Stochastic Collocation Approach to Bayesian Inference Applied to Rotating System Parameter Identification

Abstract

The analyzed problem is the identification of fault parameters taking into account the stochastic characteristic of the system. The objective is to estimate the unbalance parameters, as the unbalance moment, phase angle and axial position of the unbalance force applied to the rotor. Therefore, experimental tests with the rotor to obtain the unbalance response is performed. This work aims the comparison between Bayesian inference with Markov Chain Monte Carlo method (MCMC), using Delayed Rejection Adaptive Metropolis algorithm (DRAM), and Stochastic Collocation through Generalized polynomial chaos expansion. This method has computational cost smaller than the MCMC methods, and it could be used as an alternative method for stochastic simulation. The Bayesian inference with MCMC and DRAM is based on previous works. However, the application of the MCMC have a high computational cost. Therefore, the Stochastic collocation is introduced into the likelihood function of the Bayes theorem for a faster convergence rate. The low computational cost of the collocation is evaluated and the results of both methods are compared to determine the convergence and precision of the collocation method.