a diagnostic system for air brakes

360 IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS, VOL. 7, NO. 3, SEPTEMBER 2006

A Diagnostic System for Air Brakesin Commercial Vehicles

Shankar C. Subramanian, Swaroop Darbha, and K. R. Rajagopal

Abstract—The safe operation of vehicles on roads depends,among other things, on a properly functioning brake system.Air brake systems are widely used in commercial vehicles suchas trucks, tractor-trailers, and buses. In these brake systems,compressed air is used as the energy transmitting medium toactuate the foundation brakes mounted on the axles. In this paper,a model-based diagnostic system for air brakes is presented. Thisdiagnostic system is based on a nonlinear model for predictingthe pressure transients in the brake chamber that correlates thebrake chamber pressure to the treadle valve (brake applicationvalve) plunger displacement and the pressure of the air suppliedto the brake system. Leaks and “out-of-adjustment” of push rodsare two prominent defects that affect the performance of the airbrake system. Diagnostic schemes that will monitor the brakesystem for these defects will be presented and corroborated withexperimental data obtained from the brake testing facility.

Index Terms—Air brakes, commercial vehicles, fault diagnos-tics, modeling.

I. INTRODUCTION

ONE of the most important systems in a vehicle thatprovides for its safe operation is the brake system. In

this paper, we shall focus on air brake systems that are widelyused in commercial vehicles such as trucks, tractor-trailer com-binations, and buses. In fact, most tractor-trailer vehicles witha gross vehicle weight rating (GVWR) of over 19 000 lb, mostsingle trucks with a GVWR of over 31 000 lb, most transit andintercity buses, and about half of all school buses are equippedwith air brake systems [1]. It has been well established that oneof the main factors that increases the risk of accidents involvingcommercial vehicles is an improperly maintained brake system.For example, a report published in 2002 [2] points out that brakeproblems have been observed in approximately 31.4% of theheavy trucks involved in fatal accidents in the state of Michigan.In roadside inspections performed between October 1996 andSeptember 1999, 29.3% of all the vehicle-related violationsamong intrastate carriers and 37.2% of those among interstatecarriers have resulted due to defects in the brake system [3].

In the United States, one of the earliest air brake systemsfor trucks was developed by G. Lane in 1919 [4]. The initialair brake system consisted of storage reservoirs, control valves,and brake chambers. With time, the design of the air brake

Manuscript received September 30, 2005; revised February 23, 2006.This work was supported by the Southwest University Transportation Centerat the Texas Transportation Institute and the National Science Foundation.The Associate Editor for this paper was B. K. Johnson.

The authors are with the Department of Mechanical Engineering, TexasA&M University, College Station, TX 77843 USA (e-mail: [email protected]; [email protected]; [email protected]).

Digital Object Identifier 10.1109/TITS.2006.880645

system underwent modifications to include several featuressuch as foot-operated treadle valves, relay valves, spring brakechambers, tractor protection valves, and many more [4], [5]. Adescription of the modern air brake system including its variouscomponents and their functioning can be found in [4].

The air brake system currently found in commercial vehi-cles is made up of two subsystems, namely 1) the pneumaticsubsystem and 2) the mechanical subsystem. The pneumaticsubsystem includes the compressor, storage reservoirs, treadlevalve (or the brake application valve), brake lines, relay valves,quick release valve (QRV), brake chambers, etc. The mechani-cal subsystem starts from the brake chambers and includes pushrods, slack adjusters, S-cams, brake pads, and brake drums. Oneof the most important differences between a hydraulic brakesystem (found in passenger cars) and an air brake system isin their mode of operation. In a hydraulic brake system, theforce applied by the driver on the brake pedal is transmittedthrough the brake fluid to the wheel cylinders mounted on theaxles. The driver obtains a sensory feedback in the form of apressure on his/her foot. If there is a leak in the hydraulic brakesystem, this pressure will decrease and the driver can detect itthrough the relatively easy motion of the brake pedal. In an airbrake system, the application of the brake pedal by the drivermeters out compressed air from a supply reservoir to the brakechambers. The force applied by the driver on the brake pedal isutilized in opening certain ports in the treadle valve and is notused to pressurize air in the brake system. This leads to a lackof variation in the sensory feedback to the driver in the case ofleaks, worn brake pads, and other defects in the brake system.

Air brake systems can degrade significantly with use andneed periodic inspection and maintenance [6]. As a result, pe-riodic maintenance inspections are performed by fleet owners,and roadside enforcement inspections are carried out by stateand federal inspection teams. The performance requirements ofbrakes in newly manufactured and “on-the-road” commercialvehicles in the United States are specified by the Federal MotorVehicle Safety Standard (FMVSS) 121 [7] and the FederalMotor Carrier Safety Regulation (FMCSR) Part 393 [8], re-spectively. These regulations specify the stopping distance,deceleration, and brake force that should be achieved whenthe vehicle is braked from an initial speed of 20 mi/h. Due tothe difficulty in carrying out such tests on the road, equivalentmethods have been developed to inspect the brake system.A chronology of the development of the various commercialvehicle brake testing procedures used in the United States canbe found in [9].

Inspection techniques that are currently used to monitor theair brake system can be broadly divided into two categories,

1524-9050/$20.00 © 2006 IEEE

SUBRAMANIAN et al.: DIAGNOSTIC SYSTEM FOR AIR BRAKES IN COMMERCIAL VEHICLES 361

namely 1) “visual inspections” and 2) “performance-based in-spections” [10]. Visual inspections include observing the strokeof the push rod, thickness of the brake linings, checking forwear in other components, and detecting leaks in the brakesystem through aural and tactile means. They are subjective,time consuming, and difficult on vehicles with a low groundclearance since an inspector has to go underneath a vehicle tocheck the brake system. Performance-based inspections involvethe measurement of the braking force/torque, stopping distance,brake pad temperature, etc. A description of two performance-based brake testers—the roller dynamometer brake tester andthe flat plate brake tester—and the associated failure criteriawhen an air brake system is tested with them can be found in[11]. It is appropriate to point out that, in an appraisal of thefuture needs of the trucking industry [12], the authors call forthe development of improved methods of brake inspections.

In this paper, we present preliminary diagnostic schemes fordetecting leaks and “out-of-adjustment”1 of push rods in theair brake system. The presence of leaks and the push rodsbeing out-of-adjustment are two prominent defects that causedegradation in the performance of the brake system. Leaks inthe brake system are caused by the rupture of the brake chamberdiaphragm, defects in the brake chamber clamps, hoses, cou-plings, valves, etc. The stroke of the push rod increases due towear of the brake linings, heating of the brake drum, etc.

Detection of leaks is crucial to ensure the proper functioningof the air brake system. The response of the brake system willbe slower in the presence of a leak (i.e., the “lag time” willbe increased), and the resulting braking force generated will belower. These will, in turn, lead to increased stopping distances.The presence of leaks will lead to an increased air consumptionin the brake system. The compressor will be required to domore work than normal in order to maintain the supply pressurein the reservoirs in the presence of a leak, and this will leadto faster wear of the compressor and related components.These considerations become important when the brakes arefrequently applied, for example, when the vehicle is travelingdown a grade, in city traffic, etc.

The stroke of the push rod has to be maintained withina certain limit for the proper operation of the brake system.The fact that the brake force/torque output, and hence thebrake system performance, deteriorates rapidly when the pushrod stroke exceeds a certain length (usually referred to as the“readjustment limit”) has been well established and reported bymany authors [11], [13]–[16]. The stroke of the push rod is oneof the main performance criteria employed by the inspectionteams to evaluate the condition of the brake system. Excessivepush rod stroke has been found to be a major cause for brake-related violations, and vehicles with their push rod strokesabove the regulated limit will be placed out of service [10]. Ina safety study carried out by the National Transportation SafetyBoard in 1988 [17], it was determined that brakes being out-of-adjustment are one of the most prevalent safety issues inaccidents involving heavy trucks with brake problems.

