System Identification of Spatial Distribution of Structural Parameters Using Modified Transitional Markov Chain Monte Carlo Method

Abstract

Uncertain changes in spatial distribution of structural parameters, caused by deterioration or damage, may weaken the structure and result in unexpected losses of properties or casualties. In recent decades, to identify spatial distribution of parameters, various system identification (SI) methods have been developed based on optimization algorithms employing various regularization techniques. However, such optimization-based SI methods may suffer from ill-posedness of the optimization problem under uncertain measurement noises. Moreover, depending on boundary and traction conditions, the accuracy and robustness of SI methods may differ. In this paper, to overcome these technical challenges in identification of spatial distribution, a new SI method is developed by modifying the transitional Markov chain Monte Carlo (m-TMCMC). In addition to the modifications introduced to the sampling algorithm, the proposed method enhances robustness of the SI results by exploiting the results by the maximum likelihood estimation and finite-element updating. To identify general shapes of spatial distribution with a reasonable number of parameters, a spatial deterioration model is proposed based on the modes obtained based on a random field model called Karhunen–Loeve expansion. The proposed SI method is tested and demonstrated through numerical examples of steel plate and B-pillar structure, in which the effects of random measurement errors are also considered. The numerical examples demonstrate accuracy and robustness of the proposed method.