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Abstract

Vehicle dynamics models are widely used in many areas of the automotive industry. The usability of each model depends on how well it is able to mimic the behavior of the real vehicle. Each simulation model must go through a thorough investigation process first, which is called model validation. Although, vehicle dynamics simulation models and methodology for computational model validation are well established fields, to the best of the authors' knowledge a general framework for vehicle dynamics model validation is still lacking. The research aims to develop a comprehensive methodological framework for vehicle dynamics model validation. In this paper the aim is to present the high level layout of the proposed framework, introducing the main blocks and the tasks related, also addressing some critical issues regarding vehicle dynamics model validation such as validation metrics and vehicle parameter measurement and estimation. An important part of the proposed methodology is a sophisticated vehicle dynamics measurement system, which gives the opportunity to estimate a bunch of vehicle parameters during dynamic testing, which can be useful for several reasons, e.g. fine-tuning the parameters of the Pacejka Magic formula. As a case study some vehicle dynamics test based parameter estimations are shown to justify the raison d'être and investigate possible applications. INDEX TERMS Vehicle model validation, vehicle dynamics, vehicle parameter identification, methodological framework.
Received February 10, 2022, accepted February 24, 2022, date of publication March 8, 2022, date of current version April 6, 2022.
Digital Object Identifier 10.1109/ACCESS.2022.3157904
Framework for Vehicle Dynamics
Model Validation
ATTILA WIDNER 1,2, VIKTOR TIHANYI 3, AND TAMÁS TETTAMANTI 1,4
1Department of Control for Transportation and Vehicle Systems, Faculty of Transportation Engineering and Vehicle Engineering, Budapest University of
Technology and Economics, 1111 Budapest, Hungary
2Department of Innovative Vehicles and Materials, John von Neumann University, 6000 Kecskemét, Hungary
3Automotive Proving Ground Zala Ltd., 8900 Zalaegerszeg, Hungary
4Systems and Control Laboratory, Institute for Computer Science and Control of the Eötvös Loránd Research Network, 1111 Budapest, Hungary
Corresponding author: Tamás Tettamanti (tettamanti.tamas@kjk.bme.hu)
This work was supported by the Budapest University of Technology and Economics through the National Research Development and
Innovation Fund (TKP2020 National Challenges Subprogram) Based on the Charter of Bolster Issued by the National Research
Development and Innovation Office under the Auspices of the Ministry for Innovation and Technology under Grant BME-NC.
ABSTRACT Vehicle dynamics models are widely used in many areas of the automotive industry. The
usability of each model depends on how well it is able to mimic the behavior of the real vehicle. Each
simulation model must go through a thorough investigation process first, which is called model validation.
Although, vehicle dynamics simulation models and methodology for computational model validation are
well established fields, to the best of the authors’ knowledge a general framework for vehicle dynamics
model validation is still lacking. The research aims to develop a comprehensive methodological framework
for vehicle dynamics model validation. In this paper the aim is to present the high level layout of the proposed
framework, introducing the main blocks and the tasks related, also addressing some critical issues regarding
vehicle dynamics model validation such as validation metrics and vehicle parameter measurement and
estimation. An important part of the proposed methodology is a sophisticated vehicle dynamics measurement
system, which gives the opportunity to estimate a bunch of vehicle parameters during dynamic testing, which
can be useful for several reasons, e.g. fine-tuning the parameters of the Pacejka Magic formula. As a case
study some vehicle dynamics test based parameter estimations are shown to justify the raison d’être and
investigate possible applications.
INDEX TERMS Vehicle model validation, vehicle dynamics, vehicle parameter identification,
methodological framework.
I. INTRODUCTION
Vehicle dynamics simulations are widely used and become
more and more important in the modern era of vehicle
development (e.g. active and conventional suspensions
design, vehicle controller design, advanced driver assistance
systems, development of driving simulators, autonomous
driver algorithm development), as applying simulation is
generally more cost-efficient, safer, and faster than real-world
vehicle tests. Furthermore, in simulation a wide range of
parameters can be easily modified and tested in a short time
in a very flexible fashion.
Having a reliable and validated vehicle model is not
only important in the development phase but for the
The associate editor coordinating the review of this manuscript and
approving it for publication was Xiaogang Jin .
operation of different vehicle software components, as they
are responsible for safety-critical control processes such as
braking and cornering stability [1].
Model validation is the review and evaluation process of
how a model works, usually done by the model developer and
engineers being familiar with the given real system.
’’It refers to the processes and techniques that the model
developer, model customer and decision-makers jointly use to
assure that the model represents the real system to a sufficient
level of accuracy.’’ [2]
However, the above-mentioned advantages are only
present, when the model and its parameters are appropriately
accurate, and the simulation results well reflect the real-world
phenomenon. Sophisticated models for vehicle dynamics
have lots of parameters, some of them being difficult
to measure. The necessary validation process, therefore,
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A. Widner et al.: Framework for Vehicle Dynamics Model Validation
requires a plethora of testing as well as measurements which
are expensive and time-consuming.
Each model’s usefulness is measured by how well it can
mimic the behavior of the real vehicle. Model validation is a
process that each simulation model must go through before it
can be used. Despite the fact that vehicle dynamics simulation
models and methodology for computational model validation
are well-established topics, there is still a need for a generic
framework for vehicle dynamics model validation [3].
The aim of the research is to create a complete method-
ological framework for validating vehicle dynamics models.
The goal of this paper is to describe the proposed framework’s
high-level layout, presenting the primary blocks and activities
associated with them, as well as certain critical concerns
linked to vehicle dynamics model validation, such as
validation metrics and vehicle parameter measurement and
estimation. A sophisticated vehicle dynamics measurement
system is an important component of the proposed system,
as validation metrics - which are intended to quantify the
model’s credibility - should account for the uncertainty of
real-world measurements. As a result, precise and accurate
measurements of all relevant system response quantities
(hereinafter referred to as SRQ) are required for validation.
Furthermore, using such a measurement system allows for
the estimation of a number of vehicle parameters during
dynamic testing, which can be useful for a variety of reasons,
such as fine-tuning the Pacejka Magic Formula parameters,
tracking the change of: weight distribution, center of gravity
height (hCG), yaw inertia (θz), etc. during long dynamic tests.
To illustrate the possible applications, some vehicle dynamics
test-based parameter estimations are provided as a case study.
Vehicle simulation models become rather complex
as - besides the increasing complexity of the subsystems -
they need to reflect the entire transportation system more
and more [1]. According to this trend, the model validation
process also becomes more detailed and intricate.
A. THE STRUCTURE OF THE PAPER
The paper is organized as follows. In section II, important
works on computational model validation, vehicle dynamics,
and vehicle dynamics model validation are discussed, the
emphasis is on discovering the key elements of validation
methodology - such as validation metrics. Then, in section III
the high-level layout of our proposed vehicle dynamics
model validation framework is introduced with more detailed
discussion on parameter estimation and validation metrics.
Finally, in section IV a case study is presented, where
dynamic vehicle test-based parameter estimation is discussed
and at the end a result of a validated vehicle model is shown.
II. PRELIMINARIES AND MOTIVATION
The research domain of vehicle dynamics model validation
has two main components: computational model verification
and validation (V&V) and vehicle dynamics (vehicle models,
simulation and vehicle parameter measurements, estimation).
