Detecting Leakages in the PneumaticSystem of Heavy Vehicles: Modelling Using Simulink

UPTEC F10 057

Examensarbete 30 hp December 2010

Detecting Leakages in the Pneumatic System of Heavy Vehicles

Modelling Using Simulink

Axel Eriksson

Teknisk- naturvetenskaplig fakultet UTH-enheten

Besöksadress:

Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress:

Box 536 751 21 Uppsala Telefon:

018 – 471 30 03 Telefax:

018 – 471 30 00 Hemsida:

http://www.teknat.uu.se/student

Abstract

Detecting Leakages in the Pneumatic System of Heavy Vehicles

Axel Eriksson

In this thesis an algorithm for detecting leakages in the pneumatic system of heavy vehicles is

developed. Besides a description of this algorithm, the thesis includes a description of the pneumatic system of heavy vehicles, a review of some basic statistics and change detection analysis, and a description and analysis of some validation tests.

Heavy vehicles use compressed air for various applications, including brakes and suspensions.

Leakages in the pneumatic system are quite common and results in an increase in fuel usage, since more compressed air has to be produced.

This is of course both environmentally and economically damaging. In order to avoid this damage, leakages need to be fixed. The first step is to notice the presence of leakages.

The leakage detecting algorithm is based on a statistical deviation analysis. Inputs used are pressure measurements from the different compressed air circuits and some state variables regarding the compressed air users. All this information is communicated aboard on the vehicles’ controller area network (CAN).

The algorithm has been validated using real data measurements from test drives, some of them including a vehicle suffering from leakages. The results indicate that the algorithm manages to identify leakages, but also that there are some problems regarding incorrectly interpreting other events as leakages. The results also indicate that the algorithm fail in the ambition to locate the leakages.

If this algorithm should be implemented in a real time system to be used aboard, it is suggested that some improvements are made. These improvements mainly concern avoiding false alarms.

Tryckt av: Ångströmlaboratoriet, Uppsala Universitet Sponsor: Scania CV AB

ISSN: 1401-5757, UPTEC F10 057 Examinator: Tomas Nyberg

Ämnesgranskare: Torsten Söderström

Handledare: Martin Svensson

List of Abbreviations

APS Air Processing System CAN Controller Area Network CUSUM Cumulative Summation DC Desiccant Cartridge

ELC Electronic Levelling Control GMA Geometric Moving Average IDU Integrated Desiccant Use MCPV Multi Circuit Protection Valve MTD Mean Time to Detection

MTFA Mean Time between False Alarms PDF Probability Density Function PGN Parameter Group Number

PV Purge Valve

SAE Society of Automotive Engineers

Table of Contents

1 ! INTRODUCTION...6 !

1.1 ! B ACKGROUND ...6 !

1.2 ! P ROBLEM S TATEMENT ...6 !

1.3 ! T ASK AND L IMITATIONS ...7 !

2 ! THEORY 1: THE PNEUMATIC SYSTEM OF THE VEHICLE ...8 !

2.1 ! ^O VERVIEW OF THE S YSTEM ...8 !

2.2 ! T HE C OMPRESSOR ...8 !

2.3 ! APS ...10 !

2.3.1 ! Compressed Air Dryer...10 !

2.3.2 ! Compressed Air Distributor ...11 !

2.4 ! C OMPRESSED A IR U SERS ...14 !

2.4.1 ! Service Brakes ...14 !

2.4.2 ! Parking Brake / Trailer ...15 !

2.4.3 ! Auxiliary Equipment...16 !

2.4.4 ! ELC...17 !

2.5 ! L EAKAGES IN THE P NEUMATIC S YSTEM ...18 !

2.5.1 ! Fast Leakages and Slow Leakages...18 !

2.5.2 ! Leakages Affecting the System in Different Situations ...19 !

2.5.3 ! Common Leakage Locations ...19 !

2.6 ! CAN ...19 !

3 ! THEORY 2: SCIENTIFIC FRAMEWORK...21 !

3.1 ! C HANGE D ETECTION ...21 !

3.1.1 ! Basic Algorithms ...21 !

3.1.2 ! Parameter Tuning...22 !

3.2 ! ^{S TATISTICS} ...22 !

3.2.1 ! Regression analysis ...22 !

3.2.2 ! Hypothesis Testing ...23 !

4 ! SOLUTION LOGIC ...28 !

4.1 ! A SSIGNMENT – E XTENDED D ESCRIPTION ...28 !

4.2 ! ^{P ART 1 – L EAKAGE D ETECTION} ...29 !

4.2.1 ! Part 1 Basic Logic...29 !

4.2.2 ! Part 1 Variables ...30 !

4.2.3 ! Part 1 Calculations ...31 !

4.2.4 ! Part 1 Normal State...33 !

4.2.5 ! Part 1 Design Parameters...37 !

4.3 ! P ART 2 – L EAKAGE L OCATION E STIMATION ...44 !

4.3.1 ! Part 2 Basic Logic...44 !

4.3.2 ! Part 2 Variables ...44 !

4.3.3 ! Part 2 Calculations ...45 !

4.3.4 ! Part 2 Normal State...45 !

4.3.5 ! Part 2 Design Parameters...46 !

4.4 ! ^S YSTEM SUMMARY ...46 !

4.4.1 ! Part 1 Summary...46 !

4.4.2 ! Part 2 Summary...47 !

4.5 ! S YSTEM R ISKS AND L IMITATIONS ...48 !

4.5.1 ! Part 1 Risks and Limitations ...48 !

4.5.2 ! Part 2 Risks and Limitations ...49 !

5 ! MODEL VALIDATION ...50 !

5.1 ! ^{V ALIDATION T ESTS} ...50 !

5.1.1 ! Real Leakage Tests...50 !

5.1.2 ! False Alarm Tests...51 !

5.2 ! R ESULTS OF V ALIDATION T ESTS ...52 !

5.2.1 ! Results of Real Leakage Tests ...52 !

5.2.2 ! Results of False Alarm Tests ...62 !

5.2.3 ! Result Summary...65 !

5.3 ! S HORTCOMINGS OF V ALIDATION M ETHODS ...66 !

6 ! CONCLUSIONS ...67 !

7 ! FURTHER WORK ...70 !

7.1 ! A VOIDING F ALSE A LARMS ...70 !

7.1.1 ! False Alarms Caused Randomly ...70 !

7.1.2 ! False Alarms Caused by a Change in the Type of Driving ...73 !

