intake air path diagnostics for internal combustion engines

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Matthew A. Franchek1

Professor and Chair of Mechanical EngineeringDirector of Biomedical Engineering

University of Houston,Houston, TX 77204-4006

e-mail: [email protected]

Patrick J. BuehlerSchool of Mechanical Engineering,

Purdue University,1077 Ray W. Herrick Laboratories,

West Lafayette, IN 47907

Imad MakkiAdvanced Powertrain Control Systems,

Ford Motor Company,FPC-B, MD37,

760 Towncenter Dr.,Dearborn, MI 48126

Intake Air Path Diagnostics forInternal Combustion EnginesPresented is the detection, isolation, and estimation of faults that occur in the intake airpath of internal combustion engines during steady state operation. The proposed diag-nostic approach is based on a static air path model, which is adapted online such that themodel output matches the measured output during steady state conditions. The resultingchanges in the model coefficients create a vector whose magnitude and direction are usedfor fault detection and isolation. Fault estimation is realized by analyzing the residualbetween the actual sensor measurement and the output of the original (i.e., healthy)model. To identify the structure of the steady state air path model a process called systemprobing is developed. The proposed diagnostics algorithm is experimentally validated onthe intake air path of a Ford 4.6 L V-8 engine. The specific faults to be identified includetwo of the most problematic faults that degrade the performance of transient fuelingcontrollers: bias in the mass air flow sensor and a leak in the intake manifold. Theselected model inputs include throttle position and engine speed, and the output is themass air flow sensor measurement. �DOI: 10.1115/1.2397150�

IntroductionIn many applications, fixed coefficient controllers cannot main-

ain the level of system performance over the life of a product.his is especially true for open loop control systems with longervice lives. Consequently, adaptive control algorithms haveeen developed to maintain system performance in the presencef system aging and faults. This approach is often referred to asault-tolerant control and is typically application specific �1�. Aritical part of fault tolerant control is fault detection, isolation,nd estimation �FDIE�. The FDIE algorithm detects the fault, lo-ates the fault, and estimates the fault severity. This information ishen passed to the control system for the purpose of adaptation.

One class of systems with long service lives is internal com-ustion �I.C.� engines. Governmental regulations on the tailpipemissions and the overall health estimation of the engine and ex-aust aftertreatment systems require onboard diagnostics. Theeed for engine diagnostics can be established by considering thetandard transient fueling control problem. Transient fueling con-rol systems are open loop solutions that react to a driver’s input.his input moves the throttle plate, thereby changing the air flow

o the engine cylinders. A measurement of the air flow is accom-lished using either a mass-air flow �MAF� sensor or manifold airressure �MAP� sensor. From this air flow measurement, the fu-ling controller estimates the mass of air to be ingested into theylinder during the intake stroke using an air path model. Basedn this air mass estimate and knowing the desired air-fuel ratiohat meets the emission requirements, the transient fueling controlystem calculates the necessary mass of fuel. This mass fuel esti-ate is processed through a fuel path model whose output is a fuel

ulsewidth command given to the fuel injectors. Whether or nothe correct amount of fuel has been injected can only be ascer-ained after the combustion event has occurred. In particular, theesulting products from the combustion event are measured by anxhaust gas oxygen �EGO� sensor located in the exhaust manifold.rom this sensor measurement, the corresponding air-fuel ratioan be determined. Since an air-fuel ratio is sensed, the source forhe fueling error is not necessarily identified. For example, if theombustion mixture was lean, the EGO sensor measurement could

1Corresponding author.Contributed by the Dynamic Systems, Measurement, and Control Division of

SME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CON-

ROL. Manuscript received May 22, 2005; final manuscript received May 29, 2006.
ssociate Editor: Hemant M. Sardar.
2 / Vol. 129, JANUARY 2007 Copyright © 2

om: http://asmedigitalcollection.asme.org/ on 05/23/2014 Terms of Use: ht

not be used to ascertain if there was an error in underestimatingthe amount of air or if the commanded fuel pulsewidth is nowinjecting less fuel as a result of injector aging. This lack of infor-mation has made the adaptive feedforward fueling control prob-lem difficult since the root cause leading to fueling control adap-tation for fueling errors is elusive. Hence a diagnostic approach isnecessary to identify the root cause of these errors.

