Methodology for Optimizing First Order Markov Chains of Spectrally Decomposed Terrain Profiles

Terrain profiles are the main excitation to the chassis and the resulting loads drive vehicle designs. This motivates the need for accurate models to characterize specific terrains, enabling the generation of synthetic terrain profiles for accelerated testing and simulation. Studies of models such as power spectral density (PSD) have shown that accurately modeling spatially long and short wavelengths simultaneously is difficult. In order to better model short wavelength content separately, a spectral decomposition method is developed, where a first order Markov Chain is used to model the high-passed terrain profile. The problem is formulated as a constrained optimization problem; that is, given the constraint region where the Markov property holds, find the best model among the set of spectrally decomposed profiles. The optimization methodology consists of the comparison of statistical properties of measured and synthesized profiles. This process is demonstrated on paved and non-paved profiles taken at the Virginia Tech Transportation Institute (VTTI) and on public roads in Danville, Virginia with longitudinal resolution of 0.025 m. The results yield significant insights to further modeling terrain profiles using Markov Chains.