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Title: Damage identification from wavelet-based acceleration response sensitivity
Authors: Li, Xueyan
Subjects: Hong Kong Polytechnic University -- Dissertations
Wavelets (Mathematics)
Wave packets
Accelerometers
Engineering systems -- Testing
Non-destructive testing
Issue Date: 2008
Publisher: The Hong Kong Polytechnic University
Abstract: Early detection of damage in engineering systems during their service life has been receiving increasing attention from engineers recently because of its importance. Though vibration-based damage detection has been developed for several decades and there is a large number of literature, there are still many problems refraining it from application. The research in this thesis is on the developments of structural damage detection methods based on acceleration response sensitivity via wavelet transform. The wavelet packet component energy (WPCE) and wavelet coefficients (WC) of acceleration responses, unit impulse response function (UIR) and covariance of acceleration responses from ambient vibration are all used in the damage detection via model updating techniques. Tikhonov regularization and L-curve method are also improved for the proposed damage detection methods to solve the ill-conditioning problem. The propagation of uncertainties in the damage detection procedure is also studied with a sensitivity analysis with respect to random variables and a reliability result is finally obtained for the structure. To avoid modal extraction via the Fourier Transform which will cause structural information lost, introducing errors in the identified results, in this study, wavelet packet component energy and wavelet coefficients of acceleration responses are adopted to detect damage via sensitivity analysis and model updating techniques. The sensitivity of WPCE with respect to structural parameters has been derived analytical and the distribution and properties of the WPCE are studied. They are adopted for damage detection in a simply supported concrete beam for numerical demonstration and in a steel beam tested in the laboratory for experimental verification. The WPCE assigns the energy of the acceleration responses to different frequency bandwidth with good tolerance to noise but the associated damage detection algorithm requires more measurement locations especially in a structure with a large number of DOFs. The sensitivity of WC of acceleration response from as few as one sensor with respect to structural parameters under general excitation and support excitation are obtained analytically and computationally, and it is used for damage detection in a one-story plane frame structure and a three-dimensional frame structure for simulation study, and in a simply supported reinforced concrete beam and a three-dimensional frame structure tested in the laboratory. It is noted that time series data with a low sampling frequency also carries damage information for damage identification. Because most damage detection methods based on the acceleration responses rely on the type and the location of the force excitation, wavelet coefficient of unit impulse response function obtained via discrete wavelet transform (DWT) of the measured accelerations of a structure and the measured excitation force or measured accelerations at its support are used to assess the structural health condition. DWT is employed in the extraction procedure for UIR to avoid the end effects with Fourier transform. The sensitivity of wavelet coefficient of UIR is given numerically. In order to study the noise effect in the UIR-based method, a statistical analysis on the UIRs with measurement noise is conducted and the results compared favorably with those from Monte Carlo Technique (MCT). The proposed methods are demonstrated successfully by a 31-bar plane truss and a nine-bay three-dimensional frame structural system in a simulation study and an experimental verification.
In order to have the identification method completely independent of the external excitation, the covariance of acceleration responses of structures under ambient excitation is numerically computed and its wavelet packet energy is used to identify structural damage such that the damage detection can be performed with the response-only measurement. Covariance of acceleration responses is computed based on the unit impulse response function. Wavelet packet transform is applied to the covariance functions to find the wavelet packet energy. Damage localization is carried out firstly using the elemental modal strain energy approach. A five-bay three-dimensional cantilever truss structure is used to demonstrate the efficiency of the method, and a nine-bay three-dimensional frame structure is tested in the laboratory for verification of the proposed method. The ill-conditioning phenomenon in the inverse problem is an important factor limiting the application of damage detection methods. Tikhonov regularization and L-curve method are improved in this thesis for a better solution of the ill-conditioned problem in the proposed damage detection methods. The range of percentage damage is limited in the determination of the regularization parameter λ in the regularization method. Because there will be great similarity between the sets of results from two successive iterations, the convergence of results is further ensured by checking on such similarity using a Multiple Parameter Correlation Criteria. Numerical studies with one-story plane frame and thirty-one bar plane truss structure are performed with the proposed improved regularization techniques and satisfactory results are obtained. Uncertainties in the analytical model and the measured vibration data always exist and they affect the identified results. A statistical method for structural damage detection based on measured acceleration response is proposed in this thesis. Uncertainties in the system parameters, such as the structural parameters of the finite element model, the excitation force acting on the structure and the measured acceleration response from the perturbed state of the structure are analyzed and the analytical formula are given. The effect of each of these uncertainties on the assessment results is monitored in an updating damage detection algorithm based on the response sensitivity approach. The probability density function of the stiffness parameters in both the intact and perturbed states are compared in a subsequent reliability assessment. A three-dimensional five-bay steel frame structure is studied for illustration. In summary, the contributions of the thesis to the engineering application include: (a) As few as one accelerometer is required in the vibration measurement and it makes the damage detection be more economical, convenient and practical especially for large scale structure, (b) The study of damage detection based on response-only measurement is very useful for the case where the actual excitations may be very difficult and expensive to be measured and be generated, (c) The identified results obtained from uncertainty analysis have the higher reliability when the measurements are subject to noise and the models used have model errors.
Degree: Ph.D., Dept. of Civil and Structural Engineering, The Hong Kong Polytechnic University, 2008
Description: xvii, 333 leaves : ill. ; 30 cm.
PolyU Library Call No.: [THS] LG51 .H577P CSE 2008 Li
Rights: All rights reserved.
Type: Thesis
URI: http://hdl.handle.net/10397/3473
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