Design Optimization and Stochastic Analysis based on the Moving Least Squares Method

Many industrial design optimization and stochastic analysis problems have the following common features: (i) the response functions are evaluated as a result of expensive numerical computations, and (ii) function values may contain some level of numerical noise. In this paper these features are addressed by the use of high quality approximations of the response functions with a particular focus on the Moving Least Squares Method (MLSM). The technique is illustrated by the application of MLSM to the automatic calibration and robustness assessment of the driver's airbag inflation process. Calibration of the dynamic response of the airbag is formulated as an optimization problem. The objective is to minimize the difference between the experimental test and numerical simulation results. Once calibration has been achieved, an assessment of its robustness is performed, which utilizes the same approximation by MLSM technology as in the optimization process