Gaussian process assisted stochastic dynamic analysis with applications to near-periodic structures

Abstract

This paper characterizes the stochastic dynamic response of periodic structures by accounting for manufacturing variabilities. Manufacturing variabilities are simulated through a probabilistic description of the structural material and geometric properties. The underlying uncertainty propagation problem has been efficiently carried out by functional decomposition in the stochastic space with the help of Gaussian Process (GP) meta-modelling. The decomposition is performed by projected the response onto the eigenspace and involves a nominal number of actual physics-based function evaluations (the eigenvalue analysis). This allows the stochastic dynamic response evaluation to be solved with low computational cost. Two numerical examples, namely an analytical model of a damped mechanical chain and a finite-element model of multiple beam-mass systems, are undertaken. Two key findings from the results are that the proposed GP based approximation scheme is capable of (i) capturing the stochastic dynamic response in systems with well-separated modes in the presence of high levels of uncertainties (up to 20%), and (ii) adequately capturing the stochastic dynamic response in systems with multiple sets of identical modes in the presence of 5–10% uncertainty. The results are validated by Monte Carlo simulations.