Adaptive Kriging reliability analysis method based on extended expectation improvement strategy
-
摘要:
为了提高隐式、强非线性结构在可靠性求解时的计算效率与精度，发展一种改进的自适应Kriging可靠性分析方法。在Kriging模型加点策略中引入符号函数与距离权重函数以构建扩展期望改善学习函数，确保在极限状态曲面附近完成样本点更新。结合蒙特卡洛模拟构建自适应可靠性求解框架，确保计算稳定性并降低新增样本数量。通过经典数学算例与经典工程问题表明：所提方法相比蒙特卡洛模拟，失效概率相对误差不超过0.5%，新增样本数量较现有可靠性求解方法实现大幅降低。最后，某航空燃油离心泵汽蚀可靠性有限元算例表明：相对蒙特卡洛模拟，所提方法求解失效概率误差仅为1.06%；相较现有可靠性求解方法，所提方法实现计算成本降低51.06%。上述成果，验证了所提方法在隐式非线性结构可靠性分析中兼顾高精度与高效率的显著优势。
-
关键词:
- 结构可靠性 /
- 自适应Kriging /
- 失效概率 /
- 学习函数 /
- 主动学习
Abstract:To enhance computational efficiency and accuracy in reliability analysis for implicit and highly nonlinear structures, this study develops an improved adaptive Kriging-based reliability analysis method. in the infill strategy of the Kriging model, a sign function and a distance-based weight function were incorporated to construct an Extended Expected Improvement learning function, ensuring that sample updates are concentrated near the limit state surface. An adaptive reliability analysis framework was established by integrating Monte Carlo simulation, which improved computational stability and reduced the number of additional samples required. Validation through classical mathematical examples and engineering problems demonstrated that, compared with Monte Carlo simulation, the relative error in failure probability was within 0.5%, and the number of new samples was significantly reduced compared to existing reliability analysis methods. Finally, a finite element case study on cavitation reliability in an aviation fuel centrifugal pump showed that the error in failure probability was only 1.06% relative to Monte Carlo simulation, while the computational cost was reduced by 51.06% compared to existing reliability analysis approaches. These results verify that the proposed method achieves both high precision and high efficiency in reliability analysis of implicit nonlinear structures.
-
Key words:
- structural reliability /
- adaptive Kriging /
- failure probability /
- learning function /
- active learning
-
图 6 离心泵结构及汽蚀分布云图
Figure 6. Structure and cavitation distribution cloud diagram of centrifugal pump
表 1 算例1可靠性分析结果
Table 1. Reliability analysis results for Example 1
方法 Ncall Pf /10−3 Cov（Pf）/% $ \varepsilon /\% $ MCS 106 2.1971 4.6090 AK-MCS 12+96 2.2172 2.1214 0.91 AK-EFF-MCS 12+153 2.2901 2.0872 4.23 AK-EI-MCS 12+95 2.1664 2.1048 1.40 AK-EEI-MCS 12+79 2.2002 2.1463 0.14 
下载: 导出CSV
表 2 算例2可靠性分析结果
Table 2. Reliability analysis results of Example 2
方法 Ncall Pf/10−2 Cov（Pf）/% $ \varepsilon /{\text{%}} $ MCS 106 7.3912 2.0863 - AK-MCS 15+771 7.2111 1.1344 2.44 AK-EFF-MCS 15+776 7.3813 1.1201 0.13 AK-EI-MCS 15+686 7.2324 1.1193 2.15 AK-EEI-MCS 15+676 7.3933 1.1431 0.03
下载: 导出CSV
表 3 屋顶桁架结构输入参数分布
Table 3. Distribution of input parameters for roof truss structures
变量 分布类型 均值 标准差 q/（N/m） 正态分布 20000 2000 l/m 正态分布 13.5 0.50 $ {A}_{\mathrm{s}} $/m2 正态分布 9.82×10−4 6×10−5 $ {A}_{\mathrm{c}} $/m2 正态分布 0.04 0.008
