Crossings of Second-Order Response Processes Subjected to LMA Loadings

The focus of this paper is on the estimation of the crossing intensities of responses for secondorder 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 nonGaussian, 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.