Refined sparse Bayesian learning configuration for stochastic response analysis

Abstract

The computational intensiveness inherently associated with uncertainty quantification of engineering systems has been one of the prime concerns over the years. In order to mitigate this issue, two novel approaches have been developed for efficient stochastic computations. Both the approaches have been developed by amalgamating the advantages of two available techniques namely, high dimensional model representation (HDMR) and Kriging. These two methods are coupled in such a way that HDMR addresses the global variation in the functional space using a set of component functions and the fine aberrations are interpolated by utilizing Kriging, performing as a two level approximation. A Bayesian learning framework has been integrated with the locally refined model so as to construct a sparse configuration. In order to earn additional computational efficiency, an accelerated training algorithm for the sparse Bayesian learning framework has been fused within the refined model. Implementation of the proposed approaches have been demonstrated with two analytical problems and two large scale practical offshore structural problems. The efficiency and accuracy of the proposed approaches in stochastic response analysis have been assessed by comparison with Monte Carlo simulation. Excellent results in terms of accuracy and computational effort obtained makes the proposed methodologies potential for further complex applications.