Structural reliability analysis based on fractional moments-based iterative maximum entropy method and multiplicative exact dimension reduction integration method

Abstract

The fractional moments-based maximum entropy method (FM-MEM) is a powerful method for constructing probability density functions and is widely applied in structural reliability analysis. To ensure the satisfactory performance of this method, it is crucial to determine an appropriate number of constrained fractional moments and estimate them with a balance between accuracy and efficiency. In response to these issues, this paper proposes a fractional moments-based iterative maximum entropy method (FM-IMEM) and a multiplicative exact dimension reduction integration method (M-EDRIM). In the FM-IMEM, a nonlinear transformation is performed to allow negative limit state functions (LSFs), and the optimal number and order of constrained fractional moments and Lagrange multipliers are determined efficiently through an iterative algorithm. Moreover, to estimate fractional moments in the FM-IMEM accurately and efficiently, the M-EDRIM is developed based on a new dimension reduction model, the multiplicative exact dimension reduction model (M-EDRM). This new model can decompose the LSF into a product form of lower-dimensional component functions exactly, thereby alleviating the curse of dimensionality in fractional moments estimation while ensuring accuracy. Five examples with various LSFs are investigated to validate the proposed method. Results show that the proposed method can well balance accuracy and efficiency for structural reliability analysis.