Tutorials and surveys of fault detection, isolation, and estima-tion methodologies can be found in Refs. �2–15� and referencestherein. Although many FDIE results have been published in theliterature, the results from these particular works influenced theresults of this manuscript. There are essentially two FDIE catego-ries: model-free and model-based methods. Model-free FDIE ap-proaches consist of limit checking, special sensors, multiple sen-sors, frequency analysis, and expert systems �14�. Model-basedFDIE methods consist of parameter estimation, state estimation,and parity equations �3�. For state estimation solutions, thechanges in model states are utilized to generate residuals �10�. Forparity equation solutions, an analytic model can be used to esti-mate a sensor output based on other sensor information �6,11�.The estimated sensor output can be compared to the actual sensoroutput to generate a residual. These residuals are then processed todiagnose faults �8�. Most model-based FDIE approaches do notutilize the size of the residuals beyond comparison to a threshold.This is to say that most model-based FDIE approaches do notattempt fault estimation. Furthermore, the residuals generated area result of combined faults, noise, and modeling errors. Sensitivityand robustness properties result from these and isolability proper-ties are mainly a result of modeling errors. FDIE has receivedconsiderable attention in the past three decades and an extensiveliterature base exists concerning these methods.

Two applications of fault detection and isolation relating to in-take manifold diagnostics have appeared in the literature �16,17�.Reference �16� advances a detection filter approach to sensor di-agnostics on I.C. engines and provides a tutorial on failure detec-tion and isolation theory. Detection filter diagnostics is a model-based diagnostics approach using residuals between the actualsystem output and an observer output. The models representingactuator and sensor failures are realized using the structure of themodel to isolate various sensor/acutator scenarios. In particular, ananticipated failure mode is introduced into the observer using anappropriate Bi matrix. This matrix processes a scalar that scalesthe actual system input such that the resulting model output would
match the measured output of the dynamic system. Although not
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he sole focus of the work, an experimental validation of the pro-osed detection filter diagnostic is applied to a 1987 3.0 L Fordngine manifold air pressure �MAP� sensor. A fault of a 10% shiftn the MAP is successfully detected, although an estimate of theault size was not obtained. Another model-based residual ap-roach to fault detection of an engine intake system is developedn Ref. �17�. This work was motivated by the common fault sce-arios in engines including manifold leaks and sensor faults. Toncrease the accuracy of the residual calculation, an improvedngine intake manifold model is developed. The major contribu-ion of this work is that a nonconstant discharge coefficient for their flow over the engine throttle was proposed. With this modelmprovement, isolation logic was used to accomplish fault detec-ion using the residuals. These fault scenarios were successfullyetected during experimental trials.

The commonalities among these works include the generationf a residual and the processing of this residual for fault detectionnd isolation. For each study, a detailed dynamic model was iden-ified so that a residual could be generated. In Ref. �16� directionalnformation in the state space was exploited through the introduc-ion of the Bi matrices. In Ref. �17� an improved nonlinear modelas proposed, thereby allowing for the detection of faults at aery early stage. However, the family of faults considered in theseorks appears during steady state operation. This simplificationill be used while seeking a unifying approach to sensor andardware faults that occur in intake manifolds of I.C. enginesuring steady state operation.

Developed is a diagnostics methodology focused on the detec-ion, isolation, and estimation of faults that occur in the intake airath of internal combustion engines during steady state operation.oth engine hardware faults �leaks� and sensor faults �measure-ent bias� are investigated. Each of these fault modes in an en-

ine manifest themselves during steady state as well as transientperation. However, for the purpose of fault detection, isolation,nd estimation, steady state intake manifold models will be used.nline adaptation of the steady state intake manifold model wille used for fault detection and isolation. The residual between ariginal steady state model and the actual sensor output will besed for fault estimation. The faults to be experimentally verifiednclude the 10% sensor bias proposed in Ref. �16� and an intake

anifold leak proposed in Ref. �17�. These works have set thetandard for intake manifold diagnostics.

Main ResultsDetailed in the following sections is the development of system

robing, a process used to identify the structure of the steady stateir path diagnostic model. Following this presentation is the de-elopment of the fault detection, isolation, and estimation solu-ions. To illuminate intake air path diagnostics, the proposed

ethod is experimentally verified on the intake air path of a Ford.6 L V-8 engine. The specific steady state faults to be identifiednclude a mass air flow sensor bias and a leak in the intake mani-old.

