Gasoline engine air filter health monitoring by second-order sliding modes

INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSINGInt. J. Adapt. Control Signal Process. (2012)Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/acs.2314

Gasoline engine air filter health monitoring by second-ordersliding modes

Qadeer Ahmed*,†, Aamer Iqbal Bhatti, Muddassar Abbas Rizvi and Mohsin Raza

Control & Signal Processing Research (CASPR) Group, Department of Electronic Engineering, Faculty of Engineering,Mohammad Ali Jinnah University, Islamabad, Pakistan

SUMMARY

This paper presents a novel and cheap methodology to classify healthy and clogged air filter. Air filter isan integral part of air intake system of spark ignition engine and is responsible to deliver clean air forcombustion process. A clogged air filter may hamper engine power and its drivability performance. As aconsequence, its health monitoring becomes mandatory. This task is accomplished by modeling the air filtereffects on air flow through inlet manifold pressure by incorporating a newly introduced air filter dischargecoefficient .Caf / in its dynamics. The estimation of Caf gives an idea about the health of air filter, asno sensor can be installed to measure it. A second-order sliding mode observer is employed to estimateimmeasurable Caf . Super twisting-based sliding mode observer requires manifold pressure, engine angularspeed, and load torque as input. A successful implementation has been carried out to diagnose cloggedand healthy air filter of commercial vehicle engine compliant to on-board diagnostics version-II. Thischaracterizes ‘Caf ’ as a clean indicator of air filter health classification. Copyright © 2012 John Wiley& Sons, Ltd.

Received 5 October 2011; Revised 1 May 2012; Accepted 30 May 2012

KEY WORDS: fault diagnosis; second-order sliding mode observer (SOSMO); parameter estimation;automotive engine and air filter

1. INTRODUCTION

Modern automotive engines are smartly controlled with on-board electronics to deliver its optimumperformance. Efficient sensors are installed to precisely monitor engine functions. These sensorsalong with engine control unit (ECU) ensure flawless engine performance. Clean and sufficient airsupply is one of the main factors that can retard the engine performance. This task is the primeresponsibility of Air Intake System (AIS). AIS helps to maintain air to fuel ratio such that optimumpower and minimum exhaust pollutants are produced. Any malfunction in AIS components willlead to degraded engine performance and increased pollution. This makes health monitoring of eachcomponent involved in AIS mandatory according to strict legislations outlined by environmentalprotection agencies [1]. Moreover, fuel efficient and pollution free automobiles are always preferredby end-users.

1.1. Air filter and air filter discharge coefficient

The major components of AIS are the following: air filter, pressure manifold, throttle/butterfly valve,and various sensors. Air filter is liable to deliver clean air for combustion process. This will helpin reducing dust concentration in AIS. A serious consequence of increase in abrasive dust particle

*Correspondence to: Qadeer Ahmed, Control & Signal Processing Research (CASPR) Group, Mohammad Ali JinnahUniversity, Islamabad, Pakistan.

†E-mail: [email protected]

Copyright © 2012 John Wiley & Sons, Ltd.

Q. AHMED ET AL.

is engine wear and tear. As air filter remains exposed to environmental hazards most of the time,the natural phenomenon of clogging degrades the air filter performance with the passage of time. Aclogged air filter will hinder to deliver required amount of air to maintain AFR for optimum power,especially at high speeds and loads. The clogging phenomenon increases the pressure drop acrossair filter [2, 3]. This negatively affects the pressure dynamics of intake manifold.

Factors effecting air filter performance has been discussed in detail in [2]. The degraded air filterin open loop carbureted engine vehicles affects fuel efficiency significantly. It has been shown in[4] that the fuel economy is increased by 14% when clean air filter is used. However, in modernECU-equipped vehicles, air filter has no significant affects on fuel economy. ECU maintains thedesired AFR despite of clogged air filter. However, the acceleration/pick-up time of the vehicle isincreased if clogged air filter is used.

Keeping in view the adverse effects of clogged air filter on engine performance, its health mon-itoring becomes mandatory. In public literature, air filter health is mostly diagnosed by measuringpressure drop across it. The filter health degradation is directly related to pressure drop after airfilter. This requires installation of additional three pressure sensors [2, 4]. Similarly, a signal-baseddiagnosis of emulated clogged air filter has been carried out in [5]. However, it has been observedthat air filter health diagnosis is less practiced in available literature. One of the main reasons is thatair filter is either ignored or assumed as clean filter while modeling pressure dynamics of engine airintake path [6–9].

