Author: Zhang, Beiyang
Title: Multi-fidelity modelling based on adaptive sparse polynomial chaos expansion for bridge damage identification
Advisors: Ni, Yi-qing (CEE)
Degree: Ph.D.
Year: 2022
Subject: Structural health monitoring
Bridges -- Maintenance and repair
Hong Kong Polytechnic University -- Dissertations
Department: Department of Civil and Environmental Engineering
Pages: xxvii, 266 pages : color illustrations
Language: English
Abstract: For bridge damage identification, two types of methods are popularly used, namely, physics-based methods and data-driven approaches. Physics-based methods identify the structural damage with the aid of a physical model. The damage location and severity can be identified, but such methods are prone to the modelling error. Data-driven approaches directly interpret real observations from a structure of concern by using some statistical methods. The modelling error can be avoided, but a large amount of measurement data is required, and only the existence of damage can be detected upon most occasions. Therefore, this thesis intends to investigate a Multi-Fidelity (MF) modelling technique that can capitalise on the merits from both physics-based and data-driven methods. Accurate surrogate models will be trained to help in damage identification, in which the modelling error caused by temperature can be correctly eliminated. Moreover, the required measurements are far less than those used in data-driven approaches.
In this thesis, Polynomial Chaos Expansion (PCE) method is employed to build the PCE surrogate model owing to its simple model structure and training process. However, challenges also exist in PCE, such as the "curse of dimensionality" issue and adaptive modelling problem. Therefore, we first introduce two novel adaptive modelling techniques to facilitate the PCE method in application to engineering problems. In order to adaptively collect samples for PCE training, a hybrid sequential sampling strategy is developed, which leverages both the input information of PCE model and the output information from observations to instruct the sampling process. Meanwhile, the sparse regression procedure is used along with this strategy to train a sparse PCE model. As a result, the samples could be collected with high quality and in relatively small quantity. By evaluating on several benchmark functions, it is shown that the proposed strategy outperforms most existing methods. Next, a novel adaptive basis selection strategy is developed to adaptively determine the model structure, which consists of three procedures, basis expansion, pruning and refinement. By using this strategy, the proper truncation degree for PCE modelling can be selected automatically, and the training cost will also be reduced benefitting from removing the insignificant polynomial bases. To reconcile the sequential sampling and the adaptive basis selection in a consistent framework, a stability evaluation process which works in parallel with the sequential sampling process is introduced. As a result, this consistent PCE modelling framework can collect appropriate samples and determine the best model structure all in an automatic way. Through evaluating on several benchmark functions, this PCE modelling framework is demonstrated with satisfactory performance and high efficiency. By using this framework, the PCE models as surrogate to the physical model of the bridge structure are established, in which the pattern of frequency data concerning the structural parameters is of interest in this study.
In real applications, however, it is more practical to predict the responses of real structure rather than the physical model to help in damage identification, since the physical model will inevitably contain modelling errors. As the most influential environmental factor, temperature affects bridge structures in a complicated way, and such effect is generally difficult to be simulated correctly. Thus, to eliminate the temperature-induced modelling error in the surrogate model, a Transfer Learning (TL) based Multi-Fidelity PCE (MFPCE) modelling technique is presented. The PCE model stemming from a finite element model is regarded as Low-Fidelity (LF) model, and the frequencies collected from the real bridge under healthy condition belong to High-Fidelity (HF) data. By updating the temperature-related polynomial terms in the LF model with HF data, MFPCE model can be formulated, where the temperature effect is considered more accurately.
Based on the formulated MFPCE model, the sparse damage identification is performed and discussed in the last part of the research. Since the PCE model generally has a strong nonlinear property, traditional sparse representation approaches that work for linear systems are unsuitable for this case. Therefore, an approximate l 0 sparse damage identification approach is developed by combining a heuristic algorithm, i.e., Cuckoo Search Algorithm (CSA), with the discrepancy principle. We first give assumptions to the number of damages as prior information for the optimisation equation. Then, the optimal solution involving damage locations and severities under each assumption is obtained by using CSA. Through comparison among the optimisation residuals under different assumptions, the discrepancy principle is used to find the correct number of damages, and the damage locations and severities can thus be obtained. Finally, a numerical bridge model and an experimental beam model are explored for verification. Results demonstrate the effectiveness of the proposed MF modelling technique and the damage identification approach.
Rights: All rights reserved
Access: open access

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