Second-Order Fourth-Moment Method for Structural Reliability

In the second-order reliability method (SORM), the failure probability is generally estimated based on parabolic approximation of the performance function. In the present paper, the first four moments (i.e., the mean, standard deviation, skewness, and kurtosis) of the second-order approximation of performance functions are obtained using the definition of the probability moment. Based on the recently developed fourth-moment standardization function, an explicit second-order fourth-moment reliability index is proposed for the estimation of failure probability corresponding to both the simple and general parabolic approximations. The simplicity and accuracy of the second-order fourth-moment reliability index is demonstrated using numerical examples. It can be concluded that the proposed method is applicable to the second-order approximation of performance functions with strong nonnormality and is accurate enough to improve the existing SORM in structural reliability analysis with minimal additional computational effort.