Detection of Exhaust Manifold Leaks on a Turbocharged SI-engine with Wastegate

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1 Detection of Exhaut Manifold Leak on a Turbocharged SI-engine with Wategate Per Anderon and Lar Erikon Vehicular Sytem, Linköping Univerity, SWEDEN Copyright c 2002 Society of Automotive Engineer, Inc. ABSTRACT Emiion from modern SI-engine are reduced by a three way catalyt. However if there are leak in the exhaut ytem before the catalyt emiion increae for two reaon. irt the untreated emiion leak out. Second which i wore, due to wave in the exhaut ytem, oxygen leak into the manifold and caue an oxygen enor offet. The reult i increaed emiion a the air/fuel controller make the engine run rich. Here a method to detect leakage in the exhaut manifold i preented. The enor ued are binary oxygen enor(), intake manifold preure and temperature, and the air ma flow enor. Injection time i alo ued to etimate air/fuel ratio. Experimental reult are hown with meaurement from a turbo charged SAAB SI production engine with wategate. INTRODUCTION The three way catalyt (TWC) reduce mot of the emiion from modern park ignited (SI) engine when it i operated at a toichiometric air/fuel ratio [, 2] a input. A leak in the exhaut ytem before the catalyt increae emiion for two reaon: irt, untreated gae leak out. Second, due to wave in the exhaut ytem [3], oxygen can leak into the exhaut manifold and influence the meaured λ. The two cae are decribed in igure 2 where exhaut manifold preure i ampled with a high frequency for two different load. In the lower plot of igure 2 the minimum preure i above ambient all time which reult in a continuou leak of gae. The econd cae i hown in the top plot where the minimum preure i below ambient preure during approximately a quarter of the period. If a leak i preent in thi cae oxygen would leak in and mix with the exhaut gae. The oxygen would alo be tranported away from the hole by the velocity of the ga. Gae leaking out of the hole i therefore not necearily the ame a the gae leaking in. In the engine control ytem there i a cloed loop air/fuel ratio PI-controller, with feed-back from the binary oxygen enor. If oxygen leak into the exhaut manifold it may caue wind up of the controller or a bia on the integrating part. Running le than toichiometric alo increae fuel conumption, carbon monoxide and dioxide emiion, and hydrocarbon. Uing a rear oxygen enor the engine control ytem can compenate for the exce air. The impact on emiion can be approximated given the maximum converion efficiency. Emiion therefore increae proportional to the emiion before the TWC. To reduce the emiion a method to detect leakage before the firt oxygen enor i deirable. Current method for detecting leakage in the exhaut are e.g. litening to the engine ound, or filling the exhaut with moke injected via the tail pipe and look for preence of moke in the engine compartment. Here a computerized method to detect leakage in the exhaut manifold i preented. Detection i made poible by combining an oberver baed virtual exhaut manifold preure enor with etimated air/fuel ratio. A diagnoi framework, baed on hypothei tet [4] i then applied. Experiment with leakage are performed on a turbo charged SAAB SI production engine with wategate. The enor ued are: binary oxygen enor(), intake manifold preure and temperature enor, and the air ma flow enor. One actuator ignal i alo ued, the injection time ignal. ANALYSIS O THE IMPACT O A LEAKAGE or the cae of emiion leaking out, an approximation i made to etimate how large diameter that i required to exceed the emiion level for EURO-3 and 4. In igure chematic of the ytem i hown. Given that the maximum allowed emiion ma of pecie x after the TWC i lim x and the converion efficiency of the TWC i η x. The maximum ma fraction L that( can leak ) out i then given by the following inequality L limx m x η x +. To give an etimate of the leakage fraction L, the efficiency of the TWC η x i et to one. Thi reult in L limx m x. To etimate L a imulation of the EURO-3 driving cycle wa performed uing a longitudinal vehicle model of a SAAB 9 5. The model etimate the mean exhaut manifold preure through the cycle. Leakage i then etimated given mean exhaut preure together with Equation (). With thee aumption the emiion level for EURO-3 i exceeded

