ROAD PROFILE ESTIMATION AND
CLASSIFICATION
Design of robust H∞ observer for profile estimation and clas-
sification based on the ride comfort

Master’s thesis in Systems, Control and Mechatronics

SACHIN MADHUSUDHANA

Department of Electrical Engineering
CHALMERS UNIVERSITY OF TECHNOLOGY
Gothenburg, Sweden 2019





Master’s thesis 2019:August

Road Profile Estimation and Classification

Design of robust H∞ observer for profile estimation and classification
based on the ride comfort

SACHIN MADHUSUDHANA

Department of Electrical Engineering
Division of

Systems control and mechatronics
Chalmers University of Technology

Gothenburg, Sweden 2019



Road profile estimation and classification
Design of robust H∞ observer for profile estimation and classification based on the
ride comfort
Sachin Madhusudhana

© Sachin Madhusudhana, 2019.

Supervisor: Anton Albinson, Volvo Cars Corporation and Balazs Kulcsar, Chalmers
University of Technology
Examiner: Balazs Kulcsar, Systems Control and Mechatronics, Chalmers University
of Technology

Master’s Thesis 2019:August
Systems, Control and Mechatronics
Electrical Engineering
Chalmers University of Technology
SE-412 96 Gothenburg

iv



Sachin Madhushadhana
Systems, Control and Mechatronics
Chalmers University of Technology

v



ABSTRACT
The current active suspension systems are tuned extensively on different types of
roads to have a good vehicle comfort and handling for safety and economic savings.
Even though different modes can be chosen depending on the mode of the driver,
such as comfort or dynamic, no adaptation of these modes are made for different
road surfaces. The knowledge of the road profile estimation can be used to adapt the
damping coefficient on active or semi-active suspension control systems to improve
the ride comfort and handling of a car. Recent improvement in communication has
enabled advancement in approaches towards vehicle safety which makes it possible
for communication between the road infrastructure and the vehicle.

This master thesis involves the implementation of a road profile estimation method
with the measurements obtained from the sensors placed in the vehicle. The suspen-
sion variables used in the estimation method is obtained from a robust H∞observer
by modelling a quarter car vertical model. The robust observer is a frequency depen-
dant optimization framework providing better results of estimation in an uncertain
and noisy environment. Frequency weightings is formulated in the state space form
which prevents the cancellation of important dynamics of the system. The road ir-
regularities are further validated using Fourier analysis providing information about
the frequency components of the estimated profiles. One type of information that
is important to distinguish is the amplitude versus wavelength spectra of the road.
The road classification is done on the basis of ISO8608 standards and extended for
inclusion of more harmonic components along the road profile.

Power Spectral Density(PSD) gives the best idea for the determining the road rough-
ness and a standard for the classification of the road. Furthermore this classified
road data is stored in a cloud service, which provides an online infrastructure com-
municating with vehicle about the road surface ahead. Finally this opens a new
dimension to tune the controller adaptively to optimize the comfort and handling
of the vehicle on any stretch of road.

Keywords: PSD, H∞observer, Fourier analysis, Road profile, Semi-active suspen-
sion, ISO8608, quarter car model

vi





Acknowledgements
I would first like to thank my thesis advisor Balazs Kulcsar of Chalmers University
of Technology, Professor at Faculty of Automatic Control Research group in the
department of Electrical engineering. Balazs steered me in the right direction when-
ever I ran into a problem or had a question about my research. Consistent meeting
with the professor regarding the flow of the thesis helped me to stay on track with
my research topic.

I would also like to thank Anton Albinsson of Volvo Cars for his valuable inputs
in carrying out the research and validation of results. Without his involvement in
providing the valuable tasks to be carried out this could not have been successfully
conducted. I would also like to acknowledge Akshay Bharadwaj of Chalmers Uni-
versity of Technology for his inputs and valuable comments on the thesis.

Finally, I express my profound gratitude to my family and friends for providing
continuous encouragement throughout my years of study. This accomplishment
would not have been possible without them. Thank you

Sachin Madhusudhana, Gothenburg

viii





x



Contents

List of Figures xiii

List of Tables xv

1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Road Profile Estimation Overview . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Direct Measurement . . . . . . . . . . . . . . . . . . . . . . . 2
1.2.2 Non-contact Measurement . . . . . . . . . . . . . . . . . . . . 2
1.2.3 Indirect Measurement . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Theory 5
2.1 Vehicle Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Active Suspensions . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Semi-Active Suspensions . . . . . . . . . . . . . . . . . . . . . 5

2.1.2.1 CCD Model . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.3 Quarter Car Modeling . . . . . . . . . . . . . . . . . . . . . . 6

2.1.3.1 Observability Analysis . . . . . . . . . . . . . . . . . 8
2.1.3.2 Model Validation . . . . . . . . . . . . . . . . . . . . 9

2.2 Road Profile Estimation and Modeling . . . . . . . . . . . . . . . . . 10
2.3 Observer Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.1 µ synthesis with DK-iteration . . . . . . . . . . . . . . . . . . 13
2.4 Frequency Analysis and PSD . . . . . . . . . . . . . . . . . . . . . . . 14

3 Methodology 17
3.1 Model Based Estimation Algorithm . . . . . . . . . . . . . . . . . . . 17
3.2 Power Spectral Density . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.2.1 ISO 8608 Classification . . . . . . . . . . . . . . . . . . . . . . 23

4 Results 27
4.1 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.1.1 CarMaker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1.2 Estimation of suspension parameters . . . . . . . . . . . . . . 28
4.1.3 Road Estimation Model . . . . . . . . . . . . . . . . . . . . . 31

4.2 Frequency Analysis and Power spectrum density . . . . . . . . . . . . 33
4.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

xi



Contents

4.3.1 Frequency analysis and PSD for Experimental data . . . . . . 40
4.3.2 ISO Classification . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.3 Decision for Damper tuning for Primary and Secondary ride . 45

4.4 Future Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5 Conclusion 49

Bibliography 51

A Appendix I

xii



List of Figures

1.1 Different road estimation models . . . . . . . . . . . . . . . . . . . . 4

2.1 CCD damper force from deflecting velocity . . . . . . . . . . . . . . . 6
2.2 Quarter Car Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Suspension variables on road profile A . . . . . . . . . . . . . . . . . 9
2.4 Suspension variables on road profile B . . . . . . . . . . . . . . . . . 9
2.5 General observer structure . . . . . . . . . . . . . . . . . . . . . . . . 10
2.6 Closed loop observer structure . . . . . . . . . . . . . . . . . . . . . . 11
2.7 Difference in the observer synthesis . . . . . . . . . . . . . . . . . . . 14

3.1 Methodolgy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 System dynamic of semi active suspension with passive suspension

system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 H∞ Estimation method . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4 Road shaping filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Actuator uncertainty model . . . . . . . . . . . . . . . . . . . . . . . 20
3.6 Choice of performance weightings against the sensitivity . . . . . . . 21
3.7 Weighted noise measurements . . . . . . . . . . . . . . . . . . . . . . 21
3.8 Classification of roads from A to F . . . . . . . . . . . . . . . . . . . 24
3.9 Roughness coefficient vs velocity . . . . . . . . . . . . . . . . . . . . . 25
3.10 PSD of different classes of roads divided through center frequencies

by ISO 8608 [25] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.1 Estimates for CarMaker demo road surfaces with linear model . . . . 28
4.2 Estimates for CarMaker demo road surfaces with nonlinear model . . 29
4.3 Suspension parameters estimate for road A . . . . . . . . . . . . . . . 29
4.4 Suspension parameters estimate for road B . . . . . . . . . . . . . . . 30
4.5 Unsprung mass acceleration for road A . . . . . . . . . . . . . . . . . 31
4.6 Unsprung mass acceleration for road B . . . . . . . . . . . . . . . . . 31
4.7 Road profile estimate for road A . . . . . . . . . . . . . . . . . . . . . 32
4.8 Road profile estimate for road B . . . . . . . . . . . . . . . . . . . . . 32
4.9 PSD comparison for Road A . . . . . . . . . . . . . . . . . . . . . . . 33
4.10 PSD comparison for Road B . . . . . . . . . . . . . . . . . . . . . . . 33
4.11 PSD comparison for offsets . . . . . . . . . . . . . . . . . . . . . . . . 34
4.12 PSD comparison at varying speeds . . . . . . . . . . . . . . . . . . . 35
4.13 Suspension parameter estimate for manhole road . . . . . . . . . . . . 36
4.14 Road estimate for manhole road . . . . . . . . . . . . . . . . . . . . . 36

xiii



List of Figures

4.15 Suspension parameter estimate for roll excitation on Front left wheel 37
4.16 Road estimate for roll excitation on front left wheel . . . . . . . . . . 37
4.17 Suspension parameter estimate for low frequency road . . . . . . . . . 38
4.18 Road estimate for low frequency road . . . . . . . . . . . . . . . . . . 38
4.19 Suspension parameter estimate for high frequency road . . . . . . . . 39
4.20 Road estimate for high frequency road . . . . . . . . . . . . . . . . . 39
4.21 Primary and secondary ride roads . . . . . . . . . . . . . . . . . . . . 40
4.22 Comparison between CarMaker PSD estimate and experimental PSD

estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.23 PSD comparison when driven on same road back and forth . . . . . . 41
4.24 Displacement PSD of low frequency road . . . . . . . . . . . . . . . . 41
4.25 Primary and secondary ride roads . . . . . . . . . . . . . . . . . . . . 42
4.26 Displacement PSD of high frequency road . . . . . . . . . . . . . . . 43
4.27 Primary and secondary ride roads . . . . . . . . . . . . . . . . . . . . 43
4.28 Maneuvering frequency ranges . . . . . . . . . . . . . . . . . . . . . . 45
4.29 Primary and secondary ride roads . . . . . . . . . . . . . . . . . . . . 46

