Identifying customer usage profiles of two-wheeled vehicles

two-wheeled vehicles

vorgelegt von M.Sc. Christian Gorges geb. in Potsdam

von der Fakultät V – Verkehrs- und Maschinensysteme der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Ingenieurwissenschaften – Dr.-Ing. –

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr.-Ing. Steffen Müller Gutachter: Prof. Dr.-Ing. Robert Liebich Gutachter: Prof. Dr.-Ing. Dieter Schramm

Tag der wissenschaftlichen Aussprache: 19.11.2018

This research has been funded by BMW’s PhD ProMotion programme. This support is gratefully acknowledged.

First, I would like to thank Dr. Kemal Öztürk, expert in durability and load analysis at BMW Motorrad, Germany, who supervised this thesis. Thank you for the great support, the many constructive and fruitful discussions, keeping my back free from day-to-day business, accepting me as an equally valued employee, the unconditional trust with the direction of my project, and your personal engagement for making this research high quality.

A further thank you belongs to Prof. Dr. Robert Liebich at the Department of Engineering Design and Product Reliability at the Institute of Technology Berlin, Germany. Thank you for giving me the possibility of an industry-sponsored PhD programme and the courage for the first cumulative PhD thesis at your chair. Your knowledgeable and useful hints and comments supported me in quickly publishing the first results at relevant journals.

Additionally, I would like to thank Prof. Dr. Dieter Schramm, Head of the De-partment Chair Mechatronics and Head of the DeDe-partment Mechanical Engineering at the University of Duisburg-Essen, Germany, for reviewing this thesis and giving useful comments for improving the discussion chapter.

Finally, I would also like to thank my family and my friends for their great support.

Munich, November 2018

This cumulative PhD thesis contains the manuscripts of the following publications:

[1] – C. Gorges, K. Öztürk and R. Liebich. ‘Customer loads of two-wheeled vehicles’. In: Vehicle System Dynamics 55.12 (2017), pp. 1842–1864

[2] – C. Gorges, K. Öztürk and R. Liebich. ‘Road classification for two-wheeled vehicles’. In: Vehicle System Dynamics 56.8 (2018), pp. 1289–1314

[3] – C. Gorges, K. Öztürk and R. Liebich. ‘Impact detection using a machine learning approach and experimental road roughness classification’. In: Mechanical Systems and Signal Processing 117 (2019), pp. 738–756

This cumulative PhD thesis shows the development of methods for identifying cus-tomer usage profiles of two-wheeled vehicles utilising the vehicle’s onboard sensors. It comprises three papers that have been published to relevant journals. At present, regarding the automotive industry, customer usage profiles are mostly unknown in durability engineering and the vehicle development process. The detailed knowledge about this crowd-sourced data would improve vehicle design targets and enable a virtual load acquisition. Therefore, it is desirable to identify customer usage and customer loads for every vehicle. The first paper presents a model-based customer load acquisition system that calculates the occurring wheel forces. Therefore, the current road slope and the vehicle mass are estimated using a Kalman filter. The resulting wheel forces are subsequently counted with the rainflow method. The valid-ation was achieved by the comparison of measurements with wheel-load transducers. The second publication presents a three-part road classification system: first, a curve estimator was developed for identifying and classifying road curves; second, the road slope was utilised for counting the hilliness of a given road; and third, a modular road profile estimator was developed for classifying the road roughness according to ISO 8608. The approach uses the vehicle’s transfer functions to estimate the road excitation from the resultant vehicle motions. The third publication experimentally validates the road roughness classification method by comparing the results to laser-scanned road profiles. The comparison shows that even rough roads are detected correctly within a short time span. In addition, an impact detection strategy was developed using a supervised machine learning approach. A study of the six most popular classification algorithms was achieved for detecting mild and severe special events. The combination of the road roughness classification method and the impact detection strategy enables a holistic field-data acquisition of customer usage profiles. The methods presented are discussed in the context of the digital transformation and the increasing value of data.

Die vorliegende kumulative Dissertation zeigt die Entwicklung von Methoden zur Identifizierung der Kundennutzungsprofile von Motorrädern unter Nutzung der vor-handenen Onboard-Signale der serienmäßig verbauten Sensorik. Die Arbeit besteht aus drei Veröffentlichungen, welche in einschlägigen Fachzeitschriften veröffentlicht wurden. In der Betriebsfestigkeit und im Produktentstehungsprozess sind Kunden-nutzungsprofile weitgehend unbekannt bzw. nicht aufgezeichnet. Eine detaillierte Be-trachtung dieser Felddaten würde die Lastannahmen validieren und die Fahrzeugent-wicklung verbessern. Es ist daher erstrebenswert, Kundennutzungsprofile von allen Fahrzeugen zu erfassen und für die Entwicklung einzusetzen. Die erste Publikation stellt eine modellbasierte Radkraftberechnung vor. Dafür wurde die aktuelle Steigung der Fahrbahn und die Gesamtmasse des Fahrzeugs mit Hilfe eines Kalman-Filters geschätzt. Die berechneten Radkräfte werden mittels der Rainflow-Zählung klassiert. Eine Validierung wurde mit Hilfe von Radmessnaben durchgeführt. Die zweite Ver-öffentlichung beschreibt eine dreiteilige Streckenprofil-Klassierung. Zuerst wurde ein Klassierungsverfahren für die Kurvigkeit einer Strecke entwickelt. Anschließend wur-de die Steigung wur-der Fahrbahn zur Klassierung wur-der Hügeligkeit verwenwur-det. Abschlie-ßend wurde ein modulares System zur Klassierung der Streckenrauheit nach ISO 8608 entwickelt. Die vorgestellte Methode verwendet die Übertragungsfunktionen des Fahrzeugs, um mit Hilfe der resultierenden Bewegungen auf die Unebenheiten der Strecke zu schließen. Die dritte Publikation zeigt die experimentelle Validierung der Klassierung der Streckenrauheit durch den Vergleich mit ausgesuchten, laser-vermessenen Streckenprofilen. Zusätzlich wurde ein Machine Learning Ansatz ver-wendet, um milde und schädliche Sonderereignisse zu detektieren. Die Kombination aus Rauheitsklassierung und Detektion von Sonderereignissen, wie z.B. Hindernis-überfahrt, ermöglicht eine ganzheitliche Erfassung von Kundennutzungsprofilen. Die vorgestellten Methoden wurden abschließend in den Kontext der digitalen Transfor-mation und der steigenden Bedeutung von Daten gesetzt.

