Multiresponse Metamodeling in Simulation-Based Design Applications

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 search for the best solution to the design problem. However, system models (e.g., computational fluid dynamics (CFD) analysis, physical prototypes) are usually time-consuming and expensive to evaluate, and thus unsuited for systematic use during design. Approximate models of system behavior based on limited data, also known as metamodels, allow significant savings by reducing the resources devoted to modeling during the design process. In this work in engineering design based on multiple performance criteria, we propose the use of multi-response Bayesian surrogate models (MR-BSM) to model several aspects of system behavior jointly, instead of modeling each individually. To this end, we formulated a family of multiresponse correlation functions, suitable for prediction of several response variables that are observed simultaneously from the same computer simulation. Using a set of test functions with varying degrees of correlation, we compared the performance of MR-BSM against metamodels built individually for each response. Our results indicate that MR-BSM outperforms individual metamodels in 53% to 75% of the test cases, though the relative performance depends on the sample size, sampling scheme and the actual correlation among the observed response values. In addition, the relative performance of MR-BSM versus individual metamodels was contingent upon the ability to select an appropriate covariance/correlation function for each application, a task for which a modified version of Akaike’s Information Criterion was observed to be inadequate.