Crossings of second-order response processes subjected to LMA loadings

Abstract

The focus of this paper is on the estimation of the crossing intensities of responses for second-order dynamical systems, subjected to stationary, non-Gaussian external loadings. A new model for random loadingsthe Laplace driven moving average (LMA)is used. The model is non-Gaussian, strictly stationary, can model any spectrum, and has additional flexibility to model the skewness and kurtosis of the marginal distribution. The system response can be expressed as a second-order combination of the LMA processes. A numerical technique for estimating the level crossing intensities for such processes is developed. The proposed method is a hybrid method which combines the saddle-point approximation with limited Monte Carlo simulations. The performance and the accuracy of the proposed method are illustrated through a set of numerical examples. Copyright © 2010 Thomas Galtier et al.