Online probabilistic model class selection and joint estimation of structures for post-disaster monitoring

Online selection of the appropriate model and identifying its parameters based on measured vibrational data are among the challenging issues in dynamic system identification. After a severe earthquake, quick monitoring and assessment of structural health status play a crucial role in effective critical risk management for the building owners and decision-makers. The Bayesian multiple modeling approach is a suitable tool for optimal model class selection, which is used in this article mainly for improving data fitting precision, decreasing dimensions of structural unknown vector through removing unnecessary parameters, detecting the occurrence and type of predominant phenomenon related to degradation and pinching, and finally increasing stability and convergence rate of the used identification algorithm. In this study, a reliable and effective time-domain method is proposed for online probabilistic model class selection and joint estimation of structures using the central difference Kalman filter and Bayesian multiple modeling approach. Also, in contrast to existing studies, the performance and efficiency of the proposed algorithm are investigated in nonlinear system identification with a large number of unknowns. The proposed algorithm is implemented on three moment-frame buildings with 8, 54, and 60 unknowns. In addition, a numerical example is provided to analyze the case in which the exact model is not among the plausible models. To verify the performance of the hybrid identification method, robust simulations with synthetic measurement noises and modeling errors were generated using the Monte Carlo random simulation method. The result shows the method can be used to simultaneously select the optimal model class and identify its unknown states and parameters in an online manner.

Hierarchical Stochastic Model in Bayesian Inference for Engineering Applications: Theoretical Implications and Efficient Approximation

Hierarchical Bayesian models (HBMs) have been increasingly used for various engineering applications. We classify two types of HBM found in the literature as hierarchical prior model (HPM) and hierarchical stochastic model (HSM). Then, we focus on studying the theoretical implications of the HSM. Using examples of polynomial functions, we show that the HSM is capable of separating different types of uncertainties in a system and quantifying uncertainty of reduced order models under the Bayesian model class selection framework. To tackle the huge computational cost for analyzing HSM, we propose an efficient approximation scheme based on importance sampling (IS) and empirical interpolation method (EIM). We illustrate our method using two engineering examples—a molecular dynamics simulation for Krypton and a pharmacokinetic/pharmacodynamics (PKPD) model for cancer drug.