Vehicle crash is a highly nonlinear event in terms of the structural and dummy responses. However, Linear and quadratic polynomials regression are still widely used in the design optimization and reliability based optimization of vehicle safety analysis. This paper investigates the polynomial based subset selection regression models for vehicle safety analysis. Three subset selection techniques: all possible subset with linear polynomial, stepwise with quadratic polynomial and sequential replacement with quadratic and cubic polynomials, are discussed. The methods have been applied to data from finite element simulations of vehicle full frontal crash, side impact and frontal offset impact. It is shown subset selection with sequential replacement algorithm gives the best accuracy responses. It is also shown from limited finite element simulation data, the quadratic polynomial is good enough for most structural and dummy responses when gauges and materials are used as design variables. For vehicle weight, linear polynomial fits well.

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