7.2 ! L OWERING THE R EQUIRED C OMPUTATIONAL P OWER ...73 !

APPENDIX I – SIMULINK MODEL ...75 !

Table of Figures Figure 2.1 – An example of a pneumatic system of a vehicle, block diagram. ... 9!

Figure 2.2 – Total amount of air in system (blue line) and compressor status (red line)... 10!

Figure 2.3 – IDU, compressor and regeneration status. ... 11!

Figure 2.4 – APS block diagram ... 12!

Figure 2.5 – Pressures in circuits E21 and E25, indicating pressure compensation. ... 13!

Figure 2.6 – Pressure in circuit E21 (blue line) and service brake status (red line)... 14!

Figure 2.7 – Pressure in circuit E23 (blue line) when parking brake is activated and deactivated (red line)... 15!

Figure 2.8 – Pressure in circuit E24 (blue line) when clutch pedal is pressed down (red line). ... 17!

Figure 2.9 – Pressure in circuit E25 (blue line) when vehicle is lifted (red line). ... 18!

Figure 3.1 – Possible outcomes of a hypothesis test ... 24!

Figure 3.2 – Probability density function plots for t and normal distributions ... 27!

Figure 4.1 – Samples in one box are used to compute one k value ... 31!

Figure 4.2 – New and old k values to be used in t-test ... 32!

Figure 4.3 – Histogram of k, measuring constantly ... 33!

Figure 4.4 – Histogram of k, measuring when compressor is inactive ... 34!

Figure 4.5 – Histogram of k, measuring during normal state and compressor is inactive... 35!

Figure 4.6 – Air amount (blue curve) and k values (slope of red lines)... 35!

Figure 4.7 – Zoomed in air amount (blue curve) and k values (slope of red lines) ... 36!

Figure 4.8 – The number of samples used during a test drive (one hour long), based on the value of n 1 ... 38!

Figure 4.9 – Constructed plot of k over time, leakage occurs when t = -100 ... 39!

Figure 4.10 – Minimum leakage that the system is able to detect, leakage increment between old and new measurements ... 41!

Figure 4.11 – Required value of n 2 , as a function of n 3 , to detect a 10 l/min leakage ... 42!

Figure 4.12 – The number of samples used during a test drive (45 minutes long), based on the value of n 4 ... 43!

Figure 4.13 – Basic logic of part 1 ... 46!

Figure 4.14 – Basic logic of part 2 ... 47!

Figure 5.1 – k values obtained during real leakage test 1 (part 11) ... 53!

Figure 5.2 – t values obtained during real leakage test 1 (part 11) ... 54!

Figure 5.3 – alarms sent during real leakage test 1 (part 11) ... 55!

Figure 5.4 – histogram of k from real leakage test 1 (part 11)... 55!

Figure 5.5 – k values obtained during real leakage test 1 (part 12) ... 56!

Figure 5.6 – t values obtained during real leakage test 1 (part 12) ... 57!

Figure 5.7 – alarms sent during real leakage test 1 (part 12) ... 57!

Figure 5.8 – k values obtained during real leakage test 2 (part 11) ... 58!

Figure 5.9 – t values obtained during real leakage test 2 (part 11) ... 59!

Figure 5.10 – alarms sent during real leakage test 2 (part 11) ... 59!

Figure 5.11 – histogram of k from real leakage test 2 (part 11)... 60!

Figure 5.12 – k values obtained during real leakage test 2 (part 12) ... 60!

Figure 5.13 – t values obtained during real leakage test 2 (part 12) ... 61!

Figure 5.14 – alarm sent during real leakage test 2 (part 12)... 61!

Figure 5.15 – k values obtained during false alarm test 1 (part 11)... 62!

Figure 5.16 – t values obtained during false alarm test 1 (part 11)... 63!

Figure 5.17 – alarms sent during false alarm test 1 (part 11)... 63!

Figure 5.18 – k values obtained during false alarm test 2 (part 11)... 64!

Figure 5.19 – t values obtained during false alarm test 2 (part 11)... 65!

Figure 5.20 – alarms sent during false alarm test 2 (part 11)... 65!

Figure 6.1 – Total air amount in system during driving characterized by high air consumption. Red parts of the curve are measured during normal state. ... 68!

Figure 6.2 – Total air amount in system during driving characterized by low air consumption. Red parts of the curve are measured during normal state. ... 68!

Figure 6.3 – Pressure in circuit E24. Red parts of the curve are measured during normal state. ... 69!

Figure 7.1 – Running mean of k with different window sizes. Blue – single k values, green – mean of 21, yellow – mean of 101, red – total mean. ... 70!

Figure 7.2 – New and old k values to be used when using multiple t-tests ... 71!

Figure 7.3 – k values of fictitious false alarm 1 ... 71!

Figure 7.4 – k values of fictitious false alarm 2 ... 72!

Figure 7.5 – k values of fictitious true alarm ... 72!

1 Introduction

1.1 Background

Heavy vehicles use compressed air to a wide range of applications, including service brakes and suspensions. The pneumatic system consists of the compressor, which produces compressed air, the APS, which dries and distributes the air to the five different compressed air circuits, each of which is responsible for supplying one or more applications with compressed air.

Due to the fact that the cost (i.e. the fuel usage) of producing compressed air is low in comparison to other costs related to driving the vehicle, the amount of compressed air used has not been an important issue historically. The compressed air has more or less been seen as free. But recent year’s development has changed this viewpoint.

The development of the vehicles has made them more and more fuel efficient, and there are no longer any major improvements to be made by simple procedures. This means that every possible improvement leading to a decrease of diesel usage, even if it is just a small fraction of a litre per mile, is now of interest. This leads to the fact that the cost of producing compressed air is now an important issue to Scania.

To lower the compressed air usage, the applications using compressed air can be made more efficient, the compressor producing the compressed air can be made more efficient, and the system itself can be made more efficient, i.e. less affected by leakages. Unfortunately, as of today, Scania vehicles suffering from leakages in the pneumatic system are quite common.

The leakage could of course be minimized by making the pneumatic system more solid and robust. But since a lot of these leakages are caused by additional applications not constructed nor attached by Scania (for example cranes), some leakages would occasionally still haunt the system. To minimize the negative effects of the leakages it is important to repair them when they occur. This is usually not something that the driver can do himself, but something for a mechanic to do. Nevertheless, if the leakage is never noticed, it would never get fixed.

