Computational methods for the robust optimization of the design of a dynamic aerospace system in the presence of aleatory and epistemic uncertainties

In this paper, we consider the computational model of a dynamic aerospace system and address the issues posed by the NASA Langley Uncertainty Quantification Challenge on Optimization Under Uncertainty, which comprises six tasks. Subproblem A deals with the model calibration and (aleatory and epistemic) uncertainty quantification of a subsystem by means of a limited number of observations. A simple, two-step approach based on Maximum Likelihood Estimation (MLE) is proposed to address this task. Subproblem B requires the identification and ranking of those (epistemic) parameters that are more effective in improving the predictive ability of the computational model of the subsystem. Two approaches are compared: the first is based on a sensitivity analysis within a factor prioritization setting, whereas the second employs the Energy Score (ES) as a multivariate generalization of the Continuous Rank Predictive Score (CRPS). Since the output of the subsystem is a function of time, both subproblems are addressed in the space defined by the orthonormal bases resulting from a Singular Value Decomposition (SVD) of the subsystem observations. Subproblem C requires identifying the (epistemic) reliability (resp., failure probability) bounds of a given system design. The issue is addressed by an efficient combination of: (i) Monte Carlo Simulation (MCS) to propagate the aleatory uncertainty described by probability distributions; (ii) Genetic Algorithms (GAs) to solve the optimization problems related to the propagation of epistemic uncertainty by interval analysis; and (iii) fast-running Artificial Neural Networks (ANNs) to reduce the computational time related to the repeated model evaluations. In Subproblem D, system reliability is improved by identifying a new design point within an iterative robust optimization framework. In Subproblem E both the uncertainty model and the design obtained are tuned using additional data. Finally, a risk-based design is carried out in Subproblem F by neglecting “outliers” (i.e., less likely values of some epistemic parameters) in the design optimization.