Vehicle Ahead Property Estimation in Heavy Duty Vehicles

Institutionen för systemteknik

Department of Electrical Engineering

Examensarbete

Vehicle Ahead Property Estimation in Heavy Duty

Vehicles

Examensarbete utfört i reglerteknik vid Tekniska högskolan vid Linköpings universitet

av Henrik Felixson LiTH-ISY-EX--14/4782--SE

Linköping 2014

Department of Electrical Engineering Linköpings tekniska högskola

Linköpings universitet Linköpings universitet

Vehicle Ahead Property Estimation in Heavy Duty

Vehicles

Examensarbete utfört i reglerteknik

vid Tekniska högskolan vid Linköpings universitet

av

Henrik Felixson LiTH-ISY-EX--14/4782--SE

Handledare: Maryam Sadeghi

isy_{, Linköpings universitet}

Jonny Andersson

Scania CV AB

Examinator: Martin Enqvist

isy, Linköpings universitet

Avdelning, Institution Division, Department

Division of Automatic Control Department of Electrical Engineering SE-581 83 Linköping Datum Date 2014-06-10 Språk Language Svenska/Swedish Engelska/English   Rapporttyp Report category Licentiatavhandling Examensarbete C-uppsats D-uppsats Övrig rapport  

URL för elektronisk version

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-108341

ISBN — ISRN

LiTH-ISY-EX--14/4782--SE Serietitel och serienummer Title of series, numbering

ISSN —

Titel Title

Skattning av egenskaper hos framförvarande tungt fordon Vehicle Ahead Property Estimation in Heavy Duty Vehicles

Författare Author

Henrik Felixson

Sammanfattning Abstract

In today’s adaptive cruise controllers, the speed and distance to the vehicle ahead is based on how the vehicle ahead is driving. However, in order to optimize the driving with respect to the fuel consumption, it is very useful to be able to predict how the vehicle ahead is going to drive. By estimating the mass and maximum engine power of the vehicle ahead, its behaviour can be predicted and the own vehicle’s driving can be adjusted accordingly.

Here, method is presented that estimates the mass and maximum engine power for the heavy duty vehicle directly ahead, using topography data, data from a radar, and a camera sensor. The method is based on finding situations where the vehicle ahead rolls without any engine or braking force, and during these situations, estimating the mass with a recursive least squares method. After that, when the mass is assumed to be known, situations of maximum engine power are detected, during which the maximum engine power is estimated. The results show that it is difficult to know how long it takes before the estimates can be trusted. However, during the simulations done using real data, the methods have mostly generated a result with an error smaller than 20%.

Nyckelord

Keywords mass estimation, vehicle ahead, recursive least squares, Kalman filter, radar, vehicle dynam-ics estimation

Abstract

In today’s adaptive cruise controllers, the speed and distance to the vehicle ahead is based on how the vehicle ahead is driving. However, in order to optimize the driving with respect to the fuel consumption, it is very useful to be able to predict how the vehicle ahead is going to drive. By estimating the mass and maximum engine power of the vehicle ahead, its behaviour can be predicted and the own vehicle’s driving can be adjusted accordingly.

Here, method is presented that estimates the mass and maximum engine power for the heavy duty vehicle directly ahead, using topography data, data from a radar, and a camera sensor. The method is based on finding situations where the vehicle ahead rolls without any engine or braking force, and during these situations, estimating the mass with a recursive least squares method. After that, when the mass is assumed to be known, situations of maximum engine power are detected, during which the maximum engine power is estimated.

The results show that it is difficult to know how long it takes before the estimates can be trusted. However, during the simulations done using real data, the meth-ods have mostly generated a result with an error smaller than 20%.

Abstract

I dagens adaptiva farthållare anpassas hastigheten och avståendet till fordonet framför baserat på hur framförvarande fordon kör. För att kunna optimera sin egen körning med avseende på bränsleförbrukning är det dock mycket använd-bart att kunna prediktera hur framförvarande fordon kommer att köra. Genom att estimera framförvarande fordons vikt och maximala motoreffekt kan dess be-teende förutses och den egna körningen anpassas efter detta.

Här presenteras en metod som med hjälp av radar, kamera och topografidata skat-tar massa och maximal motoreffekt för ett framförvarande tungt fordon. Meto-den går ut på att iMeto-dentifiera situationer då framförvarande fordon rullar fritt, och under dessa situationer skatta massan med hjälp av en rekursiv minstakvadrat-metod. Därefter, när massan antas vara känd, identifieras situationer då framför-varande fordon applicerar full gas och under dessa situationer skattas maximal motoreffekt.

Resultatet visar att det är svårt att veta hur lång tid det tar innan skattningarna går att lita på, men att de i de simuleringar som gjorts på verklig data oftast generarar ett resultat med ett fel som är mindre än 20%.

Acknowledgments

This Master’s thesis has been conducted at the department of Drivers Assistance Controls, REVD at Scania CV AB in Södertälje, Sweden.

First, I would like to express my gratitude to my supervisor at Scania, Jonny An-dersson for his valuable guidance and help throughout the whole project. I would also like to thank all the other members of REVD who have helped me with dif-ferent tasks, from simulation problems to data collection, and for making me feel welcome. From Linköping University I thank Maryam Sadeghi and Martin Enqvist for valuable inputs, and guidance with the report writing.

Linköping, June 2014 Henrik Felixson

Contents

Notation xi 1 Introduction 1 1.1 Background . . . 1 1.2 Scania . . . 1 1.3 Objective . . . 2 1.4 Limitations . . . 2 1.5 Previous work . . . 2 1.6 Related work . . . 2 1.7 Outline . . . 3 2 System overview 5 2.1 can bus . . . 6 2.2 Radar . . . 6 2.3 Camera . . . 6 2.4 Topography data . . . 6

2.5 Estimator control unit . . . 7

3 Modeling and estimation theory 9 3.1 Modeling of the vehicle dynamics . . . 9

3.2 Estimation theory . . . 11

3.2.1 Kalman filter . . . 12

3.2.2 Recursive least squares . . . 12

4 Mass estimation 15 4.1 Detection of no internal forces . . . 15

4.2 rls mass estimation . . . 19

5 Maximum engine power estimation 23 5.1 Detection of maximum engine power . . . 23

5.2 Maximum engine power estimation . . . 25

5.3 Estimation of critical uphill road grade . . . 27

x Contents

6 Result 29

6.1 Experimental setup . . . 29 6.2 Experimental result . . . 29 6.2.1 Comparison to results from previous works . . . 30

7 Validation and sensitivity analysis 35

7.1 Validation . . . 35 7.2 Sensitivity analysis . . . 36

8 Conclusions and future work 43

8.1 Conclusions . . . 43 8.2 Future work . . . 44

Notation

Abbreviations

Abbreviation Meaning

hdv _{Heavy Duty Vehicle} kf _{Kalman Filter}

rls Recursive Least Squares esr Electronically Scanning Radar gps Global Positioning System ecu Electronic Control Unit

1

Introduction

In this chapter, the background and basis of the thesis are presented as well as a short summary of related and previous works.

