Efficient optimization-based method for simultaneous calibration of load and resistance factors considering multiple target reliability indices考虑多目标可靠性指标的荷载与抗力系数同时校准的高效优化方法
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Doan NS, Mac VH, Dinh HB, 2024. Efficient optimization-based method for simultaneous calibration of load and resistance factors considering multiple target reliability indices. Probabilistic Engineering Mechanics, 78: 103695.DOI: 10.1016/j.probengmech.2024.103695
本研究引入了一类新的优化过程，用于校准极限状态设计中的概率荷载与抗力因子 (load and resistance factors, LRF)，从而有效适应多目标可靠性指标。鉴于直接蒙特卡罗模拟 (Monte Carlo simulation, MCS) 不适用于此问题，因此提出了一类响应面法 (response surface method, RSM) 分别近似荷载和抗力分量，而不拟合传统安全系数。该方法无需进行额外的隐式估计，从而提高了多目标荷载与抗力因子校准效率。自适应边界算法进一步加强了该流程，该算法通过实时更新搜索域简化优化。通过三个算例 — 包括一个显式和两个隐式功能函数 (一个结构算例和一个岩土算例) — 验证表明，该方法通过动态缩小搜索范围，以更少的迭代次数获得更精确的结果。具体地，将结果与文献中显式算例的结果以及应用于初始隐式问题的基本蒙特卡罗模拟结果进行对比，可以确认所提方法的精度。算例性能表明，结构算例在十次迭代内实现了三目标校准。此外，该方法在计算岩土算例的极限状态点时无需进行约一万次隐式估计。关键词: 荷载与抗力因子校准, 可靠性分析, 响应面法, 多可靠性指标校准, 自适应边界算法This study introduces an innovative optimization process for calibrating probabilistic load and resistance factors (LRFs) in limit state designs, effectively accommodating multiple target reliability indices. Given the impracticality of direct Monte Carlo simulations (MCS) for this task, a response surface method (RSM) is proposed to approximate load and resistance components separately rather than fitting conventional safety factors. This approach eliminates the need for additional implicit evaluations, thereby improving the efficiency of LRF calibration across multiple targets. The process is further enhanced by an adaptive boundary algorithm that updates search domains in real-time, streamlining the optimization. Validation through three examples—including one explicit and two implicit performance functions (a structural and a geotechnical example)—demonstrates that the method achieves accurate results with fewer iterations by dynamically narrowing search domains. Specifically, the accuracy of the proposed method is confirmed by comparing results with those from the literature for the explicit example and with basic MCS results applied to the initial implicit problems. Performance on the illustrative examples shows that the structural example achieves calibration for three targets within ten iterations. Additionally, this method eliminates the need for approximately ten thousand implicit evaluations when calculating limit state points for the geotechnical example.Keywords: Load and resistance factor calibration; Reliability analysis; Response surface method; Calibration for multiple reliability indices; Adaptive boundary algorithm.Proposing a facile optimization for calibrating LRFs across multiple safety levels.
- Multiple target reliability indices is addressed in the calibration process of LRFs.
- Direct approximations of load and resistance significantly reduce computing time.
Sensitivity analysis reduces the number of evaluations, making faster calibrations.
Fig. 1. Sampling points for the case of two variables
Fig. 2. Necessary numbers of evaluations using initial problems for the two models
Fig. 3. Adaptive boundary algorithm for multiple targets optimization
图 4: 跨目标可靠性指标校准荷载与抗力因子的主要流程Fig. 4. Main procedure of calibrating LRFs across target RIs
Fig. 5. Validating of the design solutions using the LRFs calibrated for four targets
Fig. 6. Optimization for multiple target RIs of the simple explicit example
Fig. 7. Optimization for multiple target RIs of the simple explicit example
Fig. 8. An example of a planar truss
Fig. 9. Sensitivity analysis of the responses in the truss problem
图 10: 桁架算例中采用原始蒙特卡罗模拟与基于响应面法的蒙特卡罗模拟的荷载与抗力响应面函数对比Fig. 10. Comparison of the crude MCSs and RSMs-based MCSs applied to load and resistance RSFs in the truss example
Fig. 11. Optimization for multiple target RIs of the truss example
图 12: 桁架算例可靠性指标云图搜索下的多目标可靠性指标优化Fig. 12. Optimization for multiple target RIs of the truss example, searching on the contour plot of β
Fig. 13. A BRW example
图 14: 防波堤算例采用原始蒙特卡罗模拟与蒙特卡罗模拟的荷载与抗力响应面函数对比Fig. 14. BRW example, comparison of the crude MCSs and the MCSs applied to load and resistance RSFs
Fig. 15. Sensitivity analysis for resistance in the BRW example
Fig. 16. Optimization for multiple target RIs of the BRW example
图 17: 防波堤算例可靠性指标云图搜索下的多目标可靠性指标优化Fig. 17. Optimization for multiple target RIs of the BRW example, searching on the contour plot of β
作者信息 | Authors
越南海事大学 (Vietnam Maritime University) 土木工程学院
越南交通通信大学 (University of Transport & Communications) 土木工程学院
Huu-Ba Dinh, 通讯作者 (Corresp.)越南范朗大学 (Van Lang University) 土木工程学院Email: ba.dinhhuu@vlu.edu.vn
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)
