Outcrossing Rate Method for Nonstationary Non-Gaussian Performance Functions and Its Application to Time-Dependent Reliability Assessment

In recent decades, the outcrossing rate method has gained popularity for structural time-dependent reliability assessments (TRA). Despite numerous efforts, developing a general analytical outcrossing rate method for a nonstationary non-Gaussian performance function to estimate the failure probability within the forecast time interval remains a significant challenge. This paper introduces an analytical outcrossing rate method for non-Gaussian cases, named the three-moments-based outcrossing rate (TMO) method. The outcrossing rate is formulated based on the third-moment outcrossing rate with no assumption of the correlation between the performance function and its derivative process, allowing for a comprehensive understanding of the performance characteristics of a structure. Following the development of the proposed outcrossing rate, a TRA methodology is established to evaluate the failure probability of the nonstationary non-Gaussian performance function. Notably, the TMO method only requires statistical moments of the nonstationary non-Gaussian performance function, which are easy to calculate, facilitating efficient implementation. Three numerical examples are presented to demonstrate the applicability, efficiency, and accuracy of the proposed TMO method. It can be concluded that the proposed TMO method provides an accurate and useful approach for TRA in engineering applications.