Road Condition Predicting with Kalman Filter

for Magneto-Rheological Damper in Suspension System

Zuohai Yan Shuqi Zhao

This thesis is presented as part of Degree of Master of Science in Electrical Engineering

Blekinge Institute of Technology July 2012

Blekinge Institute of Technology School of Engineering Department of Applied Signal Processing Supervisor: Feng Wang Examiner: Sven Johansson

Abstract

This thesis develops a new way to predict the road roughness with Kalman filter. Itsuggests applying the Kalman filter to predict road condition in suspension system.According to the literature review and to the knowledge of authors, no similar appli-cations of Kalman filter in predicting the road roughness are found at the time of thewriting thesis. Most of the prediction nowadays is around the road prediction withGPS. It concentrates on avoiding the road bumps by the operator. This research isbrand new in this field. What the authors focus on is to predict the road conditionand to pass this information to the control system. By this way, the passenger comfortis improved.

This research is practical in transportation industry. Nowadays the passengercomfort is crucial. This road condition predictor can help the vehicle to improvethe passenger comfort. Furthermore, this predictor can be adjusted to different roadconditions.

A suspension system is important to improve passenger comfort. Magneto-Rheological(MR) damper, which is a controllable damper, can improve the perfor-mance of the suspension system. This thesis presents a menthod to predict the roadcondition for MR damper. Firstly, three suspension systems, passive, active andsemi-active suspension systems, are evaluated by their costs and performances. Thesemi-active suspension system has good performance with low cost. This suspensionsystem shows better performance with proper control strategy.

Additionally, two different levels of road roughness are simulated by Harmonicsuperposition method in time domain. One of the road roughness scenarios is chosento test the prediction method. The road roughness is predicted by a Kalman filter.The result shows that the Kalman filter can estimate the road condition with a highaccuracy. The prediction frequency is high in this method. The control strategy canadjust its coefficient based on the high prediction frequency. Thus, the performanceof the suspension system is enhanced and the passenger comfort is also improved.

Keywords: Suspention System, Prediction, Kalman Filter.

i

Acknowledgements

First we would like to express our sincere gratitude to our thesis supervisor, FengWang. He not only offered us the opportunity to work on this thesis but also providedvaluable orientation and direction in this field.

In addition, we would like to thank our friends Mohammad, Amy and Morce whohave supported us.

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Contents

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

1 Introduction 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.5 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Background 42.1 Primary Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Passive Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Active Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Semi-active Suspension . . . . . . . . . . . . . . . . . . . . . . . . . . 82.5 Control Schemes for a 2 Degree of Freedom (2DOF) System . . . . . 9

2.5.1 Skyhook Control . . . . . . . . . . . . . . . . . . . . . . . . . 92.5.2 Groundhook Control . . . . . . . . . . . . . . . . . . . . . . . 10

2.6 Magneto-Rheological Dampers . . . . . . . . . . . . . . . . . . . . . . 112.6.1 Magneto-Rheological Fluids . . . . . . . . . . . . . . . . . . . 112.6.2 Modes of MR Operation . . . . . . . . . . . . . . . . . . . . . 122.6.3 MR Dampers . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Road Roughness Data Realization 163.1 Road Roughness Characterization . . . . . . . . . . . . . . . . . . . . 163.2 The International Roughness Index . . . . . . . . . . . . . . . . . . . 163.3 Road Roughness Power Spectral Density . . . . . . . . . . . . . . . . 173.4 Methods of Realizating Road Roughness . . . . . . . . . . . . . . . . 18

3.4.1 Harmonic Superposition Method . . . . . . . . . . . . . . . . 183.4.2 The AR Model . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4.3 The Inverse Fourier Transform Model . . . . . . . . . . . . . . 203.4.4 The Integral White Noise Model . . . . . . . . . . . . . . . . . 20

3.5 Road Roughness Realization Results . . . . . . . . . . . . . . . . . . 20

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4 Experimental Approach and Discussion 234.1 Introduction of Kalman Filter . . . . . . . . . . . . . . . . . . . . . . 234.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.3 Road Condition Predicting Result . . . . . . . . . . . . . . . . . . . . 254.4 Passenger Comfort Comparison . . . . . . . . . . . . . . . . . . . . . 27

5 Conclusion 29

References 30

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Chapter 1

Introduction

This thesis develops a new way to predict the road roughness with Kalman filter. Itsuggests applying the Kalman filter to predict road condition in suspension system.According to the literature review and to the knowledge of authors, no similar appli-cations of Kalman filter in predicting the road roughness are found at the time of thewriting thesis. Most of the prediction nowadays is around the road prediction withGPS. It concentrates on avoiding the road bumps by the operator. This research isbrand new in this field. What the authors focus on is to predict the road conditionand to pass this information to the control system. By this way, the passenger comfortis improved.

This research is practical in transportation industry. Nowadays the passengercomfort is crucial. This road condition predictor can help the vehicle to improvethe passenger comfort. Furthermore, this predictor can be adjusted to different roadconditions.

The purpose of this chapter is to provide an overview of the whole thesis. Itbriefly discusses the road condition prediction for vehicles equipped with semi-activesuspension system.

1.1 Overview

The vibration phenomenon has gained a huge expansion in the past few years. Thevibration theory expands from discrete systems to continuous systems, from harmonicvibration analysis to random vibration problems, from linear vibration theory tononlinear vibration analysis, and from vibration analysis to vibration control systemdesign [1].

With all these control systems and suspension systems, the comfort of passengershas been improved significantly. A good suspension system should achieve three goals:

• Isolating the vehicle from uneven road

• Guaranteeing the stability of vehicle

• Improving the operation of the vehicle

1

Suspension systems support the weight of the vehicle and enhance the traction forcebetween the tires and the road surface [2]. They have been developed significantly inrecent years.

Many kinds of suspension systems have been implemented. For example, passive,active and semi-active suspension systems have been applied in real vehicle design.The active suspension system is an efficient one with high cost. In order to reducethe cost, semi-active suspension is designed as a substitute. This kind of suspensionsystem costs less when implemented in the vehicle, while the performance is close tothat of active suspension system. By implementing semi-active suspension system,the requirement on compromise between the ride comfort and vehicle stability isreduced.