2.1 Steady State Model Identification. The success of aodel-based diagnostic solution is contingent upon model struc-

ure �8,14,15�. When first-principle-based models are used, thetructure of the model naturally emerges provided the actual dy-amics are fully understood. In the case of input/output �I/O�odels, model structure must be established. To develop a sys-

ematic approach for model structure identification, the method ofystem probing is developed. This method is developed as a gen-ral procedure for model structure identification for a class ofeakly nonlinear dynamic systems �18�. Here weakly nonlinear

mplies that the actual system response gradually departs frominear system behavior as the input size grows.

2.1.1 System Probing: Identification of Model Structure. Aroad class of weakly nonlinear �i.e., physical� systems can be
epresented by a Volterra series model �18�. The following extends
ournal of Dynamic Systems, Measurement, and Control


standard single-input-single-output �SISO� structure identificationof a truncated Volterra series ��18,19�� to a multi-input-single-output �MISO� formulation. One MISO truncated Volterra Seriesmodel is

y�t� = g0 + �a=0

N1

�b=0

N2

¯ �c=0

Nr

a=b=¯=c�0

�−�

�

ga,b,. . .,c�t�

�u1a�t − ��u2

b�t − �� ¯ urc�t − �� d� �1�

where r denotes the number of inputs, Ni is the highest power ofthe ith input ui�t� for i� I+/�r+1�, g0 is a constant, and ga,b,. . .,c�t�� l1 denotes causal, stable impulse response functions. Here the

�·� symbol denotes an estimated value from a model output. Thesteady state model for �1� is

ySS�t� = C0 + �a=0

N1

�b=0

N2

¯ �c=0

Nr

a=b=. . .=c�0

Ca,b,. . .,cu1a�t�u2

b�t� ¯ urc�t� �2�

where the C’s are constants.To identify the structure of �1� or equivalently �2�, that is, which

input combinations denoted as u1a�t−��u2

b�t−��¯urc�t−�� are

needed to accurately model a dynamic system, a frequency-basedapproach called system probing is developed. System probing ex-ploits the property of nonlinear systems forced by a harmonicinput. In particular, SISO nonlinear systems forced by a sinusoidalinput will produce an output comprised of that frequency as wellas integer multiples of that frequency. To identify which regres-sors are needed to represent a dynamic system, each input ui�t�will be comprised of a single distinct excitation frequency. Oncethe system response has settled to its particular solution com-prised of sinusoids, the power spectral density �PSD� of y�t� willreveal the needed model regressors. The regressor identificationprocess is recursive and is based on those regressors that producedsignificant amplitude peaks in the PSD of y�t�. Those regressorswith the largest peaks are included in the model. The model ac-curacy is recursive where additional regressors are identifiedbased on the remaining PSD amplitudes and the correspondingfrequencies. Such an approach for a SISO nonlinear system isadvanced in Ref. �19�. This investigation will focus on a class ofMISO nonlinear systems.

The development of MISO system probing begins by consider-ing the system defined in �1� and by letting each input be definedas

ui�t� = Ui sin��it�, i � I+/�r+1� �3�

where �1��2� ¯ ��r nor are these frequencies integer mul-tiples of each other. To identify the regressors, the steady stateoutput y�t� due to �3� will be analyzed. The steady state harmonicoutput of �1� due to �3� is

limt→�

y�t� = g0 + �a=0

N1

�b=0

N2

¯ �c=0

Nr

a=b=¯=c�0

�k=−a,−a+2,. . .

a

�l=−b,−b+2,. . .

b

¯ �m=−c,−c+2,. . .

c

��a,b,. . .,c,k,l,. . .,m

U1aU2

b¯ Ur

c

jk+l+¯+m �Ga,b,. . .,c�j�k�1 + l�2 + ¯

+ m�r��exp�j�Ga,b,. . .,c�j�k�1 + l�2 + ¯

+ m�r��exp�j�k�1 + l�2 + ¯ + m�r�t� �4�

where �a,b,. . .,c,±k,±l,. . .,±m=�a,b,. . .,c,�k,�l,. . .,�m, Gi=L�gi�t�, and j=−1. From �4�, the steady state output of y�t� due to �3� willcontain frequency components that are a combination of the inputfrequencies multiplied by their integer powers and subsequent in-teger powers that are reduced by a factor of 2 until the fundamen-
tal frequency or DC is reached. Furthermore, each PSD frequency
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omponent corresponds to regressors, namely u1au2