Therefore, to prevent an unnecessary high fuel usage caused by leakages in the pneumatic system, a system detecting those leakages would be beneficial.

1.2 Problem Statement

A warning system similar to the one described above exists in today’s vehicles, but it is not very good. The existing warning system is only based on the amount of compressed air produced by the compressor (which is controlled by the pressure in the pneumatic system). If the compressor is producing more air than what is considered to be normal, the driver receives a warning on the dashboard. There are two different degrees of the warning, depending on how much air is produced. This system is actually not designed to detect leakages, but to warn if the pneumatic system is under dimensioned relative to the vehicle and its applications. A leakage must therefore be extremely large to be detected by the current system.

This warning system only tells the driver that the compressed air usage is higher (or much higher) than normal. This might be because of a leakage in the system, but it is not for certain.

It could also be caused by the type of driving. For example, more air will be used if the driver

uses the service brakes more frequently than normal. Even other, less obvious, factors will affect the compressed air usage.

If the abnormal usage of compressed air is in fact due to leakages in the pneumatic system, the warning doesn’t give any information regarding where those leakages are most likely to be. This means that the mechanic has to search the entire system for leakages, which is of course not efficient.

These shortages of the existing warning system have created a demand for a more sophisticated one: a system that first of all provides reliable information about whether the system is leaking or not, but also provides information regarding where the leakages are most likely to be.

The first step towards such a warning system is a model for detecting/estimating leakages in the pneumatic system.

1.3 Task and Limitations

The aim for this thesis is to create a foundation for a more sophisticated warning system regarding leakages in the pneumatic system of heavy vehicles. This will be done by constructing a Simulink model for detecting those leakages. The model shall be able to provide information about whether the pneumatic system leaks or not, and if it does, it should be able to provide information regarding where the leakages are most likely to be.

To be able to use the model in the vehicles, to detect leakages while driving, the model must be compatible with the software used in the vehicles and built to operate in real time. This is, however, not part of the task. Instead, the task is limited to construct a model which detects leakages in the pneumatic system based on stored data.

The model should be able to estimate where the leakages are (or at least where they are most likely to be). This is a question which could be answered with various precision. For this thesis, the model requirements are limited to provide information regarding which of the five compressed air circuits are most likely to leak. Estimating exactly where the leakages are, within the circuits, is not part of the task.

In conclusion, the task is to construct a Simulink model which, based on stored data information, tells if the pneumatic system is leaking, and in that case, in which of the five different compressed air circuits the leakage is most likely to be.

Available information to be used as input to the model is all information communicated at the

vehicles’ CAN, the local network within the vehicles. This information consists of various

data regarding the driving characteristics and the current state of the vehicle.

2 Theory 1: The Pneumatic System of the Vehicle

This chapter will provide brief overlooking information regarding the pneumatic system in general, and more detailed information regarding those parts considered more relevant for this specific thesis.

2.1 Overview of the System

The pneumatic system of the vehicle consists of all parts producing, distributing, storing or consuming compressed air. Figure 2.1 shows a simplified model of the entire system. Fresh air enters the system and goes straight to the compressor. From the compressor (which compresses the air) the air flows via the APS and the tanks and ducts to the compressed air users. After or during the usage the compressed air leaves the system. In a perfect system the air only leaves through the compressed air users or through the purge valve during regeneration (regeneration will be explained later in this chapter). A perfect system, however, only exists in theory, meaning that there will always be some leakages. These leakages may occur at any part of the system.

The heart of the system, the compressor and the APS, is usually placed near by the engine.

The entire system though, because of the placement of the compressed air users, covers practically the entire vehicle. Figure 2.1 only shows the logic of the system. The physical placement of and distances between different parts are hence not taken in consideration. How the system actually appears on the vehicle is not considered relevant information for this thesis.

After the APS, the air enters one of five different compressed air circuits, each with its own sphere of responsibility. Circuit E21 supplies the rear service brake with air, circuit E22 the front service brake, circuit E23 the parking brake and trailer, circuit E24 the auxiliaries and circuit E25 the ELC. As seen in figure 2.1, circuits E21, E22 and E23 contain tanks for storing the compressed air, whereas circuits E24 and E25 connect the compressed air users straight to the APS (in some vehicles, also E25 contains tanks). Of course, some air will be stored in the ducts, but this is a small amount compared to the tanks.

2.2 The Compressor

The function of the compressor is to supply the pneumatic system with compressed air, to

maintain the pressure in the system at a point where the applications using compressed air

function as well as required. The compressor only has two states, active and inactive, meaning

that the rate at which compressed air is produced when active is not possible to control

directly. The amount produced is however not constant, but dependent on the current engine

speed and the pressure in the system. The dependence on the engine speed is directly

proportional. The dependence on the system pressure is not completely proportional, but it is

quite linear in the region of interest. The relative compressed air production (at 10 bar it is

100%) is known for some values of the pressure (and the rest can be obtained approximately

by interpolating).

Figure 2.1 – An example of a pneumatic system of a vehicle, block diagram.

The compressor is controlled by the APS using a quite complex logic. A simplified description is that it is turned on when the system pressure falls below a certain predefined limit, and turned off when the system pressure reaches another predefined limit. This logic gives the amount of air in the system an approximately periodical variation, which is easily observed in figure 2.2. Another observation from figure 2.2 is that the limits at which the compressor is activated and deactivated varies. This limit is dependent of the current state of the vehicle (and the load on the engine).

The length of the inactive periods is of course related to the usage of compressed air, and varies from a couple of seconds to a couple of minutes. The usage itself is related to the type of driving and, possibly, to leakages.

Figure 2.2 – Total amount of air in system (blue line) and compressor status (red line).

2.3 APS

The APS has three functions, to dry the compressed air, to distribute the compressed air and to control the compressor. The APS also contains devices to measure the pressures in circuits E21, E22 and E23. (The APS will possibly, in a near future, also be able to measure the pressure in circuit E24). This information is communicated at CAN and used as input in the system developed in this thesis. Besides controlling the compressor and measuring circuit pressures, the APS can be divided into two parts, one drying the compressed air and one distributing the compressed air.

2.3.1 Compressed Air Dryer

It is important that the air entering the system is dry. Moister in the system is a safety issue,

especially during winter when it might freeze. To dry the air, a desiccant cartridge (DC) is

placed right after the compressor. The desiccant absorbs the moister while letting the air pass

through. After a while the desiccant will be saturated, meaning that it needs to be dried to function as required.