Considering general model validation, the field is well
established. Carson states in [2]:
’’The goal of verification and validation is a model
that is accurate when used to predict the performance of
the real-world system that it represents, or to predict the
difference in performance between two scenarios or two
model configurations. The process of verifying and validating
a model should also lead to improving a model’s credibility
with decision-makers.’ [2]
This idea is also supported in [4] and [5].
According to many experts there is no absolute valid
model [4]–[7]. Therefore, there will always be discrepan-
cies between the measured physical phenomenon and the
simulation results. The purpose of the simulation is to
give an answer to a specific question, or give information
for engineers in a decision making process, therefore as
defined in [3] the model only needs to be validated in the
domain which is suitable for the application. Any further
work on the validation can improve the predictability of
the model, but if this is not required for the purpose,
then it unnecessarily increases the cost and time of the
process.
Vehicle dynamics models have well established mathemat-
ical background, one of the earliest works on this topic is [8]
from Olley (1946), and one of the first vehicle dynamics
models was proposed by Segel (1956) [9]. Since then several
works have been presented in the field of vehicle dynamics
including Millikens’ Race Car Vehicle Dynamics [10],
Vehicle Dynamics by Zomotor [11], Pacejka’s tire and
Vehicle Dynamics [12], Vehicle dynamics: Theory and
Application from Jazar [13], and plenty of more.
There is a broad range of publications and books regarding
vehicle dynamics and vehicle dynamic simulations. Many
papers can be found on the topic of vehicle model validation
as well, but according to Kutluay - who did a comprehensive
literature review in this field in 2014:
’’Many of the publications which claim to present a
validation methodology or technique tend to only offer the
application of a methodology to an individual case.’’ [3].
To the best of the authors’ knowledge, the full method-
ological connection between simulation and real measured
data comparison, as well as the method of error detection
and parameter identification - in other words, a compre-
hensive general framework for vehicle dynamics model
validation - is still lacking.
’’Existent works on validation methodologies for vehicle
dynamics simulations focus on different aspects of the
question. Neither there is a standard in experimentation and
data handling processes in vehicle dynamics modeling, nor is
there a standard reasoning process in the vehicle dynamics
modeling application in validation analysis. Most of the
applications rely only on visual comparison and subjective
judgment. Diagrams types used in visual comparison also do
not follow any recognizable pattern and their contents and
structures are determined at will by the research team. Most
of the time, the team which developed the model also decides
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A. Widner et al.: Framework for Vehicle Dynamics Model Validation
if the simulation is valid. This whole process chain diminishes
the credibility of these models.’’ [3]
One of the first studies regarding vehicle dynamics
simulation model validation methodology is [14] from 1990.
The validity of the model is defined as the agreement between
the simulation’s predictions of a vehicle’s responses and
the actual measured vehicle’s responses within a previously
specified level of accuracy. It is stated that the simulation
results may only be valid within a range of the operating
conditions. A model is probably only valid for a specific
task, for example, a validated lateral dynamics model with
suspension degree of freedom is not necessarily valid for ride
quality analysis [3]. The methodology presented in [14] is
based on statistical analysis, therefore several experimental
test runs need to be carried out for each test case to gather
sufficient data and to reduce the influence of random error.
The data should be investigated in time and frequency
domains as well.
Since then several other authors - including [14]–[17] - also
support the idea that the validation of a vehicle dynamics
model should include steady-state and transient tests and
consider analysis in time and frequency domain as well.
In [18] Bernard and Clover defined three topics to
investigate during a model validation:
Conceptual validity - Is the model appropriate for the
vehicle and maneuver to be tested?
Verification - Are the equations in the simulation fully
replicating the model?
Data validity - Are the input parameters reasonable?
Running the simulation claims to be the only way for veri-
fication due to the high complexity of the simulation models,
as it is not possible to check each of the equations [18].
The methodology presented in [19] defines four possible
areas causing discrepancies between simulation model results
and real world data:
Mathematical model.
Computational model programming.
Vehicle or environment input data.
Numerical accuracy and stability.
The model validation should consider the domain of
application of the model, since the degree of validation
always has a limit and the model should be useful for a
specific question (in a specific range). Care should be taken if
the previously validated model would be used for a different
task, especially when the behavior of a subsystem needs to
be investigated in more depth, as a valid model according to
the analysis of general system response does not guarantee
sufficiently valid subsystem models [19].
Although in [2] Carson stated that ’’a model is not
valid until all of its subsystems are valid’’. We can see
that in the case of highly complex systems - such as
vehicles - a model that is considered valid for a general
analysis, is not necessarily valid for subsystem analysis.
For example, a model that is accurate enough and useful
for general longitudinal, lateral, and combined (braking and
cornering or acceleration and cornering) behavior analysis,
does not need a sophisticated brake model, that considers
energy dissipation, brake pad and disc temperatures, and the
variation of the coefficient of friction between the two due
to temperature and sliding velocity. But for example, if the
braking performance needs to be analyzed in a long run, the
above-mentioned model is probably not valid for the task.
The validation method presented in [19] is summarized in
four steps:
The mathematical model’s conceptual validity.
Face validity (reasonableness) of the simulation model
response.
Input, intermediate, and output variable consistency.
Agreement between the simulated and the reference
system responses.
The works presented in [14] and [15] are about vehicle
parameter measurement and vehicle model validation. The
validation process consists of three main phases:
Collection of experimental test data (Steady-state,
transient, and frequency domain responses).
Independent vehicle parameter measurement
Comparison of simulation results with test data using the
same driver inputs.
A. PARAMETER MEASUREMENTS
The model can only be validated under a limited number
of operational conditions, as previously stated. In their
2002 paper, Wade-Allen et al. [17] discussed the importance
of parameter measurement according to the operating condi-
tions. If the vehicle model is used for analyzing the vehicle
behavior on the grip limit of the tires, then the parameter
measurements must be carried out taking into consideration
the operating conditions that can occur in these situations.
Therefore in this case, for example, the tire characteristics
must be measured in a higher slip angle range - in the tire
saturation region - and at a wider normal load range (because
of the higher normal load variation due to load transfer).
The importance of independent parameter measurement is
emphasized in [15] and [14]. Complex vehicle simulation
models can only provide adequate results if the subsystem
parameters are set to an appropriate level of accuracy.
According to [18] faulty data entry is an important risk
factor - even if the parameter measurements are reliable. The
most endangered part is tire and suspension data, as both have
many parameters and this step is tend to have human error.
Extra care should be taken during the parametrization of the
model.
B. VEHICLE DYNAMICS TESTS
In this section, various viewpoints on the type of vehicle test
required for model validation are investigated.
In [16] the following five test cases are defined as primary
validation maneuvers:
steady-state lateral dynamics (low-frequency cornering)
Transient lateral dynamics (wide frequency range
steering input)
Longitudinal acceleration (throttle inputs)
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FIGURE 1. Validation flow chart from [20], which illustrates the
interaction between computation and experimentation that should occur
in a validation process.
Longitudinal deceleration (braking inputs)
Road disruption input (suspension kinematics and ride
dynamics)
A sixth group is defined as well, called ’other maneuvers’
- which are imitations of a real-life situations such as double
lane change or a fishhook - but are not considered as a primary
validation maneuvers.
