Probabilistic machine learning and Bayesian inference for vibration-based structural damage identification

Abstract

Vibration-based structural damage detection involves the acquisition of vibration data, extraction of damage-sensitive features, and identification of novelty. These procedures intrinsically contain uncertainties arising from the measurement noise, varying environmental and operational conditions, and modeling errors. Probabilistic machine learning (ML) techniques have the ability of autonomous feature extraction and model optimization from uncertain data, thus stand out as the natural approach for vibration-based damage detection. This thesis attempts to develop advanced techniques for structural damage identification based on probabilistic ML techniques and Bayesian inference. The vibration-based damage detection methods have two branches, data-based and inverse model-based. The Bayesian theorem can be introduced to both kinds of methods by incorporating the engineering knowledge or researcher's belief about the unseen model parameters as the prior information for the damage detection. The Bayesian theorem is first introduced to the data-driven data normalization techniques for automatic model optimization. A linear sparse Bayesian factor analysis (FA) method is developed to discriminate the environmental effects on structural dynamic features from damage. The automatic relevance determination (ARD) prior is defined on the factor loading matrix to determine the number of underlying environmental factors automatically. The method is applied to two laboratory-tested examples (a reinforced concrete slab and a steel frame) under changing environmental conditions for damage detection. Later, an improved method on the basis of the probabilistic kernelized model is developed to remove nonlinear environmental effects. The unknown kernel parameters and the latent variables are estimated automatically in the Bayesian probabilistic framework. The method is finally applied to the benchmark Z24 bridge for damage detection. Next, the sparse Bayesian learning (SBL) technique is introduced to the finite element (FE) model updating-based damage identification. An SBL technique is developed using the normalized damage sensitive modal parameters. The ARD prior is defined on the damage index to induce sparsity to the results. Due to the nonlinear relationship between the damage index and modal parameter, the evidence involves a complex integral that cannot be calculated directly. The Laplace approximation method and the combination of variational Bayesian inference (VBI) and delayed rejection adaptative Metropolis (DRAM) algorithm are developed to circumvent the intractable evidence. Both methods are applied to the laboratory-tested steel frame for damage detection. The comparison indicates that the analytical Laplace approximation technique is markedly efficient for low-dimensional problems as no sampling is required. The VBI-DRAM algorithm is substantially efficient in dealing with high-dimensional problems. The last contribution of the thesis is to develop a cutting-edge domain adaptation (DA) technique for structural damage detection that can transfer knowledge from the numerical FE model to the experimental structure and from one structure to the other with different sizes, in which re-collecting the labeled damage data from the new structure is not required. A re-weighting mechanism is introduced to deal with inconsistent label spaces between the labeled source domain and unlabeled target domain, given that structural damage scenarios may be different. The numerical and experimental studies demonstrate the effectiveness of the proposed method. The comparison analysis indicates the superiority of the method, as compared with the models without DA or without the re-weighting mechanism.