Journal of Probability and Statistics
Volume 2010 (2010), Article ID 752452, 22 pages
Research Article

Crossings of Second-Order Response Processes Subjected to LMA Loadings

1Mathematical Sciences, Chalmers University of Technology, SE-41296 Gothenburg, Sweden
2Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600 036, India

Received 26 October 2009; Accepted 1 February 2010

Academic Editor: Tomasz J. Kozubowski

Copyright © 2010 Thomas Galtier et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 loadings—the 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.