The tests performed in [14] and [15] include steady-state,
transient and frequency domain responses. The following
maneuver sequence was followed:
Quasi-steady-state
Step response
Pulse response (evaluated in frequency domain)
Real-world like maneuver: lane change
Regarding data comparison time domain was used for steady-
state, low-frequency, and nonlinear effects, then frequency
domain was used for high-frequency transient maneuvers.
Wade-Allen et. al. [17] used both steady-state and transient
maneuvers:
Quasi-steady-state steering wheel ramp input
Pulse response (in frequency domain)
Double lane change
Fishhook maneuver
C. VALIDATION METRICS
’’In most of the papers no validation metrics or confidence
intervals are used and no statistical analysis is performed in
relation with validation. Instead, a subjective and qualitative
judgment is reached through visual graphical comparison
of overlaid time histories of test and simulation results
usually.’’ [3]
A proper model validation framework should contain a
method for comparing time histories in order to quantify
the discrepancies and get a picture of the degree of validity.
Oberkampf and Barone in [20] discussed various features that
should be incorporated or excluded in validation metrics and
developed validation metrics that are based on the statistical
concept of confidence intervals.
Oberkampf [21] and Trucano [22] argued that when
comparing computational and experimental results, both
uncertainties and errors should be quantified.
Accordingly, Fig. 1illustrates the flowchart of comparing
system response quantity (SRQ) obtained from both the
simulation and real-life experiment. As stated in [20]:
’’The SRQ can be any type of physically measurable
quantity, or it can be a quantity that is based on, or inferred
from, measurements. For example, the SRQ can involve
derivatives, integrals, or more complex data processing of
computed or measured quantities such as the maximum or
minimum of functionals over a domain. When significant
data processing is required to obtain an SRQ, it is important to
process both the computational results and the experimentally
measured quantities in the same manner.’’ [20]
They refer to validation metric, as the ’’mathematical pro-
cedure that operates on the computational and experimental
SRQs.’’ [20]
The main task to validation is comparing the validation
metrics’ results with the accuracy requirements (which
depends on many factors) for the intended use of the model.
In [20] three validation metrics approaches were reviewed:
parameter estimation and system identification, hypothesis or
significance testing, Bayesian analysis, or Bayesian statistical
inference. They proposed six properties that validation
metrics should include to be useful in the engineering
decision-making process. The six attribution are presented
here in a manner that only includes the information relevant
to our current vehicle simulation domain:
Validation metrics should either:
explicitly include an estimation of numerical error
in the SRQ resulting from the computational
simulation - such as including the upper and lower
estimated bound on the error in the SRQ, but it
would add significant complexity to the calculation
and interpretation of the metric.
Or exclude the numerical error in the SRQ, only if
the numerical error was previously estimated to be
small compared to the experimental uncertainty.
The metrics should be a quantitative evaluation of the
aggregate accuracy for a specific SRQ, including:
the combined modeling assumptions,
the physics approximations,
the physical parameters of the model.
A metric should include, an estimate of the error
resulting from post-processing of the experimental data
that is compared to the simulation result.
A metric should explicitly incorporate an estimate of the
measurement errors in the experimental data for the SRQ
that are the basis of comparison with the computational
model. There are two types of measurement errors:
bias (systematic) errors and precision (random) errors.
The minimum requirement for validation metrics is to
include an estimation of precision errors. As much as
possible, the metrics should include an estimate of bias
errors as well.
A metric should take into account the number of
experimental measurements. The authors emphasize the
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importance of multiple measurements and estimating the
accuracy of the experimental result.
A metric should not include any indications of the level
of agreement between computational and experimental
results (e.g. characterizing them as ‘‘good’’ or ‘‘excel-
lent’’). Validation metrics should be used to assess the
degree of agreement between computational models and
experimental measurements. The metric should be kept
separate from how satisfying the results are.
In [23] common measures are evaluated used to quantify
the discrepancy between time histories in fields such as
statistics, computational mechanics, signal processing, and
data mining. The following existing metrics were evaluated:
Vector norms
Average residual and its standard deviation
Coefficient of correlation and cross-correlation
Sprague and Geers (S&G) metric
Russell’s error
Normalized Integral Square Error (NISE)
Dynamic Time Warping (DTW)
Their proposal is a structured combination of some of
these measures. The new metrics classify error components
associated with three physically meaningful characteristics
(phase, magnitude, and topology), and utilizes norms,
cross-correlation measures, and algorithms such as dynamic
time warping to quantify discrepancies. [23]
For phase error cross-correlation method is used with a
tunable penalty function to have a linear penalty for small
time-step (local errors) and larger time-step (global errors)
differences. Magnitude error is analyzed after minimizing
the global, local phase difference between the data sets
and also the slope differences - because slope difference is
a topological error, not a magnitude error. Dynamic Time
Warping is used to reduce local phase and slope differences.
After that L1 vector norm is used to measure the relative
magnitude differences. The topology error - the measure of
discrepancies in the slope - is calculated on the derivative of
the time-shifted, warped channels. Then L1 norm is used to
quantify the topology error. [23]
D. CONCLUSION OF THE LITERATURE REVIEW
The validation of computational models is well established.
Several papers have been published in this field in the
last decades. Recently, the quantification of discrepancies
between simulated and experimental measurements’ time
histories improved a lot. Also, significant efforts have
been undertaken to develop the so-called validation metrics.
However, only a fragment of these methodologies has been
implemented in the practice of vehicle dynamics.
The mathematical background of vehicle dynamics is also
well established and simulation models in the field are used
in a wide range of applications. Several methods and ideas
can be found regarding parameter measurements and vehicle
dynamics tests for model validation. The problem is that
usually, they are only applicable for a narrow range of
scenarios - for example only for lateral dynamics in the linear
range of the tire. However, there is no general framework
that gives a concise guideline for the wide range of vehicle
dynamics model validation - that includes the determination
of validity criteria, vehicle parameter measurements, vehicle
dynamics tests, validation metrics for a given simulation
model domain.
According to the above, the main research gap targeted
in this paper is the general idea for a comprehensive
vehicle dynamics model validation framework, which is
based on a sophisticated vehicle dynamics measurement
system. In this paper, besides the framework, some automated
parameter estimation methods are also presented as practical
use cases to demonstrate the idea. Finally, the result of
model validation is shown, where the previously mentioned
estimated parameters were used.
III. FRAMEWORK PROPOSED FOR VEHICLE DYNAMICS
MODEL V&V
In this chapter, the proposed V&V framework for vehicle
dynamics models is presented with a high-level system
layout and some general explanation. Our goal is to create
a sophisticated system that gives a guideline for the majority
of vehicle model validation.
