Application of a Bayesian hierarchical model to system identification of structural parameters

Abstract

System identification (SI) is a key step in the process of evaluating the status or condition of physical structures and of devising a scheme to sustain their structural integrity. SI is typically carried out by updating the current structural parameters used in a computational model based on the measured responses of the structure. In the deterministic approach, SI has been conducted by minimizing the error between calculated responses (using the computational model) and measured responses. However, this brought about unexpected numerical issues such as the ill-posedness of the inverse problem, which likely results in non-uniqueness of the solutions or non-stability of the optimization operation. To address this issue, Bayesian updating enhanced with an advanced modeling technique such as a Bayesian network (BN) was introduced. However, it remained challenging to construct the quantitative relations between structural parameters and responses (which are placed in conditional probability tables: CPTs) in a BN setting. Therefore, this paper presented a novel approach for conducting the SI of structural parameters using a Bayesian hierarchical model (BHM) technique. Specifically, the BHM was integrated into the Bayesian updating framework instead of utilizing a BN. The primary advantage of the proposed approach is that it enables use of the existing relations between structural parameters and responses. This can save the computational effort needed to construct CPTs to relate the parameter and response nodes. The proposed approach was applied to two experimental structures and a realistic soil-slope structure. The results showed that the proposed SI approach provided good agreement with actual measurements and also gave relatively robust estimation results compared to the traditional approach of maximum likelihood estimation. Hence, the proposed approach is expected to be utilized to address SI problems for complex structural systems and its computational model when integrated with a statistical regression approach or with various machine learning algorithms.