Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and control strategies based on simulation or prediction results. However, in the surrogate model, preventing overfitting and incorporating reasonable prior knowledge of embedded physics and models is a challenge. Suspended Nonstructural Systems (SNS) pose a significant challenge in the inverse problem. Research on their seismic performance and mechanical models, particularly in the inverse problem and uncertainty quantification, is still lacking. To address this, the author conducts full-scale shaking table dynamic experiments and monotonic & cyclic tests, and simulations of different types of SNS to investigate mechanical behaviors. To quantify the uncertainty of the inverse problem, the author proposes a new framework that adopts machine learning-based data and model driven stochastic Gaussian process model calibration to quantify the uncertainty via a new black box variational inference that accounts for geometric complexity measure, Minimum Description length (MDL), through Bayesian inference. It is validated in the SNS and yields optimal generalizability and computational scalability