2 m x ( L)m x TWC Efficiency η x Lm x ( L)( η x)m x Low Load, no Leakage High Load, no Leakage Low Load, Leakage may be Preent High Load, Leakage may be Preent Low and High Load igure : Given a ma of emiion m x where x can be e.g. carbon monoxide. The ma fraction that pae through the leak i L and the converion efficiency of the TWC for pecie x i η x. Meaured Mean p e [kpa] Low Load High Load Preure [kpa] Preure [kpa] Low Exhaut Manifold Preure High Exhaut Manifold Preure igure 2: Exhaut preure variation during the cycle. Top: The lowet part of the preure wave i below ambient. Thi i referred to a low preure. Bottom: All of the preure wave i above ambient preure and thi cae i referred to a high preure. by leakage out of a 6 mm hole and EURO-4 by a 4 mm leak. DEINITION O LOW AND HIGH EXHAUST PRESSURE The deign of the diagnoi ytem i baed on a partition of exhaut preure into high and low preure, ee igure 2. Let tart by oberving that mean exhaut back preure i almot linear in ma flow through the engine [, 5]. The firt cae occur when the minimum of the exhaut preure wave are below ambient. If a leak i preent here air leak in. Hence low preure will be ued in the text to refer to operating point where the preure in the exhaut manifold i below ambient for part of the time. Thi condition i hown in the top of igure 2. High preure appear when the lowet preure i higher than the ambient preure all the time, which i the cae in the lower plot of igure 2. A leak in thi cae will caue emiion to leak out all the time and hence the exhaut manifold preure to drop Air Ma low [kg/] igure 3: Mean exhaut manifold preure plotted againt air ma flow for low and high exhaut manifold preure. There i a ditinct border between the elected limit for high and low load, which i hown a vertical line in the plot above. or low load the lowet exhaut manifold preure i below 98 kpa and for high load the lowet preure i above 02 kpa. Uing Air Ma low to Partition Exhaut Preure Low preure are defined from meaurement a where the minimum exhaut manifold preure wa below 98 kpa and high preure are defined for preure above 02 kpa. The limit are here arbitrarily choen a ambient preure i approximately 00 kpa and a limit of ± 2 kpa i added. The intantaneou preure i not eaily obtained and the mean exhaut manifold preure depend trongly on the ma flow through the engine. The reult i hown in igure 3. or air ma flow le than 25 g/ the lowet exhaut manifold preure wa below 98 kpa and for air ma flow above 32.5 g/ the minimum exhaut manifold preure wa over 02 kpa. low in between thee limit are not categorized a low or high uing thi method. However thi categorization capture the majority of the operating condition. DESIGN O DIAGNOSIS SYSTEM To diagnoe the leakage a framework with hypothei tet i ued [4]. irt the tatement of the diagnoi ytem i decided: Abbreviation N EML Explanation No fault Exhaut Manifold Leakage ault mode are initially decribed in word and then model are preented for the two tatement. A the ytem behave differently depending on exhaut manifold preure there are two cae. One for low preure, where air can leak into the exhaut manifold. The econd cae i for high preure where exhaut gae continuouly leak out. To apply the methodology ome aumption are made regarding the ytem needed 2

3 .02 Air/uel Ratio λ for Low Exhaut Preure W e Exhaut manifold W ecat Calculated λ [] Meaured Preure [kpa] No Leakage Leakage Air Ma low [kg/] Meaured Exhaut Manifold Preure for High Exhaut Preure No Leakage Leakage Air Ma low [kg/] igure 4: Top: Calculated air/fuel ratio. When there i a leakage the extra oxygen reult in a richer mixture to the engine. Bottom: Exhaut manifold preure for the different meaurement. When there i a leak preent at high ma flow the exhaut preure will drop lightly. Here it drop at mot 9 kpa. to deign the tet tatitic. No ault (N) Depending on the exhaut manifold preure two cae have to be conidered: Low preure No oxygen preent in the exhaut gae. High preure There i no exhaut manifold preure drop compared to what wa expected. Exhaut Manifold Leakage (EML) A for the no fault tate there are two cae: Low preure Oxygen i preent in the exhaut gae. High preure Due to the increaed flow of gae out of the exhaut manifold the preure drop compared to the fault free cae. Aumption irt the engine i aumed to be run tationary, that i the ame peed and load i held contant for approximately 20 econd. The engine model are only valid for a warmed up engine and the TWC doe not work for a cold engine, which mean that a warmed up engine i required. The dicrete oxygen enor i only ueful if the engine run toichiometric and thi will alo be required. Meaured data i time dicrete and the ample are aumed to be independent. W aleak A leak W eleak igure 5: Model of leakage in the exhaut manifold. Exhaut gae coming from the engine are W e and are paing through the exhaut