1 Introduction 1

1.1 Durability in vehicle engineering . . . 1

1.2 The need for customer usage profiles . . . 3

1.3 Approach and experimental set-up . . . 6

1.4 Vehicle dynamics . . . 9

1.5 A brief literature survey . . . 11

1.6 Overview of published papers . . . 13

2 Customer loads of two-wheeled vehicles 15 2.1 Introduction . . . 15

2.2 Experimental set-up and data analysis . . . 18

2.3 Methods . . . 20

2.4 Validation . . . 36

2.5 Summary and Conclusion . . . 42

References . . . 44

3 Road classification for two-wheeled vehicles 47 3.1 Introduction . . . 47

3.2 Experimental set-up . . . 49

3.3 Road curve estimator. . . 50

3.4 Road slope classification . . . 53

3.5 Road profile estimator . . . 54

3.6 Results and Validation . . . 70

3.7 Summary and Conclusion . . . 76

References . . . 78

4 Impact detection using a machine learning approach and experimental road roughness classification 83 4.1 Introduction . . . 84

4.2 Longitudinal road profiles . . . 89

4.3 Measurement campaign . . . 91

4.5 Impact detection . . . 103

4.6 Results and Discussion . . . 106

4.7 Conclusion. . . 114

References . . . 116

5 Discussion 123 5.1 Summary of the developed methods . . . 123

5.2 Implementation into the vehicle development process . . . 126

5.3 Statistical considerations . . . 131

5.4 Application to four-wheeled vehicles . . . 135

5.5 Data as a resource . . . 137 5.6 Outlook . . . 138 Bibliography 143 A Onboard signals 147 B Vehicle dynamics 151 C Kalman filter 157

1.1 Vehicle development process. . . 2

1.2 Classification of customer loads. . . 3

1.3 Approach for the online identification of customer usage profiles. . . 6

1.4 Test motorcycle of type BMW R1200GS.. . . 8

1.5 2D data-logging device and GPS-module. . . 8

2.1 Distribution of customer loads, survey sampling, and structural strength. 17 2.2 Test motorcycle with the global reference coordinate system.. . . 18

2.3 Amplitude spectrum of vertical wheel forces. . . 19

2.4 Road slope estimation physics. . . 21

2.5 Model of the driveline dynamics. . . 24

2.6 External forces acting on the motorcycle.. . . 26

2.7 Motorcycle model with three rigid bodies. . . 31

2.8 Flow chart of the customer load estimation model. . . 35

2.9 Validation of the road slope estimator at the proving ground. . . 37

2.10 Validation of the road slope estimator at the mountain track. . . 37

2.11 Validation of the mass estimator. . . 38

2.12 Validation of the longitudinal wheel forces.. . . 39

2.13 Validation of the resultant wheel forces in the Y -Z-plane. . . 41

2.14 Detailed extract of the resultant wheel forces. . . 41

2.15 Rainflow matrices of the resultant rear-wheel forces in the Y -Z-plane. 42 3.1 Road curve estimation physics. . . 52

3.2 Definition of longitudinal road profiles. . . 56

3.3 PSD and straight line fit of an artificial road profile according to ISO 8608. . . 58

3.4 Pseudo random test track comprising road classes A–H and a detailed extract of class C.. . . 60

3.5 Full-vehicle model with four DOFs. . . 61

3.6 Bodeplot of transfer functions for v = 15 m s−1. . . 65

3.7 Flow chart of the road profile estimation algorithm. . . 67

3.9 Results of the road curve estimator. . . 70

3.10 Properties of road curve No. 7. . . 71

3.11 Results of the road curviness classification.. . . 72

3.12 Results of the road slope classification. . . 73

3.13 Validation of the road profile estimator. . . 75

4.1 Classification of customer loads. . . 85

4.2 Test tracks for the road roughness classification.. . . 94

4.3 Road profile and histogram of test track No. 4. . . 95

4.4 Smoothed PSDs of selected test tracks. . . 96

4.5 Road obstacles. . . 97

4.6 Derivation of reduced stiffness and damping coefficients. . . 100

4.7 Lower and upper bound of spatial frequency n depending on the ve-locity v. . . 102

4.8 Schematic view of an impact. . . 103

4.9 Onboard signals during kerb crossing. . . 104

4.10 Scatter plot of the training set. . . 105

4.11 Results of the road roughness classification for test tracks No. 1–6. . 107

4.12 Results of the road roughness classification for test tracks No. 7–9. . 108

4.13 Decision surfaces for different classifiers. . . 111

4.14 Binary decision tree. . . 113

4.15 Flowchart of the impact detection strategy. . . 116

5.1 Information value loop.. . . 127

5.2 Durability test rig for motorcycles. . . 130

5.3 Annual mileage of a population of vehicles. . . 131

5.4 Median air temperature of different regions. . . 133

5.5 Statistical treatment of distributed variables. . . 134

5.6 Statistical derivation of personas. . . 139

5.7 Three components of a virtual load acquisition. . . 140

A.1 Block diagrams and signal flow of developed methods. . . 148

B.1 Quarter of Vehicle (QoV). . . 152

1.1 Features of customer usage profiles. . . 5

2.1 Required onboard signals for the wheel force calculation. . . 32

2.2 Pseudo damage ratio.. . . 42

3.1 Properties of the road classes according to ISO 8608 and Sayers and Karamihas. . . 60

3.2 Full-vehicle model properties. . . 63

3.3 Octave bands and geometric mean values for road classification. . . . 68

3.4 Properties of the classified road curves. . . 71

3.5 Confusion matrix of the road profile estimator. . . 76

4.1 Properties of test tracks. . . 93

4.2 Properties of measured special events. . . 98

4.3 Results of the road roughness classification. . . 107

4.4 Properties of classification methods. . . 110

4.5 Confusion matrix of binary decision tree. . . 113

Abbreviation Description

2D Debus & Diebold Meßsysteme GmbH

ABS Anti-lock Braking System

ACEM European Association of Motorcycle Manufacturers ANFIS Adaptive Neuro-Fuzzy Inference System

ANN Artificial Neuronal Network

ARAS Advanced Rider Assistance Systems

ASTM American Society for Testing and Materials

BMW Bayerische Motoren Werke

CAN Controller Area Network

CBM Condition-Based Monitoring

CE Consumer Electronics

CMC Connected Motorcycle Consortium

COG Centre of Gravity

CPU Central Processing Unit

CRG Curved Regular Grid

DOF Degree of Freedom

DTC Dynamic Traction Control

eCall Emergency Call

ECU Electronic Control Unit

EKF Extended Kalman Filter

EU European Union

FFT Fast Fourier Transform

FIR Finite Impulse Response

GPS Global Positioning System

HoV Half of Vehicle

ICA Independent Component Analysis IIR Infinite Impulse Response

IMU Inertial Measurement Unit

IOT Internet of Things

IRI International Roughness Index

ISO International Organization for Standardization

KF Kalman Filter

LTI Linear Time Invariant

MIRA Motor Industry Research Association

ML Machine Learning

OBIS On Bike Information System ODE Ordinary Differential Equation

QoV Quarter of Vehicle

PPV Positive Predictive Value

PSD Power Spectral Density

RLS Recursive Least Square

SIM Subscriber Identity Module

SVM Support Vector Machine

TPR True Positive Rate

UKF Unscented Kalman Filter

VMC Virtual Measurement Campaign

1.1 Durability in vehicle engineering

Durability is an essential discipline in engineering. Johannesson and Speckert [4] offered a rather general definition of the term: “Durability is the capacity of an item to survive its intended use for a suitable long period of time”. In order to evaluate the durability of a product, the occurring loads during the product’s life need intense investigation, namely through load analysis. According to Johannesson and Speckert, load analysis in vehicle engineering comprises three steps: First, evaluating and quantifying the customer service loads. Second, deriving design loads for vehicles, sub-systems and components. Third, define verification loads and test procedures for the verification of components, sub-systems and vehicles. Thus, the process of durability engineering coincides with the well known v-model of product development [5], see Figure 1.1. Initially, the product concept must be defined, which comprises the class of vehicle, market segment, target cost, volume, size, weight, wheel base, etc. After the initial concept phase passed, the vehicle engineering process consists mainly of two phases: product design and product validation.

The product requirements must be defined at the beginning of the design pro-cess. Thus, overall targets are defined for the physical properties of the product; for example, performance, durability, safety, acoustics and vibration comfort. In the case of durability, targets, in the form of occurring loads, are usually defined with measurements from predecessors and load assumptions. Subsequently and follow-ing the cascade down, design targets are derived for sub-systems and components; for example, chassis, engine and suspension systems. After the first test parts are produced, strength and durability tests are conducted on test rigs based on load assumptions and simulations. The strength of these components is influenced by the design, the manufacturing process and the material properties.

