Chapter 43 Optimal Restraint Conditions for the SID-IIs Dummy with Different Objective Functions Yibing Shi, Jianping Wu, and Guy S. Nusholtz Abstract This study formulates and numerically solves the optimal restraint condition problem for the SID-IIs side impact crash dummy under given impact conditions. It extends a previous study (Shi, Y., Wu, J., Nusholtz, G.S.: ASME J. Dyn. Syst. Meas. Control 135, 031007-1–031007-8, 2013) on the optimal restraint for this dummy which has the peak of the thoracic compression as the objective function. This extension allows for the peak of the different responses of the dummy, or their weighted average to be used as the objective function to reflect different strategies for reducing the impact load on the dummy. The requirements of the FMVSS 214 regulation are considered with these formulations. At the center of these formulations is a spring-mass model of the SID-IIs dummy established previously. The loading on the dummy, i.e., the restraint condition, is optimized through a discretization scheme which reduces the problem to a linear programming problem. Numerical examples are presented which illustrate the numerical effectiveness of the formulation. The results from these identify the optimal restraint action under different objectives and different impact conditions. They also combine to provide insight on some fundamental response characteristics of this dummy, such as the relationship between thoracic loading and pelvic loading. Additional optimization results are presented which identify the minimum restraint space requirement under given impact conditions. Such information can be referenced in practical engineering of side impact protection. Keywords Optimal control • Impact response • SID-IIs crash dummy • FMVSS • Side impact 43.1 Introduction The SID-IIs [2] is a side impact crash test dummy used in vehicle side crash tests to represent small-stature occupants. It is currently used in the Federal Motor Vehicle Safety Standard 214 (FMVSS 214) [3] and the Insurance Institute of Highway Safety (IIHS) side crash tests. These applications lead to an interest in understanding the characteristics required of the restraints to reduce force/acceleration and/or rib compressions as measured by this dummy in a crash. At the theoretical limit of this is the question: What is the optimal restraint that will produce the lowest dummy response under a given impactor motion history? The answer to this question promises to provide direction for restraint design, and the bound of the possible performance. This question is the topic of the study reported in [1]. The peak thoracic compression during the transient impact loading, which is an injury assessment measure in the existing IIHS side impact test that often requires particular engineering efforts to ensure a satisfactory level of performance, was used as the objective function—the optimal restraint condition in that case therefore is the one that provides the lowest peak thoracic compression. In the formulation and numerical solution in [1], the peak thoracic acceleration and the pelvic force were subjected to given limits which are realized in the optimization formulation as constraints. Thoracic compression, however, is not included as one of the performance measures in the FMVSS214 regulation; instead, included are the peak thoracic acceleration and peak pelvic force. This regulation requires each of these two measures not to exceed their respective “injury assessment reference value” (IARV, which is crash performance limit), which are 82 g and 5.525 kN. With this background, the work reported in [1] is modified in this study to provide information specifically pertinent to this regulation. A modification in this case could follow several possible approaches. If the single-objective scheme is kept, the objective function would need to be changed from the peak thoracic compression in [1] to the peak thoracic acceleration, or the peak pelvic force. With such a scheme, with either of the two requirements as the objective function, the other would need to be brought into the picture in the form of a constraint condition. Therefore, conceivably, two alternative optimization problems Y. Shi ( ) • J. Wu • G.S. Nusholtz FCA US LLC, CIMS 483-05-10, 800 Chrysler Drive, Auburn Hills, MI 48375, USA e-mail: yibing.shi@fcagroup.com © The Society for Experimental Mechanics, Inc. 2016 M. Allen et al. (eds.), Dynamics of Coupled Structures, Volume 4, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29763-7_43 425
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