For a semi-active suspension system, a good control strategy is crucial. With agood control strategy, unwanted vibration is isolated. There are many kinds of controlstrategies. Skyhook control is one of the most commonly used ones. The semi-activesuspension system is built with the skyhook control strategy.

The semi-active suspension system is easy to implement with the controllabledamper. The Magneto-Rheological (MR) damper is a damper controlled by magneticfield. Nowadays, a lot of researchers are working on Magneto-Rheological fluid forthe MR damper.

1.2 Motivation

This thesis concerns the prediction of road condition for the vehicle suspension system.The passive suspension system only controls the damper with one fixed coefficient.Unlike the passive suspension system, the semi-active suspension system controls thedamper by the control system. For a semi-active suspension system, the controlstrategy is fairly important as it affects the performance of the system.

The MR damper is commonly used in a semi-active suspension system. It isa controllable damper controlled by the magnetic field. Thus, the strategy of thecoefficient control becomes really important. Nowadays the customers focus more oncomfort and safety. A better strategy for the suspension system is able to provideboth comfort and safety.

Additionally, MR damper reduces the cost of the system with better performance.The road condition prediction can improve the performance of the semi-active sus-pension system. It helps the system to decide the coefficient of the suspension system.Furthermore, it is important to verify the prediction with true road data. The coeffi-cient of the prediction system determines the quality of experiment result. It shouldbe carefully chosen.

1.3 Objective

This thesis is focused on two tasks:

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• The first one is to simulate the true road data. A model of the road conditionis built to provide current data. This data is set as the input of the predictorto test the prediction. Road roughness classification based on the Power Spec-tral Density (PSD) has been proposed by the International Organization forStandardization (ISO). The true road data is built based on this road rough-ness classification. Harmonic superposition method is chosen to build the timedomain model.

• The second one is to predict the road condition with measurement data froma road. The measurement data is built based on true road data with randommeasurement noise. In this thesis, the Kalman filter is chosen to predict theroad condition. The prediction filter is then built to get the future data.

1.4 Outline

The next chapter describes the theoretical aspects of suspension system. A primarysuspension system is introduced. It gives a fundamental knowledge of the suspensionsystem. There is always compromise between passenger comfort and stability insuspension system. It is impossible to avoid the compromise. A few suspensionsystems are discussed including semi-active suspension system. This brings in thestudy of the control strategy and controllable damper.

In chapter 3, simulation of the road roughness is discussed. The harmonic super-position simulation method is chosen to build the road roughness. This simulationmethod is easy to implement.

Chapter 4 presents the solution to the prediction. The F level road is close tothe rough road condition in reality. This kind of roughness is much more commonin daily life. A Kalman filter is built to predict this level road roughness. The inputof the Kalman filter is the measurement data. The result of the prediction is thenevaluated.

Chapter 5 gives out a overview of this thesis. It concludes the main achievementof this thesis and presents recommendations for future study.

1.5 Contribution

This thesis makes the following contributions:

• Study the theory of suspension system.

• Simulate the road roughness data based on power spectral density.

• Develop a new way to predict the road roughness with Kalman filter.

• Suggest applying Kalman filter to predict road condition in suspension system.

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Chapter 2

Background

During these years, the automobile industry is growing quickly. Instead of concen-trating on price, customers pay more attention to both comfort and safety than ever.Then, the comfort and safety should be considered in the design of the vehicles. Thismakes the designing of suspension system becoming trickier.

The suspension system designers have to consider two things. One is the highoperability of vehicle. The other is the feeling of smooth ride for passengers. In thischapter, the background of suspension system is provided.

The suspension systems are divided into three categories: passive, active and semi-active suspension systems. And, these three different kinds of suspension systems arediscussed and compared.

2.1 Primary Suspension

A conventional suspension system usually consists of two components: a spring anda damper [3]. The spring is chosen depending on the whole weight of vehicle. Itis used to pass the force and torsional force between the tire and the vehicle frame.While the damper aims to cancel the impact force from bad road conditions. Theprimary suspension system isolates the vehicle body from the uneven road. Thus, thevibration is reduced and the safety of the passenger is also guaranteed.

However, it is difficult to decide the constant of the damper in a suspension system.Because it is hard to do the trade-off analysis between comfort and stability, theirrelationship is shown in Figure 2.1. For an instance, if a higher constant damper isequipped in a suspension system, more stability is achieved but with less comfort andvice versa.

According to Figure 2.1, the design of the constant of damper is very tricky.The compromise between comfort and stability is hard to decide by designers. Theprimary suspension systems can only provide solution with limitation. In the last fewdecades, many types of suspension systems have been designed to solve this dilemma.Primary suspension systems are divided into categories, which are passive, active andsemi-active suspension systems, by its structure. And those systems are discussed inthe following subsections.

4

Comfort

Stability

Low Damping High Damping

Figure 2.1: Trade-off between comfort and stability

2.2 Passive Suspension

A passive suspension system, as shown in Figure 2.3, contains two elements, springand damper [4]. Once the spring and damper are chosen, the character of this sus-pension system is fixed. So a challenge for designers is to make a trade-off betweenthe spring and damper.

The frequency response of a passive suspension system is shown in Figure 2.2.Higher constant of damper equipped in a vehicle, less comfort is felt by passengerswhile the vehicle passing the uneven road. Most of the energy from the bumpy roadis transmitted to the passengers and the cargo in the vehicle. The more stable systemis, the more uncomfortable passengers feel. But it is easier to operate the vehicle inthis situation

On the contrary, if the designer choses a damper with small coefficient, it resultsin comfort for passengers. In this case, the stability of the suspension system isconspicuously reduced [5]. With a less stable suspension system, the vehicle behavioris affected, especially when it comes to turns and road condition with side force. Thevehicle body roll might happen in some driving situation, for example, acceleratingand braking. Designers should try to optimize the character of the suspension systemwith guidance of the compromise between comfort and stability.