b¯ur

c, con-ained in the model. Note that each frequency component is scaledy a constant comprised of input magnitude information and theagnitude of Ga,b,. . .,c�s� evaluated at s= j�k�1+ l�2+ ¯ +m�r�.Steady State Model Example: Consider the nonlinear static sys-

em

f„u1�t�,u2�t�… = u12�t� + u1

2�t�u22�t�

f ui�t�=Ui sin��it� for i=1, 2 and �1��2, nor are they integerultiples of each other, then f�·� is

f„u1�t�,u2�t�… =U1

2

2�cos�2�1t� − 1� +

U12U2

2

4�1

2cos�2��1 + �2�t�

+1

2cos�2��1 − �2�t� − cos�2�1t� − cos�2�2t� + 1�

emark. From �4�, it can be seen that the magnitude of a fre-uency component produced by a specific regressor in y�t� couldask the contribution of a different regressor producing magni-

ude information at that frequency. Note that the above regressors

12�t� and u1

2�t�u22�t� both contribute frequency components at 2�1.

herefore, to probe the system each input is excited individuallyhile holding all other inputs constant to determine the individual

egressors uia. This individual input probing is then followed by

imultaneous input excitations to identify the significant crossroduct regressors u1

au2b¯ur

c. Note that when exciting multiplenputs, both the individual regressors and the cross product regres-ors will be seen in the PSD of the output y�t�. Hence, the choicef input frequencies should be chosen such that the sum and dif-erence of the integer powers of the excitation frequencies due tohe cross product regressors �see �4�� do not equal the integerower of the individual regressors multiplied by their correspond-ng input frequency. Although this development is applicable tooth transient and steady state system operation, the focus of thisaper will be limited to steady state operation. Identifying thei�t�’s in �1� for transient conditions is detailed in Ref. �20�.

2.2 Fault Detection, Isolation, and Estimation. Presented ishe proposed fault detection, isolation, and estimation methodol-gy for intake air paths of I.C. engines. Fault detection and isola-ion are realized by adapting the steady state air path models on-ine. A coefficient error vector is produced by comparing healthy

odel parameters to the adapted model parameters. The magni-ude of the coefficient error vector will be used to indicate

ig. 1 Power spectral density of MAF sensor output with en-ine speed fixed and a 10 rad/s throttle excitation

hether a fault exists. The direction of the coefficient error vector

4 / Vol. 129, JANUARY 2007


will be used to “point” to the fault location. Fault estimation isaccomplished by analyzing the residual between the health modeloutput and the actual sensor output.

One concern with fault detection is that of false positives. Is-sues that may contribute to the possibility of false detections in-clude model accuracy, sensor noise/accuracy, and system variabil-ity. Correctly identifying the model structure via system probingpartly addresses the model accuracy issue. In addition, changes inthe coefficients are used to establish fault detection instead ofusing the absolute values of the coefficients. Concerning sensornoise issues, the algorithm only considers steady state faults. Con-sequently sensor noise is attenuated by averaging and/or filteringof the sensor output. However, normal system variability that ap-pears during steady state conditions must be incorporated into theproposed process. This is accomplished by establishing a thresh-old where the magnitude of the coefficient error vector must begreater than a precalculated tolerance before a fault is declared.The details are presented herein.

2.2.1 Fault Detection. Let the healthy system steady statemodel coefficients construct the vector H defined as

Fig. 2 Power spectral density of MAF sensor output withthrottle fixed and a 6 rad/s engine speed excitation

Fig. 3 Power spectral density of the MAF sensor output with 6and 10 rad/s sine wave excitation from engine speed and
throttle
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H = �a1 a2 ¯ ai ¯ aX�T � RX�1 �5�

here X is the number of model coefficients. Next, define theteady state model coefficient vector for the adapted model, po-entially containing a fault, as

F = �b1 b2 ¯ bi ¯ bX�T � RX�1 �6�

sing �5� and �6� defines the model coefficients error vector, E, as

E = S�H − F� � RX�1 �7�here

S = diag� 1

a1

1

a2¯

1

ax� �8�

efining E as in �7� essentially expresses a normalized change inhe model coefficients. Therefore steady state models having co-fficients that differ in magnitude can be effectively addressed.

