Kernel and Metamodel Based Methods for Analysis and Optimization of Systems under Uncertainty

In many engineering applications, the predictions of system responses are uncertain due to our incomplete knowledge related to the system and its environment. For robust analysis and design, all these uncertainties must be explicitly accounted for. A probabilistic approach provides a rational and consistent framework for achieving this goal. In this setting, the analysis and optimization of engineering systems involves a high computational demand, considered prohibitive for complex applications, despite recent advances in computer/computational science. To alleviate these computational challenges, this research investigates the development/use of kernel and metamodel based methodologies within a stochastic simulation framework to facilitate efficient computation in three different tasks: a) probabilistic sensitivity analysis, b) optimization under uncertainty, and c) real-time risk assessment. The implementation and optimization of metamodels for efficient probabilistic performance assessment is studied, focusing on systems with very high dimensional output (something that becomes increasingly relevant with the trend of increasing complexity and scale of modern engineering problems), on the explicit incorporation of the metamodel prediction error in the performance predictions, and on real-time implementation that can support development of standalone applets. Additionally, the formulation of adaptive kernels exploiting information from stochastic sampling is investigated. In particular, kernel density estimation (KDE) is explored to approximate probability densities within multiple settings (sensitivity analysis, optimization), addressing challenges such as boundary reflections, implementation within domains with complex boundaries, and optimal selection of KDE characteristics when used as proposal densities in a stochastic simulation setting. The proposed KDE framework is first utilized to facilitate an efficient global sensitivity analysis, to identify the importance towards the overall probabilistic performance of the different uncertain model parameters or of groups of them, exploring concurrently different measures to quantify this importance (and how they can be robustly evaluated). Then supported by the probabilistic sensitivity analysis, KDE is used to develop an adaptive stochastic sampling algorithm with optimal sampling efficiency in the context of a sequential/iterative application. Finally, KDE is implemented to support the development of a new optimization under uncertainty algorithm, called Non-parametric Stochastic Subset Optimization (NP-SSO). The extension of the algorithm to reliability-based design optimization problems is also explored.