The desiccant is dried by letting air pass from inside the system, the back way through the DC, and out of the system carrying the moister. For every 10 litres dried by the DC, the DC needs one litre to be dried itself. To keep track of how much air is needed to dry the desiccant, and control when it should be dried, a counter called integrated desiccant use (IDU) is used.

IDU constantly add one to its count for every 10 litres of air entering the system, and subtracts one for every litre leaving the system through the DC. The relationship between IDU, compressor status and regeneration status is presented in figure 2.3. Regeneration occurs when the IDU reaches a certain predefined limit, which is set to regenerate quite long before the desiccant gets saturated. This limit is however dependent of the current pressure in the system in order to secure the system pressure before regenerating. Hence, when the system pressure, for some reason, is low even though the compressor has been active a lot lately, regeneration will not occur.

Figure 2.3 – IDU, compressor and regeneration status.

The regeneration is managed by opening the purge valve (PV), which is placed on a duct connected on the duct connecting the compressor and the DC (see figure 2.4). When the PV is open, air will automatically, due to the pressure, leave the system this way.

2.3.2 Compressed Air Distributor

After getting dried, the air enters the multi-circuit protection valve (MCPV). The MCPV is

responsible for distributing the air to the five different circuits. It contains one pressure

limiter, five charge valves and three bypass bleeds. These are organised in a quite complex logic, presented in the block diagram in figure 2.4.

The pressure in the system depends on the usage, the compressor and the regenerations. It usually varies between around 10 and 12 bars. Circuits E23 and E24 contains devices which may break, or not function as required, at these high pressures. Therefore, the inflow to these circuits is equipped with a pressure limiter, limiting the pressure in the circuits to a maximum of 8.5 bars.

To avoid a situation where a major leakage in one of the five circuits also affects the supply pressure in the rest of the circuits, the inflow to all circuits are controlled by charge valves.

When open, air can pass through a charge valve in either direction. If the pressure in a circuit falls below a certain level, the charge valve closes, thus preventing more air to enter that circuit. If the pressure decay is caused by a leakage, this prevents the air in the other circuits to leave the system in the same leakage. This means, for example, that a huge leakage in circuit E21, making the rear service brake unusable, will not affect the performance of the front service brake.

Figure 2.4 – APS block diagram

The charge valve on the inflow to circuit E23 is also controlled by an additional logic; it is

only open when the sum of the pressures in circuit E21 and E22 exceeds 7.2 bars. This is a

safety precaution. If the vehicle has been standing unused for a while (over a night for example) even a small leakage may cause the system pressure to drop to low levels. When this happens, the applications using compressed air will not fully function. This can be problematic if it affects critical applications, for example the service brakes. The charge valve makes sure that, when starting the car with empty compressed air tanks, the service brakes circuits (E21 and E22) will charge before the parking brake circuit (E23). Since the parking brake needs compressed air to be released (this will be explained in greater detail later in this chapter), this means that it is impossible to release the parking brake before the supply pressure is high enough to operate the service brake. It is thus not possible to start driving before the service brakes start working.

The bypass bleeds are open all the time, but limits the flow rate and some of them only let air pass in one direction (according to the arrows in figure 2.4). The function of the bypass bleeds parallel to the charge valves in circuits E24 and E25 is to assure that there is some pressure in the system, even when the charge valve is closed. The one connecting E23 to E22 is a safety precaution. If the pressure in E22 is lower than the pressure in E23, this will even out. The reason for this is that the supply pressure in E22 is more critical to the vehicle than the one in E23.

Figure 2.5 – Pressures in circuits E21 and E25, indicating pressure compensation.

In a normal state, when all charge valves are open, all circuits are connected to each other

through open ducts. This means that pressure decay in one of the circuits will be compensated

by the other circuits, and the pressures in all circuits will follow each other. This is easily

observed in figure 2.5, showing pressure in circuits E21 and E25 over time. Even though the

pressures may appear to be identical, they are actually not. The small difference between them

is caused by the time the pressure compensation takes.

2.4 Compressed Air Users

When leaving the APS, the compressed air enters one of the five different circuits, whose function is to supply one or more of the compressed air users. To understand how the compressed air usage depends on the compressed air users, it is necessary to understand how they work and how they use compressed air.

2.4.1 Service Brakes

Circuit E21 supplies the rear service brake whereas circuit E22 supplies the front service brake. Since the rear and front service brakes work analogous, they will be described together.

Scania vehicles use drum or disc brakes. The basic idea is that a brake shoe is pressed against the inside of a spinning drum/disc (in the wheel), adding friction and creating a deceleration.

Compressed air is used to manage the brake shoe. When the brake pedal is pressed down, a valve opens letting compressed air to flow into the brake chamber. When the pressure in the brake chamber rises it pushes the brake shoe against the spinning drum/disc. Figure 2.6 shows the pressure in circuit E21 (rear brake) before, during and after braking.

Figure 2.6 – Pressure in circuit E21 (blue line) and service brake status (red line).

Given that no leakages exist, air will only leave the system through the service brakes when

the brakes are released, i.e. when brake pedal is released after being pressed down. The small

decrease in pressure when the brake is not activated seen in figure 2.6 might be caused by a

leakage, pressure compensation to other circuits, or a combination of them both.

2.4.2 Parking Brake / Trailer

Circuit E23 supplies the parking brake and trailer (when one is attached) with compressed air.

They work and use compressed air differently and will thus be described separately.

2.4.2.1 Parking Brake

The parking brake works in the opposite of the service brakes. Instead of using compressed air to brake it needs compressed air not to brake. This works mechanically by a brake shoe attached to a spring. The spring presses the brake shoe against the wheel unless a chamber is filled with compressed air pushing it back. This makes it impossible to release the parking brake without enough pressure in the system, as described in section 2.3.2. This also makes a leakage in the system not affecting the parking brake while the vehicle is standing unused.

Figure 2.7 shows the pressure in circuit E23 when the parking brake is switched on and off.

Figure 2.7 – Pressure in circuit E23 (blue line) when parking brake is activated and deactivated (red line).

When released, it is obvious that the pressure will decrease. This is easily observed in figure 2.7. From inspecting figure 2.7, it is also apparent that there is a small decrease in pressure when the parking brake is switched on. This is caused by the trailer as described below.