A.1 Comparison of PSD for road profile A at varying velocities with ISO
standard classification . . . . . . . . . . . . . . . . . . . . . . . . . . I

xiv



List of Tables

2.1 Vehicle Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.1 Road level definition by ISO . . . . . . . . . . . . . . . . . . . . . . . 24

4.1 Parameters of low frequency road classification . . . . . . . . . . . . . 42
4.2 Parameters of high frequency road classification . . . . . . . . . . . . 43

xv



List of Tables

xvi



1
Introduction

1.1 Motivation

In today’s world we have highest number of vehicles on road, and this number
seems to ever increase with the advancement in technologies in the automotive in-
dustry with autonomous vehicles and electro-mobility. Vehicle dynamics is a major
area with continuous development in the handling and comfort of the vehicle. One
such important factor which is the primary input to the vehicle is the road profile
which determines the vehicle performance.This information is used to adapt differ-
ent suspension features. The estimated road profile is used to adaptively change the
damping coefficient in the semi-active or the active suspensions control to tweak the
handling and the stability of the car.
A bad road might cause severe damage to the vehicle components at different fre-
quencies, which results in increase in the operational costs when there is a damage.
According to the report [1] the road expenses is about 20 billion Euros in EU each
year and in Germany is said to reach from 2.7 billion Euros in 2015 to 3.6 billion
Euros in 2025 [2]. Hence such a method is necessary to estimate the road profile
beforehand. The federal highway administration (FHA) under U.S development of
transportation started the long term pavement performance (LTTP) in 1987 [3]. It
has standard data collection procedures divided into two sets namely general pave-
ment studies (GPS) and specific pavement studies (SPS), where GPS is for existing
profiles and SPS included ten levels built for specific designs of the road. This mo-
tivates for a lot of research on the importance of the road profile information. A
route planning algorithm is proposed [4] based on the passenger feeling, improving
overall time and ride comfort. [5] proposed a precision enhancement of pavement
roughness localization among the connected vehicles. The semi-active suspensions
present in the current market assume the road conditions to be unknown because
the relation between to the ride comfort and the handling are difficult to be satisfied
simultaneously [6].
Therefore an adaptive estimation is important for commercial applications of semi-
active suspension systems. Another scope of the thesis is to have a preview knowl-
edge of the road for control of the dampers through a cloud based service. This
provides an important bandwidth of the road profile as it is a primary input of
vehicle dynamics for control of handling and comfort.

1



1. Introduction

1.2 Road Profile Estimation Overview
The road estimation has attracted major interest between the automotive manufac-
turers and government in recent decades[23]. There are different methods to classify
roads which are:

1.2.1 Direct Measurement
Currently the adopted standards to determine the road profile uses a specially de-
signed device which comes in contact with the road irregularities. These devices are
called as profilometers or profilographs [7]. The accuracy of the estimation is very
high in this case. However, this is really expensive and can be affected by adverse
change in the environment. Two examples of the equipment used for the estimations
are:

• Dipstick profiler : A dipstick profiler consists of an inclinometer with two legs
collecting relatively very small quantity of road profile measurements. It has
two digital displays on the end of both the legs to provide relative elevation
between them. This method requires a person to walk through the elevation in
the pavement profile by pivoting around each leg of the profiler.These instru-
ments usually have accuracy around 0.1mm and sometimes used in calibration
of more sophisticated profilers.

• Profilographs : A profilograph is mounted with a sensing wheel to provide free
vertical movement at the center frame to determine the undulations from the
road roughness. The recorded profile is then obtained in a graph. They have a
different structure to that of the dipstick profiler and data processing methods.
The accuracy of such is around 100mm with a range from 0.05cycles/m to 2
cycles/m [8].

1.2.2 Non-contact Measurement
There are several existing methods that uses visual inspections to determine the
road depths through either camera or depth sensors.These generally are non contact
sensors like lasers and infrared transceivers mounted on the vehicle to determine the
distance between the light from the lasers and the road surface. In current commer-
cialized laser displacement sensors for road profilometry it is possible to measure
the road surfaces for upto 200mm with accuracy of 1% of the measurement range
[9]. Similar concepts can be seen which is based on the non contact measurement
[11, 12].

1.2.3 Indirect Measurement
An alternative method used is the response based system. With advancement of
technologies and stricter rules for the automotive industries, it has led to increase in
the sensors used in the vehicles. This is an indirect method that uses the information
from the sensors equipped in the vehicle such as the suspension deflection sensors

2



1. Introduction

and the accelerometers. An observer based techniques are used to determine the
road conditions. The generated road profiles in time domain can be used to mod-
ify controller parameter gains [10] . Many different methods are proposed for road
profile estimation.
Hrovat et al[13] proposes rattle space deflection to determine road conditions. Fre-
quency based estimation using sprung mass accelerations was proposed by Yi et
al [14]. A sliding mode observer was proposed by comparing it with a profilo-
graph [15]. Doumiati et al [16] used Kalman filter to determine road excitation in
real time. Time domain estimation for semi-active suspension systems using Youla
parametrization was proposed by Martinez et.al [17].

The response based systems are classified into two categories:
• Road profile estimation in time domain
• Road level classification

The profile estimation uses observer based models to reconstruct the road irregu-
larities. These models uses inverse based modelling with no prior knowledge of the
road surface profile. Whereas road classification refers to algorithms to determine
the level of the road excitation estimated.

A transfer function based approach road classification using just the measurement
of the unsprung mass accelerations was proposed by [24]. It was then extended by
Wang et al [18] to include varying velocities and experimental validation was done
to validate the algorithm. A speed independent road classification algorithm was
proposed by Qin et al [19] without any prior information of the road profile. The
results showed the robustness towards the change in the parameters and vehicle
velocity. With greater development in the fields of the Machine learning there are
many papers which uses neural networks to classify roads. Ngwangwa et al [20] uses
Back propagation and neural networks to classify road irregularities.

For time domain profile estimation Kang et al. used a discrete Kalman filter with
unknown road input and compared the results with laser profilometer form a test
vehicle [21]. Wang et al. combined a model error with Kalman filter and used
simulation results to validate with the proposed algorithm [22].

3



1. Introduction

Figure 1.1: Different road estimation models

Figure 1.1 represents the different ways of classifying roads as discussed above. The
scope in this thesis makes use of the response based systems where the sensors used
for measurements are sprung mass accelerations and unsprung mass accelerations.

1.3 Summary
A literature review of different estimation methods were presented. The growing
importance in road safety and interest in research of different methods for estima-
tion and classification is shown. The current methods to estimate the road profile
include direct measurement, non contact measurement and indirect measurement.
The indirect measurement i.e response based measurement are the best among the
three categories since they provide marginal accuracy with lower cost. Therefore a
system based on the indirect measurement for road profile estimation is built in this
thesis.

4



2
Theory

2.1 Vehicle Modeling
Vehicle system models are presented in this chapter. Vertical dynamics of the vehicle
is considered to model the system since the impact of a road input on the vehicle is
vertical. The major part of the vertical dynamics includes the automotive suspension
systems which rests the vehicle body on its axles. Modeling can be done with a 7
degree full car vertical model, or a 4 degree half car model or a 2 degree quarter car
model. A quarter car model represents a suspension system at each wheels of the
vehicle. Some of the functions of this system is to isolate the vehicle body from the
external road disturbance to give good ride quality, to provide good handling and
support the vehicle’s static weight. We will consider two systems on to which the
damper settings can be controlled i.e. active and semi-active suspension systems.

2.1.1 Active Suspensions
The passive suspension systems have significant trade-offs between ride quality and
suspension deflection. Improvements in one of the factors will deteriorate other
factor. The active suspension uses electronically controlled dampers to provide
superior ride quality.It offers more refined riding experience. An active suspension
system has the ability to store, dissipate and introduce energy into the system.
These systems help in effectively reduce the body roll,pitch and heave. Though a
fully active system will consume more power than semi-active suspension systems.

2.1.2 Semi-Active Suspensions
A semi active suspension system in the vehicle uses a variable damper by controlling
the damper force based on the continuously varying road surface, where the road
surface is not measured directly. It is similar to active suspension systems but with
an adjustable shock absorber. A semi active suspension model can be employed by
several control strategies, where the most common control strategy still used is a
skyhook controller. An example of a semi-active suspension is a magneto rheological
(MR) damper. The MR damper uses an MR fluid which reacts to changes in the
magnetic field. The dissipative force for the damper can be obtained by varying the
electromagnetic field to cause an effect in the movement of the fluid in the container.
Another type of semi-active dampers
The semi active suspension use less power when compared to active suspension
systems. Here the power is used only to change the electromagnetic field using the

5



2. Theory

current through the coil in the MR damper. No external power is used unlike the
active systems to counter the vibratory forces. In case of the semi-active dampers
with control valves, the damping force depends on the piston speed, the damping
force is directly proportional to the piston speed. The degree by which the piston
motion moves is controlled by the valves. This thesis will make use of semi active
suspensions with internal valves, but can also be used with the passive dampers as
long as the damping force is characterized.

2.1.2.1 CCD Model

The CCD damper model can be continuously adjusted according to the ride modes
required and continuous information regarding the body and wheel motion in the
vehicle. The dissipative force obtained from this model is a function of the de-
flecting velocity. At different values of current different forces can be obtained. A
damper model characteristic is usually non-linear as seen in figure 2.1.The effective
damping must be lowered for high velocities to minimize the transmissibility of the
disturbances to the passengers. Similarly lower velocities the damping should be
larger. Having higher damping is not necessary during compression as additional
energy will get stored in the springs. Therefore lower damping is given for positive
velocities since the springs will resist any further compression. But is not the case
in negative velocities as it will further increase the effective damping.

