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Many passenger vehicles are equipped with automatic safety features. One system, Electronic Stability Control (ESC), saved 7,024 lives from 2011 to 2015. While effective, ESC and other similar control systems are reactionary in nature and require knowledge of a vehicle's current state to determine the response at the next state. Also, many control systems do not take the road characteristics into account, despite being an important contributor to a vehicle's dynamics. This work presents a predictive vehicle controller to help prevent roadside departures during cornering that incorporates the road's geometry and roughness to estimate the vehicle's safe operating speed. An Optimized Speed Profile generates a speed trajectory to allow the vehicle to successfully navigate the corner while preserving ride quality. Simulation results demonstrate cases in which vehicles equipped with ESC would depart from the road while the proposed system does not. Simulations demonstrate that road roughness effects account for up to 10% of the velocity changes in the maximum allowable cornering speed; simulations based on a real-world highway off-ramp measurement demonstrate that the proposed control system is capable of lane-keeping while maintaining stability.

Hydroplaning is a phenomenon that occurs when a layer of water between the tire and pavement pushes the tire upward. The tire detaches from the pavement, preventing it from providing sufficient forces and moments for the vehicle to respond to driver control inputs such as breaking, accelerating, and steering. This work is mainly focused on the tire and its interaction with the pavement to address hydroplaning. Using a tire model that is validated based on results found in the literature, fluid–structure interaction (FSI) between the tire-water-road surfaces is investigated through two approaches. In the first approach, the coupled Eulerian–Lagrangian (CEL) formulation was used. The drawback associated with the CEL method is the laminar assumption and that the behavior of the fluid at length scales smaller than the smallest element size is not captured. To improve the simulation results, in the second approach, an FSI model incorporating finite element methods (FEMs) and the Navier–Stokes equations for a two-phase flow of water and air, and the shear stress transport k–ω turbulence model, was developed and validated, improving the prediction of real hydroplaning scenarios. With large computational and processing requirements, a grid dependence study was conducted for the tire simulations to minimize the mesh size yet retain numerical accuracy. The improved FSI model was applied to hydroplaning speed and cornering force scenarios.

This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents the unknown function as a member of a reproducing kernel Hilbert space (RKHS) and defines a distributed parameter system (DPS) that governs state estimates and estimates of the unknown function. This paper 1) derives sufficient conditions for the existence and stability of the infinite dimensional online estimation problem, 2) derives existence and stability of finite dimensional approximations of the infinite dimensional approximations, and 3) determines sufficient conditions for the convergence of finite dimensional approximations to the infinite dimensional online estimates. A new condition for persistency of excitation in a RKHS in terms of its evaluation functionals is introduced in the paper that enables proof of convergence of the finite dimensional approximations of the unknown function in the RKHS. This paper studies two particular choices of the RKHS, those that are generated by exponential functions and those that are generated by multiscale kernels defined from a multiresolution analysis., Comment: 24 pages, Submitted to CMAME

The interaction between the tire and terrain has long been of interest for vehicle dynamic simulation. Detailed tire models produce accurate results, but are too computationally intensive for the iterative vehicle design process. The objective of this work is to develop a computationally efficient way to estimate the tire's deformed shape, from which the tire forces can be evaluated. A novel, planar, quasi-static, constraint mode tire model is developed to address this objective. The required model parameters are reduced to two non-dimensional shape parameters and an overall stiffness factor. An admissible domain of the shape parameters is developed based on the deformation limitations of a physical tire. Specifically, no single harmonic may dominates the tire shape and the low spatial frequency components must contribute more than higher frequency components to the overall tire shape. The ability of the model to accurately predict the spindle force is evaluated by comparing simulation and experimental responses for quasi-static flat plate and cleat tests. This work provides a simple, accurate tire model for circumferential displacement and vertical spindle force prediction to improve the vehicle design process.

Engineers of off-road equipment, on-road vehicles, pavement and tyres must assess the roughness of a terrain surface for the design of their products. A ubiquitous roughness index is the International Roughness Index (IRI), which quantifies the roughness of a section of road based on the average suspension travel for a particular vehicle at a prescribed speed. The Discrete Roughness Index (DRI) developed in this work addresses a fundamental limitation of the IRI. Specifically, the DRI is calculated for each discretely measured location along a terrain surface; furthermore, the DRI is applicable to vehicles travelling at varying speeds and parameters other than the Golden Quarter-Car on which the IRI is based. The development begins with a consistent discretisation of the terrain surface, vehicle response and the IRI. The Fractional Response Coefficient is then developed which serves a fundamental role in the development of the DRI. Finally, the DRI is developed and its properties are discussed thr...

