Confidence Level Estimation and Design Sensitivity Analysis for Confidence-Based RBDO
Confidence Level Estimation and Design Sensitivity Analysis for Confidence-Based RBDO
复制标题
基于置信度的 RBDO 的置信度估计和设计敏感性分析
DOI：
10.1115/detc2012-70725
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
D. Gorsich
中科院分区：
文献类型：
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作者：
Hyunkyoo Cho;K. Choi;Ikjin Lee;D. Gorsich
在实际工程问题中，通常只有有限的输入数据可用于生成输入分布模型。输入数据不足会导致输入分布模型的不确定性，而这种不确定性将使我们对使用基于可靠性的设计优化（RBDO）方法获得的最佳设计失去信心。输入分布模型的不确定性要求我们考虑可靠性分析输出（定义为故障概率）遵循概率分布。本文提出了基于置信度的 RBDO 方法的新公式以及置信度的设计敏感性分析。使用贝叶斯方法通过输入分布参数和输入分布类型的连续条件概率获得可靠性分析输出的概率。在某些假设下建议输入分布参数和类型的近似条件概率。应用蒙特卡罗模拟来实际计算输出分布，并使用联结函数来描述相关的输入分布类型。使用导出的输出分布来制定基于置信度的 RBDO 问题。在这个新的公式中，概率约束被修改为包括目标可靠性和目标置信水平。最后，推导出置信水平的敏感性，这是一种新的概率约束，以支持有效的优化过程。使用准确的代理模型，该方法不需要在 RBDO 迭代期间生成额外的代理模型；它只需要对相同的替代模型进行多次评估。因此，获得了该方法的效率。对于数值示例，当只有有限的数据可用时，会计算置信水平并验证导出灵敏度的准确性。版权所有 © 2012 ASME
In practical engineering problems, often only limited input data are available to generate the input distribution model. The insufficient input data induces uncertainty on the input distribution model, and this uncertainty will cause us to lose confidence in the optimum design obtained using the reliability-based design optimization (RBDO) method. Uncertainty on the input distribution model requires us to consider the reliability analysis output, which is defined as the probability of failure, to follow a probabilistic distribution. This paper proposes a new formulation for the confidence-based RBDO method and design sensitivity analysis of the confidence level. The probability of the reliability analysis output is obtained with consecutive conditional probabilities of input distribution parameters and input distribution types using a Bayesian approach. The approximate conditional probabilities of input distribution parameters and types are suggested under certain assumptions. The Monte Carlo simulation is applied to practically calculate the output distribution, and the copula is used to describe the correlated input distribution types. A confidence-based RBDO problem is formulated using the derived the distribution of output. In this new formulation, the probabilistic constraint is modified to include both the target reliability and the target confidence level. Finally, the sensitivity of the confidence level, which is a new probabilistic constraint, is derived to support an efficient optimization process. Using accurate surrogate models, the proposed method does not require generation of additional surrogate models during the RBDO iteration; it only requires several evaluations of the same surrogate models. Hence, the efficiency of the method is obtained. For the numerical example, the confidence level is calculated and the accuracy of the derived sensitivity is verified when only limited data are available.Copyright © 2012 by ASME