Author: Hou, Rongrong
Title: Vibration-based structural damage identification using sparse recovery and sparse bayesian learning
Advisors: Xia, Yong (CEE)
Degree: Ph.D.
Year: 2019
Subject: Hong Kong Polytechnic University -- Dissertations
Structural health monitoring
Structural failures
Department: Department of Civil and Environmental Engineering
Pages: xxii, 193 pages : color illustrations
Language: English
Abstract: Numerous vibration-based structural damage detection methods have been developed over the past decades. The basic idea of these methods is that structural damage may induce changes in vibration characteristics, such as frequencies, mode shapes, and their variants. Finite element model updating is a widely used technique to identify damage location and quantify damage extent. Most of these studies have achieved limited success in small civil structures or scaled models in laboratory only. There are two major difficulties and challenges, among others, that hinder successful applications of vibration-based damage detection methods to practical civil structures: First, civil structures generally contain a large number of elements or components whereas the number of vibration measurement data is limited in general. To avoid this underdetermined problem in mathematics, super-elements are usually employed in numerical modelling and model updating. However, the use of such elements hinders the direct quantification of local damage with the updating parameter of the entire super-element. Second, the vibration-based damage detection is essentially an inverse problem and typically ill-posed. A small perturbation in the input data (for example, measurement noise) would lead to a significant change in the solution. Most previous model updating techniques employ the Tikhonov regularization (or l₂ regularization), which causes the identified damage distributed to many structural elements. However, this result does not match the practical situation in which damage usually occurs at several locations only especially at the early stage of damage development. Taking these difficulties into consideration, this PhD study exploits the sparsity of structural damage and aims to develop accurate and reliable structural damage detection methods based on sparse recovery and sparse Bayesian learning. The damage index is defined as the elemental stiffness reduction and thus can be regarded as a sparse vector with several non-zero items at the damaged elements but many zeros at others. Consequently the sparse recovery theory can be applied to obtain the sparse damage index. An l1-regularized model updating technique is first developed to identify sparse damage using the first several natural frequencies and mode shapes. In regularization methods, the regularization parameter controls the trade-off between data fidelity and solution size and thus exerts a crucial effect on the solution. Two strategies of selecting the regularization parameter for the l₁-regularized damage detection problem are proposed. Further, an optimal sensor placement technique is proposed using the combinatory genetic algorithm such that the columns of the resulting sensitivity matrix are of the maximum independence. Next, an iteratively reweighted l₁ regularization algorithm is proposed for structural damage detection. The regularization parameter in one step is revised according to the identification results in the previous iteration, making the technique resemble the l0 regularization technique and outperform the l₁ regularization for sparse recovery. The last contribution of the study is to develop a sparse Bayesian learning method, in which the sparsity of structural damage is exploited as the prior information from the Bayesian perspective. Since structural modal parameters have a nonlinear relation with structural damage, the evidence function cannot be obtained explicitly. An expectation-maximization based technique is developed to obtain the structural damage index and hyper-parameters iteratively. The proposed structural damage detection methods are applied to several numerical and laboratory structures. The results demonstrate that the proposed methods are able to locate and quantify the sparse damage accurately, even when the number of measurement data is much less than the number of structural elements. The other advantage of the proposed damage detection methods is that the structure of interest can be modelled using a relatively large number of elements. This enables the local damage be appropriately modelled and directly quantified, which is unable to achieve through the conventional l₂ regularization methods.
Rights: All rights reserved
Access: open access

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