manifold. A leak with area A leak may caue air to leak in, W aleak or emiion to leak out, W eleak. The gae, W ecat, are then paed on to the front oxygen enor and then to the catalyt. AULT MODELS ault are decribed by a model to which the meaured or etimated data are teted againt. If the fault model explain the data the tatement of the diagnoi ytem can be decided. In thi cae fault model are developed for the fault free cae (N) and for the exhaut manifold leakage cae (EML). When the model of the fault are fixed, tet tatitic are developed for the fault model. A tet tatitic i a function of the ampled data. A framework of hypothei tet are then applied to the tet tatitic. or a decription of the ymbol ued, pleae ee the nomenclature at the end. irt the exhaut manifold leakage model i decribed. Exhaut Manifold Leakage Model A mentioned earlier for low preure in the exhaut manifold air may leak in. or thi purpoe a model of the oxygen content i deired for low preure. Information of the oxygen content in the exhaut manifold i upplied by the binary oxygen enor(). or higher exhaut preure there i a contant flow out of the exhaut manifold cauing a drop in exhaut manifold preure. Here a virtual preure enor i ued to detect the change in preure without introducing any new enor. Change in exhaut manifold preure i called p em, and p em i calculated below: p em = p eexpected + p em Depending on the preure ratio, π = pem p a, between the exhaut manifold and the ambient air may flow into the exhaut manifold or exhaut emiion flow out. A traight forward approximation i to aume that the exhaut ga i an ideal ga flowing through a retriction with area A leak. If the exhaut preure i larger than the ambient preure emiion will flow out W eleak = p ( ) em Ψ A leak C d, π > () Re T em π The other cae occur when the ambient preure i higher than the exhaut manifold preure and air leak into the exhaut manifold. 3

4 W aleak = p a Ra T a Ψ(π) A leak C d, π < (2).0 Etimated and Meaured Change in air/fuel Ratio at Low Preure Meaured Change Etimated Change Ψ(π) = 2γ γ 2γ γ ) (π 2 γ+ γ π γ ( ( ) 2 γ 2 γ+ ( for π> ( ) 2 γ+ ) γ+ γ 2 γ+ ) γ γ otherwie λ Exhaut Preure Difference Model 0.95 or higher ma flow the minimum exhaut preure i above the atmopheric preure and therefore exhaut gae will leak out continuouly. Thi contant leak will decreae the exhaut manifold preure, which can be modeled uing the firt law of thermodynamic [6]. Exhaut manifold preure influence the ma of reidual gae remaining in the cylinder at exhaut valve cloing (EVC). The ma of air that can fill the cylinder depend on, among other, the ma of reidual gae. More reidual ga ma reult in le air ma to the cylinder and the other way around. The derivation of exhaut manifold preure uing enor on the intake ide can be briefly decribed a follow. Calculate whether the cylinder i filled with the expected ma of air. If not the offet m will differ from zero, ee Equation (3a). Since the air ma offet m i influenced by the exhaut manifold preure [6] a correponding change in exhaut manifold preure can be etimated, Equation (3b). m = η vol (N,p im ) p imv d R c T }{{ im } Expected air ma W at n r N }{{} Meaured air ma (3a) p em (T im,m )= kt im m (3b) In Equation (3b) k i a contant which i identified uing a leat quare technique. Oxygen Content Model or the fault free cae (no leakage) the influence of a leakage could be approximated uing meaurement of the preure wave in the exhaut and meaured air ma flow: λ new ( A ) W c + W aleak W f = λ no leak W c + W aleak W c (4) or the meaurement in igure 2 with application of Equation (2, 4) the change in air/fuel ratio can be approximated, ee igure 6. In the approximation of flow in and out of the manifold C d =wa ued in Equation () to give an approximation of the leakage. A known diturbance in thi experiment wa that only 0.5 econd of meaured data wa ued to etimate the leakage flow of air into the exhaut manifold Meaured Air Ma low [kg/] igure 6: Etimated change in λ in percent for different load and leakage area (4 mm and 5 mm diameter leak). The etimated change in λ i of the ame magnitude a the meaured. Since the lambda enor i enitive to oxygen in the exhaut gae and the lambda-controller ha an integration part which tore information of the air/fuel ratio. The reult i an offet in the integrating part of the air/fuel controller during a leak. Two ource are candidate for information on offet from the toichiometric: irt the integrating part of the air/fuel ratio controller. Second ource i etimated air/fuel ratio uing meaured air ma flow and injection time. Which of thee method i mot