Experience With Response Surface Methods for Occupant Restraint System Design

Response surface methodologies (RSMs) have been proposed as surrogate models in vehicle design processes to gain insight and improve turnaround time for optimization and robust design. However, when studying the vehicle occupants during crash events, nonlinearities in responses, coupled with the relatively high dimensionality of vehicle design, can yield misleading results with little or no warning from the response surface algorithms. To ensure the accuracy and reliability of RSMs, fast and dependable error estimation procedures are essential for enlightening how well a response surface predicts highly nonlinear phenomena, given a limited number of model simulations. Such error estimation methods are also useful for providing guidance on how many simulation runs are needed for reliable RSM construction. In this paper, a fast cross validation error estimate procedure is first presented, applied to the multivariable adaptive regression spline (MARS) response surface method. The fast error estimation procedure is then compared to a more thorough and time-consuming validation procedure. Several types of occupant restraint system models, such as belted and unbelted cases and 5^th and 50^th percentile occupants, are considered. Finally, an error reduction approach which employs a more computationally expensive Kriging RSM instead of MARS is investigated. Throughout, guidelines and thumb-rules for applying MARS and other RSMs to occupant crash models are proposed.