This paper presents the formulation of an uncertainty quantification challenge problem consisting of five subproblems. These problems focus on key aspects of uncertainty characterization, sensitivity analysis, uncertainty propagation, extreme-case analysis, and robust design.

This paper develops techniques for constructing metamodels that predict the range of an output variable given input–output data. We focus on models depending linearly on the parameters and arbitrarily on the input. This structure enables to rigorously characterize the range of the predicted output and the uncertainty in the model’s parameters. Strategies for calculating optimal interval predictor models (IPMs) that are insensitive to outliers are proposed. The models are optimal in the sense that they yield an interval valued function of minimal spread containing all (or, depending on the formulation, most) of the observations. Outliers are identified as the IPM is calculated by evaluating the extent by which their inclusion into the dataset degrades the tightness of the prediction. When the data generating mechanism (DGM) is stationary, the data are independent, and the optimization program (OP) used for calculating the IPM is convex (or when its solution coincides with the solution to an auxiliary convex program); the model’s reliability, which is the probability that a future observation would fall within the predicted range, is bounded tightly using scenario optimization theory. In contrast to most alternative techniques, this framework does not require making any assumptions on the underlying structure of the DGM.

This paper presents a robust control design methodology for systems with probabilistic parametric uncertainty. Control design is carried out by solving a reliability-based multi-objective optimization problem where the probability of violating design requirements is minimized. Simultaneously, failure domains are optimally enlarged to enable global improvements in the closed-loop performance. To enable an efficient numerical implementation, a hybrid approach for estimating reliability metrics is developed. This approach, which integrates deterministic sampling and asymptotic approximations, greatly reduces the numerical burden associated with complex probabilistic computations without compromising the accuracy of the results. Examples using output-feedback and full-state feedback with state estimation are used to demonstrate the ideas proposed.

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