In this paper, a realistic modeling of engine has been carried out by considering the effects of airfilter on intake manifold dynamics. It can be visualized in Figure 1 that the restrictions in flow can beeither due to throttle body or air filter. Generally, throttle discharge coefficient .CD/ is used to mea-sure flow limitations caused by throttle body. Under steady state conditions, CD remains a constantvalue [10]. Other fluctuations in air flow under steady state operation can be due to air filter behav-ior. In order to incorporate the effects of air filter health on air flow through inlet manifold, Caf hasbeen proposed in this paper. Smaller Caf means lesser air will flow through air intake manifold andvice versa. Mathematically, Caf can be defined as (See Table I for symbols description.)

Caf DPmin.actual/

Pmin.ideal/

The actual degraded air flow rate due to air filter is determined experimentally and ideal massflow rate is given by the flow equation. Under steady state conditions, none of the flow rates willbe equal to zero. Hence, this parameter will always be greater than 0 and less than 1. As Caf is animmeasurable parameter, it cannot be routinely sensed by any sensor. Therefore, its estimation can

Figure 1. Air intake system of gasoline engine showing its major components like air filter, intake manifold,throttle valve, and so on.

Copyright © 2012 John Wiley & Sons, Ltd. Int. J. Adapt. Control Signal Process. (2012)DOI: 10.1002/acs

GASOLINE ENGINE AIR FILTER HEALTH MONITORING

Table I. Symbols, description, and their values for mean valueengine model.

Symbol Description Values/Units

�vol Volumetric efficiencyCaf Air filter discharge coefficientPa Ambient pressure 101,325 PaPm Manifold pressure PaTm Manifold temperature 325 KTa Ambient temperature 298 KPmin Air flow entering the manifold kg/secPmout Air flow entering the cylinder kg/sec˛cl Throttle angle at closed position 9.8°˛ Throttle angle °AE Throttle effective area m2

D Inlet diameter 0.054 mR Specific gas constant 287 J/kg.KCD Throttle discharge coefficient 0.8� Ratio of heat capacities 1.4Vd Displaced volume 0.001294 m3

Vm Manifold volume 0.001127 m3

�c Combustion efficiency 0.9!e Engine speed rad/secJe Engine inertia 0.25 kg.m2

Ti Indicated torque N.mTl Load torque N.mTf Frictional torque N.mTp Pumping torque N.mQ Heat value of fuel 44 kJ/kgCr Compression ratio 10

be carried out using robust second-order sliding mode observer (SOSMO). The estimated value ofCaf will help in diagnosing air filter health.

1.2. Fault diagnosis and second-order sliding mode observer

Fault diagnosis (FD) of engineering systems is currently one of the active research areas [11]. It hasbeen shown in [12, 13], that for a highly nonlinear system, a nonlinear FD technique is mandatory.AIS of gasoline engine exhibits highly nonlinear behavior because of its components like throttlebody, pressure manifold, and so on. Therefore, a nonlinear methodology for engine FD remains anopen research area.

Among various FD techniques [14, 15], linear and nonlinear observers are extensively used fordiagnosis, estimation, and control of mechatronic systems [16–19]. In case of nonlinear FD tech-niques, SOSMO-based FD techniques are widely practiced [10, 20]. The key attribute of a robustnonlinear SOSMO is that it may or may not require system dynamics for its application in FD.The required system dynamics can either be nonlinear or linear in nature. Unlike, other method-ologies that only work on linear model like proportional observers, proportional integral observers,Kalman filter (KF), and so on. Even the variants of KF like extended KF require linearized versionsof the nonlinear model. This linearization can be inaccurate for a system with large nonlinearitiesfor short period [21]. Furthermore, KF-based estimation and diagnosis scheme requires manda-tory initial information about system and noise distribution for its convergence. The parity-basedFD approaches do utilize nonlinear dynamics but this approach is highly sensitive to measure-ment noise and process noise, because these are not taken into consideration in the design ofthe parity space [22]. However, SOSMO are robust against such noise and disturbances. Amongparameter estimation-based FD techniques, least squares, and its variants work efficiently for linearsystems only. First-order sliding mode observers utilize multiple filters for state/parameter estima-tion that may lead to corruption in results. Similarly, model-free FD techniques only work on sensor