1A push rod is said to be in “out-of-adjustment” when its stroke exceeds acertain length.

Motivated by these issues, we have developed preliminarymodel-based diagnostic schemes that detect leaks and estimatethe stroke of the push rod. We have developed an experimen-tally corroborated “fault-free” model that predicts the pressuretransients in the brake chamber of the air brake system [18].This model relates the pressure transients in the brake chamberwith the treadle valve plunger displacement and the pressure ofair supplied to the treadle valve. Our diagnostic schemes utilizepressure measurements and predictions of this model in orderto monitor the brake system for the defects mentioned above.The guideline issued by the Federal Motor Carrier SafetyAdministration (FMCSA) to check for the push rod stroke[19] states that “Stroke shall be measured with engine off andreservoir pressure of 80 to 90 psi with brakes fully applied.” Italso specifies the readjustment limits for various types of brakechambers. We have been developing our diagnostic schemes toconform to these regulations. Such an inspection procedure isalso recommended in air brake maintenance manuals [20].

Our long-term objective is to integrate these diagnosticschemes into a portable diagnostic tool that can be used tomonitor the performance of the air brake system and help inautomating the brake inspection process. Such a diagnostictool can be used for preventive maintenance by fleet ownersand drivers, and also for enforcement inspections by state andfederal inspection teams. Current brake inspection methodsrequire an inspector to get underneath the vehicle and checkfor push rod stroke, brake pad wear, leaks, etc. Such a diag-nostic tool will speed up the brake inspection process since,according to [21], the average time required for a typical currentroadside inspection of a commercial vehicle is 30 min, withapproximately half of the time spent on brakes. A reductionin the inspection time will result in reduced lead times ofthe vehicles and also smaller lines at the roadside inspectionstations. Also, fleet operators can ensure that the brake systemof their vehicles meets the required standards and thus reducesthe risk of their vehicles being put out of service. Defects inthe brake system can be identified and corrected immediately.An accident involving a commercial vehicle often results in theirreplaceable loss of life and is also monetarily expensive interms of loss of property. It is reported in [22] that, betweenthe years 1998 and 2002, an average of 5530 fatalities haveoccurred every year due to accidents involving commercialvehicles. In 2002, the average cost of an accident involvinglarge trucks was reported to be approximately $59 153 [23].Also, commercial vehicle accidents will have a negative impacton the economy since they constitute the single largest mode(in terms of monetary value) for transporting commodities inthe United States [24]. If the commercial vehicle involved in anaccident is transporting hazardous materials, the environmentalimpact would be tremendous, and there will be huge cleanupcosts associated with it. A well-maintained and diagnosed brakesystem will reduce the chances of occurrence of such accidents.

II. DESCRIPTION OF THE AIR BRAKE SYSTEM AND

THE EXPERIMENTAL SETUP

A layout of the air brake system found in a typical tractoris presented in Fig. 1. Compressed air is provided by an


Fig. 1. General layout of a tractor air brake system.

Fig. 2. S-cam foundation brake.

engine-driven compressor and is collected in storage reservoirs.A governor serves to control the pressure of the compressed airstored in the reservoirs. Compressed air is supplied from thesereservoirs to the treadle and relay valves. The driver applies thebrake by pressing the brake pedal mounted on the treadle valve.This action meters the compressed air from the supply portsof the treadle valve to its delivery ports from where it travelsthrough hoses to the brake chambers mounted on the axles.

The S-cam foundation brake, found in more than 85% of theair-braked vehicles in the United States [1], is shown in Fig. 2.Compressed air metered from the reservoirs enters the brakechamber and acts against the diaphragm, generating a forceresulting in the motion of the push rod. The motion of the pushrod serves to rotate, through the slack adjuster, a splined shafton which a cam in the shape of an “S” is mounted. The endsof two brake shoes rest on the profile of the S-cam, and therotation of the S-cam pushes the brake shoes outward so thatthe brake pads make contact with the rotating drum. This actionresults in the deceleration of the rotating drum. When the brakepedal is released by the driver, air is exhausted from the brakechamber to the atmosphere, causing the push rod to stroke backinto the brake chamber, and the S-cam rotates in the oppositedirection. The contact between the brake pads and the drum isnow broken, and the brake is thus released.

Fig. 3. Schematic of the experimental facility.

Fig. 4. Photograph of the experimental facility.

A schematic of the experimental setup is provided in Fig. 3and a photograph of the same is provided in Fig. 4. Two“Type-20” brake chambers (having an effective cross-sectionalarea of 20 in2) are mounted on a front axle of a tractor and two“Type-30” brake chambers (having an effective cross-sectionalarea of 30 in2) are mounted on a fixture designed to simulatethe rear axle of a tractor. The air supply to the system isprovided by means of two compressors and storage reservoirs.The reservoirs are chosen such that their volume is more than12 times the volume of the brake chambers that they provide to,as required by FMVSS 121 [7]. Pressure regulators are mountedat the delivery ports of the reservoirs to control the supplypressure to the treadle valve. A cross-sectional view of thetreadle valve used in the experiments is illustrated in Fig. 5. Thetreadle valve consists of two circuits—the primary circuit andthe secondary circuit. The delivery port of the primary circuit


Fig. 5. Sectional view of the treadle valve.

is connected to the control port of the relay valve (referred toas the service relay valve in Fig. 1) and the delivery ports ofthe relay valve are connected to the two rear brake chambers.The relay valve has a separate port for obtaining compressed airsupply from the reservoir. The delivery port of the secondarycircuit is connected to the Quick Release Valve (QRV) and thedelivery ports of the QRV are connected to the two front brakechambers (FBCs).

A closed-loop position feedback control system is used toapply and release the brakes by regulating the displacement ofthe treadle valve plunger. An EC2 electric cylinder (mountedwith a B23 brushless, servo motor) manufactured by IndustrialDevices Corporation/Danaher Motion is used for actuation[25]. The actuator shaft is interfaced with the servo motorthrough a belt drive and lead screw assembly. The actuatoris controlled by a B8501 Servo Drive/Controller [26], [27].A linear potentiometer is built into the electric cylinder, andits output is provided to the servo drive. The servo drive alsoreceives a feedback signal from an encoder mounted on themotor shaft to regulate the torque input to the motor. The de-sired plunger motion trajectory is provided from the computerto the servo drive through the analog output port of a dataacquisition (DAQ) board. The servo drive compares the desireddisplacement and measurement from the linear potentiometerat each instant in time and provides the suitable control inputto the actuator. The position control system is tuned to obtainthe desired performance using IDC’s Servo Tuner softwareprogram [28].

A pressure transducer is mounted at the entrance of eachof the four brake chambers by means of a custom-designedand fabricated pitot tube fixture. A displacement transducer ismounted on each of the two FBC push rods through appro-priately fabricated fixtures in order to measure the push rodstroke. All the transducers are interfaced with a connector blockthrough shielded cables. The connector block is connected to aPCI-MIO-16E-4 DAQ board [29] (mounted on a PCI slot inside

a desktop computer) that collects the data during experimentaltest runs. An application program is used to collect and storethe data in the computer.

III. MODEL OF THE PRESSURE TRANSIENTS IN THE

BRAKE CHAMBER

A “fault-free” model of the pressure transients in a brakechamber of the pneumatic subsystem of the air brake systemwas developed by the authors and reported in [18]. In thissection, we present a summary of the main governing equationsof the model. We also present an improvement in the modelthat relates the stroke of the push rod to the pressure in thebrake chamber. A detailed derivation of the model along withpertinent assumptions, terminology, and nomenclature can befound in [18]. We consider the configuration of the brakesystem in which the delivery port of the primary circuit isdirectly connected to one of the two FBCs.

