Mathematical Modeling and Numerical Optimization of Three Vehicle Crashes Using a Single-Mass Lumped Parameter Model

In this paper mathematical modelling of a vehicle crash based on a lumped parameter model is studied. The vehicle is modelled as a single mass connected to a non-linear spring and damper system. The characteristics of the non-linear behaviour of the model is identified with a hybrid Firefly/Harmony Search optimization algorithm that minimizes the deviation between experimental test data and a simulated response. The experimental data is taken from three crashes of an identical vehicle that crashes into a wall at different initial velocities. The aim of this paper is to find a piecewise-linear function for the spring and damper coefficients which is scaleable to reconstruct the three different experimental crashes at different impact velocities. Numerical results are provided to illustrate the applicability of the proposed algorithm. Three data sets will be used for parameter identification and a fourth data set will be used for verification