The concept of simulation-based engineering has been embraced by virtually every research and industry sector (Sinha, Liang et al. 2001; Mocko and Fenves 2003). Engineering and science communities have become increasingly aware that computer simulation is an indispensable tool for resolving a multitude of scientific and technological problems. It is clearly desirable to gain a reliable perspective on the behaviour of a system early in the design stage, long before building costly prototypes (Chul and Ro 2002; Letherwood, Gunter et al. 2004; Makarand Datar 2007; Ersal, Fathy et al. 2008; Mueller, Ferris et al. 2009). Simulation tools have become a critical part of the automotive industry due to their ability to reduce the time and money spent in the development process. Terrain is the principle source of vertical excitation to the vehicle and must be accurately represented in order to correctly predict the vehicle response in simulation. In this dissertation, non-deformable terrain surfaces are defined as a sequence of vectors, where each vector comprises terrain heights at locations oriented perpendicular to the direction of travel. The evolution and implications of terrain surface measurement techniques and existing methods for correcting INS drift are reviewed as a framework for a new compensation method for INS drift in terrain surface measurements. Each measurement is considered a combination of the true surface and the error surface, defined on a Hilbert vector space, in which the error is decomposed into drift (global error) and noise (local error). It is also desirable to develop a compact, path-specific, terrain surface representation that exploits the inherent anisotropicity in terrain over which vehicles traverse. In order to obtain this, a set of analytic basis vectors is formed from Gegenbauer polynomials, parameterized to approximate the empirical basis vectors of the true terrain surface. It is also desirable to evaluate vehicle models and tire models over a wide range of terrain types, but it is computationally impractical to store long distances of every terrain surface variation. This dissertation examines the terrain surface, rather than the terrain profile, to maximize the information available to the tire model (i.e. wheel path data). A method to decompose the terrain surface as a combination of deterministic and stochastic components is also developed. / Ph. D.

Terrain surface measurement is an important tool in vehicle design work as well as pavement classification and health monitoring. �Non-deformable terrains are the primary excitation to vehicles traveling over it, and therefore it is important to be able to quantify these terrain surfaces. Knowledge of the terrain can be used in combination with vehicle models in order to predict force loads the vehicles would experience while driving over the terrain surface. �This is useful in vehicle design, as it can speed the design process through the use of simulation as opposed to prototype construction and durability testing. �Additionally, accurate terrain maps can be used by highway engineers and maintenance personnel to identify deterioration in road surface conditions for immediate correction. �Repeated measurements of terrain surfaces over an extended length of time can also allow for long term pavement health monitoring. Many systems have been designed to measure terrain surfaces, most of them historically single line profiles, with more modern equipment capable of capturing three dimensional measurements of the terrain surface. �These more modern systems are often constructed using a combination of various sensors which allow the system to measure the relative height of the terrain with respect to the terrain measurement system. �Additionally, these terrain measurement systems are also equipped with sensors which allow the system to be located in some global coordinate space, as well as the angular attitude of that system to be estimated. �Since all sensors return estimated values, with some uncertainty, the combination of a group of sensors serves to also combine their uncertainties, resulting in a system which is less precise than any of its individual components. �In order to predict the precision of the system, the individual probability densities of the components must be quantified, in some cases transformed, and finally combined in order to predict the system precision. �This thesis provides a proof-of-concept as to how such an evaluation of final precision can be performed. / Master of Science