1.1

Background

In today’s Heavy Duty Vehicles (hdvs), an adaptive cruise control is often used to adjust the speed to the vehicle ahead based on its longitudinal motion. How-ever, in order to minimize the fuel consumption and make as good adjustments as possible, prior information about how the vehicle ahead is going to move is beneficial. For instance, knowing in advance that the vehicle ahead is going to slow down in the next uphill due to insufficient engine power, is critical when optimizing the driving with respect to fuel consumption.

There are several parameters that determine the longitudinal motion of a vehicle and two of the most decisive ones are the mass and the engine power. There-fore, knowledge of these parameters for the vehicle directly ahead would greatly enhance the optimality potential of an adaptive cruise controller.

1.2

Scania

The thesis project is conducted at Scania CV AB in Södertälje, at the department of vehicle control systems. Scania is a leading manufacturer of HDVs and coaches, and industry and marine engines. The company is active in around 100 countries and has more than 35 000 employees, of which 2400 work with research and development.

2 1 Introduction

1.3

Objective

The goal of this thesis is to develop a method that can be used to estimate the mass and maximum engine power of a heavy vehicle directly ahead, from now on denoted as the target vehicle, based on the road grade data from a digital topography map, the data from a radar, and a camera sensor.

1.4

Limitations

The focus of this thesis is on estimating key properties of the target vehicle, not on how these estimates can be used to control the vehicle. Furthermore, the as-sumed usage is during highway driving, and the estimators are adjusted to these conditions. The maximum engine power estimator will not produce any result at velocities below 70 km/h, and the mass estimator will not produce any result at velocities below 50 km/h.

1.5

Previous work

There has not been a lot of papers written on the subject of estimating properties of a heavy vehicle directly ahead of the own vehicle. However, one example is Slettengren [2006], where data from the radar are used to classify different prop-erties of the target vehicle. By the use of a Kalman filter, the driving force over mass and a lumped aerodynamic drag coefficient are estimated.

1.6

Related work

However, estimating properties of the own vehicle has been the subject of nu-merous papers. Most of the ones of interest to this thesis are based on Newton’s second law applied to the longitudinal dynamics of the vehicle. In Jonhed [2013] and Lundin and Olsson [2012], some methods to estimate the vehicle mass are presented. The former uses a recursive least squares method on signals that have been noise reduced by stepwise integration into 10 second intervals, and low-pass filtered, while the road grade is known. The latter uses an extended Kalman filter and additional measurements from an inclination sensor. Nyqvist [2011] evaluates an approach that disregards the external forces depending on the road grade, the foundation of the road, and the wind, acting on the vehicle.

In Jonsson Holm [2011] and Ardalan et al. [2005], methods for on-line estimation of the vehicle mass as well as the road grade are presented, using a Kalman filter and recursive least squares with forgetting, respectively. Knowledge of the road grade adds information to the longitudinal dynamics, making more accurate es-timates possible. If the road grade is not known, as in Jonhed [2013], estimating the road grade as well as the mass is an option. This is done in several papers. For example, in Bae et al. [2001], two methods for estimating the road grade using

1.7 Outline 3

Global Positioning System signals, (gps), are presented. The resulting grade mea-surements are used to produce an estimate of mass, rolling resistance and air drag from the longitudinal force balance. Feng et al. [2014] propose a vehicle mass es-timator that adapts to changing conditions in the surrounding by first estimating the combined resistances and then estimating the vehicle mass. The resistance is estimated at low accelerations and the mass during high accelerations, both by the use of recursive least squares. In Mahyuddin et al. [2014], an observer-based parameter estimation scheme with a sliding mode term is described, which esti-mates the road gradient and vehicle mass using only the vehicle’s velocity and engine torque. The estimation scheme is augmented to an adaptive observer and analysed using Lyapunov theory.

Some methods have been proposed that are not based on the longitudinal motion of the vehicle. In Fathy et al. [2008], an algorithm is proposed inspired by pertur-bation theory that is based on the idea that the inertial dynamics dominate the vehicle motion during certain manoeuvres. Those certain manoeuvres are found and data are fed to a recursive least squares-based estimator. Daeil et al. [2012] present two types of mass estimation algorithms based on the roll dynamics. The first uses adaptation law from a roll angle observer and Lyapunov stability analy-sis. The second is based on a recursive least squares method.

A slightly different application is presented in Sadeghi et al. [2013], where the au-thors suggest a method for detecting and estimating changes in a vehicle’s sprung mass as well as the roof load based on a physical model of the roll dynamics. The unknown parameters are estimated with a greybox and an ARMAX approach. Estimation of other vehicle properties than the mass have also been the subject of numerous scientific papers. In Sebasadji et al. [2008], the vehicle dynamics are estimated using an extended Kalman filter, as well as the road grade which is estimated by the use of an Luenberger observer. Rhode and Gauterin [2013] propose a recursive generalized total least squares algorithm with exponential forgetting for estimating the vehicle driving resistance parameters. More specific, these resistance parameters are the vehicle mass, two coefficients for the rolling resistance, and a coefficient for aerodynamic drag.

1.7

Outline

The relevant system and its components are described in Chapter 2. In Chap-ter 3, a physical model of the longitudinal dynamics is derived and the theory behind the estimation methods used in the project is briefly described. Chapter 4 presents a method to estimate the mass of the target vehicle, and Chapter 5 de-scribes a method to estimate the maximum engine power as well as the critical value of the road grade at which positive acceleration is still possible. The results from a test drive are presented in Chapter 6, and a validation and sensitivity analysis is performed in Chapter 7. In Chapter 8, conclusions and suggestions for future work are presented.

2

System overview

In this chapter an overview of the system and its components is presented. The most relevant components in this project are the different Electronic Control Units (ecus) that are responsible for gathering and processing data describing the longitudinal motion of the target vehicle. These are the camera, radar, topog-raphy data, and the estimator control units. They communicate with each other via a Controller Area Network (can). A visual overview of the system and its components can be seen in Figure 2.1, and a more detailed description of the components follows below.

Camera Control Unit Radar Control Unit Topography Data Control Unit Estimator Control Unit CAN bus

Figure 2.1:Visual overview of the system with the components relevant for the project.

6 2 System overview

2.1

CAN

bus

The can bus is a standard message-based communication protocol for vehicle buses, allowing micro-controllers, or ecus, to communicate without a host com-puter. Each node, connected to the bus, is able to send and receive messages, but not simultaneously. A message consists of the identity of the sending control device, and its message. The identity also represents the priority of the mes-sage. This enables the control units with higher priority than that of the current sending control unit, to interrupt the current message and gain access to the bus [BOSCH, 2012].

2.2

Radar

A radar is commonly used in HDVs to detect and track target vehicles. It provides information regarding distance, relative velocity and direction to one or more targets. The radar used in many Scania vehicles is an Electronically Scanning Radar (esr). More specifically, the radar is a multi mode esr that combines a wide field of view at mid range with long range coverage. In Table 2.1 some technical specifications are presented [Delphi, 2014].