When the driver presses the brake pedal, the primary pistonin the treadle valve (see Fig. 5) first closes the primary exhaustport (by moving a distance equal to xpt) and then opens upthe primary inlet port (when xpp > xpt). This action servesto meter the compressed air from the reservoir to the brakechamber. We shall refer to this phase as the “apply phase.”When the pressure in the primary circuit increases to a levelsuch that it balances the force applied by the driver, the primarypiston closes the primary inlet port with the exhaust port alsoremaining closed (when xpp = xpt). We shall refer to this phaseas the “hold phase.” When the driver releases the brake pedal,the primary piston opens the exhaust port, and air is exhaustedfrom the brake chamber to the atmosphere (when xpp < xpt).We shall refer to this phase as the “exhaust phase.”

A lumped parameter model of the treadle valve has beendeveloped and presented in [18]. The treadle valve opening hasbeen modeled as a nozzle. The friction at the sliding surfaces ofthe treadle valve is assumed to be negligible since these surfacesare well lubricated. The springs in the treadle valve have beentested and found to be linear in the region of their operation(except the rubber graduating spring). The governing equationof the primary piston during the apply and hold phases of thebrake application process is given by

(Mpp + Mpv)(

d2xpp(t)dt2

)+ K2xpp(t)

= Kssxp(t) + Fgs + F1 − Ppd(t)(App − Apv)

− PpsApv1 + PatmApp (1)

F1 = Kpvxpt + Fkssi − Fkppi − Fkpvi (2)

K2 = Kss + Kpp + Kpv (3)

where Mpp and Mpv denote, respectively, the mass of theprimary piston and the primary valve assembly gasket, xp

and xpp denote, respectively, the displacement of the treadlevalve plunger and the primary piston from their respectiveinitial positions, xpt is the distance traveled by the primarypiston before it closes the primary exhaust, Kss, Kpp, and Kpv

denote, respectively, the spring constants of the stem spring, the


Fig. 6. Calibration curve of the rubber graduating spring.

primary piston return spring, and the primary valve assemblyreturn spring, Fkssi, Fkppi, and Fkpvi denote, respectively, thepreloads on the same, App is the net area of the primary pistonexposed to the pressurized air at the primary delivery port, Apv

is the net cross-sectional area of the primary valve assemblygasket exposed to pressurized air at the primary delivery port,Apv1 is the net cross-sectional area of the primary valve as-sembly gasket exposed to the pressurized air at the primarysupply port, Fgs is the force transmitted from the plunger tothe primary piston by the rubber graduating spring, Pps is thepressure of air being supplied to the primary circuit, Ppd isthe pressure of air at the primary delivery port, and Patm isthe atmospheric pressure. The mechanical response of the rub-ber graduating spring has been tested to obtain the calibrationcurve illustrated in Fig. 6.

The deflection of the rubber graduating spring is denotedby xpd(t) = (xp(t) − xpp(t)). From the calibration curve, thefollowing relationship is obtained between Fgs and xpd:

Fgs =

m1xpd + n1, if xpd ≤ l1m2xpd + n2, if l1 < xpd ≤ l2m3xpd + n3, if l2 < xpd ≤ l3a1x

2pd + a2xpd + a3, if xpd > l3

(4)

where the calibration constants are obtained from Fig. 6. Inthe above equation, l1 is the value of the deflection of therubber graduating spring until which its response is describedby the first subequation. The second subequation describes theresponse of the rubber graduating spring when its deflectionlies between l1 and l2. The third subequation describes itsresponse when its deflection lies between l2 and l3. The fourthsubequation describes its response when its deflection is greaterthan l3.

The mass of the primary piston was found out to be ap-proximately 0.16 kg, and the magnitude of the spring andpressure forces was found to be in the order of 102 N. Thus, theacceleration required for the inertial forces to be comparablewith the spring force and the pressure force terms has to be in

Fig. 7. Simplified pneumatic subsystem under consideration.

Fig. 8. Sectional view of the brake chamber.

the order of 102–103 m/s2, which is not the case. Hence, theinertial forces are neglected, and (1) reduces to

K2xpp = Kssxp + Fgs + F1 − Ppd(App − Apv)

− PpsApv1 + PatmApp. (5)

The treadle valve opening is modeled as a nozzle. The flowthrough the nozzle is assumed to be one-dimensional (1-D) andisentropic. We also assume that the fluid properties are uniformat all sections in the nozzle. Under the above assumptions, thepart of the pneumatic subsystem under consideration can bevisualized as illustrated in Fig. 7. It should be noted that whenthe primary delivery port is connected directly to an FBC, theterm Ppd in the above equations is taken to be the same asthe pressure in the brake chamber (denoted by Pb). For thisconfiguration, the supply pressure term, denoted by Pps in theabove equations, is denoted by Po in the equations that follow.

When the brake pedal is applied, the air from the reservoirtravels through the treadle valve opening to the brake chamber.A cross-sectional view of the brake chamber is presented inFig. 8. In [18], we assumed the following relationship betweenthe push rod stroke (xb) and the brake chamber pressure (Pb):

xb =(Pb − Patm)Ab − Fkbi

Kb(6)

where Ab is the cross-sectional area of the brake chamberdiaphragm, Fkbi is the preload on the brake chamber returnspring, and Kb is the spring constant of the brake chamberreturn spring.


Fig. 9. Push rod stroke and brake chamber pressure at 653 kPa (80 psig)supply pressure.

We have installed displacement transducers for measuringthe push rod stroke, and the data obtained from these sensorshave given us a better understanding of the relationship betweenthe brake chamber pressure and the push rod stroke. A plot ofthe transients of the push rod stroke and the brake chamberpressure from recent experiments performed at a supply pres-sure of 653 kPa (80 psig) is shown in Fig. 9. We note thatthe evolution of the push rod stroke with the brake chamberpressure can be divided into three phases. The push rod startsto move only after a “threshold pressure” (Pth) is reached inthe brake chamber. This is the first phase, and Pth representsthe amount of pressure needed to overcome the preload on thebrake chamber diaphragm. In the second phase, the push rodmoves and rotates the S-cam such that the clearance betweenthe brake pads and the brake drum decreases. The brake padscontact the brake drum at a certain pressure in the brakechamber. We shall refer to this pressure as “contact pressure”and denote it by Pct. In the third phase, further stroke of thepush rod with increasing brake chamber pressure is caused dueto the deformation of the mechanical components of the brakesystem. Thus, the total stroke of the push rod is made up of twocomponents—one that is required to overcome the clearancebetween the brake pads and the brake drum, and another that isdue to the deformation of the mechanical components after thebrake pads make contact with the brake drum. Thus, the totalstroke of the push rod depends both on the clearance betweenthe brake pads and the brake drum and the steady-state pressurein the brake chamber. We have included these effects in ourmodel and approximated the corresponding regions with linearmodels (see Fig. 10) to obtain a calibration curve relating thepush rod stroke to the brake chamber pressure. In Fig. 9, thearrows represent the steady-state condition in each of the threesets of data presented. We note that the steady-state push rodstroke in each case depends on the corresponding steady-statebrake chamber pressure. The calibration curve relating the pushrod stroke and the brake chamber pressure in Test 3 of Fig. 9 isshown in Fig. 10. The calibration constants are obtained fromthis curve and used for all the subsequent test runs. Thus, it can

Fig. 10. Calibration curve at 653 kPa (80 psig) supply pressure.

be noted that the value of Pct depends on the clearance betweenthe brake pads and the brake drum. This clearance will increaseduring the operation of the vehicle due to the wear of the brakepads and the brake drum and also due to the expansion of thebrake drum due to heating. We note that once we determine thethreshold pressure (Pth) from experiments, the final push rodstroke can be found out if the parameter Pct and the steady-state pressure are known. We shall use this feature to obtain anestimate of the push rod stroke from the measurement of thebrake chamber pressure.

From the calibration curve illustrated in Fig. 10, we obtainthe following relationship between the push rod stroke and thebrake chamber pressure:

xb ={

M1Pb + N1, if Pth ≤ Pb < Pct

M2(Pb − Pct) + M1Pct + N1, if Pb ≥ Pct

(7)

where the constants M1, M2, and N1 are obtained from thecalibration curve.

