Patent ID: 12215645

DETAILED DESCRIPTION

InFIG.1B, the internal combustion engine1is shown in a more detailed schematic view. The internal combustion engine1has cylinders Z1, Z2, Z3and Z4, wherein all cylinders Z provide their torque contribution M to a crankshaft of a crank drive KT. The internal combustion engine1additionally comprises a control means2according to an exemplary embodiment of the invention, optionally comprising a computing unit4if the control means2is not formed as part of an engine control unit. The control means2further comprises a speed detection unit6and a cylinder pressure detection unit7for the reference pressures from the surrounding environment and air collector or crankcase. The control means2also has a cylinder volume determination unit and a cylinder temperature determination unit and can access measured values of all lambda sensors of the internal combustion engine1.

FIG.1Bshows, inter alia, that, depending on the particular cylinder pressure p, each cylinder Z can cyclically apply a torque contribution M to the crankshaft drive KT. The totality of the torque contributions results in a time-variable speed n of a crankshaft of the crank drive KT.

The reference pressure p can be used by means of the pressure detection unit7, the instantaneous speed n can be used by means of the speed detection unit6, and the computing unit4can be used by the device2.

FIG.1Cshows a graph of a torque development Mgeswith an exemplary torque curve10at the crankshaft drive KT during normal operation over the crank angle KW. It is evident that the torque contribution M comes alternately from different cylinders Z. A torque limit value14is drawn in the illustration and is set in particular arbitrarily and determines below which torque a torque contribution of a cylinder is considered insignificant, so that a low-torque range12in the sense of the invention then exists. Consequently, a low-torque range12in the sense of the invention can be identified if, at a certain time interval, the torque contributions of each cylinder are below the limit value14.

In the embodiment ofFIG.1C, low-torque ranges12of slightly different lengths result. Within each of these low-torque ranges12, in particular, a diagnosis time window112can be defined and may comprise the entire period of the low-torque range or a part thereof.

FIG.2shows a sketch of an exemplary graph150of a development in the speed101of a four-stroke cycle (=one operating cycle (ASP): top dead center charge change (LOT)→intake→bottom dead center (UT)→valve closure and compression→top dead center ignition (ZOT)→expansion→UT→exhaust) of the internal combustion engine1.

The sequence diagram150shows the curve101of the engine speed n over an operating cycle (ASP) of a 4-cylinder gasoline engine. The ignition timing points (ZZP) and an example of a possible diagnosis time window112for the cylinder Z1to be diagnosed in the compression phase are marked. Below this, the associated power strokes of the physical cylinders Z1-Z4are shown.

This example of a four-cylinder engine shows which range112of the crank angle scale can be used for charge change diagnosis. The diagnosis time window112for the cylinder Z1to be diagnosed is in the compression phase, i.e. when the intake phase has already been completed and there is also a low-torque range (cf. limit value14inFIG.1C).

In particular, the diagnosis time window112must be selected so that the last cylinder performing work no longer achieves acceleration of the crankshaft and the next cylinder performing work has not yet fired.

In the exemplary embodiment, the diagnosis time window comprises a time interval in which the inlet valves of the cylinder Z1to be diagnosed are closed again after the intake of the charge air or the combustion mixture, and in addition a low-torque range of the internal combustion engine1is present. The limits depend on an applied engine operating point and can be flexibly adapted thereto. Dynamic adaptation of the limits of the diagnosis time window112is also possible for dynamic driving operation in dependence on boundary conditions such as an ignition angle and the cylinder pressure curve.

In the exemplary embodiment, therefore, the diagnosis time window112is determined to be 660° KW to 690° KW, relative to a crank angle value of cylinder Z1. In the illustration ofFIGS.1C and2—which is based on the entire internal combustion engine with four cylinders—this crank angle value corresponds to −60° to −30° before top dead center of ignition (ZOT). In the following, only 660° KW to 690° KW is concerned.

FIG.3shows the detail X fromFIG.2, i.e. the development in the speed101over the crank angle KW during the diagnosis time window112with the limit points P1and P2of the diagnosis time window of cylinder Z1. The pressure p1prevails in the cylinder at point P1, and pressure p2at point P2.

A diagnosis time point113in the diagnosis time window112is determined, for example in the middle of the diagnosis time window at 675° KW. For this time point, the temperature T* in the combustion chamber of cylinder Z1is calculated, for example. For the determination of the diagnostic cylinder pressure pdiagin dependence on the development in the speed101, on the other hand, a time window such as the diagnosis time window112is required because the determination is based on a difference consideration.

FIGS.2to6explain an exemplary embodiment of methods according to the invention for determining a fresh-air mass parameter rf in a cylinder Z of the internal combustion engine1in driving operation with the aid of the crankshaft speed n of the crankshaft drive KT.

