Improving Markov Chain models for road profiles simulation via definition of states

Road profiles are a major excitation to the chassis and the resulting loads drive vehicle designs. The physical resources needed to measure, record, analyze, and characterize an entire set of real, spectrally broad roads is often infeasible for simulation. This motivates the need for more accurate models for characterizing roads and for generating synthetic road profiles of a specific type. First order Markov Chain models using uniform sized bins to define the states have been previously proposed to characterize and synthetically generate road profiles. This method, however, was found to be unreliable when the number of states is increased to improve resolution. In an effort to solve this problem, this work develops a method by which states are defined using nonuniform sized, percentile-based bins which results in a more fully populated transition matrix. A statistical test is developed to quantify the confidence with which the estimated transition matrix represents the true underlying stochastic process. The order of the Markov Chain representation of the original and synthetic profiles is checked using a series of preexisting likelihood ratio criteria. This method is demonstrated on data obtained at the Virginia Tech VTTI location and shows a considerable improvement in the estimation of the transition properties of the stochastic process. This is evidenced in the subsequent generation of synthetic profiles.