Road surface measurement plays a crucial role in the modelling and simulation of vehicles as the road surface is one of the primary means of excitation. A prevalent technique for measuring road surfaces utilises scanning lasers whose measurements produce a non-uniform, 3-dimensional point cloud representation, in which statistical outliers typically manifest. In this work, a novel, axiomatic, probabilistic method for simultaneously identifying outliers and estimating the road surface height at uniformly spaced grid nodes is developed. The method expands on the concepts used in the seminal model fitting algorithm, random sampling and consensus (RANSAC), to address a situation in which multiple underlying models may exist in a neighbourhood of the data. The proposed method, called random sampling and probabilistic consensus (RSPC), is evaluated on a 2-dimensional simulated road surface dataset containing 60% outliers in order to demonstrate its effectiveness at identifying outliers and simultaneously estimating grid node heights.

The fast-paced, iterative, vehicle design environment demands efficiency when simulating suspension loads. Towards that end, a computationally efficient, linear, planar, quasi-static tyre model is developed in this work that accurately predicts a tyre's lower frequency, reasonably large amplitude, nonlinear stiffness relationship. The axisymmetric, circumferentially isotropic, stiffness equation is discretised into segments, then parameterised by a single stiffness parameter and two shape parameters. The tyre's deformed shape is independent of the overall tyre stiffness and the forces acting on the tyre. Constraint modes capture enveloping and bridging properties and a recursive method yields the set of active constraints at the tyre–road interface. The nonlinear stiffness of a tyre is captured by enforcing unidirectional geometric boundary conditions. The model parameters are identified semi-empirically; simulated cleat test loads match experiments within 7% including nonlinear stiffness when simulating ...

Modeling customer usage in vehicle applications is critical in performing durability simulations and analysis in early design stages. Currently, customer usage is typically based on road roughness (some measure of accumulated suspension travel), but vehicle damage does not vary linearly with the road roughness. Presently, a method for calculating a pseudo damage measure is developed based on the roughness of the road profile, specifically the International Roughness Index (IRI). The IRI and pseudo damage are combined to create a new measure referred to as the road roughness-insensitive pseudo damage. The road roughness-insensitive pseudo damage measure is tested using a weighted distribution of IRI values corresponding to the principal arterial (highways and freeways) road type from the Federal Highway Administration (FHWA) Highway Performance Monitoring System (HPMS) dataset. The weighted IRI distribution is determined using the number of unique IRI occurrences in the functional road type dataset and the Average Annual Daily Traffic (AADT) provided in the FHWA HPMS data.

Modeling and simulation of vehicles can be improved by using actual road surface data acquired by Road Surface Measurement Systems. Due to inherent properties of the sensors used, the data acquired is often ridden with outliers. This work addresses the issue of identifying and removing outliers by extending the robust outlier rejection algorithm, Random Sampling and Consensus (RANSAC). Specifically, this work modifies the cost function utilized in RANSAC in such a way that it provides a smooth transition for the classification of points as inliers or outliers. The modified RANSAC algorithm is applied to neighborhoods of data points, which are defined as subsets of points that are close to each other based on a distance metric. Based on the outcome of the modified RANSAC algorithm in each neighborhood, a novel measure for determining the likelihood of a point being an outlier, defined in this work as its exogeny, is developed. The algorithm is tested on a simulated road surface dataset. In the future this novel algorithm will also be tested on real-world road surface datasets to evaluate its performance.

Recent developments in high-fidelity three-dimensional terrain surface measurements have necessitated the development of interpolation methods that are specific to different ground vehicle applications. The objective of this work is the development of application-dependent methods to convert non-uniformly spaced data to uniformly spaced data. This work develops techniques for applying interpolation methods to on-road and off-road terrain surfaces that are used in vehicle simulations. The interpolation methods examined to create uniformly spaced terrain surfaces are mean, median, Inverse Distance to a Power, and Kriging. Each method is judged in four areas: computational efficiency, outlier sensitivity, location sensitivity, and trend sensitivity. The results of this work show that for applications where the resolution of interest is coarse (25 mm or greater) the mean and median are advantageous for creating a uniform grid; but for data applications where fine resolution is required (less than 25 mm) the Inverse Distance to a Power and Kriging have advantages.