As shown inFIG.6, the method carried out in the exemplary embodiment is described below: S10: Determine whether at least quasi steady-state operation SB or transient operation TB of the internal combustion engine1is present.

S20: If transient operation TB of the internal combustion engine is present, the cylinder Z1which is at the end of the intake stroke or at the beginning of the compression stroke is identified.

S30: Determine the diagnosis time window112for the identified cylinder Z1in the low-torque range12of the internal combustion engine1.

S40: Determine the development of the speed101of the internal combustion engine during the specified diagnosis time window112with a real-time-capable sampling quality. A live engine control function continuously reads out speed values n for the crankshaft KT during driving operation (due to gas friction delay (and for the present purposes disregarded delay due to mechanical friction), an increased speed drop from one to a subsequent point in time is to be expected in a compression phase of a cylinder) and determines a development in the speed from this—cf.FIGS.1-3.

S50: Determine the pressure characteristicpcyl,diagfor the cylinder Z1in diagnosis time window112in dependence on the determined development in the speed101.

S60: Determine the simplified cylinder load parameter rf* in dependence on the determined pressure characteristicpcyl,diagfor the cylinder Z1in the diagnosis time window112.

S70: Determine the fresh-air mass parameter rf for transient operation TB in the identified cylinder Z1in dependence on the determined simplified cylinder load parameter rf*, in the exemplary embodiment additionally in dependence on a steady-state cylinder load parameter rfSBand/or an offset prediction rfOFFSETof the fresh-air mass parameter derived therefrom and determined in a manner known per se by means of the engine control unit for steady-state operation (cf. step S160for steady-state operation SB). Depending on the operating state of the internal combustion engine—in particular depending on the degree of transience of engine operation—control of the fuel quantity to be injected purely on the basis of the determined, simplified cylinder load variable may be sufficient; or the injection quantity may already be subject to feedforward control on the basis of known methods for determining the fresh air quantity in the cylinder in steady-state operation or for offset prediction on the basis of such values.

S160: A steady-state cylinder load parameter rfSBand/or an offset prediction rfOFFSETof the fresh-air mass parameter derived therefrom are determined in a manner known per se by means of the engine control unit. The step can also be carried out to support the feedforward control of the fuel injection quantity if transient operation TB is present; cf. input variables for determining the fresh-air mass parameter rf according to step S70.

S170: Determine the fresh-air mass parameter rf for steady-state operation SB in the identified cylinder Z1in dependence on a steady-state cylinder load parameter rfSBalready determined (in a manner known per se) by means of the engine control unit for steady-state operation and/or an offset prediction rfOFFSETof the fresh-air mass parameter derived therefrom. The simplified cylinder load parameter rf* is not used for steady-state operation SB.

In the exemplary embodiment, various options are provided for using the determined values of the fresh-air mass parameter rf for onboard diagnostics204and/or offboard diagnostics208and/or control tasks206by means of the engine control unit2(cf.FIG.6).

For this purpose, the values determined are continuously stored in a non-volatile memory202of the engine control unit2during driving operation of the motor vehicle or are stored for further use. If, for example, the associated value for the fresh-air mass parameter rf is evaluated for each cylinder Z at each ignition, a new value of the fresh-air mass parameter rf is stored in the memory202for each ignition—in particular with a time stamp and/or output values for determining and/or specifying the diagnosed cylinder, for example Z1.

The stored values of the fresh-air mass parameter rf can be provided in real time, i.e. in particular immediately during driving operation, for example to an online diagnostic component204and/or an engine closed-loop control206of the engine control unit2. Also, the values of the fresh-air mass parameter rf can be made available to an offboard diagnostic computer208at a later time, for example in the workshop.

In the following, it is explained in detail—inter alia on the basis of the illustrations inFIGS.4and5—how the simplified cylinder load parameter rf* and, on that basis, the fresh-air mass parameter rf are determined in the exemplary embodiment.

As can be seen fromFIG.4, the following relationship applies to the composition of the gas mass in cylinder Z1in diagnosis time window112:
m=mtot=mair+mfuel+mresidual gas(1)

The following relationship exists here between the air mass and the fuel mass:

mfuel=ma⁢i⁢rλ·Lst(2)

Formula symbolMeaningλmeasured combustion air ratio (<1 =“rich”, 1 = stoichiometric, >1 = “lean”)Lstfuel-dependent chemical constant, so-called stoichiometric fuel-air ratio,typically between 14-16

Equation (2) in (1) gives

mt⁢o⁢t=mair·(1+1λ·Ls⁢t)+mresidual⁢gas(3)

In the exemplary embodiment, a substitution of the residual gas mass takes place via typical engine control variables:
mresidual gas=xrg·mtot(4)

The residual gas mass can be interpreted as fraction xrg of the total mass.