Detecting the existence of a fault is accomplished by evaluatinghe magnitude of E and ensuring that this error is not due totandard system variability. The presence of a system fault can beccomplished by calculating the residual

M = y�t� − ySSH �t� , if �E�2 − � � 0

0, �E�2 − � 0� �9�

here y�t� is the steady state filtered sensor output, ySSH �t� is the

teady state healthy intake air path model having the structureefined in �2�, � is a threshold value that represents system vari-bility �developed below�, and �E�2=�i=1

x �E�i ,1��2i� I+/�X+1�. Aonzero value for M whose 2-norm is greater than � indicates theresence of a fault.

Quantifying system variability. The degree of normal systemariability lower bounding � in �9� can be established when deter-ining the ai values in �5�. To identify the coefficients for the

ealthy model, a series of experiments is performed. For the ithest, the healthy model coefficient vector Hi is calculated. Mul-iple experiments produce a family of Hi’s where the mean valueor each element in H serves as a healthy model parameter in �5�.imultaneously a standard deviation calculation can be performed,

hereby establishing normal system variability. Hence, one defini-ion for the � parameter in �9� is

� = ��a1a2

¯ aX�T�2 �10�

ig. 4 Comparison of MAF sensor output and predicted out-ut before and after adaptation with a MAF sensor bias

here denotes standard deviation and ��1.



2.2.2 Fault Isolation. Once the fault has been detected �i.e.,�E�2−��0 in �9��, fault isolation will be realized through theprojection of E onto predefined vectors that facilitate isolation.Let these predefined vectors be denoted as Dirj where j� I+/�m+1� and m is the number of model input�s� plus one �for thesensor bias case�. The fault assessment vectors are defined to iso-late a fault to a specific path among the various paths that existbetween the steady state model input�s� and output. For the airpath application considered, m=3 since there are two inputs andits output.

Let the general unity fault direction vector for the jth path bedefined as

Dirj =1

�Dirj�2�d1 d2 ¯ di ¯ dx�T �11�

where di is either 0 or 1. Choosing the value of di is based on theinfluence of the jth input on the model regressors. Those steadystate model coefficients in �2� whose corresponding regressor con-tains the jth input will have unity entered in its location of theDirj direction vector. Else a zero will be entered.

Fault isolation can now be limited to a specific path throughprojection of E on each Dirj, namely

��j� = E · Dirj �12�

The location of the detected fault, denoted as ��l�, will be iso-lated as the largest projection

l = �j�max��j�� 13�

2.2.3 Fault Estimation. Fault estimation is accomplished byestablishing a proxy for the fault size. Letting the influence of thefault manifest itself as a multiplicative uncertainty in the steady

Fig. 5 Comparison of MAF sensor output and predicted out-put before and after adaptation with an intake manifold leak

state air path model gives

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y�t� = �1 + ��ySSH �t� �14�

his proxy is meaningful since the actual correction to the MAFstimate needed by the fueling control system is directly calcu-ated. From �14�, � can be calculated as

� =y�t� − ySS

H �t�ySS

H �t�=

M

ySSH �t�

�15�

here M is defined in �9�. The � metric is essentially a percentrror in the mass air flow predicted by the healthy steady state airath model.

2.3 Experimental Validation. The proposed fault detection,solation, and estimation process is applied to an internal combus-ion engine intake air path. The engine studied is a 1999 Ford.6 L V-8 fuel injected engine. The two faults to be identifiednclude a MAF sensor bias and a leak in the intake manifold.

2.3.1 Steady State Model Development for the Air Intake Path.ased on the dynamics of the engine intake air path, both throttleosition sensor �TPS� and engine speed signals �RPM� will besed as inputs to the steady state air path model. The model outputs the mass air flow �MAF� signal. The resulting steady state airath model from �2� is

VMAF = C0 + �a=0

N1

�b=0

N2

a=n�0

Ca,bVRPMa VTPS

b �16�

here C0 ,Ca,b’s are the model coefficients, VMAF is the MAFensor voltage, VRPM is the voltage of the engine speed sensor,nd VTPS is the throttle position sensor voltage.

