7th IEEE International Symposium on Applied (omputationallntelligence and Informatics· May 24-26, 2012 • Timi�oara, Romania Searching for a nonlinear ODE model of vehicle crash with genetic optimization Andras Horvath*, Mikos F Hatwagner t , Istvan A. Harati + Szechenyi Istvan University, Gyor, Egyetem ter 1., H-9026, Hungary *Depaent of Physics and Chemistry t Depaent of Information Technology + Department of Mathematics and Computational Science Email: { horvatha.hatwagnf.harati } @sze.hu Abstct-Vehicle crash is a very complex process, which can be modelled in detils using the fnite element method (FEM), but a simple, quasi-heuristic model with a limited number of parameters is ofen more benefcial. In this paper we propose a relatively simple dynamic model for deformation and force during a frontal collision process, which has very similar behavior to the experimental data. A genetic-type optimization of model parameters is executed on thre car crash experimental data sets. I. INTRODUCTION The analysis of crash events plays a key role in several felds of vehicle engineering practice. Some of the most important are accident reconstruction, accident analysis, development of active and passive vehicle safety systems, and in general vehicle crashworthiness design [1], [2], [3]. A certain vehicle crash event can be examined in many diferent points of view, for example the before and after impact speed of the vehicles, the movement of the damaged cars, the main characteristic of the road, the amount and distribution of te absorbed energy, deformation and deformation force during the collision [4], [5]. From the above mentioned, in the feld of developing passive vehicle safety the absorbed energy and the deforation force are the most important quantities. A detailed model of the highly nonlinear deformation pro cesses is usually based on the fnite element method [6], [7], [8]. This approach gives a complete description of te process, but requires a detailed knowledge of geometry and material properties, which are not known exactly in general, and as a consequence of the huge number of degrees of freedom te simulation requires extremely large computational power. However, if we a contented with less detailed information about the process, a simple model is more suitable [4], [9], [10], [11], [12]. Altough we a looking for an 'as simple as possible' dynamic model of deforation force, there are some natural expectations for this quasi-heuristic model: 1) Limited number of model variables, e.g. 10-15, such tat present computers can solve the system of equations (diferential or algebraic) in fractions of a second and complexity is tractable to the human mind. 2) Limited number of model parameters, e.g. 10-15. 3) Model parameters and equations should have physical meaning. A completely theoretical multivariable func tion approximation of measured data may be useful in some situations, but it is better if the majority of the model parameters and equations is in simple relation with the real world, e.g. "efective spring constant". 4) The model should produce qualitively similar behavior to the real system. 5) The parameters of the model can be identifed in a car crash experiment and the model with the identifed pa rameters should reproduce te experimental data witin moderate (5-10%) relative eror. There are a lot of very simple fnite dimension models in the literature for vehicle crash events, for example the linear force model, the bilinear force model [13], [14], the power law force model [15], te elasto-plastic spring-mass model [16], the viscoelastic model [17], or diferent stifess calculations [18]. These models fulfll the expectations 1-3 above, but there a signifcant phenomena that are not caught by them, e.g. elastic recovery at the end of a process, or oscillations in force time function. Harmati et. al. [19] proposed a more theoretical approach, which is good at reproducing measured data and uses a limited number of parameters but these parameters of LPV (linear parameter varying) model have no physical meaning, and the whole model is not based on physical laws, and tus does not satisfy expectation 3. In this paper we propose a model that fts all the re quirements above. The proposed "sliding base point" model is a six-variable ODE system with a physically meaningful background with 7 parameters. We show that this system produces the same qualitative behaviour as real experiments. A genetic algorithm for parameter identifcation is presented and applied to three experimental data sets. The results show that the model with the identifed paeters can reproduce measured force and deformation data witin 6-7% relative error. II. EXPERIMENTAL DATA One of the many vehicle crash tests is the so called load cell barier (LCB) test. The examined vehicle is driven into a special barer which is equipped with force-sensors. During the collision a well designed set of sensors in the back of 978-1-4673-1014-7/12/$31.00 ©2012 IEEE -131-