During the vehicle design process, excitation loads are needed to correctly model the system response. The main source
of excitation to this dynamic system comes from the terrain. Characteristic models of terrain topology, therefore, would
allow for more accurate models and simulations of the system response. Terrain topology can be characterized as a
realization of an underlying stochastic process. It has been demonstrated that ARIMA modeling can be used to
characterize non-stationary road profiles. In this work it is suggested that ARIMA models of terrain topology can be
further developed by characterizing the previously deterministic autoregressive coefficients as random variables. In this
way uncertainty is introduced into the system parameters and propagated through the process to yield a distribution of
terrain topology. This distribution is then dependent on the distribution of the residuals as well as the distribution of the
ARIMA coefficients. The use of random variables to classify road types is discussed as possible future work.
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