2.4.2.2 Trailer

If a trailer is attached to the vehicle, this will also be supplied with compressed air by circuit

E23. The trailer uses compressed air mainly for its service brakes, which work analogous with

the service brakes of the vehicle. Some trailers, mainly outside Sweden, are also equipped

with parking brakes. The trailer service brakes can be controlled in two ways, by the brake

pedal, in which case both vehicle and trailer brake, and by a special trailer brake switch, in

which case only the trailer brakes.

The trailer is connected to two compressed air ducts. One of them is used to supply the applications with compressed air, called the feeding part, and the other is used to control the applications, called the operating part. For example, when using the service brakes, a valve has to be opened to let air flow from the feeding part into the brake chamber. This valve is opened by a compressed air signal through the operating part. The operating part works regardless if a trailer is attached or not. This is the reason for the small decrease in pressure when the parking brake is switched on, as seen in figure 2.7, even though no trailer was attached.

Just like the service brakes and the parking brake on the vehicle, no air is used unless the service brakes are used or the state of the parking brake is changing. It is possible, however, for a trailer to use compressed air for more applications than the brakes, for example air suspension. Because of the fact that trailers are being swapped between drivers, the information about the trailer and its compressed air usage is usually limited. But given that no leakages exist, the trailer air consumption should be low except for when braking.

2.4.3 Auxiliary Equipment

Circuit E24 supplies the auxiliary equipments with compressed air. Auxiliary equipments include the applications not included in the other circuits, with the common characteristic that their compressed air consumption is quite limited. The different applications will be described separately.

2.4.3.1 Engine

The engine uses compressed air to a number of applications. It has three compressed air controlled dampers; one controlling the exhaust gas brake, one controlling the exhaust gas recirculation (EGR damper) and one controlling the fresh air inflow (to avoid cooling down the engine more than necessary). It uses compressed air to dose the reducing agent to lower the amount of NO x in the exhaust gas (called selective catalytic reduction technology or SCR technology). It also uses compressed air to clean the diesel particulate filter. This is, however, limited to around 20 minutes every other day.

The engine application using most compressed air is the NO x reduction. This is constantly activated and the usage is not directly related to any driving characteristics. Overall, the compressed air usage by the engine is quite constant.

2.4.3.2 Cab suspension

The cab suspension consists of air bellows attaching the cab to the chassis. The compressed air works as a spring reducing the bounces. For the suspension to function as good as required, the bellows need to be kept at a certain level (height). Therefore, the bellows contain valves connecting them to circuit E24. The valve opens, letting more compressed air into the bellow, if the bellow level falls bellow a certain limit. If the bellow rises over another limit the valve opens, letting air out of the bellow. The valve is mechanical, meaning that there is no dynamic in the control of the bellow level. Hence, when for example driving on a bumpy road, there will flow air through the valve, with changing direction, almost constantly.

Nevertheless, the compressed air usage of the cab suspension will in general be low and quite

constant over time. Even when driving on a bumpy road, the usage is not big enough to

observe just by inspecting a pressure graph of the entire circuit.

For the comfort of the driver and passenger (if any), the seats are equipped with their own additional suspensions.

2.4.3.3 Clutch

When the clutch pedal gets pressed down, a valve is opened letting compressed air in to a cylinder, pushing the clutch lever arm forward. Figure 2.8 shows the pressure decrease in circuit 24 when the clutch pedal is pressed down. It is apparent that the decrease is momentarily when pressing it down, i.e. the compressed air usage is independent of how long the clutch switch is pressed down.

Figure 2.8 – Pressure in circuit E24 (blue line) when clutch pedal is pressed down (red line).

2.4.3.4 Air horn

Some vehicles are equipped with horns using compressed air. The usage is limited to when the horn is used, which is usually quite rarely, and even then the air amounts are not considerable.

2.4.4 ELC

Circuit E25 supplies the air suspension, also called electronic levelling control (ELC). Just like the cab, the entire vehicle rests on air bellows. These are located between the wheel axles and the chassis. The ELC has two functions; besides damping bounces it also makes it possible to lift or lower the vehicle.

Just like for the cab suspension, the bellows need to be kept at a certain level, but the control

mechanism differs. The ELC uses an electronic control, with the deviation from the normal

level integrated over the last minute as input. This gives a smoother control and lowers the

compressed air usage. It also makes the usage more constant over time. Theoretically, more air will be used when driving on a bumpy road. This is, however, not something that could be observed by inspecting a pressure graph.

Figure 2.9 – Pressure in circuit E25 (blue line) when vehicle is lifted (red line).

The vehicle can be lifted or lowered using the ELC. This is done by letting air flow into the bellows (to lift the vehicle) or by releasing air from the bellows (to lower the vehicle).

Lowering the vehicle only affects the air in the bellows, i.e. the system pressure remains the same as before. Lifting the vehicle, on the other hand, requires a quite large amount of air.

This is easily observed by inspecting figure 2.9. After the lift in figure 2.9, the pressure rises to a bit below the level before the lift. This is so because of pressure compensation from the other circuits.

2.5 Leakages in the Pneumatic System

Leakages in the pneumatic system might differ a lot from each other. The type of leakage can be described using two characteristics, how it develops and when it affects the system. For the first characteristic there are two options. The leakage may occur suddenly (a fast development), or it may slowly become bigger and bigger (a slow development). For the second characteristic, there are also two main options. The leakage may affect the system constantly (leak all the time) or only in some special situations (for example only when the service brakes are active or while driving on a bumpy road). Of course a leakage could have the characteristics of any combination of these four options.

2.5.1 Fast Leakages and Slow Leakages

Fast leakages might occur, for example, at the workshop when work is done to the vehicle or

while driving if hitting a bump or something equivalent. This kind of leakages is less common

than the slow ones. They are also in general easier to detect. If they occur while driving (given that the leakage is big enough) the driver will most often notice them immediately.

Slow leakages might occur, for example, when a valve or gasket has gotten old. This kind of leakages is both more common and harder to detect than the fast ones. The development of the leakages might take days or even weeks, which of course makes it (practically) impossible for the driver to detect them. A leakage is affecting the fuel usage even if it causes a quite small waste of compressed air compared to the air usage of some the applications. A leakage is considered important to fix when it reaches a leaking rate of around ten litres per minute.

This could be compared to the usage during a full power brake, which is around 25 litres per axle. It is obvious that this calls for a quite sophisticated leakage detection system.