In order to perform a substitution of the absolute air mass in equation 3, the following relationship is introduced based on typical engine control variables:

mair=rfS⁢B·p0·VmaxR·T0(5)

Formula symbolMeaningrfSBSteady-state fresh-air mass parameter,relative air charge of the cylinder in %p0atmospheric pressure under standardconditions (1013 hPa)Vmaxmaximum cylinder volume at bottomdead center of the crankshaftRideal gas constantT0ambient temperature under standardconditions (293 K)

The current air mass in the cylinder is determined in advance in the engine control unit as the steady-state fresh-air mass parameter rfSBfor the purpose of correct fuel addition.

The function known per se and already present in the engine control unit for this purpose is the so-called load detection for steady-state engine operating states. It estimates a relative filling in percent.

The aim of the exemplary method described here is to improve the estimation of the reference variable rf. (The filling rf is defined as 100% if the max. cylinder volume were completely filled with air under standard conditions, cf. ideal gas equation):

mair=rf·p0·VmaxR·T0(5.5)

The total cylinder mass in turn results from the current thermodynamic ratios of cylinder pressure p*, cylinder volume V* and temperature T* in the cylinder, since the cylinder is not only filled with air and the components of fuel and residual gas lead to an increase in pressure:

Formula symbolMeaningp*Cylinder pressure in diagnosis timewindowV*Cylinder volume at time of diagnosisRideal gas constantT*Temperature T* in the cylinder at thetime of diagnosis

mtot=p*·V*R·T*(6)

Insertion of (6), (5.5) and (4) into (3) including rearrangement and truncation leads to this relationship:

p*·V*·1-xrgT*=rf·p0·VmaxT0·(1+1λ·Ls⁢t)(7)

Based onFIGS.5A-E, it is explained below how—starting from equation (7)—a simplified relationship is established which manages with a smaller number of variable quantities and thus also with significantly lower computing power in the engine control unit, so that a simplified cylinder load parameter rf* can be determined in real time. In this exemplary embodiment, real-time capability means that the simplified cylinder load parameter rf* can be used to determine a fuel injection quantity for the next cycle on the basis of the values determined for one cycle.

FIGS.5A-Fshow a graphical derivation of simplifying assumptions for the interrelationships of the cylinder content parameters and the state variables.

Starting from the complete relationship shown inFIG.5A, a further simplification is introduced with each furtherFIGS.5B,5C,5D and5E, so that finally inFIG.5Fa simplified relationship is shown which nevertheless still permits a statement accuracy sufficient for the purposes of the invention.

The simplifications for equation (7) are aimed at parameterizing the residual gas fraction xrg and the cylinder temperature T*.

FIG.5Ashows the full relationship of the variables. The line thickness represents the correlation strength. Each line is considered in first approximation as an approximation of a proportionality relation, in order to simplify again the existing equation set later. Dashed lines indicate inverse proportionality (and are marked “indirect” accordingly).

The cylinder Z1is filled with a fresh-air mass mair, which is represented by the fresh-air mass parameter rf. In addition, the cylinder is filled with the fuel mass mruei and a residual gas mass mresidual gas, which is represented by the residual gas fraction xrg.

Indirectly or directly, all three parameters of the cylinder content act on at least one of the two relevant state variables of the mixture in the cylinder Z1, namely p* and V*.

The residual gas fraction xrg has a medium influence on the total mass mtotin the cylinder; likewise on the temperature T*. The residual gas fraction xrg also has a small influence on the pressure p* in the cylinder. Both are known from experimental observations and can be regarded as generalizable.

The fresh-air mass parameter rf has a major influence in each case on the total mass mtotin the cylinder and thus also on the fuel mass mfuel.

The total mass mtotalin the cylinder in turn has a large influence on the cylinder pressure p* via the ideal gas equation.

The cylinder pressure p* in turn has a large influence on the temperature T* star in the cylinder.

FIG.5Bshows a change in the use of the residual gas fraction xrg to an inversely proportional consideration to allow for a later simplification step in which an indirect influence of the residual gas fraction on the cylinder pressure is introduced (cf. Figure D).

InFIG.5C, a removal of “weak” connections and then solitary adjacent elements occurs.

InFIG.5D, the intermediate quantity mtotis substituted as shown.

InFIG.5E, a “weak” connection resulting from the substitution step is removed.

