A Study of Covariance Functions for Multi-Response Metamodeling for Simulation-Based Design and Optimization

The optimal design of complex systems in engineering requires the availability of mathematical models of system’s behavior as a function of a set of design variables; such models allow the designer to find the best solution to the design problem. However, system models (e.g. CFD analysis, physical prototypes) are usually time-consuming and expensive to evaluate, and thus unsuited for systematic use during design. Approximate models, or metamodels, of system behavior based on a limited set of data allow significant savings by reducing the resources devoted to modeling during the design process. In our work in engineering design based on multiple performance criteria, we propose the use of Multi-response Bayesian Surrogate Models (MRBSM) to model several aspects of system behavior jointly, instead of modeling each individually. By doing so, it is expected that the observed correlation among the response variables can be used to achieve better models with smaller data sets. In this work, we study the approximation capabilities of several covariance functions needed for multi-response metamodeling with MRBSM, performing a simulation study in which we compare MRBSM based on different covariance functions against metamodels built individually for each response. Our preliminary results indicate that MRBSM outperforms individual metamodels in 46% to 67% of the test cases, though the relative performance of the studied covariance functions is highly dependent on the sampling scheme used and the actual correlation among the observed response values.