Our goal is to develop a system where the majority of
the iterative tasks are swapped by automated systems. The
general idea is shown by Fig. 2. Following the definition of
the validity criteria, individual parameter estimations for each
important subsystem are performed to the most sufficient
level, implying that the subsystems with a significant impact
on vehicle behavior in the investigation domain should be
thoroughly measured. In addition to the individual parameter
measurements, the measurement system constants - such
as the position of the acceleration sensor in the chassis
coordinate system - must be measured since they are critical
for proper post-processing of the vehicle dynamics measure-
ments. In the next block vehicle dynamics measurements are
carried out with a sophisticated measurement system - which
is capable of measuring all the important movements,
phenomenons such as vehicle body movement, suspension
movement, tire forces and moments, side-slip angle, camber,
etc. Then based on the measurements - in the previous two
blocks - the vehicle model parameter identification is solved
by an automated system (denoted by the dashed line on
Fig. 2), as an output, it gives the base parameter set for the
simulation environment, also after the post-processing the
driver inputs (steering wheel angle, throttle position, brake
pedal force/position, gear) and the measured system outputs
(vary for each model, but usually vehicle speed, longitudinal
and lateral acceleration, yaw velocity, etc.) are present for the
comparison of simulation and real-world response quantities.
Finally, the recursive process of validation (denoted by doted
line on Fig. 2) is to be fulfilled by appropriate machine
learning algorithm [24], the main steps of the iterative
validation process are presented with the blue and red shapes
on Fig. 2. As an output of the parameter estimation, the mean
value of the parameters and the uncertainty of the estimation
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are given. This will define the base parameter set for the
simulation. The iterative loop is the following:
Running the simulation using the driver inputs from
vehicle tests.
Compare the two SRQ set by computing the previously
defined validation metrics.
Compare each metric with the belonging validity
criteria.
If the criteria is not met, then fine-tune the vehicle
parameters, in the range given by the uncertainty of the
estimation.
The process ends when the validity criteria is met.
In the following subsection, the validation metrics and
validity criteria for vehicle dynamics models are discussed
in more detail.
A. SPECIFICATION
In Fig. 2the steps of the validation process are defined, but
in order to have a complete framework, some preparatory
tasks need to be included which are not in the figure. The
first step - following the nomenclature of the widely used
V-model [25] - is the specification, which contains all
the initial information gathering regarding the real-world
system, the simulation environment, and the purpose of
the simulation. This information all necessary to define the
following:
initial vehicle parameter set,
the required vehicle dynamics measurement system
(sensors, accuracies),
the list of individual parameter measurements (if
necessary),
the vehicle dynamics test cases,
the validation metrics and validity criteria.
An important and one of the initial steps is to define
the validity criteria. Prior in this paper, a literature review
regarding validation metrics are presented. The suggestions
presented in section II-C should be implemented when
these metrics are defined for vehicle dynamics models.
As discussed previously in the above-mentioned section,
a validation metric is the quantification of the discrepancies
between the measured and simulated system responses.
Each validity criteria defines the desired maximum value
of the belonging validation metric. It is easy to see, that the
defined metrics and criteria can be different for each vehicle
dynamic model and application. For example, different SRQ
is important for ride-comfort analysis, than lateral dynamics,
also different accuracy is required for a high-level analysis
of the vehicle dynamics, than for a deeper investigation of a
subsystem.
Each computational model has several input and output
quantities, but depending on the use case the importance -
and required accuracy - for each SRQ can be different. Also,
the input parameters and the model operating conditions
(e.g. lateral and longitudinal acceleration, speed) can be in
different ranges. Answering the following questions: ’’What
question needs to be answered using the simulation-based
FIGURE 2. High level layout of the proposed framework for vehicle
dynamics model validation.
investigation?’’ and ’’What engineering decision needs to be
supported with its data?’’ will give information about:
Which system response needs to be investigated during
the validation process,
and what the required accuracy is.
The validity criteria is a list of the specified maximum
values of the different validation metrics for the given
application. These values need to be defined based on the
previously gathered information, basically, the validation
process will end if these criteria are met - meaning the model
will mimic the real system with the desired accuracy.
When defining the required accuracy of the validation
metrics the following factors should be considered according
to [20]:
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A. Widner et al.: Framework for Vehicle Dynamics Model Validation
TABLE 1. Examples for validation metrics and validity criteria.
complexity of the model, and the engineering system;
difference in hardware and environmental conditions
between the engineering system and the validation
experiment;
increase in uncertainty due to extrapolation of the model
from the validation conditions to the conditions of the
intended use;
the risk tolerance of the decision-makers involved;
the consequence of failure or under-performance of the
system.
The validity criteria for a vehicle dynamics simulation
model in our system is the set of SRQs and the acceptable
discrepancy in the given input range and the weight of
the SRQ. See an example in table 1. Where VMxis the
validation metric containing the three quantities presented
in [23]: phase, magnitude, and topology, VCxis the validity
criteria for that metric - the maximum of the validation metric
for a given SRQ, the weight represents how important the
given criteria is. For example, the second row of table1is
meaning that in the 5..5m/s2lateral acceleration range the
discrepancy of chassis roll angle (VM2) should be below
the validity criteria (VC2), and the weight of this indicator
is 0.7. As there are no standard metrics and criteria for
vehicle dynamics model validation, determining the required
accuracy is part of the validation work.
In order to have one specific value that represents how
accurate the model is, we introduce the ’’degree of validity’’
that is defined as the weighted sum of the discrepancies of
each validation metric from the validity criteria.
DoV =
w1VM1
VC1+w2VM2
VC2+. . . +wnVMn
VCn
w1+w2+. . . +wn
(1)
where
DoV is the degree of validity,
VMnis validation metric n,
VCnis the validity criteria n,
wnis the weight for validation metric n.
This is important for the conventional model validation
methods where parameters are modified manually in an
iterative way, as well as for a machine-learning based
validation systems. In the latter case, the DoV can be used
for the reward function/ cost function.
If the SRQs necessary for the validation and the SRQs
for the parameter estimation are defined, then besides the
vehicle dynamics tests, the list of sensors can be defined for
the vehicle dynamics measurement system. As mentioned
in section II, the validation metric should consider the
uncertainty of the measurement system. Therefore if the
validity criteria is defined, the required accuracy of each
sensor in the vehicle dynamics measurement system can be
defined.
At the end of the specification step, the below-listed
elements are at our disposal:
Validity criteria.
Requirements for the vehicle dynamics measurement
system.
Requirements for the vehicle dynamics tests.
List of simulation model parameters.
List of vehicle parameters that need to be measured.
B. VALIDATION CONCEPT
The following step - also based on the V-model - is the
validation concept. This step is the comprehensive planning
of the measurement and validation processes. Here basic
decisions need to be taken, that have an effect on the whole
following processes, for example: defining the layout of
the measurement system, deciding the estimation/measuring
method for each parameter, detailed planning of the vehicle
dynamics tests.
Based on the requirements from the previous step, the
vehicle dynamics measurement system can be specified
and composed in more detail. Also, parameter measure-
ment/estimation can be detailed. Our approach for parameter
determination is the following. For sufficient data from
vehicle dynamics measurement - which is also important for
the accurate validation metrics - a sophisticated measurement
system is essential. This allows measuring, estimate vehicle
parameters during the dynamic tests, which are required
anyway for the validation. With well-planned vehicle test
scenarios, we can gather sufficient information for each
vehicle parameter estimation. Therefore, the separate mea-
surements such as mass, weight distribution, inertial param-
eter measurements, suspension K&C, engine dynamometer
etc. can be augmented with the a merged dynamic test based
estimation or in some cases the dynamic estimation may
replace some individual measurements. It is important to
note that each subsystem that has a significant effect on
vehicle behavior must be measured individually with the
greatest accuracy possible. For example, if the suspension
elasto-kinematic behavior is to be investigated using vehicle
dynamics simulation, then the dynamic test based method is
probably insufficient.
