Computational methods for system optimization under uncertainty

In this paper, Subproblems A, B and C of the NASA Langley Uncertainty Quantification (UQ) Challenge on Optimization Under Uncertainty are addressed. Subproblem A deals with the model calibration and (aleatory and epistemic) uncertainty quantification of a subsystem, where a characterization of the parameters of the subsystem is sought by resorting to a limited number (100) of observations. Bayesian inversion is here 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 (and, thus, that deserve a refinement in their uncertainty model). Two approaches are here 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: in other words, a multivariate dynamic problem in the real domain is translated into a multivariate static problem in the SVD space. Finally, Subproblem C requires identifying the (epistemic) reliability (resp., failure probability) bounds of a given system design point. The issue is addressed by an efficient combination of: (i) Monte Carlo Simulation (MCS) to propagate the aleatory uncertainty described by probability distributions; and (ii) Genetic Algorithms (GAs) to solve the optimization problems related to the propagation of epistemic uncertainty by interval analysis.