Quantile-based sequential optimization and reliability assessment method under random and interval hybrid uncertainty随机与区间混合不确定性下分位数序列优化可靠性评估方法
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Li XL, Lu ZZ, Wei N, 2024. Quantile-based sequential optimization and reliability assessment method under random and interval hybrid uncertainty. Probabilistic Engineering Mechanics, 76: 103631.DOI: 10.1016/j.probengmech.2024.103631
摘要 | Abstract
在随机和区间混合不确定性条件下，求解混合可靠性设计优化 (hybrid reliability based design optimization, HRBDO) 可以在结构性能和可靠性之间获得最佳权衡。求解混合可靠性设计优化包含功能函数 (performance function, PF) 最小分析、失效概率约束分析和设计参数优化的三重嵌套框架，因此混合可靠性设计优化计算复杂性很高，尤其是对于复杂结构。因此提出了一种分位数序列优化可靠性评估方法 (quantile-based sequential optimization and reliability assessment, QSORA) 来降低混合可靠性设计优化的计算复杂性。在所提分位数序列优化可靠性评估方法中，首先将失效概率约束转化为与目标失效概率相对应的最小功能函数 (minimum PF, MPF) 分位数。然后，通过近似当前迭代中功能函数与其目标分位数之差与前一迭代中二者之差，将失效概率约束分析与设计参数优化解耦。此外，通过近似当前迭代中相对于区间输入的功能函数最小点与前一迭代中最小点，将功能函数最小分析与设计参数优化分离。通过在分位数序列优化可靠性评估方法中将最小分析、失效概率约束分析与设计参数优化分离，将混合可靠性设计优化的三重嵌套框架依次解耦为确定性设计优化、功能函数最小分析和目标最小功能函数分位数估计，将混合可靠性设计优化从三重嵌套框架重构为三个单层框架，这种方式可以显著提高混合可靠性设计优化的求解效率。此外，当前设计参数下的最小功能函数分位数通过基于随机选点的统计矩方法估计，其中随机选点方法用于有效估计最小功能函数矩以近似最小功能函数的概率密度函数。最后，通过四个数值和工程实例验证了分位数序列优化可靠性评估的效率和精度。关键词: 混合不确定性, 分位数, 序列优化可靠性评估, 随机选点方法Under random and interval hybrid uncertainties, solving hybrid reliability based design optimization (HRBDO) can acquire an optimal balance between structural performance and reliability. Since solving HRBDO includes a triple nested framework involving minimum analysis of performance function (PF), failure probability constraint analysis and design parameter optimization, the computational complexity of HRBDO is high, especially for dealing with complex structures. Therefore, a quantile-based sequential optimization and reliability assessment method (QSORA) is proposed for reducing the computational complexity of HRBDO. In the proposed QSORA for HRBDO, failure probability constraint is firstly transformed into minimum PF (MPF) quantile one corresponding to target failure probability. Then, approximating the difference between PF and its target quantile at current iteration by that at previous one, the failure probability constraint analysis is decoupled from the design parameter optimization. Moreover, by approximating the minimum point of the PF with respect to the interval input in the current iteration by that in the previous one, the minimum analysis of PF is separated from the design parameter optimization. By the separation of minimum analysis and failure probability constraint analysis from the design parameter optimization in the proposed QSORA, the triple nested framework of HRBDO is decoupled sequentially as the deterministic design optimization, the minimum analysis of the PF and the target MPF quantile estimation, and this way of reconstructing the HRBDO from the triple nested framework to three single-loop frameworks can significantly enhance the efficiency of solving HRBDO. Furthermore, the MPF quantile at the current design parameter is estimated by stochastic collocation based statistical moment method, in which the stochastic collocation method is employed to efficiently estimate the MPF moment to approximate the probability density function of MPF. The efficiency and accuracy of the QSORA are validated by four numerical and engineering examples finally.Keywords: Hybrid uncertainty; Quantile; Sequential optimization and reliability assessment; Stochastic collocation method![]()
Fig. 1. Relationship between P^T_f_j and the MPF quantile F_{Y_j|θ}^{-1}(P^T_f_j)
图 2: 求解混合可靠性设计优化的分位数序列优化可靠性评估流程图Fig. 2. Flowchart of QSORA for solving HRBDO model
图 3: 区间输入仅影响极限状态曲面平移的算例中参考最优设计参数附近的目标可靠性指标圆与极限状态带Fig. 3. β^T circle and limit state bands near the reference optimal design parameter for example 1
图 4: 区间输入仅影响极限状态曲面平移的算例中目标函数的收敛过程Fig. 4. Convergence history of the objective function for example 1
图 5: 区间输入仅影响极限状态曲面平移的算例中两个约束函数的收敛过程Fig. 5. Convergence history of the two constraint functions for example 1
图 6: 区间输入仅影响极限状态曲面旋转的算例中参考最优设计参数附近的极限状态带Fig. 6. Limit state bands near the reference optimal design parameter for example 2
图 7: 区间输入仅影响极限状态曲面旋转的算例中目标函数的收敛过程 Fig. 7. Convergence history of the objective function for example 2
图 8: 区间输入影响极限状态曲面平移与旋转的算例中目标函数的收敛过程Fig. 8. Convergence history of the objective function for example 3
图 9: 区间输入影响极限状态曲面平移与旋转的算例中三个约束函数的收敛过程Fig. 9. Convergence history of the three constraint functions for example 3
图 10: 区间输入影响极限状态曲面平移与旋转的算例中参考最优设计参数附近的目标可靠性指标圆与极限状态带Fig. 10. β^T circle and limit state bands near the reference optimal design parameter for example 3
Fig. 11. A vehicle side impact problem
作者信息 | Authors
西北工业大学 (Northwestern Polytechnical University) 航空学院
吕震宙 Zhen-Zhou Lu, 通讯作者 (Corresp.) 西北工业大学 (Northwestern Polytechnical University) 航空学院Email: zhenzhoulu@nwpu.edu.cn
西北工业大学 (Northwestern Polytechnical University) 航空学院
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)