Compression<---------------Velocity(m/s)---------------> Expansion

D
a
m

p
e
r 

F
o
rc

e
(N

)

i=0.38

i=0.90

i=1.60

Figure 2.1: CCD damper force from deflecting velocity

2.1.3 Quarter Car Modeling
One of the most used vertical model for the study of vehicle suspension is the quarter
car model shown in figure 2.2. The vertical model uses two solid suspended masses
denoted as sprung mass ms and unsprung mass mus. The sprung mass denotes 1

4
th

of the body of the vehicle and the unsprung mass represents the mass of the wheel
and the components connected to it. The spring is considered to be linear because
the application it has in automotive applications is almost 95% in linear region. The
spring stiffness coefficient of the spring ks and that of the wheel kt. The damping

6



2. Theory

coefficient is bs.

ms

mus

ks bsemi

kt

zs

zus

zr

Figure 2.2: Quarter Car Model

The dynamics of motion governing the two degree of freedom vertical model is given
by

msz̈s(t) + bsemi(t)(żs(t)− żus(t)) + ks(zs(t)− zus(t)) = 0
musz̈us(t)− bsemi(t)(żs(t)− żus(t)) + kt(zus(t)− zr(t))− ks(zs(t)− zus(t)) = 0

(2.1)

Here, bsemi(t)(zs(t) − zus(t)) is considered to be the variable damper force Fd to
adjust the handling or comfort. Therefore the dynamics can be re-written as

msz̈s(t) + ks(zs(t)− zus(t)) = −Fd(t)
musz̈us(t) + kt(zus(t)− zr(t))− ks(zs(t)− zus(t)) = Fd(t)

(2.2)

The state space model of the quarter car model for the semi active suspension model
can be written as:

ẋ(t) = Ax(t) +Bu(t) + Lzr(t) (2.3)

States of the model are considered to be

x1(t) = zs(t) Sprung mass displacement
x2(t) = żs(t) Sprung mass velocity
x3(t) = zus(t) Unsprung mass displacement
x4(t) = żus(t) Unsprung mass velocity

And, inputs
u(t) = Fd(t) Damper Force
zr(t) Road profile

7



2. Theory

State space representation of the model is given by

ẋ(t) =


żs(t)
z̈s(t)
żus(t)
z̈us(t)

 (2.4)

ẋ(t) =


0 1 0 0

−ks/ms 0 ks/ms 0
0 0 0 1

ks/mus 0 −(ks + kt)/mus 0



zs(t)
żs(t)
zus(t)
żus(t)

+


0 0

1/ms 0
0 0

−1/mus kt/mus


[
u(t)
zr(t)

]

(2.5)

[
y1(t)
y2(t)

]
=
[

1 0 −1 0
−ks/ms 0 ks/ms 0

] 
zs(t)
żs(t)
zus(t)
żus(t)

+
[

0 0
1/ms 0

] [
u(t)
zr(t)

]
+
[
n1(t)
n2(t)

]
(2.6)

Where y1 and y2 are the observed data with n1 and n2 are the corresponding noises
from the sensor modules. The parameters used in designing the model is given in
table 2.1

ms 608.7
mus 52.611
ks 45356.3
kt 286882

Table 2.1: Vehicle Parameters

The states that are used to determine the vehicle performance in the vertical dy-
namics are hard to obtain. Hence a H∞ observer is designed to estimate the the
states and handle the uncertainties and disturbances.

2.1.3.1 Observability Analysis

This analysis is used to determine how well the internal states are easy to deduce
based on the system input and output. Since the system designed above is a linear
system, the observability condition can be checked by Kalman test

O =
[
C CA CA2 CA3

]
(2.7)

For the system to be observable the rank of the matrix must be equal to the number
of states of the system i.e rank(O) = n. For the above system the observability
condition holds true.

8



2. Theory

2.1.3.2 Model Validation

In control applications all the types of model needs to be validated to ensure that the
region around which it is operated should be very similar to that of the non-linear
model. Therefore it is necessary that the model is applicable for the designed oper-
ation. Hence, the output of the linear models should match that of the non-linear
model in the respective time domain.

To test the linear model, the vehicle is run on two road profiles A and B in the
Carmaker. The algorithm is written in Matlab, where the linear model is built. It is
possible to collect data from Carmaker to Simulink. Results for which can be seen
in figures 2.3 and 2.4. The model outputs are in red color whereas the Carmaker
model is in blue color. The four states match that of the non linear model. The
similar roads A and B will be used for the analysis of observer.

Figure 2.3: Suspension variables on road profile A

Figure 2.4: Suspension variables on road profile B

9



2. Theory

2.2 Road Profile Estimation and Modeling
The standard definition of road profile is the distance between the road surface and
the base of the measuring device in a contact based instruments. Unsprung mass
accelerations measurements are close to determination of the road profile zr(t). By
using the estimated states from the observer, it is possible to determine the road
profile from the static equation of the unsprung mass acceleration

ẑr(t) = (mus
¨̂zus(t)− ks(ẑs(t)− ẑus(t)) + ktẑus(t) + Fd(t))/kt (2.8)

Since the measurement that is used from the sprung mass accelerations (z̈s) and
suspension deflection alone, the unsprung mass accelerations ˆ̈zus is estimated. Fd is
the damper force that is obtained form the CCD model.
The statistical characteristics of such road surfaces based on amplitude and fre-
quency can be used to classify the type of road. Power spectral densities is one such
way to give a better understanding of the road irregularities.

2.3 Observer Design
A general structure of an observer to estimate the unobservable states is shown in
figure 2.5, where the measurements are the input to an observer which estimate the
states based on an estimation algorithm. The error term that is obtained as result
of difference between true states and the observer output has to be reduced. There
are many such observer structures for state estimation. In this thesis H∞ observer
is the one chosen.

ẋ(t) = Ax(t) +Bu(t) + Fzr(t)
y(t) = Cx(t) + Du(t)

˙̂x(t) = Af x̂(t) +Bfy(t)
ŷ(t) = Cf x̂(t)

x

y x̂ = ŷ z = x̂− ŷ

zr

u

Figure 2.5: General observer structure

The H∞ observer is a Luenberger state observer which is an extension of H∞ con-
troller optimization framework. Therefore, a linearised search algorithm for the H∞
can be straight forwardly applied to this problem.
The general LTI plant used for the synthesis of H∞ observer is given by

P =


ẋ(t) = Ax(t) +Bu(t) + Fzr(t)
y(t) = Cx(t) +Du(t)
z(t) = Wei(t)(x(t)− x̂i(t))

(2.9)

10



2. Theory

where x(t) is the states, u(t) is the control input and zr(t) is the unknown road input
to the system. y(t) is the measured outputs and z(t) is the performance outputs.
Wei is the performance dynamic weightings on the states for error minimization.

An augmented model for the quarter car system is built for this observer design to
establish the disturbance rejection and reduce integration drift in the states. The
updated measurement equation of which along with the performance outputs as
mentioned in 2.9 is augmented as

y(t) =



1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
0 1 0 −1
1 0 −1 0

−ks/ms 0 ks/ms 0


︸ ︷︷ ︸

C2


zs(t)
żs(t)
zus(t)
żus(t)

+



0 0
0 0
0 0
0 0
0 0
0 0

1/ms 0


︸ ︷︷ ︸

D2

[
u(t)
zr(t)

]
(2.10)

The augmented plant model now consists of the measured outputs and perfor-
mance outputs useful for the observer synthesis. The observer dynamics is given
by ˙̂x = Af x̂(t) +Bfy(t), which is quadratically stable.

ẋ(t) = Ax(t) +Bu(t) + Fzr(t)
y(t) = Cx(t) +Du(t)
z(t) = Wei(t) (x(t)− x̂(t))

˙̂x(t) = Af x̂(t) +Bfy(t)
ŷ(t) = Cf x̂(t)

yx̂ = ŷ

z = x− x̂u

N

Figure 2.6: Closed loop observer structure

With reference to general controller configuration in 2.6, the central controller has
same number of states as the generalized plant P . Therefore the central controller
can be divided into state observer and a state feedback control. For this thesis re-
quires just the design of state observer. The general algorithm for the H∞ synthesis

11



2. Theory

is given by a law satisfying the optimal law ||Fl(P,K)||∞ < γ where γ is the per-
formance level and Fl is the lower fractional transformation i.e the interconnection
between the plant and the controller (N = Fl(P,K)). K is a stabilizing controller if
and only if,
(i) X∞ > 0 is a solution to riccati equation

ATX∞ +X∞A+ CT
1 C1 +X∞(γ−2B1B

T
1 −B2B

T
2 )X∞ = 0 (2.11)

such that Re λi[A+ (γ−2B1B
T
1 −B2B

T
2 )X∞] < 0, ∀i, and

(ii) Y∞ > 0 is a solution to riccati equation

ATY∞ + Y∞A+BT
1 B1 + Y∞(γ−2C1C

T
1 − C2C

T
2 )Y∞ = 0 (2.12)

such that Re λi[A+ ((γ−2C1C
T
1 − C2C

T
2 )Y∞], ∀i, and

(iii) ρ(X∞Y∞) < γ2

Such controllers are given by K = Fl(Kc, Q) where

Kc(s) = L
 A∞ −Z∞ L∞ Z∞ B∞

F∞ 0 I
−C2 I 0



F∞ = −BT
2 X∞, L∞ = −Y∞CT

2 , Z∞ = (I − γ−2Y∞X∞)−1 (2.13)

A∞ = A+ γ−2B1B
T
1 X∞ +B2F∞ + Z∞L∞C2 (2.14)

where Q(s) is a stable transfer function, such that ||Q||∞ < γ and L is the Laplace
transform.
If Q(s) = 0 then

K(s) = Kc11(s) = −Z∞L∞(sI − A∞)−1F∞ (2.15)

we obtain the central controller. As explained in the beginning a central controller
has same number as the plant model and can be separated into a state observer

˙̂x(t) = Ax̂(t) +B1 γ
−2BT

1 X∞(t)x̂︸ ︷︷ ︸
worst case

+B2u(t) + Z∞L∞(C2x̂(t)− y(t)) (2.16)

and a state feedback

u(t) = F∞x̂(t) (2.17)

The worst case disturbance is an exogenous input to the system as shown in 2.16.
The H∞ algorithm is carried out generally by using the Matlab toolboxes. This
allows to have a γ iteration to determine the best performance of the observer.