Integration & Implementation Vehicle Testing

Level of maturity

Le

vel

of

de

ta

il

Design

Validation

Simulation System Testing

Initial Phase

Specs

Scope

Figure 1.1 – Vehicle development process.

cascade up. After the components were validated, sub-systems are evaluated; for ex-ample, on different test rigs. Finally, after all sub-tests passed, the complete vehicle is validated with endurance tests, which simulate a vehicle’s life in a short time period. The test environment for endurance tests is designed close to the previously-defined vehicle requirements and load assumptions; for example, a given mix of different road types is driven with pre-defined velocity ranges. This simplified description of the vehicle engineering process does not include the essential development loops and the influence of virtual product development methods. For similar descriptions of the v-model, see Johannesson and Speckert [4] and Pötter [6].

However, the pre-defined product requirements and load assumptions influence the complete vehicle engineering process, beginning from the product design and ending with the vehicle validation. In the past, measurements from predecessors and load assumptions lead to incrementally improving products. Given that measurements are cost- and time-consuming, and in terms of lightweight design, the product require-ments should be defined as precise as possible to meet the customer requirerequire-ments. At the present, the customer requirements are mostly unknown. A well-defined product requirement will only be optimal when the occurring loads are known in advance; otherwise, the requirements remain as assumptions and are not optimal in sense of

Figure 1.2 – Classification of customer loads.

durability and lightweight design. In this context, the present research addresses the first and last step of the product development, which is, quantifying the requirements and subsequently, testing the vehicle.

1.2 The need for customer usage profiles

The distribution of customer loads is often unknown. As mentioned above, it is standard practice to estimate customer loads with survey sampling and measure-ments with predecessors, where selected test vehicles are equipped with additional measurement devices. It is common to choose customers or even test drivers who are characterised by a forced driving style. Figure 1.2 illustrates the broad probability distribution of customer loads in comparison to the narrower probability distribu-tions of survey sampling, endurance tests and structural strength. Obviously, survey sampling cannot reveal the complete distribution of customer loads. In addition, it is not guaranteed, in which relation the selected drivers are with the distribution of customers, which means more precisely, which quantile the measured loads repres-ent. Moreover, survey sampling is expensive due to the additional equipment costs. Furthermore, the endurance tests at the end of the vehicle development process, cannot be assigned to specific quantiles without a detailed knowledge of the under-lying distribution. These aspects raise the demand of revealing the customer load distribution.

entire distribution of customer loads. Consequently, every customer would have to be evaluated. Second, defining individual load targets and endurance tests for the individual customer quantiles. This is more a statistical problem and differs from manufacturer, product, and component and is not part of the present scope. The current publication addresses the first task by presenting methods that collect customer loads in real time by using the onboard sensors.

The distribution of customer loads is affected by variability, as illustrated in Fig-ure 1.2. Load variability has different sources, as Johannesson and Speckert [4] discussed. According to the authors, controlled variation is given by different vehicle specifications, markets or regions. This controlled variation can be distinguished by classification. In contrast, uncontrolled variation can only be handled by statistical considerations. A population of the same type of vehicles will be subjected to a various number of road irregularities, curves and obstacles, depending on their usage and environment. In addition, different driving styles ranging from restrained to ag-gressive increase the variability. This variation is even more present at two-wheeled vehicles, since they are characterised by diverse application possibilities, compared to passenger cars.

In the automotive industry and referring to Matz [7] and Pötter [6], customer loads are divided in three categories: service loads, special events and misuse events, as illustrated in Figure1.2. This separation is characterised by statistical considerations and is necessary for product liability and warranty. Service loads occur during the normal use of the vehicle, which is called the intended purpose. They can be described by a continuously distributed load spectra during the life of the vehicle. In the case of a motorcycle, service loads comprise acceleration and brake manoeuvres, cornering and loads that occur due to the roughness of the road surface. In addition to the service loads, the intended purpose also includes the occurrence of special events, which are rare compared to service loads. Special events induce a higher load on the vehicle components and they are often characterised by impacts from sudden events; for example, driving over a pothole. By definition, misuse events are not part of the intended purpose, but they are also considered during the vehicle design process. Figure1.2shows that the load severity of misuse events typically coincides with the structural strength of the components. Thus, the components will be over exposed and damaged. Misuse events are also often the consequence of impacts; for example,

Table 1.1 – Features of customer usage profiles.

Classification method Continuous signal Event

Direct

Mileage Gear shifts

Velocity Controls

Engine speed Throttle Gear position (Location & time)

Model-based

Vehicle loading[1] Curves[2]

Wheel forces[1] Special events[3] Curviness[2]

Hilliness[2]

Road roughness[2,3]

riding against, or over a significant obstacle. The collection of both service loads and special events is addressed by this publication.

The present research extends the term of customer loads to the more general concept of customer usage profiles, because the methods presented capture more than merely loads. Table 1.1 shows the components of customer usage profiles de-pending on their classification method. Direct classification defines features that can simply be classified from the sensor signals; for example, velocity and gear position. In the case of a continuous signal, the classification is often realised using a time-at-level counting in one or two dimensions. For more information about classification methods, see Köhler et al. [8]. In contrast, model-based classification requires mul-tiple sensor signals and an underlying model for calculating or estimating advanced features and vehicle states. These model-based features are the focus of this PhD thesis and they comprise vehicle loading, wheel forces, road curviness, road hilliness, road roughness and the occurrence of special events. The superscripts in Table 1.1

indicate the publication, which present the respective methods. Direct classification of sensor signals is state of the art in the automotive industry and is not part of the present research. Furthermore, location- and time-based motion profiles are also not part of the present research.

All of the mentioned aspects can be categorised as external loads. Internal loads are also part of customer usage profiles; for example, vibrations induced by the

en-ABS sensor Acceleration

sensor _Suspension sensor

CAN bus Online processing

Methods for classification and counting

©_{BMW AG}

Figure 1.3 – Approach for the online identification of customer usage profiles.

gine. However, they are not in the scope of this research. Johannesson and Speckert [4] describe the external load environment with three aspects: longitudinal input, which means braking and accelerating; transversal input, which means loads in-duced by driving curves and; vertical input, which means loads inin-duced due to road roughness and dynamic wheel loading. All three external load inputs are addressed by this cumulative PhD thesis to reveal complete customer usage profiles in terms of durability.

1.3 Approach and experimental set-up

The number of onboard sensors increases based on the development of functions of two-wheeled vehicles such as anti-lock braking system (ABS), dynamic traction control (DTC), curve assistant, as well as driving assistance systems in the near future. Consequently, the connected motorcycle comprises various signals that can be accessed by the vehicle’s Controller Area Network (CAN) bus, as shown in Fig-ure 1.3. Following, the main approach of this research is gathering the individual components of customer usage profiles using the onboard sensors. Therefore, dif-ferent methods were developed to estimate advanced vehicle states in real time; for example, vehicle loading and wheel forces. Subsequently, the estimated values are counted and stored in the vehicle’s electronic control units (ECUs). An online im-plementation of the counting algorithms is mandatory, since the time series of the CAN bus signals cannot be stored in the control units due to memory efficiency. In

addition, various vehicle applications could use the revealed information for changing vehicle settings and improving existing functions. Up to this point, a dataset will be created which represent the individual customer-specific behaviour. It is also called a customer usage profile on the small scale. The vehicles will send the collected clas-sification results to the manufacturer; for example, during workshop appointments. BMW Motorrad already released an eCall system in 2017, which comes along with a built-in SIM card. Such a system could also be used to send the customer usage profiles via mobile communication to the manufacturer. Subsequently, the customer usage profiles can be derived offline from the overall distribution of the individual customer usage components. As a result, these derived customer usage profiles rep-resent the customer behaviour on the large scale; for example, for a given statistic, which is often the median or the 99 % quantile. The definition of design targets and product requirements is a statistical problem and is demonstrated in the discussion (see Chapter 5). By implementing this type of field-data acquisition, almost every customer will be evaluated, as these sensors and the respective signals are part of almost all produced vehicles. Further information about the development of driving assistance systems for two-wheeled vehicles can be found at ACEM1 and the CMC2.

