Unified Hermite Polynomial Model and Its Application in Estimating Non-Gaussian Processes

Abstract

Non-Gaussian processes beset many aspects of structural engineering analysis. To estimate non-Gaussian processes, various third-order Hermite polynomial models have been proposed and widely applied. Different forms of expressions have been proposed for hardening and softening processes in existing Hermite polynomial models, which makes them inconvenient to implement. Furthermore, these models are either too simple to ensure accurate results or too complicated to implement conveniently. Thus, a unified third-order Hermite polynomial model that achieves a good balance between accuracy and convenience for both hardening and softening processes is proposed in this study. Explicit expressions for translations of the marginal distributions between the non-Gaussian and Gaussian processes using the proposed Hermite polynomial model are deduced, and the applicable ranges are provided. The accuracy of the proposed model is demonstrated by comparing the coefficients and estimated moments with those obtained from the moment-matching method. Furthermore, the application of the proposed model in evaluating first passage probability, analyzing fatigue damage, and estimating peak factors of non-Gaussian wind pressure coefficient histories is demonstrated with numerical and practical examples.