HDMR-Based Bayesian Structural System Identification

Abstract

This paper presents a method for faster identification of structural systems within a Bayesian framework with the use of High-Dimensional Model Representations (HDMR). For system identification problems solved within Bayesian framework, the intractable multidimensional integrals involved always pose a problem. To address this issue, the multidimensional integrands are expanded approximately by HDMR, an exact hierarchical representation for the multivariable functions, thereby significantly reducing the computational expenditure and ensuring the applicability of the procedure to systems of infinite dimensionality. The proposed method combines HDMR with Bayesian inference and follows an iterative procedure for convergence. In the present study, a stochastic plane strain field and a single degree of freedom system are analyzed. The results obtained are compared with the estimates from Extended Kalman Filter. In future, the proposed method will be tested on structural identification problems involving nonlinearity, non-Gaussianity, and high dimensionality.