结构输出响应概率密度估计中分数矩求解方法

摘要

For the fact that the fractional moment based principle of maximum entropy for structural relia-bility analysis has some advantages in computational efficiency and precision,in this paper,three computa-tional methods for accurately estimating the fractional moments of constraint condition output response involved in the principle of maximum entropy,are studied and presented,including the dimension reduction integration (DRI)method,the sparse gird integration (SGI)method and the unscented transformation (UT)method. The computational theory and process are expounded,the calculation efficiency of each method is given,and the applicability of each method is analyzed in the paper.The presented three methods can greatly reduce the number of structural input-output model estimates and ensure the accuracy of calculation at the same time,so the efficiency of statistical analysis can be greatly improved.Besides,compared with the Monte Carlo simula-tion method,the accuracy and efficiency of the presented methods are verified according to the applied exam-ples.%鉴于概率不确定性背景下基于分数矩极大熵准则的结构可靠性分析方法具有较大的效率与精度优势,综合研究并给出了可以用于极大熵准则中约束条件输出响应分数矩求解的3 种分数矩求解方法,包括降维积分(DRI)方法、稀疏网格积分(SGI)方法和无迹变换(UT)方法.阐述了分数矩求解原理及过程,给出了方法的计算效率,并分析了方法的适用性.3 种分数矩求解方法在确保计算精度的同时可以很大程度减少结构输入-输出模型的调用次数,大幅提高统计分析效率.通过与 Monte Carlo 仿真分析法对比,验证了3 种分数矩求解方法的正确性与高效性.