Thus, the volume of the brake chamber (Vb) is given by

Vb =

Vo1, if Pb < Pth

Vo1 + Ab(M1Pb + N1), if Pth ≤ Pb < Pct

Vo1 + AbM2(Pb − Pct)+ Ab(M1Pct + N1), if Pb ≥ Pct

(8)

where Vo1 is the initial volume of the brake chamber. Thus, wewill now use (7) instead of (6) in our model. This is the minormodification that we have made to the model presented in [18].

Thus, the equation describing the flow of air in the brakesystem during the apply and hold phases is given by (refer to[18] for a detailed derivation) that shown in (9) at the bottom ofthe next page, where

Ap = 2πrpv(xpp − xpt) (10)

where rpv is the external radius of the primary valve inletsection.


TABLE IVALUES OF THE PARAMETERS USED IN THE DIAGNOSTIC SCHEMES

The above equations are solved numerically using the fourth-order Runge–Kutta method to obtain the pressure transients inthe brake chamber during the apply phase of a brake appli-cation cycle. The input data to the numerical scheme are thedisplacement of the treadle valve plunger (xp). This model hasbeen corroborated for various test runs, and the results havebeen presented in [18]. Here, we compare the prediction of themodel with the experimental data for one of the recent test runsfor illustration. The numerical values of the various parametersused in the model and the diagnostic schemes are presented inTable I.

We observe from Fig. 11 that the model predicts the startof the pressure rise and the steady-state value well. For theparticular test run illustrated in this figure, the brake applicationis started at approximately t = 4.1 s (refer to Fig. 12). Thevalue t = 0 s corresponds to the instant of time at which thecomputer program for collecting the data is started. We alsonote that the second phase of the pressure transients (wherethere is a decrease in the slope of the pressure growth curve) isalso captured. One of the assumptions that we made in derivingthe model is that the second phase of the pressure transientsis caused by the increase in the volume of the brake chamber

Fig. 11. Pressure transients at 722 kPa (90 psig) supply pressure.

due to the stroke of the push rod. We support this assumptionwith the data presented in Fig. 13. Here, we have plotted themeasured brake chamber pressure and push rod stroke for thetest run illustrated in Fig. 11. We observe that majority ofthe push rod stroke falls in the second phase of the pressuregrowth curve. The latter part of the push rod stroke is dueto the deformation of the brake pads and other mechanicalcomponents as the brake lining contacts the brake drum andis pressed against it.

The response of the pneumatic subsystem of the air brakesystem is such that it can be classified as what is usuallyreferred to as a “sequential hybrid system.” In this paper,the term “hybrid systems” is used to denote those systemswhose mathematical representation involves a finite set ofgoverning ordinary differential equations corresponding to afinite set of modes of operation. The governing equation ineach mode is different, and the transition/switch from onemode to another occurs when some conditions involving oneor more of the following—system’s states, inputs, system para-meters, etc.—are satisfied. These conditions are referred to as“transition/switch conditions.” These conditions may be knowna priori or unknown. In a sequential hybrid system, the possible

((2γ

γ − 1

)1

RTo

∣∣∣∣∣[(

Pb

Po

)( 2γ )

−(

Pb

Po

)( γ+1γ )]∣∣∣∣∣

) 12

ApCDPo sgn(Po − Pb)

=

(Vo1P

( γ−1γ )

o

γRToP( γ−1

γ )b

)Pb, if Pb < Pth(

VbP( γ−1

γ )o

γRToP( γ−1

γ )b

+ P1γ

bAbM1P

( γ−1γ )

o

RTo

)Pb, if Pth ≤ Pb < Pct(

VbP( γ−1

γ )o

γRToP( γ−1

γ )b

+ P1γ

bAbM2P

( γ−1γ )

o

RTo

)Pb, if Pb ≥ Pct

(9)


Fig. 12. Treadle valve plunger displacement for the test run shown in Fig. 11.

Fig. 13. Pressure and push rod stroke measurements for the test run shownin Fig. 11.

modes are ordered in a specific sequence. From a given mode,there can only be one forward transition to the next mode in thisordered set or one backward transition to the previous mode.Thus, the system can switch from a given mode to either theprevious mode or the following mode.

Many automotive systems have recently been described byhybrid models. Balluchi et al. [30] have proposed a hybridmodel for the automotive engine and power train that takes intoaccount the four strokes of the pistons in the engine cylinders.They use this hybrid model to develop a variety of enginecontrollers. Borrelli et al. [31] have used a linearized hybridvehicle model to develop traction control systems. Tractioncontrol systems improve the driver’s ability to control thevehicle under wet and/or icy road conditions. Altafini et al. [32]have developed a linearized hybrid model for the motion ofa miniature tractor-trailer combination along straight line andcircular arc trajectories. In [33], the authors have developed a

hybrid model for the drive line of an automotive power trainand designed observers based on this model.

There are three modes of operation in the pneumatic sub-system of the air brake system [refer to (9)] when the brakeis applied. In “Mode 1,” the pressure in the brake chamber(Pb) increases to Pth. In “Mode 2,” the push rod starts to movewith further increase in pressure, and the clearance between thebrake pads and the brake drum starts to decrease. When thebrake chamber pressure is equal to Pct, the brake pads contactthe brake drum and “Mode 3” begins with further increase inpressure. In this mode, the stroke of the push rod increases withpressure due to the deformation of the mechanical componentsof the brake. These three modes are illustrated in Fig. 14.

The following features of our model should be noted:1) The governing equation in each mode for each brake

chamber is a nonlinear first-order ordinary differentialequation in Pb and is different in each mode.

2) The transition conditions from one mode to anotherare linear equalities/inequalities involving the state (Pb),a known parameter (Pth), and an unknown parameter(Pct). Thus, the transition condition between Mode 2 andMode 3 is not known. But the range of values of Pct isknown from the possible range of values of the push rodstroke.

3) Hence, a transition detection problem and a parameterestimation problem have to be solved simultaneously.Also, the governing equations in Mode 3 involve theunknown parameter (Pct).

We will use this hybrid model that predicts the pressure tran-sients in the air brake system to develop schemes for estimatingthe push rod stroke. The problems of transition detection andparameter estimation in such classes of nonlinear sequentialhybrid systems are currently open.

IV. DETECTION OF LEAKS

A leak is introduced in the system by loosening the hose cou-plings at the entrance of the brake chamber. Brake applicationsare made at different supply pressures, and the prediction ofthe model is compared with the corresponding brake chamberpressure measurement in each case.

Designing a fault detection and isolation (FDI) scheme fora physical system involves the tasks of residual generationand residual processing. Exhaustive surveys of various FDIschemes have been provided by Willsky [34], Gertler [35],[36], Basseville [37], Isermann [38], and Frank [39]. Economicconstraints require that a reliable diagnostic tool be obtainedwith the least number of sensors. For the proposed diagnosticsystem, a pressure transducer is required at each brake chamber,and a displacement transducer is required to measure the treadlevalve plunger displacement. The investment on these sensorswill be justified by the availability of a fast, reliable, andautomatic diagnostic system. For a given brake application, thegoverning equations of the model will be solved numerically toobtain the solution for the brake chamber pressure. This will becompared with the experimental data to generate the values ofthe residuals. The diagnostic schemes will generate the pressureresiduals and process them to detect leaks and estimate the push


Fig. 14. Air brake system modeled as a sequential hybrid system.

rod stroke. The features of the diagnostic schemes proposed inthis paper include the following:

1) The presence of a leak will be determined from measure-ments of the steady-state brake chamber pressure and thesupply pressure taken during a full brake application. Thedifference between these two values serves as an indicatorof the absence or presence of leaks.

2) The stroke of the push rod will be estimated from theparameter estimation and transition detection schemesdeveloped using the hybrid model for the pressure tran-sients in the brake chamber.

