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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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A. Widner et al.: Framework for Vehicle Dynamics Model Validation

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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A. Widner et al.: Framework for Vehicle Dynamics Model Validation

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

35426 VOLUME 10, 2022

A. Widner et al.: Framework for Vehicle Dynamics Model Validation

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).

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