Monte Carlo Dynamically Weighted Importance Sampling For Finite Element Model Updating

Abstract

The Finite Element Method (FEM) is generally unable to accurately predict natural frequencies and mode shapes of structures (eigenvalues and eigenvectors). Engineers develop numerical methods and a variety of techniques to compensate for this misalignment of modal properties, between experimentally measured data and the computed result from the FEM of structures. In this paper we compare two indirect methods of updating namely, the Adaptive Metropolis Hastings and a newly applied algorithm called Monte Carlo Dynamically Weighted Importance Sampling (MCDWIS). The approximation of a posterior predictive distribution is based on Bayesian inference of continuous multivariate Gaussian probability density functions, defining the variability of physical properties affected by forced vibration. The motivation behind applying MCDWIS is in the complexity of computing normalizing constants in higher dimensional or multimodal systems. The MCDWIS accounts for this intractability by analytically computing importance sampling estimates at each time step of the algorithm. In addition, a dynamic weighting step with an Adaptive Pruned Enriched Population Control Scheme (APEPCS) allows for further control over weighted samples and population size. The performance of the MCDWIS simulation is graphically illustrated for all algorithm dependent parameters and show unbiased, stable sample estimates.