基于首次穿越PDF自适应估计的时变可靠性分析方法

doi:10.3901/JME.2024.05.264

机械工程学报 ›› 2024, Vol. 60 ›› Issue (5): 264-275.doi: 10.3901/JME.2024.05.264

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基于首次穿越PDF自适应估计的时变可靠性分析方法

俞水^1,2, 吴晓^1,2, 郭鹏^1,2, 王志华³

1. 西南交通大学机械工程学院成都 610031;
2. 轨道交通运维技术与装备四川省重点实验室成都 610031;
3. 航空工业成都飞机工业(集团)有限公司成都 610091

收稿日期:2023-03-25 修回日期:2023-10-15 出版日期:2024-03-05 发布日期:2024-05-30
通讯作者: 俞水，男，1990年出生，博士，讲师。主要研究方向为结构可靠性分析与设计。E-mailh2oyu@swjtu.edu.cn
基金资助:
四川省自然科学基金(2022NSFSC0433)和中央高校基本科研业务费(2682022CX012)资助项目。

Adaptive Approximation of the First-crossing PDF for Time-variant Reliability Analysis

YU Shui^1,2, WU Xiao^1,2, GUO Peng^1,2, WANG Zhihua³

1. School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031;
2. Technology and Equipment of Rail Transit Operation and Maintenance Key Laboratory of Sichuan Province, Chengdu 610031;
3. Chengdu Aircraft Industrial (Group) Co. Ltd, Chengdu 610091

Received:2023-03-25 Revised:2023-10-15 Online:2024-03-05 Published:2024-05-30

摘要/Abstract

摘要： 针对机械产品全寿命周期的时变可靠性问题，提出了自适应首次穿越点(First-crossing time point，FCTP)的概率分布模型，可获得寿命周期内可靠性的演化规律，为机械产品在全寿命周期内可靠性分析和设计提供了工具。对于传统时变可靠性首次穿越法中首次穿越率模型估计困难的问题，首先基于支持向量回归提出首次穿越时间点自适应代理模型；其次，采用拉丁化部分分层抽样(Latinized partially stratified sampling，LPSS)估计首次穿越时间点代理模型的四阶原点矩；再次，以距离代理模型一阶矩最近的点为中心，结合均匀分布构建自适应学习函数；然后，以相邻两次迭代的各阶矩最大误差为收敛条件，建立最优的首次穿越时间点的代理模型；最后，基于最优代理模型，利用核密度函数求解首次穿越点的概率密度函数(Probability density function，PDF)，获得产品寿命周期内时变可靠性的演化趋势。通过三个算例验证了所提方法的有效性。

关键词: 时变可靠性, 全寿命周期, 首次穿越时间点, 自适应代理模型, 核密度函数

Abstract: An adaptive probability distribution model of first-crossing time point is proposed for the time-varying reliability of mechanical products over their whole life cycle, which can obtain the evolution of reliability during the life cycle and provide a tool for reliability analysis and design of mechanical products over their whole life cycle. To address the difficulty of estimating the first crossing rate model in the traditional first-crossing time-variant reliability method. Firstly, an adaptive surrogate model is proposed for the first-crossing time point based on support vector regression. Secondly, Latinized partially stratified sampling (LPSS) is employed to estimate the fourth origin moments of first-crossing time point surrogate model. The adaptive learning function is constructed by combining the uniform design with the nearest point to the first-order moment of the surrogate model as the center. Then, the maximum error of each order moment of two adjacent iterations is used as the convergence condition to build the optimal surrogate model for the first-crossing time point. Finally, based on the optimal surrogate model, the probability distribution function of the first-crossing time point is solved using the kernel density function to obtain the time-variant reliability trend during the product life cycle. The effectiveness of the proposed method is verified by three examples.

Key words: time-variant reliability, whole life cycle, first-crossing time point, adaptive surrogate model, kernel density function

中图分类号:

TH122

俞水, 吴晓, 郭鹏, 王志华. 基于首次穿越PDF自适应估计的时变可靠性分析方法[J]. 机械工程学报, 2024, 60(5): 264-275.

YU Shui, WU Xiao, GUO Peng, WANG Zhihua. Adaptive Approximation of the First-crossing PDF for Time-variant Reliability Analysis[J]. Journal of Mechanical Engineering, 2024, 60(5): 264-275.

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基于首次穿越PDF自适应估计的时变可靠性分析方法

Adaptive Approximation of the First-crossing PDF for Time-variant Reliability Analysis

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