工程力学 ›› 2019, Vol. 36 ›› Issue (5): 166-175.doi: 10.6052/j.issn.1000-4750.2018.04.0223

• 土木工程学科 • 上一篇    下一篇

基于自适应点估计和最大熵原理的结构体系多构件可靠度分析

李正良1,2, 祖云飞1, 范文亮1,2, 周擎宇1   

  1. 1. 重庆大学土木工程学院, 重庆 400045;
    2. 山地城镇建设与新技术教育部重点实验室(重庆大学), 重庆 400045
  • 收稿日期:2018-04-10 修回日期:2018-12-12 出版日期:2019-05-25 发布日期:2019-04-16
  • 通讯作者: 李正良(1963-),男,江苏人,教授,博士,博导,从事结构工程和工程力学方面的研究(E-mail:lizhengl@hotmail.com). E-mail:lizhengl@hotmail.com
  • 作者简介:祖云飞(1988-),男,重庆人,博士生,从事结构工程、随机系统分析和可靠度分析方面的研究(E-mail:windzyf@aliyun.com);范文亮(1979-),男,江西人,教授,博士,博导,从事结构工程、随机系统分析和可靠度分析方面的研究(E-mail:davidfwl@126.com);周擎宇(1991-),男,江西人,博士生,从事结构工程、随机系统分析和可靠度分析方面的研究(E-mail:403668549@qq.com).
  • 基金资助:
    国家自然科学基金项目(51478064,51678092)

RELIABILITY ANALYSIS OF MULTI-COMPONENTS IN STRUCTURAL SYSTEM BASED ON THE ADAPTIVE POINT ESTIMATE METHOD AND THE PRINCIPLE OF MAXIMUM ENTROPY

LI Zheng-liang1,2, ZU Yun-fei1, FAN Wen-liang1,2, ZHOU Qing-yu1   

  1. 1. School of Civil Engineering, Chongqing University, Chongqing 400045, China;
    2. Key Laboratory of New Technology for Construction of Cities in Mountain Area(Chongqing University), Ministry of Education, Chongqing 400045, China
  • Received:2018-04-10 Revised:2018-12-12 Online:2019-05-25 Published:2019-04-16

摘要: 准确而高效地求解结构体系中多个构件的可靠度水准对结构维护和优化具有重要意义,目前已有学者将蒙特卡洛法和响应面法用于此类可靠度分析。然而,蒙特卡洛法所需结构分析次数取决于失效概率的量级,通常计算成本较高。而响应面法的所需结构分析次数取决于杆件数量,当其数量较多时同样有较高的成本。鉴于此,该文提出了一种基于自适应点估计和最大熵原理的结构体系多构件可靠度分析方法,其所需的结构重分析次数上限与杆件数量无关,计算过程简便无需迭代。首先,通过引入自适应交叉项判定和双变量降维近似模型求解各杆件的前四阶矩;然后,根据各杆件的前四阶矩,采用最大熵原理求解各杆件的可靠度指标;最后,通过多个算例对比了蒙特卡洛法、响应面法和建议方法的精度和效率。结果表明建议方法所需的结构重分析次数远少于蒙特卡洛法和响应面法,实现过程简便,且精度能够满足工程要求。

关键词: 结构体系多构件可靠度, 蒙特卡洛法, 响应面法, 自适应点估计, 最大熵原理, 矩方法

Abstract: It is important to analyze the reliability level of multi-components in a structural system accurately and efficiently. Monte Carlo method and response surface method are usually used in such reliability analysis. However, the number of structural analysis in Monte Carlo method depends on the value of the reliability index, which usually requires large computation cost. The number of structural analysis in response surface method depends on the number of components, which also needs significant computation cost when the number of components is large. A reliability method for multi-components in a structural system based on the adaptive point estimate method and the principle of maximum entropy is proposed. In this method, the upper limit of the required number of structural analysis is irrelevant to the number of components, and the computation process is easy to implement without iterations. Firstly, the first four moments of each component are calculated based on the combination of adaptive delineation of cross terms and bivariate dimensional decomposition. Then, the principle of maximum entropy is induced to evaluate the reliability index of each component according to the first four moments. Finally, several cases are investigated to compare the accuracy and efficiency of the Monte Carlo method, the response surface method and the proposed method. The results demonstrate that the proposed method has significant advantages in efficiency when compared with Monte Carlo method and response surface method, and can be implemented with satisfactory accuracy for engineering problems.

Key words: reliability analysis of multi-components in structural system, Monte Carlo method, response surface method, adaptive point estimate method, principle of maximum entropy, moment method

中图分类号: 

  • TU311.2
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