Table 2.1:Some technical specifications for the radar [Delphi, 2014]. Specification Long range: 174 m Short Range: 60 m Field of view +/- 10 deg +/- 45 deg

Update rate 50 ms 50 ms

Range rate -100 to 25 m/s -100 to 25 m/s

2.3

Camera

A camera, used for vision based driver assistance, can work as a complement to the radar. It handles visual recognition and scene interpretation, aiding the track-ing of a target. The visual recognition makes it possible to disttrack-inguish between hdvs and passenger cars. The digital camera, used in many Scania vehicles, is operating at 332MHz. The vehicle detection algorithm running on the processor recognises most types of motorized vehicles such as motorcycles, cars and trucks. The algorithm works both in night and day time. It detects targets up to a dis-tance of 100 meters when using a camera with a field of view of 38 degrees and a resolution of 640x480 pixels [Mobileye, 2014a,b].

2.4

Topography data

The topography data control unit calculates the vehicle position with the help of a gps, gyroscope and wheel speed information. On this basis the relevant topography data is retrieved from a database of map data and transmitted via

2.5 Estimator control unit 7

the can bus. The receiving control unit then recreates the virtual topography profile from each new data package, as well as deletes the oldest data package, reducing the memory management requirements of the receiving control unit. [Continental, 2014].

2.5

Estimator control unit

The estimator suggested in this thesis is implemented in a Scania developed con-trol unit suitable for driver assistance systems. The code running on the embed-ded system is generated from matlab.

3

Modeling and estimation theory

A necessary condition for determining the properties of the target vehicle is a sufficiently accurate physical model of the dynamics, which together with the measured signals can lead to the desired estimates. In this chapter, a model de-scribing the longitudinal dynamics of the target vehicle is presented, and two common estimation methods are described.

3.1

Modeling of the vehicle dynamics

The longitudinal dynamics of a vehicle are governed by Newton’s Second Law as

X

Fi = ma, (3.1)

whereP Fiis the sum of all forces acting on the vehicle, and m and a are the mass

and acceleration of the vehicle, respectively.

The forces acting on a moving vehicle can be divided into internal and external forces. The internal forces are, for example, the driving and braking forces, and the external forces are, for example, the aerodynamic drag, the rolling resistance and the gravity induced force. An overview of all the forces acting on the vehicle in the longitudinal direction can be seen in Figure 3.1, and the individual forces are described below. By applying (3.1) and the forces displayed in Figure 3.1, the longitudinal dynamics are described as

Fw−Fair−Fg −Froll= ma, (3.2)

where Fw are the internal forces acting on the wheels, originating from braking 9

10 3 Modeling and estimation theory

and the engine torque. Fair is the aerodynamic drag, Fg is the gravity induced

force and Frollis the rolling resistance.

α

F

g

F

air

F

w

F

roll

Figure 3.1:Forces acting on a moving vehicle.

The external forces, the aerodynamic drag, the rolling resistance and the grav-ity induced force, generally depend on the surrounding conditions on one hand, and the predefined vehicle properties on the other hand. The surrounding con-ditions are, for example, the speed and the road grade, where the speed mainly influences the aerodynamic drag and the road grade influences both the gravity induced force and the rolling resistance. The vehicle properties that influence the external forces are, for example, the shape and the weight of the vehicle, where the shape influences the aerodynamic drag and the mass affects the rolling resis-tance and the gravity induced force.

A common model of the aerodynamic drag depends on a number of constant vehicle specific parameters and the vehicle speed as

Fair =

1

2ρairCdAv

2_{, (3.3)}

where ρair is the air density, Cd is the aerodynamic drag coefficient, A is the

vehicle front area, and v is the vehicle speed. Cdlies within the range of 0.64-1.1

for hdvs [Wong, 2008].

The rolling resistance for an hdv driving on a hard surface is mainly caused by the hysteresis of the tires (approximately 90-95%). A small part is caused by the friction between the tires and the ground, as well as some air resistance. Frollis

3.2 Estimation theory 11

well as a tire specific parameter as

Froll = mgcrcos(α), (3.4)

where cr is the coefficient of rolling resistance and α is the road grade. cr lies

within 0.006-0.01 for hdvs [Wong, 2008]. The gravity induced force, modeled as

Fg = mg sin(α), (3.5)

can either be a resistance or an assistance to the forward motion depending on the road grade. If the road grade is negative, the gravity induced force contributes to the propulsive force of the vehicle.

The most important internal forces related to the longitudinal motion of a vehicle are the braking and driving forces acting on the wheels, Fw. The braking force is

generally unknown in a standard hdv, but the driving force of the own vehicle can usually be derived from models of the driveline and measurements of the engine torque. However, since measuring the engine torque of the target vehicle is not possible in practice, both of these forces are generally unknown in this project. Therefore, modeling of the internal forces Fwfor the target vehicle is not

necessary. However, as presented in Chapter 4, it is possible to get around this problem by finding driving situations where Fwcan be assumed to be either zero,

or at its maximum positive value.

If the engine torque was known, a common expression giving the driving force of an hdv in steady state is

Fpropulsion= (Mm−Mf r:m)

igifηgηf

rw

, (3.6)

where Mm is the output torque from the engine, Mf r:m is the engine friction

torque, ig and if are the ratios of the transmission and the final gear, ηg and ηf

are the efficiencies of the transmission and the final gear, respectively, and rwis

the wheel radius. This equation will be used for the own vehicle in Chapter 7 [Eriksson and Nielsen, 2012].

By combining equations (3.2), (3.3), (3.4) and (3.5), the complete vehicle model, describing the longitudinal dynamics of an hdv used in this project, becomes

Fw−

1

2ρairCdAv

2_−mgc

rcos(α) − mg sin(α) = ma. (3.7)

3.2

Estimation theory

In order to calculate valid estimates based on a physical model and measured sig-nals under the influence of noise, many different methods have been developed. In this section, two methods frequently used in on-line estimation problems are briefly presented.

12 3 Modeling and estimation theory

3.2.1

Kalman filter

The Kalman Filter (kf) is a common computational tool to handle real-time es-timation problems. It was developed by Rudolf Kalman in 1960 and has be-come popular due to its recursive nature that suits real-time implementations well [Gustafsson et al., 2010]. The kf estimates the states in a linear state space model and a full derivation can be found in Gustafsson et al. [2010] or Gustafsson [2012].

