Reliability optimization using probabilistic sufficiency factor and correction response surface

Abstract

Reliability-based design optimization for low failure probability often requires millions of function analyses. Response surface approximation of the response functions (analysis response surface(ARS)) is often used to reduce the cost of failure probability calculations. Failure probabilities obtained from numerical sampling schemes are noisy and unsuitable for gradient-based optimization. To overcome this, response surfaces have been fitted to the failure probability of the designs (design response surface (DRS)) as a function of the design variables and used in optimization. Two shortcomings of the approach are that (i) the ARS fitting is extremely expensive for a large number of variables, especially for the high accuracy required to obtain very accurate reliability estimates, and (ii) DRS introduces fitting errors which affect the tails of the distributions which are significant for low failure probabilities. An approach to obtaining high-accuracy reliability estimates using the probabilistic sufficiency factor and correction response surface is investigated in this article. The method is demonstrated using a thin-walled box beam structure designed for minimum weight with failure probability constraints. The design is subjected to buckling, strength, and displacement constraints. Two methods of correcting low-fidelity analyses are compared for accuracy and efficiency. It is shown that correction to the response function is more accurate than the correction fitted to the probabilistic sufficiency factor.

Review of multi-fidelity models

“…a second order polynomial) is correct but the data points response has noise. In MFM context, RSMs can be found in an outstanding number of papers, just to cite some of them, Chang et al, 1993 [31], Burgee et al, 1994 [27], Venkatarman et al, 1998 [179], Balabanov et al, 1998 [12], Balabanov et al, 1999 [13], Mason et al, 1998 [124], Vitali et al, 1998 [182], Knill et al, 1999 [93], Vitali et al, 2002 [183], Umakant et al, 2004 [176], Venkatarman et al, 2006 [178], Choi et al, 2008 [36], Sharma et al, 2008 [162], Sharma et al, 2009 [163], Sun et al, 2010 [166], Goldsmith et al, 2011 [67] and Chen et al, 2015 [33].…”

Survey of Multi-fidelity Surrogate Models and their Applications in the Design and Optimization of Engineering Equipment

“…除了拓展 EI、 LCB、 PI 准则外， BEACHY 等 [151] 提出了一种适用于低精度模型不可分层的序贯采样 准则-期望效力(Expected effectiveness，EE)准则， 综合考虑期望提升、不同低精度分析模型主导系数 变化、模型不确定性以及模型的计算成本；WANG 等 [152] 在变可信度近似模型的高效全局优化过程 中， 局部搜索准则为最小化变可信度近似模型的预 估响应， 全局搜索准则为最大化变可信度近似模型 的预估均方误差； GHOREISHI 等 [153] 提出一种适用 于不可分层低精度模型的变可信度近似建模方法， 对目标函数和约束条件中变可信度近似模型采用 不同的准则进行序贯更新， 目标函数的更新基于两 步前瞻实用函数和模型计算成本， 约束条件的更新 基于信息获取策略和模型计算成本；SHI 等 [154] 提 出一种双目标导向的自适应填充策略， 将有约束的 单目标优化问题转化为双目标优化问题， 同时最大 化目标函数的期望改善以及约束条件中的约束违 背；KEANE 等 [155] [64] 在该方法的基础 上引入 K 均值聚类算法对种群划分，通过在局部区 域内建立变可信度近似模型，以提高该方法求解高 维问题的能力； JIANG 等 [165] 提出了三阶段变可信度 近似模型辅助多目标进化算法，该方法对适应度值 的评价时，逐步自适应的选用低精度模型-变可信度 近似模型-高精度近似模型；ZHOU 等 [166] 总结了变 可信度近似模型辅助多目标进化算法的基本框架 (图 9)， 并提出了考虑变可信度近似模型预估不确定 性的个体更新策略和考虑优化解离散程度的种群更 新策略，有效降低了寻优成本。当低精度分析模型 相较于高精度分析模型成本不可忽略时： SHU 等 [167] [60] 在小失效概率的可靠性 优化过程中，采用基于乘法标度函数的变可信度近 似模型替代极限状态函数，以降低优化所需的高精 度分析样本点数目；GANO 等 [46] 提出了基于变可信 度近似模型的双环嵌套可靠性优化设计方法； 随后， LI 等 [178] 在此基础上，利用优化算法求解加法和乘 法标度函数的权重系数以在混合标度过程中反映它 们之间的相对贡献率，显著提升了变可信度近似模 [179] 提出了基于 Co-Kriging 的稳健性优 化设计方法，该方法中目标函数的均值和方差被当 作独立的目标构建多目标优化数学模型，稳健性优 化过程中 Co-Kriging 用于预测目标函数的均值和方 差；PADRON 等 [180] 在稳健性优化设计方法中，利 于基于多项式混沌展开的变可信度近似模型预测目 标函数的均值和方差； TAO 等 [44] [54] ；2D/3D [183] 仿真求解器 Cart3D/Linearized panel [51] ；VLM/VRM [184] ； BLFP/RANS [185] ；AVL/AADL-3D [52] ； RANS/XFOIL [29] ；ADSP/AADL-3D [67] ； FUN2D/Vortex panel method [135] ；Cart3D/Modied Newtonian Method [186] ；BEMT/RANS [187] ； HOST/elsA [188] ；ASWING/VABS [189] ； RANS/ADSP [190] ；AVL/Euler [191] ；STAGS-A/ BOCS [133] 粗网络/细网络 [57, 70-72, 84, 86, 90, 154, 192-194] 仿真/试验 [44,124,…”