2.3 Active Suspension

In an active suspension system as illustrated in Figure 2.3, the damper, sometimeseven the damper and the spring is replaced by an actuator [6]. Even though thedamper is replaced, the spring still plays the role to hold the whole weight of the

5

0 50 100 1500

1

2

3

4

5

6

Frequency (Hz)

Tra

nsm

issi

bilit

y

damper constant=0.9damper constant=0.5damper constant=0.1

Figure 2.2: Frequency response of primary suspension system

vehicle. The suspension system consists of an electromagnetic actuator, a spring,a piezoelectric accelerometer and an analog control circuit [4]. When the vehicleis running on the road, the piezoelectric accelerometer collects the road condition.It passes the data to the electromagnetic actuator with the analog control circuit.With this data, the actuator can adjust itself according to the road condition. Theadjustment of the actuator improves the passenger comfort.

The active suspension system not only dissipates energy, but also gives out force toreduce the vibration. Based on the message given by the accelerometer, the actuatoradjusts itself in order to minimize the vibration of vehicle. For instance, it changesthe character of actuator and spring to a larger value when the vehicle just starts.Through changing the character, the suspension system dissipates the recoil.

In addition, the system also takes actions when the vehicle reaches certain speed.The system prevents the vehicle from nose-diving by adjusting the spring. Figure 2.4shows a comparison between a passive system and an active system in two-degree-of-freedom system.

Figure 2.4 is the comparison between passive and active suspension system. Theactive suspension system has both advantages and disadvantages. The advantage ofthis system is that it is easy to know how the system works. Within short time, theoperator is able to be pretty familiar with the behavior and response to the differentsituations.

The disadvantage of active suspension system is that it does not work for reducingthe vibration when it reaches its limitation. In this circumstance, the system is worsethan passive system. Assumed suspension system works like without actuator orspring, consequently both the vehicle and the passengers are dangerous.

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MASS

spring

Force actuator

F

MASS

springDamper

Passive Suspention Active Suspension

Figure 2.3: Passive and Active Suspensions [4]

In addition, the active suspension system is not widely used because the cost ishigh and it requires higher power consumption. And it is commonly used in luxuryvehicle.

Figure 2.4: Passive and Active Suspensions Comparison [7]

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2.4 Semi-active Suspension

The semi-active suspension system was first proposed by Crosby and Karnopp in the1970s [8]. This suspension system was applied in the 1980s [9].In an active suspensionsystem, both actuator and spring are controllable. Being similar with the activesuspension system, the semi-active suspension system also adjusts the vibration andthe height of vehicle frame. The different part is that the system can only adjuststhe character of the damper.

The Semi-active Suspension system is simply implemented due to its simple struc-ture [10]. Semi-active suspension system functions with only a little amount of energyfrom the vehicle. The prospect of applying the system is good.

1m

2m

tK

sK

c

Figure 2.5: Semi-active Suspensions

There are two kinds of damper in this system:

• One is continuously variable semi-active suspension system [2]. The coefficientof damper is controlled continuously from the minimum to the maximum value.According to the acceleration, velocity or displacement, the system calculatesthe corresponding damper coefficient. The system adjusts the damper accordingto the calculated coefficient. The semi-active suspension system does not needexternal energy supply device. But the cost of this system is expensive since itrequires more sensors than conventional system.

• The other kind of damper is controllable damper with varies damping levels.The damping level changes according to the control strategies. There are manydifferent kinds of control strategies [5]. These control schemes are discussed inthe following subsection.

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2.5 Control Schemes for a 2 Degree of Freedom

(2DOF) System

In this section, the control schemes for a 2DOF system are introduced. There are threebasic ways to control the semi-active suspension system. These control strategies areskyhook control strategy, ground-hook control strategy and hybrid control strategy.

2.5.1 Skyhook Control

Skyhook control is the most commonly used strategy in semi-active suspension sys-tem. The ideal model of skyhook control is shown in Figure 2.6. The damper isconnected to an inertial reference in the sky. It is impossible to implement the idealmodel in real vehicle. The designer usually uses a controllable damper to reach thesimilar performance of the idal model in a semi-active suspension system.

M

K

BASE

skyC

Figure 2.6: Ideal Model of Skyhook Control System

As shown in Figure 2.6, the basic model of skyhook includes a spring with coef-ficient of k and a damper with coefficient of C. The velocity of m and base is Vmand Vb which are upwards. The velocity is defined as positive. For the first situation,assuming m is separating with a positive upwards. The force given by the skyhookdamper should eliminate the vibration. Considering of that, the force should be

F = −C × VmNext is to calculate the coefficient of a controllable damper in a semi-active sus-

pension system. They are defined positive when the direction is as shown in Figure2.6. It is known that m is moving faster than the base. This means the relativevelocity

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V = Vm − Vb > 0

Considering the force should eliminate the vibration, the force given by the con-trollable damper is

Fcon = −Ccon × V

The force given by these two systems should be the same. This means

F = Fcon

Ccon = CVmV

Based on the definition above, Vm and V are positive, then Ccon should equal toC Vm

V. It proves that the semi-active suspension system works as a skyhook system

in this situation. In other situation, the system is separated with a negative velocity.This means both the mass and the base are moving downward. So V m < 0 ,C > 0,Ccon < 0, which is physically impossible. The direction is the same as the forceprovided by skyhook damper. The semi-active system cannot provide force withnegative direction. The ideal solution is to make Ccon = 0. This is also hard torealize. In reality, the system sets the controllable damper to a minimum coefficient.The capability of system is optimized.

To sum up, the control strategy is

Ccon =

high damping, for V × Vm > 0

low damping, for V × Vm < 0

This is the simplest control strategy. With this strategy, the skyhook controlsuspension system is built up with semi-active damper.

2.5.2 Groundhook Control

The damper is connected to the unsprung mass instead of the sprung mass to modifythe skyhook control system. This modified system is then defined as ground-hookcontrol system. Although, the system has similar character as skyhook control, thevibration of unsprung mass is reduced and sprung mass is increased. This shows abetter capability of isolating the unsprung mass. The structure is shown in Figure2.7.