A state space model without any known control input can be written as

xk = Axk−1+ vk, (3.8a)

yk = Cxk+ ek, (3.8b)

with

Cov(vk) = Qk, Cov(ek) = Rk, (3.8c)

Cov(x0) = P1|0, E(x0) = ˆx1|0, (3.8d)

where vk and ek are the process noise and the measurement noise, respectively,

and x0is the initial value of the states. Both the process noise and the

measure-ment noise are assumed to be Gaussian, which means that the estimates can be assumed to have Gaussian distributions. The kf equations are

Time update ˆ xk+1|k = A ˆxk|k, (3.9a) Pk+1|k = APk|kAT + Qk, (3.9b) Measurement update ˆ xk|k= ˆxk|k−1+ Pk|k−1CT(CPk|k−1CT + Rk) −₁ (yk−C ˆxk|k−1), (3.9c) Pk|k= Pk|k−1−Pk|k−1CT(CPk|k−1CT + Rk) −₁ CPk|k−1. (3.9d)

If x0, vk and ek are Gaussian variables, the kf is the best possible unbiased

es-timator in the sense of minimum variance. If x0, vk and ek have an unknown

distribution, the kf is still the best possible linear filter. In practice, since the noise variance can be hard to know, Qkand Rk become tuning parameters for the

filter and are commonly given constant values. Q decides how much the model is trusted, and the larger Q is, the less the model is trusted. R decides how much the measurements are trusted, and the larger it is, the less the measurements are trusted. It is common to choose constant values for Q and R [Gustafsson et al., 2010].

3.2.2

Recursive least squares

A signal model that is linear in its parameters can be written as

3.2 Estimation theory 13

where yt are the measurements, et is an unknown noise, ϕt is the known noise

free regression vector, and θ contains the parameters to be estimated. The Recur-sive Least Squares (rls) method finds the estimates

ˆ

θN = argmin θ

VN(θ), (3.11)

where VN(θ) is the loss function, in discrete time defined as

VN(θ) = N

X

k=1

λN −k(y(k) − ϕT(k)θ)2. (3.12)

The parameter λ is called the forgetting factor, causing the old measurements to lose their influence on the future estimates. The steps of the recursion in discrete time are ˆ θk= ˆθk−1+ Kk(yk−ϕkTθˆk−1), (3.13a) where Kk = Pk−1ϕk λ + ϕ_kTPk−1ϕk , (3.13b) Pk = 1 λ(Pk−1− Pk−1ϕkϕTkPk−1 λ + ϕ_kTPk−1ϕk ). (3.13c)

Equation (3.13) is a recursive algorithm where the number of calculations and the memory requirement do not increase over time, making it suitable for on-line applications. Pk is related to the covariance matrix of θ, and the choice of

its initial value affects how fast the estimates converge. A large value results in fast convergence. For a full derivation of the rls algorithm see, for example, Gustafsson et al. [2010].

4

Mass estimation

As explained in Chapter 3, the internal forces of the target vehicle are generally unknown. Therefore, it is impossible to perform any mass estimations for the target vehicle in the general case. However, if the internal forces were known to be zero in a specific driving situation, the only unknown parameter would be the mass and could thereby easily be estimated. Intuitively, the internal forces would be approximately zero in a steep enough downhill. In Slettengren [2006], an ap-proach based on predefined limits for the target acceleration and road grade is used to isolate the situations of no internal forces. This idea works as a comple-ment to the more measurecomple-ment-based method presented below.

4.1

Detection of no internal forces

Since the intuitive idea that a vehicle is subject to no internal forces during a steep enough downhill is only an assumption, the target vehicle might very well be applying either gas or brake for different reasons. For example, this depends on how fast the target vehicle wants to drive, or if it has to slow down because of a slower vehicle driving in front of it. Furthermore, many of the hdvs have an upper allowed speed limit at which a braking force might be applied. Because of these factors, information about how the target vehicle actually is driving is useful as a complement to how it should be driving given the road grade circum-stances.

By starting from the complete vehicle model (3.7), and rearranging the terms with known signals on the right-hand side, and the terms with unknown

16 4 Mass estimation

ables on the left-hand side, one gets

Fw mv2 − ρairCdA 2m = a + g sin(α) + gcrcos(α) v2 | {z } := κ . (4.1)

According to (4.1) it is clear that when Fw = 0, the only term remaining on the

left-hand side is −ρairCdA

2m . Even though this term is unknown, it is clear that it

is constant and negative since all of its individual parameters are constant and positive. Therefore, the signals on the right-hand side, denoted by κ, will reach the same constant value, −ρairCdA

2m , whenever Fw = 0. This means that if time

intervals of this value could be identified, situations of no internal forces could be detected as well.

To find the intervals where κ is constant, the time derivative of κ is calculated by the use of a kf. By introducing the states x1 = κ, x2 = ˙κ, and using a constant

velocity motion model to describe the dynamics, a state space model of the system can be written as xk = Axk−1+ vk, (4.2a) yk = Cxk+ ek, (4.2b) where A ="1 T 0 1 #

, T is the sample time of the system, C =h1 0i, and yk = κ at

time instance k. The constant velocity motion model is used since κ is assumed to be approximately constant during the intervals of interest. By following the kf equations stated in Section 3.2.1, the states and thereby the time derivative of κ, can be estimated. Q and R in the kf equations are chosen based on a compromise between filter speed and noise sensitivity, to

Q ="10 −₈ 0 0 10−₄ # , (4.3)

and R = 1, respectively. The initial variance P0is set to

P0="0.1_{0 0.1}0 # , (4.4) and x0is set to x0 = "0 0 # . (4.5)

Several different sets of logged data from different hdvs were used to find the values for Q and R. The time derivative of κ will be approximately zero when κ is constant, hence when x1< 0 and x2≈0 there is a possibility that Fw= 0.

Further analysis of (4.1) reveals that it is not guaranteed that Fw= 0 just because

κ is constant and negative for a period of time. In fact, as long as Fw mv2 <

ρairCdA

2m , κ

4.1 Detection of no internal forces 17

torque during constant speed, will also result in a constant negative value of κ. Some of the unwanted situations with a small amount of gas, are avoided by using a condition on the road grade which must be fulfilled in order to enable the detection of no internal forces algorithm. The steeper the road grade is, the more probable it is that Fw = 0, up to a certain limit. After that limit is it likely

that a braking force is applied. Therefore a limit for the acceleration is used to rule out situations of distinct braking. The road grade limit is set to -0.9%, where steeper downhill is allowed. The acceleration limit is set to -0.35 m/s2_,

where higher acceleration is allowed. These values are a satisfactory compromise between avoiding misclassification, and missing correct situations, in a similar manner as in Slettengren [2006].

Further on, some more of these unwanted situations can be avoided by only look-ing at possible values that κ could reach durlook-ing situations of no internal forces. For a light hdv, weighing for example 15 tons, with a large front area of 12m2, and suboptimal aerodynamic properties with cr = 1.1, κ would reach

approxi-mately −5 · 10−4. For a heavy hdv of 60 tons, with a small front area of 9m2, and a small rolling resistance with cr = 0.006, κ would reach approximately −5 · 10

−₅

. It is concluded that κ most likely will be in the interval −5 · 10−4< κ < −5 · 10−5, and by only looking at this interval, some misclassification should be avoided. However, misclassification could still occur during, for example, a period with a small enough driving force. In order to investigate the possibility to avoid that, measured values of κ have been compared to the measured internal forces from the same vehicle. This has been done for two different vehicles with different masses. The first one has a mass of 15000 kg according to the vehicle’s own mass estimation, and the second one has a mass of 57000 kg according to its mass estimation. In Figures 4.1 and 4.2 the comparison is displayed. From these figures it is clear that it is possible to visually find the situations where Fw = 0.

