Multiobjective Robust Parameter Design with Kernel Density Estimator of Noise Distribution Based on Computer Experiments
DescriptionThis project will develop statistical methods that utilize the Gaussian process (GP) model to perform robust parameter design (RPD) with multiple loss functions that measure the quality of multiple responses, and noise factors that have probability density function estimated by a kernel density estimator (KDE).Due to the widespread availability of computers and physical modeling software, computer models, also called simulators, are increasingly used for designing engineering systems. These models are often computer codes that implement numerical algorithms, notably the finite element method, to solve partial differential equations (PDEs). Due to the complexity of engineering systems, simulators for such systems can be timeconsuming to run. To circumvent this difficulty, an emulator constructed with data obtained by running the simulator according to an experimental design can be employed.In design of engineering systems, there is always the need to study multiple responses with quality level measured by several loss functions (or equivalently, desirability functions), and input factors can often be classified into two types, i.e., control factors and noise factors. Control factors are inputs set by designers while noise factors vary randomly in the actual system. The average quality level is quantified by the expectation of the loss functions with respect to the distribution of the noise factors. Note that it is not always easy or desirable to combine all loss functions into a single objective function. Thus, it can be preferable to seek the Pareto frontier, which is an idea that has been scarcely considered in RPD. Moreover, it can be important to use a realistic estimate of the noise distribution than simply assuming the noise factors follow some standard distribution such as the normal distribution.This project will develop an approach based on the GP model to seek the Pareto frontier for multiple expected loss functions for RPD with time-consuming simulators. Our approach will assume the noise factor distribution is estimated from data with a mixture normal KDE. We shall develop analytical expressions for the posterior mean and covariance functions of the expected quality loss vector using appropriate modeling assumptions so that computations are simplified. We shall use a model-based approach to solve the experimental design problem posed by the nonstandard distribution of the noise factors. Finally, we shall develop an expected improvement (EI) criterion for seeking the Pareto frontier via sequential experimental design together with a fast and deterministic way to compute the criterion to ease optimization.
|Effective start/end date||1/01/20 → …|