12



2. Theory

This H∞ optimization technique is used to shape the singular values of the weight-
ing function over a desirable bandwidth by minimizing energy in the error signals
included by the uncertainty, noise and other disturbances. The difficult part of the
optimization technique is the choice of the weighting function i.e to choose a good
trade off at conflicting objectives in frequency ranges, which is described in the
section 3

2.3.1 µ synthesis with DK-iteration
In general, two observer design is possible to achieve robustness to error H∞ synthe-
sis along with µ synthesis, of which H∞ is already studied in the previous section.
The main difference is, the H∞ deals with minimizing the uncertainty in the plant.
If the uncertainty in the plant is unstructured then it means that the uncertainty in
the plant couples with each other. For example, in case of the mass damper system
of the suspension the uncertainty in the mass does not couple with that of the spring
constant, but H∞ assumes so. Whereas µ synthesis assumes structured uncertainty
where the actuator uncertainty as considered in this observer design does not couple
with suspension parameters. The structured value of µ is a powerful tool for robust
performance analysis. DK-iteration is one such technique that is used to synthesize
the observer which combines H∞ and µ synthesis to get good results.
The DK method applies upper bound on the µ in terms of scaled singular value

µ(N) ≤ min
DεDs

σ̄(DND−1) (2.18)

where N is the interconnection matrix of the closed loop and D, the dynamic weight
is the applied upper bound. Ds is the domain of the stable weighting.
This operation minimizes the peak over frequency of this upper bound, such as

min
K

(min
DεD
||(DN(K)D−1||∞) (2.19)

The DK-iteration process happens as follows:
• K-step: H∞ synthesis for the scaled problem with a constant Dmin

K
||(DN(K)D−1||∞

• D-step: Finding D(jw) to minimise at each frequency ¯σ(DND−1(jw)) with
fixed N.

The iteration continues until a satisfactory result is obtained ||(DN(K)D−1||∞ < 1
or until the norm will no longer decrease. Matlab uses function called dksyn to
perform this iteration and give the best µ value.

13



2. Theory

One such example can be seen in figure 2.7, which shows the difference between
the H∞ synthesis and µ synthesis. It is clear to see that µ sythensis gives the best
performance to uncertainties and errors in the systems.

Figure 2.7: Difference in the observer synthesis

2.4 Frequency Analysis and PSD
A road profile is a collection of many different periodic sinusoidal signals, which
contains many frequency irregularities. This thesis aims to classify the roads in terms
of spectral densities. The power spectral density(PSD) is the magnitude squared
of the Fourier transform of a continuous time and finite power signal. The PSD
describes the amount of power present in each frequencies unlike the energy spectral
densities which is suitable only for transient signals where energy is concentrated
only in a single time window. For signals such as continuous time signals such as
stationary process PSD is defined.
In general the average power of a signal say x(t) over a time period is given by

Px = lim
T 7→∞

1
T

∫ T

0
|x(t)|2dt (2.20)

To get the frequency component of the signal a Fourier transform has to be applied
over the time period [0,T] as mentioned above.

x̂(w) = 1√
T

∫ T

0
x(t)e−jwtdt (2.21)

shows the amplitude spectral density of the signal.
And the power spectral density is given by

Sxx = lim
T 7→∞

E[|x̂(w)|2] (2.22)

14



2. Theory

where, E is the expected value given by the Fourier transform

E[|x̂(w)|2] = 1
T

∫ T

0

∫ T

0
E[x∗(t)x(t′)]e−jw(t−t′)dtdt′ (2.23)

Eqn 2.23 represents the auto-correlation function of the signal x(t)

Rxx(τ) = (X(t)∗X(t+ τ)) (2.24)

PSD is defined by the auto-correlation function by

Sxx =
∫ T

0
Rxx(τ)e−jwτdτ = R̂xx(w) (2.25)

provided Rxx(τ) is integrable.

15



2. Theory

16



3
Methodology

3.1 Model Based Estimation Algorithm
The design methodology implemented in this thesis is shown in figure 3.1.

Vertical
dynamics

Road profile
estimation

Transformation
to space domain

Power spectral
density

Classifier

Descision
level

Averaging
with more
measurements

Road
Class

Profile Estimation

Frequency Analysis

ISO 8608
Classfication

Cloud storage

Figure 3.1: Methodolgy

As seen from the figure above the process involves estimation of the road profile and
classification obtained from the sensor data of a vehicle with semi-active suspension
system

• Profile Estimation : To estimate the suspension parameters usingH∞observer
as discussed in section 2 and thereafter estimate the road profile based on the
static equation of the unsprung mass accelerations (2.8).

• Frequency analysis : By using the profile estimate in the time domain,
Frequency components of the road signals is determined and the corresponding
power acquired in each frequency is determined.

• ISO 8608 Classification : Classification standard of the type of roads based
on power spectral densities. Given an idea about the road surface irregularity.

17



3. Methodology

The quarter car model represented as state space representation is used for the
estimation of road profile. The best way to understand the performance of a model
for respective inputs is through the singular value of frequency response of the
system. The linear plant model dynamics with road and damper force as inputs can
be can be seen in figure 3.2.

10
-1

10
0

10
1

10
2

10
3

-100

-50

0

50

100

150

200

250

semi-active suspesion

passive suspension

Singular Values

Frequency (Hz)

S
in

g
u
la

r 
V

a
lu

e
s
 (

d
B

)

Figure 3.2: System dynamic of semi active suspension with passive suspension
system

Figure 3.2 also shows the difference between the semi-active suspension and the
passive suspension system. Since the damper force is considered as a continuously
changing input to the model and not included in the state space dynamic model
we can observe the invariant peaks at two frequencies. The figure shows two plots
obtained from the two inputs. The plot with higher singular values is due to the
road input on body displacement and the other is due to the damper force input on
the body displacement. The transfer function between damper force input to the
body displacement and velocity has imaginary zeros with resonance at 73.84rad/s
(12Hz), this frequency is called the wheel hop frequency. And the transfer function
between the suspension deflection and damper force produces imaginary zero with
resonance at 20.82rad/s(3Hz) is called the rattle space frequency.

Hence in a semi-active suspension system it is assumed to have an actuator con-
nected between unsprung and sprung mass to control the suspension over complete
bandwidth of the two frequencies, to provide a better ride performance. In case of
the passive suspension system, since there is no assumption of controlled damper
force between the two masses, the peaks at the two frequencies are highly damped.

The overall estimation model of a closed loop structure with an observer as a feed-
back and control inputs are estimated states as outputs is then built.

18



3. Methodology

Wzr

WFd

Wei

Wd

LTI plant model (G)

H∞observer
(K)

zr

Fd

z
e = x− x̂

nx̂

y

System
interconnection

Figure 3.3: H∞ Estimation method

Optimized observer is synthesized in order to make the H∞norm as low as possi-
ble. To obtain this condition three weighting functions are added to the plant for
loop shaping as shown in figure 3.3. A loop-shaping technique to design perfor-
mance filters in the optimization setting is used for the observer design. This thesis
does not deal with robustness issues with a controller design and focuses more on
H∞optimization to the frequency dependant loop-shaping state observers. The op-
timized state observer estimates the suspension parameters as control inputs fed
back to the plant model which in turn minimizes the error dynamics and reducing
the effect of the measurement noise.

The filter specifications used in the design of H∞observer is explained below. Find-
ing an appropriate weighting function is a crucial step in the robust control design
which requires few trials.

From fig 3.3 the weighting matrix denoted by Wzr is the loop shaping transfer func-
tion responsible to shape the irregularities of the road in the frequency band of
interest. This is shown in 3.4. The road variability consists of slow changing profiles
and high frequency irregularities, a relevant part of the road spectrum is a suitable
choice to affect the dynamics of the vehicle. The slow variability in the road profile
less than 0.01 cycles/m (0.3Hz) or wavelength above 100 m and similarly the high
frequency irregularities greater that 5 cycles/m (30Hz) or wavelength below 0.5m
are filtered out since it is difficult to measure high frequencies with the sensors used
and very low frequencies do not affect the vehicle dynamics, hence they are not
included in the spectrum. The region covered with boundary in the red color shows
the region of interest.

