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Probability-space surrogate modeling for fast multidisciplinary optimization under uncertainty

机译：不确定条件下快速多学科优化的概率空间替代模型

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摘要

This paper proposes a probability-space surrogate modeling approach for computationally efficient multi-disciplinary design optimization under uncertainty. This paper uses a probability-space surrogate as opposed to an algebraic surrogate so that the probability distributions of the required outputs at a given design input can naturally be obtained without repeated Monte Carlo runs of an algebraic surrogate at different realizations of the uncertain variables. We consider three probability-space surrogates with analytical solutions for prediction and inference - Multivariate Gaussian, Gaussian Copula, and Gaussian Mixture Model, and investigate their applicability to perform multidisciplinary design optimization under uncertainty. All the input design and random variables, coupling variables, objective and constraint functions are incorporated within the probability-space surrogate, which helps analytically obtain the distributions of coupling variables, objective and constraint functions at desired design inputs while enforcing multidisciplinary compatibility. The training points for the probability-space surrogates are obtained by performing one-pass analysis through the disciplinary models at different realizations of the input variables. The proposed methodology is demonstrated for reliability-based design optimization (RBDO) and reliability-based robust design optimization (RBRDO) in an aircraft design example. The performance of the probability-space surrogates is compared against a Kriging algebraic surrogate and fully coupled Monte Carlo analysis.
机译：本文提出了一种在不确定性条件下用于计算有效的多学科设计优化的概率空间替代建模方法。本文使用的是概率空间替代方法，而不是代数替代方法，因此在不确定变量的不同实现下，无需重复进行代数替代方法的蒙特卡罗运算，自然就可以获得在给定设计输入下所需输出的概率分布。我们考虑了具有预测和推理分析解决方案的三种概率空间替代物-多元高斯，高斯Copula和高斯混合模型，并研究了它们在不确定性下执行多学科设计优化的适用性。所有输入设计和随机变量，耦合变量，目标函数和约束函数都包含在概率空间代理中，这有助于在期望的设计输入处分析性地获得耦合变量，目标函数和约束函数的分布，同时加强多学科兼容性。通过在输入变量的不同实现下通过学科模型进行单次分析来获得概率空间替代物的训练点。在飞机设计实例中，针对基于可靠性的设计优化（RBDO）和基于可靠性的鲁棒设计优化（RBRDO）演示了所提出的方法。将概率空间代理的性能与Kriging代数代理和完全耦合的蒙特卡洛分析进行比较。

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