Currently, the only available indicator for leaks is in theform of a low-pressure warning signal that is activated whenthe air pressure in the storage reservoirs falls below around549.5 kPa (65 psig) [the normal range of pressure in the storagereservoirs of a typical air brake system is between 790.9 kPa(100 psig) and 997.7 kPa (130 psig)]. But such an indicator willbe activated only when the compressor fails to operate properlyand thus is a “worst case” indicator of leakage. Visual push rodadjustment indicators are required on all commercial vehiclesmanufactured from 1994 [7], [8], but the use of these indicatorsalso involves manual inspection. The diagnostic schemes pre-sented in this paper will use the measurement of pressure in thebrake chamber along with the model for the pressure transientsto automatically monitor the brake system for leaks and out-of-adjustment of push rods.

During “partial” brake applications (by “partial” application,we refer to a brake application where, in the absence of anyleaks and other faults, the steady-state brake chamber pressureis less than the supply pressure to the treadle valve) made inthe absence of a leak, the inlet port of the primary circuit of thetreadle valve will close at some point in the brake applicationprocess [which is determined in the simulations from the forcebalance equation (5)], and there is no further flow of air in thesystem until the brakes are applied further or released. It is

Fig. 15. Pressure transients at 653 kPa (80 psig) supply pressure—partialapplication with leak.

observed that at partial brake applications made in the presenceof a leak, the brake system tends to make up for the lossof air due to leakage by continuously bleeding air from thereservoir until the brakes are released. This can be observedfrom Fig. 15, where we can hardly observe any differencebetween the steady-state pressure predicted by the “fault-free”model and that from the experimental data for a partial brakeapplication test run despite the presence of a leak in the system.Also, the response of the treadle valve is such that the fullrange of the brake chamber pressure is realized in a very narrowrange of the plunger displacement. This is illustrated in Fig. 16,where the steady-state values of the brake chamber pressureand the treadle valve plunger displacement have been plottedfor a wide range of test runs performed at a supply pressure


Fig. 16. Steady-state treadle valve plunger displacement and brake chamberpressure at 722 kPa (90 psig) supply pressure.

Fig. 17. Pressure transients at 515 kPa (60 psig) supply pressure—partialapplication with leak.

of 722 kPa (90 psig). We note that a major portion of thepressure range is achieved within a span of 0.002 m of theplunger displacement. Thus, the prediction of the steady-statebrake chamber pressure by the model at partial applications issensitive to measurements from the treadle valve displacementtransducer. External factors such as noise, temperature, etc.,affect these measurements, and there is invariably some errorbetween the prediction of the model and the measured steady-state brake chamber pressure. This is illustrated in Fig. 17,where the steady-state brake chamber pressure predicted by themodel is lower than the measured value during a partial brakeapplication carried out in the presence of a leak.

It has been found that a reliable and repeatable manner ofdetecting leaks in the current configuration of the air brakesystem is to make a “full” brake application (by “full” appli-cation, we refer to a brake application where, in the absence

Fig. 18. Pressure transients at 653 kPa (80 psig) supply pressure—full appli-cation without leak.

of any leaks and other faults, the steady-state brake chamberpressure is almost equal to the supply pressure to the treadlevalve). In such an application made in the presence of a leak,it has been observed that the air still keeps flowing throughthe system as long as the brake is applied. But, it should benoted that the maximum steady-state brake chamber pressurethat can be reached during a brake application is the supplypressure to the treadle valve. This can happen only during fullbrake applications with no leaks in the system. Our “fault-free”model reliably predicts that during full brake applications, thesteady-state brake chamber pressure is the supply pressure tothe treadle valve. We have observed from experiments that,during a full brake application made in the presence of a leak,the measured steady-state brake chamber pressure is alwayslower than that predicted by the fault–free model. This behavioris illustrated in the following figures for full brake applicationscarried out at supply pressures of 653 kPa (80 psig) and722 kPa (90 psig).

We can infer from Figs. 18 and 19 that in the absence ofleaks, the steady-state brake chamber pressure predicted by themodel and the actual measurement are in good agreement. Weobserve a marked difference between these two values when aleak is introduced in the system as can be seen from Figs. 20and 21. Also, the pressure rise (observed from the measureddata) becomes “sluggish” when there is a leak in the systemcompared to cases without a leak. This effect is very pro-nounced at 722 kPa (90 psig) supply pressure when comparedwith the test run at the supply pressure of 653 kPa (80 psig).It should be noted that the pressure capacity of the reservoirused in our experiments is between 756.4 kPa (95 psig) and825.3 kPa (105 psig); hence, this behavior is more prominent asthe supply pressure approaches the maximum pressure capacityof the reservoir. We can note that there are differences betweenthe predictions of the model and the experimental data duringMode 3 of the pressure transients. But our model reliablypredicts that the steady-state brake chamber pressure is equalto the supply pressure in all the cases. Thus, checking for leaks


Fig. 19. Pressure transients at 722 kPa (90 psig) supply pressure—full appli-cation without leak.

Fig. 20. Pressure transients at 653 kPa (80 psig) supply pressure—full appli-cation with leak.

involves measurement of the supply pressure and comparing itwith the measured steady-state brake chamber pressure whilemaking a full brake application.

Next, we take a quantitative look at the differences betweenthe steady-state brake chamber pressure predicted by the modeland the measured value for a group of test runs. The results arepresented in Table II. In this table, Pssim refers to the steady-state brake chamber pressure predicted by the model for abrake application, and Psmeas is the steady-state brake chamberpressure measured for that brake application. The percentagedifference is calculated by using the formula

% difference =(Pssim − Psmeas)

Pssim∗ 100. (11)

Fig. 21. Pressure transients at 722 kPa (90 psig) supply pressure—full appli-cation with leak.

TABLE IIERROR BETWEEN PREDICTED AND MEASURED STEADY-STATE

BRAKE CHAMBER PRESSURE

Fig. 22. Comparison of test runs with and without leaks at 653 kPa (80 psig)supply pressure.

We note from Table II that there is an appreciable increase inthe percentage error when a leak is introduced in the systemwhen compared to the case when there is no leakage.

We had mentioned in Section I that current federal reg-ulations require inspections to be made under a full brakeapplication carried out a supply pressure of between 653 kPa(80 psig) and 722 kPa (90 psig) [19]. In Figs. 22 and 23, we


Fig. 23. Comparison of test runs with and without leaks at 722 kPa (90 psig)supply pressure.

present data collected from a number of test runs performed atsupply pressures of 653 kPa (80 psig) and 722 kPa (90 psig),respectively. In these figures, the term “normalized steady-statepressure” has been plotted on the ordinate. This is obtained bydividing the measured steady-state pressure for a particular testrun by the supply pressure for that test run. An appreciabledifference can be observed between the test runs made in thepresence of a leak and those made in the absence of a leak.With a supply pressure of 653 kPa (80 psig), this value is alwaysbelow 0.97 in the presence of a leak. When the supply pressureis 722 kPa (90 psig), this value is always below 0.93 in thepresence of a leak. At supply pressures of 653 kPa (80 psig)and 722 kPa (90 psig), this value is above 0.98 in the absenceof a leak. This value is not equal to 1 in the absence of a leakdue to the presence of measurement errors and noise. But thereis a clear demarcation in the range of this value when there isa leak in the brake system compared to the case when thereis no leakage. Since the current regulations for air brake testingprescribe a full brake application with a supply pressure of80–90 psig, a suitable threshold for detecting leaks in theconfiguration of the brake system under consideration can bechosen to be 0.97.

