Criteria Determining the Number of Estimate Points of Moment Method for Performance Functions Including Non-differentiable Points

Abstract

Moment method is famous for its calculation efficiency. Moments of the performance function are obtained by point estimates based on Hermite Integration. The reliability index and probability of failure can be obtained using existing standardization function or existing distribution systems. The precision of moment method increases monotonously with the increasing number of estimating points. The performance functions with non-differentiable points are frequently encountered when elasto-plastic behavior dominates for a structure under loading. Thus the accuracy and efficiency of moment method should be addressed for performance functions with non-differentiable points. In this paper, an example of structural performance functions is presented to show the existence of non-differentiable points. Two example performance functions are used to verify the accuracy and efficiency of moment method. The MCS method is employed to obtain the accurate results of probability of failure. The relative errors of probability of failure from moment method are obtained through a comparison with the results from MCS method. The fluctuation of the relative errors with the number of estimate points is also presented. The required number of estimate points for performance functions with non-differentiable points is discussed through the above two examples. Finally, criteria to determine the estimate points for performance functions with non-differentiable points are proposed and verified the applicability.