下载: 导出CSV
表 4 某屋顶桁架结构可靠性分析结果
Table 4. Reliability analysis results of a certain roof truss structure
方法 Ncall Pf /10−2 Cov（Pf）/% $ \varepsilon /{\text{%}} $ MCS 106 4.1092 1.1529 AK-MCS 8+252 4.1446 1.5347 0.86 AK-EFF-MCS 8+384 4.1181 1.4786 0.22 AK-EI-MCS 8+119 4.1125 1.5270 0.08 AK-EEI-MCS 8+75 4.1072 1.5178 0.05
下载: 导出CSV
表 5 Non-linear Oscillator系统参数分布
Table 5. Distribution of parameters of non-linear oscillator system
变量 分布类型 均值 标准差 m 正态分布 1 0.05 c1 正态分布 1 0.1 c2 正态分布 0.1 0.01 F1 正态分布 1 0.2 r 正态分布 0.5 0.05 t1 正态分布 1 0.2
下载: 导出CSV
表 6 Non-linear Oscillator可靠性分析结果
Table 6. Reliability analysis results of non-linear oscillator
方法 Ncall Pf /10−2 Cov（Pf）/% $ \varepsilon /{\text{%}} $ MCS 106 2.7761 1.8714 AK-MCS 50+221 2.8670 1.8407 3.27 AK-EFF-MCS 50+384 2.6901 2.0148 3.10 AK-EI-MCS 50+288 2.8210 1.8560 1.62 AK-EEI-MCS 50+45 2.7862 1.8680 0.36
下载: 导出CSV
表 7 离心泵随机不确定性参数描述
Table 7. Description of random uncertainty parameters of centrifugal Pumps
变量名称 分布类型 均值 标准差 叶轮入口直径$ {D}_{\mathrm{j}} $/mm 正态分布 40.662 0.3 叶轮出口直径$ {D}_{2} $/mm 正态分布 116.330 0.3 叶轮出口宽度$ {b}_{2} $/mm 正态分布 4.004 0.3 叶片出口角度$ {\beta }_{2} $/° 正态分布 15.80 0.03
下载: 导出CSV
表 8 离心泵汽蚀可靠性分析结果
Table 8. Cavitation reliability analysis results of centrifugal pump
方法 Ncall Pf /10−4 Cov（Pf）/% $ \varepsilon /{\text{%}} $ MCS 106 6.6516 4.0051 AK-MCS 50+128 6.8323 3.8251 2.72 AK-EFF-MCS 50+129 7.0102 3.6973 5.39 AK-EI-MCS 50+94 6.3440 3.7463 4.62 AK-EEI-MCS 50+46 6.5811 4.0019 1.06
下载: 导出CSV
-
[1] 葛福林, 吴宗辉, 何建. 基于少数类合成的过采样算法和贝叶斯优化神经网络的结构可靠性分析方法[J]. 船舶力学, 2025, 29(5): 767-775. Ge Fulin, Wu Zonghui, He Jian. Structural reliability analysis method based on synthetic minority over-sampling technique algorithm and Bayesian optimization neural network[J]. Journal of Ship Mechanics, 2025, 29(5): 767-775. (in Chinese doi: 10.3969/j.issn.1007-7294.2025.05.009Ge Fulin, Wu Zonghui, He Jian. Structural reliability analysis method based on synthetic minority over-sampling technique algorithm and Bayesian optimization neural network[J]. Journal of Ship Mechanics, 2025, 29(5): 767-775. (in Chinese) doi: 10.3969/j.issn.1007-7294.2025.05.009 [2] 刘泽清, 程鑫, 杨旭锋. 基于ALK模型与子集模拟的主动学习可靠性分析方法[J]. 机械强度, 2024, 46(1): 96-106. Liu Zeqing, Cheng Xin, Yang Xufeng. Active-learning method based on alk model and subset simulation[J]. Journal of Mechanical Strength, 2024, 46(1): 96-106. (in Chinese doi: 10.16579/j.issn.1001.9669.2024.01.013Liu Zeqing, Cheng Xin, Yang Xufeng. Active-learning method based on alk model and subset simulation[J]. Journal of Mechanical Strength, 2024, 46(1): 96-106. (in Chinese) doi: 10.16579/j.issn.1001.9669.2024.01.013 [3] Luo Changqi, Zhu Shunpeng, Keshtegar B, et al. Active Kriging-based conjugate first-order reliability method for highly efficient structural reliability analysis using resample strategy[J]. Computer Methods in Applied Mechanics and Engineering, 