Shortly the approach is that for example, during a
straight-line test (acceleration, constant speed, coast-down,
braking) sufficient data can be gathered from the following
vehicle subsystems. By measuring the tire forces and
moments, wheel angular velocities, and vehicle speed,
we can estimate parameters for the powertrain (engine torque
characteristics, gear ratios, efficiencies), tire (longitudinal
slip characteristics, rolling radius, rolling resistance, loaded
radius), aerodynamic parameters (drag and lift forces), brake
system parameters (brake force distribution, brake pressure -
braking torque characteristics). During J-turn maneuver, tire
lateral characteristics can be measured, also vehicle transient
turning behavior. With a step steer maneuver the vehicle yaw
inertia and also some tire parameter (relaxation length) can
be estimated.
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The estimations discussed in the above two paragraphs can
create additional requirements for the measurement system.
Based on the requirements for test cases given by the
previous step (III-A) and the test requirements for parameter
estimation, the detailed vehicle dynamic test plan can be
created, including all the test cases that are necessary for the
parameter estimation, for the validation process and system
warm-up, initialization as well.
Also based on this information the necessity of the
individual parameter measurements can be decided.
At the end of this block the following information is at our
disposal:
Specification and detailed composition of the vehicle
dynamics measurement system.
Specification and detailed plan for the vehicle dynamics
tests.
List of vehicle parameters with the measurement or
estimation method.
C. VEHICLE PARAMETER ESTIMATION
The idea is that utilizing the information gathered during
dynamic test events some of the necessary vehicle subsys-
tem parameters can be estimated with sufficient accuracy.
Furthermore, by knowing the uncertainty of each estimation
during the iterative model validation part we can further
improve the accuracy of these parameters, by fitting the
vehicle model SRQs.
In the proposed system we would mostly rely on the
dynamic test-based parameter estimations, but ’workshop
measurements’ are inevitable. Besides the case discussed
in the previous section, some measurements also necessary
for the vehicle dynamics measurement system as well,
for example defining damper potentiometer motion ratios,
positions, and orientation of the GPS and IMU (Inertial
Measurement Unit) systems in the vehicle coordinate system.
Also, some parameters are hard to estimate but very easy to
measure instead, such as wheelbase and wheel track.
The different subsystem parameter measurements and
estimations are discussed in the following subsections,
beginning with the tire - as it has a significant impact on
vehicle behavior - and then moving on to all of the vehicle
subsystems.
1) TIRE
Tire characteristics have a major effect on vehicle behavior,
it influences grip, balance, control, and stability, hence the
tire model is a crucial part of each vehicle model [12], [26].
The goal here is to gather information about the force and
moment characteristics to fit the Pacejka Magic Formula.
Basically, there are two options for tire characterization
measurements: indoor and outdoor testing.
Indoor testing is carried out on a ’’flat-trac’’ tire force
and moment measurement system such as [27]. In this case,
the test conditions are well-controlled in large ranges. This
means that the tire can be tested under a wide range of normal
load, slip ratio, slip angle, inclination angle, pressure, etc.
Also, the temperature of the tire can be well-monitored and
controlled. For example between two side slip angle sweep
tests, a condition can be set that the next measurement only
starts if the tire surface cooled down to a specific temperature.
But there is also a downside to this method, although the
surface of the rotating belt is normally covered with an
abrasive coating to better represent a real road surface, it is
still different from it and this has a significant effect on the
measurement results [12], [28].
Outdoor testing is executed with a real vehicle equipped
with a measurement system (acquiring information of the
following: tire forces and moments, side-slip angles, dynamic
camber angles, tire pressures, tire temperatures, etc.) usually
on a proving ground. The advantage is that it is on a
real road surface, therefore the tire operating conditions are
realistic. The downside is that the parameters that have a big
influence on the grip are hardly controlled, also the ranges
are usually smaller. For example, the normal load is limited
by the vehicle static corner weights and the load transfer,
the inclination angle is limited by the static camber, chassis
roll, and suspension/steering kinematics, and compliance.
The maneuvers need to be chosen with care to have desired
operating conditions for the tires.
Obtaining data from only outdoor testing should consider
that, the side-slip angle sensor is mounted to the wheel,
therefore it measures the wheel’s side slip, not the tire’s.
If lateral force is acting on the tire, the contact patch
moves sideways relative to the wheel, therefore during this
movement, there will be a discrepancy between the tire and
wheel slip angles. This phenomenon can be modeled and
taken into account if there is information regarding tire lateral
stiffness. This may need to be measured separately before the
dynamic tests.
The most accurate option is to obtain information from
both measurements, create a tire model parameterization
based on flat belt measurements and use the vehicle-based
tire test data to scale this model to the real road surface [28].
2) STEERING, SUSPENSION KINEMATICS AND COMPLIANCE
Suspension subsystem - similarly to the tire - has significant
effect on vehicle behavior as it directly influences the tire
operating conditions (normal load, camber angle, etc.). The
most complete and most accurate method for suspension
kinematics and compliance measurements is using K&C test
machines such as [29].
However by measuring the
chassis movement (yaw, pitch, roll angles, ride height),
each wheel position relative to the chassis (wheel travel,
steering angle),
the wheel orientation relative to the ground (slip angle,
inclination angle loaded radius),
and the tire forces and moments,
and steering wheel angle,
during vehicle dynamic testing, the steering and suspension
kinematics and compliance characterization can be estimated,
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although the measurement precision falls behind the previ-
ously mentioned K&C testing.
Also some basic measurements need to be taken in the
workshop regarding the the starting suspension geometry
(camber, toe, ride height, etc.).
3) AERODYNAMICS
Wind tunnel testing is the ultimate solution for aerodynamics
because it provides complete information about aerodynamic
drag, lift, center of pressure, and so on. However, basic
aerodynamic parameters can be estimated by measuring the
tire normal forces during dynamic tests. The normal forces
on the two axles plotted against vehicle speed can give
information about the downforce and downforce distribution
(in other words center of pressure) of the vehicle. Also
aerodynamic drag can be estimated during coast down tests.
Speed must be measured with caution since, in most cases, the
speed of the vehicle is measured, but in this case, the speed
of the airflow must be measured. The effect of wind can be
reduced by conducting testing in both directions and having
accurate data regarding wind conditions, but it is preferable if
the system is equipped with pitot tubes that can measure the
speed of the airflow.
4) POWERTRAIN
Engine-powertrain dynamometers provide the most accurate
solution for the powertrain measurements. If the vehicle
dynamics measurement system is utilized for this operation,
additional data from the vehicle on-board diagnostics (OBD)
such as engine rpm, throttle position, clutch application,
selected gear, and so on are required. By measuring throttle
position, engine rpm and driving torques on the wheel -by
a wheel force transducer - the engine torque map can be
obtained during a straight run acceleration test. This has also
the drivetrain efficiency included, as measured on the wheel.
The gear ratios can be defined by seeing the relation between
the engine and wheel rpm.
