Computing Sensitivity Analysis of Vehicle Dynamics Based on Multibody Models

Vehicle dynamics simulation based on multibody dynamics techniques has become a powerful tool for vehicle systems analysis and design. As this approach evolves, more and more details are required to increase the accuracy of the simulations, to improve their efficiency, or to provide more information that will allow various types of analyses. One very important direction is the optimization of multibody systems. Sensitivity analysis of the dynamics of multibody systems is essential for design optimization. Dynamic sensitivities, when needed, are often calculated by means of finite differences but, depending of the number of parameters involved, this procedure can be very demanding in terms of time and the accuracy obtained can be very poor in many cases if real perturbations are used. In this paper, several ways to perform the sensitivity analysis of multibody systems are explored including the direct sensitivity approaches and the adjoint sensitivity ones. Finally, the techniques proposed are applied to the dynamical optimization of a five bar mechanism and a vehicle suspension system. ∗Address all correspondence to this author. INTRODUCTION Multibody dynamics has become an essential tool for vehicle systems analysis and design. The evolution during the last decades leaded to complex multibody vehicle models that consider phenomena difficult to take into account years ago and impossible to achieve with analytical models. One interesting application of the state-of-the-art multibody models of vehicles, is the design optimization of certain parts of the vehicle. Sensitivity analysis of the dynamics of multibody systems is essential for design optimization. In general, the multibody dynamics equations, constitute an index-3 differential algebraic system of equations (DAE) that it is not usually directly solved because of the numerical difficulties involved [1, 2]. Some of the most advanced families of formulations used nowadays are based on some ideas presented in the eighties and nineties. One of this families comprise penalty and augmented Lagrangian formulations introduced in [3, 4]. The sensitivity equations for the mentioned penalty and augmented Lagrangian formulations were developed by [5] for the direct sensitivity calculation. In this paper the approach is extended to compute sensitivities using the adjoint variable theory [6]. The validity of the theoretical results introduced in the paper to calculate the sensitivities is checked comparing the di1 Copyright c ⃝ 2013 by ASME Proceedings of the ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference IDETC/CIE 2013 August 4-7, 2013, Portland, Oregon, USA