uitable for detection of oxygen leaking into the exhaut manifold? Let tart with the integration part of the air/fuel ratio controller. The advantage of thi information i that no additional computation are neceary a thi information i already available in the control unit. In ECU there are alo ome model decribing the ma of fuel to be injected given information of intake manifold preure and temperature, engine peed, and meaured air ma flow. Thi kind of information i often repreented by an engine map. If ome kind of tationary error i preent in thi map it i handled by the feed-back from the oxygen enor. However the error in the map then how up in the integrating part of the air/fuel ratio controller which i a le deirable property. Another drawback i that the integrating part may alo be influenced by the rear oxygen enor. Epecially if there i a leak of oxygen diturbing the front enor, the rear enor information will indicate preence or abence of oxygen. If the value of the integrator i to be ued, detailed knowledge of the rear enor feed back i neceary. The econd method i to ue knowledge of meaured air ma flow and injection time to etimate the current air/fuel ratio called λ calc. λ calc = W at ( A ) K inj (t inj t 0 ) N n r (5) Here additional knowledge of toichiometric air/fuel ratio i neceary a well a a model of the injector. One major advantage i that the air/fuel ratio till can be calculated regardle 4

5 of how the front and rear feed back from the oxygen enor influence the controller. Thi mean that no information of how controller are implemented i neceary. A diadvantage i that it ha two additional parameter K inj and t 0. Model error in K inj ha the ame impact a error in the toichiometric air/fuel ratio ( ) A. Error in the needle lift time t 0 are mot evident for mall injection time which unfortunately i the cae for low exhaut preure where the air ma flow i low. A drawback of the later method i it enitivity to fuel with different toichiometric air/fuel ratio ( ) A. To enure proper operation of the method a known fuel i neceary. Since the econd method with etimated air/fuel ratio i independent of the implementation of the air/fuel ratio controller it i choen a method to detect preence of oxygen. However if the tationary error in the ECU engine map are mall and detailed knowledge exit of how rear enor feed-back influence the value of the integrator it i the deirable method. The reaon i that it ha a poibility to handle change in fuel by combining information from the front and rear oxygen enor. Deign of Tet Statitic Two tet tatitic are ued. irt for the oxygen content the mean of λ calc i a a tet tatitic. The econd i the etimated exhaut manifold preure change p em. Both tet tatitic are modeled a contant parameter µ x. The parameter i etimated from a meaured ignal y(t), which i ubjected to noie v(t) originating from meaurement and model error. Noie i aumed to have a normal ditribution N(0,σ v ) and to be independent. Time dicrete meaurement are ued to etimate the contant parameter. A etimate of the contant parameter µ x, the mean value of the meaured ignal y(t) i ued. The etimated parameter i called ˆµ x. ˆµ x = N N y i = µ x + N i= N v i N(µ x, σ) N i= The tandard deviation of the etimate ˆµ x i σˆµx = σv N. Low Exhaut Preure Here the etimate of oxygen content i modeled uing the mean value of ampled λ calc a a parameter. λ calc = N λ calci (6) N High Exhaut Preure Etimate of change in exhaut manifold preure from expected preure i made by the virtual exhaut manifold preure enor p em. The change i etimated a the mean value of etimated preure change. i= [] [] Meaured Data Ditribution Compared to Normal Ditribution Normal Ditribution Meaured Data Ditribution Calculated λ [] Meaured Data Ditribution Compared to Normal Ditribution Normal Ditribution Meaured Data Ditribution Calculated p [kpa] e igure 7: Top: Ditribution of λ calc in the fault free cae. A normal ditribution wa aumed. Bottom: Exhaut manifold preure ditribution in the fault free cae. Value have been calculated for different tationary operating point. The hape reemble that of a normal ditribution. Hypothei Tet The preent fault i denoted p and a hypothei tet i formulated to tet whether there i a leakage in the exhaut manifold preent (EML) or if no fault i preent (N). H 0 : p {N} H : p {EML} Thi correpond to tet whether the variable i within a pecified region or not. If it i within the pecified region the nullhypothei H 0 can not be rejected. A threhold, denoted J, will be ued to uppre noie and model error. Value of the threhold i calculated uing theory from tatitical hypothei