19



3. Methodology

10
-4

10
-3

10
-2

10
-1

10
0

10
1

10
2

10
3

4

5

6

7

8

9

10

11

12

13

Road shaping filter

Wzr

Frequency (Hz)

S
in

g
u
la

r 
V

a
lu

e
s
 (

d
B

)

Region of interest

Figure 3.4: Road shaping filter

The actuator CCD model is an approximation of the behaviour the physical sys-
tem which accounts for varying displacements and modelling errors. There exists
a nominal behaviour with frequency dependant amount of uncertainty. At lower
frequency around 0.1Hz a 40% uncertainty of the nominal model is applied and at
frequency greater than 3Hz the uncertainty is greater than 100% of the nominal
value. An input multiplicative uncertainty model is developed as a weighting to the
actuator which can be seen in figure 3.5. The nominal model is represented with
black color in the right half of the figure. The uncertainties shown are respective
to that nominal model. These input uncertainties are included in the filter design
since factors such as change in current reading due to external parameters such as
temperatures or small displacement errors in the deflection velocity brings changes
in the damper force. Therefore to account for this changes an input multiplicative
uncertainty is considered for the actuator model.

10
-2

10
-1

10
0

10
1

10
2

10
3

10
4

10
5

-120

-100

-80

-60

-40

-20

0

20

nominal filter

unceratinty

Singular Values

Frequency (Hz)

S
in

g
u
la

r 
V

a
lu

e
s
 (

d
B

)

Figure 3.5: Actuator uncertainty model

Another weighting from the figure 3.3 represents the performance weightings. It
is used in the minimization of the estimation error in the frequency region of the

20



3. Methodology

suspension operation. To achieve a desired performance of noise reduction it is
necessary to satisfy the inequality condition ||Wei(I +GK)−1||∞ < 1. The singular
values of the sensitivity function (I + GK)−1 must lie below the inverse of the
weighting function ( 1

Wei
) for all frequencies as shown in figure 3.6. Hence a precisely

tuned performance weighting has to be chosen

10
-4

10
-2

10
0

10
2

10
4

10
6

-60

-40

-20

0

20

40

60

80

100

120

Inverse performance

sensitivity

Singular Values

Frequency (Hz)

S
in

g
u
la

r 
V

a
lu

e
s
 (

d
B

)

Figure 3.6: Choice of performance weightings against the sensitivity

In general case, the measurement noise is a complementary sensitivity function from
a classical closed loop transfer equation 3.1 which describes that less weightage is
given to the noise signals which are generally present in the higher frequencies of
the sensor signals.

y = (I +GK)−1GK︸ ︷︷ ︸
T

r + (I +GK)−1︸ ︷︷ ︸
S

Gdd− (I +GK)−1GK︸ ︷︷ ︸
T

n (3.1)

10
0

10
2

10
4

-80

-70

-60

-50

-40

-30

-20

-10

W
n1

Frequency (Hz)

S
in

g
u
la

r 
V

a
lu

e
s
 (

d
B

)

10
0

10
2

10
4

-80

-70

-60

-50

-40

-30

-20

-10

W
n2

Frequency (Hz)

S
in

g
u
la

r 
V

a
lu

e
s
 (

d
B

)

10
0

10
2

10
4

-70

-60

-50

-40

-30

-20

-10

0

W
n3

Frequency (Hz)

S
in

g
u
la

r 
V

a
lu

e
s
 (

d
B

)

Figure 3.7: Weighted noise measurements

All these filters are used in support of loop shaping techniques to operate the system
in the frequency region of interest. Whereas, for lower frequencies which includes

21



3. Methodology

slower dynamics of the road it might account to small drift from an accelerometer
sensor. The structure of the open loop system is then interconnected with all the
weightings. By taking into account the the performance outputs and weights given

[
z
y

]
= P

d1
d2
u

 (3.2)

Here d1 is an input to the weighting matrices Win = diag(WFd,Wzr), d2 is the
disturbance input to Wd and u = x̂ the control input.
By using the equations for inputs and outputs i.e the performance output and the
measurement output

z = WeiGWind1 −Weiu

y = GWind1 +Wdd2
(3.3)

the interconnected block P will take the form
[
z
y

]
=
[
WeiGWin 0 −Wei

GWin Wd 0

] d1
d2
u

 (3.4)

where,

P =
[
WeiGWin 0 −Wei

GWin Wd 0

]
(3.5)

The system interconnected block P is then used in the H∞ synthesis with measure-
ments as inputs and estimated states as the number of outputs System interconnec-
tion can also be done by using sysic command from the MATLAB.

3.2 Power Spectral Density
Road profile data zr(t) is converted to frequency domain by using Fourier trans-
formation to determine the frequency components of the signal. By knowing the
vehicle velocity equivalent road profile zr(x) is determined in spatial domain and
spatial angular frequency domain can also be determined, since space domain is the
best way to classify the roads according to ISO 8608 classification.

By using a Matlab function "pwelch" it is possible to determine the power spectral
density of the spatial domain signal directly. This uses a similar method as explained
in section 2.4 The pwelch() method uses a moving window technique where FFT is
computed and then PSD is computed as average of FFT’s over all windows. This
method is dependant on three parameters.

• Window length (N) : The convention of choosing the window size N is set to
the power of 2 greater than the length of the signal. But this procedure would
make it less efficient and faster implementation of the FFT. If N is less than

22



3. Methodology

the length of the signal then FFT will utilize only N samples to estimate the
PSD. An effective utilization of the window size is to be chosen such that the
number of windows used over the data is effective. This will help in obtaining
a smooth PSD. Frequency resolution (distance between two frequency points)
is another factor that should be taken care of such that important frequency
components are not lost.
A suitable window size is chosen in this thesis considering 2000 samples per
second of signals of varying length. By using a window function such as Ham-
ming window it is possible to have very less side-lobes and makes it better
option for frequency selective analysis.

• Overlap percentage : The change in the overlap percentage varies the effects
of noise in the signal. Lower overlap percentage with 0% increases the overall
noise in the PSD, and with increase in the overlap percentage to 50% increases
the number of windows and helps in the averaging of the effects of noise.
Increasing it further to 100%, the correlation between the windows samples
increases, thus averaging brings no effect on the noise.
Therefore 50% noise is taken into consideration

• Number of FFT points : The number of FFT points chosen is equal to the
length of the window

3.2.1 ISO 8608 Classification

ISO is a worldwide federation of national standards designated to form standards of
rules for the specified work. The committee responsible for the document related to
road classification is "Mechanical vibration, shock and condition monitoring". The
road profile classification is done by standards mentioned in the ISO 8608 [25]. The
power spectral density of a road profile is defined by

Gq(n) = Gq(n0)
(
n

n0

)−w
(3.6)

n is the spatial frequency and n0 is the reference spatial frequency of 0.1m−1 and
Gq(n) is the power spectral density at spatial frequency n. The reference PSD
Gq(n0) determines the differences in the road classes, where smallest value shows
better roads and greater values the bad roads. w represents the waviness of the
road with greater values of w representing higher amplitudes and lower frequency
and smaller values of w representing higher frequency and lower amplitudes. But
ISO 8608 uses w=2 as the waviness.
The ISO road level definition is given by

23



3. Methodology

Road Class Gq(n0)10−6m3

A 16
B 64
C 256
D 1024
E 4096
F 16,384

Table 3.1: Road level definition by ISO

The representation of all the classes from A to F with values given in table 3.1 can
be seen in the figure 3.8. The road profile estimates will be described by the PSD
of its vertical displacement. As seen in the figure 3.8 the PSD is in m3 versus the
spatial frequency in cycles/m are on the logarithmic scale. The below figure also
represents the fitted PSD which describes the region around the type of road.

Since the spatial frequency range is important for vehicle dynamics analysis, the
range for which is chosen between nε[0.01 4]cycles/m.

Figure 3.8: Classification of roads from A to F

For the vehicle driven at a velocity of V ms−1 the spatial PSD can be transformed
into time domain PSD as in equation 3.7

Gq(f) = 1
v
Gq(n) = Gq(n0)n2

0
V
f 2 (3.7)

where f is the frequency in Hz. The relation between the excitation energy of the
PSD coefficient Gq(n0)n2

0 and the vehicle velocity can be seen in 3.9. The figure
shows that the increase in vehicle velocity increases the the roughness coefficient.
Therefore, the vehicle velocity is directly proportional to the roughness coefficient.

24



3. Methodology

Figure 3.9: Roughness coefficient vs velocity

The PSD of the road profile is not always a straight line, since the frequency com-
ponent of the irregularity differ in different octave bands. Therefore, the spatial
frequency range is divided into six segments for easier classification. The figure 3.10
shows the mean and limit values of Gd(n) for different octave bands. This figure
is the PSD representation divided throughout the center frequencies by the ISO
standards. Here only segments for valid spatial frequency range between 0.00625
cycles/m to 4 cycles/m.

Figure 3.10: PSD of different classes of roads divided through center frequencies
by ISO 8608 [25]

25



3. Methodology

26



4
Results

The results of the estimation and the classification for the roads are presented in
this section. Results are divided into simulation results i.e testing it on the Car-
Maker and experimental results (sensor data collected by driving the vehicle on test
tracks). High frequency roads and low frequency roads are both part of the experi-
mental result structure. In the experimental data, the speed of the vehicle is almost
maintained as a constant. Later a classification study is done comparing the roads
with the ISO standard roads. The effect of these on the primary ride and secondary
ride is also studied and definition of how it helps in the damping control is also
analyzed.
The available tools and sensors used during this thesis are limited to existing vehicle
sensors. The effect of this limitation is studied and the results are discussed.

4.1 Estimation Results

4.1.1 CarMaker
CarMaker is a software tool which consists of entire vehicle dynamics comprising
of suspension, vertical, lateral, longitudinal and tire dynamics. Hence the obtained
results will be considered to be behaving very close to the CarMaker data. Therefore,
the roads are considered from this software for testing.
The road models from CarMaker is used in order to test the estimation results.
Several road conditions are included in order to determine the classification on the
type of the road to be determined. High frequency disturbance roads and roads
having very slow change in the topography i.e low frequency disturbance are some
of the roads used for the classification.
Whilst having the road model built, there are certain parameters needed to be set
in the CarMaker.

