 i m; 1 j d, andd Dmin .m; d/, m Dmax .m; d/, n DmC.d 1/ , then the matrix .Xi/m d can be transferred to a series y1; y2 yn according to Eq. (2.3): yk D 8 ˆ ˆ ˆ ˆ ˆ ˆ< ˆ ˆ ˆ ˆ ˆ ˆ: 1 k k X pD1 y p; k pC1 1 d d X pD1 y p; k pC1 1 n k C1 n m C1 X pDk m C1 y p; k pC1 1 k <d d k m m <k n (2.3) After the four steps, the original time series is decomposed into p independent superimposed components with different trend and frequency band. The trend in certain scale can be employed to eliminate the effects of changing environmental and operational changes 2.3 Application of the SGSA to a Simply Supported Beam In this section, temperature variation in a yearly cycle will be introduced to a beam along with damage and the beam frequency change induced by the damage is totally masked by the temperature change. SGSA method is then used to decompose the frequency change into five components. The first component is employed to eliminate the variation of temperature change and damage is identified. 2.3.1 Brief Introduction of the Model The length of the simply supported beam is 6 m (LD6 m), rectangular section with the size of 0.2 m 0.3 m. The density of the material is 2500 kg/m3. The simply supported beam is divided into 40 elements with equal length, Consistent mass matrix are used. The relationship between temperature and the elastic modulus of the material is shown in Fig. 2.1. 2.3.2 Temperature Variation and the First Natural Frequency of the Beam The temperature in Beijing from Jan 1, 2011 to Jan 31, 2012 is selected in our simulation. The sampling period T is set as 2 h and there are totally 4752 sampling points as shown in Fig. 2.2a. Per unit length on the horizontal axis is set to represent 2 h long for analysis convenience. At 6000 h after Jan 1, 2011 (the 3000th point on the horizontal axis), the stiffness of the eighth element is reduced to 60 % to simulate the structure damage. The vibration frequency of the beam is influenced
12 D.-S. Li and X.-H. Li -20 1.9 1.95 2 2.05 2.1 2.15 -10 0 10 temperature( ˚C ) elastic modulus (1011pa) 20 30 40 50 Fig. 2.1 Elastic modulus variation with temperature. (a) Temperature variation with time. (b) First natural frequency of the beam 0 -20 -10 10 20 30 40 a time ( h ) temperature (˚C) 0 1000 2000 3000 4000 5000 33 33.5 34 34.5 35 35.5 b frequency (Hz) time ( h ) 0 1000 2000 3000 4000 5000 Fig. 2.2 Temperature variation and the first natural frequency of the beam both by environmental temperature and damage. The frequency variation with time is shown in Fig. 2.2b. Compared with Fig. 2.2a, it is found that in Fig. 2.2b there is a strong correlation between the frequency and the temperature, and that the structural damage is completely submerged in the temperature’s influence. 2.3.3 Damage Identification of the Simply Supported Beam First, the temperature data is decomposed by SGSA with the embedding dimension set to five. The decomposed five components are shown in Fig. 2.3. Figure 2.3a shows the original temperature signal, whereas Fig. 2.3b–f shows the five components of the original temperature decomposed by the SGSA. As illustrated in Fig. 2.3, the first component shown in Fig. 2.3b represents temperature seasonal trend, whereas the second component shown in Fig. 2.3c is the daily temperature fluctuation which is an approximately simple harmonic signal as shown in the enlarged picture of Fig. 2.4. The daily temperature fluctuates within around 10ı. The amplitude of the components shown in Fig. 2.3d–f are very small compared with the first two components and they can be neglected as noise. Second, decomposing the first natural frequency of the beam by SGSA and the embedding dimension also set to five. The decomposed five components are shown in Fig. 2.5. Figure 2.5a shows the original frequency, whereas Fig. 2.5b–f