The emergence of high-fidelity vehicle and tyre models has raised the requirements for 3D terrain measurement capabilities. Inaccuracies that were once tolerable for measurement of general terrain roughness are no longer acceptable for these new applications. The data inaccuracies that arise from small inertial errors are compounded by difficulties in managing massive file sizes. These faults are most apparent when combining multiple lanes of data in the post-processing phase. This work develops two correction techniques: a general method for any terrain type and a more computationally efficient method for smooth terrain. The general terrain correction method uses overlapping points in the horizontal plane to build a discontinuity vector and applies that vector to correct adjacent lanes. While this method effectively eliminates lane-to-lane discontinuities, it is computationally inefficient for terrain that lacks localized disturbances. For simulations using smooth terrain surfaces, such as racetracks or highways, data can be down-sampled through a mean interpolation method to smooth the artefacts of inertial errors. This work provides the vehicle test engineer with guidelines to minimize inertial errors during the data collection phase as well as a post-processing tool to combine multiple lanes of high-fidelity 3D terrain surfaces.

The principal excitation to a vehicle's chassis system is the road profile. Simulating a vehicle traversing long roads is impractical and a method to produce short roads with given characteristics must be developed. An autoregressive model of non-stationary road profile data has been developed previously. This work examines the residual process of such an ARIMA model. Statistical techniques are developed and used to examine the distribution of the residual process and the preliminary results are demonstrated. Implications of this work to characterizing road profiles and future studies are discussed.

With the advent of terrain surface mapping capabilities comes the necessity to extract useful information from the copious data, particularly localized events. Digital image processing methods for edge detection are applied to road surfaces to locate localized road events. A novel method of edge detection is developed based on the Nodal Uncertainty in which the probability distribution of the nodal heights determines the edges of an event. An example demonstrates that the new method performs at least as well as the best digital image processing methods available. Future development of this work is planned for integration with event characterization and identification methods.Copyright © 2014 by ASME and Chrysler Group LLC

A Location-Aware Adaptive Vehicle Dynamics System (LAAVDS) is currently being developed to predict and maintain vehicle handling capabilities through upcoming maneuvers. This system depends heavily on an understanding of the interplay between the vehicle’s longitudinal, lateral, and vertical forces, as well as their resulting moments. These vehicle dynamics impact the Performance Margin metric and ultimately the point at which the Intervention Strategy will modulate the throttle and brake controls. Real-time implementation requires the development of computationally efficient predictive models of the vehicle dynamics. A method for predicting future vehicle states for smooth but tortuous roads is developed in this work using perturbation theory. An analytical relationship between the change in these forces and the resulting change in the Performance Margin is also derived. This model is implemented in the predictor-corrector algorithm of the Intervention Strategy. Corrections to the predicted states are made at each time step using a detailed, full, non-linear vehicle model; this full vehicle model is a precursor to incorporation of the LAAVDS in a real vehicle. Eventually, this work will be expanded to include the impact of rough terrain.Copyright © 2014 by ASME

The critical link between two powerful modeling techniques, component mode synthesis and large admissible perturbation theory, Is established. This new redesign process allows structural systems that are composed of several substructures to be redesigned. The process is developed in three steps. First, the analytical first-order perturbation relationships between the structural system eigenvalues and the eigenvalues of each independent substructure are developed. Second, a transformation matrix is developed for each perturbation relationship, then combined to form the ultimate structural transformation matrix. Third, a minimization problem is defined that uses the ultimate transformation matrix as a set of constraint equations. The result of this minimization is a set of changes to the substructure eigenvalues that approximately affect the objective changes to the structural system eigenvalues. The success of the redesign process is demonstrated by an isolated platform example. The changes in the substructure eigenvalues are predicted via the redesign process, then substituted back into the full nonlinear equations for the structural system, and the results are discussed. This work forms the basis for future redesign developments when other static and dynamic objectives are to be achieved for structural systems.

A method to improve the ability of design engineers to generate proper dynamic models of systems from sets of component models is developed. This two stage method, called Eigenvalue MODA, is a new model deduction procedure for developing proper models of hybrid systems. The first stage in Eigenvalue MODA consists of using a previously published Model Order Deduction Algorithm (MODA) to systematically increment the complexity of each component model in the system. The first stage continues until a set of Critical System Eigenvalues (CSE) has been defined. During the second stage, the complexity component models is incremented based on the convergence of the CSE. The second stage continues until each CSE has converged to within a user specified tolerance. Component models may be represented by first-order (state space) or second-order equations and may be modal expansion or finite segment models. An example shows that the deduction of the proper system model depends on the interactions between the component model representations and the model deduction method. Eigenvalue MODA is a model deduction method that facilitates the generation of models of sufficient accuracy with physically meaningful parameters and states. This makes the models useful for system design and, as such, Eigenvalue MODA would be a useful tool in an automated modeling environment for design engineers.