V. EFFECT OF PUSH ROD STROKE ON

PRESSURE TRANSIENTS

A set of experimental test runs is carried out by connectingthe secondary delivery port of the treadle valve to the QRV,and the delivery ports of the QRV are connected to each of thetwo FBCs. We label these two FBCs as FBC # 1 and FBC # 2for convenience. The stroke of the push rod of each of thesebrake chambers is adjusted by rotating the manual adjustmentnut on the corresponding automatic slack adjuster mounted onthe S-cam shaft associated with that brake chamber. In thisset of experiments, the stroke of the push rod of FBC # 2is kept fixed and that of FBC # 1 varied over a wide rangeto observe the effects of the push rod stroke variation on thepressure transients. The measured pressure transients for these

Fig. 24. Pressure transients at 515 kPa (60 psig) supply pressure—x1 =0.016 m (0.63 in), and x2 = 0.02398 m (0.944 in).


various test runs are presented in Figs. 24–27. In these figures,x1 refers to the steady-state stroke of the push rod of FBC# 1, and x2 refers to the steady-state stroke of the push rodof FBC #2.

We can observe from Figs. 24–27 that the pressure transientsin both chambers start simultaneously. The steady-state valuesare also equal in both brake chambers. The major difference canbe observed in the second phase of the pressure growth curve,which corresponds to the phase when the push rod strokesout. The stroke of the push rod of FBC # 2 is kept fixed ataround 0.02388 m (0.94 in), and the stroke of the push rod ofFBC # 1 is varied. We can observe from Fig. 24 that when x1

is less than x2, the second phase of the pressure transients inFBC # 1 is shorter than that in FBC # 2. Fig. 25 illustratesthat when the strokes of both push rods are almost equal,the pressure transients in both chambers almost overlap oneanother. When x1 is increased to a value greater than x2, the




second phase of the pressure transients in FBC # 1 is longerthan that in FBC # 2. This is shown in Fig. 26. This differencebecomes more pronounced when x1 is increased even furtheras can be observed from Fig. 27. Thus, we can observe theeffect of the variation of the push rod stroke on the secondphase of the pressure transients in the brake chamber. Thiseffect will be used to develop schemes for estimating the pushrod stroke.

VI. SCHEMES FOR ESTIMATING THE STROKE

OF THE PUSH ROD

We stated in Section III that the final stroke of the pushrod is made up of two parts—the first part is for overcomingthe clearance between the brake pads and the brake drum andthe second part is due to the subsequent deformation of the

mechanical components. Thus, from (7), the steady-state strokeof the push rod (xbss) can be written as

xbss = M2(Pbss − Pct) + M1Pct + N1 (12)

where Pbss is the steady-state brake chamber pressure. Thevalue of Pbss can be found from the measured pressure data.Thus, the problem of estimating the final stroke is equivalentto obtaining a good estimate of the parameter Pct (which isthe brake chamber pressure at which the clearance between thebrake pads and the brake drum is overcome).

We present below two schemes that provide an estimate ofPct and thus an estimate of the push rod stroke. In the firstscheme, the range of possible values of Pct is discretized intosufficiently small intervals. Then, a pressure residue measureis calculated for each possible value of Pct, and the one thatminimizes this measure is taken to be the estimate of Pct.In the second scheme, a method is proposed for detectingthe transition from Mode 2 to Mode 3, and subsequently, anestimate of Pct is obtained.

A. Scheme 1—Estimation of Push Rod Stroke by Discretization

In this scheme, we propose the following procedure to obtainan estimate of Pct:

1) From the physical limits on the stroke of the push rod,we can obtain bounds on the value of Pct. Let Pctl andPctu denote, respectively, the lower bound and the upperbound on Pct. We note that the lower bound correspondsto zero clearance between the brake pads and the brakedrum, and the upper bound is obtained from the maxi-mum possible push rod stroke. The maximum push rodstroke for the “Type-20” brake chamber that is beingused in our experiments is 0.05715 m (2.25 in) [40]. Thevalue of Pctl is found from experiments to be 142.73 kPa(6 psig), and the value of Pctu is calculated to be184.1 kPa (12 psig).

2) We note that the estimate of Pct, denoted by Pct, will liein the interval between Pctl and Pctu. In order to obtainthis value, we discretize the interval [Pctl, Pctu] into finerintervals by using a step size (δP ) of 689.5 Pa (0.1 psi).Thus, we obtain a set P with its elements equally spacedby a step size of δP , and whose first and last elementsare Pctl and Pctu, respectively. We note from Section IIIthat the push rod stroke needed to overcome the clearancebetween the brake pads and the brake drum is reflected inthe second region (Mode 2) of the pressure growth curve.Hence, we shall restrict our attention to this region forobtaining Pct.

3) Next, we numerically solve the governing equations ofthe model [(5) and (9)] for each element in the set P toobtain the corresponding solution of the brake chamberpressure. Then, we calculate the following pressure error/residue measure:

eP (Pcti) =k∑

j=0

|Pmeas(j) − Pb(Pcti)(j)| (13)


Fig. 28. Normalized pressure residue at 653 kPa (80 psig) supply pressure.

where Pmeas(j) is the measured brake chamber pressureat the jth instant of time, and Pb(Pcti)(j) is the solutionof the model (at the same instant of time) correspondingto Pcti, which is given by

Pcti = Pctl + (δP )i, i = 0, . . . , N (14)

where δP = (Pcti − Pctl)/N .4) The choice of k in (13) is determined by the maximum

possible dwell time of the system in Mode 2. Dependingon the clearance between the brake pads and the brakedrum, this time interval will vary. But we have observedfrom experiments that this time interval is usually notmore than 0.3–0.35 s. The sampling time used in ourexperiments is 2 ms. Hence, we have chosen the valueof k to be 200 (which corresponds to a time interval of0.4 s). We should mention here that j = 0 correspondsto the time instant at which Mode 2 starts. Hence, westart at the beginning of Mode 2 [which occurs when thebrake chamber pressure reaches the threshold pressure(Pth)] and calculate the quantity eP (Pcti) given by (13).This procedure is repeated for each value of Pcti, andfinally, we generate an array of values representing theresidue measure given by (13). Then, the estimate Pct isobtained as

Pct = arg minPcti∈P

eP (Pcti). (15)

We illustrate the results obtained by using this scheme ontwo test runs in Figs. 28 and 29. Before discussing the results,we point out some practical issues involved in implementingthe scheme. Obtaining accurate measurements of the brakechamber pressure and the treadle valve plunger displacementis critical to the successful implementation of this scheme. Inreality, measurements are corrupted by noise and environmentalfactors. We have tried to minimize the effects of noise by usingshielded twisted pair cables for transmitting electrical signals.We have also used a shielded connector block for interfacing the

Fig. 29. Normalized pressure residue at 722 kPa (90 psig) supply pressure.

transducers with the DAQ board. Environmental effects such astemperature, humidity, etc., try to shift the initial reading (“zeroreading”) of the transducers and also affect their calibrationcurves. We try to minimize these effects by obtaining the initialreadings at the start of each and every set of experiments andtaking their variation into account while converting voltagesignals into physical quantities (such as pressure, displacement,etc.). Also, we use a digital filter with a cutoff frequency of10 Hz to further minimize the effect of noise.

In Fig. 28, we have plotted the results obtained for a testrun made at 653-kPa (80 psig) supply pressure. The array ofthe pressure error/residue is calculated, the minimum valueis located, and the estimate Pct is obtained from P as thevalue corresponding to this minimum residue. On the ordinate,we have plotted the term “normalized pressure residue.” Weobtain these values by dividing the array of the residues by itsminimum value (thus the minimum residue will always be givena value of 1). Once the value of Pct is determined, we obtainan estimate of the final push rod stroke by using (12). In thiscase, we obtain the best estimate of the push rod stroke to be0.03381 m (1.3311 in), while the measured value of the stroke is0.03114 m (1.2262 in). We observe that the normalized pressureresidue corresponding to the actual stroke is around 1.007,which differs by 0.7% from the residue corresponding to theestimated stroke. In Fig. 29, we have plotted the results obtainedfrom a test run performed at a supply pressure of 722 kPa(90 psig) on a different day from the above test run. We observethat the estimated push rod stroke in this case is 0.03684 m(1.4506 in), while the measured stroke is 0.03181 m (1.2525 in).We also note that the normalized pressure residue correspond-ing to the actual stroke is around 1.009, i.e., a difference of 0.9%from the minimum value.

