Probability-space surrogate modeling for fast multidisciplinary optimization under uncertainty

Abstract

This paper proposes a probability-space surrogate modeling approach for computationally efficient multidisciplinary 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.