数学
Kullback-Leibler散度
分歧(语言学)
概率密度函数
最大熵原理
算法
熵(时间箭头)
序列(生物学)
B样条曲线
应用数学
可靠性(半导体)
概率分布
花键(机械)
数学优化
计算机科学
统计
数学分析
工程类
生物
物理
哲学
结构工程
功率(物理)
量子力学
遗传学
语言学
作者
Wanxin He,Yiyuan Wang,Gang Li,Jinhang Zhou
标识
DOI:10.1016/j.ress.2023.109909
摘要
The maximum entropy method (MEM) is a powerful tool for the recovery of unknown probability density functions (PDF) and has growing popularity in the reliability analysis community. However, MEM may be inaccurate for PDFs with a complex shape (e. g. multiple modals or a long tail), influencing the accuracy of the reliability analysis greatly. To overcome this deficiency, this study proposes a novel MEM paradigm based on the B-spline theory and the low-discrepancy sequence. Firstly, to enhance the performance of MEM for complex PDFs, the B-spline functions are used to construct the MEM PDF. Correspondingly, the iteration formulation is derived for the undetermined parameter estimation of the B-spline-based MEM PDF based on the closed solution for minimizing the Kullback-Leibler divergence. Then, we adopt the low-discrepancy sequence to calculate the objective function of minimizing the Kullback-Leibler divergence efficiently. Compared with MEM and other moment-based reliability analysis methods, the proposed method does not require the statistical moments, and integrates the advantages of the B-spline theory and MEM. To illustrate the benefits of our method, five examples are analyzed and compared with some classical reliability analysis methods.
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