In the top plot, the internal forces can be seen, and during the situations where the engine torque and the braking force are at zero percent, κ, as seen in the bottom plot, recurrently reaches approximately the same negative value, marked with the dashed line. For instance, after approximately 300 seconds the internal forces reach zero percent in the top plot, and κ reaches the recurrent negative value.

In order to automatically find the correct situations of no internal forces, or in-tervals where κ reaches the same recurrent negative value, an algorithm is used that follows the following steps. First, the mean value of κ is calculated during an interval which fulfils the following conditions.

• The road grade at the target vehicle is below -0.9% indicating a downhill. • The acceleration of the target vehicle is above -0.35 m/s2ruling out distinct

braking.

• κ is constant and within the interval −5 · 10−4< κ < −5 · 10−5.

18 4 Mass estimation 0 100 200 300 400 500 600 700 800 −100 −50 0 50 100

Percent of internal forces at use over time

Time [s]

Percentage applied Engine torque

Brakes 0 100 200 300 400 500 600 700 800 −1 −0.5 0 0.5 1

x 10−3 The signal κ over time

Time [s]

Value of

κ

κ

Recurrent constant negative value

Figure 4.1:Plot showing the percentage of the internal forces used (above), as well as the signal κ and the returning negative constant value marked as the dashed line (below), for a vehicle with a mass of 15000 kg.

not hold, this new value is compared to the median of the old stored values of

κ from previous situations. Since some old values could either be values from

situations of braking or situations of small enough engine torque, the median of the previous values is assumed not to be affected by these misclassified situations. If the comparison is considered to be close enough, it is assumed that Fw was

really zero, and the new value is stored with the old values. Otherwise the new value is just stored for later comparison, and it is assumed that Fwwas not zero.

The interaction between the detection of no internal forces and the mass esti-mation can be seen in Figure 4.3. As soon as κ is constant, negative and the previously specified conditions are fulfilled, the mass estimation starts, but the mass estimate is only saved if the assumption Fw = 0 was considered valid at the

end of the situation. The situation is considered to have ended when any of the conditions on κ, ˙κ, the road grade α or the acceleration a are not fulfilled any

4.2 rls_{mass estimation} 19 0 100 200 300 400 500 600 700 800 −100 −50 0 50 100

Percent of internal forces at use over time

Time [s]

Percentage applied Engine torque

Brakes 0 100 200 300 400 500 600 700 800 −1 −0.5 0 0.5 1

x 10−3 The signal κ over time

Time [s]

Value of

κ

κ

Recurrent constant negative value

Figure 4.2:Plot showing the percentage of the internal forces used (above), as well as the signal κ and the returning negative constant value marked as the dashed line (below), for a vehicle with a mass of 57000 kg.

more.

4.2

RLS

mass estimation

The mass estimation is performed with the rls method which means that suit-able physical varisuit-ables and known signals need to be represented by the linear model y = ϕTθ according to Section 3.2.2. The mass estimation is assumed to be

performed at times when Fw = 0. Starting from (3.7), by dividing both sides of

the equation by mass, m, and assuming Fw= 0 one gets

a + g sin(α) + gcrcos(α) = −

1

2ρairCdAv

21

20 4 Mass estimation

Figure 4.3: State flow diagram for the interaction between the automatic detection of the situation where Fw = 0 and the mass estimation.

In order to avoid noise in ϕ, and thereby the errors in variables problem, the speed is removed from the right-hand side, resulting in a linear model suitable for rls: a + g sin(α) + gcrcos(α) v2 | {z } y = −1 2ρairCdA | {z } ϕT 1 m. |{z} θ (4.7)

Since the mass is constant, there is no need to forget old values during the estima-tion, hence λ in (3.13) is set to one. The fact that v2is a part of y in (4.7) means that if v is noisy, the noise is no longer additive which could affect the uncertainty and the standard deviation of the estimates. However, the signal-to-noise ratio was found to be high for v, which suggests that the impact of its noise is small. Additionally, the estimation error due to this problem is not likely to have a sig-nificant effect on the total estimation error, which is assumed to depend mostly on how well the detection of no internal forces works.

The nominal values used for mass estimation are displayed in Table 4.1. Two values of the rolling resistance coefficient are used, depending on the last mass estimation. Even though the model for the rolling resistance in (3.4), states that the rolling resistance is proportional to the vehicle mass, a common perception within the vehicle industry is that it in fact depends on the number of axles

[Sand-4.2 rls_{mass estimation} 21

berg, 2001]. Increased number of axles seems to increase the rolling resistance [Leduc, 2009]. This modeling issue will not be further investigated in this thesis, but in order not to lose generality, two different values of cr are used depending

on the last mass estimation. If the mass is estimated to be above 31 tons, it is as-sumed that the target has a trailer, and thus extra axles. The maximum allowed weight in Sweden for an hdv without a trailer is 31 tons [Transportstyrelsen, 2014].

Table 4.1:Nominal values used for the mass estimation.

Parameters Symbol Value Unit

Aerodynamic drag coefficient Cd 0.7

-Vehicle front area A 10 m2

Air density ρair 1.125 kg m−3

Rolling resistance coefficient cr 0.007/0.009

-Gravitational constant g 9.82 m s−2

The rls filter follows the recursive algorithm presented in (3.13) initialized with

5

Maximum engine power estimation

Much like during the mass estimation where it is important to isolate suitable situations, it is important to isolate situations suitable for maximum power esti-mation, since the maximum power is only applied on occasion. These occasions should occur rather frequently when driving on a highway with varying road grade. Intuitively, the engine power would be at its maximum value in a steep enough uphill. However, the uphill performance of hdvs varies gravely depend-ing on both the mass and the engine power. Because of this, knowdepend-ing in advance what a steep enough uphill for a specific target vehicle is, is usually very difficult. As well as in the case of finding situations of no internal forces, situations of max-imum engine power are found through a measurement based method presented below.

5.1

Detection of maximum engine power

hdv_{s drive at their maximum engine power much more frequently than} passen-ger cars. The heavier the truck is, the more often it needs to apply full power. For a typical heavy duty vehicle with a 420 hp engine, weighing 20 tons and driv-ing at 80 km/h, the road grade limit at which positive acceleration is no longer possible, is around 4 percent. Weighing 40 tons, the limit is around 2 percent for the same vehicle [Slettengren, 2006]. This implies that information about how the target vehicle actually is moving is needed also for the detection of the max-imum engine power. With similar reasoning, as in the case of no internal forces, situations of maximum engine power can be found. An expression of the internal forces is obtained by rearranging (3.7) into

24 5 Maximum engine power estimation

Fw= m(a + g sin(α) + gcrcos(α)) +

1

2ρairCdAv

2_{. (5.1)}

If all of the parameters but Fw were known, this expression would produce a

value of Fw and thus a means to identify situations of maximum engine power,

simply by comparing Fw to the previous values of Fw = Fw,max. A condition for

this to work is of course that Fw= Fw,maxactually has occurred before. However,

before the mass is known, (5.1) will not produce any valid data. Instead of wait-ing until the mass has been estimated and then use (5.1) to look for situations of maximum engine power, a nominal value of m in equation (5.1) is used, resulting in

Fw,nominal= mnominal(a + g sin(α) + gcrcos(α)) +

1

2ρairCdAv

2_{. (5.2)}

Even though this expression will not produce any valid values, it will reach its maximum value precisely at the same time as (5.1), when using the true mass. In this way, situations of Fw = Fw,max can be found even before the mass is known,

given that Fw,max indeed has occurred. After that, as soon as the mass has been

estimated, Fw,maxcan be estimated during the right situation.