A motorcycle of the type BMW R1200GS was chosen as the test vehicle, since it is the most sold motorcycle of BMW, and all required onboard sensors are available, see Figure1.4. This motorcycle was prepared with data-logging devices for experimental tests and validation of the algorithms. Therefore, a CAN logging device from 2D3 was mounted together with a global positioning system (GPS) logging device, which provides information about the position and the altitude of the vehicle. Figure 1.5

shows the data-logging device and the GPS module. Both devices are sufficient small to mount them without restrictions on the motorcycle. The data-logging device needs a power supply and a CAN signal as inputs. The data logging of vehicle internal signals is standard practice at developing applications for ECUs. It ensures the recording of all necessary information for a posterior offline evaluation of the vehicle dynamics and the driven manoeuvres. In the present case, the signals recorded were used to develop methods for collecting the individual customer usage profiles.

1_{ACEM, the European Association of Motorcycle Manufacturers, seewww.acem.eu.}

2

CMC, the Connected Motorcycle Consortium, seewww.cmc-info.net.

Figure 1.4 – Test motorcycle of type BMW R1200GS⃝cBMW AG.

Data-logging device

GPS-module

Figure 1.5 – 2D3_{data-logging device and GPS-module.}

This is possible, because the methods presented do not interact with the vehicle, or more precisely, they are not designed to be feedback control loops. By contrast, the development of applications that do interact with the vehicle, specific hardware-in-the-loop (HIL) test beds would be required, but this is not the scope of the present research. An overview of the recorded signals can be found in Appendix A.

After the onboard signals had been logged, they were imported in a Simulink⃝R environment. The discrete models use the same time step size as the vehicle’s onboard system, which is set to ts = 0.01 s. Consequently, the offline test environment can simulate the vehicle and its signals as they appeared during the test manoeuvres. This enables the development of algorithms that in principle work in real time, and

can be implemented in new vehicles. However, it is not part of the present study to evaluate specific hardware requirements for the implementation of the developed methods. In general, this is merely a cost factor of memory and CPU capacity.

1.4 Vehicle dynamics

Vehicle dynamics is an essential discipline in engineering and it plays a fundamental role at the development of motor vehicles. According to Schramm et al. [9], vehicle dynamics deals “with the motional actions necessary for moving road vehicles and their resulting forces under consideration of the natural laws”. It describes the re-actions of a vehicle due to the re-actions of the driver and the interaction with the road surface and the driving unit [10]. It is common to divide the problem of vehicle dynamics into three subdomains: longitudinal, vertical, and lateral dynamics [11]. Longitudinal vehicle dynamics comprises:

• Acceleration and braking events

• Driving resistance forces due to air resistance, slope, friction and inertia • Dynamic wheel loading due to longitudinal acceleration

• Transmission of traction and brake moments

Vertical vehicle dynamics is characterised by:

• Vertical oscillation due to the road excitation

• Assessment of comfort and safety due to vertical oscillation • Dynamic wheel loading due to pitch and roll effects

Lateral vehicle dynamics evaluates the dynamic behaviour of the vehicle during cornering and comprises:

• Lateral acceleration of the vehicle mass • Yaw effects

• Dynamic wheel loading during cornering

The forces acting between the road surface and the tyre are of major importance in vehicle dynamics, since all required loads for vehicle dynamics are transmitted by this contact patch. The investigation of the wheel forces is thus often the first

quantitative load assumption in terms of load analysis. A method for calculating the wheel forces with the onboard signals is shown in the first publication [1]. Various techniques for the modelling and simulation of vehicle dynamics exist, while they differ in complexity and purpose. For example, simple vibration models evaluate the comfort and safety of the vehicle due to the road excitation. Thus, they aim to investigate vertical vehicle dynamics.

The most commonly-employed model is the Quarter of Vehicle (QoV) with two degrees of freedom. It is made up of a sprung mass, which represents the vehicle mass, and an unsprung mass, which represents the wheel mass. The QoV model is often the very beginning of a deep model understanding in vertical vehicle dynamics. It exists in a variety of modifications and is suitable for simple comfort analyses and the evaluation and optimisation of the suspension characteristics. The extended Half of Vehicle (HoV) model includes a second wheel on the same track and is designed for investigating pitch effects and coupled oscillation phenomena. In the case of a motorcycle, this model is already considered as a full-vehicle model, since a motorcycle is a single-track vehicle. The major effects of vertical vehicle dynamics can be investigated with such models, as shown in the second publication [2]. Further information about the detailed modelling of two-wheeled vehicles can be found in Cossalter [12]. More complex models are common in multi-body simulations, which are composed of various rigid or elastic bodies and connection elements; for example, joints, springs and dampers. These models enable a detailed investigation of all subdomains of vehicle dynamics and the interaction between the single components. Mathematical models and the numerical treatment can be found for example -in Schramm et al. [9]. Often, the first step in modelling vehicle dynamics is the formulation of the equations of motion:

M ¨x(t) + C ˙x(t) + Kx(t) = F (t). (1.1)

The equations of motion can be obtained from free body diagrams, based on Newton’s second law of motion. M is defined as the mass matrix, C is the damping matrix, K is the stiffness matrix, F is the force vector of external forces, and x is the position vector comprising the degrees of freedom. Once the equations of motion are derived, they can be transformed to first-order ordinary differential equations (ODEs). This makes a numerical treatment more applicable. In the case of linear

time-invariant system matrices, the linear state-space representation can be derived:

˙

q(t) = Aq(t) + Bu(t), (1.2)

y(t) = Cq(t) + Du(t). (1.3)

Such a system is said to be linear and time-invariant, or LTI for short. The state variables are gathered in the state vector q, the control variables in the control vector u, and the measured signals in the measurement vector y. The constant matrices A, B, C, and D, are called the system matrix, control matrix, measurement matrix and direct matrix. This system representation is often used, because even complex models can be described by these two equations. The use of state-space models is presented in the first [1] and second publication [2]. Another most common and useful method of representing an LTI system, is by its transfer function H(s), which relates the output Y (s) to the input U (s) in the frequency domain. Therefore, the Laplace transformation of the system equations needs to be derived:

H(s) = Y (s) U (s) =

L {y(t)}

L {u(t)}. (1.4)

The application of transfer functions is often used in signal processing and con-trol theory and was employed by the second publication [2] for mapping the road excitation (input) to the response of the vehicle (output). The equations of motion, state-space models and the transfer functions of the frequently-used QoV and HoV models are shown in AppendixB.

1.5 A brief literature survey

The present publication aims to collect customer usage profiles in terms of durability, rather than monitoring the vehicle conditions. However, the methods presented are similar to the model-based condition monitoring systems and they follow the same approach. Condition-based monitoring (CBM) aims to observe a system’s condition to provide prognosis and diagnosis of component degradation, and the detection of in-service failures. Charles et al. [13] annotated that “Condition monitoring uses some level of knowledge of the system of interest. This may be in the form of a

model, expert system, experience, learnt behaviour, etc.”. In general, two different techniques have been established: signal-based condition monitoring, and model-based condition monitoring.

