基于降维可视化技术的结构可靠性灵敏度分析

doi:10.3969/j.issn.1000-1093.2014.11.020

兵工学报 ›› 2014, Vol. 35 ›› Issue (11): 1876-1882.doi: 10.3969/j.issn.1000-1093.2014.11.020

基于降维可视化技术的结构可靠性灵敏度分析

李皓川¹，孙志礼¹，王海²

（1.东北大学机械工程与自动化学院，辽宁沈阳 110819；2.沈阳金鑫宏美物资有限公司，辽宁沈阳 110001）

收稿日期:2014-03-03 修回日期:2014-03-03 上线日期:2015-01-05
作者简介:李皓川(1987—)，男，博士研究生
基金资助:
国家自然科学基金项目(51135003)

Analysis of Structural Reliability Sensitivity Based on Dimensionality Reduction and Visualization Technique

LI Hao-chuan¹, SUN Zhi-li¹ , WANG Hai²

(1.School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, Liaoning，China；2.Shenyang Jinxin Hongmei Materials Co. Ltd.，Shenyang 110001, Liaoning，China）

Received:2014-03-03 Revised:2014-03-03 Online:2015-01-05

摘要/Abstract

摘要： 针对多维隐式结构可靠性问题，应用降维可视化技术进行可靠性灵敏度分析。基于iHLRF法求解设计点，根据模型计算精度确定有限差分步长。用一条直线将平面分为安全域和失效域两部分，通过计算直线初始位置附近数据点对应的响应量，来调整并确定直线的最终位置，根据直线上方数据点提供的信息计算可靠性灵敏度。提出的可靠性灵敏度分析方法的准确性不受维度以及非线性的影响，且效率较高。最后计算了两个结构系统的可靠度及各个变量的可靠性灵敏度，为结构设计提供了理论依据。算例表明了文中所给出的计算公式的正确性和有效性。

关键词: 应用统计数学, 结构可靠性, 可靠性灵敏度, 设计点, 降维可视化技术, iHLRF法

Abstract: For the implicit reliability problem with multiple dimensions, the reliability sensitivity of structure is analyzed by applying the dimensionality reduction and visualization technique. The design point is found based on iHLRF method, and the step size of finite difference is determined according to the modeling computational precision. The plane is divided into two parts of safe domain and failure domain by a straight line, and the final position of the straight line is determined by calculating the responses corresponding to several data points nearby its initial position. The dimensionality and nonlinearity do not affect the accuracy of the proposed method, which also has relatively high efficiency. Finally, the reliabilities of two structural systems and the reliability sensitivities of various influencing factors are calculated, which provides a theoretical basis for designing the structural systems. The examples show that these theories and formulas are rational and efficient.

Key words: applied statistical mathematics, structural reliability, reliability sensitivity, design point, dimensionality reduction and visualization technique, iHLRF method

中图分类号:

TB114.3

李皓川，孙志礼，王海. 基于降维可视化技术的结构可靠性灵敏度分析[J]. 兵工学报, 2014, 35(11): 1876-1882.

LI Hao-chuan, SUN Zhi-li , WANG Hai. Analysis of Structural Reliability Sensitivity Based on Dimensionality Reduction and Visualization Technique[J]. Acta Armamentarii, 2014, 35(11): 1876-1882.