In order to find an interval where Fw = Fw,max, the time derivative of Fw,nominal

is calculated by the use of a kf. By expanding (4.2) with the two states x3 =

Fw,nominaland x4= ˙Fw,nominal, and setting

A =             1 T 0 0 0 1 0 0 0 0 1 T 0 0 0 1             , (5.3a) C ="1 0 0 0 0 0 1 0 # , (5.3b) and yk= " κ Fw,nominal # , (5.3c)

the intervals where Fw = Fw,maxare assumed to be found when x3 ≥ x3,max and

x4 ≈0, where x3,maxis the maximum recorded value of x3so far. Q and R in the

kf_{equations are extended to}

Q =             10−8 0 0 0 0 10−4 _{0 0} 0 0 10−4 0 0 0 0 10−3             (5.4) and R ="1 0 0 1 # , (5.5)

5.2 Maximum engine power estimation 25

respectively. P0and x0are extended to

P0=             0.1 0 0 0 0 0.1 0 0 0 0 0.1 0 0 0 0 0.1             (5.6) and x0=             0 0 0 0             , (5.7)

which produced a sufficient result. The value in Q for x3 did not need to be as

small as the one for x1, since x3is much larger than x1, which is close to zero, and

therefore more sensitive to noise.

A condition for the suggested detection algorithm to work is that the maximum value of Fwhas been reached at some point, as stated earlier. In order to minimize

the risk that the algorithm misclassifies a situation, the detection of the maximum engine power is only active when the road grade circumstances indicate that pos-itive acceleration might not be possible, i.e. when the road grade has passed a certain limit. This limit is chosen to 0.4%. Furthermore, in this project it is only interesting to know the maximum engine power during highway driving. Since the power generated by the engine depends on Fwand the speed, the maximum

engine power detection is only active when the speed is above 70 km/h.

In Figure 5.1, the interaction between the detection of suitable estimation situa-tions and the maximum engine power estimation can be seen. Starting in the top left state, the detection of the maximum engine power algorithm runs continu-ously when enabled by the road grade and speed limit conditions. The maximum power estimation is begun when the correct state is reached.

5.2

Maximum engine power estimation

The relation between the power P , the force F and the speed v is P = Fv. Hence, in order to estimate the maximum engine power, Pmax, the maximum engine force

needs to be known. From that, a speed dependent value of the maximum engine power can be calculated. Since the speed of interest in this thesis is the speed during highway driving, a fixed speed of 80 km/h is used when calculating Pmax

based on Fw,max. The obtained value will be an approximation of the net

maxi-mum engine power after losses, during highway driving. Since Pmaxhere depends

on the speed as well as Fw,max, it is not guaranteed that Pmaxoccurs at the same

time as Fw,max. However, since only highway driving is of interest in this thesis

where the speed variations are limited, which is assumed here, Pmaxis assumed

to occur at the same time as Fw,max.

26 5 Maximum engine power estimation

Figure 5.1:State flow diagram showing the interaction between the detection of maximum engine power and the maximum power estimation.

during situations when Fw = Fw,max and the mass has already been estimated.

The same nominal values as in the mass estimation, specified in Table 4.1, are used. Re-writing (3.7) into

m(a + g sin(α) + crg cos(α)) +

1 2ρairCdAv 2 | {z } y = 1 |{z} ϕT · Fw,max | {z } θ , (5.8)

a linear model suitable for the rls is obtained, which generates the mean value of

Fw,maxof the situation. From this value, the maximum engine power is calculated

as Pmax =3.680Fw,max.

The rls filter for the maximum engine power estimation follows the recursive algorithm presented in (3.13), initialized with θ0 = 12000 and P0 = 4, which

5.3 Estimation of critical uphill road grade 27

5.3

Estimation of critical uphill road grade

A convenient property to look at is the maximum road grade at which positive acceleration is possible. It depends mainly on the mass and the maximum engine power. Knowledge of this critical road grade will immediately reveal whether an uphill is steep enough to cause the target vehicle to slow down.

One way to find this critical road grade is to constantly store the maximum value of the road grade where the target has nonnegative acceleration. As soon as a steep enough uphill has been passed, while driving at full engine power, this value will be accurate. Another way is to calculate it when the mass and the maximum engine power are known. By rearranging (3.7), setting a to zero, and using the small angle approximation, i.e. sin(α) ≈ α and cos(α) ≈ 1, the critical road grade is found as

αcritical =

Fw,max

mg −

ρairCdAv2

2mg −cr (5.9)

By using both of these methods, a comparison between the two different values of αcritical will not only validate the estimation of αcritical, but also give an idea

6

Result

In this chapter the experimental setup is described and the result is presented.

6.1

Experimental setup

A test drive was performed with two trucks where the first truck, i.e. the target vehicle had a known mass of 21120 kg. The two vehicles drove the part of the path between Södertälje and Nyköping that can be seen in Figure 6.1. The target vehicle was driving in a normal manner, meaning that it was using an adaptive cruise controller. Some of the time it meant following the vehicle in front of it, and when no vehicle was in front of it, a set speed was kept. The road grade can be seen in Figure 6.2. The estimates were both computed on-line in the real time embedded system on the vehicle, and re-simulated on the logged data from the experiment. The results presented here are from the re-simulation.

6.2

Experimental result

The re-simulated result is presented in Figure 6.3. The estimation methods are interrupted and the estimates are reset each time a new target is discovered. This happened, for instance, each time another vehicle overtook the own vehicle and placed itself between the own vehicle and the target vehicle. This can be seen when the estimates return to zero in Figure 6.3. However, all the estimates are of the same known target vehicle. This means that there are six different inter-vals with mass estimates, and three different interinter-vals with maximum power es-timates, as if there was a new target vehicle during each interval. The top plot in Figure 6.3 shows that the mass estimates approximately lie within 20 percent of

30 6 Result

the true mass in five of the six intervals of mass estimates. The second attempt is the most inaccurate, most likely because the estimations are performed at a time where the target vehicle applies some driving force. The fact that there are vari-ations between all the different intervals of estimates, could depend of a number of reasons. There might be some occurrence of driving or braking force, which affects the estimations. Furthermore, external influences, like wind, would also affect the estimates.

