Optimal Frontal Vehicle Crash Pulses - - a Numerical Method for Design

In a frontal vehicle crash, for a given crash velocity and given maximum vehicle crush, with a known restraint characteristic, what is the vehicle pulse, subject to lower and upper bound constraints, that produces the lowest peak occupant deceleration? A solution procedure using numerical optimization is proposed. The pulse is discretized in the vehicle crush domain. The optimization search is facilitated by a specially developed algorithm that is a hybrid of the sequential quadratic programming (SQP) algorithm for nonlinear constrained optimization and the genetic algorithm (GA). Optimization examples are shown with linear and nonlinear occupant restraints. Numerical results from the examples indicate that when the number of pulse discretization segments is less than five, the solution method is effective in providing pulse improvements for practical problems. A discussion on the theoretical and practical aspects of optimal pulses is also given, with reference to a theoretical optimal pulse recently published by Wu et al. [1]. INTRODUCTION Occupant protection in vehicle crash is an important aspect in automobile design. It has been a continuing endeavor on the part of automobile manufactures. Some occupant crash-test responses are also regulated by crash safety standards in many countries and geo-political regions. Engineering design in this field is generally executed with integrated testing and analytical modeling. Analytical modeling at present generally includes finite element, rigid-body dynamics, and simple spring-mass model analyses. Each of these approaches reduces the vehicleoccupant restraint problem to a different level of abstraction that is best suited to answering questions raised from a particular perspective concerning the central occupant response issue. These predictive models, in their most direct applications, simulate the occupant response under given vehicle structure and restraint specifications. Given this capability, a question that is naturally expected is then: what is the best structure and restraint design for the occupant? This optimal design question is the focus of this study. A definition of "best for the occupant" is in order at this point. What metrics most comprehensively and accurately reflect the level of occupant protection is in itself a topic that still requires considerable investigation. Nevertheless, the peak occupant thorax acceleration has been used in the industry. This metric has also been one of the injury assessment values in the US Federal Motor Vehicle Safety Standard 208 for frontal crash occupant protection. It serves as an indicator of the force acting on the occupant if the occupant is approximated as a single point mass. In the scope of this study, "best for the occupant" means a condition that gives the lowest possible peak occupant thoracic acceleration. The frontal vehicle crash design optimization problem may be dealt with analytically with two approaches. The first would use physical vehicle parameters as the optimization variables, and would therefore involve the solution of the dynamic crash response of the vehicle in addition to the solution of the occupant response to the vehicle motion. This makes an efficient and accurate structural dynamic solver a prerequisite, which at the present time, still represents a challenge. The alternative approach is to use a two-step strategy by first finding an optimal structural response for the occupant. The second step is to either solve an inverse structural design problem based on the optimal structural response, or provide a direction for structural design. The study in this paper assumes this two-step approach, and deals only with the first step, i.e., finding the optimal structural crash response for the occupant. Many studies have been published in the last three decades or so on this optimal pulse problem. Several [1-11] of these are particularly relevant to the current work, and a brief review is given here. In [2-3], different simple theoretical vehicle acceleration pulses are evaluated analytically in terms of their effect on the occupant. In contrast, in [4-9], numerical methods are used to compute the occupant response (based on either single-degree-of-freedom (SDOF) spring-mass model or multi-body occupant dynamics simulation), allowing for vehicle pulses of general shapes. The vehicle pulses are in general preselected for evaluation; therefore, these are not optimization studies in the sense of the lack of an automatic search. In [10], a sensitivity analysis is used, which is in essence a gradient-based iterative search. The vehicle pulse is discretized in the crash displacement domain. Overall, to date, the optimal