And the control strategy is drawn with the same method as skyhook control,which is

Ccon =

high damping, for V × Vb > 0

low damping, for V × Vb < 0

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BASE

M

bK

mK

groundC

Figure 2.7: Groundhook Control System

2.6 Magneto-Rheological Dampers

In recent years, Magneto-Rheological (MR) damper has been approved to be used invibration control applications [11]. MR damper is very popular among all kinds ofcontrollable dampers. It is designed as part of the semi-active suspension system. Inthis section, the MR damper is introduced as well as the background and applicationof MR Fluids.

2.6.1 Magneto-Rheological Fluids

MR fluids and Electro-Rheological(ER) fluids are both smart materials. The char-acters of these fluids change due to external reason. They respond to magnetic andelectric field separately. ER fluids are discovered before MR fluids. They are highlysensitive to high yield stress. Due to this reason, MR fluids are more widely usedthan ER fluids [11].

MR was invented by Jacob Rabinow at the US National Bureau of Standardsin 1948 [12]. MR fluid is a type of oil which changes state from liquid to semi-solid. Compared to ferrofluids, the MF fluids particles are much bigger. The sizeof ferrofluids particle is 1 ∼ 2microns and the size of MF fluids particle is 20 ∼50microns. There was little research about MR fluids until the early 1990s [13].

Usually, MR fluids are composed of carrier oil, activator and magnetic particles.The magnetic particles are ferrous particles coated with anti-coagulant material. Thecarrier oil is mineral oil or silicone oil. The activator here is to keep the magneticparticles suspending in the oil and increase the MR effect.

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The MR fluids are divided into four kinds according to their compositions andcapabilities [14]:

• First one is micron magnetic particles with non-magnetic carrier MR fluids. Itis a typical MR fluid. The magnetic particles are paramagnetic materials. Inthis case, magnetic particles are usually carbonyl iron dust. The percentageof magnetic particles in the fluid is from 20% ∼ 40%, even up to 50%. Thediameter of particles is usually from 0.1um to 100um. The typical range isfrom 3um to 5um. The corresponding carrier oils are silicone oil, mineral oil,synthetic oil, water and glycol.

• The second type of MR fluid is Nano-meter magnetic particles with non-magnetic carrier MR fluids. The fluid is composed of Nano-scale magneticparticles with non-magnetic carrier MR fluids.

• The third type is magnetic particles with magnetic carrier MR fluids. The fluidis consisted of micron magnetic particles and magnetic carrier.

• And there is another kind of MR fluid called non-magnetic particles with mag-netic carrier MR fluids. The fluid is composed of Nano-scale non-magneticparticle sand magnetic carrier MR fluids.

MR fluids display Newtonian-like behavior when deactivated. Without the mag-netic field, the particles disperse to the fluid without direction. When applied witha powerful magnetic field, the particles align themselves along the line of magneticflux. It is shown in Figure 2.8. The particles form the particles chains. These chainsrestrict the movement of the fluid. They lead to an increase of the viscosity, plasticityand yield stress. The chains break with certain amount of shear stress. The shearstress is defines as the yields stress.

However, the reason of viscosity is still unsolved. There are two theories whichare phase transformation theory and dipole moment under field theory. One of thetheories is widely accepted while the other theory only explains part of the effect ofMR fluids. Most of scientists believe that each particle is polarized to magnetic dipolewith the fluency of magnetic field. With the magnetic attraction, the dipole attractseach other into a line. The strength of this effect is determined by many factors. Thistheory is based on that all the particles are in regular shape. In fact, the particlesare in irregular shape. This fact is important when analyzing of the motion of theparticles.

2.6.2 Modes of MR Operation

It is known that the MR fluids have three application modes which are valve, directshear and squeeze modes. All of these modes have been applied on MR damper. Eachof them is designed for different purpose.

Valve mode and shear mode are the most commonly used. Valve mode is shownin Figure 2.9. The controllable viscosity of fluids determines how quickly the fluidpasses through a damper or valve. This is the basic premise of valve mode operation.

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Figure 2.8: MR fluid Ferrous Arrangement when applied in magnetic field [15]

The flow is directed perpendicularly between two magnetic pole plates [16]. The flowof the fluid absorbs the energy. The speed of the flow is determined by the variation ofthe magnetic field. With the changing of the magnetic field, the MR damper becomescontrollable.

Figure 2.9: MR fluid in valve mode with an applied magnetic field [15]

It is widely known that the direct shear mode is also very popular. The shearmode is shown in Figure 2.10. The plates are perpendicular to the magnetic field.The particle chain prevents relative motion of the pole plates. The particles try toprevent the chain from broken. The MR fluid only reduces the relative motion withthe normal amount. The operation is deactivated when it is not applied in magneticfield.

While the shear mode does not work in the circumstance that requires high stiff-ness with less displacement, squeeze mode is designed for these circumstances. Thesqueeze mode utilizes the analogy of a buckling columnar structure.

In this mode, the lateral force applied is parallel to the magnetic field lines [15] [17].The damper becomes more efficient with both squeeze mode MR fluid and anothermaterial. The other material provides support when the MR fluid is not activated.

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Figure 2.10: MR fluid in shear mode with an applied magnetic field [15]

After activated, the MR fluid hinders the energy with the power magnetic chain.Normally, the magnetic chain tries to stay in line. The chain breaks when applied withcertain amount of displacement. Figure 2.11 gives a clear procedure of the squeezemode operates.

Figure 2.11: MR fluid in squeeze mode with an applied magnetic field [15]

2.6.3 MR Dampers

Nowadays, MR damper is the most commonly usage of the MR fluids. Its charactermakes it perfectly suitable for the semi-active suspension system. It changes rheo-logical properties due to the changes of the magnetic field. Since the changing of therheological properties makes the damper easy to be controlled. The design of controlsystem is based on velocity or acceleration. With this quality, the semi-active systemhas more advantages than other suspension systems.

In most of time, the MR fluids work with valve mode. The damper also workswith a combination of valve mode and direct-sheer mode. With this combination,the system benefits both advantages of these two modes [6]. The structure of value

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model is simple and the design of the magnetic circuit is easy to implement. Figure2.12 shows the structure of the basic MR damper with valve mode.