The maximum power estimation, displayed in the bottom plot of Figure 6.3, can only be performed after the mass has been estimated, There is only enough time during three of the mass estimation intervals, before the estimates are reset. It can be seen that the maximum power estimation depends on the mass estimation, since the higher the mass estimate is, the higher the maximum power estimate becomes. The true maximum engine power presented in Figure 6.3 is the engine power specified by the manufacturer, and due to different losses, it is not likely that this value is reached during highway driving.

The critical value of the road grade can be seen in Figure 6.4. The estimated value, i.e. calculated from the estimated mass and maximum engine power, can be seen as the dashed line. Both the measured value and the estimated value is set to zero each time a new target is discovered. The result indicates that the last interval of estimates in Figure 6.3 is the most accurate one, since the measured and estimated value of the critical road grade are the most similar. The measured value is constantly updated as soon as the road grade increases and positive ac-celeration is registered. Therefore, the first measured values of the critical road grade are most likely the most accurate ones, since they reveal the highest value of the critical road grade that actually has occurred. Even for the second interval of estimates of the mass and the maximum engine power, which were the most in-accurate, the estimated critical road grade is close to the highest measured value. This could be explained by the fact that since the estimation of the maximum en-gine power is based on the mass estimation, the relation between these could still be accurate, resulting in an accurate value of the estimated critical road grade.

6.2.1

Comparison to results from previous works

The most relevant previous work to this project is the thesis by Slettengren [2006]. The author describes a way to estimate the driving force over mass, described as,

Fw

m −gcr, as well as a lumped airdrag parameter, ρC2mdA, denoted by Cair. The

driv-ing force over mass estimation is done durdriv-ing steep enough uphill. The estima-tion of Cair is performed during steep enough downhill where Fw is assumed to

be zero. He presents a result where the driving force over mass estimations give a mean absolute error of approximately 5%, and the Cair estimation produces a

result with a mean absolute error of 25%. The most accurate way to compare the methods in this project to the result in Slettengren [2006], would be to apply the methods presented in this project on the data used in Slettengren [2006], or vice versa. Unfortunately that data is not available, and an implementation of the method from Slettengren [2006] was not performed due to unknown

imple-6.2 Experimental result 31

Figure 6.1:Drive path during the experiment. Courtesy of Google Maps.

mentation details and lack of time. However, an attempt is made to review the differences of the performances from the two different projects.

A comparison between the maximum engine power estimation in this thesis and the drive force over mass estimation from Slettengren [2006] is rather difficult to perform, mainly because the actual maximum engine power for the target ve-hicle was not known during the experiments in this thesis. However, the value

32 6 Result 0 500 1000 1500 2000 2500 3000 −6 −4 −2 0 2 4 6 Time [s] Road slope [%]

Figure 6.2:Road grade variation of the experiment.

of Fw

m −gcr for the target vehicle in this thesis can be calculated. Based on the

three intervals with estimates of the mass and the maximum engine power in Figure 6.3, the value of Fw

m −gcr is calculated to 0.46, 0.64 and 0.68 respectively.

This value varies considerably more than the value in Slettengren [2006], which indicates that the mean absolute estimation error is greater that 5%. A possible explanation to this is that almost all logged signals in Slettengren [2006] were low-pass filtered off-line in matlab before being used during the simulations, whereas all the steps of the signal processing and estimations in this thesis could be done on-line in the real time embedded system of an hdv.

The result of the Cair estimation is roughly the same as the result of the mass

esti-mation in this thesis. The mean absolute error of the mass estimates in this thesis is approximately 23%. By estimating Cair instead of the mass, Slettengren [2006]

avoids using nominal values for ρ, Cdand A. Hence some uncertainty is avoided.

This should lead to a more accurate estimate. Since the behaviour of a vehicle without any internal forces is governed by all the parameters in Cair, it might be

a better idea to estimate Cair directly instead of the mass, at least if the purpose

of the estimation is to predict how the target vehicle is going to behave. Given the fact that the signals are low-pass filtered off-line, and that there are less

un-6.2 Experimental result 33

Figure 6.3:Estimation result from simulation using logged data from a drive following a target with known mass and maximum engine power. Above are six intervals with mass estimates compared to the true mass. Below are three intervals with maximum power estimates compared to the value specified by the manufacturer.

known parameters when estimating Cairin Slettengren [2006], one would expect

that the result would be more accurate than in this thesis. One possible reason as to why that is not the case might be that the detection of no internal forces works better in this thesis than in Slettengren [2006]. In Slettengren [2006] situations of no internal forces are identified when the road grade is below -1.3% and the target vehicle accelerates more than -0.02m/s2_{for more than 2 seconds. In this}

project situations of no internal forces are found by studying the longitudinal behaviour of the target vehicle in more detail. The only predefined conditions are a small downhill and no distinct braking. Otherwise the method of finding situations of no internal forces sets dynamic limits that are adjusted to the cur-rent target vehicle. These dynamic limits are formed by the comparison between

34 6 Result 0 500 1000 1500 2000 2500 3000 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Time [s] Critical value of α Measured value Estimated value

Figure 6.4:The measured critical value of α compared to the estimated crit-ical value of the road grade, α. There are only three sets of estimated critcrit-ical road grade, since there were only three intervals with both mass and maxi-mum engine power estimates, as can be seen in Figure 6.3.

older values of κ as explained in Chapter 4. This way, situations of no internal forces can be found more often, and misclassification can more easily be avoided.

7

Validation and sensitivity analysis

Since the experimental results earlier still leave some uncertainties regarding the maximum engine power estimations and whether the estimations are performed during the right driving situations, this chapter presents a validation of the esti-mation methods as well as a sensitivity analysis.

7.1

Validation

The algorithms were tested on logged data of the own vehicle, for three different vehicles. That is, the mass and maximum engine power were estimated for the own vehicle using the signals available for the target vehicle. In this way the re-sult could be compared to the true parameters of the mass and maximum engine power available via can, and the detection of no and maximum internal force could be validated against the signals for braking and engine torque. The three trucks are denoted A, B and C, and some specifications are displayed in Table 7.1. The net Pmaxfrom can is calculated based on the engine torque and a model of

the driveline specified in (3.6), which means that this is the net value after losses. Vehicle True mass from can Engine type NetPmaxfrom can

A 42 tons DC16 102/580 hp 490 hp

B 15 tons DC13 116/370 hp 270 hp

C 57 tons DC16 102/580 hp 560 hp

Table 7.1:Specifications for the three trucks used for validation.

Figures 7.1, 7.2 and 7.3 present three different plots of the estimations performed during approximately 20 minutes of driving for trucks A, B and C, respectively.

36 7 Validation and sensitivity analysis

The top plot shows the estimated mass compared to the true mass from can. The second plot shows the estimated maximum engine power compared to the true value of the maximum engine power from can, when driving at 80 km/h. The third plot shows the estimated occurrences of no internal force and the maximum driving force, compared to the internal forces available from can. The bottom plot shows a comparison between the measured and estimated value of the criti-cal uphill road grade.