Probing the system will identify the significant regressors in16� needed for the steady state model. The engine throttle waserturbated at a frequency of 10 rad/s �via a Jordan electronichrottle controller� and the engine speed was perturbated at a fre-uency of 6 rad/s �via an eddy current dynamometer�. The result-ng PSDs of the MAF sensor voltage are shown in Figs. 1–3.ased on the content of the PSDs, the structure of the steady stateodel is

VMAF = C0 + C0,1VTPS + C0,2VTPS2 + C0,3VTPS

3 + C1,0VRPM

+ C1,1VTPSVRPM �17�

able 1 Model coefficients for normal and fault engineperation

Normal Bias % difference Leak % difference

c0 −3.88 −3.48 10.3 −4.03 3.9c0,1

7.62 6.83 10.4 7.55 0.9c0,2 −3.30 −2.96 10.3 −3.31 0.5c0,3

0.429 0.385 10.3 0.448 4.6c1,0 −0.292 −0.264 9.7 −0.039 86.8c1,1

0.422 0.379 10.3 0.318 24.6

wing to the recursive nature of the model structure identifica-

6 / Vol. 129, JANUARY 2007


tion, additional regressors can be included in �17� if the modelaccuracy is not sufficient. This lack of model accuracy will pro-duce larger standard deviations used in �10� to determine �.

The engine speed/load conditions used to estimate the param-eters in �17� are based on the Federal Test Procedure �FTP� �21�drive cycle. One hundred six speed/load combinations spanningthe FTP speed/load envelope were used for model identification.By operating the engine at each speed-load point, the resultingmodel coefficients are identified as

VMAF = − 3.88 + 7.62VTPS − 3.30VTPS2 + 0.429VTPS

3 − 0.292VRPM

+ 0.422VTPSVRPM �18�

Five separate test runs of the 106 FTP operating points were per-formed to calibrate �18�. The 2-norm for the standard deviationsfor the healthy model coefficient calculations is

��a1a2

¯ aX�T�2 = 0.06 ⇒ � = 0.1 �19�

where � was rounded up to 0.1. The mean value of the absoluteerror at each speed/load point is 1.2% with a standard deviation of1.1%.

2.3.2 Phenomenological Intake Manifold Dynamic Model.Presented in this section is a review of a recent advancement inimproving a phenomenological model of an intake manifold. Thismodel will validate the results from system probing. The intake airpath model reviewed here is the one proposed in Ref. �17�. Thismodel builds upon well established intake manifold models devel-oped from the continuity equation for the intake manifold volume,the ideal gas law for the intake air, and the one-dimensional steadystate compressible flow through an orifice. However, in the modelof Ref. �17�, the discharge coefficient Cd is approximated with thepolynomial. The resulting equations are

mai =Cd� ,N�PatmAth� �

RTa

g�Pm� �20�

Cd� ,N� = �0�0�1 +�1

�0N� + �1�0�1 +

�1

�0N�

+ �2�0�1 +�1

�0N� 2 �21�

Table 2 Projections of the faults

Fault Direction EBias ELeak

MAF Bias Dir10.25 0.5

Leak before throttle Dir20.21 0.05

Leak after throttle Dir30.14 0.79

Ath� � = A0„1 − cos� + 0�… �22�

g�Pm� =�� 2

� + 1��+2�/��−2�

ifPm

Patm� � 2

� + 1��/��−1�

� Pm

Patm� 2�

� − 1�1 − � Pm

Patm��−1�/�

otherwise � �23�


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here mai is the mass air flow, Pm is the intake manifold pressure,atm is the atmospheric pressure, Ta is intake manifold tempera-

ure, � is the specific heat ratio, Ath� � is the open throttle area, s throttle angle, and N is engine speed. The parameters in �21� aredentified via engine testing.

To validate the model structure identification results obtainedrom the system probing process, let =sin��1t� and N=sin��2t�,here �1��2 nor are they integer multiples of each other. Sub-

tituting these signals into �21� gives

Cd� ,N� = C1 + C2 sin��2t� + C3 sin��1t�

+ C4 cos��1 + �2�t�cos��1 − �2�t�

+ C5�cos�2�1t� − 1� + C6�cos�cos�2�1 + �2�t�

− cos��2�1 − �2�t� − 2 sin��2t� �24�

here the Ci coefficients are a function of the �’s and �’s given in21� as well as constants. The difference between the steady stateodel structure identified in �18� and the steady state behavior of

he model in �20�–�23� is the N 2 regressor in �21� and the regres-or 3 �denoted as VTPS

3 � in �18�. Referring to Fig. 3, the N 2

egressor would place magnitude peaks at 14 and 26 rad/s. Theagnitude peak at 14 rad/s is about −55 dB and the peak at

6 rad/s is −52 dB and therefore neglected. In general, however,he polynomial nature of the steady state model in �16� matcheshe steady state behavior of the model developed in Ref. �17�.