tet [7]. A ignificance level of 0.5% i ued in the deciion of the threhold. The elected threhold i a compromie between mied detection and fale alarm. The mied detection rate decreae a the fale alarm rate increae and vice vera. Low Exhaut Preure or low preure the oxygen content i teted uing: λ calc <J λcalc (8) If λ calc i above J λcalc no concluion can be drawn. Exhaut manifold leakage can be preent if λ calc i below the threhold a it indicate the preence of oxygen in the exhaut. The ditribution of λ calc in the fault free cae i hown in the top of igure 7 together with an approximation of a normal ditribution N(, 0.02). With the deired ignificance level the normal ditribution give the threhold J λcalc =0.95. p em = N N p em i (7) i= High Exhaut Preure At higher exhaut manifold preure, the preure drop compared to the no leak cae i tudied. If the preure in the exhaut manifold i lower than a pecified 5

6 Air filter.02 Low Exhaut Preure Experimental Reult Intercooler W a Air flow meter Compreor Throttle p em Turbine Shaft Turbine Calculated λ [] W c 0.94 p im, T im Intake Manifold Engine Wate Gate Exhaut Manifold λ Catalyt % Significance Level % Significance Level No Leak 4mm Leak 0.9 5mm Leak 6 and 6 mm Leak Air Ma low [g/] igure 8: Engine Schematic igure 9: Experimental reult uing calculated λ calc for low load. The line indicate different ignificance level. No fale alarm are preent but only 5% of the leakage are detected. threhold a leakage could be preent. p em <J pem (9) To decide the value of J pem the ditribution of p em in the fault free cae wa tudied, ee the lower plot in igure 7. A normal ditribution wa aumed and hence p em N(0,.7). With the deired ignificance level the threhold wa et to J pem = 4.3 kpa. Diagnoi Deciion In the diagnoi ytem there i one hypothei tet and two tet tatitic ued depending on the exhaut preure (low or high). The tet i rejected when the tet tatitic i within the rejection region, µ x >J x, and the deciion i EML. If the tet i not rejected the preence of an exhaut manifold leakage can not be dimied, and the deciion i N. EXPERIMENTAL SETUP In igure 8 a ketch of the engine ued i hown. It i a 2.3 dm 3 turbo charged SAAB 9 5 engine with additional enor for preure and temperature. In the exhaut ytem there i only one production enor before the catalyt and that i the oxygen enor. The engine i equipped with additional preure enor in the intake ytem before the throttle and in the intake manifold. Preure enor are alo preent in the exhaut ytem before and after the turbine There are alo extra temperature enor of PT200 type, in the intake manifold, between the intercooler and the throttle, and in the exhaut manifold cloe to the turbine. All meaurement are performed with a VXI-baed intrument HPE-45A. The engine i connected to an aynchronou Dyna 220 NT dynamometer, which i operated in contant peed mode. The dynamometer i controlled by a PC and the engine i controlled by a reearch engine management ytem called Trionic 7. The engine management unit i connected to a PC in the control room uing a CAN-bu. EXPERIMENTAL RESULTS The reearch engine i equipped with an exhaut manifold with additional plug in which leakage can be introduced. Leakage are created by removing a plug or replace it with another plug with a drilled hole. The leakage i applied on the exhaut manifold of cylinder 3. In the meaurement the engine i run tationary for 25 econd to allow for temperature and controller to tabilize. Data i then ampled for 30 econd which wa ued to evaluate the diagnoi ytem. Low Preure or low preure the etimated air/fuel ratio λ calc i the evaluated tet tatitic and the reult i hown in igure 9. or low preure there are no fale alarm but the mied detection rate i 85% for thee mall leakage. The ue of etimated air/fuel ratio λ calc require a defined fuel, ince different fuel may not have the ame toichiometric ratio. An example of uch diturbance i fuel which contain of alcohol. A changed air/fuel ratio caue the etimated λ calc to deviate from it nominal value and caue either a mied detection or a fale alarm. The outcome depend on the direction of air/fuel ratio change. uel with lower ( ) A increae the rik of fale alarm and fuel with higher ( ) A increae the rate of 6