Q. AHMED ET AL.

measurements without considering underlying working model and actual inputs to the systems.Knowledge-based models require experience to develop model rules. FD using data-based modelsrequire extensive training data sets. Insufficient training sets may lead to imprecise health monitor-ing. Another problem with data-based schemes is their off-line execution for FD, whereas SOSMOdoes not require any training data sets and other prerequisites. The nonlinear framework of SOSMO-based FD technique is also efficient, computationally cheap and online implementable as it is freeof multiple matrices evaluation and multiplication like in prediction stage of KF. In addition, it doesnot involve the system to be Jacobian linearized as required in extended KF. Similarly, SOSMOis free of transformations, computation of sigma points, Cholesky factor updating, efficient leastsquares, and decompositions as mandatory in unscented KF and its variants [23]. Therefore, onecan implement SOSMO using a low cost embedded system very easily.

Second-order sliding mode observer inherits the same robustness as first-order sliding mode andensures reduced chattering phenomenon [24]. Super twisting algorithm-based SOSMO operates onerror between actual measurement and observed state only. It does not require any derivative of erroras required in other higher-order sliding mode algorithm like real twisting algorithm. The SOSMOalso makes the states observation without filtering and parameters estimation with just one first orderlow pass filter.

Keeping in view the attributes of SOSMO and SI engine malfunctions caused by air filter, a noveland cheaper strategy is proposed to monitor air filter health. The condition monitoring is carried outby estimating newly introduced parameter Caf in air flow dynamics. The estimation is carried outusing super twisting-based SOSMO. The proposed scheme requires ˛, Pm, Tl , and !e as inputs.These inputs are accessible on any on-board diagnostics (OBD-II) compliant engine. The strengthof incorporating Caf can be visualized when its estimated value helps in diagnosing healthy andclogged air filter. The presented scheme is cheaper as it does not require installation of extra pres-sure sensors. It is computationally inexpensive and simple enough for online implementation for airfilter health diagnosis.

The rest of the paper is arranged as follows: Section 2 contains mean value engine model (MVEM)with the incorporation of Caf in air flow dynamics. Section 3 discusses second-order sliding mode-based estimation scheme of Caf . Experimental trails for diagnosis of healthy and clogged air filterare discussed in Section 4, followed by concluding remarks in Section 5, Appendix, and References.

2. MEAN VALUE ENGINE MODELING

The proposed nonlinear health monitoring scheme operates on a nonlinear model of AIS. Figure 1gives a brief idea about the AIS of gasoline automotive engine. The air flow across the AIS can bemodeled on basic fluid dynamics laws. The adiabatic flow across the throttle body/butterfly valvecan be modeled as air flow from orifice. The assumptions are as follows: one-dimensional com-pressible flow has no friction and inertial effects in the flow and there is no change in temperatureand pressure (lumped parameter approach) during the flow [6, 9]. Moreover, the fuel and tempera-ture dynamics involved in AIS are assumed to be uniform. The mass and energy of the air servesas inputs and outputs of the receivers. It is assumed that no substantial changes occur in energyand no mass and heat transfers through the manifold walls. The manifold pressure dynamics can bemodeled on the basis of filling and emptying of air behaving as perfect gas as shown in (1).

PPm DRTm

VmŒ Pmin � Pmout � (1)

The flow across the throttle body . Pmin/ can be modeled as

Pmin D Caf CDAEPa�cf .Pm/ (2)



where

AE .˛/D �D2

4

�1� cos

�˛C ˛cl

˛cl

��

�c D

s1

.RTa/

vuut�

�2

� C 1

� �C1��1

f .Pm/D

�1� e

�PmPa�1��

The engine itself acts as a volumetric pump, a device that enforces a volume flow approximatelyproportional to its speed [9, 25]. Therefore, the air mass flow across the engine can be modeled as

Pmout DVd!e

4��m�vol (3)

where

�m DPm

RTm

The rotational speed dynamics can be developed from combustion process modeled by Otto cycleas given in (4) [9,26]. The available brake torque is the difference of torque produced by combustionTi and other agents. These agents include Tf , Tp , and Tl .