2.3.3 Online Model Adaptation. The goal for online modeldaptation is for the model output to track the sensor output dur-ng steady state conditions. There are many techniques that can betilized for online adaptation �see Refs. �19,22,23� and referencesherein�. The approach proposed in this manuscript is the recur-ive least squares formulation using a forgetting factor �22�.

There are two primary issues associated with online parameterstimation. The first issue is sensor noise and the resulting bias inhe parameter estimates. This issue will be addressed by obtainingn ensemble average for each model input at a given steady stateperating condition. The second issue concerns numerical issuesf the recursive least squares solution, which are addressed byatisfying a persistency of excitation condition �22�. Persistencyf excitation will be achieved through two separate means. First,teady state model adaptation will only be executed when therror between the model output and the corresponding measuredensor output is greater than prespecified tolerance. Thus the cur-ent sensor/controller actuation information that serve as inputs tohe steady state model will contain information that is not redun-ant. Secondly, adaptation happens only once at a given steadytate operating condition provided an error exists. Once the steadytate operating condition has changed, online parameter estima-ion can be executed again �if need be�. To identify the modeloefficients online, the recursive least squares with exponentialorgetting formulation is used where the forgetting factor � washosen as 0.9997.

2.3.4 Mass Air Flow Sensor Fault Detection, Isolation, andstimation. To identify the existence of a fault, isolate its location,nd estimate its size, the results in Sec. 2.2 will be applied. First,efine the vector H in �5� with the model coefficients given in18�

Eleak = �0.039 0.009 0.005 0.046



H = �− 3.88 7.62 − 3.30 0.429 − 0.292 0.422�T

The value for � has been established as 0.1 in �19�. Next define thedirection vectors of �11� as

Dir1 = 6−1/2 · �1 1 1 1 1 1�T �25�

Dir2 = 4−1/2 · �1 1 1 1 0 0�T �26�

Dir3 = 2−1/2 · �0 0 0 0 1 1�T �27�

where Dir1 will correspond to MAF sensor bias �since all thecoefficients are influenced�, Dir2 indicates a leak between theMAF sensor and the throttle plate, and Dir3 indicates a leak in theair path between the throttle plate and the intake valves ultimatelyleading the engine speed.

Discussion. The vector Dir1 corresponding to a sensor bias isimmediate. For Dir2, not all of the air flow crossing the throttleplate comes from the MAF sensor intake. Instead there are at leasttwo sources of air, the leak and the MAF sensor intake. The per-cent contribution from each air source is contingent upon the flowresistance of the air filter and the size of the leak. Therefore, themodel coefficients relating VTPS to VMAF will be influenced. Nowconsider Dir3, which indicates a leak downstream of the enginethrottle. When a leak is introduced in the air path after the throttle,the amount of air being ingested through the leak is dependent onthe pressure difference between atmospheric pressure and the in-take manifold pressure. Engine speed will increase beyond what ispredicted by the air path model since additional air and hence fuelwill be going into the cylinders. However, the path between theMAF sensor and the throttle remains healthy. Thus the modelparameters between VRPM and VMAF will significantly change.

Validating the fault detection and isolation. To validate the faultvectors defined in �25�–�27�, an experimental investigation of thetwo faults are performed. Shown in Figs. 4 and 5 are the MAFsensor output and steady state model output before and after on-line adaptation. For the case of MAF sensor bias, a 10% bias wasadded to VMAF. The intake manifold leak after the throttle platewas introduced by unplugging the by-pass air valve hose feedingthe throttle body. The by-pass air value is used to siphon airaround the engine throttle for the purpose of idle speed control.This opened a half-inch diameter hole in the manifold. The result-ing model coefficients are summarized in Table 1. From Table 1 itcan be seen that the corresponding changes in the steady statemodel coefficients for the sensor bias case essentially changed bythe same percentage. The vectors �defined in �6�� for the MAFsensor bias and intake manifold leak are

Fbias = �− 3.48 6.83 − 2.96 0.385 − 0.264 0.379�T

and

Fleak = �− 4.03 7.55 − 3.31 0.448 − 0.039 0.318�T

where Fbias contains the coefficients of the model when a biasedMAF sensor is present in the engine and Fleak contains the coef-ficients of the model when an intake manifold leak is present inthe engine. The error vector can be computed from �7�

Ebias = �0.103 0.104 0.103 0.103 0.097 0.103�T, �Ebias�2 = 0.25

T
0.868 0.246� , �Eleak�2 = 0.90
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he projections of each error vector on each fault direction vectorre given in Table 2. Each fault was correctly isolated to its ap-ropriate path.

