| Parallel to significant advances in sensor hardware, there have been recent developments of sophisticated methods for quantitative assessment of measured data that explicitly deal with all of the involved uncertainties, including inevitable measurement errors. The existence of these uncertainties often causes numerical instabilities in inverse problems that make them ill-conditioned.;The Bayesian methodology is known to provide an efficient way to alleviate this ill-conditioning by incorporating the prior term for regularization of the inverse problem, and to provide probabilistic results which are meaningful for decision making.;In this work, the Bayesian methodology is applied to inverse problems in earthquake engineering and especially to structural health monitoring. The proposed methodology of Bayesian earning using automatic relevance determination (ARD) prior, including its kernel version called the Relevance Vector Machine, is presented and applied to earthquake early warning, earthquake ground motion attenuation estimation, and structural health monitoring, using either a Bayesian classification or regression approach.;The classification and regression are both performed in three phases: (1) Phase I (feature extraction phase): Determine which features from the data to use in a training dataset; (2) Phase II (training phase): Identify the unknown parameters defining a model by using a training dataset; and (3) Phase III (prediction phase): Predict the results based on the features from new data.;This work focuses on the advantages of making probabilistic predictions obtained by Bayesian methods to deal with all uncertainties and the good characteristics of the proposed method in terms of computationally efficient training, and, especially, prediction that make it suitable for real-time operation. It is shown that sparseness (using only smaller number of basis function terms) is produced in the regression equations and classification separating boundary by using the ARD prior along with Bayesian model class selection to select the most probable (plausible) model class based on the data. This model class selection procedure automatically produces optimal regularization of the problem at hand, making it well-conditioned.;Several applications of the proposed Bayesian learning methodology are presented. First, automatic near-source and far-source classification of incoming ground motion signals is treated and the Bayesian learning method is used to determine which ground motion features are optimal for this classification. Second, a probabilistic earthquake attenuation model for peak ground acceleration is identified using selected optimal features, especially taking a non-linearly involved parameter into consideration. It is shown that the Bayesian learning method an be utilized to estimate not only linear coefficients but also a non-linearly involved parameter to provide an estimate for an unknown parameter in the kernel basis functions for Relevance Vector Machine. Third, the proposed method is extended to a general case of regression problems with vector outputs and applied to structural health monitoring applications. It is concluded that the proposed vector output RVM shows promise for estimating damage locations and their severities from change of modal properties such as natural frequencies and mode shapes. |
