Developing Compact Models of Terrain Surfaces

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Heather M. Chemistruck ◽  
John B. Ferris
Keyword(s):  
Stochastic Process ◽  
Compact Form ◽  
Tire Model ◽  
Vertical Excitation ◽  
Vehicle System ◽  
Wide Range ◽  
Principal Source ◽  
Stochastic Representations ◽  
Tire Models ◽  
Terrain Surface

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.

Compact Models of Terrain Surfaces

2010 ◽  
Author(s):  
Heather Chemistruck ◽  
John B. Ferris
Keyword(s):  
Stochastic Process ◽  
Tire Model ◽  
Vertical Excitation ◽  
Vehicle System ◽  
Wide Range ◽  
Principal Source ◽  
Compact Models ◽  
Stochastic Representations ◽  
Tire Models ◽  
Terrain Surface

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.

Stability and Interpretation of Autoregressive Models of Terrain Topology

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Shannon Wagner ◽  
John B. Ferris
Keyword(s):  
Infinite Impulse Response ◽  
Mathematical Framework ◽  
Spatial Derivative ◽  
Model Order ◽  
Vertical Excitation ◽  
Wide Range ◽  
Principal Source ◽  
Infinite Impulse Response Filter ◽  
The Stability ◽  
Impulse Response Filter

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.

Residual Analysis of Autoregressive Models of Terrain Topology

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Shannon Wagner ◽  
John B. Ferris
Keyword(s):  
Stochastic Process ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Statistical Test ◽  
Joint Probability Distribution ◽  
Mathematical Framework ◽  
Reference Distribution ◽  
Goodness Of Fit Test ◽  
Vertical Excitation ◽  
Wide Range

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.

A Modified Dugoff Tire Model for Combined-slip Forces

2010 ◽  
Vol 38 (3) ◽  
pp. 228-244 ◽  
Author(s):  
Nenggen Ding ◽  
Saied Taheri
Keyword(s):  
Vehicle Dynamics ◽  
Tire Model ◽  
Magic Formula ◽  
Model Based ◽  
Proposed Model ◽  
Road Friction ◽  
On Line ◽  
Double Lane Change ◽  
Tire Forces ◽  
Tire Models

Abstract Easy-to-use tire models for vehicle dynamics have been persistently studied for such applications as control design and model-based on-line estimation. This paper proposes a modified combined-slip tire model based on Dugoff tire. The proposed model takes emphasis on less time consumption for calculation and uses a minimum set of parameters to express tire forces. Modification of Dugoff tire model is made on two aspects: one is taking different tire/road friction coefficients for different magnitudes of slip and the other is employing the concept of friction ellipse. The proposed model is evaluated by comparison with the LuGre tire model. Although there are some discrepancies between the two models, the proposed combined-slip model is generally acceptable due to its simplicity and easiness to use. Extracting parameters from the coefficients of a Magic Formula tire model based on measured tire data, the proposed model is further evaluated by conducting a double lane change maneuver, and simulation results show that the trajectory using the proposed tire model is closer to that using the Magic Formula tire model than Dugoff tire model.

A Double Interaction Brush Model for Snow Conditions

2019 ◽  
Vol 47 (2) ◽  
pp. 118-140
Author(s):  
Artem Kusachov ◽  
Fredrik Bruzelius ◽  
Mattias Hjort ◽  
Bengt J. H. Jacobson
Keyword(s):  
Low Complexity ◽  
Large Set ◽  
Tire Model ◽  
Vehicle Handling ◽  
Real Time Applications ◽  
Snow Conditions ◽  
Double Interaction ◽  
Tire Models ◽  
Force Characteristics ◽  
Model Approach

ABSTRACT Commonly used tire models for vehicle-handling simulations are derived from the assumption of a flat and solid surface. Snow surfaces are nonsolid and may move under the tire. This results in inaccurate tire models and simulation results that are too far from the true phenomena. This article describes a physically motivated tire model that takes the effect of snow shearing into account. The brush tire model approach is used to describe an additional interaction between the packed snow in tire tread pattern voids with the snow road surface. Fewer parameters and low complexity make it suitable for real-time applications. The presented model is compared with test track tire measurements from a large set of different tires. Results suggest higher accuracy compared with conventional tire models. Moreover, the model is also proven to be capable of correctly predicting the self-aligning torque given the force characteristics.

scholarly journals Prediction of Wide Range Two-Dimensional Refractivity Using an IDW Interpolation Method from High-Altitude Refractivity Data of Multiple Meteorological Observatories

2021 ◽  
Vol 11 (4) ◽  
pp. 1431
Author(s):  
Sungsik Wang ◽  
Tae Heung Lim ◽  
Kyoungsoo Oh ◽  
Chulhun Seo ◽  
Hosung Choo
Keyword(s):  
High Altitude ◽  
Korean Peninsula ◽  
Interpolation Method ◽  
Atmospheric Condition ◽  
Propagation Path ◽  
Two Dimensional ◽  
Data Set ◽  
Wide Range ◽  
Atmospheric Data ◽  
Terrain Surface

