Calculation of road profiles by reversing the solution of the vertical ride dynamics forward problem

Road profiles are an important input into vehicle simulation studies and a key part of road surface condition. However, their availability is often limited by the insufficient existence of simpler road profiling procedures. Therefore, the main purpose of this paper is to present a simple analytical procedure for the calculation of road profiles from given or measured vehicle accelerations. In the paper, an analytical procedure is derived based on a quarter car ride model, which uses accelerations obtained from sprung mass only, unsprung mass only and both sprung and unsprung masses to inversely calculate road profiles. The performance of the approach is demonstrated through a numerical and experimental study at different vehicle speeds, for different suspension settings, under various levels of noise and for a nonlinear LuGre damping model. The developed procedure produces very good results at lower vehicle speeds and it is further shown to produce correlations of above 97% with actual profiles when both the actual and reconstructed profiles are low-pass filtered at a cut-off frequency of one-third of the sprung mass resonance. The need for system characterisation makes this procedure suitable for use with light vehicles. Furthermore, its speed limitations make it suitable for application on township or suburb roads, or unpaved rough terrains where low speeds are often recommended