The estimation of the driving situation for all of the vehicles produces a satis-factory result. However, in some cases when a situation of no internal forces is detected, a small part of the situation includes some driving force. For vehicles A and B, the first situations of maximum engine power are slightly misclassified, but that is to be expected since the estimator really finds the maximum engine power situations that have occurred so far. The mass estimation eventually comes within approximately 20 percent of the true mass for all vehicles.

The most accurate estimation is performed on vehicle B. An indication that these estimates are accurate is the fact that the measured and estimated critical uphill road grade are very similar, which can be seen in the bottom plot of Figure 7.2.

7.2

Sensitivity analysis

Since the nominal values of the parameters cr, Cd and A used during the

esti-mations may differ from the true values for the target vehicle, there is a risk of errors in the estimates. In order to investigate how sensitive the estimates are to deviations in these parameters, the mass estimation is performed on the same set of data from vehicle B with two additional sets of values of the parameters cr, Cd

and A. The result can be seen in Figure 7.4 where the top plot shows the influence of variations in CdA and the bottom plot shows the influence of variations in cr.

Since the estimation of the maximum engine power is based on the estimation of the mass, these errors affect the estimation of the maximum engine power as well. The plots show that the mass estimation is very sensitive to variations in these pa-rameters. However, in an application that is used to predict how a target vehicle is going to move, a faulty mass obtained because of a faulty value of cr, Cdor A,

can still produce a sufficiently good prediction of the future behaviour. The mass estimate could be interpreted as the best fit to the measured data, given certain values of the parameters cr, Cd and A. Hence, even if the mass estimate itself

deviates from the true mass, combined with cr, Cdand A an accurate prediction

of the target vehicle behaviour might still be found.

The values used for the sensitivity analysis are the minimum and maximum com-mon values for an hdv specified in Chapter 3 and are displayed again in Ta-ble 7.2.

7.2 Sensitivity analysis 37

Table 7.2:Different values of c_r, Cdand A used in the sensitivity analysis.

Parameter Symbol Minimum value Maximum value

Aerodynamic drag coefficient Cd 0.64 1.1

Vehicle front area A 9m2 12m2

38 7 Validation and sensitivity analysis 0 500 1000 1500 0 2 4 6x 10 4 Time [s] Mass [kg]

Mass estimation for the own vehicle

True mass Estimated mass 0 500 1000 1500 0 200 400 600 Time [s] Power [Hp]

Maximum engine power estimation for the own vehicle

True maximum engine power Estimated maximum engine power

0 500 1000 1500 −100 −50 0 50 100

Percent of maximum torque

and braking in use

Torque and brakes in use for the own vehicle

Engine torque Brakes Estimated F w = 0/Fw,max 0 500 1000 1500 0 2 4 6 Critical value of α Time [s] α Measured value Estimated value

Figure 7.1: Validation of the mass and the maximum engine power estima-tions for truck A. The top plot shows the estimated mass compared to the true mass. The second plot shows the estimated maximum engine power compared to the true maximum engine power. The third plot shows the in-ternal forces compared to the estimated situations of no inin-ternal forces and maximum engine power. The bottom plot shows the estimated and mea-sured critical value of the road grade.

7.2 Sensitivity analysis 39 0 200 400 600 800 1000 1200 0 0.5 1 1.5 2x 10 4 Time [s] Mass [kg]

Mass estimation for the own vehicle

True mass Estimated mass 0 200 400 600 800 1000 1200 0 100 200 300 Time [s] Power [Hp]

Maximum engine power estimation for the own vehicle

True maximum engine power Estimated maximum engine power

0 200 400 600 800 1000 1200 −100 −50 0 50 100

Percent of maximum torque

and braking in use

Torque and brakes in use for the own vehicle

Engine torque Brakes Estimated F w = 0/Fw,max 0 200 400 600 800 1000 1200 0 2 4 6 Critical value of α Time [s] α Measured value Estimated value

Figure 7.2:Validation of the mass and the maximum engine power estima-tions for truck B. The top plot shows the estimated mass compared to the true mass. The second plot shows the estimated maximum engine power compared to the true maximum engine power. The third plot shows the in-ternal forces compared to the estimated situations of no inin-ternal forces and maximum engine power. The bottom plot shows the estimated and mea-sured critical value of the road grade.

40 7 Validation and sensitivity analysis 0 200 400 600 800 1000 1200 0 2 4 6x 10 4 Time [s] Mass [kg]

Mass estimation for the own vehicle

True mass Estimated mass 0 200 400 600 800 1000 1200 0 200 400 600 Time [s] Power [Hp]

Maximum engine power estimation for the own vehicle

True maximum engine power Estimated maximum engine power

0 200 400 600 800 1000 1200 −100 −50 0 50 100

Percent of maximum torque

and braking in use

Torque and brakes in use for the own vehicle

Engine torque Brakes Estimated F w = 0/Fw,max 0 200 400 600 800 1000 1200 0 1 2 3 Critical value of α Time [s] α Measured value Estimated value

Figure 7.3: Validation of the mass and the maximum engine power estima-tions for truck C. The top plot shows the estimated mass compared to the true mass. The second plot shows the estimated maximum engine power compared to the true maximum engine power. The third plot shows the in-ternal forces compared to the estimated situations of no inin-ternal forces and maximum engine power. The bottom plot shows the estimated and mea-sured critical value of the road grade.

7.2 Sensitivity analysis 41 0 200 400 600 800 1000 1200 0 1 2 3 4x 10 4 Time [s] Estimated mass [kg] Variations in C dA 0 200 400 600 800 1000 1200 0 0.5 1 1.5 2x 10 4 Time [s] Estimated mass [kg] Variations in c r

Figure 7.4:Sensitivity analysis on variations in the parameters cr, Cdand A.

The top plot shows the mass estimation for vehicle B with changes in CdA.

The bottom plot shows the mass estimation for vehicle B with deviations in

cr. The green full curve in the two plots are from using the nominal values

8

Conclusions and future work

In this chapter the conclusions drawn from the results are presented, and some alternatives for future work are suggested.

8.1

Conclusions

Previously, different methods of mass estimation for hdvs have been thoroughly investigated and several methods have been implemented and presented in nu-merous scientific reports. However, the estimations can only be as accurate as the underlying physical model of the vehicle system allows. During the simula-tions in this project, there have been several uncertainties concerning the vehicle model, since very few parameters are known. Several assumptions have been made, for example, regarding the aerodynamic properties and the rolling resis-tance properties of the target vehicle. Additionally, since no measurement of the target engine torque has been available, the internal forces have usually been un-known, except at times when situations of no internal forces or maximum engine power have been detected.

It has been shown in a sensitivity analysis that the mass estimation is rather sen-sitive to variations in the parameters Cd, A and cr, and that the accuracy of the

mass and maximum engine power estimations depends completely on how well the classification of the driving situation works. In particular, the mass estima-tion is very sensitive to misclassified situaestima-tions of no internal forces, especially situations which partly or completely include a small engine torque. These mis-classified situations can cause the mass to be over-estimated.

The estimator suffers a bit from the fact that only a few situations are suitable for estimations. There is no guarantee that the first mass estimation has been