• Maneuvering : The speed at which the vehicle moves on the road profile is set
here. To account offset of the vehicle position is also set here.

• Road bumps : The road bumps are set in the parameters section. Beams or
waves is chosen to test in order to have single or multiple bumps. Another
option used is a CRG file i,e a built in model of certain roads which replicate
the real road scenario is also chosen.

• Vehicle Parameters : Mass of the vehicle, suspension parameters are needed
to be set.

• Sensors : For obtaining the measurements from the maneuver of the vehicle,

27



4. Results

respective sensors such as body accelerometers and position sensors placed in
the vehicle are used.

4.1.2 Estimation of suspension parameters
The suspension parameters comprising of the states used to determine the road pro-
file is estimated here. CarMaker software tool as explained above is used to verify
and analyze the estimated parameters of the suspension from the observations. The
observer is built by considering measurements used from the vehicle sensor data.
The mounted senors provide information about the suspension behaviour in real
time which is useful in validation and verification of the estimates. In order to first
validate the observer, measurements are chosen from the linear model and tested, the
results for which can be seen in figure 4.1. Different bumps and symmetrical/unsym-
metrical roads are part of the result. The car in the simulation is run at a different
speeds, On the wavy road (a) the vehicle speed is 50kmph, Unsymmetrical waves(b)
at 35kmph, Road roughness(c) at 30kmph and on Belgian road(d) at 70kmph. The
measurements sprung deflection and velocity and the sprung mass accelerations are
chosen from the linear model and given as an input to the observer. The outputs are
the state estimates sprung mass displacements ẑs, sprung mass velocity ˆ̇zs, unsprung
mass displacement ẑus, and unsprung mass velocity ˆ̇zus. The linear model outputs
are shown in blue and the estimates are in red.

(a) Waves (b) Unsymmetrical Waves

(c) Road Roughness (d) Belgian Road

Figure 4.1: Estimates for CarMaker demo road surfaces with linear model

The same observer is tested with the non-linear model from the CarMaker, the
results for which can be seen below. The results show the states matches precisely
with that of the CarMaker sensor data. These are further used in estimation of the
road profile. Figure 4.2 shows the similar roads tested with the linear model. The
vehicle speed is the same as used for verification with the linear model.

28



4. Results

(a) Waves (b) Unsymmetrical Waves

(c) Road Roughness (d) Belgian Road

Figure 4.2: Estimates for CarMaker demo road surfaces with nonlinear model

Two roads are further chosen to compare and analyze the road estimate and the
frequency components of the profile. The roads chosen are the best example to
study the effects of the road irregularities affecting the control of the damper as a
result of the ride quality. The two roads are given the names Road A and road
B. They have symmetrical and unsymmetrical wavelengths of profile irregularities
which could be distinguished by the frequency components.
Road A has track width of 3m and driven on the center lane with no offset. The
length of entire road is around 550m and the vehicle is driven at a speed of 65 kmph.
Road B has a track width of 3m and driven on center lane without any offset. The
length of the road is around 300m and speed of the vehicle is 70 kmph. Figures 4.3
and 4.4 shows the state estimates of Road A and Road B in comparison with actual
state values from the CarMaker.

Figure 4.3: Suspension parameters estimate for road A

29



4. Results

Figure 4.4: Suspension parameters estimate for road B

Further these estimates are used to construct the road profile, which is presented in
the next section.

30



4. Results

4.1.3 Road Estimation Model
The road estimation is done based on the estimations obtained from the observer.
The profile estimate obtained is a proximity of the real road profile. Since the
unsprung mass accelerometer is not a part of the observed vehicle measurement, It
is determined from the estimated states by taking the derivative of the unsprung
velocity and then filtered to obtain the data only from the range of interest.
Equation 2.8 is used to estimate the road profile. The estimated unsprung mass
accelerations ˆ̈zus for the two roads A and B is shown in figure 4.5 and 4.6.

15 20 25 30 35 40 45 50 55

time(s)

-15

-10

-5

0

5

10

15

U
n
s
p
ru

n
g
 m

a
s
s
 a

c
c
e
le

ra
ti
o
n
s
 (

m
/s

^2
)

Time Series Plot:

CarMaker unsprung acceleration

Estimated unsprung acceleration

37 38 39 40 41
-6

-4

-2

0

2

4

Figure 4.5: Unsprung mass acceleration for road A

5 10 15 20 25 30 35 40 45 50 55 60

time(s)

-60

-50

-40

-30

-20

-10

0

10

20

U
n
s
p
ru

n
g
 m

a
s
s
 a

c
c
e
le

ra
ti
o
n
s
 (

m
/s

^2
)

Time Series Plot:

CarMaker unsprung acceleration

Estimated unsprung acceleration

37 38 39 40 41
-10

-5

0

5

10

15

Figure 4.6: Unsprung mass acceleration for road B

The road profile ẑr(t) shown is in the time domain, therefore, with the speed of
the vehicle it is possible to determine an equivalent road profile ẑr(x) as a function
of the road length x. The estimate is then passed through a moving average filter
which acts as a simple low pass(FIR) filter. A suitable filter length is chosen such
that any important modulations in the profile data is not affected. Road estimate
for road A is shown in 4.7 and road B is shown in 4.8

31



4. Results

0 10 20 30 40 50 60

time (s)

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

P
ro

fi
le

 H
e
ig

h
t 
(m

)

Estimated

road

Figure 4.7: Road profile estimate for road A

10 15 20 25 30 35 40 45 50 55

time (s)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

P
ro

fi
le

 H
e
ig

h
t 
(m

)

Estimated

road

Figure 4.8: Road profile estimate for road B

32



4. Results

4.2 Frequency Analysis and Power spectrum den-
sity

Frequency analysis is carried out for the road estimates in the previous subsection
4.1. It is necessary to study the frequency components of these roads as they build
the notion of any prolonged disturbances from the road, which could be plausible
harm to the vehicle or human body. They even provide information for the control
of the vehicle suspension on a specific length of the road, helping in improving the
ride quality and the handling of the car. Human body is another such complex
structure with different organs resonating at different frequencies. Hence knowing
the frequency components of the road is vital aspect of vehicle dynamics.

10
-1

10
0

cycles/m

10
-9

10
-8

10
-7

10
-6

10
-5

10
-4

10
-3

10
-2

10
-1

10
0

P
S

D
(m

3
)

CarMaker road profile PSD

Estimated road profile PSD

X: 0.05307

Y: 0.003141

Figure 4.9: PSD comparison for Road A

10
-1

10
0

cycles/m

10
-9

10
-8

10
-7

10
-6

10
-5

10
-4

10
-3

10
-2

P
S

D
(m

3
)

CarMaker road profile PSD

Estimated road profile PSD
X: 0.03708

Y: 0.006862
X: 0.06181

Y: 0.001513

Figure 4.10: PSD comparison for Road B

Since the scope of the thesis remains to classify these roads based on its condition,

33



4. Results

power spectral density is the best way to define the road’s spatial frequency compo-
nent because it is independent of the velocity of the vehicle. The PSD for Road A
shown in figure 4.9 clearly represents a low frequency disturbance in the road with a
peak around 0.053 cycles/m, with the vehicle moving at a velocity of 75 kmph and
the PSD for road B is shown in 4.10 with multiple frequency disturbances with peaks
at 0.03 cycles/m and 0.06 cycles/m. The figures also show the comparison between
the real road profile from the CarMaker road sensor data and the estimated road
profile. It is clear to see the similarities between the estimated spectral densities.

The vehicles travelling on a single lane won’t always be travelling in the same width
of the track. For example if a lane has a width of 3m, the vehicle might travel with
some offset of 0.5m, 1m or greater. A test is done to check the similar circumstance.
Road A is considered for this. Figure 4.11 shows the vehicle travelled on the same
track but having some offsets in the track position. The offset of 1m is set for the
car position. Although the PSD of the shown road profile almost remains the same.
The power spectral density of road with an offset shown is for the left wheel, similar
experiment is carried out with an observer at the right wheel.

10
-1

10
0

cycles/m

10
-9

10
-8

10
-7

10
-6

10
-5

10
-4

10
-3

10
-2

10
-1

10
0

P
S

D
(m

3
)

No track offset

1m track offset

Figure 4.11: PSD comparison for offsets

The spatial frequency is used in the ISO standard classification of the roads and the
importance of representing the spectral density in spatial frequency can be seen from
figure 4.12. Road A is considered in this case as well. The vehicle is driven on the
same track at different speeds i.e 48kmph, 75kmph, 90kmph, 120kmph and 150kmph.
Since moving at different speeds on the same road profiles would have different time
domain frequency disturbance, whereas the spatial frequency would show the same
peak for all varying velocities which is easy to understand and represent. Although
there arises few differences when vehicle is moving at higher speeds which is due to
the suspension settings on the vehicle. Comparison with the ISO standards is shown
in the appendix.

34



4. Results

10
-1

10
0

cycles/m

10
-9

10
-8

10
-7

10
-6

10
-5

10
-4

10
-3

10
-2

10
-1

10
0

P
S

D
(m

3
)

48kmph

75kmph

90kmph

120kmph

150kmph

Figure 4.12: PSD comparison at varying speeds

4.3 Experimental results
Section 4.2 explains about the examples considering the measurements form the Car-
Maker sensor data. This would still consider an ideal case in real world with very
less uncertainties and disturbances. Therefore, real world measurements are col-
lected from the sensors placed on vehicle and driven on test tracks. Similar observer
model is used for estimation of the states using these sensor measurements with
more uncertainties and disturbances present in them. The measurements sprung
mass accelerations z̈s and suspension deflection zdef from the sensors are sampled at
2000Hz and an offline estimation is done in Simulink. These measurements sprung
mass acceleration is low pass filtered at 30Hz to include the region of interest for
the dynamics. This filtered data in turn removes additional noise affecting the esti-
mation. In turn the deflecting velocity of the suspension which is differentiated and
filtered from the suspension deflection data is another measurement passed as an
input to the observer.