B. Scheme 2—Detection of the Transition FromMode 2 to Mode 3

An estimate of the push rod stroke can be obtained oncethe transition from Mode 2 to Mode 3 is detected. For the


purpose of detecting this transition, we consider a time intervalthat is smaller than the minimum possible dwell time of thesystem in Mode 2. Since the measurements are acquired at aconstant sampling time of 2 ms, we shall denote time intervalsin terms of the equivalent number of samples in this section.The following steps are involved in this scheme:

1) Let T1 denote the instant of time at which transitionoccurs from Mode 1 to Mode 2. Since we are going tofocus only on Mode 2 and Mode 3, let us provide thesample number 1 to the data collected at this instant oftime. In the first iteration, we take the estimate of Pct

to be equal to Pth and numerically solve the governingequations for Modes 2 and 3 over the next K time steps.The value of K is chosen such that it is less than theminimum number of time steps that the system will spendin Mode 2. This can be obtained from experiments, andin our case, we have chosen K = 5.

2) We note that the initial value of the pressure in Mode 3will be Pct. The input to the numerical scheme is thetreadle valve plunger displacement over the time intervalcorresponding to these K time steps. We solve the gov-erning equations in both modes over K time steps andthen calculate the residue measures

e2 =K∑

j=1

|Pmeas(j) − Pb2(j)| (16)

e3 =K∑

j=1

|Pmeas(j) − Pb3(j)| (17)

where Pb2(j) and Pb3(j) are the solutions of the govern-ing equations in Mode 2 and Mode 3, respectively.

3) If e2 < e3, it can be concluded that the system is still inMode 2. We update the value of Pct to be equal to Pb2(K)and repeat the previous step over the next K time steps.

4) If e2 ≥ e3, we can declare that a transition has takenplace from Mode 2 to Mode 3. Then, the best estimateof Pct will be the value used at the start of this particulariteration. Once this is known, we can obtain an estimateof the push rod stroke from (12).

Figs. 30 and 31 illustrate the results on the two test runs thathave been considered in Section VI-A. We note that we havetaken an initial time interval corresponding to 50 time steps.This is done due to practical considerations since we know thatthe clearance between the brake pads and the brake drum isnever zero and usually a minimum stroke of around 0.0127 m(0.5 in) is present. Such a choice also ensures that any initialdisagreement between the model and the experiment at theend of Mode 1 will not affect the transition detection process.Additionally, it reduces the computation time involved.

We provide in Table III a comparison of the push rod strokeestimate obtained from these two schemes with the measuredstroke. It should be pointed out that the computation timeinvolved in implementing Scheme 2 is much less than that ofScheme 1, and this would be beneficial for implementing thediagnostic scheme in practice. Also, the complexity of Scheme1 will increase if we need to estimate more than one unknown

Fig. 30. Transition detection at 653 kPa (80 psig) supply pressure.

Fig. 31. Transition detection at 722 kPa (90 psig) supply pressure.

TABLE IIICOMPARISON OF ACTUAL AND ESTIMATED PUSH ROD STROKE

parameter. For example, if the value of Pth was unknown inaddition to that of Pct, we need to obtain the pressure residuemeasure for each possible pair of values of Pth and Pct usingScheme 1. But, using Scheme 2, an estimate of Pth can beobtained by detecting the transition from Mode 1 to Mode 2.

Thus, we can provide a range of values for the best estimatedepending on a chosen range for the tolerated normalizedpressure residue. For example, we can identify the region of thepush rod stroke estimate as that corresponding to the interval[1, 1.01] for the normalized pressure residue (i.e., till 1% morethan the minimum). A range of possible estimates of the actual


push rod stroke is practically valuable since we can determinethe state of the push rod adjustment from it.

VII. CONCLUDING REMARKS

In this paper, we have presented methods for detecting leaksand obtaining estimates of the push rod stroke in the air brakesystem of a commercial vehicle. A hybrid model for predictingthe pressure transients in the air brake system has been pre-sented. Experimental test runs are performed over a wide rangeof supply pressures, and full brake applications are made bothin the absence and presence of leaks. The predictions of themodel and the experimental data are compared in both cases,and the differences in the results due to the introduction of theleak have been identified. The effect of the variation of the pushrod stroke on the pressure transients in the brake chamber isalso studied through appropriate experiments. Two schemes forestimating the stroke of the push rod have been presented andcompared with experimental data.

ACKNOWLEDGMENT

The authors would like to thank Dr. C. Hatipoglu of BendixCommercial Vehicle Systems for providing some of the neces-sary hardware.

REFERENCES

[1] S. F. Williams and R. R. Knipling, “Automatic slack adjusters for heavyvehicle air brake systems,” Nat. Highway Traffic Safety Administration,Washington, DC, Tech. Rep. DOT HS 807 724, Feb. 1991.

[2] D. Blower and K. L. Campbell, “The large truck crash causation study,”Federal Motor Carrier Safety Administration, Washington, DC, Tech.Rep. UMTRI-2002-31, Nov. 2002.

[3] “Safety report: Analysis of intrastate trucking operations,” Nat. Trans-portation Safety Board, Washington, DC, Tech. Rep. NTSB/SR-02/01,Mar. 2002.

[4] L. C. Buckman, “Commercial vehicle braking systems: Air brakes, ABSand beyond,” presented at the Society Automotive Engineers, 43rd L. RayBuckendale Lecture, Int. Truck and Bus Meeting and Exposition, Soc.Automotive Eng., Indianapolis, IN, Nov. 1998, Paper SP-1405.

[5] “Heavy vehicle airbrake performance,” Nat. Transportation Safety Board,Washington, DC, Tech. Rep. NTSB/SS-92/01, Apr. 1992.

[6] R. W. Radlinski, “Braking performance of heavy U.S. vehicles,” presentedat the SAE International Congress and Exposition, Detroit, MI, 1987,Paper 870492. Trans. Soc. Automotive Eng.

[7] Motor vehicle safety standard no. 121, Air brake systems, Oct. 2003. Codeof Federal Regulations, Title 49, Part 571, Section 121.

[8] “Federal motor carrier safety regulations: Part 393,” Oct. 2003. Code ofFederal Regulations, Title 49, Part 393.

[9] S. J. Shaffer and R. W. Radlinski, “Braking capability requirements forin-use commercial vehicles—A chronology,” presented at the SAE Inter-national Truck and Bus Meeting and Exposition, Ft. Worth, TX, 2003,Paper 2003-01-3397. Trans. Soc. Automotive Eng.

[10] S. J. Shaffer and G. H. Alexander, “Commercial vehicle braketesting—Part 1: Visual inspection versus performance-based test,” pre-sented at the SAE International Truck and Bus Meeting and Exposition,Winston-Salem, NC, 1995, Paper 952671. Trans. Soc. Automotive Eng.

[11] ——, “Commercial vehicle brake testing—Part 2: Preliminary resultsof performance-based test program,” presented at the SAE InternationalTruck and Bus Meeting and Exposition, Winston-Salem, NC, 1995, Paper952672. Trans. Soc. Automotive Eng.

[12] R. M. Braswell, J. F. Broder, P. J. Fisher, R. D. Flesher, D. Foster,S. Gooch, K. F. Johnson, H. T. Pannella, R. L. Rak, G. H. Rood,J. Salas, C. O. Summer, V. Suski, and J. Thrift, “Tomorrow’s trucks:A progress review and reappraisal of future needs,” presented at the SAEInternational Truck and Bus Meeting and Exposition, Detroit, MI, 1993,Paper 932975. Trans. Soc. Automotive Eng.

