Abstract

Despite the tremendous advancements in computational resources and techniques over the last several decades, the computational cost of using high-fidelity physics-based simulations remains prohibitive to broad-scale adoption and application of probabilistic design and analysis methods in industry applications. Response surface models (also known as surrogate models) make it feasible to perform decision-critical probabilistic analysis and sensitivity studies that would otherwise be too costly. Effective response surfaces must efficiently represent the relationships between the inputs and output of a computationally intensive simulation and often must be based on a very limited set of training points. Since a response surface model is trained on a limited number of data points, it is important to be able to account for this inherent uncertainty in rigorous uncertainty quantification (UQ) analyses. Of the many response surface approaches that exist (e.g., linear and nonlinear regression, neural networks), Gaussian process (GP) regression has proved to be a valuable methodology as they are nonparametric and provide the necessary flexibility to model a wide range of complex nonlinear relationships present in engineering applications. In addition, once trained, GP models capture both the prediction mean and prediction uncertainty. Not only applicable as surrogate models for noise-free physics-based simulations, GP regression models can accommodate noisy training data from experiments and also account for it in prediction. These characteristics of GP models make them ideal for integration in probabilistic, UQ, and verification and validation (V&V) frameworks. To facilitate the creation and verification of both parametric response surface models and GP regression models, the NESSUS® Response Surface Toolkit (RST) was developed. NESSUS RST also has built-in capabilities to create a space-filling design of experiments using Latin-hypercube sampling, provides both quantitative and visual goodness-of-fit assessments, and offers variance-based sensitivity indices of the response surface to guide V&V and UQ activities. This paper will explore the creation, evaluation, and usage of response surface models in engineering examples.