Figure 2.12: MR damper operating in valve mode [6]

According to the discussion above, it is known that there are two working statusesof the MR damper. When the damper status is on, the variation of the magnetic fieldchanges the apparent viscosity of the fluid. The reason of calling it apparent viscosityis that the true viscosity does not change [6]. Only the layout of particles changedwhen the magnetic field changes. The fluid changes into solid in particular conditions.

In the valve mode case, the electromagnetic coils are turned on. Thus the magneticfield is created. The paramagnetic poles are inspired by the activation regions. TheNorth and South Poles are activated by the paramagnetic poles. The MR fluid changesinto solid with the change of the magnetic field. The movement of the piston becomesslower. When the status of the MR damper is off, the piston only works with normalmode.

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Chapter 3

Road Roughness Data Realization

3.1 Road Roughness Characterization

Road roughness has influence on passenger comfort, operation of driver, maintenancecosts, fuel consuption and fatigue, etc. It is widely known that the cost on fuel isless when the road is smoother [18]. The random process of road roughness char-acterization is commonly assumed as a zero-mean, stationary and ergodic Gaussianprocess [19].

The purpose of this thesis is to predict the road roughness data in time domain.The prediction is based on an uneven road surface. This chapter describes realizationof road roughness data. The road roughness data is set as the input of the predictorwhich is simulated in time domain in this thesis.

There are two menthods to obtain these data. One is to record the data bymeasuring the true road. The other one is to simulated road roughness. It is builtbased on PSD when the measurement data are not provided. Here, road roughnessis realized by the simulation.

3.2 The International Roughness Index

Simulation of road roughness is important for analyzing and evaluating the vehicleride quality. Some organizations have made different classifications of road roughnessin the past. The PSD method and International Roughness Index (IRI) method inevaluating road roughness are well-accepted in classifying the road condition.

The IRI is the most popular road roughness index. It has been adopted by mostroad authorities around the world [20]. The mathematical model of IRI is a quarter-car vehicle model.

The IRI does not provide a comprehensive and detailed description of roaddata[21]. It cannot be used to simulate the degrees of road roughness.

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3.3 Road Roughness Power Spectral Density

A road roughness classification based on the PSD has been proposed by the Interna-tional Organization for Standardization (ISO).

The general form of fitted PSD is

Gd (n) =Gd (n0) ·(n/n0)−w (3.1)

orGd (Ω) =Gd (Ω0) ·(Ω/Ω0)

−w (3.2)

where n0 (n0= 0.1cycle/m) is the reference spatial frequency, Ω0 (Ω0= 1 rad/m) isthe reference angular spatial frequency, n is the spatial frequency, w is the exponentof the fitted PSD and Gd (n0) is the displacement PSD.

When the w = 2, the

Gd (n) =Gd (n0) ·(n/n0)−2 (3.3)

Considering the influence of velocity v, the spatial frequency spectrum is usuallytransformed into a temporal frequency spectrum.

Gd (f) =Gd (n) /v (3.4)

As f = v × n,

Gd(f) = n20

v

f 2Gd(n0) (3.5)

Gd(f) depends on velocity, temporal frequency and the value of displacement PSD.According to the value of displacement PSD, the road roughness is divided into

eight degrees. The classifications are shown in Table 3.1 [22].

Table 3.1: Road Classification

Road classDegree of roughnessGd (n0) (10−6m3)

Lower limit Geometric mean Upper limitA — 16 32B 32 64 128C 128 256 512D 512 1024 2048E 2048 4096 8192F 8192 16384 32768G 32768 65536 131072H 131072 262144 —

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3.4 Methods of Realizating Road Roughness

There are many menthods to stimulate stochastic excitation in time domain to formroad roughness. For example, Harmonic superposition method, integral white noisemodel, AR model and inverse Fourier transform model are the commonly used.

3.4.1 Harmonic Superposition Method

The main idea of the Harmonic superposition method is an approximation of a targetrandom process by the Discrete Spectral. In temporal frequency (f1, f2), the powerspectrum density is Gd (f). The variance σ2 of this interval is simulated by Gd (f).

σ2=

∫ f2

f1

Gd (f) df (3.6)

In order to derive the discretion formula, the interval (f1, f2) is divided into nintervals. The value of middle frequency fmid−i is considered as the power spectrumof each small interval. Then the function is transformed as

σ2=n∑

i=1

Gd (fmid−i)·4fi (3.7)

The standard deviation PSD of each small interval is expressed based on sinefunction as

σ=√

2Gd (fmid−i)4fi·sin(2πfmid−it+θi) (3.8)

Then the stationary-zero mean value-stochastic process is simulated by the sumof the sine function of each small interval.

q (t) =n∑

i=1

√2Gd (fmid−i)4fi·sin(2πfmid−it+θi) (3.9)

where q(t) is the road roughness height and θ is a uniform random number in theinterval [0, 2π].As n tends to infinity, the accuracy increases. This means large amountof calculation is needed to obtain an acceptable signal. Z. Yonglin proposed that theoperational frequencies range from 0.139 to 39.3Hz in vehicle analysis [23].

3.4.2 The AR Model

The autoregressive-moving-average model is

q (k) = −m∑k=1

ak·q (n−k)+w(n) (3.10)

where ak is parameter to be determined, m is the order of AR model and n is then-th sample time. Here q(k) is considered as a linear combination of the m previous

18

samples and a white noise process w(n). The mean of the white noise process w(n)is zero. The variance is of w(n) is σ2. After Z-transform, the equation is

H (z) =Q(Z)

A(Z)=

1

1+∫ m

k=1ak·Z−1

=1

(1−z1Z−1) (1−z2Z−1) · · · (1−zmZ−1)(3.11)

When all the poles z1, z2, . . . , zm are inside the unit circle, the signal of the ARmodel is stable. According the property of the autocorrelation function, the value ofRq (m) is

Rq (m) =E [q (n) q (n+m)] = E

q (n)

[−

m∑k=1

ak·q (n−k+m)+w (n+m)

]

= −m∑k=1

akRq (m−k)+E[q (n)w (n+m) ]

(3.12)

Then the Rq (m) is

Rq (m) = −m∑k=1

akRq (m−k)+σ2, if m = 0 (3.13)

or

Rq (m) = −m∑k=1

akRq (m−k), if m 6= 0 (3.14)

If m = 1, 2, . . . , p, the equation is transformed into matrix below.Rq(0) Rq(−1) Rq(−2) · · · Rq(−p)Rq(1) Rq(0) Rq(−1) · · · Rq(−p+ 1)Rq(2) Rq(1) Rq(0) · · · Rq(−p+ 2)

......