Signal-based condition monitoring is common at the observation of continuously running machines and engines; for example, wind turbines, railway vehicles and stationary turbines. It is characterised by the use of signal-processing techniques in the time and frequency domain. Therefore, several sensors are mounted in the near of critical parts; for example, rotor shafts and bearings. A comparison between the current signals and the measurements of an accurate system, indicates malfunction and machine deterioration. It is also possible to compare the current state with simulated values of the proper system. The detection of malfunction is often realised using threshold detection, trend analysis and spectral analysis. An example of signal-based condition monitoring is the work of Mei and Ding [14]. They developed a fault detection system of rail vehicle suspensions based on the cross-correlation of acceleration signals. An example of vibrational analysis for the detection of faults in engine bearings can be found in Tandon et al. [15]. Aliustaoglu et al. [16] developed a tool wear condition monitoring using a sensor fusion model based on fuzzy logic.

Model-based condition monitoring is characterised by the comparison of the cur-rent machine state to a simulated ideal system behaviour, based on a system model. In general, model-based approaches are more complex, since they require a detailed knowledge about the system, which is often dynamic, complex and non-linear. An example of model-based systems can be found in the PhD thesis from Schlechtingen [17]. He uses an ANFIS model to analyse the behaviour of a wind power plant. Furthermore, Liu et al. [18] developed a recursive least square algorithm (RLS) in combination with a Kalman filter and machine learning (ML) methods to detect a vertical suspension fault on railway vehicles. Li et al. [19] utilised a linear model of a railway vehicle to estimate suspension parameters for condition monitoring. An ex-ample of an automotive application is the work of Börner et al. [20]. They discussed the comparison of an ideal linear damping constant with the measured suspension travel to detect deterioration of the suspension system. Various examples of CBM exist and in times of industry 4.0 and data-driven decisions, many others will follow. The “’Applied Condition Monitoring’ series of Haddar et al. [21] publishes the latest applications of condition monitoring.

The methods presented within this PhD thesis can be classified as model-based collection of customer usage profiles. Several of these systems have already been published in vehicle engineering. Rupp et al. [22] used linear transfer functions derived from previous measurements for estimating stresses on components with acceleration signals as inputs. Müller [23] simulated operative stresses on critical parts of commercial vehicles within a multi-body system model in real time. She used measured acceleration signals as input for the simulation and counted the resultant stresses online with the help of the rainflow counting method. In contrast to Müller, Matz [7] directly calculated the wheel forces of passenger cars and then translated these forces acting on components with kinematic transfer functions. As well as the present publication, he also used onboard signals as inputs. The first publication [1] of this cumulative PhD thesis transfers his method to the application on two-wheeled vehicles.

1.6 Overview of published papers

Customer loads of two-wheeled vehicles

The first publication [1] presents methods for estimating the vehicle loading and the current road slope to calculate the occurring wheel forces. Information about the vehicle loading is especially important for two-wheeled vehicles, because the vehicle’s empty weight is low in comparison to the additional loading comprising the driver, passenger and luggage weight. Finally, the first publication shows that the wheel forces can be calculated merely with the signals of the onboard sensors. A validation of the simulated wheel forces was achieved by comparison with measured wheel forces using wheel-load transducers. The knowledge about wheel forces is an improvement for the product development, because they can be used do derive design loads and verification loads for test rigs.

Road classification for two-wheeled vehicles

The second publication [2] aims to classify the driven roads in terms of curviness, hilliness and road roughness. The study shows the vehicle-independent collection of road properties using the onboard sensors. First, the driven curves are counted and classified on a scale of curviness. Second, the road slope is classified in terms of

hilliness. Third, a modular road roughness estimator is presented, which utilises the vehicle’s transfer functions to estimate the current road roughness in terms of the ISO 8608 [24] classification. Information about the road characteristics helps defining test and endurance tracks for product verification. This means that verification tracks and tracks for survey samplings can be optimised for the actual customer behaviour. For example, the Virtual Measurement Campaign (VMC) project from Speckert et al. [25] aims at the planning of measurement campaigns. In addition, knowledge about the road characteristics enables a virtual load acquisition, where customer loads are simulated on virtual test tracks.

Impact detection using a machine learning approach and experimental road roughness classification

The third publication [3] presents the experimental validation of the modular road roughness estimator. Therefore, a measurement campaign was carried out, where previously measured road surfaces were ridden to experimentally validate the pro-posed method. The propro-posed method of road roughness classification was successfully validated even on rough test tracks. In addition, the study presents a ML approach to detect and classify impacts in terms of mild and severe special events. Knowledge about the number and intensity of occurred special events during the product’s life helps deriving design loads and enables a virtual load acquisition.

vehicles

Customer loads of two-wheeled vehicles Christian Gorgesa, Kemal Öztürka, Robert Liebichb a_{BMW AG, Munich, Germany;}b_{Chair of Engineering Design and Product}

Reliability, Berlin Institute of Technology, Berlin, Germany

(This is an Accepted Manuscript of an article published by Taylor & Francis in Vehicle System Dynamics on 13/06/2017, available online: http: // www. tandfonline. com/ 10. 1080/ 00423114. 2017. 1335874.)

Customer usage profiles are the most unknown influences in vehicle design targets and they play an important role in durability analysis. This publication presents a customer load acquisition system for two-wheeled vehicles that utilises the vehicle’s onboard signals. A road slope estimator was developed to reveal the unknown slope resistance force with the help of a linear Kalman filter. Furthermore, an automated mass estimator was developed to consider the correct vehicle loading. The mass estimation is performed by an extended Kalman filter. Finally, a model-based wheel force calculation was derived, which is based on the superposition of forces calculated from measured onboard signals. The calculated wheel forces were validated by measurements with wheel–load transducers through the comparison of rainflow matrices. The calculated wheel forces correspond with the measured wheel forces in terms of both quality and quantity. The proposed methods can be used to gather field data for improved vehicle design loads.

Keywords: Customer loads, motorcycle dynamics, road slope estimation, mass estimation, load acquisition, Kalman filter

2.1 Introduction

Two-wheeled vehicles are characterised by diverse application possibilities, given that motorcycles have changed from means of transportation to general purpose vehicles, at least in the modern world. Scooters and small-sized motorcycles remain the first choice for personal mobility in urban traffic, whereas more specific vehicle segments

such as Enduro, Sport, Cross, Tour, Roadster and Cruiser exist for individual pur-poses. Since mass reduction and lightweight design play an important role in vehicle engineering, the components are optimised to their individual design targets. Con-sequently, every product segment needs its own requirements regarding durability and operating strength. Furthermore, different markets with varying regional de-mands influence product design [1]. The most unknown influences to determine vehicle design targets are customer usage profiles. Detailed knowledge of customer usage profiles improves design loads and ultimately the vehicle development process. Customer usage profiles describe the unknown distribution comprising wheel forces, vehicle loading, road profile characteristics, engine loads, brake events, and special events. In this paper, customer loads are defined as wheel forces and vehicle load-ing. Knowledge about the vehicle loading is particularly important for two-wheeled vehicles and has a strong impact on the customer loads, given that the vehicle’s empty weight is low in comparison to the additional loading comprising the driver, passenger, and luggage weight.