Different examples of various roads are provided below. These are the roads from the
experimental test tracks. The suspension estimates and the respective road profiles
are shown. The unsprung mass acceleration used in determining the road estimates
are obtained from the suspension estimates.

35



4. Results

Figure 4.13 and 4.14 represents the state and road estimates respectively for road
with manholes on the left side of the track present at a distance of 40m approxi-
mately. It shows that the amplitude is quite small which makes the sprung mass
movement very negligible compared to the unsprung mass movement.

Figure 4.13: Suspension parameter estimate for manhole road

The road estimates shows very such small dips representing profile irregularity.

2 4 6 8 10 12

time(s)

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

P
ro

fi
le

 h
e

ig
h

t(
m

)

Figure 4.14: Road estimate for manhole road

36



4. Results

Figure 4.15 and 4.16 represents the state and road estimates respectively for road
with roll excitation on left side of the track. It shows a constant dip at an equidistant
distance. These roads create discomfort when the vehicle body rolls to the left. Since
the measurements used are limited and the vehicle roll is not plotted here.

Figure 4.15: Suspension parameter estimate for roll excitation on Front left wheel

The road estimates shows the dips from the left wheel representing profile irregu-
larity.

5 10 15 20 25 30 35

time(s)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

P
ro

fi
le

 h
e

ig
h

t(
m

)

Figure 4.16: Road estimate for roll excitation on front left wheel

37



4. Results

Figure 4.17 and 4.18 represents the state and road estimates respectively for road
with low dips at equidistant distance. These are the low frequency disturbances
affecting the primary rides in vehicle dynamics. These roads are similar to road A
of the section 4.2.

Figure 4.17: Suspension parameter estimate for low frequency road

The road estimates shows the low frequency long dips representing profile irregular-
ity.

5 10 15 20 25 30 35 40 45 50 55 60

time(s)

-1

-0.5

0

0.5

1

P
ro

fi
le

 h
e

ig
h

t(
m

)

Figure 4.18: Road estimate for low frequency road

38



4. Results

Figure 4.19 and 4.20 represents the state and road estimates respectively for road
with high frequency disturbances which affects the secondary ride in vehicle dynam-
ics. These roads have unsymmetric wavelengths of road profiles.

Figure 4.19: Suspension parameter estimate for high frequency road

The road estimates shows high frequency profile irregularity.

0 5 10 15 20 25 30 35 40 45 50

time(s)

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

P
ro

fi
le

 h
e

ig
h

t(
m

)

Figure 4.20: Road estimate for high frequency road

39



4. Results

4.3.1 Frequency analysis and PSD for Experimental data
Two roads representing low frequency and high frequency disturbance i.e road es-
timates from figures 4.18 and 4.20 are considered. Frequency components of these
two roads can be seen below.

0 5 10 15 20 25 30

Frequency (Hz)

-20

-10

0

10

20

30

40

50

60

70

80

M
a
g
n
it
u
d
e
 (

d
B

)

Magnitude Response (dB)

Frequency: 0.7324219

Magnitude: 51.07753

(a) Symmetric Wavelength

0 5 10 15 20 25 30 35 40 45

Frequency (Hz)

-30

-20

-10

0

10

20

30

40

50

60

M
a
g
n
it
u
d
e
 (

d
B

)

Magnitude Response (dB)

Frequency: 14.03809

Magnitude: 36.62762

(b) Random wavelength

Figure 4.21: Primary and secondary ride roads

As already discussed the power spectral density in spatial domain is the region of
interest, further results will feature comparison of the spectral density in units of
wavenumber. One road to easily compare the data from CarMaker and experimental
data is the low frequency road. Figure 4.22 show the PSD of the roads, although
at higher frequencies few uncertainties and different damping controls might be few
reasons of small differences. The peak obtained from CarMaker is at 0.058 cycles/m
and the peak obtained from the experimental data is at 0.06 cycles/m which shows
not much difference between them. This would be an ideal case for the classification
of road.

Figure 4.22: Comparison between CarMaker PSD estimate and experimental PSD
estimate

In order to verify power spectral density of the experimental data for high frequency
road, the car is driven on the same track twice first at 60kmph and then 70kmph, the
result of which can be seen in the 4.23. The figure shows the PSD for the same road
width for left and right wheel. The result shows that the power spectral densities of

40



4. Results

the same road matches hence it could be useful for classification of the type of the
road.

10
-1

10
0

cycles/m

10
-10

10
-9

10
-8

10
-7

10
-6

10
-5

10
-4

10
-3

10
-2

10
-1

P
S

D
(m

3
)

PSD for left wheel

PSD for right wheel

Figure 4.23: PSD comparison when driven on same road back and forth

4.3.2 ISO Classification
The power spectral densities of the road estimates is compared to ISO standards
as explained in the section 3.2.1. This makes it easier to classify the roads at
different spatial frequency and provide an idea for the control of the dampers. Figure
4.24 shows the PSD for low frequency roads on the fitted PSD classes of the ISO
standards. The low frequency road is the experimental road estimate represented
in figure 4.18. The peak frequency in spatial domain is around 0.06 cycles/m or
0.74Hz with the vehicle travelling at 15.5 m/s.

Figure 4.24: Displacement PSD of low frequency road

In figure 4.25(a) shows type of classes for all points of spectral density in spatial fre-
quency range and 4.25(b) shows the peak frequency at a particular central frequency

41



4. Results

of in the spatial frequency octave bands. The central frequencies for division into
frequency segments is given in figure 3.10. The classification based on the central
frequency will provide clear information for setting the damper control for primary
and the secondary ride. As it can be seen the the central frequency 0.06 cycles/m
shows the peak for the low frequency disturbance.

0 0.5 1 1.5 2 2.5 3

cycles/m

ISO-A

ISO-B

ISO-C

ISO-D

ISO-E

ISO-F

IS
O

 r
o
a
d
 c

la
s
s
e
s

(a) PSD for specified frequencies

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

cycles/m

ISO-A

ISO-B

ISO-C

ISO-D

ISO-E

ISO-F

IS
O

 r
o
a
d
 c

la
s
s
e
s

(b) PSD only for central frequencies

Figure 4.25: Primary and secondary ride roads

The parameters for such classification can be seen in table 4.1. The standard of the
road is said to be ISO-C class at lower frequencies.

RMS speed 15.5 m/s
Peak Frequency 0.74 Hz
Spatial frequency 0.06 cycles/m

Road Class ISO-C

Table 4.1: Parameters of low frequency road classification

Similarly, figure A.1 shows the PSD of high frequency road on the fitted ISO stan-
dards, The high frequency road is the experimental road one shown in figure A.1.
The peak frequency is at 1.075 cycles/m or 14.03 Hz. The velocity of the vehicle
moving is at 14 m/s.

42



4. Results

Figure 4.26: Displacement PSD of high frequency road

In figure 4.27(a) shows type of classes for all points of spectral density and 4.27(b)
shows the peak frequency at a particular central frequency of in the spatial frequency
octave bands. The parameters of such classification can be seen in table 4.2. It can
be seen that the peak can be seen for a central frequency of around 1 cycle/m.

0 0.5 1 1.5 2 2.5 3

cycles/m

ISO-A

ISO-B

ISO-C

ISO-D

ISO-E

ISO-F

IS
O

 r
o
a
d
 c

la
s
s
e
s

(a) Symmetric Wavelength

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

cycles/m

ISO-A

ISO-B

ISO-C

ISO-D

ISO-E

ISO-F

IS
O

 r
o
a
d
 c

la
s
s
e
s

(b) Random wavelength

Figure 4.27: Primary and secondary ride roads

The parameters for this classification can be seen in table 4.2. The standard of the
road is said to be ISO-F class at higher frequencies.

RMS speed 14 m/s
Peak Frequency 14.03 Hz
Spatial frequency 1.075 cycles/m

Road Class ISO-F

Table 4.2: Parameters of high frequency road classification

Similarly, classification could be done for all the estimated road profile based on the
PSD as given by the ISO standardization. Meanwhile the ISO standardized classi-
fication considers the waviness of any type of road to be fixed at 2. A classification

43



4. Results

algorithm to include different waviness for different roads is included in the future
scope.

44



4. Results

4.3.3 Decision for Damper tuning for Primary and Secondary
ride

The operation condition of a vehicle is subjected to many vibrations in the vehicle
body caused by many things at different frequencies. The vibration that creates
discomfort to passengers can be distinguished by different ways as seen in figure
4.28

Figure 4.28: Maneuvering frequency ranges

In automotive industry the ride behaviour is described by primary and secondary
ride. The primary ride would describe the road with bumps having higher ampli-
tudes and lower frequencies. Such topographic variation would be visible to the
naked eye whilst driving. Such riding conditions of the road is termed as the pri-
mary ride. Which includes suspension movement over undulations related to the
bound and rebound of the dampers.

Secondary ride is small irregularities with low amplitudes but higher frequencies
Which is slightly difficult to be seen from the moving vehicle. Such irregularities are
mainly due to combination of damper and bushing control. The tuning in secondary
ride involves the dampers and bushings to work well.