7 Etimated Preure Drop [kpa] High Exhaut Preure Experimental Reult 6 0.5% Significance Level 5% Significance Level 0% Significance Level 7 No ault 4 mm Leak 5 mm Leak Air Ma low [g/] igure 0: Experimental reult uing etimated exhaut manifold preure drop. No fale alarm are encountered, but only one leakage i detected. mied detection. High Preure At higher exhaut manifold preure the etimated preure drop p em i the evaluated tet tatitic and the experimental reult are hown in igure 0. Here only one leakage i detected and that i one that differ ignificantly from the other meaurement, which indicate that it may be an etimation error ince the preure drop for the urrounding operating point doe not how thi behavior. The mied detection rate wa alo here 85%. The virtual exhaut manifold preure enor relie on information from the air ma meter and enor in the intake manifold. Change and uncertaintie in the enor reading caue error in the etimation of exhaut manifold preure. Thi can alo reult in mied detection or fale alarm. UTURE WORK The uggeted method how promiing reult for low exhaut manifold preure. At higher preure more data i needed to tudy the behavior of the exhaut manifold preure. Another intereting topic i how to merge the information from low and high exhaut manifold preure and make the diagnoi deciion baed on information fuion. CONCLUSIONS A diagnoi method for detecting leakage in the exhaut manifold have been developed uing the etimated air/fuel ratio and a mean value model of the exhaut manifold preure. A hypothei tet i ued to decide whether there i a leak or not. The ue of hypothei tet feature a poibility to uppre noie and modeling error by etting a ignificance level of the tet. The firt reult are encouraging but the experiment are not concluive yet. Low Preure or low exhaut manifold preure, the oxygen content of the exhaut gae i monitored. An increae in oxygen indicate a leakage. Detection of exhaut manifold leakage ha uccefully been hown for even mall leakage (4mm diameter). The mied detection rate i high but detection are made at low engine load. The method i very enitive to fuel change a it etimate the current air/fuel ratio, but it i independent of the implementation of the air/fuel controller and feed back from a rear oxygen enor. High Preure At high exhaut manifold preure, there i a continuou flow out of the exhaut manifold cauing the preure to drop, which can be detected uing a virtual exhaut manifold preure enor. Exhaut manifold preure etimation relie on accurate enor on the intake ide together with an good decription of the volumetric efficiency. No additional enor in the exhaut manifold are neceary. More validation data i however needed a the ytem wa not ufficiently excited. ACKNOWLEDGMENTS Thi work wa financially funded by the Swedih Agency for Innovation Sytem (VINNOVA). REERENCES [] John B. Heywood. Internal Combution Engine undamental. McGraw-Hill International Edition, 988. [2] P. Degobert. Automobile and Pollution. Society of Aoutomotive Engineer, Inc., 995. [3] R.J. Pearon D.E. Winterbone. Deign Technique for Engine Manifold Wave Action Method for IC Engine. SAE International, 999. [4] Mattia Nyberg. Model Baed ault Diagnoi: Method, Theory, and Automotive Engine Application. PhD thei, Linköping Univerity, June 999. [5] Johan Bergtröm and Jan Brugård. Modeling of a turbo charged park ignited engine. Mater thei, Linköping, 999. LiTH-ISY-EX

8 [6] Per Anderon and Lar Erikon. Exhaut manifold preure etimation on a turbocharged SI-engine with wategate. In IAC Workhop - Advance in Automotive Control; Karlruhe, Germany, March 200. [7] G. Caella and R. L. Berger. Statitical Inference. Duxbury Pre, 990. NOMENCLATURE Symbol m x η x lim x L p im p em p em p em m π J x T im T em T a η vol W a W at W c W f C d m λ λ calc λ calc ( A ) V d n r N t inj K inj t 0 Decription Raw emiion ma of pecie x, e.g. carbon monoxide. Efficiency of the TWC for the pecie x Emiion regulation for pecie x. Specifie maximum allowed ma of pecie x. Ma fraction of total emiion that leak out of an exhaut manifold leakage. Intake manifold preure Exhaut manifold preure Exhaut manifold preure difference from nominal (no leak). Mean value of exhaut manifold preure difference from nominal (no leak). Difference in air to cylinder from expected. Preure ratio Threhold in the hypothee tet. Temperature of gae inide the intake manifold Temperature of gae inide the exhaut manifold Ambient air temperature Volumetric efficiency Meaured air ma flow Air ma flow through throttle Air ma flow to cylinder uel ma flow Dicharge coefficient Air ma to cylinder offet, calculated uing mapped volumetric efficiency Normalized air/fuel ratio Etimated air/fuel ratio Mean value of etimated air/fuel ratio Stoichiometric air/fuel ratio Diplacement volume Number of revolution per cycle Engine peed i revolution per econd Time in econd where the injector i open Maximal delivered fuel ma per econd Time in econd for the injector needle lift 8