Crossing statistics of quadratic transformations of LMA processes

► Development of a numerical method for estimating crossing statistics of quadratic transformations of LMA processes.
► LMA processes model non-Gaussian features such as skewness and kurtosis.
► Neglecting non-Gaussian features underestimates the crossing statistics.
► Proposed method is computationally cheaper than full scale Monte Carlo simulations.

Random loads that exhibit significant non-Gaussianity in terms of asymmetric distributions with high kurtosis can be modeled as Laplace Moving Average (LMA) processes. Examples of such loads are the wave loadings in ships, wind loads on wind turbines, loads arising due to surface roughness in vehicular systems, etc. The focus of this paper is on estimating the crossing statistics of second-order response of structures subjected to LMA loads. Following the Kac–Siegert representation, a second order approximation of the Volterra expansion of the system enables representing the response as a quadratic combination of vector LMA processes. The mean crossing rate of the response is then computed using a hybrid approach. The proposed method is illustrated through two numerical examples.