Efficient computing technique for reliability analysis of high-dimensional and low-failure probability problems using active learning method基于主动学习方法的高维小失效概率问题可靠性分析高效计算技术
![]()
Rajak P, Roy P, 2024. Efficient computing technique for reliability analysis of high-dimensional and low-failure probability problems using active learning method. Probabilistic Engineering Mechanics, 77: 103662.DOI: 10.1016/j.probengmech.2024.103662
尽管可靠性分析方面有很多最新进展，但由于获得精确结果需要大量样本和函数调用，高维小失效概率问题仍是一个挑战。函数调用会导致时间方面的计算成本急剧增加。为此，提出了一种基于 Kriging 元模型的主动学习算法，该算法在前两次迭代中使用无监督算法从随机样本中选择训练样本。随后，通过极限状态函数附近样本和填充设计空间获得样本丰富相关域，迭代改进元模型。这样通过使用主动学习算法，能以最少的函数调用数实现快速收敛。此外，提出了一种有效停止准则，以避免元模型的过早或过迟终止，并调节失效概率估计的精度。通过五个基于高维小失效概率的随机和区间变量算例的相对误差、函数调用次数和效率系数来检验该算法的表现。关键词: 无监督聚类算法, Kriging 元模型, 样本选取策略, 填充设计空间, 主动学习算法, 停止准则In spite of recent advancements in reliability analysis, high-dimensional and low-failure probability problems remain challenging because many samples and function calls are required for an accurate result. Function calls lead to a sharp increase in computational cost in terms of time. For this reason, an active learning algorithm is proposed using Kriging metamodel, where an unsupervised algorithm is used to select training samples from random samples for the first and second iterations. Then, the metamodel is improved iteratively by enriching the concerned domain with samples near the limit state function and samples obtained from a space-filling design. Hence, rapid convergence with the minimum number of function calls occurs using this active learning algorithm. An efficient stopping criterion has been developed to avoid premature or late-mature terminations of the metamodel and to regulate the accuracy of the failure probability estimations. The efficacy of this algorithm is examined using relative error, number of function calls, and coefficient of efficiency in five examples which are based on high-dimensional and low-failure probability with random and interval variables.
Keywords: Unsupervised clustering algorithm; Kriging metamodel; Sample selection strategy; Space-filling design; Active learning algorithm; Stopping criterion.- An active learning algorithm is proposed to estimate failure probability with less computational effort.
A stopping criterion is suggested to overcome the shortcoming of premature for high-dimensional and low-failure probability problems.
The efficacy of the active learning procedure is examined using relative error (ϵ_P_f), number of function calls (N_call) and coefficient of efficiency (CoE).
Fig. 1. Training samples selected for first iteration
Fig. 2. Training samples increased in the concerned domain for second iteration
图 3: 第三次迭代为减少错误分类增加的四组训练样本Fig. 3. Four training samples increased to reduce misclassification for third iteration
Fig. 4. Flowchart to estimate the failure probability
Fig. 5. Pseudocode of the proposed method
图 6: 四类失效模式串联系统的实际与预测极限状态函数Fig. 6. Actual and predicted LSF for the series system with four failure modes
图 7: 四类失效模式串联系统: (a) 失效概率的收敛; (b) 不同方法的相对误差Fig. 7. Series system with four failure modes: (a) Convergence of failure probability (P_f); (b) Relative error (ϵ_P_f) of different methods
图 8: 高维扁球函数: (a) 失效概率的收敛; (b) 不同方法的相对误差Fig. 8. High-dimensional oblate spheroid function (d = 50): (a) Convergence of failure probability (P_f); (b) Relative error (ϵ_P_f) of different methods
图 9: 高维问题: (a) 失效概率的收敛; (b) 不同方法的相对误差Fig. 9. High-dimensional problem (n = 40): (a) Convergence of failure probability (P_f); (b) Relative error (ϵ_P_f) of different methods
图 10: 高维问题: (a) 失效概率的收敛; (b) 不同方法的相对误差Fig. 10. High-dimensional problem (n = 100): (a) Convergence of failure probability (P_f); (b) Relative error (ϵ_P_f) of different methods
Fig. 11. Nonlinear oscillator
图 12: 非线性振子: (a) 失效概率的收敛; (b) 不同方法的相对误差Fig. 12. Nonlinear oscillator: (a) Convergence of failure probability (P_f); (b) Relative error (ϵ_P_f) of different methods
Fig. 13. Schematic view of the roof truss
图 14: 屋架结构: (a) 上界失效概率的收敛; (b) 不同方法的相对误差Fig. 14. Roof truss structure: (a) Convergence of upper bound failure probability (P_f^max); (b) Relative error (ϵ_P_f^max) of different methods
图 15: 屋架结构: (a) 下界失效概率的收敛; (b) 不同方法的相对误差Fig. 15. Roof truss structure: (a) Convergence of lower bound failure probability (P_f^min); (b) Relative error (ϵ_P_f^min) of different methods
作者信息 | Authors
印度杜尔加布尔技术学院 (National Institute of Technology Durgapur) 土木工程系
Pronab Roy, 通讯作者 (Corresp.)印度杜尔加布尔技术学院 (National Institute of Technology Durgapur) 土木工程系Email: proy.ce@nitdgp.ac.in
律梦泽 M.Z. Lyu | 编辑 (Ed)
P.D. Spanos | 审校 (Rev)
陈建兵 J.B. Chen | 审校 (Rev)
彭勇波 Y.B. Peng | 审校 (Rev)