.... . .

...Rq(p) Rq(p− 1) Rq(p− 2) · · · Rq(0)

1a1a2...aq

=

σ2

00...0

(3.15)

The Rq (m) =Rq (−m), the matrix is transformed asRq(0) Rq(1) Rq(2) · · · Rq(p)Rq(1) Rq(0) Rq(1) · · · Rq(p− 1)Rq(2) Rq(1) Rq(0) · · · Rq(p− 2)

......

.... . .

...Rq(p) Rq(p− 1) Rq(p− 2) · · · Rq(0)

1a1a2...aq

=

σ2

00...0

(3.16)

This is the Yule—Walke function. If the value of each Rq(q = 1, 2, . . . , p) is known,the ak can be calculated from the Yule—Walke function. It is solved by Levinson-Durbin in Matlab. At last, road roughness is simulated by the AR model.

19

3.4.3 The Inverse Fourier Transform Model

The power spectrum density of road roughness is replaced by the square of Fouriertransform of random sequence.

Gd (fk) =2

Nfs|Xk|2 (3.17)

where k = 0, 1, 2, 3, . . . , N/2, Xk is a discrete Fourier transform of road random signalin time domain, fk is the frequency of the Fourier transform, fs is the sample frequencyand N is the number of sample points. Therefore,

|Xk|=√Gd (fk)Nfs

2(3.18)

|Xk| is the magnitude-frequency characteristic of Xk. For an n-point discrete signal,the discrete Fourier transform is a complex number. Xk is transformed as

Xk = |Xk| ejϕk (3.19)

where ϕk is a phase of Xk.The first N/2 + 1 value of ϕk is its phase in the Inverse Fourier Transform model.

To simulate the road roughness based on inverse Fourier transform, |Xk| and ϕk arecombined. Then, xt is obtained by inverse Fourier transform of Xk.

3.4.4 The Integral White Noise Model

The road roughness is considered as the result of a white noise filtered by an appro-priate filter. The mathematical model of a single-point time domain model is

q (t) = w (t) (3.20)

And the variance of w(t) is defined as

σ2w = E[w − E[w]]2 = 4π2Gd (n0)n0

2v (3.21)

So,q (t) = 2πn0

√Gd (n0) v·w1(t) (3.22)

where w1(t) is the Gaussian white noise with σ2 = 1, q(t) is the road roughness andv is the velocity of the vehicle. The solution of the differential equation is the roadroughness in the vertical direction. There are two the road roughness data. One usesan integrator, and the other uses a forming filter.

3.5 Road Roughness Realization Results

Some researchers have compared and analyzed these models in calculation, stability,application and expansibility [24]. The Harmonic superposition method requires a

20

Table 3.2: Roas roughness Simulation Parameters

Road classParameters

Velocity(m/s) Displacement PSD (×10−6m−3)C 15 256F 15 16384

large amount of calculation. But it is widely used in different road situations. Itprovides good simulation precision. In this thesis, the road roughness is re-constructedby this method.

In this thesis, the C and F degrees of road roughness are simulated. The roadsimulation parameters are shown in Table 3.2. The simulation results are shown inFigure 3.1 and Figure 3.2.

0 50 100 150−0.04

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05

The length of the road (m)

Roa

d ro

ughn

ess

(m)

Road roughness in time domain

Figure 3.1: C degree road roughness

From these two figures, the F degree road is rougher than the C degree road. Themaximum value of C degree is 0.049m. The F degree road roughness is chosen asinput of the prediction.

21

0 50 100 150−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

The length of the road (m)

Roa

d ro

ughn

ess

(m)

Road roughness in time domain

Figure 3.2: F degree road roughness

22

Chapter 4

Experimental Approach andDiscussion

4.1 Introduction of Kalman Filter

The Kalman filter is a remarkable method to predict and estimate the state of astationary process by minimizing the mean square error [25].

The results of Kalman filter have very small error. The Kalman filter has appli-cations in spacecraft orbit determination, estimation and prediction of target trajec-tories, simultaneous localization and mapping, etc [25].

The discrete Kalman filter cycle is shown in Figure 4.1. It consists of two steps:

• Prediction step. In prediction step, the goal is to obtain the predicted state fornext time step by forward projection of the current state and error covarianceestimates [26].

• Correction step. In correction step, the aim is to correct the estimate state anderror covariance.

4.2 Modelling

In this thesis, the random road roughness is a zero-mean, stationary and ergodicGaussian process. The road roughness, xk , is measured by the displacement sensor attime k. The discrete-time process can be expressed as the linear stochastic differenceequation:

xk= Axk−1 + wk−1 (4.1)

with measurement data z,zk = Hxk + vk (4.2)

where A is a time-variant matrix relating the state at the previous time step k− 1 tothe state at the current step k and H is a time-variant matrix relating the state to

23

Prediction step: project the state and the priori error covariance

Correction step：correct the estimate state and the priori error covariance

Initial value

Figure 4.1: The prediction and correction steps of Kalman filter

the measurement zk [26]. they are assumed as constant, here. The random variablewk is a zero-mean white noise with normal distribution which is defined as

wk ∼ N(0, Q)

vk is the noise from measurement. It is a zero-mean white noise with normal distri-bution independent of wk. It is defined as

vk ∼ N(0, R)

Where Q is covariance of the process noise and R is covariance of the measurementnoise.