P!e D1

Je

�B1Pm � Tf � Tp � Tl

�(4)

where

B1 D

VdQ�c

�1�

�c��1r

��1��c2��r

� ��c��1r

�� 1

�4�AFR.� � 1/.cr � 1/cvTm

Tp DVd

4�.Pa �Pm/

Tf D 11.72C 5.69� 10�5!e C 2.33� 10�14!2e

Remark 1The aforementioned frictional torque Tf expression is adapted from [26]. The constants of the givenexpression are identified using least squares for the particular engine used in experiment [14].

Finally, a four-stroke spark ignition engine can be explained based on (1) and (4). More details ofengine modeling can be seen in [6, 9, 25].

2.1. Model verification

The pressure and angular speed dynamics in (1) and (4) were validated against a 1.3-L gasolineengine of commercial vehicle. The inputs and outputs of the engine were accessed by OBD-IIdata scanning and logging software. The operating temperature of the engine was around 89ıCand unwanted loads were avoided to ensure steady state conditions. Keeping in view the experimen-tation limitations, the throttle was manipulated and kept constant for several times at 110, 170, and230 s. The response of MVEM and a 1.3-L engine to the same inputs is shown in Figure 2. It canbe observed that the MVEM in (1)–(4) exhibits same response as actual engine in steady state con-ditions. The error of pressure and angular speed dynamics remains within 5% and 8%, respectively.Therefore, the verified model can now be used for air filter health monitoring scheme.


Q. AHMED ET AL.

Figure 2. MVEM validation with a 1.3-L engine in steady conditions under uniform temperature andfuel dynamics.

3. AIR FILTER DISCHARGE COEFFICIENT ESTIMATION SCHEME

As claimed in Section 1.1, Caf can be explored to diagnose the air filter health. This section dealswith the SOSMO-based estimation scheme for Caf . In this paper, a credible approach is adopted byfirst estimating �vol dynamically and then it will be used to identify Caf . Dynamic estimation of�vol can lead to precise calculation of Caf as static relationships for �vol may hinder to model thedynamics induced by manipulating throttle angle [26]. For this task, air intake manifold pressuredynamics given in (1) can be exploited efficiently.

If we consider the following states, input and outputs of gasoline engine

xD�x1x2

D

�PmPPm

2 <2 (5)

y D x1 D Pm 2 < (6)

uD ˛ 2 < (7)

Then, the pressure dynamics given in (1) can be written as follows:

Px1 D g1.x, t ,u/

D x2

D A1�˛,Caf

�f .x1/�A2x1!e�vol

(8)

Px2 D g2.x, t ,u/

D A7 .x1,!e/ �vol2 �

�A5�x1,!e ,˛,Caf

�CA6

�x1,!e ,˛,Caf

�CA8 .x1,!e// �vol CA4

�x1,˛,Caf

�(9)

y D x1 (10)

where A./i are defined in the Appendix,The previously mentioned pressure dynamics can be reformulated as

Px1 D x2

Px2 D f .x, t ,u/C �.x, t ,u/

y D x1 (11)

where initially known nonlinear dynamics of pressure manifold are

f .x, t ,u/D A4�x1,˛,Caf

�(12)



and the unknown dynamics to be estimated are

�.x, t ,u/D A7 .x1,!e/ �vol2 �

�A5�x1,!e ,˛,Caf

�CA6

�x1,!e ,˛,Caf

�CA8 .x1,!e/

��vol

(13)the dynamics in f .x, t ,u/ and �.x, t ,u/ are Lebesgue measurable in a compact region of x.

3.1. AIS observability and identifiability analysis

Under steady state conditions, gasoline engine states and parameters, listed in Table I, are nonzero.The following observability matrix (JPO ) and identifiability matrix (JPI ) are full ranked as jJPO j D18.406� 0¤ 0 and jJPI j D 1.1014� .�0.4685/¤ 0, respectively. This ensures pressure manifolddynamics to be observable and identifiable with respect to the parameters to be estimated [27].

JPO D

"A3�x1,˛,Caf

��A2!e�vol 0

@g2@x1

A3�x1,˛,Caf

��A2!e�vol

#(14)

JPI D

"A9.x1,˛/f .x1/

�A2x1!e@g2@Caf

@g2@�vol

#(15)

where @g2@x1

, @g2@Caf

and @g2@�vol

are given in Appendix.

3.2. AIS boundedness analysis

An ECU-equipped SI engine is operating under bounded input (˛ < 90°), the pressure dynamics willalways remain bounded. This characterizes the system as bounded input and bounded output sys-tem. Therefore, the uncertain function �.x, t ,u/ and its time derivative will always remain boundedby positive �C and ı�C, respectively.

