Nonprobability-based Design Optimization Considering Reliability Robustness for Structures
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摘要: 传统基于概率模型可靠性设计优化（Reliability-based design optimization，RBDO）通过制定结构性能的概率约束，使得设计结果符合可靠性要求。然而，在参数信息缺乏时，准确的参数概率密度函数难以获取，且在不确定性因素影响下可靠性的稳健性并未被考虑。在参数信息缺乏的情况下，本文中利用非概率凸模型去有效地度量参数的不确定性。根据非概率可靠性分析理论，将极限状态函数进行泰勒展开，利用非概率可靠性指标的灵敏度分析，建立非概率可靠性的鲁棒性指标。将非概率可靠性设计优化与非概率鲁棒性设计集成到统一的设计模型中，结合SORA（Sequential optimization and reliability assessment）方法和微型多目标遗传算法进行求解。最后，通过两个工程算例分析结果，表明所提优化模型的可行性。Abstract: The traditional reliability-based design optimization (RBDO), which is based on probabilistic model, can guarantee the reliability of structure by formulating probabilistic constraints. However, it is difficult to obtain the accurate probability density function of parameter when the parameter information is limited. Meanwhile, the reliability robustness is not fully considered in optimization. In this paper, the non-probabilistic convex model is utilized to measure the uncertainty of parameter with insufficient information. Based on the theory of non-probabilistic reliability analysis, Taylor expansion is conducted for the limit-state function, and the robustness index of non-probabilistic reliability is formulated through the sensitivity analysis of non-probabilistic reliability index. Then, a unified design framework integrating the reliability-based design with robust design is established. The optimization can be implemented efficiently by combining the sequential optimization and reliability assessment (SORA) and the micro multi-objective genetic algorithm. Two engineering applications are presented to demonstrate the effectiveness of the optimization model.
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表 1 数值算例1的部分优化解
序号 设计点 f1 增加 f2 减少 β1 β2 1 [2.70, 3.91] 10.55 - 16.10 - 3.00 3.55 2 [3.41, 3.27] 11.14 5.64% 14.55 9.66% 3.17 3.15 3 [3.66, 3.15] 11.55 9.47% 14.15 12.11% 3.36 3.01 4 [3.73, 3.14] 11.71 11.06% 14.06 12.66% 3.48 .04 5 [3.90, 3.10] 12.09 14.67% 13.86 13.93% 3.71 3.08 6 [4.11, 3.04] 12.49 18.42% 13.63 15.34% 3.88 3.02 7 [4.34, 2.98] 12.92 22.54% 13.42 16.63% 4.06 3.00 8 [4.59, 2.98] 13.69 29.83% 13.24 17.80% 4.54 3.28 9 [4.87, 2.92] 14.21 34.77% 13.04 19.01% 4.67 3.20 
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表 2 数值算例2的部分优化解
序号 设计点 f1 增加 f2 减少 β1 β2 1 [1.01, 0.71, 1.64] 3.36 - 44.12 - 3.05 3.74 2 [1.02, 0.86, 1.68] 3.56 6.10% 36.40 17.49% 3.28 3.92 3 [1.04, 1.00, 1.74] 3.78 12.41% 30.64 30.56% 3.27 3.86 4 [1.03, 1.03, 1.75] 3.80 13.22% 29.62 32.87% 3.08 3.66 5 [1.01, 1.14, 1.89] 4.04 20.39% 26.10 40.85% 4.48 5.03 6 [1.05, 1.23, 1.87] 4.15 23.55% 24.22 45.10% 3.18 3.71 7 [1.06, 1.38, 1.99] 4.43 31.82% 21.22 51.90% 3.27 3.76 8 [1.29, 1.44, 1.95] 4.68 39.33% 20.72 53.04% 3.25 3.73 9 [1.40, 1.48, 1.95] 4.83 43.79% 20.31 53.98% 3.41 3.89
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