In this model, the road roughness xk is assumed as a linear process. The dis-placement sensor assembled on the tires is used to measure the displacement. Thisdisplacement is assumed as the road roughness over time. z is road roughness mea-surement data with noise. The parameter H = 1 and A = 1 .

x represents the road roughness and z is the measurement value of road roughness.The prediction update step can be expressed as

X−k = AXk−1 (4.3)

P−k = APk−1A

T +Q (4.4)

In the equation 4.3, X−k is a priori estimate to predict the statement forward from

step k-1 to step k. X−k is considered as the predicted road roughness. P−

k is the priori

24

error covariance. It is used to calculate the Kalman gain in the correction step. Thecorrection update steps are

Kk = P−k H

T (HP−k H

T +R)−1 (4.5)

Xk = X−k +Kk(Zk −HkX

−k ) (4.6)

Pk = (I −KkH)P−k (4.7)

where Kk is the Kalman gain that minimizes the posteriori error covariance, Xk is aposteriori estimated state, Pk is posteriori error covariance and I is unit matrix.

4.3 Road Condition Predicting Result

The F level of road roughness was assumed as the true roads data in the predic-tion experiment prediction. The vehicle speed is assumed as 15m/s over an entiredistance of 20m. The response time of the Magneto-rheological Fluids is within sixmilliseconds. So, the prediction frequency is assumed as 100Hz. If the predictionfrequency is higher, it requires the MR damper with shorter response time which isnow impossible to implement. The parameters are shown in Table 4.1.

Table 4.1: F level load roughness experimental parameters

Parameters ValuesVelocity 15m/sUpdated state estimate 0.01sQ covariance of the process noise 81− 250mm2

R covariance of the measurement noise 25− 900mm2

Gd (n0) 16384× 10−6m3

Figure 4.2 and Figure 4.3 show the performance of Kalman with the varied processnoise covariance Q and measurement noise covariance R on predicting the F level roadroughness.

In Figure 4.2, it shows that Kalman filter is more accurate with a lower processnoise Q on road prediction. According to Figure 4.3, Kalman filter predicts roadroughness less accurate in noisy measurement environment(R). The predicted roadroughness approaches the actual value quickly. Figures 4.2 and 4.3 also indicate theactual road roughness character.

Table 4.2 shows the mean error with variant measurement noise covariance R andprocess noise covariance Q in F level road roughness. These coefficients are chosento test the performance of the predictor.

According to Figures 4.4, Kalman filter performans better on predicting F levelroad roughness with assumed Q and R.

Figure 4.5 shows the Kalman gains with variant measurement noise covarianceR and process noise covariance Q. R and Q varies every time. The Kalman gains

25

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.3

−0.2

−0.1

0

0.1R1,Q1

Time [s]R

oad

roug

hnes

s (m

)

Predicted road roughnessTrue road roughness

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.3

−0.2

−0.1

0

0.1R1,Q2

Time (s)

Roa

d ro

ughn

ess

(m)

Predicted road roughnessTrue road roughness

Figure 4.2: The performance of Kalman with measurement noise covariance R1=25mm2 and varied process noise covariance Q1=100 mm2,Q2=250 mm2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2

−0.1

0

0.1

0.2R3,Q3

Time (s)

Roa

d ro

ughn

ess

(m)

Predicted road roughnessTrue road roughness

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2

−0.1

0

0.1

0.2R4,Q3

Time (s)

Roa

d ro

ughn

ess

(m)

Predicted road roughnessTrue road roughness

Figure 4.3: The performance of Kalman with process noise covariance Q3=100 mm2

and varied measurement noise covariance R3=100 mm2,R4=900 mm2

convergence very fast with different R values and Q values. It takes no more than 10iterations. This advantage makes the predictor applicable.

This predictor system has fast response time and converge speed. It reaches therequirement of the real time application. This predictor method is applicable in thevehicle.

26

Table 4.2: Mean error with variant R values and Q values

R (mm2) Q(mm2) error Mean (m)25 100 0.016425 250 0.0180100 100 0.0181900 100 0.030925 81 0.0152

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−0.2

−0.1

0

0.1

0.2R5,Q5

Time [s]

Roa

d ro

ughn

ess

[m]

Predicted road roughnessTrue road roughness

Figure 4.4: The performance of Kalman with the process noise covariance Q=25mm2

and measurement noise covariance R=81mm2

4.4 Passenger Comfort Comparison

The vehicle runs through the road at speed of 15m/s. The process noise Q is 81mm2

and the measurement noise R is 25mm2. The passenger comfort comparison is shownin Figure 4.6.

In Figure 4.6, the red line shows the absolute value of true road roughness. Thisroad has three large bumps and three valleys. The maximum peak is 20cm. Thepassenger feels uncomfortable on this road.

The blue line displays error between predicted and true road roughness. Thiserror is the left-over after the roughness is compensated by the semi-active suspensionsystem. Compared to the red line, the big bumps and valleys are reduced into smallvibrations. The comfort of passenger is proportional to the error. The comfort ofpassenger is improved significantly.

27

0 5 10 15 20 25 30 35 40 45 500.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Iteration

vaul

ekalman gain

R1,Q1R1,Q2R3,Q3R4,Q3R5,Q5

Figure 4.5: Kalman gains with different R values and Q values

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Time (s)

Roa

d ro

ughn

ess

(m)

absolute value of true road roughnesserror between predicted and true data

Figure 4.6: Error between the true road roughness and the predicted road roughness

28

Chapter 5

Conclusion

The implementation of the research is constructed as follows. Firstly, the data oftrue road and the model of Kalman filter are built. Then Kalman filter is applied topredict the road condition. The result shows the passenger comfort is optimized.

A new solution of road condition prediction is proposed in this thesis. It needsless calculation and only real-time data. The system response is fast. The Kalmanfilter is also capable of predicting the real-time road condition with accurate response.This leads to a better performance of the suspension system. The system providesmore comfort with less trade off to stability.

This thesis realizes the road roughness model to simulate the road condition asthe input of road condition predictor. The random process of the road roughness isa stationary random process.

Predictor is built based on Kalman filter. The simulation result is fairly close tothe true road data. The prediction of road condition is considered as predicting theroughness of the road.

The advantage of the Kalman filter is that the filter only needs the current data.It gives the Kalman filter an outstanding performance in the real-time prediction.The calculation is fast and easy to implement. This reduces the energy consumptionof the control system.