2.5.2 Leakages Affecting the System in Different Situations

As stated above, a leakage may affect the system either constantly or in some special situations only. The more common of these two cases are leakages affecting the system constantly. Leakages affecting the system constantly will also, obviously, cause a bigger compressed air waste and will hence have a bigger effect on the fuel usage (given that it is compared to a special situation leakage of similar size). When considering the aforementioned comparison between a leakage and a full power brake, it is easy to understand that a normal size leakage only affecting the system in some special situations will not cause any big problems.

2.5.3 Common Leakage Locations

Leakages can of course occur anywhere in the system, but some circuits and applications are more prone to leak than others. The circuit most often suffering from leakages is the auxiliary equipment circuit (E24). This is because it contains so many different applications (the risk of leakages is increasing with the number of components), and they are located in different environments (for example, heat will affect the applications in the engine). One of the more common applications to leak is the seat suspension.

2.6 CAN

The controller area network (CAN) is a local network used for communication between the different components and control units within the vehicle. The communication is event driven and uses a priority system. CAN is standard in the vehicle industry, hence it is not only used by Scania.

The CAN messages are binary vectors which follow a distinct structure consisting of three

parts, the header, the data field and the end of frame. The header consists of 29 bits including

information about priority, message type (identifier) and source address. The data field

consists of 64 bits which carries the actual information of the message. The end of frame

contains 15 bits which distinguishes the end of the message, and includes a cyclic redundancy

check. Even though the messages always follow this structure, the binary vector itself can be

longer due to bit stuffing. Bit stuffing is a security check meaning that a one is automatically

inserted after five consecutive zeros, and vice versa. This means that six consecutive ones or

zeros is considered a signal error. The inserted bits do not carry any information (other than

confirming the validity of the signal) and is automatically terminated by the reader while

decoding.

For the information in the data field to be usable, the reader must understand what it means.

That is why the identifier is there. Every message type has its own identifier code. The identifier should tell what every single one of the 64 bits in the data field stands for. This is done by a general convention of the identifier codes.

The convention used by Scania is built on the one presented by the SAE-J1939 (the society of automotive engineers - truck bus control and communications network subcommittee), which is standard in the heavy vehicle industry. This convention consists of around 400 messages, of which Scania uses the majority. In addition to these messages, Scania also uses some own designed messages which are not in SAE-J1939.

In Scania trucks CAN is divided into three smaller local networks, red CAN, yellow CAN and green CAN. This breakdown is based on the importance of the communicated information.

Red CAN carries the most critical information, for example information regarding the engine and the gearbox system. Green CAN carries the least critical information, for example information regarding distance sensor and the automatic climate control. Yellow CAN is right between red and green regarding importance.

Besides the aforementioned breakdown, every message also gets classified into one of two internal priority categories. The messages are labelled 3 for control (high priority) or 6 for information (low priority). If a control message and an information message are trying to use the same band with at the same time, the control message will be sent and the information message will be held. The information will still be sent but maybe a bit later than what was intended.

Since there are a lot of different applications in the vehicle using compressed air, there are a lot of different messages containing information concerning the pneumatic system. For example, the APS and the suspension management system are part of the yellow CAN, whereas the brake management system is part of the red CAN.

As said before, the communication on CAN is event driven. All messages, however, have

upper and lower limits on the time between two messages are sent. For some messages these

two limits coincide, meaning that the message is sent at a constant rate. The messages that

will be used in this thesis are all sent at a constant rate of 10 Hz.

3 Theory 2: Scientific Framework

This chapter contains a review of the theoretical framework needed to complete the task for this thesis. Since detecting leakages in the pneumatic system is to detect changes in the system, change detection theory is considered a crucial concept. To fully use the theory of change detection, and to be able to customize the algorithms for this specific task, an understanding of some basic statistics will also be needed.

3.1 Change Detection

This part will mainly be focusing on the parts of the theory needed for this specific thesis. For a deeper and more general review, see Gustafsson [3].

3.1.1 Basic Algorithms

Detecting changes in some system is to detect when the system deviates from its normal state.

This can be done by either signal estimation, parameter estimation or state estimation. In this thesis, signal estimation will be used. This means that some output signal from the system is measured to see when it deviates from its normal state. A basic assumption made when using this method is that the output signal can be represented as a sum of a deterministic part (the actual signal) and a stochastic part (white noise)

(3.1)

A common approach to signal estimation is to use an adaptive filter transforming the signal into a sequence of residuals. The sequence of residuals should resemble white noise. For this reason, the filter is also called a whitening filter. When the system changes this sequence will change, meaning that either the mean or variance (or both) will change. Unless the change is that the variance is smaller (which is unlikely), the signal (or at least its absolute value) will be larger.

Due to the noise it is not always trivial to detect when the signal has become larger. The change detection algorithm will therefore need some predefined rule about when to send an alarm that a change has occurred, i.e. a stopping rule. Two ways of doing this is the cumulative summation (CUSUM) test and the geometric moving average (GMA) test.

The CUSUM test is based on the recursive algorithm (3.2). The idea is that all samples that deviate from what is considered to be normal (which is zero due to the whitening filter) are summarized. An alarm is sent if/when this sum (i.e. g t ) exceeds some predefined threshold h.

(3.2)

! t is called a drift parameter and is used to prevent a positive random walk caused by the white noise. s t is the tested variable, if the aim is to detect changes in the mean value it equals the residual itself.

The GMA test is also based on a recursive function and just as in the CUSUM test an alarm is

sent if g t exceeds some predefined threshold h (i.e. if some average of the latest samples are

too far away from what is considered to be normal, which is zero due to the whitening filter).

(3.3)

" is called the forgetting factor and decides the shape of the moving average window (i.e. how the samples used to compute an average are weighted), it can be set to any value between 0 and 1. s t is the same as above.

3.1.2 Parameter Tuning

An important part in both the CUSUM and the GMA tests is to set the threshold value h. This will decide how sensitive the system is when detecting changes. A low value of h will ensure that most of the changes will be detected in good time, but at the same time the risk of sending false alarms will be high. A high value of h will lower the frequency of false alarms, but at the same time the risk of not detecting real changes (or detecting them only after a long time) will be high.

The tradeoff between detecting real changes and avoiding false alarms is called the fundamental limitation of change detection [3]. In some situations, a false alarm will be no big deal whereas not detecting a real change would be catastrophic, and in some situations it will be the other way around. h must therefore always be chosen specifically for the current conditions and circumstances. The same also holds for the other design parameters, " and !.