Terrain topology is the principal source of vertical excitation to the vehicle system and must be accurately represented in order to correctly predict the vehicle response. It is desirable to evaluate vehicle and tire models over a wide range of terrain types, but it is computationally impractical to simulate long distances of every terrain variation. This work seeks to study the terrain surface, rather than the terrain profile, to maximize the information available to the tire model (i.e., wheel path data), yet represent it in a compact form. A method to decompose the terrain surface as a combination of deterministic and stochastic components is presented. If some, or all, of the components of the terrain surface are considered to be stochastic, then the sequence can be modeled as a stochastic process. These stochastic representations of terrain surfaces can then be implemented in tire and vehicle models to predict chassis loads.

The vehicle terrain measurement system (VTMS) allows highly detailed terrain modeling and vehicle simulations. Visualization of large-scale terrain datasets taken from VTMS provides better insights into the characteristics of the pavement or road surface. However, the resolution of these terrain datasets greatly exceeds the capability of traditional graphics displays and computer systems. Large high-resolution displays (LHRDs) enable visualization of large-scale VTMS datasets with high resolution, large physical size, scalable rendering performance, advanced interaction methods, and collaboration. This paper investigates beneficial factors, implementation issues, and case study applications of LHRDs for visualizing large, high-fidelity, terrain datasets from VTMS. Two prototype visualizations are designed and evaluated with automotive and pavement engineers to demonstrate effectiveness of LHRDs for multiscale tasks that involve understanding pavement surface details within the overall context of the terrain. [DOI: 10.1115/1.4024656]

The interaction between the tire and road has long been of interest for vehicle dynamic simulation. A planar tire model is developed to capture the tire circumferential displacements and calculate the spindle force according to the tire shape. The tire is discretized into segments and Hamilton’s principle is used to derive the model mathematical expression. It is shown that the static constraint modes are functions of two non-dimensional parameters; a third parameter defines the overall stiffness. These parameters are experimentally identified for a specific tire. The bridging and enveloping properties are examined circumferentially. The prediction accuracy of spindle force with respect to tire-road interference is evaluated by comparing the simulation and experimental response for a quasi-static cleat test. The simulation result of spindle force agrees with the experimental data and the process can be implemented as a morphological pre-filter of road profiles for more efficient vehicle modeling and simulation.Copyright © 2012 by ASME

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.Copyright © 2012 by ASME

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.

Terrain topology is the principal source of vertical excitation into the vehicle system and must be accurately represented in order to correctly predict the vehicle response. It is desirable to evaluate vehicle models over a wide range of terrain, but it is computationally impractical to simulate long distances of every terrain type. A method to parsimoniously characterize terrain topology is developed in this work so that terrain can be grouped into meaningful sets with similar topological characteristics. Specifically, measured terrain profiles are considered realizations of an underlying stochastic process; an autoregressive model and a residual process provide the mathematical framework to describe this process. A statistical test is developed to determine if the residual process is independent and identically distributed (IID) and, therefore, stationary. A reference joint probability distribution of the residuals is constructed based on the assumption that the data are realizations of an IID stochastic process. The distribution of the residuals is then compared to this reference distribution via the Kolmogorov–Smirnov “goodness of fit” test to determine whether the IID assumption is valid. If the residual process is IID, a single probability distribution can be used to generate residuals and synthetic terrain of any desired length. This modeling method and statistical test are applied to a set of U.S. highway profile data and show that the residual process can be assumed to be IID in virtually all of these cases of nondeformable terrain surfaces.