At present, a common method to obtain field data is survey sampling, where a certain number of test vehicles are equipped with additional measurement devices to perform a measurement campaign with selected or randomly chosen customers. However, survey sampling cannot reveal the complete probability distribution of customer loads. Moreover, it is expensive due to the additional equipment costs. Figure 2.1 illustrates the broad probability density function of customer loads in comparison to the structural strength of the components and the narrow distribu-tion of survey samplings. To reveal the entire distribudistribu-tion of customer loads, every customer would have to be evaluated. Johannesson and Speckert [1] highlight that there are two scales when discussing customer loads: on the small scale the profile of a specific customer needs to be evaluated; while on the large scale, the problem is to identify the severity of a population of customers. The final vehicle design loads in-volve combining survey sampling, measurements on test tracks, and experience from previous product designs.

The number of onboard sensors rises due to the increased functions of motorcycles, such as an anti-lock braking system (ABS), dynamic traction control (DTC), or curve assistant. Hence, the main approach of this study is to gather information from every customer with the help of these onboard signals. Onboard signals are defined

Customer loads Structural strength Survey sampling

?

Figure 2.1 – Distribution of customer loads, survey sampling, and structural strength.

as signals that can be accessed by the vehicle’s Controller Area Network (CAN) bus and are part of every production vehicle. This type of field data collection can be classified as a model-based online monitoring system with integrated counting of durability-related values. Online implies that the customer loads are estimated while the vehicle is in use, meaning that there is no long-term logging of the signals. Several of these systems have already been published in vehicle engineering. Müller [2] simulated operative stresses on critical parts of commercial vehicles within a multi-body system model in real time. She has used measured acceleration data as input for the simulation and counted the resultant stresses online with the help of the rainflow counting method. In contrast to Müller, Matz [3] directly calculated the wheel forces of passenger cars and then translated these forces acting on components with kinematic transfer functions. His approach also has used onboard signals as inputs. Karlsson [4] has presented different methods to model loads for customer usage profiles with the help of road classification.

In contrast to specific application-driven publications, the main contribution of this study is to develop a holistic approach to collect customer loads with onboard signals of two-wheeled vehicles. There is neither the ambition to realise a real-time control system nor to intervene vehicle dynamics. Therefore, no specific hardware requirements will be discussed. This paper is organised as follows. Section 2.2

describes the reference motorcycle with measurement equipment and analyses previ-ously measured wheel forces which serve as reference values. Section2.3derives the algorithms for road slope estimation, mass estimation, and the calculation of wheel

Figure 2.2 – Test motorcycle with the global reference coordinate system c⃝BMW AG.

forces. Section2.4discusses and compares the results from simulation to their refer-ence measurements to validate the method. Finally, Section2.5provides a summary and conclusion about the developed methods.

2.2 Experimental set-up and data analysis

A motorcycle with data-logging devices was prepared for experimental tests and val-idation of the algorithms. Onboard signals were logged during pre-defined tracks for offline simulation of vehicle dynamics. Figure 2.2 shows the test and reference motorcycle (BMW R1200GS) together with the global reference coordinate system. The reference frame will not rotate around the roll axes during banking of the mo-torcycle, which means that it is aligned with the road plane. When the motorcycle is upright, it coincides with the vehicle’s coordinate system. The test motorcycle has the following onboard signals available, which are required for the developed algorithms:

• 5 DOF Inertial Measurement Unit (IMU) to measure

– Acceleration in X, Y , and Z in the vehicle coordinate system.

– Angular velocity around X (roll) and Z (yaw) in the vehicle coordinate system.

• wheel velocities, • brake pressures,

Frequency

F

o

rc

e

I. Domain II. Domain

fc

Figure 2.3 – Amplitude spectrum of vertical wheel forces.

• spring deflections,

• model-based signals (e.g. engine torque and roll angle).

These signals were logged through the CAN bus. Additionally, the vehicle was equipped with a Global Positioning System (GPS) logging device, which provides information about the position and the altitude for later validation.

Wheel forces were measured with wheel–load transducers [5] during previous meas-urement campaigns. These forces were used for data analysis and validation of the wheel force calculation. Figure 2.3 shows a generic amplitude spectrum of vertical wheel forces. The amplitude spectrum can be divided into two domains: the first domain contains driver-induced forces and low-frequency path excitation from road undulations; and the second domain contains track-induced forces from stochastic road excitation. These two domains are separated by the crossover frequency f_c. It is well known that these two domains belong to the different modes of the motorcycle [6]. The first domain contains bounce and pitch mode of the sprung mass, while the second domain contains wheel hop modes of unsprung masses. Driver-induced forces are defined as forces directly dedicated to driver manoeuvres, such as accelerating, braking, and cornering. The main aspect of this analysis is to highlight the cros-sover frequency f_c, which is used to set up the filter frequency for the wheel force calculation, see Section2.3.4.

The logged signals from the previous measurement campaigns were used in a Simulink⃝ model to simulate vehicle dynamics and validate the developed algorithms.R

The discrete model uses the same time step size as the vehicle’s onboard time step size. This in principle enables an online application of the developed algorithms. It is not part of the present study to evaluate specific hardware requirements for implementation of the methods into existing or new production vehicles.

2.3 Methods

The wheel force calculation requires all resistance forces that act on the motorcycle. Therefore, two unknown resistance forces had to be determined first: the slope res-istance force and the inertial force. A road slope estimator based on a linear Kalman filter (KF) was developed, which estimates the current road slope angle. The total vehicle mass comprises the motorcycle and the loading, including the driver, pas-senger, and luggage weight. The estimation of the total vehicle mass was developed with the help of an extended Kalman filter. The mass estimator requires the road slope angle and the traction force as input signals. A stiff driveline model was used to calculate the traction force from the internal engine torque. Once the vehicle mass and the road slope had been determined, the wheel force calculation was feas-ible. The wheel forces were calculated by a superposition of forces calculated from measured motions. Subsequently, the wheel forces were counted with the rainflow method, which reduces the memory requirements and enables a classification of the customer loads.

2.3.1 Road slope estimator

Estimation of the road slope is essential for the wheel force calculation, since road slope can cause a major driving resistance force. Different methods for the estimation of road slope have already been published. Boniolo et al. [7] utilised a 6-DOF IMU to describe the state of the motorcycle with Euler angles. Moreover, they used an extended KF to estimate the vehicle states. Since a 6-DOF IMU is not yet part of the onboard signals, this method will not be adopted for the present work. Vahidi et al. [8] estimated the road slope together with the mass of a heavy-duty vehicle using a recursive least-square estimation with forgetting factor. Lingman and Schmidtbauer [9] reported another example for this type of slope estimation, while they used an extended KF. The aforementioned methods use driving resistance forces

α

𝑣 𝑎𝑥

𝑔

Figure 2.4 – Road slope estimation physics.

and longitudinal dynamics for the estimation problem. This paper uses a similar approach described by Corno et al. [10], because it is more suitable for the application to motorcycles. The idea is that the gravitational acceleration is measured by the IMU in longitudinal direction while riding up- or downhill, see Figure2.4. Assuming a rigid motorcycle, the estimated pitch angle is the road slope angle α. In contrast to the other methods, this approach makes the estimation of the road slope independent from the mass estimation. The road slope angle can be calculated directly with the help of the inertial acceleration a_x and the vehicle acceleration ˙v, which is derived from the wheel velocities. Hence, the road slope angle α is given by

α = arcsinax− ˙v

g . (2.1)

Since the input signals are affected by noise from both measurement and differen-tiation, a linear KF [11] was implemented to estimate the road slope. Many applica-tions have been realised with Kalman filtering, particularly in navigation problems, as well as vehicle dynamics. Maybeck [12] describes the KF as a recursive data-processing algorithm that minimises the error statistically [13]. To estimate the road slope with the linear KF, the discrete linear difference equation needs to be derived. Therefore, the problem was formulated in state-space representation. The state vector xs∈ Ren comprises the velocity v and Φ, as shown in Equation (2.2).

xs= ( v Φ ) , Φ = sin α. (2.2)

The subscript ‘s’ indicates that the state vector is formulated to estimate the slope. The substitution of Φ = sin α leads to a linear formulation of the system, which is essential to apply the linear KF. The measurement vector zs∈ Remis defined by the measured velocity v, which can be derived from the rotational speed of the wheels and is part of the onboard signals. Transformation of Equation (2.1) yields the state-space representation of the problem, see Equation (2.3).