2024, 423: 116863. doi: 10.1016/j.cma.2024.116863 [4] Hu Zhangli, Mansour R, Olsson M, et al. Second-order reliability methods: a review and comparative study[J]. Structural and Multidisciplinary Optimization, 2021, 64(6): 3233-3263. doi: 10.1007/s00158-021-03013-y [5] Phan H C, Le T T, Duong H T, et al. Reliability-based optimization for concrete-filled steel tubular columns incorporating multi-advanced techniques and model constraints[J]. Advances in Mechanical Engineering, 2024, 16(10): 16878132241293508. [6] Saraygord Afshari S, Enayatollahi F, Xu Xiangyang, et al. Machine learning-based methods in structural reliability analysis: a review[J]. Reliability Engineering & System Safety, 2022, 219: 108223. doi: 10.1016/j.ress.2021.108223 [7] Teixeira R, Nogal M, O’connor A. Adaptive approaches in metamodel-based reliability analysis: a review[J]. Structural Safety, 2021, 89: 102019. doi: 10.1016/j.strusafe.2020.102019 [8] Gao Shuzhi, Zhao Yunkun, Zhao Xudong, et al. Application of response surface method based on new strategy in structural reliability analysis[J]. Structures, 2023, 57: 105202. doi: 10.1016/j.istruc.2023.105202 [9] Wang Yahui, Zhang Cai, Su Yongqiang, et al. Structure optimization of the frame based on response surface method[J]. International Journal of Structural Integrity, 2019, 11(3): 411-425. doi: 10.1108/IJSI-07-2019-0067 [10] 胡伟飞, 廖家乐, 郭云飞, 等. 基于物理信息神经网络的时变可靠性分析方法[J]. 机械工程学报, 2024, 60(13): 141-153. Hu Weifei, Liao Jiale, Guo Yunfei, et al. Time-dependent reliability analysis based on physics-informed neutral network[J]. Journal of Mechanical Engineering, 2024, 60(13): 141-153. (in Chinese doi: 10.3901/JME.2024.13.141Hu Weifei, Liao Jiale, Guo Yunfei, et al. Time-dependent reliability analysis based on physics-informed neutral network[J]. Journal of Mechanical Engineering, 2024, 60(13): 141-153. (in Chinese) doi: 10.3901/JME.2024.13.141 [11] Jia Dawei, Wu Ziyan. A Laplace asymptotic integral-based reliability analysis method combined with artificial neural network[J]. Applied Mathematical Modelling, 2022, 105: 406-422. doi: 10.1016/j.apm.2021.12.043 [12] Roy A, Chakraborty S. Support vector machine in structural reliability analysis: a review[J]. Reliability Engineering & System Safety, 2023, 233: 109126. doi: 10.1016/j.ress.2023.109126 [13] Zheng Xiaohu, Yao Wen, Zhang Xiaoya, et al. Parameterized coefficient fine-tuning-based polynomial chaos expansion method for sphere-biconic reentry vehicle reliability analysis and design[J]. Reliability Engineering & System Safety, 2023, 240: 109568. doi: 10.1016/j.ress.2023.109568 [14] 宋海征, 周长聪, 李磊, 等. 一种基于AK-MCS-K的失效概率函数估计方法[J]. 