Dynamic System Identification using HDMR-Bayesian Technique

This paper presents a novel HDMR-Bayesian technique for dynamic system identification in a Bayesian framework. This technique is based on Bayesian Inference. Direct application of Bayesian inference in estimation and identification involves evaluation of multi-dimensional integrals in multidimensional systems. This is computationally complex and tedious. The proposed technique addresses this challenge by using the HDMR expansions of the multivariable integrands. The expanded representations can be easily integrated. High Dimensional Model Representations(HDMR) are the finite, hierarchical expansions of nonlinear functions of any number of variables. These representations neglect higher order correlations between variables. In this paper, we consider the identification of vibration properties of linear multi degree of freedom systems subjected to stochastic excitations, by the proposed method. Various examples are solved using the proposed method and compared against the results from Kalman Filter methods and Monte Carlo methods. This technique is faster and more accurate for linear multi-dimensional systems. We can use this technique to solve nonlinear and high dimensional systems, in faster pace.