Kriging quick adaptive sampling for multivariate optimization

The paper describes a general adaptive sampling methodology useful in multivariate optimization involving finite element analysis that typically requires a long time. The proposed adaptive sampling method was obtained by starting from a model-based statistical methodology developed to design an adaptive inspection plan for the geometric control of mechanical parts. The novelty of the new kriging adaptive sampling procedure consists in overcoming some critical issues, such as the reduction of the estimation time to have an efficient tool for quick application. The others are related to how to set up a kriging-based adaptive sampling, how to choose the stopping rule, and how to remove the dependence on the statistical variability. These issues are the subject of this work to develop a useful tool for multivariate optimization. By improving the methodology in these aspects, it was possible to obtain a feasible and useful instrument for the application in a quick sampling procedure within the inspection process. After this enhancement process, the method is sufficiently general to be extended in the multivariate optimization field that requires a multi-factorial finite element analysis. To demonstrate this, an illustrative real case study from an industrial application is presented and it was found that the proposed method reduces significantly the time required to reach the optimal solution.