5) BRAKE SYSTEM
In most of the vehicle dynamics simulation software usually
a ’’brake factor’’ is defined, which is the amount of brake
torque produced per unit brake pressure. This can be
estimated by measuring the brake torque on the wheels, brake
pressures at each brake line. Measuring brake torques and
pressures gives information also about the brake distribution
of the vehicle. Adding pedal travel and force the ’’brake
interface’’ can be characterized. Because brake disc temper-
ature has a substantial effect on braking performance, disc
temperature sensors should be installed in order to explore
the temperature dependency of the disc-pad coefficient of
friction.
D. VALIDATION PROCESS
Final step is the iterative validation (see on Fig2in dashed
frame). The base parameter set for the vehicle containing
most of the crucial parameters such as tire characteristics,
inertial parameters, suspension geometry and kinematics,
powertrain parameters are given. Also, the test track needs
to be parametrized, this information usually can be obtained
from the track operating company.
In this automated step, the previously estimated parameter
set is filled in the vehicle model. A test run is carried out using
the driver inputs from the real test. Then by comparing the
two time-histories an algorithm will calculate the degree of
validity then, modify the parameters to achieve the validity
criteria. For sure, some constraints need to be defined,
to avoid unreal values during this process. As mentioned
in a previous chapter, this validation algorithm will modify
the parameters within the measurement/estimation accuracy
range. For example, if the estimated vehicle yaw inertia
is 3200kgm2and the uncertainty is +/200kgm2, then the
algorithm can modify this parameter in that range.
In the beginning of section III the block diagram of
the proposed framework is presented augmented with the
preparatory steps. In sub-section III-A and III-B these
preparatory steps are defined. Than in sub-sectionIII-C the
parameter estimation is discussed. Finally, the iterative steps
of the validation is presented in this section.
In the following, a case study is presented for parameter
estimation utilizing the above-described principles.
IV. CASE STUDY: PARAMETER ESTIMATION
As a case study, a model validation was carried out using
some of the above-mentioned principles. In this section,
some examples are presented from the automated parameter
estimation part of our model validation system (see the block
denoted by the dashed line in Fig. 2). During the validation
process some parameters were automatically estimated from
the vehicle dynamics test data, but some of them were
measured manually in a conventional way. Most of the
estimation methods are based on statistical estimation and
carried out in Motec i2 data analysis program [30].
The vehicle used for the validation is a Mercedes-Benz Cla
250 7G-DCT, which was equipped with the vehicle dynamics
measurement system of John von Neumann University. The
test cases were carried out on the Dynamic Platform of
ZalaZONE Proving Ground.
A. MEASUREMENT SYSTEM INTRODUCTION
As mentioned before, to execute proper validation of a
sophisticated vehicle model, an advanced vehicle dynamics
measurement system is crucial. The measurement system
contains several sensors, the followings were used for the
presented estimation methods:
Kistler RoaDyn S625 - wheel force transducer
Race Technology Speedbox INS - GPS and IMU
Motec 58043 - brake pressure sensor
Motec 59006 - steering angle sensor
Using these sensors the parameters presented in Table 2
can be measured during the tests.
The data logging system was based on Motec products.
Each channel is logged by an ACL (Advanced Central
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TABLE 2. Measured parameters and accuracies.
FIGURE 3. Mass and CG position measurement with weight scale and
wheel force transducers at John von Neumann University’s laboratory.
Logger). The post-processing and parameter estimation was
carried out in Motec i2 software. Math channels were
defined to calculate vehicle inertial parameters powertrain
and brake parameters, and to visualize tire force and moment
characteristics, etc. In the followings, some of the methods
are presented.
B. MASS AND CENTER OF GRAVITY (CG) POSITION
ESTIMATION
The inertial parameters (mass, weight distribution, CG posi-
tion, etc.) are generally easy to measure with weight scales.
Our approach - as previously described - is to estimate these
parameters during dynamics tests by utilizing the data from
the advanced measurement system - which is necessary for
proper model validation anyway - to track the changes during
long test events.
In order to have a baseline value for comparing the
dynamic estimation method, a conventional mass and CG
position measurement was carried out. During this measure-
ment, the vehicle was already equipped with the measurement
system. Therefore, the corner weights were measured with a
Breda Racing weight scale set and the Kistler wheel force
transducers as well. See the measurement layout in Fig. 3.
As it can be seen, the weight scales on the front axle are
equipped on a vehicle lift, this way the height of the CG can
be measured using the method described from pages 27 to
33 in [31].
TABLE 3. Comparison of Breda and Kistler measurements.
1) ESTIMATION OF MASS AND AXLE LOAD
First, the mass and CG longitudinal position estimation is
presented. The conventional method is presented first as a
baseline. For this measurement, the weight scales were on a
level plane. Corner weights were recorded from Breda and
Kistler as well. It is important to note that the corner weights
measured by Kistler need to be compensated - by adding the
mass of the wheel’s outer part. This is necessary, because
the structure of the measuring wheel, it is not capable of
measuring its own weight. All measurements were repeated
three times. See the results in table 3. For corner weights and
total mass, the differences of the two methods were below
0.6%.
In the following, the dynamic test-based method is
presented. The basic principle of the parameter estimation
system is that as an initial step, the calculation channel
filters out situations - with an ’’if’’ function - that are not
suitable for determining the given parameter. Then, using the
measured channels the math channel calculates the parameter
in each time step, then a separate math channel determines the
statistical mean value and standard deviation of the channel.
In case of mass and weight distribution, the wheel forces
are close enough to the static load if the vehicle is moving
straight on level ground without any acceleration and with
a low speed - to avoid aerodynamic lift effects, or standing
on a level surface and the wheels are not tensioned (such as
after braking while still applying brake pressure). The corner
weight channels give the calculated value if the following
criteria are met:
The absolute value of the longitudinal acceleration is
less than 0.5m/s2.
The absolute value of the lateral acceleration is less than
0.5m/s2.
The absolute value of the steering angle is less than 10.
The vehicle speed is less than 50km/h.
The first two conditions ensure a steady-state, the third
filters out the effect of the steering geometry (normal force
variation due to king-pin inclination), the fourth condition
filters out the effect of aerodynamic forces. Then, using
the filtered data, the parameters can be calculated with the
appropriate equation.
Total mass of the vehicle:
m=FzFL +FzFR +FzRL +FzRR
G+4·mwft (2)
The mass on the front axle:
mF=FzFL +FzFR
G+2·mwft (3)
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FIGURE 4. Visualization of the parameters used in the equations. WB:
wheelbase; a: longitudinal distance of the front axle from the CG; b:
longitudinal distance of the rear axle from the CG; t: lateral distance of
each wheel from the CG.
The mass on the rear axle:
mR=FzRL +FzRR
G+2·mwft (4)
where Fz-s are the wheel normal forces and mwft (20kg) is
the mass of the outer part of the wheel force transducer, Gis
the gravitational acceleration. In the lower indexes FL is front
left, FR is front right, RL is rear left, and RR is rear right.
The front weight distribution is:
WDF=mF
m(5)
where mFis the mass on the front axle.
For each parameter two channels calculate the statistical
mean and standard deviation for the entire data set. This
gives a specific value and the standard deviation provides
information about the accuracy of the estimate. After the
weight distribution is given the longitudinal position of the
CG can be calculated as follows:
a=WB ·(1 WDF) (6)
and the rear
b=WB a(7)
where
ais the longitudinal distance of the front axle from the
CG.
bis the longitudinal distance of the rear axle from the
CG.