The passenger comfort is proportional to the error. A passenger feels more com-fortable when the error is small. According to the result of prediction, the comfort ofpassengers is improved significantly with the proposed method.

The performance of the semi-active suspension system is optimized with the roadcondition prediction. To our knowledge, until now there are no other comparablesolution to predict the road roughness.

29

References

[1] X. Song, “Design of adaptive vibration control systems with application ofmagneto-rheological dampers,” Ph.D. dissertation, Dept. Mech. Eng., VirginiaPolytechnic Institute and State Univ., Blacksburg, Virginia, 1999.

[2] T. Rao, G. Rao, k.S. Rao, and A. Purushottam, “Analysis of passiveand semi active controlled suspension systems for ride comfort in anomnibus passing over a speed bump,” vol. 5, 2010. [Online]. Available:http://www.arpapress.com/Volumes/Vol5Issue1/IJRRAS 5 1 02.pdf

[3] N. McLellan, “On the development of a real-time embedded digital controller forheavy truck semiactive suspensions,” Master’s thesis, Faculty of Virginia Tech,1998.

[4] D. Simon, “An investigation of the effectiveness of skyhook suspensions forcontrolling roll dynamics of sport utility vehicles using magneto-rheologicaldampers,” Ph.D. dissertation, Dept. Mech. Eng., Virginia Polytechnic Instituteand State Univ., Blacksburg, Virginia, 2001.

[5] C. A. Par, “Experimental evaluation of semiactive magneto-rheological suspen-sions for passenger vehicles,” Master’s thesis, Dept. Mech. Eng., Virginia Poly-technic Institute and State Univ., Blacksburg, Virginia, 1998.

[6] J. W. Gravatt, “Magneto-rheological dampers for super-sport motorcycle appli-cations,” Ph.D. dissertation, Dept. Mech. Eng., Virginia Polytechnic Instituteand State Univ., Blacksburg, Virginia, 2003.

[7] R. Chalasani, “Ride performance potential of active suspension systems-part i:Simplified analysis based on a quarter-car model,” in Proceedings of the 1986ASME Winter Annual Meeting, 1986.

[8] E. Guglielmino, T. Sireteanu, C. Stammers, G. Ghita, and M. Giuclea, Semi-active suspension control: improved vehicle ride and road friendliness. SpringerVerlag, 2008.

[9] D. Guo, H. Hu, and J. Yi, “Neural network control for a semi-active vehicle sus-pension with a magnetorheological damper,” Journal of Vibration and Control,vol. 10, no. 3, pp. 461–471, 2004.

30

[10] L. Jansen and S. Dyke, “Semiactive control strategies for mr dampers: compar-ative study,” Journal of Engineering Mechanics, vol. 126, no. 8, pp. 795–803,2000.

[11] T. Butz and O. Von Stryk, “Modelling and simulation of rheological fluid de-vices,” Sonderforschungsbereich, vol. 438, pp. 1–35, 1999.

[12] J. Rabinow, “The magnetic fluid clutch,” Transactions of the American Instituteof Electrical Engineers, vol. 67, no. 2, pp. 1308–1315, 1948.

[13] C. Hirunyapruk, B. Mace, and M. Brennan, “Vibration control using an adaptivetuned magneto-rheological fluid vibration absorber,” 2008.

[14] J. Wang and G. Meng, “Research advances in magnetorheological fluids,” ActaAeronautica Et Astronautica Sinica, vol. 23, no. 1, pp. 6–12, 2002.

[15] S. Mazlan, N. Ekreem, and A. Olabi, “The performance of magnetorheologicalfluid in squeeze mode,” Smart Materials and Structures, vol. 16, pp. 1678–1682,2007.

[16] J. Carlson and M. Jolly, “MR fluid, foam and elastomer devices,” Mechatronics,vol. 10, no. 4, pp. 555–569, 2000.

[17] F. D. Goncalves, J. H. Koo, and M. Ahmadian, “A review of the state of the artin magnetorheological fluid technologies-part I: MR fluid and MR fluid models,”The Shock and Vibration Digest, vol. 38, no. 3, pp. 203–219, 2006.

[18] M. Yousefzadeh, S. Azadi, and A. Soltani, “Road profile estimation using neu-ral network algorithm,” Journal of Mechanical Science and Technology, vol. 24,no. 3, pp. 743–754, 2010.

[19] C. J. Dodds and J. D. Robson, “The description of road surface roughness,”Journal of Sound and Vibration, vol. 31, no. 2, pp. 175–183, 1973.

[20] R. Hesami and K. McManus, “Signal processing approach to road roughnessanalysis and measurement,” in TENCON 2009-2009 IEEE Region 10 Conference.IEEE, 2009, pp. 1–6.

[21] A. Ayenu-Prah and N. Attoh-Okine, “Comparative study of hilbert–huang trans-form, fourier transform and wavelet transform in pavement profile analysis,”Vehicle System Dynamics, vol. 47, no. 4, pp. 437–456, 2009.

[22] ISO, ISO 8608:1995(E): Mechanical Vibrationroad surface profilesreporting ofmeasured data. Geneva, Switzerland: International Organization for Stan-dardization, 1995. [Online]. Available: http://www.iso.org/iso/iso catalogue/catalogue tc/catalogue detail.htm?csnumber=15913

31

[23] X. Wang and R. Wang, “A novel modeling method of virtual lunar surface basedon lunar surface roughness,” in Remote Sensing, Environment and Transporta-tion Engineering (RSETE), 2011 International Conference on. IEEE, 2011, pp.17–20.

[24] J. Peng, J. He, X. Li, Y. Chen, and Y. Cong, “Simulation comparison andevaluation of common time domain models under road irregularity excitation,”Journal of PLA University of Science and Technology (Natural Science Edition),vol. 10, no. 1, pp. 77–79, 2009.

[25] M. Gruber, “Statistical digital signal processing and modeling,” Technometrics,vol. 39, no. 3, pp. 335–379, 1997.

[26] G. Welch and G. Bishop, “An introduction to the kalman filter,” University ofNorth Carolina at Chapel Hill, Chapel Hill, NC, vol. 7, no. 1, 1995.

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