Terrain is the principal source of vertical excitation to the vehicle and must be accurately represented in order to correctly predict the vehicle response. Ideally, an efficient terrain surface definition could be developed that maintains the high-fidelity information required to accurately excite vehicle models. It is also desirable to minimize the effect of the choice of measurement system used to sample the terrain surface. Nondeformable, anisotropic (path-specific) terrain surfaces are defined as a sequence of vectors, where each vector comprises terrain heights at locations oriented perpendicular to the direction of travel. A vector space is formed by the span of these vectors and a corresponding set of empirical basis vectors is developed. A set of analytic basis vectors is formed from Gegenbauer polynomials, parameterized to approximate the empirical basis vectors. A weighted inner product is defined to form a Hilbert space and the terrain surface vectors are projected onto the set of analytic basis vectors. The weighting matrix is developed such that these projections are insensitive to the number and placement of the discrete transverse locations at which the terrain heights are defined. This method is successfully demonstrated on sets of paved road surfaces to show that a high-fidelity but compact definition of terrain surfaces is developed. This representation is applied to an example of off-road terrain to demonstrate the representation’s scope of applicability. Future work will investigate generating stochastic terrain surfaces with these vectors.

Modern terrain measurement systems use an inertial navigation system (INS) to measure and remove vehicle movement from laser measurements of the terrain surface. Instrumental and environmental biases inherent in the INS produce noise and drift errors in these measurements. 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). The global and local subspaces are constructed such that the drift is modeled as a random walk process and the noise is a zero-mean process. This theoretical development is coupled with careful experimental design to identify the drift component of error and discriminate it from true terrain surface features, thereby correcting the INS drift. It is shown through an example that this new compensation method dramatically reduces the variation in the measured surfaces to within the resolution of the measurement system itself.

Terrain topology is the principal source of vertical excitation into the vehicle system and must be accurately represented in order to correctly predict the vehicle response. It is desirable to evaluate vehicle models over a wide range of terrain, but it is computationally impractical to simulate long distances of every terrain type. A method to characterize terrain topology is developed in this work so that terrain can be grouped into meaningful sets with similar physical characteristics. Specifically, measured terrain profiles are considered realizations of an underlying stochastic process; an autoregressive model provides the mathematical framework to describe this process. The autocorrelation of the spatial derivative of the terrain profile is examined to determine the form of the model. The required order for the model is determined from the partial autocorrelation of the spatial derivative of the terrain profile. The stability of the model is evaluated and enforced by transforming the autoregressive difference equation into an infinite impulse response filter representation. Finally, the method is applied to a set of U.S. highway profile data and an optimal model order is determined for this application.

The development of new stochastic terrain gridding methods are necessitated by new tire and vehicle modeling applications. Currently, grid node locations in the horizontal plane are assumed to be known and only the uncertainty in the vertical height estimates is modeled. This work modifies the current practice of weighting the importance of a particular measured data point (the terrain height at some horizontal location) by the inverse distance between the grid node and that point. A new weighting function is developed to account for the error in the horizontal position of the grid nodes. The geometry of the problem is described and the probability distribution is developed in steps. Although the solution cannot be determined in closed form, an estimate of the median distance is developed within 1% error. This more complete stochastic definition of the terrain can then be used for advanced tire modeling and vehicle simulation.

Terrain topology is the principal source of vertical excitation to the vehicle system and must be accurately represented in order to correctly predict the vehicle response. It is desirable to evaluate vehicle models and tire models over a wide range of terrain types, but it is computationally impractical to simulate long distances of every terrain variation. This work seeks to study 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 presented. If some, or all, of the components of the terrain surface are considered to be stochastic, then the sequence can be modeled as a stochastic process. These stochastic representations of terrain surfaces can then be implemented in tire and vehicle models to predict chassis loads.Copyright © 2010 by ASME

Traditionally, terrain profilers have been evaluated based on their ability to reproduce measurements made from some reference device (e.g., a rod and level). The measurement error inherent in these reference measurements has become significant as terrain profilers have become more accurate. The fundamental technical challenge in the design of terrain profilers is the removal of vehicle body motion from the height sensor measurement. The objective of this work is to develop design criteria for an excitation event that will quantitatively highlight the abilities and inadequacies of terrain profilers by testing the profilers under adverse measurement conditions. The design of a characteristic excitation event must fulfill two requirements. First, the event should excite the terrain profiler chassis at its primary ride and wheel-hop frequencies. Using these first two ride frequencies and the suspension damping ratio, relationships are developed that relate these parameters to the geometric excitation event dimensions. The terrain profiler's test velocity is also determined based on these frequencies. Second, the excitation event should be simple, light, inexpensive, and reproducible to ensure that it is used. The result of this work is an excitation event that insures that the terrain profiler will be excited to its highest attainable amplitude (near resonance). This excitation event provides the first step in developing an accuracy test for modern terrain profilers.