WB is the wheelbase.
The above mentioned parameters can be seen on figure 4.
The dynamic mass and weight distribution estimation
method allows taking into account the changing conditions
during a longer test case such as changes in mass and weight
distribution due to fuel consumption or passenger changes.
Based on the results it can be concluded that the dynamic
estimation method can measure the mass and CG x and y
position of the vehicle in motion with sufficient level of
accuracy.
2) ESTIMATION OF CG HEIGHT
Center of gravity height affects the dynamic load transfer,
hence the load transfer can be measured - by measuring all
the tire normal forces - the (hCG) can be estimated. For this,
any steady-state behavior is suitable where the vehicle has
sufficient acceleration. Here data from a steady-state braking
maneuver was used. In steady-state the longitudinal load
transfer can be calculated with the following equation:
1Fz =m·ax·hCG
WB ,(8)
where axis the longitudinal acceleration and WB is the
wheelbase. By rearranging the equation we get the following:
hCG =WB ·1Fz
m·ax·,(9)
This equation only true in steady-state, therefore all
transient data needs to be filtered. This was done with the
following conditions:
To filter out cornering: The absolute value of lateral
acceleration is below 0.5m/s2.
To have sufficient load transfer: The longitudinal
acceleration is above 5m/s2.
To ensure steady-state
Absolute value of pitch velocity is below 1/s
Absolute value of the derivative of longitudinal
acceleration is below 20m/s3
Fig. 5shows the results of the estimation during a braking
maneuver. The estimated and filtered calculation channel
can be seen at the top, which displays value only when the
previously described requirements are met.
In a previous work [32], this method was compared to the
widely used ’’Lifted axle’’ method, which is based on the
static load transfer due to axle lifting. The difference between
the two measurements was 9,2mm (1,7%).
C. YAW INERTIA ESTIMATION
This parameter was estimated using data from a step-steer
maneuver. If we consider the car as one rigid body, then
the yaw acceleration is proportional to the yaw moment and
the yaw inertia. The yaw inertia can be calculated by the
following equation:
θz=Mz
βz
,(10)
where
θzis the vehicle yaw inertia,
Mzis the yaw moment acting on the chassis,
βzis the yaw acceleration of the chassis.
The yaw moment was calculated with the following
equation:
Mz =MzFyFL +MzFyFR +MzFyRL +MzFyRR
+MzFxFL +MzFxFR +MzFxRL +MzFxRR
+MzFL +MzFR +MzRL +MzRR (11)
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FIGURE 5. CG Height estimation during straight line braking. On top the
actual and the mean value of the estimation channel can be seen. The
three middle chart shows some of the motion parameters (vehicle speed,
longitudinal acceleration, and pitch velocity) that are used for filtering
out the transient states. Then, on the bottom the longitudinal load
transfer channel which is used of the estimation.
where MzFL ,MzFR,MzRL ,MzRR are the tire aligning torques
and
MzFyFL =(FyFL ·cos(δFL )FxFL ·sin(δFL )) ·a(12)
MzFyFR =(FyFR ·cos(δFR)+FxFR ·sin(δFR )) ·a(13)
MzFyRL = −(FyRL ·cos(δRL )FxRL ·sin(δRL )) ·b(14)
MzFyRR = −(FyRR ·cos(δRR)+FxRR ·sin(δRR )) ·b(15)
MzFxFL = −(FxFL ·cos(δFL )+FyFL ·sin(δFL )) ·tFL (16)
MzFxFR =(FxFR ·cos(δFR)FyFR ·sin(δFR )) ·tFR (17)
MzFxRL = −(FxRL ·cos(δRL )+FyRL ·sin(δRL )) ·tRL (18)
MzFxRR =(FxRR ·cos(δRR)+FyRR ·sin(δRR )) ·tRR (19)
where
Fy is the lateral force in the wheel coordinate system for
each wheel;
Fx is the longitudinal force in the wheel coordinate
system for each wheel;
δis the steering angle of each wheel including steering,
static toe, kinematic toe, elastic toe;
tis the lateral position of each wheel from the CG.
The lateral and longitudinal forces given by the wheel force
transducers are converted into the chassis coordinate system
to correct the effect of wheel steering angles. Also, there is a
lag in the signal due to the wireless communication between
the measuring wheels and the on-board electronics. Therefore
all the channels from the Kistler system were adjusted with
a ’’time shift’’ function in Motec i2 by -63ms. As the yaw
velocity change occurs rapidly during a step-steer maneuver
all the channels used for the estimation must be synchronized.
For the proper estimation, the data set needed to be filtered
so that the math channel only uses data when there are
sufficient yaw moment, and yaw acceleration.
Absolute value of the yaw moment is above 4000 Nm
Absolute value of the yaw acceleration is above 50/s2
If the above-mentioned conditions are true then the channel
gives the calculated yaw inertia, if not true, then gives no
value. Finally, the mean value and standard deviation of
the channel are calculated. The result of the estimation is
2960 kgm2, and the standard deviation of the estimation
channel is 330kgm2.
D. ENGINE TORQUE CHARACTERISTICS ESTIMATION
In concerns of the powertrain, some values are available
from any vehicle database, such as gear and final drive
ratios, as well as engine torque characteristics at full throttle.
Although engine max load characteristics are insufficient
for a vehicle model, also real values frequently differ from
catalog values.
We have information about the propulsion torque on the
wheels due to the measurement system, therefore we cannot
measure the pure engine characteristics but rather with the
overall drivetrain efficiency.
The propulsion torque was calculated with the following
equation:
MyF=MyFR +MyFL (20)
where My-s are the driving torques on the wheels.
Then this channel was filtered by the following conditions
to only have pure acceleration without brake application and
to only investigate the required conditions: throttle position
and gear:
Throttle position (from OBD) is more than 95%.
Brake pressure (front and rear) is below 1bar.
Gear is 2 (in the example).
From the filtered wheel torque channel then the engine
estimated torque was calculated with the following equation:
ENGtorque(G2,TP100) =MyF
GearRatio(2) (21)
The results of full-throttle characteristics in second gear
can be seen in Fig. 6.
The test scenario was an acceleration from standstill with
different throttle positions. This way sufficient information
can be gathered to have full and part load characteristics in
all gears. Measuring in all gears is important because we can
get a picture of the efficiency of each gear.
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FIGURE 6. Estimated powertrain torque characteristics measured on the
wheels in second gear.
E. ESTIMATION OF BRAKE PARAMETERS
In the simulation software, one of the main brake parameters
is the so-called ‘brake factor’, which gives the braking torque
exerted by unit brake pressure. Its unit is Nm/bar. In addition,
we need to specify the brake torque distribution, which is
a percentage of brake torque on the front axle divided by
the total braking torque. Finally, the value of the maximum
braking torque that can be applied by the braking system shall
be defined. To determine these, the following math channels
were created.
Braking torque on each wheel is the My channel filtered by
the following conditions:
Brake pressure at the given wheel is more than 10bar.
Throttle pedal position is below 5%.
The brake factor is calculated with the following equation:
BrakeFactorFL =MyFL
BrakePresFL
(22)
The brake torque distribution is calculated with the
following equation:
BrakeTorqueDist =MyFL +MyFR
MyFL +MyFR +MyRL +MyRR
(23)
The results of the estimation can be seen in Fig. 7
F. MANUAL VALIDATION OF THE VEHICLE DYNAMICS
BASED ON THE ESTIMATED PARAMETERS
In this section, we present the results of the vehicle model
validation referring to Fig 2denoted by dotted line.