Validating the fault estimation. Experimental validation of faultstimations is presented. As detailed in Sec. 2.2.3, fault estimations accomplished by calculating � in �15�. The online comparisonor fault estimation is completed using the postadaptation condi-ions shown in Figs. 4 and 5. For the MAF sensor bias case, the

Fig. 6 Estimation of the fau

Fig. 7 Estimation of the fault

8 / Vol. 129, JANUARY 2007


difference between the actual biased MAF signal and the healthymodel prediction of �18� is shown in Fig. 6. The MAF sensorsignal is also provided to indicate the engine operating condition.The large amplitude spikes evident in the � transients are duringsignificant transients in the engine mass-air flow. This is expectedsince the model in �18� is for steady state engine operation. Themean value for the � in Fig. 6 is 0.11, which is to be compared to0.10, the 10% bias. The 0.11 value is based on transient as wellassteady state information. If the steady state information is

ize due to MAF sensor bias
lt s
size due to a manifold leak


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arsed from the data set, an estimate of 0.1 is recovered for �.The � between �18� and the actual MAF signal for the intakeanifold leak case is shown in Figs. 7 and 8. Again, the MAF

ensor signal is included in the figure. The mean value for �hown in Fig. 7 is 0.04. Based on the results of the MAF sensorias case, this could lead to a possible conclusion that an average% more mass-air flow is due to the leak. However, an overallverage is not as useful since the amount of additional mass airow will be contingent upon engine speed and throttle opening.onsider a more detailed view of Fig. 7 given in Fig. 8. At higherass air flow rates, the magnitude of the � is on the order of 4%

t=800 s, for example�. At the lower mass air flow rates, around00 s, the � size is approximately 10%. This observation can bexplained by considering the amount of mass air flow through a/2 in.-diameter hole in comparison to that flow through a throttle

hat is largely open �high mass air flow rates� and one that isostly closed �lower mass air flow rates�. It is expected that the

eak contributes more of a percentage to the total mass air flowhen the throttle opening is small.

ConclusionsDeveloped is a steady state intake air path diagnostics. In par-

icular, this work focuses on the development and adaptation ofhe steady state air path models that track the MAF sensor output.

model regressor identification technique called system probings introduced for a MISO Volterra Series model structure identifi-ation. The FDIE algorithm is developed to utilize the informationenerated by the adapted steady state model. Specifically, theodel coefficients are utilized to detect and isolate a fault. Analy-

is of the residual between the actual sensor output and theealthy model output provides fault estimation. This approach toDIE addresses issues associated with the model-based diagnos-

ics such as system to system variation, and diagnosing both thehysical system hardware �i.e., intake manifold leak� health andensor faults �i.e., MAF sensor bias�. Basing system diagnosticsnformation on the evolution of the steady state air path modeloefficients has advantages in addressing system variability, initialodel calibration, and reducing the potential for false detections.

Fig. 8 Estimation of the fault size

he FDIE algorithm is demonstrated on a Ford 4.6 L V-8 engine



where the focus is the diagnosis of the MAF sensor used fortransient engine fueling control. For the two engine faults consid-ered in this experimental study, it is demonstrated that each lead toa unique change in the model coefficients. As a result the rootcause and degree of intake air path degradation can be captured.

AcknowledgmentThe authors would like to thank Steve Smith and Fai Yeung at

Ford Motor Company for the donation of the 4.6 L V-8 engine,and Fritz Peacock and R. J. Brown of the Ray W. Herrick Labo-ratories for their technical support. The financial support under theNational Science Foundation Grant No. CMS0097807 and a grantfrom the Texas Learning and Computation Center at the Univer-sity of Houston are also gratefully acknowledged.

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�12� Patton, R. J., and Chen, J., 1996, “Robust Fault Detection and Isolation �fdi�Systems,” Control. Dyn. Syst., 74, pp. 171–224.

�13� Patton, R. J., and Ding, X., 1997, “Survey of Robust Residual Generation andEvaluation Methods in Observer Based Fault Detection,” J. Process Control,7, pp. 403–424.

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Glasgow, Scotland, U.K., pp. 719–724.�18� Schetzen, M., 1980, The Volterra and Wiener Theories of Nonlinear Systems,

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intake air path diagnostics for internal combustion engines

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