First passage probability assessment of stationary non-Gaussian process using the third-order polynomial transformation

Abstract

In this article, an analytical moment-based procedure is developed for estimating the first passage probability of stationary non-Gaussian structural responses for practical applications. In the procedure, an improved explicit third-order polynomial transformation (fourth-moment Gaussian transformation) is proposed, and the coefficients of the third-order polynomial transformation are first determined by the first four moments (i.e. mean, standard deviation, skewness, and kurtosis) of the structural response. The inverse transformation (the equivalent Gaussian fractile) of the third-order polynomial transformation is then used to map the marginal distributions of a non-Gaussian response into the standard Gaussian distributions. Finally, the first passage probabilities can be calculated with the consideration of the effects of clumping crossings and initial conditions. The accuracy and efficiency of the proposed transformation are demonstrated through several numerical examples for both the “softening” responses (with wider tails than Gaussian distribution; for example, kurtosis > 3) and “hardening” responses (with narrower tails; for example, kurtosis < 3). It is found that the proposed method has better accuracy for estimating the first passage probabilities than the existing methods, which provides an efficient and rational tool for the first passage probability assessment of stationary non-Gaussian process.