For the validation, conventional manual method was used.
Our goal was to test the output correlation with the previously
estimated parameter set. Generally, it is an iteration process,
where the main steps are the following: run the simulation,
compare the outputs with the real logged data, based on the
differences look for the reasons, then change the parameter
that affect that particular phenomenon. For the simulation,
a high fidelity vehicle dynamics simulation software - AVL
VSM [33] - was used which is frequently applied by the
automotive industry. We considered that the software has
FIGURE 7. Estimation of brake parameters. The first and second charts
show the braking torques and brake pressures for each wheels. The third
is the calculated brake factor. Then on the bottom, the brake torque
distribution and brake pedal position are shown.
well established computational base and is used by several
industrial parties. Therefore during the validation process,
we focused on the fine-tuning of the vehicle parameters and
not on the equations behind the model.
The following test cases in the simulation model was
carried out: First test case is stand-still equilibrium, the
vehicle stands on a level road, then steering is turned both
sides. This test is for checking the standstill equilibrium: ride
heights, static normal forces, etc. and to check the suspension
geometry and steering characteristics: steering angle vs wheel
angle, camber variation due to steering, etc.
Then a straight run test (acceleration, constant speed,
coast-down, braking) for checking the rolling resistance,
aerodynamic drag, propulsion characteristics, braking perfor-
mance, longitudinal characteristics of the tire.
The next test was a steady-state cornering test to investigate
the over-, understeer characteristics of the vehicle, tire lateral
performance, roll gradient, and roll stiffness distribution.
Then transient steering input (sinusoidal, step steer) to
investigate the transient response, tire lateral performance,
etc. and combined test cases (acceleration or braking in turn).
Finally combined test case with the driver input from real
logged data that can be seen in Fig. 8. The graph shows the
vehicle speed and the tire longitudinal forces, red is measured,
green is the simulated result.
As an example, the final values of the parameters - pre-
sented in the previous subsections - are presented in Table 4.
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FIGURE 8. Example of the validation’s results: Vehicle speed and tire longitudinal forces. Comparison of experimental measurements (red) and
simulation results (green).
TABLE 4. The final value of the estimated parameters - which are
presented in this paper - after the validation.
The values were modified during the iterative validation
process within the measurement/estimation accuracy range.
V. CONCLUSION AND FUTURE WORK
First a literature review was presented which concluded that
there is no standard general framework for vehicle dynamics
model validation. The topics of validation metrics and vehicle
parameter measurement and estimation was investigated
more deeply.
A high level layout for a vehicle dynamics model validation
framework was presented. Also insights regarding parameter
estimation and validation metrics, validity criteria were
discussed. Then, a part of the proposed framework was
demonstrated via a case study using real-world vehicle mea-
surements and high-fidelity automotive simulation software.
The goal is to create a framework with predominantly
automated processes. For this as a base, the validation metric
and validity criteria need to be further developed. The task
of determining which parameters should be examined and
what level of accuracy is appropriate for the validation of
a given simulation model is not trivial. Investigating this
topic and developing a comprehensive metric for vehicle
dynamics model validation metric is part of the future
work. Also, the automated parameter estimation needs to
be further developed and augmented for more parameters.
Finally, the iterative process of parameter fine-tuning and data
comparison is to be automated.
In the future, the validation of a single track model will be
performed using the entire validation methodology outlined
in this article.
ACKNOWLEDGMENT
The model validation and the preliminary measurements
were carried out at John von Neumann University, the
vehicle dynamics measurements were carried out with the
university’s vehicle dynamics measurement system.
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vsm-4-
ATTILA WIDNER received the M.Sc. degree
in vehicle engineering from Széchenyi István
University, in 2020. He is currently pursuing the
Ph.D. degree with the Budapest University of
Technology and Economics. In parallel, he is
working both at John von Neumann University and
the HUMDA Laboratory (which is the Research
Institution of the Hungarian Motorsport Devel-
opment Agency) as a Researcher in the field of
vehicle dynamics simulation and model validation.
VIKTOR TIHANYI received the degree in elec-
trical engineering from the Faculty of Electric
Machines and Drives, Budapest University of
Technology and Economics, in 2005, the Ph.D.
degree, in 2012, and the B.Sc. degree in mechan-
ical engineering from the Vehicle Technology
Faculty, University of Óbuda, in 2014. He has
been working with Hyundai Technology Center
Hungary for five years, since 2008. In 2013,
he changed to the automotive sector at Knorr-
Bremse Fékrendszerek Kft., as the Project Leader and the Team Leader
of Electromobility and Autonomous Vehicle-Related Projects, until 2019.
Since 2020, he has been working at ZalaZONE Proving Ground as the
Team Leader of Research and Innovation Activities. Besides his industrial
employment, he has been also working with the Department of Automotive
Technologies, Budapest University of Technology and Economics, as the
Research Leader of Autonomous Vehicle-Related Research Projects, since
2016, as an Associate Professor.
TAMÁS TETTAMANTI received the M.Sc. and
Ph.D. degrees in traffic engineering, in 2007 and
2013, respectively. He acts as an Associate
Professor and also participates in research and
industrial projects as a Researcher and a Project
Coordinator. He is the coauthor of over 140 sci-
entific papers, two patents, and several books. His
research interests include road traffic modeling,
estimation, control with applications in intelligent,
and autonomous transportation systems. He is a
member of the Public Body of Hungarian Academy of Sciences (Committee
on Transport Engineering). He is a Management Committee Member at
European Cooperation in Science and Technology COST Action CA162222
(Wider Impacts and Scenario Evaluation of Autonomous and Connected
Transport).
35436 VOLUME 10, 2022
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This intermediate textbook is appropriate for students in vehicle dynamics courses, in their last year of undergraduate study or their first year of graduate study. It is also appropriate for mechanical engineers, automotive engineers, and researchers in the area of vehicle dynamics for continuing education or as a reference. It addresses fundamental and advanced topics, and a basic knowledge of kinematics and dynamics, as well as numerical methods, is expected. The contents are kept at a theoretical-practical level, with a strong emphasis on application. This third edition has been reduced by 25%, to allow for coverage over one semester, as opposed to the previous edition that needed two semesters for coverage. The textbook is composed of four parts: • Vehicle Motion: covers tire dynamics, forward vehicle dynamics, and driveline dynamics • Vehicle Kinematics: covers applied kinematics, applied mechanisms, steering dynamics, and suspension mechanisms • Vehicle Dynamics: covers applied dynamics, vehicle planar dynamics, and vehicle roll dynamics • Vehicle Vibration: covers applied vibrations, vehicle vibrations, and suspension optimization Vehicle dynamics concepts are covered in detail, with a concentration on their practical uses. Also provided are related theorems and formal proofs, along with case examples. Readers appreciate the user-friendly presentation of the science and engineering of the mechanical aspects of vehicles, and learn how to analyze and optimize vehicles’ handling and ride dynamics.
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The definitive book on tire mechanics by the acknowledged world expert. © 2012 Hans Pacejka Published by Elsevier Ltd All rights reserved.