Multidisciplinary Analysis and Optimization under Uncertainty

Abstract

This study proposes an optimization framework to include different sources of uncertainty in the design of multidisciplinary analysis with feedback coupling. To achieve this goal, four objectives were pursued, two related to multidisciplinary analysis and two related to design optimization. A likelihood-based decoupling approach is first proposed for probabilistic feedback coupled analysis to include both aleatory and epistemic uncertainty, using an auxiliary variable method. No convergence analysis is needed in this approach, so it achieves great computational efficiency. Secondly, A novel uncertainty propagation approach is proposed when individual disciplinary analyses are connected to each other by a large number of coupling variables. The Bayesian network with a copula-based (BNC) sampling strategy is adopted for efficient probabilistic multi-disciplinary analysis that satisfies interdisciplinary compatibility condition. The BNC approach is then exploited as a surrogate model in reliability-based design optimization (RBDO). The joint probability of multiple objectives and constraints is included in the formulation. The Bayesian network along with conditional sampling is also exploited to select training points that enable effective construction of the Pareto front. A comprehensive multidisciplinary optimization under uncertainty framework is finally developed based on the BNC approach. In this fourth objective, the BNC approach is extended for simultaneous interdisciplinary compatibility enforcement and the objectives/constraints evaluation within MDO. The proposed methodology is observed to achieve significant computational efficiency in solving several engineering examples, including an electronic packaging problem, an aeroelastic wing analysis and design problem, and a vehicle side impact problem.