3.3. Proposed SOSMO for AIS

In order to estimate the state vector x and to extract unknown variables, the observer in (17) basedon [28] has been proposed for automotive engine inlet manifold dynamics

POx1 D Ox2C ´1 (16)

POx2 D f .Ox, t ,u/C ´2Oy D Ox1 (17)

where Ox represents the observer states and ´1 & ´2 are the observer injectors based on super twist-ing algorithm. These injectors aim to eliminate the error between the estimated states and the actualstates, that is, .eD x� Ox/. These injectors are defined as

´1 D �1je1j1=2sign .e1/C 1

P1 D ˛1sign .e1/ (18)

and

´2 D 0 if e1 ¤ 0 & Pe1 ¤ 0´2 D �2 j´1j

1=2 sign .´1/C 2 if e1 D 0 & Pe1 D 0

P2 D ˛2sign .´1/ (19)


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Remark 2It can be seen that the proposed SOSMO for pressure manifold calculates the pressure derivative( Ox2) using (17) and then utilizes it in (16) for the calculation of manifold pressure ( Ox2).

The state x1 is available for measurement from the pressure sensor installed in inlet mani-fold that can be accessed from OBD-II scanner. The gains �1, ˛1 are the observer gains. TheSOSMO inherits anti-peaking structure, where e1 and e2 reach the sliding manifold one by one in arecursive way.

It can be observed in (18) that the chattering is reduced because of smart structure of the injec-tor. The super twisting-based injector consists of two parts. The first part contains je1j1=2; asthe error approaches to zero, this term vanishes out. As a consequence, the chattering magnitudecaused by sign.e1/ is greatly reduced. The second term contains integral of discontinuous term,that is, sign.e1/. The chattering caused by sign.e1/ is eliminated by integrating it (Low pass filteraction). Same procedure is adopted for ´2 in (19) with ´1 as sliding surface. Thus, the chatteringphenomenon is significantly reduced as compared with the first-order sliding mode techniques.

3.4. SOSMO convergence analysis

In order to analyze the convergence of the proposed observer for inlet manifold, 9 ˛ < 90°,8 t 2 <C

and 8 x19 k1 and k2, such that

f .x, t ,u/� f .Ox, t ,u/6 k1 jx1 � Ox1jdf .x, t ,u/� df .Ox, t ,u/

dt6 k2 jx2 � Ox2j (20)

is satisfied.Therefore, 8 t 2 <C, 8 x, Ox, u, intake pressure manifold dynamics satisfies

jF .x, Ox, t ,u/j< k1 je1j C �C (21)

d jF .x, Ox, t ,u/j

dt< k2 je2j C ı�

C (22)

where F.x, Ox, t ,u/D f .x, t ,u/� f .Ox, t ,u/.The condition (21) holds for engine manifold dynamics in (11), and the parameters of the pro-

posed observer in (17) are selected according to (23) for the convergence of Ox1 to x1 in finitetime [28].

˛1 >pk1 Pe1o C �

C

�1 >4˛1p˛1 � �C

(23)

Remark 3The choice of ˛1 and �1 depends on the bound of uncertainty and the initial state estimation error( Pe1o) in the worst case [28]. The observer parameters are taken as shown in Table II as F../ isbounded for engine pressure dynamics.

The error dynamics before converging to the surface, that is, e1 D 0 comes out to be

Pe1 D e2 � ´1

Pe2 D F .x, Ox, t ,u/ (24)

When e1 reaches the sliding manifold which means e1 D 0, ´1 D e2, the dynamics of e2 becomes

Pe2 D F .x, Ox, t ,u/� ´2 (25)

The constants .˛2,�2/ (Given in Table II) in ´2 can be chosen in a similar way as discussed for.˛1,�1/ in ´1 and convergence of e2 will be ensured in similar fashion [28].



Table II. Second-order slid-ing mode observer parameters

for Caf estimation.

Parameter Value

Ox1.0/ 25 kPaOx2.0/ 0˛1 10�1 40˛2 10�2 190

3.5. Estimation of Caf and �vol

After the second-order sliding mode has been achieved, that is, . Ox1, Ox2/! .x1, x2/. From (24), thesecond-order sliding mode dynamics can be written as

N1 D e2

N1 D x2 � Ox2 (26)

as the convergence of e1 is achieved, the convergence of e2 is also guaranteed. Under theconvergence of e2, the following sliding mode dynamics will be available then.

