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

doi:10.3901/JME.2024.05.264

Abstract

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

CLC Number:

TH122

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.

References

[1] 张义民. 机械可靠性设计的内涵与递进[J]. 机械工程学报，2010，46(14)：167-188. ZHANG Yimin，Connotation and development of mechanical reliability-based design[J]．Journal of mechanical engineering，2010，46(14)：167-180.
[2] 蒋琛，邱浩波，高亮. 随机不确定性下的可靠性设计优化研究进展[J]. 中国机械工程，2020，31(2)：190-205. JIANG Chen，QIU Haobo，GAO Liang. Research progresses in reliability-based design optimization under aleatory uncertainties[J]. China Mechanical Engineering，2020，31(2)：190-205.
[3] ANDRIEU-RENAUD C，SUDRET B，LEMAIRE M. The PHI2 method：a way to compute time-variant reliability[J]. Reliability Engineering & System Safety，2004，84(1)：75-86.
[4] YU Shui，ZHANG Yanwei，LI Yun，et al. Time-variant reliability analysis via approximation of the first-crossing PDF[J]. Structural and Multidisciplinary Optimization，2020，62(5)：2653-2667.
[5] MENG Zeng，ZHAO Jingyu，JIANG Chen. An efficient semi-analytical extreme value method for time-variant reliability analysis[J]. Structural and Multidisciplinary Optimization，2021，64(3)：1469-1480.
[6] WANG Jian，CAO Runan，SUN Zhili. Importance sampling for time-variant reliability analysis[J]. IEEE Access，2021，9：20933-20941.
[7] YUAN Xiukai，LIU Shaolong，FAES M，et al. An efficient importance sampling approach for reliability analysis of time-variant structures subject to time-dependent stochastic load[J]. Mechanical Systems and Signal Processing，2021，159：107699.
[8] JIANG Chen，WANG Dapeng，QIU Haobo，et al. An active failure-pursuing Kriging modeling method for time-dependent reliability analysis[J]. Mechanical Systems and Signal Processing，2019，129：112-129.
[9] SHI Yan，LU Zhenzhou，XU Liyang，et al. An adaptive multiple-Kriging-surrogate method for time-dependent reliability analysis[J]. Applied Mathematical Modelling，2019，70：545-571.
[10] RICE S O. Mathematical analysis of random noise[J]. The Bell System Technical Journal，1945，24(1)：146-156.
[11] SUDRET B. Analytical derivation of the outcrossing rate in time-variant reliability problems[J]. Structure and Infrastructure Engineering，Taylor & Francis，2008，4(5)：353-362.
[12] SHI Yan，LU Zhenzhou，ZHANG Ke，et al. Reliability analysis for structures with multiple temporal and spatial parameters based on the effective first-crossing point[J]. Journal of Mechanical Design，2017，139：121403.
[13] HU Zhen，DU Xiaoping. Mixed efficient global optimization for time-dependent reliability analysis[J]. Journal of Mechanical Design，2015，137：051401.
[14] JIANG Chao，WEI Xinpeng，HUANG Zhiliang，et al. An outcrossing rate model and its efficient calculation for time-dependent system reliability analysis[J]. Journal of Mechanical Design，2017，139：041402.
[15] 王丕东，张建国，阚琳洁，等. 基于时变区间和穿阈模型的机械时变可靠性分析方法[J]. 机械工程学报，2017，53(11)：1-9. WANG Pidong，ZHANG Jianguo，KAN Linjie，et al. Time variant reliability approach with time-variant interval and up crossing model[J]. Journal of Mechanical Engineering，2017，53(11) ：1-9．
[16] FENG Kaixuan，LU Zhenzhou，LING Chunyan，et al. Efficient computational method based on AK-MCS and Bayes formula for time-dependent failure probability function[J]. Structural and Multidisciplinary Optimization，2019，60(4)：1373-1388.
[17] DU Weiqi，LUO Yuanxin，WANG Yongqin. Time-variant reliability analysis using the parallel subset simulation[J]. Reliability Engineering & System Safety，2019，182：250-257.
[18] YU Shui，WANG Zhonglai，LI Yun. Time and space-variant system reliability analysis through adaptive Kriging and weighted sampling[J]. Mechanical Systems and Signal Processing，2022，166：108443.
[19] WANG Zequn，WANG Pingfeng. A new approach for reliability analysis with time-variant performance characteristics[J]. Reliability Engineering & System Safety，2013，115：70-81.
[20] JIANG Chen，QIU Haobo，GAO Liang，et al. Real-time estimation error-guided active learning Kriging method for time-dependent reliability analysis[J]. Applied Mathematical Modelling，2020，77：82-98.
[21] ZHANG Dequan，HAN Xu，JIANG Chao，et al. Time-dependent reliability analysis through response surface method[J]. Journal of Mechanical Design，2017，139(041404).
[22] ZHANG Dequan，ZHOU Pengfei，JIANG Chen，et al. A stochastic process discretization method combing active learning Kriging model for efficient time-variant reliability analysis[J]. Computer Methods in Applied Mechanics and Engineering，2021，384：113990.
[23] WANG Zequn，CHEN Wei. Time-variant reliability assessment through equivalent stochastic process transformation[J]. Reliability Engineering & System Safety，2016，152：166-175.
[24] WANG Jinsheng，LI Chenfeng，XU Guoji，et al. Efficient structural reliability analysis based on adaptive Bayesian support vector regression[J]. Computer Methods in Applied Mechanics and Engineering，2021，387：114172.
[25] DANG Chao，XU Jun. A mixture distribution with fractional moments for efficient seismic reliability analysis of nonlinear structures[J]. Engineering Structures，2020，208：109912.
[26] KESHTEGAR B，BEN SEGHIER M E A，ZIO E，et al. Novel efficient method for structural reliability analysis using hybrid nonlinear conjugate map-based support vector regression[J]. Computer Methods in Applied Mechanics and Engineering，2021，381：113818.
[27] FANG Kaitai，LIN D，WINKER P，et al. Uniform design：theory and application[J]. Technometrics，Taylor& Francis，2000，42(3)：237-248.
[28] DANG Chao，XU Jun. Unified reliability assessment for problems with low- to high-dimensional random inputs using the Laplace transform and a mixture distribution[J]. Reliability Engineering & System Safety，2020，204：107124.
[29] YANG Xufeng，LIU Yongshou，MI Caiying，et al. Active learning Kriging model combining with kernel-density-estimation-based importance sampling method for the estimation of low failure probability[J]. Journal of Mechanical Design，2018，140(5)：051402.
[30] LING Chunyan，LU Zhenzhou，ZHU Xianming. Efficient methods by active learning Kriging coupled with variance reduction based sampling methods for time-dependent failure probability[J]. Reliability Engineering& System Safety，2019，188：23-35.
[31] YU Shui，WANG Zhonglai. A Novel Time-variant reliability analysis method based on failure processes decomposition for dynamic uncertain structures[J]. Journal of Mechanical Design，2018，140(5)：051401.