˙ xs= ( ax− gΦ 0 ) , zs= v. (2.3)

To apply the linear KF, the explicit discrete time-invariant formulation of the prob-lem must be derived. This is achieved by using the explicit Euler forward integration, whereby s is the time step size:

x_s|k = ( vk Φk ) = ( vk−1+ s[ax|k−1− gΦk−1] + qs1|k−1 Φk−1+ qs2|k−1 ) . (2.4)

Process and measurement noise is represented by qsand rs, respectively. They are assumed to be independent and uncorrelated with a normal white noise probability distribution [13]:

p(qs) ∼ N (0, Q_s), (2.5)

p(rs) ∼ N (0, Rs). (2.6)

Q_s is the process noise covariance matrix and Rs is the measurement noise cov-ariance matrix. Equation (2.4) is reformulated into the linear stochastic difference Equation (2.7) with measurement Equation (2.8).

x_s|k = [ 1 −sg 0 1 ]    As ( vk−1 Φk−1 )    xs|k−1 + [ s 0 ]  Bs a_x|k−1    us|k−1 + [ 1 0 0 1 ] ( qs1|k−1 qs2|k−1 )    qs|k−1 , (2.7) z_s|k =[1 0 ]    Hs ( vk Φk )    xs|k +r_s|k. (2.8)

The n × n linear system matrix As relates the state xs at the previous time step k − 1 to the state at the current time step k. The linear n × l input matrix Bs relates the control input vector us ∈ Rel to the state xs, while the inertial acceleration ax is defined as the control input. The linear m × n measurement matrix H_srelates the state x_s to the measurement z_s.

In comparison to the direct computation, see Equation (2.1), this formulation does not require a differentiation of the velocity v to obtain the road slope. The meas-urement noise covariance matrix was estimated from previous measmeas-urements of the velocity v and was thus set to Rs = 0.01. The system covariance matrix Qs was tuned empirically, which is a standard practice in KF application. In contrast to the rigid motorcycle model, a real motorcycle has a degree of freedom around the Y -axis (pitch). Therefore, an on/off logic was implemented to restrict the pitch in-fluence on the road slope estimation. Since the test motorcycle has no pitch signal available, the longitudinal acceleration was utilised to detect acceleration and brake events. Thus, the road slope estimation pauses when a certain value of longitudinal acceleration is exceeded. Furthermore, the model assumptions are only valid for mo-torcycles without steering action. The algorithm thus also pauses when the measured angular yaw rate exceeds a certain value. To sum up, the following restrictions were formulated for the road slope estimator:

• Absolute value of the angular yaw rate is lower than a given threshold. • Absolute value of the longitudinal acceleration is lower than a given threshold.

When at least one condition is violated, the algorithm holds the road slope estim-ation until the conditions are true again. In the meantime, the last valid value of the road slope is delivered for the mass estimator and the wheel force calculation.

𝑇t

Engine & Clutch Transmission

Rear wheel Cardan drive & Differential 𝐼rr 𝜔_rr 𝐹T 𝑇w 𝑟_rr 𝑇e 𝑇f 𝑇w 𝐼e, 𝜔e 𝐼f, 𝜔f, 𝑖f 𝐼t, 𝑖t

Figure 2.5 – Model of the driveline dynamics.

Please note that these limitations are only valid for the road slope estimator. They are independent of the mass estimator and the wheel force calculation.

2.3.2 Driveline model

The mass estimation and the wheel force calculation require the traction force F_T. Thus, the traction force was derived from the rotational equations of motion from both the driveline and the rear-wheel dynamics, as illustrated in Figure 2.5. The engine torque Te is provided by the engine electronic control unit (ECU). It is cal-culated by the engine speed and the throttle position. The engine torque already considers the necessary amount of slip to accelerate the vehicle, because the engine torque is adapted to the current road conditions due to the DTC. The driveline is assumed to be stiff, whereby driveline oscillation and torsional effects are neglected. The transmission torque T_t can be calculated by subtracting the rotational inertia of the engine components Iefrom the engine torque Te, as shown in Equation (2.9).

Tt= Te− Ieω˙e, (2.9)

Tf= (Tt− Itω˙e)it, (2.10) Tw= (Tf− Ifω˙f)if. (2.11)

The final drive torque T_fcan be calculated by subtracting the inertial losses of the transmission parts Itfrom the transmission torque Tt. Furthermore, it is amplified by the gear ratio i_t, see Equation (2.10). The wheel torque T_w is derived from the final

drive torque T_f reduced by the inertial losses of the cardan drive and the differential If. Furthermore, it is amplified by the fixed final drive ratio if, see Equation (2.11). The traction force FT can be derived from the rotational equation of motion of the rear wheel, see Equation (2.12), where r_rr is the dynamic rolling radius of the rear wheel. Irrωrr˙ = Tw− FTrrr, (2.12) ˙ ωrr= ˙v rrr , u = itf rrr

, itf= itif, µeff = efficiency parameter. (2.13)

Moreover, it is assumed that the rolling condition is valid. The gear ratio it, the final drive ratio if, and the dynamic rear-wheel radius rrr are condensed into the coefficient u. The rotational acceleration of the rear wheel ˙ωrr can be derived from the rear-wheel velocity v. Mechanical losses of the driveline are reduced to the efficiency parameter µeff, see Equation (2.13). Finally, the traction force FT can be partitioned into two parts: the steady-state traction force and the losses of the traction force due to the driveline inertia, as shown in Equation (2.14).

FT= Tw− Irrωrr˙ rrr = Teuµeff   Steady–state − (Ie+ It+ If i2 t +Irr i2 tf )u2    Rotational mass ˙v. (2.14)

These losses are reduced to an equivalent rotational mass, which is multiplied by the rear-wheel acceleration ˙v to obtain a force component. The validation of the traction force F_T is made within the wheel force validation in Section 2.3.4. In the case of acceleration, the longitudinal rear-wheel force is the traction force.

2.3.3 Mass estimator

As mentioned in the introduction, estimation of the vehicle mass is particularly im-portant for motorcycles. The empty weight of two-wheeled vehicles is less compared to passenger cars and thus the influence of the vehicle loading on customer loads increases. Furthermore, the vehicle mass is essential for the wheel force calculation. Several algorithms have already been published. Rozyn and Zhang [14] measured

α

𝑣 𝑚

Figure 2.6 – External forces acting on the motorcycle.

the sprung mass response to estimate the inertial parameters of the vehicle, which requires detailed knowledge about the suspension stiffness and the damping char-acteristics. Lingman and Schmidtbauer [9] used longitudinal vehicle dynamics and a KF that estimates both the road slope and the vehicle mass. Fathy et al. [15] developed a recursive least-square model to estimate the vehicle mass. This study uses an approach based on resistance forces and longitudinal dynamics for mass estimation, as Ritzen et al. [16–18] proposed for heavy-duty vehicles. Figure 2.6

illustrates the longitudinal dynamics with external forces acting on the motorcycle. The dynamic equation of motion can be solved for the vehicle mass m, see Equa-tions (2.15)–(2.17). m ˙v = FT− FD− FS− FR, (2.15) FD= 1 2ρcxAv 2 _{= κv}2_{, F} S = mg sin α, FR = mgfrcos α, (2.16) m = FT− κv 2 ˙v + g(sin α + frcos α) . (2.17)

FD is the aerodynamic drag force and FT is the traction force acting on the rear wheel, as derived in Equation (2.14). The aerodynamic coefficients were obtained from measurements in a wind tunnel of BMW. They are substituted by the single constant κ. The slope resistance force F_Sdepends on the road slope angle α, which is estimated with the road slope estimator. The rolling resistance force FR is calculated with a constant rolling resistance coefficient f_r.

