Nonlinear random vibration analysis: A Bayesian nonparametric approach

Random vibration analysis aims to estimate the response statistics of dynamical systems subject stochastic excitations. Stochastic differential equations (SDEs) that govern general nonlinear are often complicated, and their analytical solutions scarce. Thus, a range approximate methods simulation techniques have been developed. This paper develops hybrid approach approximates governing SDE using small number simulations information available priori. The main idea is identify set surrogate linear such probability distributions collectively distribution original system. To systems, proposed method integrates simulated responses system with priori about parameters systems. There will be epistemic uncertainty in because limited data. proposes Bayesian nonparametric approach, called Dirichlet Process Mixture Model, capture these uncertainties. process models over an infinite-dimensional parameter space, representing infinite potential Specifically, allows grow indefinitely as observed dynamic unveil new patterns. quantified estimates unknown model propagates into distribution. then shows that, under some mild conditions, estimated approaches, close desired, system’s As measure accuracy, provides convergence rate Because posterior not analytically tractable, Gibbs sampling algorithm presented draw samples from Variational inference also introduced derive closed-form expression for illustrates through random elastic hysteretic