There are two common measures to evaluate the performance of the test. The first one is called mean time between false alarms (MTFA) and measures how often false alarms occurs on average. The second is called mean time to detection (MTD) and measures the average time from a system change until the alarm is sent. When designing a change detection test usually one of these (the most crucial one) is set to a satisfying level and then the algorithm is chosen and the parameters are tuned to minimize the other one.

3.2 Statistics

As in the previous section, this part will mainly be focusing on the parts of the theory needed for this specific thesis. For a deeper and more general review, see for example Blom and Holmquist [1] and Blom [2].

3.2.1 Regression analysis

Regression analysis is a statistical method used to examine and describe dependencies between one dependent variable and one or more independent variable(s), by using a sample from an observation. This is done by modelling a curve (i.e. a mathematical function) that fits with the observed sample, also called curve fitting. The most common approach to this is the least squares method. The idea is to find the function that minimizes the squares of the vertical distances between the function and the sample points, mathematically expressed as

!

c min

,...,c

( y i ( ) ^{" f x} ( 1 ( ) i ^{,..., x} k ( ) i ^,c 1 ,...,c _m ) ) ²

i=1 n

$ #

% & '

( ) (3.4)

In (3.4), variables c 1 to c m are the constants (parameters) in the function f. y i is the value of the

dependent variable in sample point i, whereas x1 i to xk i are the values of the independent

variables in the same sample point. n is the number of sample points, m is the number of parameters in f and k is the number of independent variables. The format of function f must always be decided before numerically computing the values of the parameters. The function f can take any form (polynomial, trigonometric, exponential etc.)

A special, and maybe the most common, case is when there is only one independent variable and f is a polynomial of degree one (hence m equals two and k equals one in (3.4)). This special case is called a simple linear regression, and the least squares method equation looks like

(3.5)

Even if the relationship between two variables is not linear, a linear regression analysis can provide some useful information. For example it can tell if a growth (decrease) in one variable leads to a growth or decrease in the other. The method is thus widely used.

Another common special case is when the independent variable (x) is some time measurement. The analysis will then give information about the variable’s tendency (growth or decrease) during the measured time span. In this special case the regression is a form of time series analysis.

3.2.2 Hypothesis Testing 3.2.2.1 General Hypothesis Testing

Hypothesis testing is a statistical method for making decisions regarding some measured variable. From this variable a test statistic (denoted T) is defined. The test statistic may for example be the mean or variance of the data sample obtained when measuring the variable of interest. Besides T, the foundation is two hypotheses regarding T, the null hypothesis (denoted H 0 ) and the alternative hypothesis (denoted H 1 ). H 0 and H 1 have to deviate from each other, but they do not need to be each others exact opposites.

A hypothesis test always focuses on H 0 , which is the only of the two hypotheses that is actually tested. The test is conducted by forming a critical region (denoted c, sometimes also called rejection region) for the test statistic T. If T is part of c, then H 0 is rejected with some predefined level of certainty. Since H 0 and H 1 do not need to be each others exact opposites, rejecting H 0 does not necessarily imply that H 1 is true. It only means that H 1 might be true.

Analogously, not rejecting H 0 does not necessarily imply that H 1 is false (and hence neither that H 0 is true). In conclusion, not rejecting H 0 does not provide any new information. Of course, this situation differs a bit in the special case when H 0 and H 1 are each others exact opposite (when (3.7) is true).

(3.6) If (3.6) is true, then:

• H 0 is rejected => H 0 is not true (with some predefined level of certainty), H 1 might be

true but it is not implied.

• H 0 is not rejected => Either of H 0 and H 1 (but not both at the same time) might be true but it is not implied (no new information).

(3.7) If (3.7) is true, then:

• H 0 is rejected => H 0 is not true, H 1 is true (with the same predefined level of certainty).

• H 0 is not rejected => H 0 or H 1 (but not both at the same time) is true (no new information).

Given that H 0 can be either true or false (the correct value, not the calculated) and that it could be either rejected or not rejected, there are in total four different outcomes of a hypothesis test. These are summarized in figure 3.1.

Figure 3.1 – Possible outcomes of a hypothesis test

As seen in figure 3.1, there are two different types of errors. Type one error is to reject H 0

when it is in fact true. A type two error is to not reject H 0 when it is in fact false. The predefined level of certainty mentioned earlier is set to get the probability of either of these errors below a desired value. The probability of a type one error is denoted # whereas the probability of a type two error is denoted $.

The probability of a type one error, #, is called the significance level of the test and is usually the fixed parameter when constructing the test (this is because $ is often much more complex to deal with than #). # is quite often set to one of the values 0.05, 0.01 or 0.001. It is not, however, necessary to use one of these standard values. Instead # should be chosen to suit the current conditions of the test situation. The probability of correctly rejecting H 0 (i.e. one minus $) is called the power of the test. Notice that a high test power corresponds to a low probability of a type 2 error.

! = P(type I error) (3.8)

" = P(type II error) (3.9) 1- " = test power (3.10)

Typically, it is considered more important to have a low significance level than a high test

power. This is caused by the fact that not rejecting H 0 does not provide any new information,

and that it is usually worse to say something that is incorrect than to say nothing at all. If #,

however, is set to a value arbitrarily close to zero, H 0 will never be rejected and the test would

be useless.

Choosing # is thus always a tradeoff between the probability of a type one and a type two error, respectively. In that sense, choosing # reminds a lot of choosing the parameters in the change detection algorithms described in section 3.1 (the fundamental limitation of change detection).

Another alternative is to calculate the value of the test statistic first, and then use this to derive a threshold value (usually called p-value) of # for when H 0 would be rejected or not. The p- value gives information of for what significance level H 0 can be rejected. In some sense this gives more information. But most of the time a yes or no answer (whether or not to reject H 0 ) is of more interest, and then a value for # must be decided.

3.2.2.2 Normal Approximation and the Central Limit Theorem

For many statistical methods it is a requirement that, and in some situations when it is not a requirement it makes calculations easier if, the examined variable follows a normal distribution (sometimes also called Gaussian distribution). The normal distribution depends on two parameters, the mean (denoted µ) and the variance (denoted % ² ). The distribution (denoted N(µ, % ² )) has the following probability density function, where x is the variable. This is also shown in figure 3.2.

(3.11)

The probability density function (3.11) appears quite complex and it is hard to intuitively see that any process should follow this distribution. Nevertheless, the normal distribution is very useful. This is because of the central limit theorem, as stated below.