2 Damage Detection with Symplectic Geometry Spectrum Analysis in Changing Environment 13 time ( h ) a b c d e f tempereture (˚C) -20 -10 0 10 20 30 0 20 40 tempereture (˚C) -20 -10 0 10 20 tempereture (˚C) 0 2000 4000 6000 time ( h ) 0 2000 4000 6000 time ( h ) 0 1000 2000 3000 4000 5000 -20 -10 0 10 20 tempereture (˚C) time ( h ) 0 1000 2000 3000 4000 5000 -20 -10 0 10 20 tempereture (˚C) time ( h ) 0 1000 2000 3000 4000 5000 -20 -10 0 10 20 tempereture (˚C) time ( h ) 0 1000 2000 3000 4000 5000 Fig. 2.3 Temperature decomposed by SGSA tempereture (˚C) -6 -4 -2 0 2 4 6 time ( h ) 1960 1980 2000 2020 2040 2060 2080 Fig. 2.4 Partially enlarged picture of the Fig. 2.3c time ( h ) 0 1000 2000 3000 4000 5000 c frequency (Hz) -1 -0.5 0 0.5 1 time ( h ) 0 1000 2000 3000 4000 5000 f frequency (Hz) -1 -0.5 0 0.5 1 time ( h ) 0 1000 2000 3000 4000 5000 e frequency (Hz) -1 -0.5 0 0.5 1 time ( h ) 0 1000 2000 3000 4000 5000 d frequency (Hz) -1 -0.5 0 0.5 1 time ( h ) a frequency (Hz) 33 33.5 34 34.5 35 35.5 0 1000 2000 3000 4000 5000 time ( h ) b frequency (Hz) 33 33.5 34 34.5 35 35.5 0 1000 2000 3000 4000 5000 Fig. 2.5 First natural frequency of the beam decomposed by SGSA
14 D.-S. Li and X.-H. Li time ( h ) 0 1000 2000 3000 4000 5000 time ( h ) 0 1000 2000 3000 4000 5000 time ( h ) a b c frequency (Hz) 33 33.5 34 34.5 35 35.5 frequency (Hz) frequency (Hz) -1 -0.5 0 0.5 1 33 33.5 34 34.5 35 35.5 0 1000 2000 3000 4000 5000 Fig. 2.6 Filter of frequency changes induced by temperature and damage identification shows the five components of the first nature frequency decomposed by the SGSA. Similar to the analysis of the temperature decomposition, the first two components shown in Fig. 2.5b and c represent the main trend and fluctuation amplitude of the original frequency signal. Compared with the first two components of the temperature in Fig. 2.3, it can be concluded that the first frequency component shown in Fig. 2.5b reflects the frequency variation influenced by the seasonal trend of temperature and structural damage whereas the second component in Fig. 2.5c represents the frequency variation induced by the daily temperature fluctuation. The other frequency components shown in Fig. 2.5d–f can be neglected as noise due to their tiny amplitude. To finally identify structural damage, the first component shown in Fig. 2.5b that includes both temperature and damage influences are further analyzed. If the frequency variation induced by the temperature trend can be filtered out from this component, the remaining part of the frequency changes can be inferred as induced from structural damage. To filter out the frequency change induced by seasonal temperature trend, a cross validation approach is adopted to fit the frequency variation induced only by temperature. The temperature data in Fig. 2.5b are divided into ten segments. The length of first nine segments is set to 500 and the last segment 250. Nine segments of data are then sequentially taken as fitting data and the remaining segment for validation data in turn. A quartic curve is then obtained as shown in red in Fig. 2.6b. The red curve in Fig. 2.6b represents the frequency change induced by temperature and the blue curve shows the frequency change induced both by temperature and damage, which is the same curve as that in Fig. 2.5b. Figure 2.6b shows that the frequency change by temperature trend can be eliminated. Subtracting the blue cure from the red curve in Fig. 2.6b, the blue curve in Fig. 2.5c is obtained, which is the frequency of the beam induced only by the damage. It is easily observed that there is a relatively large change at about the 3000th point (6000 h after Jan 1, 2011). Therefore, it can be deduced that at the 3000th moment, damage occurs in the beam. 2.4 Conclusions A symplectic geometric spectral analysis method is applied to structural damage identification considering the influences of environmental influences. The frequency change induced by seasonal temperature is filtered out through SGSA and damage is identified. It shows that the SGSA method can detect structural damage in the presence of environmental and operational variations successfully. The advantage of this method is that it does not need to directly measure the environment parameters and if feasible to practical damage identification. Acknowledgement The authors appreciate the support by the National Natural Science Foundation of China (Grant No. 51121005, 51578107) and 973 Project (2015CB057704).
RkJQdWJsaXNoZXIy MTMzNzEzMQ==