Using Cross Validation to Design Conservative Surrogates

The use of surrogates (also known as metamodels) for facilitating optimization and statistical analysis of computationally expensive simulations has become commonplace. Surrogate models are usually fit to be unbiased (i.e., the error expectation is zero). However, in certain applications, it might be important to safely estimate the response (e.g., in structural analysis, the maximum stress must not he underestimated in order to avoid failure). In this work we use safety margins to conservatively compensate for tilting errors associated with surrogates. We propose the use of cross validation for estimating the required safety margin for a desired level of conservativeness (percentage of safe predictions.). The approach was tested on three algebraic examples for two basic surrogates: namely, kriging and polynomial response surface. For these examples we found that cross validation is effective for selecting the safety margin. We also applied the approach to the probabilistic design optimization of a composite laminate. This design under uncertainty example showed that the approach can be successfully used in engineering applications.