This article proposes a method for the prediction of wide range two-dimensional refractivity for synthetic aperture radar (SAR) applications, using an inverse distance weighted (IDW) interpolation of high-altitude radio refractivity data from multiple meteorological observatories. The radio refractivity is extracted from an atmospheric data set of twenty meteorological observatories around the Korean Peninsula along a given altitude. Then, from the sparse refractive data, the two-dimensional regional radio refractivity of the entire Korean Peninsula is derived using the IDW interpolation, in consideration of the curvature of the Earth. The refractivities of the four seasons in 2019 are derived at the locations of seven meteorological observatories within the Korean Peninsula, using the refractivity data from the other nineteen observatories. The atmospheric refractivities on 15 February 2019 are then evaluated across the entire Korean Peninsula, using the atmospheric data collected from the twenty meteorological observatories. We found that the proposed IDW interpolation has the lowest average, the lowest average root-mean-square error (RMSE) of ∇M (gradient of M), and more continuous results than other methods. To compare the resulting IDW refractivity interpolation for airborne SAR applications, all the propagation path losses across Pohang and Heuksando are obtained using the standard atmospheric condition of ∇M = 118 and the observation-based interpolated atmospheric conditions on 15 February 2019. On the terrain surface ranging from 90 km to 190 km, the average path losses in the standard and derived conditions are 179.7 dB and 182.1 dB, respectively. Finally, based on the air-to-ground scenario in the SAR application, two-dimensional illuminated field intensities on the terrain surface are illustrated.

Radial-Interradial Spring Tire Models

1988 ◽  
Vol 110 (1) ◽  
pp. 70-75 ◽  
Author(s):  
J. M. Badalamenti ◽  
G. R. Doyle
Keyword(s):  
Test Data ◽  
Close Agreement ◽  
Tire Model ◽  
Drag Forces ◽  
Tire Models

Two radial-interradial spring tire models are developed to predict vertical and drag forces produced by a tire as it rolls over an obstacle. Interradial springs are used to interconnect radial linear or quadratic springs to make each tire element’s deflection dependent upon its adjacent element’s deflections. Forces predicted by these two models are compared with a previously developed quadratic radial spring tire model and test data. The newly developed quadratic radial-linear interradial spring tire model predicts vertical and drag forces that are in close agreement with the test data.

Weighted Orthogonal Distance Regression for Tire Models Parameters Identification

2015 ◽  
Author(s):  
JoseLuis Olazagoitia ◽  
Alberto López
Keyword(s):  
Test Data ◽  
Measured Data ◽  
Model Parameters ◽  
Tire Model ◽  
Optimum Parameters ◽  
Ordinate Axis ◽  
Orthogonal Distance Regression ◽  
Independent Variable ◽  
Tire Models ◽  
Least Squares Techniques

Determining the parameters in existing tire models (e.g. Magic Formula (MF)) for calculating longitudinal and lateral forces depending on the tire slip is often based on standard least squares techniques. This type of optimization minimizes the vertical differences in the ordinate axis between the test data and the chosen tire model. Although the practice is to use this type of optimization in adjusting those model parameters, it should be noted that this approach disregards the errors that have been committed in the measurement of tire slips. These inaccuracies in the measured data affect the optimum parameters of the model, producing non optimum models. This paper presents a methodology to improve the fitting of mathematical tire models on available test data, taking into account the vertical errors together with errors in the independent variable.

Insensitivity and product-form decomposability of reallocatable GSMP

1993 ◽  
Vol 25 (2) ◽  
pp. 415-437 ◽  
Author(s):  
Masakiyo Miyazawa
Keyword(s):  
Stochastic Process ◽  
Stationary Distribution ◽  
Jump Process ◽  
Product Form ◽  
Balance Equations ◽  
Independent Components ◽  
Extended Sense ◽  
Wide Range ◽  
Standard Models

A stochastic process, called reallocatable GSMP (RGSMP for short), is introduced in order to study insensitivity of its stationary distribution. RGSMP extends GSMP with interruptions, and is applicable to a wide range of queues, from the standard models such as BCMP and Kelly's network queues to new ones such as their modifications with interruptions and Serfozo's (1989) non-product form network queues, and can be used to study their insensitivity in a unified way. We prove that RGSMP supplemented by the remaining lifetimes is product-form decomposable, i.e. its stationary distribution splits into independent components if and only if a version of the local balance equations hold, which implies insensitivity of the RGSMP scheme in a certain extended sense. Various examples of insensitive queues are given, which include new results. Our proofs are based on the characterization of a stationary distribution for SCJP (self-clocking jump process) of Miyazawa (1991).

scholarly journals QUASI-HAMILTONIAN METHOD FOR COMPUTATION OF DECOHERENCE RATES

2011 ◽  
Vol 25 (16) ◽  
pp. 2115-2134 ◽  
Author(s):  
ROBERT JOYNT ◽  
DONG ZHOU ◽  
QIANG-HUA WANG
Keyword(s):  
Field Theory ◽  
Stochastic Process ◽  
Mean Field Theory ◽  
Mean Field ◽  
Hamiltonian Method ◽  
Single Qubit ◽  
Pure Dephasing ◽  
Wide Range ◽  
Two Level Systems ◽  
Arbitrary Quantum

We present a general formalism for the dissipative dynamics of an arbitrary quantum system in the presence of a classical stochastic process. It is applicable to a wide range of physical situations, and in particular it can be used for qubit arrays in the presence of classical two-level systems (TLS). In this formalism, all decoherence rates appear as eigenvalues of an evolution matrix. Thus the method is linear, and the close analogy to Hamiltonian systems opens up a toolbox of well-developed methods such as perturbation theory and mean-field theory. We apply the method to the problem of a single qubit in the presence of TLS that give rise to pure dephasing 1/f noise and solve this problem exactly.

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