The sample mean of any set of random variables, that is independent and identically distributed with finite mean and variance, will converge to a normal distribution as the sample size goes to infinity. [2]

More precisely, if the variables follow any distribution with mean µ and variance % ² , the sample mean will converge to a normal distribution with mean µ and variance % ² /n (i.e. N(µ,

% ² /n)), where n is the sample size.

The central limit theorem thus says that the sample mean of any set of variables that is independent and identically distributed (usually noted iid) can be approximated as normally distributed, given that the sample size is sufficiently large. This is a very useful theorem. The main problem while using it is to know what sufficiently large means. This will vary from situation to situation and is of course dependent of the required accuracy. It can sometimes also be difficult to decide whether two measurements are independent or not. Even in situations where it is not clear that the measurements are totally independent or that the sample size is big enough, normal approximation is often implemented due to lack of alternatives.

3.2.2.3 The Student t-test

The student t-test is a type of hypothesis test where the null hypothesis H 0 is that two different

samples, both assumed to be normally distributed, come from the same distribution

H 0 : X 1 = X 2 , H 1 : X 1 # X 2 (3.12)

The t-value computed in the test (equation (3.13)) follows the t distribution. The t distribution is very similar to the normal distribution, but with the difference that it is applied as an approximation when the theoretical variance is unknown.

In (3.12), X 1 and X 2 are the theoretical means of the distributions of the samples {x 11 ,…, x 1n } and {x 21 ,…, x 2m }. H 1 does not necessarily need to be that X 1 is unequal to X 2 (as in (3.12)), it could also, for example, be that X 1 is less than X 2 or that X 1 is greater than X 2 . H 0 is usually rewritten to X 1 – X 2 = 0, which makes the difference between the sample means the test statistic. The first part of the test is done by computing

(3.13)

In (3.13), the numerator is the difference between the two sample means (i.e. the test statistic).

In the denominator, s ² denotes the sample variances and n denotes the sample sizes. The t- value in (3.13) corresponds to a p-value described in section 3.2.2.1. In contrast to the normal distribution, however, the t-distribution is depending on one more parameter, the degrees of freedom (denoted !). ! is computed by

(3.14)

Notice that the degrees of freedom always should be an integer, meaning that the value obtained in (3.14) has to be rounded (it is usually rounded downwards). After computing t and

!, the corresponding # is obtained from either the probability density function of the t- distribution, or straight from a table. Since the probability density function is quite complex, the later is usually to prefer.

The shape of the probability density curve of the t-distribution reminds a lot of the one of a normal distribution. The difference is that the t-distribution is more spread out. When the degrees of freedom go to infinity, however, the t-distribution will converge to a normal distribution, as shown in figure 3.2.

The degrees of freedom is increasing when the sample sizes are increasing, it is not dependent

of the magnitudes the variances but the relationship between them. This is easily seen in

equation (3.14) if dividing both nominator and denominator with either s 1 4 or s 2 4 . The degrees

of freedom parameter should be interpreted as a rectification of the probability density

function (and hence the critical region) due to the fact that the variances are unknown. The

PDF will be more spread out and the critical region smaller (hence the complement to the

critical region, the region where H 0 is not rejected, will be larger). As the sample sizes go to

infinity, the sample variances will converge to the theoretical variances of the distributions (given by the law of large numbers), and ! will go to infinity. When ! goes to infinity, the t distribution will converge to a normal distribution and the critical region will thus converge to one constructed with known theoretical variances.

Figure 3.2 – Probability density function plots for t and normal distributions

As mentioned earlier, the t-value calculated in (3.13) corresponds to a p-value. This means that the # obtained with it is a threshold value for on what confidence level H 0 could be rejected. The critical region for the test statistic (i.e. the difference between the two sample means), given a predefined #, is computed by

(3.15)

It is easy to see that equation (3.15) is derived from equation (3.13). To compute the critical

region, the first step is to calculate ! with equation (3.14). Then ! is used together with the

predefined # to get t. When t is obtained, equation (3.15) can be computed.

4 Solution Logic

This chapter describes how the theory reviewed in chapter three has been applied to solve the specific task of this thesis. First is a description of the assignment, a bit more detailed than the one in the introduction chapter. The rest of the chapter will contain a review of the logic of how the assignment has been solved, i.e. the logic of the system. The last part of the chapter contains a brief summary of the system logic and a review of the system limitations and shortcomings. A description of how the model has been implemented in Simulink is presented in appendix I.

4.1 Assignment – Extended Description

The assignment is to create a Simulink model which shall be able to detect leakages in the pneumatic system of Scania vehicles. The model should also be able to say in which of the five circuits the leakage is most likely to be.

As stated in chapter one, the assignment is limited to create a model which uses stored data as input. However, in the end the goal is to be able use the model on vehicles operating in real time. This means that, even though it is not part of this thesis to make it work in real time, the model should be made so that its logic could be a foundation for a model working in real time.

A necessary requirement for the model is thus to be causal (which is not a necessary requirement when using stored data). Another, more interesting, aspect is the computational power required when using the model. Since there are a lot of different control units in the vehicle, and since there is a limited computational power, this is a crucial aspect. For this assignment, there is no predefined upper limit for the computational power required to use the model. Instead, the aim is to try to keep this number low, without negatively affecting the performance of the model.

As mentioned in chapter three, the accuracy of a change detection model will always be a trade off between some fundamental performance measurements. In this case it will mainly concern how big changes have to be to be detected, how fast they will be detected and the probability of sending false alarms (and also, when it is taken under consideration, the computational power required to run the model). Since leakages are considered important to fix when they reach a leakage rate of about ten litres per minute, the goal is to make the system accurate enough to detect leakages of this size.

In section 2.5, some different kinds of leakages were mentioned. The first distinction was whether the leakage develops suddenly or slowly. For this assignment, the slowly developing leakages are considered most important to detect. This is because they are more common and usually harder to detect. A system able to detect slowly developing leakages is probably also able to detect faster developing leakages. The main focus when tuning the parameters will thus be to detect the slowly developing leakages. The second distinction was whether the leakage affects the system constantly or only in some special situations. The only leakages not affecting the system constantly that is considered important to detect are those only affecting the system while the compressor is active. The other special cases are considered less important because the amounts of air lost through them are usually quite low in comparison.

What pressure measurements are available at CAN is stated in section 2.3. Since the system

developed in this thesis will not be implemented in the vehicles very soon (if it will be