中国机械工程, 2024, 35(5): 784-791. Song Haizheng, Zhou Changcong, Li Lei, et al. An estimation method of failure probability function based on AK-MCS-K[J]. China Mechanical Engineering, 2024, 35(5): 784-791. (in Chinese doi: 10.3969/j.issn.1004-132X.2024.05.003Song Haizheng, Zhou Changcong, Li Lei, et al. An estimation method of failure probability function based on AK-MCS-K[J]. China Mechanical Engineering, 2024, 35(5): 784-791. (in Chinese) doi: 10.3969/j.issn.1004-132X.2024.05.003 [15] Huang Ying, Zhang Jianguo, Wang Bowei, et al. AOK-ES: Adaptive optimized Kriging combining efficient sampling for structural reliability analysis[J]. Quality and Reliability Engineering International, 2024, 40(4): 1502-1525. doi: 10.1002/qre.3493 [16] Prentzas I, Fragiadakis M. Quantified active learning Kriging model for structural reliability analysis[J]. Probabilistic Engineering Mechanics, 2024, 78: 103699. doi: 10.1016/j.probengmech.2024.103699 [17] 刘骁骁, 肖杰杰, 冯威, 等. 基于自适应Kriging和直接概率积分方法的复合材料层合板分层可靠度研究[J]. 振动与冲击, 2025, 44(7): 293-304. Liu Xiaoxiao, Xiao Jiejie, Feng Wei, et al. Study on delamination reliability of composite laminate based on adaptive Kriging and direct probability integration methods[J]. Journal of Vibration and Shock, 2025, 44(7): 293-304. (in Chinese doi: 10.13465/j.cnki.jvs.2025.07.034Liu Xiaoxiao, Xiao Jiejie, Feng Wei, et al. Study on delamination reliability of composite laminate based on adaptive Kriging and direct probability integration methods[J]. Journal of Vibration and Shock, 2025, 44(7): 293-304. (in Chinese) doi: 10.13465/j.cnki.jvs.2025.07.034 [18] 王珏, 窦唯, 姜绪强, 等. 基于临界转速避开率的涡轮泵转子系统可靠性快速评估[J]. 宇航学报, 2025, 46(3): 580-588. Wang Jue, Dou Wei, Jiang Xuqiang, et al. A rapid assessment method for the reliability of turbopump rotor systems based on critical speed avoidance rate[J]. Journal of Astronautics, 2025, 46(3): 580-588. (in Chinese doi: 10.3873/j.issn.1000-1328.2025.03.015Wang Jue, Dou Wei, Jiang Xuqiang, et al. A rapid assessment method for the reliability of turbopump rotor systems based on critical speed avoidance rate[J]. Journal of Astronautics, 2025, 46(3): 580-588. (in Chinese) doi: 10.3873/j.issn.1000-1328.2025.03.015 [19] 陈吉清, 张钰奇, 兰凤崇, 等. 基于主动学习PC-Kriging模型的复杂结构可靠性分析方法[J]. 汽车工程, 2025, 47(2): 383-390. Chen Jiqing, Zhang Yuqi, Lan Fengchong, et al. Reliability analysis method of complex structures based on active learning PC-Kriging model[J]. Automotive Engineering, 2025, 47(2): 383-390. (in Chinese doi: 10.19562/j.chinasae.qcgc.2025.02.019Chen Jiqing, Zhang Yuqi, Lan Fengchong, et al. Reliability analysis method of complex structures based on active learning PC-Kriging model[J]. Automotive Engineering, 2025, 47(2): 383-390. (in Chinese) doi: 10.19562/j.chinasae.qcgc.2025.02.019 [20] Hu Yingshi, Lu Zhenzhou, Wei Ning, et al. Importance sampling enhanced by adaptive two-stage Kriging model and active subspace for analyzing rare probability with high dimensional input vector[J]. Reliability Engineering & System Safety, 2024, 245: 110019. doi: 10.1016/j.ress.2024.110019 [21] Echard B, Gayton N, Lemaire M. AK-MCS: an active learning reliability method combining Kriging and Monte Carlo Simulation[J]. Structural