N2 D �.x, t ,u/

N2 D A7 .x1,!e/ �vol2 �

�A5�x1,!e ,˛,Caf

�CA6

�x1,!e ,˛,Caf

�CA8 .x1,!e/

��vol (27)

It can be observed that the only unknown in (27) is �vol that can be calculated as

�vol Dc1˙

qc21 � 4A7 .x1,!e/ N2

A7 .x1,!e/(28)

where

c1 D�A5�x1,!e ,˛,Caf

�CA6

�x1,!e ,˛,Caf

�CA8 .x1,!e/

�Once �vol has been estimated, it can lead to identification of Caf from (26) as

Caf D. N1C Ox2CA2�volx1!e/

A9 .x1,˛/(29)

whereA./i are defined in the Appendix. TheseA./i are formulated based on validated engine modelin (1)–(4).

Finally, the SOSMO-based estimation scheme for Caf and �vol can be summarized in Figure 3.

Remark 4The estimation of �vol involves an initial value of Caf , but later on the value of Caf , it is updatedwith an estimated value from (29). The recursive estimation of parameters involves iterative calcu-lations. For the calculation of Caf , �vol is replaced in (29) by (28) and vice versa. The new value ofCaf is updated as Caf .kC1/D ".Caf , where j"j< 1 is guaranteed for manifold pressure dynamics.Hence, the convergence and stability of Caf estimation is ensured.

Remark 5It may be kept in mind that N1 and N2 are the low pass filtered versions of ´1 and ´2, respec-tively. These low pass filters are employed to cater for switching affects of discontinuous injectorsin estimation results. The time constant of first-order low pass filter was chosen as 1 s.


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Figure 3. SOSMO-based estimation scheme for Caf and �vol .

Remark 6Equation (28) has two solutions in general; however, we are not interested in negative values havingno physical significance.

4. EXPERIMENTAL RESULTS

The estimation method formulated for Caf in the previous section was tested and implementedfor air filter health monitoring of a 1.3-L commercial vehicle engine. The vehicle is equipped withan OBD-II compliant ECU. The air intake path of the vehicle is equipped with pressure sensorto measure pressure inside the intake manifold. The pressure is sensed due to change in electricalresistance as the silicon chip in the sensor flexes with variable pressure. The rotational speed of theengine is measured by hall effect-based crankshaft sensor. Similarly, throttle valve manipulationscan be measured by the installed position sensor. The sensors measurements provide enough infor-mation for air filter health status. Each sensor is communicating with ECU and one can acquire thesesensor measurements using OBD-II scanner. The whole communication network is exchanging theinformation using ISO 9141-2 protocol. The OBD-II scanner connects the computer to ECU usingOBD-II cable. By OBD-II scanner, the experiment data can be recorded and analyzed for air filterhealth status.

Figure 4 shows the healthy and clogged air filter used in the diagnostic procedure. An experi-ment was performed in such a manner that the health diagnosis can be carried out accurately. Thispractice is termed as Active Diagnosis [29]. During the experiments, it was observed that at lowangular speeds, both air filters provided sufficient amount of air required by engine to carry out nor-mal operations. So, it was not possible to diagnose air filter health at low operating angular speeds.Finally, an experiment was conducted in steady state conditions at high angular speeds and loads.The throttle angle was kept at 18ı and loads were induced by turning on air conditioner, headlights,screen wipers, and fan. This practice helped to identify the health of air filter efficiently.



Figure 4. Air filters used in experimentation.

Figure 5. Input data acquired from OBD-II Scanner/Logger.

Remark 7The available OBD-II kit calculates the load torque according to a static relationship which is pro-portional to MAP sensor readings [30–32]. The load torque values acquired from OBD-II kit are thepercantage of the peak available torque, that is, 119 Nm.

Figure 5 shows the mean values of the ECU-equipped engine variables accessed by OBD-II kit. Itcan be observed that under steady state conditions, throttle valve remained at 18ı. With these inputsto the engine, the manifold pressure and angular speed can be seen as well. It can be observed thatthe measurements are corrupted with acquisition noise and engine behavior even in steady stateconditions. The same trends are observed in estimation results.

