Stochastic modeling of nonlinear random vibrations using heavy-tailed mixture distribution

Abstract

In this study, we propose a simple probability density function (PDF) model of Gaussian-Laplacian mixture type, which is capable of parameterizing a heavy-tailed data easily. We construct our model of a convex combination of Gaussian and Laplacian PDFs and derive a minimal parameterization of it. Next, we conduct least-squares fitting of our model to a heavy-tailed data generated by a random Duffing oscillator and obtain over 94% of residual sum of squares (RSS) fitness. The resulting model is applied to predicting transient moment responses and yields over 97% of RSS fitness to Monte{Carlo simulation results of the original system.