Improved Methods for Gridding, Stochastic Modeling, and Compact Characterization of Terrain Surfaces

Abstract

Accurate terrain models provide the chassis designer with a powerful tool to make informed design decisions early in the design process. During this stage, engineers are challenged with predicting vehicle loads through modeling and simulation. The accuracy of these simulation results depends not only on the fidelity of the model, but also on the excitation to the model. It is clear that the terrain is the main excitation to the vehicle [1]. The inputs to these models are often based directly on physical measurements (terrain profiles); therefore, the terrain measurements must be as accurate as possible. A collection of novel methods can be developed to aid in the study and application of 3D terrain measurements, which are dense and non-uniform, including efficient gridding, stochastic modeling, and compact characterization.

Terrain measurements are not collected with uniform spacing, which is necessary for efficient data storage and simulation. Many techniques are developed to help effectively grid dense terrain point clouds in a curved regular grid (CRG) format, including center and random vehicle paths, sorted gridding methods, and software implementation. In addition, it is beneficial to characterize the terrain as a realization of an underlying stochastic process and to develop a mathematical model of that process. A method is developed to represent a continuous-state Markov chain as a collection of univariate distributions, to be applied to terrain road profiles. The resulting form is extremely customizable and significantly more compact than a discrete-state Markov chain, yet it still provides a viable alternative for stochastically modeling terrain. Many new simulation techniques take advantage of 3D gridded roads along with traditional 2D terrain profiles. A technique is developed to model and synthesize 3D terrain surfaces by applying a variety of 2D stochastic models to the topological components of terrain, which are also decomposed into frequency bandwidths and down-sampled. The quality of the synthetic surface is determined using many statistical tests, and the entire work is implemented into a powerful software suite. Engineers from many disciplines who work with terrain surfaces need to describe the overall physical characteristics compactly and consistently. A method is developed to characterize terrain surfaces with a few coefficients by performing a principal component analysis, via singular value decomposition (SVD), to the parameter sets that define a collection of surface models.