The acquired data sets (Figure 5) served as input for the proposed estimation and diagnosisscheme. In the first phase, observers convergence was achieved. Figure 6 shows the Pm of a 1.3-L engine and observers output and the convergence error for both air filters. It can be seen thatthroughout the experiments, SOSMOs efficiently tracked the actual values of manifold pressure.The estimators error remained close to zero.


Q. AHMED ET AL.

Figure 6. SOSMO convergence for both experiments of healthy and clogged air filter.

Figure 7. Estimated parameters for experiments with clogged and healthy air filter.

Remark 8The robustness of the observer can be visualized in Figure 6. Even with variations in enginebehavior, the designed observer tracked the engine outputs efficiently.

Once the observers were successfully running in second-order sliding modes, the computed uncer-tainty in injection signals ( N1, N2) were used for the estimation of air filter health. The observer in(17) for pressure dynamics was used to estimate �vol and Caf . In the first phase, �vol was com-puted through the uncertainty modeled in N2 as shown in (28). The estimated �vol was then fedback in (29) along with uncertainty modeled in N1 to compute Caf . The sequence of instantaneousvalues of both parameters acquired from (28) and (29) would represent sampled version of theircontinuous-time nonlinear representations. The smaller the sample time, each parameter will con-verge to its continuous time representation. Therefore, a reasonable sampling of time 0.01 s wasused to evaluate the observers in this paper.

Figure 7 depicts the estimated parameters. It can be observed that �vol remained around 0.7 forboth air filters. The value of Caf differed in case of healthy and clogged air filter. Caf remainedaround 0.3 for clogged air filer and for healthy air filter, it remained around 0.9. As the engine wasoperating under closed loop, �vol was maintained around 0.7 by ECU for both air filters. However,the interruption in air flow due to air filter remained the same even in closed loop. This uncertainhindrance in air flow was modeled under N1 by the designed SOSMO. Later on, Caf was calculatedbased on N1. That is why Caf varied in both cases as it is the measure of obstruction in air flow dueto air filter.

The estimated value of Caf reveals the realistic behavior of air filter. The healthy air filter allowsmaximum amount of air to pass through it, instead of all amount of air, where as clogged air filter



Figure 8. Air filter health monitoring strategy.

provided maximum hindrance to the air flow. Practically, Caf can never be equal to ‘1’ as some ofthe air flow will be blocked by porous material of air filter. Similarly, Caf can never be equal to ‘0’,as some of the air will always flow though air filter termed as clogged by the experts.

4.1. Air filter health monitoring methodology

The SOSMO-based estimation of Caf provides solid grounds to monitor air filter health. Figure 8outlines discrete steps necessary to classify air filter as clogged or healthy. The pressure dynam-ics of intake manifold in AIS can be exploited to generate information about air filter health. Themeasurements acquired from OBD-II scanner are used as input for SOSMO. The estimated value ofCaf measures the hindrance caused by air filter. On the basis of experimental results, a value below‘0.30’ of Caf indicates air filter replacement and a value closer to ‘1’ refers to healthy air filter.

4.1.1. Advantages of the proposed scheme. The proposed diagnostic scheme is cheaper and doesnot require extra pressure sensors as suggested in [4]. It is computationally inexpensive and possesthe potential for online implementation as it involves ‘sample by sample’ processing of the OBD-IIscanner data unlike other estimation schemes (Line Search, Levenberg Marquardt, Powell‘s DogLeg) that require a batch of samples for curve fitting to develop empirical relations. Moreover, theproposed diagnosis scheme remains valid for production line spread of a single make as it does notinvolve curve fitting.

5. CONCLUSION

A SOSMO-based SI engine air filter health monitoring scheme is proposed and demonstrated withactual implementation. The proposed scheme is computationally cheap and friendly to OBD-II com-pliant engines. The scheme depends on the estimated value of Caf to predict status of the filter anddoes not require any extra pressure sensors. Experimental results declared Caf as a clean indicator,as it successfully identified the healthy and clogged air filters of a 1.3-L commercial vehicle engine.


Q. AHMED ET AL.

APPENDIX

A1�˛,Caf

�DR.TmVm

CafAEPaCD�c

A2 DVd

Vm4�

A3�x1,˛,Caf

�D A1

1

Pa

��e

�x1Pa�1��

A4�x1,˛,Caf

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Gasoline engine air filter health monitoring by second-order sliding modes