As computational power builds to meet the needs of ground vehicle designers, the focus has begun to shift from laboratory testing of prototype parts and subsystems to computational simulations of the vehicle. In the automotive and defense industries, large strides have been made in simulating full vehicle responses, such as durability. These simulations are most meaningful when excited by proper mathematical models that accurately characterize the terrain. It is important to understand the roughness indices that are used to judge the terrain profiles. The state-of-the-art in terrain characterization and modeling is reviewed in this work for models including Power Spectral Density (PSD), Markov Chains, Autoregressive Integrated Moving Average (ARIMA), Parametric Road Spectrum (PRS), Shifted Spatial Range Spectrum (SSR), Direct Spectrum Estimation (DSE) and Transformed Direct Spectrum Estimation (TrDSE). The applicability, limitations, and benefits of these models are assessed based on their effectiveness in capturing the stochastic nature of the terrain being characterized. A discussion of terrain characterization usage to advance reliability testing concludes this work as an example of the applicability of this technology.

The principal excitation to a vehicle's chassis system is the road profile. Simulating a vehicle traversing long roads is impractical and a method to produce short roads with given characteristics must be developed. There are many methods currently available to characterize roads when they are assumed to be homogeneous. This work develops a method of characterizing non-stationary road profile data using ARIMA (Autoregressive Integrated Moving Average) modeling techniques. The first step is to consider the road to be a realization of an underlying stochastic process. Previous work has demonstrated that an ARIMA model can be fit to non-stationary road profile data and the remaining residual process is uncorrelated. This work continues the examination of the residual process of such an ARIMA model. Statistical techniques are developed and used to examine the distribution of the residual process and the preliminary results are demonstrated. The use of the ARIMA model parameters and residual distributions in classifying road profiles is also discussed. By classifying various road profiles according to given model parameters, any synthetic road realized from a given class of model parameters will represent all roads in that set, resulting in a timely and efficient simulation of a vehicle traversing any given type of road.

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.

This work establishes a new method for predicting the deformed shape of a tire with unilateral geometric constraints imposed by the road surface. Specifically, a method is developed for determining the static constraint mode that captures the planer enveloping properties of a tire for uneven road surfaces. This new method uses a recursive algorithm for determining which geometric constraints are active. A simple planer tire model, described by a linear ring on an elastic foundation, is used to demonstrate the method. The result of this method is a set of active geometric constraints on the tire and the static constraint modes that compose the deflection of the tire along its circumference. The success of the method is demonstrated by an example. This work forms the basis for developing nonlinear dynamic tire models that accurately account for active, unilateral, geometric constraints on the tire.Copyright © 2006 by ASME

Every time we measure the terrain profiles we would get a different set of data due to the measuring errors and due to the fact that the linear tracks on which the measuring vehicle travels can not be exactly the same every time. However the data collected at different times from the same terrain should share the similar intrinsic properties. Hence it is natural to consider statistical modeling of the terrain profiles. In this paper we shall use the time series models with time being the distance from the starting point. We receive data from the Belgian Block and the Perryman3 testing tracks. The Belgian Block data are shown to behave like a uniformly modulated process ([7]), i.e. it is the product of a deterministic function and a stationary process. The modeling of the profiles can be done by estimating the deterministic function and fit the stationary process with a well-known ARMA model. The Perryman3 data are more irregular. We have to use the intrinsic mode function decomposition method ([2]). The first few intrinsic mode functions could be modeled in the same way as the the Belgian Block data. The residue part is a very smooth function which we may consider as a deterministic function.

Load data representing severe customer usage is required during the chassis development process. The use of road profiles and vehicle models to predict chassis loads is currently being researched; this research hinges on the ability to accurately measure road profiles. This work focuses on detecting possible signal defects such as leaves on the ground, reflecting surfaces, or narrow roadway gaps. The objective of this work is to develop a simulation procedure that checks the measured road profile for plausibility. The position of the vehicle body is recorded as part of the typical road profiling process. Ideally, a mathematical model can predict the body position from a road profile. The first step in verifying the plausibility of road profiles is to predict the body position. Next, the measured body position is compared to the predicted body position for the road profile in question. New criteria for plausibility checking are a major contribution of this work. These criteria include examination of the amplitude, duration, and phase relationships of the measured/simulated body position and velocity. Plausibility bounds are placed on a new representation of these relationships as well as on bandwidth-specific areas of the vehicle transfer function. These plausibility bounds are another major contribution of this work. A set of characteristic signal defects are defined and added to existing road profiles to demonstrate the effectiveness of this method. This is the seminal work for plausibility checking of measured road profiles.