参考文献

［1］ Hurtado J E, Alvarez D A.A method for enhancing computational efficiency in Monte Carlo calculation of failure probabilities by exploiting FORM results［J］. Computers & Structures, 2013, 117(2): 95-104.
［2］ Zhao Y G, Ono T. A general procedure for first/second-order reliability method (FORM/SORM)［J］. Structural Safety, 1999, 21(2): 95-112.
［3］ Zhao Y G, Ono T. New approximations for SORM: Part 1［J］. Journal of Engineering Mechanics, 1999, 125(1): 79-85.
［4］ Zhao Y G, Ono T. New approximations for SORM: part II［J］. Journal of Engineering Mechanics, 1999, 125(1):86-93.
［5］ Bourinet J M, Deheeger F, Lemaire M. Assessing small failure probabilities by combined subset simulation and support vector machines［J］. Structural Safety, 2011, 33(6): 343-353.
［6］ Balesdent M, Morio J, Marzat J. Kriging-based adaptive importance sampling algorithms for rare event estimation［J］. Structural Safety, 2013, 44(9): 1-10.
［7］刘瞻，张建国. 基于优化Kriging模型和重要抽样法的结构可靠度混合算法［J］. 航空学报，2013, 34(6): 1347-1355.
LIU Zhan, ZHANG Jian-guo. Hybrid structure reliability method combining optimized Kriging model and importance sampling［J］. Acta Aeronautica et Astronautica Sinica, 2013, 34(6): 1347-1355.(in Chinese)
［8］ Bucher C. Asymptotic sampling for high-dimensional reliability analysis［J］. Probabilistic Engineering Mechanics, 2009, 24(4): 504-510.
［9］ Sichani M T, Nielsen S R K, Bucher C. Efficient estimation of first passage probability of high-dimensional nonlinear systems［J］. Probabilistic Engineering Mechanics, 2011, 26(4): 539-549.
［10］ Pettit C L, Wilson D K. Full-field sensitivity analysis through dimension reduction and probabilistic surrogate models［J］. Probabilistic Engineering Mechanics, 2010, 25(4): 380-392.
［11］ Zhang X, Pandey M D. Structural reliability analysis based on the concepts of entropy, fractional moment and dimensional reduction method［J］. Structural Safety, 2013, 43(3): 28-40.
［12］ Valdebenito M A, Pradlwarter H J, Schuller G I. The role of the design point for calculating failure probabilities in view of dimensionality and structural nonlinearities［J］. Structural Safety, 2010, 32(2): 101-111.
［13］ Hurtado J E. Dimensionality reduction and visualization of structural reliability problems using polar features［J］. Probabilistic Engineering Mechanics，2012, 29: 16-31.
［14］ Liu P L, Der Kiureghian A. Optimization algorithms for structural reliability［J］. Structural Safety, 1991, 9(3): 161-177.
［15］李皓川，孙志礼，闫明. 高精密滚动轴承游隙的可靠性保障研究［J］. 东北大学学报:自然科学版, 2014, 35(10)：1516-1520.
LI Hao-chuan, SUN Zhi-li, YAN Ming. Research on the reliability assurance of highly precise rolling bearing clearance［J］. Journal of Northeastern University:Nature Science, 2014, 35(10): 1516-1520. (in Chinese)

[1]	邱继伟，罗海胜. 结构可靠性分析的自适应共轭非线性近似方法[J]. 兵工学报, 2021, 42(3): 648-654.
[2]	陈鹏霏，和鹏，于泰龙，刘巧伶. 基于梯度搜索法的非线性结构可靠性分析方法[J]. 兵工学报, 2021, 42(1): 175-184.
[3]	朱达伟, 周金宇, 庄百亮. 结构可靠性优化的通用生成函数-序列优化与可靠性评估方法[J]. 兵工学报, 2020, 41(2): 398-405.
[4]	邱涛，张建国，邱继伟，魏娟，游令非. 基于二参数寻优设计点的混合结构可靠性分析算法[J]. 兵工学报, 2019, 40(4): 865-873.
[5]	孟广伟，魏彤辉，周立明，李锋. 基于泰勒展开法的结构混合可靠性分析[J]. 兵工学报, 2018, 39(7): 1404-1410.
[6]	荣吉利，宋乾强，杨国孝，张涛. 正态应力-正态强度下可靠度精确置信下限[J]. 兵工学报, 2015, 36(2): 332-336.
[7]	张志华, 李大伟, 钟强晖, 梁胜杰. 考虑维修的产品可靠性模型研究[J]. 兵工学报, 2014, 35(7): 1131-1136.
[8]	宋保维, 董华超, 王鹏. null[J]. 兵工学报, 2013, 34(5): 605-610.

基于降维可视化技术的结构可靠性灵敏度分析

Analysis of Structural Reliability Sensitivity Based on Dimensionality Reduction and Visualization Technique

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 8

编辑推荐

Metrics

本文评价