[13] R. J. Morse, “Brake system performance at low operating pressures,”presented at the SAE Mid-Year Meeting, Detroit, MI, 1970, Paper 700512.Trans. Soc. Automotive Eng.

[14] P. Fancher, Z. Bareket, D. Blower, C. Mink, and K. Campbell, “Evaluationof brake adjustment criteria for heavy trucks,” Federal Highway Admin-istration, Washington, DC, Tech. Rep. FHWA-MC-94-016, Feb. 1995.

[15] R. M. Clarke, W. A. Leasure, Jr., R. W. Radlinski, and M. Smith, “Heavytruck safety study,” Nat. Highway Traffic Safety Administration, Wash-ington, DC, Tech. Rep. DOT HS 807 109, Mar. 1987.

[16] R. B. Heusser, “Heavy truck deceleration rates as a function of brakeadjustment,” presented at the SAE International Congress and Exposition,Detroit, MI, 1991, Paper 910126. Trans. Soc. Automotive Eng.

[17] “Braking deficiencies on heavy trucks in 32 selected accidents,”Nat. Transportation Safety Board, Washington, DC, Tech. Rep. NTSB/SS-88/06, Nov. 1988.

[18] S. C. Subramanian, S. Darbha, and K. R. Rajagopal, “Modeling thepneumatic subsystem of an S-cam air brake system,” ASME J. Dyn. Syst.,Meas. Control, vol. 126, no. 1, pp. 36–46, Mar. 2004.

[19] Minimum Periodic Inspection Standards. (2005 Apr.). [Online]. Avail-able: http://www.fmcsa.dot.gov/rules-regulations/administration/fmcsr/appng.htm

[20] Bendix ASA-5 Automatic Slack Adjuster. (2005 Apr.). [Online]. Avail-able: http://www.bendix.com/downloads/service_data_sheet/051269.pdf

[21] D. Middleton and J. Rowe, “Feasibility of standardized diagnostic devicefor maintenance and inspection of commercial motor vehicles,” Transp.Res. Rec., no. 1560, pp. 48–56, 1996.

[22] A. Matteson, D. Blower, and J. Woodrooffe, “Trucks involved in fatalaccidents factbook 2002,” Transp. Res. Inst., Univ. Michigan, Ann Arbor,Tech. Rep. UMTRI-2004-34, Oct. 2004.

[23] E. Zaloshnja and T. Miller, “Revised costs of large truck- and bus-involvedcrashes,” Federal Motor Carrier Safety Administration, Washington, DC,Nov. 2002. Tech. Rep.

[24] “Commodity flow survey,” 1997 Economic Census, 1997, Washington,DC: U.S. Census Bureau.

[25] EC Series Electric Cylinders: User’s Manual, Industrial DevicesCorp./Danaher Motion, Rockford, IL. PN CUS10050, Version 1.0.

[26] B8501: Brushless Analog Position Control Manual Supplement,Industrial Devices Corp./Danaher Motion, Rockford, IL. Jun. 1995.PN PCW-4712, Rev. 1.01.

[27] B8001 Brushless Servo Drive: Operator’s Manual, Industrial De-vices Corp./Danaher Motion, Rockford, IL, May 1998. PN PCW-4679,Rev. 1.5.

[28] IDC Servo Tuner: Operator’s Manual, Industrial Devices Corp./DanaherMotion, Rockford, IL, Apr. 1995. P/N PCW-4710, Rev. 1.00.

[29] PCI E Series User Manual: Multifunction I/O Devices for PCI Bus Com-puters, Nat. Instruments, Austin, TX, Jul. 2002.

[30] A. Balluchi, L. Benvenuti, M. D. Di Benedetto, C. Pinello, and A. L.Sangiovanni-Vincentelli, “Automotive engine control and hybrid systems:Challenges and opportunities,” Proc. IEEE, vol. 88, no. 7, pp. 888–912,Jul. 2000.

[31] F. Borrelli, A. Bemporad, M. Fodor, and D. Hrovat, “A hybrid control ap-proach to traction control,” in Hybrid Systems: Computation and Control,ser. Lecture Notes in Computer Science, vol. 2034, M. D. Di Benedettoand A. Sangiovanni-Vincentelli, Eds. Berlin, Germany: Springer-Verlag,2001, pp. 162–174.

[32] C. Altafini, A. Speranzon, and K. H. Johansson, “Hybrid control of atruck and trailer vehicle,” in Hybrid Systems: Computation and Control,ser. Lecture Notes in Computer Science, vol. 2289, C. J. Tomlin and M. R.Greenstreet, Eds. Berlin, Germany: Springer-Verlag, 2002, pp. 21–34.

[33] A. Balluchi, L. Benvenuti, M. D. Di Benedetto, and A. L. Sangiovanni-Vincentelli, “A hybrid observer for the driveline dynamics,” in Proc. Eur.Control Conf., Porto, Portugal, 2001, pp. 618–623.

[34] A. S. Willsky, “A survey of design methods for failure detection in dy-namic systems,” Automatica, vol. 12, no. 6, pp. 601–611, 1976.

[35] J. Gertler, “Residual generation in model-based fault diagnosis,” ControlTheory Adv. Technol., vol. 9, no. 1, pp. 259–285, 1993.

[36] J. J. Gertler, Fault Detection and Diagnosis in Engineering Systems.New York: Marcel Dekker, 1998.

[37] M. Basseville, “Detecting changes in signals and systems—A survey,”Automatica, vol. 24, no. 3, pp. 309–326, 1988.

[38] R. Isermann, “Process fault detection based on modeling and estimationmethods—A survey,” Automatica, vol. 20, no. 4, pp. 387–404, 1984.

[39] P. M. Frank, “Fault diagnosis in dynamic systems using analytical andknowledge-based redundancy—A survey and some new results,” Auto-matica, vol. 26, no. 3, pp. 459–474, 1990.

[40] Bendix Brake Chambers. (2005 Apr.). Accessed. [Online]. Available:http://www.bendix.com/downloads/service_data_sheet/021302.pdf


Shankar C. Subramanian received the B.E. degreein mechanical engineering from the University ofAllahabad, Allahabad, India, in 2000 and the M.S.and Ph.D. degrees in mechanical engineering fromTexas A&M University, College Station, in 2003and 2006, respectively.

He is currently a Post-Doctoral Research Asso-ciate with the Department of Mechanical Engineer-ing, Texas A&M University. His research interestsinclude modeling, control, and fault diagnosis ofdynamic systems.

Swaroop Darbha received the B.Tech. degree inmechanical engineering from the Indian Institute ofTechnology, Madras, India, in 1989 and the M.S. andPh.D. degrees in mechanical engineering from theUniversity of California, Berkeley, in 1992 and 1994,respectively.

He is currently an Associate Professor of mechan-ical engineering at the Texas A&M University, Col-lege Station, where he conducts research in modelingthe dynamics of the flow of ground traffic and in thedevelopment of control and diagnostic algorithms forground vehicles.

K. R. Rajagopal received the B.Tech. degree inmechanical engineering from the Indian Institute ofTechnology, Madras, India, in 1973, the M.S. degreein mechanical engineering from the Illinois Instituteof Technology, Chicago, in 1974, and the Ph.D. de-gree in mechanical engineering from the Universityof Minnesota, Minneapolis, in 1978.

He is currently a University Distinguished Pro-fessor and the Forsyth Chair with the Departmentof Mechanical Engineering, Texas A&M University,College Station. He has authored or coauthored over

300 archival papers on a variety of subfields in continuum mechanics thatincludes, among them, non-Newtonian fluid mechanics, finite elasticity, vis-coelasticity, turbulence, mixture theory, mechanics of granular material, elec-trorheology, and continuum thermodynamics. He has coauthored three booksand coedited several others in the field of mechanics.

Dr. Rajagopal is a Fellow of the American Society of Mechanical Engineersand a past President of the Society for Natural Philosophy. He currently serveson the editorial advisory boards of 30 archival journals and book series.

a diagnostic system for air brakes

Documents