Since the input signals are affected by measurement noise as well as model uncer-tainties from the road slope estimator and the driveline model, a direct calculation of the vehicle mass is infeasible. For this reason, the estimation problem was formu-lated with the help of an extended Kalman filter (EKF). The application of a linear KF is infeasible because the process equations are nonlinear. The EKF can handle nonlinear stochastic difference equations, such as Equations (2.18)–(2.19).

xk= f (xk−1, uk−1, qk−1), (2.18)

zk= h(xk, rk). (2.19)

Welch and Bishop [13] highlight that the EKF linearises around the current mean and covariance and that the most interesting and successful applications have been solved with EKFs. Jacobian matrices A, W, H, and N are required for the linear-isation. The basic operations for the EKF are the same as for the linear KF. To define the problem in state-space representation, Equation (2.17) can be solved for the vehicle acceleration ˙v, see Equation (2.20).

˙v = (FT− κv 2₎

m − g(sin α + frcos α). (2.20)

The state vector xm is defined by the velocity v and the reciprocal mass Θ, as shown in Equation (2.21). The subscript ‘m’ indicates that the state vector is for-mulated to estimate the vehicle mass.

xm= ( v Θ ) , Θ = 1 m. (2.21)

The substitution of Θ = 1/m leads to a more robust formulation of the estimation problem. The measurement vector zm∈ Rem is defined by the measured velocity v. Finally, the state-space representation is obtained, see Equations (2.22)–(2.24).

˙ xm= ( ΘΓ − gΛ 0 ) with (2.22) Γ = FT− κv2, Λ = sin α + frcos α, (2.23) zm= v. (2.24)

The explicit discrete time-invariant formulation of the problem can be derived with the use of explicit Euler forward integration, see Equations (2.25)–(2.29), where s is the time step size.

x_m|k= f (x_m|k−1, u_m|k−1, q_m|k−1) = ( vk−1+ s[Θk−1Γk−1− gΛk−1] Θk−1+ qm4|k−1 ) with (2.25) Γk−1= FT|k−1(1 + qm1|k−1) − κ(vk−1+ qm2|k−1) 2_{, (2.26)} Λk−1= sin (αk−1+ qm3|k−1) + frcos (αk−1+ qm3|k−1), (2.27) um= ( FT α ) , (2.28) zm|k= h(xm|k, rm|k) = [ 1 0 ]    Hm ( vk Θk )    xm|k +rm|k. (2.29)

While the process equations are nonlinear, the measurement equation remains linear. The process noise q_m is modelled as normally distributed white noise. The noise influence qm1 is modelled as a percentage amount of the traction force FT, since the model uncertainties for the traction force increase with a higher engine torque. The unknown wind speed is considered with the noise q_m2. Additionally, the noises qm3 and qm4 are added to the road slope angle α and the reciprocal vehicle mass Θ to consider model uncertainties. The measurement noise r_m is added to the measured velocity v. The control input vector umcomprises the traction force FTand the road slope angle α. The Jacobian matrices Am, Wm, Hm, and Nmneed to be derived to apply the EKF, see Equations (2.30)–(2.34).

A_m[i,j] = ∂f[i] ∂x_m[j](xm|k−1, um|k−1, 0), Wm[i,j]= ∂f_[i] ∂q_m[j](xm|k−1, um|k−1, 0), (2.30) H_m[i,j] = ∂h[i] ∂xm[j] (x_m|k, 0), N_m[i,j]= ∂h[i] ∂rm[j] (x_m|k, 0), (2.31) A_m= [ 1 − 2κsvk−1Θk−1 sΓk−1 0 1 ] , (2.32) Wm= [ sΘk−1FT|k−1 −2sκΘk−1vk−1 −sg(cos αk−1− frsin αk−1) 0 0 0 0 1 ] , (2.33) H_m= [ 1 0 ] , N_m= 1. (2.34)

The model assumes valid acceleration events that are suitable for the mass es-timation. Hence, a second on/off logic was formulated for the mass estimator. The restrictions are designed to be strict to identify evaluable acceleration events, which makes the mass estimation more robust. For this reason, the algorithm pauses dur-ing cornerdur-ing of the motorcycle. Additionally, the engine torque model is only valid for steady-state conditions of the engine. For the mass estimation, this means that the traction force FT must not change more than a given threshold. To sum up, the conditions to identify valid acceleration events are as follows:

• Absolute value of the angular yaw rate is lower than a given threshold. • Traction force is higher than a given threshold.

• Derivative of the traction force is lower than a given threshold.

The thresholds were evaluated empirically and as a consequence, they can differ for other motorcycles and underlying models. If a condition is violated, the algorithm holds the mass estimation until all conditions are true again. Despite these strict conditions, the results can still vary for different acceleration events since several other influences are not considered. Therefore, another linear filter was implemented to calculate the running mean of the estimated mass. When the conditions are violated or no converged mass estimate is available, the last valid mass estimate is forwarded to the wheel force calculation. The start value for the algorithm is defined

as a standard mass with a normal rider weight. Please note that these restrictions are valid for the mass estimator only. Nevertheless, there is a continuous output of the mass estimate for the subsequent wheel force calculation.

2.3.4 Wheel force calculation

A model-based wheel force calculation was developed, whereby the individual mech-anical effects are calculated for the particular rigid bodies. This modular approach makes a subsequent composition of the wheel forces possible. The method is based on the following assumptions: A motorcycle is modelled with three rigid bodies for sprung mass, rear unsprung mass, and front unsprung mass, as Cossalter described in [19]. These models exist in a variety of publications, see e.g. [6,10,19,20]. They differ in complexity and degrees of freedom for their individual application. The sprung mass comprises the frame, the engine, and the rider. Additionally, parts of the front and rear suspension system are counted to the sprung mass. The sprung mass is lumped in the centre of gravity (COG). The rear unsprung mass comprises the rear wheel, the rear brake, and parts of the rear suspension. The front unsprung mass comprises the front wheel, the front brake, and parts of the front suspension. Figure2.7shows the motorcycle model together with the three rigid bodies and the global reference frame. Furthermore, the main geometric dimensions are illustrated: wheelbase p, height of the COG h_cog|0 and perpendicular distance lcog of the COG from the rear wheel Z-axis. The degrees of freedom of the rigid bodies were formu-lated according to their equivalent onboard sensor. This means that every degree of freedom is represented by a signal from the onboard sensors. The sprung mass has the following four degrees of freedom:

• Displacement in X and Z.

• Roll motion around tyre contact patch line. • Yaw motion around vehicles Z-axis.

The unsprung masses have one degree of freedom in vertical direction, while the wheels can rotate around their axes. Steering and rotation of the handlebars are neglected, because they are not yet part of the onboard signals. This means that every roll motion acts on the three bodies with the same amount. The illustrated model considers no springs or dampers, because they are not required for the modular