Safety, 2011, 33(2): 145-154. doi: 10.1016/j.strusafe.2011.01.002 [22] Bichon B J, Eldred M S, Swiler L P, et al. Efficient global reliability analysis for nonlinear implicit performance functions[J]. AIAA Journal, 2008, 46(10): 2459-2468. doi: 10.2514/1.34321 [23] Zheng Peijuan, Ming W C, Zong Zhouhong, et al. A new active learning method based on the learning function U of the AK-MCS reliability analysis method[J]. Engineering Structures, 2017, 148: 185-194. doi: 10.1016/j.engstruct.2017.06.038 [24] Lu Pengzhen, Hong Tao, Wu Ying, et al. Kriging–KNN hybrid analysis method for structural reliability analysis[J]. Journal of Bridge Engineering, 2022, 27(4): 04022009. doi: 10.1061/(ASCE)BE.1943-5592.0001837 [25] Zhang Xufang, Wang Lei, Sørensen J D. REIF: a novel active-learning function toward adaptive Kriging surrogate models for structural reliability analysis[J]. Reliability Engineering & System Safety, 2019, 185: 440-454. doi: 10.1016/j.ress.2019.01.014 [26] Lv Zhaoyan, Lu Zhenzhou, Wang Pan. A new learning function for Kriging and its applications to solve reliability problems in engineering[J]. Computers & Mathematics with Applications, 2015, 70(5): 1182-1197. doi: 10.1016/j.camwa.2015.07.004 [27] Jones D R, Schonlau M, Welch W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13(4): 455-492. doi: 10.1023/A:1008306431147 [28] Zhan Dawei. Expected coordinate improvement for high-dimensional Bayesian optimization[J]. Swarm and Evolutionary Computation, 2024, 91: 101745. doi: 10.1016/j.swevo.2024.101745 [29] Shi Yan, Lu Zhenzhou, He Ruyang, et al. A novel learning function based on Kriging for reliability analysis[J]. Reliability Engineering & System Safety, 2020, 198: 106857. doi: 10.1016/j.ress.2020.106857 [30] 洪林雄, 李华聪, 彭凯, 等. 基于改进学习策略的Kriging模型结构可靠度算法[J]. 西北工业大学学报, 2020, 38(2): 412-419. Hong Linxiong, Li Huacong, Peng Kai, et al. Structural reliability algorithms of Kriging model based on improved learning strategy[J]. Journal of Northwestern Polytechnical University, 2020, 38(2): 412-419. (in Chinese doi: 10.3969/j.issn.1000-2758.2020.02.023Hong Linxiong, Li Huacong, Peng Kai, et al. Structural reliability algorithms of Kriging model based on improved learning strategy[J]. Journal of Northwestern Polytechnical University, 2020, 38(2): 412-419. (in Chinese) doi: 10.3969/j.issn.1000-2758.2020.02.023 [31] Krige D G. A statistical approach to some basic mine valuation problems on the Witwatersrand[J]. Journal of the Southern African Institute of Mining and Metallurgy, 1951, 52(6): 119-139. [32] Lophaven S N, Nielsen H B, Søndergaard J. DACE - A Matlab Kriging Toolbox, Version 2.0: IMM-TR-2002-12[R]. Kongens Lyngby: Informatics and Mathematical Modelling, Technical University of Denmark, 2002. [33] ISO 9906: 2012: Rotodynamic pumps-Hydraulic performance acceptance tests - Grades 1, 2 and 3[S]. -
点击查看大图
计量
- 文章访问数: 16
- HTML浏览量: 9
- PDF量: 1
- 被引次数: 0