The frequency content of the primary ride is less than 6Hz, with the wavelength
greater than the wheel base of the vehicle. These roads mostly have symmetric
profile. An example of such road profile can be seen in figure 4.29(a) The fre-
quency component of the secondary ride has medium frequency range around 8Hz
and greater. The irregularities in the road profile is continuously varying in large
spectrum of wavelengths. This can be seen in figure 4.29(b)

45



4. Results

(a) Symmetric Wavelength (b) Random wavelength

Figure 4.29: Primary and secondary ride roads

Influence of the low frequency and high frequency roads from the results on primary
and secondary ride can be

• Low frequency roads in the primary ride must have a suspension damping
increased to get better damping at frequencies below 6Hz which eliminates
the peak frequencies in that region and improves the ride quality. But with
same settings if the vehicle is driven on the high frequency roads then the ride
quality is deteriorated causing a slower roll-off and harshness.

• High frequency roads in the secondary ride must have a suspension damping
decreased to get better damping at higher frequencies from 8Hz to above elim-
inating the peak frequencies improve the ride quality. If with same setting the
vehicle is driven on low frequencies then it will have a large impact on the
passenger.

46



4. Results

4.4 Future Scope
• The suspension parameter estimation uses a quarter car model which operates

in a lower frequency region where the accelerometer data tends to drift with a
very slow varying slope, hence a full car model can be used to build an observer
to handle the case of slow varying topographies.

• The estimated states can also be used to the control the damper force.
• Here a classification is done using a continuous time observer model. An online

estimation can be done by discretising the model and the observer at a specific
sampling rate.

• The ISO classification uses the waviness of the road to be 2 for all sets of
road. A different classification standards could be considered for varying sets
of waviness of the roads depending on the reference classes of the road.

47



4. Results

48



5
Conclusion

The main objective of this thesis was to to estimate the road profile and classify
the road based on the roughness of the road. The first chapter introduced many
techniques used in the current market for estimation of the classes of the road and
road profile. Response based road profile estimation was the one considered. The
second chapter gives insight into the vehicle modeling. The continuous damper in
the semi-active suspension model is explained along with a quarter car model of
the left wheel suspension model. Road profile estimation model is also defined. The
robust observer H∞model is derived for the estimation of the suspension parameters
later used to estimate the road profile. The third chapter explains about the method
in which the estimation and classification is done. The choice of filter specifications
and loop shaping for the robust observer is explained. The ISO standards for classi-
fication of the road profile based on power spectral density in the spatial frequency
domain is introduced. The last chapter is used to explain the results obtained from
the simulations from Carmaker data and the experimental results from the sensor
data collected from the measurements run on the test tracks.

49



5. Conclusion

50



Bibliography

[1] DGIP. EU road surfaces: Economic and safety impact of the lack of regular
road maintenance, study. Policy Department Structural and Cohesion Policies,
European Parliament,2014.

[2] S. Gerwens. European Manifesto: Need for road maintenance. Pavement Preser-
vation and Recycling, Summit, 2015.

[3] US department of transportation. Long-term pavement performance program
[4] Z. Zhang, C. Sun, R. Bridgelall, et al. Application of a machine learn-

ing method to evaluate road roughness from connected vehicles. Journal of
Transportation Engineering, Part B: Pavements, 144(4):04018043, 2018. DOI:
10.1061/jpeodx.0000074.

[5] R. Bridgelall, Y. Huang, Z. Zhang, et al. Precision enhancement of pavement
roughness localization with connected vehicles. Measurement Science and Tech-
nology, 27(2):025012, 2016. DOI: 10.1088/0957-0233/27/2/025012

[6] Y. Qin, M. Dong, F. Zhao, et al. Comprehensive analysis for influence of control-
lable damper time delay on semi-active suspension control strategies. Journal
of Vibration and Acoustics Transactions of ASME, 139(6):031006, 2017. DOI:
10.1115/1.4035700.

[7] K. Mcghee. Automated pavement distress collection techniques. Transportation
Research Board, 2004.

[8] H. Imine, Y. Delanne, and N. K. M’sirdi. Road profile input estimation in
vehicle dynamics simulation. Vehicle System Dynamics, 44(4):285–303, 2006.
DOI:10.1080/00423110500333840.

[9] Acuity AR600/RP: Laser displacement sensor for road profilometry.
https://www.Acuitylaser.Com/Docs/Ar600-Road-Profiling.Pdf

[10] M. Ahmed and F. Svaricek. Preview optimal control of vehicle semi-active sus-
pension based on partitioning of chassis acceleration and tire load spectra. Proc.
of the Control Conference (ECC), 2014. DOI: 10.1109/ecc.2014.6862615.

[11] Z. Yuan, X. Zhang, S. Liu, et al. Laser line recognition for autonomous road
roughness measurement. Proc. of the Cyber Technology in Automation, Con-
trol, and Intelligent Systems (Cyber), 2015. DOI: 10.1109/cyber.2015.7287977.

[12] M. Aki, T. Rojanaarpa, K. Nakano, et al. Road surface recognition using laser
radar for automatic platooning. IEEE Transactions on Intelligent Transporta-
tion Systems, 17(10):2800–2810, 2016. DOI: 10.1109/tits.2016.2528892.

[13] D. Hrovat and W. Tseng. Adaptive active vehicle suspension system. US
Patents. 1995.

[14] K. Yi and B. Song. A new adaptive sky-hook control of vehicle
semi-active suspensions.Proc. of the Institution of Mechanical Engineers,

51



Bibliography

Part D: Journal of Automobile Engineering, 213(3):293–303, 1999. DOI:
10.1243/0954407991526874.

[15] H. Imine, Y. Delanne, and N. K. M’sirdi. Road profile input estimation in
vehicle dynamics simulation. Vehicle System Dynamics, 44(4):285–303, 2006.
DOI: 10.1080/00423110500333840

[16] D. Moustapha, V. Alessandro, A. Charara, et al. Estimation of road profile for
vehicle dynamics motion: Experimental validation. American Control Confer-
ence, San Francisco, CA, 2011. DOI: 10.1109/acc.2011.5991595.

[17] J. Tudon-Martinez, S. Fergani, O. Sename, et al. Adaptive road profile esti-
mation in semiactive car suspensions. IEEE Transactions on Control Systems
Technology, 23(6):2293– 2305, 2015. DOI: 10.1109/tcst.2015.2413937.

[18] S. Wang, S. Kodagoda, L. Shi, et al. Road-terrain classification for land vehi-
cles: Employing an acceleration-based approach. IEEE Vehicular Technology
Magazine, 12(3):34–41, 2017. DOI: 10.1109/mvt.2017.2656949.

[19] Y. Qin, Z. Wang, C. Xiang, et al. Speed independent road classifica-
tion strategy based on vehicle response: Theory and experimental valida-
tion. Mechanical Systems and Signal Processing, 117:653–666, 2019. DOI:
10.1016/j.ymssp.2018.07.035.

[20] H. Ngwangwa, P. Heyns, H. Breytenbach, et al. Reconstruction of road defects
and road roughness classification using artificial neural networks simulation
and vehicle dynamic responses: Application to experimental data. Journal of
Terramechanics, 53:1–18, 2014. DOI: 10.1016/j.jterra.2009.08.007.

[21] S. Kang, J. Kim, and G. Kim. Road roughness estimation based on discrete
Kalman filter with unknown input. Vehicle System Dynamics, 2018. DOI:
10.1080/00423114.2018.1524151.

[22] Z. Wang, M. Dong, Y. Qin, et al. Road profile estimation for suspension system
based on the minimum model error criterion combining with kalman filter.
Journal of Vibroengineering, 2017.

[23] G. Xue, H. Zhu, Z. Hu, et al.(2017) Pothole in the dark: Perceiving pothole
profiles with participatory urban vehicles. IEEE Transactions on Mobile Com-
puting, 16(5):1408–1419, 2017. DOI: 10.1109/tmc.2016.2597839.2,

[24] A. Gonzalez, E. O’brien and K. Cashell. The use of vehicle acceleration measure-
ments to estimate road roughness. Vehicle System Dynamics, 46(6):483–499,
2008. DOI:10.1080/00423110701485050.6

[25] Mechanical vibration — Road surface profiles — Reporting of measured data,
second edition ISO 8608:2016

52



A
Appendix

The figure represents comparison of the PSD for road profile A at varying velocities
with the ISO standard classification. Although most of the classification shows
similar classes for the roads at velocities 48kmph, 75kmph and 90kmph but at
higher velocities at 120kmph and 150kmph the peak shows road class as Class D,
the small uncertainties might be due to the coupling of the front and rear axles.

Figure A.1: Comparison of PSD for road profile A at varying velocities with ISO
standard classification

I


	List of Figures
	List of Tables
	Introduction
	Motivation
	Road Profile Estimation Overview
	Direct Measurement
	Non-contact Measurement
	Indirect Measurement

	Summary

	Theory
	Vehicle Modeling
	Active Suspensions
	Semi-Active Suspensions
	CCD Model

	Quarter Car Modeling
	Observability Analysis
	Model Validation


	Road Profile Estimation and Modeling
	Observer Design
	 synthesis with DK-iteration

	Frequency Analysis and PSD

	Methodology
	Model Based Estimation Algorithm
	Power Spectral Density
	ISO 8608 Classification


	Results
	Estimation Results
	CarMaker
	Estimation of suspension parameters
	Road Estimation Model

	Frequency Analysis and Power spectrum density
	Experimental results
	Frequency analysis and PSD for Experimental data 
	ISO Classification
	Decision for Damper tuning for Primary and Secondary ride

	Future Scope

	Conclusion
	Bibliography
	Appendix