Advanced metamodeling techniques applied to multidimensional applications with piecewise responses

Due to digital changes in the solution properties of many engineering applications, the model response is described by a piecewise continuous function. Generating continuous metamodels for such responses can provide very poor fits due to the discontinuity in the response. In this paper, a new smart sampling approach is proposed to generate high quality metamodels for such piecewise responses. The proposed approach extends the Sequential Approximate Optimization (SAO) procedure, which uses the Radial Basis Function Network (RBFN). It basically generates accurate metamodels iteratively by adding new sampling points, to approximate responses with discrete changes. The new sampling points are added in the sparse region of the feasible (continuous) domain to achieve a high quality metamodel and also next to the discontinuity to refine the uncertainty area between the feasible and non-feasible domain. The performance of the approach is investigated through two numerical examples, a two dimensional analytical function and a laser epoxy cutting simulation model.