InFIG.5F, only a conversion to the temperature T* as the target variable is shown. Since each line was considered as an approximation of a proportionality relation, two borrowable substitution equations result from the diagram shown. The first substitution equation is:
T*=C2·p*(8)

With the further relationship
(T*)C1·(1−xrg)1=C0|C1>1
this gives
(C2·p*)C1·(1−xrg)=C0
and by combining the constants
p*C1·(1−xrg)=C3
or converted to the second substitution equation
1−xrg=C3·p*−C1(9)

Equations (8) and (9) are now used for the corresponding variables of equation (7) and, in addition, an amalgamation of the constants is provided:

C⁢4·p*C⁢5·V*=rf·p0·VmaxT0·(1+1λ·Ls⁢t)(10)

The determination of the constants C4, C5, etc. in the model equations was carried out in the exemplary embodiment on the development engine with the aid of the following procedure: a complete characteristic map (speed/load) is measured; evaluation of cylinder indexing p* and calculation of xrg and T* via corresponding gas exchange analyses; then, accordingly, a calculation of the respective characteristic values is carried out from the results and plotting over mean engine speed (characteristic curve).

The combining of the constant C4with the fixed values p0, T0and Vmaxgives in the following:

C⁢6·p*C⁢5·V*=rf·(1+1λ·Ls⁢t)(11)

Lastly, it is now possible to convert to rf and thus derive the determination rule for the relative load, in this case initially the simplified fresh-air mass parameter rf*:

rf*=C⁢6·p*C5+C⁢71+1λ·Ls⁢t·V*(12)

The constant C7was introduced subsequently in the application of equation (12) to make the model as adaptable as possible. (The constant C7can also be assumed to be C7=0 in the initial application and can later take on other values accordingly for improved model accuracy).

Below is a table for determining the open parameters for rf estimation:

ValueUnitDescriptionC6[%/Nm]Scaling factor: working term to loadC5[—]Exponential scaler: pressure to loadC7[bar]Offset: pressure to load (Default = 0)

The values for λ, LStand V*, in each case for a time defined by the crankshaft position of the diagnosis time point113, can be taken from known engine control units, including that of the exemplary embodiment.

A diagnostic cylinder pressure valuepcyl,diagfor the diagnosis time window112is determined as the value for p*.

How this is possible can be taken from the following description for equations (13)-(28), wherein, from the determined diagnosis time window (see explanations forFIG.2) φ1corresponds to the crank angle KW=660°0of P1and p2corresponds to the crank angle KW=690° of P2, and accordingly in the shown exemplary embodimentpcyl,diag=pcyl1, diag, 660-690.

The determination is based on a pressure balancing of the diagnosed cylinder on the basis of the measured speed curve:

ddt⁢(12·J0·ω2)=(Mtan-MR-ML)·ω

Formula symbolMeaningJ0, JGeneral/proportional mass moment ofinertiaφAngular position of crankshaftωAngular velocityMtanMoment due to gas force in cylinderand oscillating mass forceMRMoment due to friction lossesMLMoment due to load reductionMMProportional moment due to rotationalmass inertianmotCurrently applied motor speed

By differentiation, substitution and introduction of a mass moment (division of inertia components), the following equation is obtained:

J·ω.=∑iMi=Mtan-MR-ML-MM

If the equation is divided sensibly into a “constant component” and an “alternating component”, the following sub-equations are obtained:
“Constant component”:Mtan=MR−ML

The balancing of the constant component assumes a steady-state operating point. The mean provided torque keeps the mean speed constant because it corresponds to the torque demands from load and friction.
“Alternating component”:J·{dot over (ω)}={tilde over (M)}tan−{tilde over (M)}R−{tilde over (M)}M(13)

A conversion from time-based derivation to crank-angle-based differencing is performed using the relationship

ω=d⁢φdt=π·nmot3⁢0⁢per(14)ω˙≈(π3⁢0)2·nmot·Δ⁢nmotΔφ

The decisive quantities from equation (13) are further detailed for the evaluation. The relationship for the resulting moment from the inner-cylindrical gas force results in:

=[AK·[Pcyl(φ)-p0]-mosc·s¨(φ)]·rK·sin⁡(φ+β)cos⁢β(15)

Formula symbolMeaningAKPiston top surface = const.rKEffective radius of the crankshaftcorresponds to half stroke = const.lPlConnecting rod length = const.moscOscillatory mass part corresponds topiston assembly and proportionalconnecting rod mass = const.pcylPressure prevailing in cylinderp0Reference pressure, crankcase pressureB(φ)Connecting rod pivot angle independence on crank angle position{umlaut over (s)}(φ)Piston acceleration in dependence onpiston position

A further detailing of the variable factors from equation (15) gives:
{umlaut over (s)}(φ,{dot over (φ)},{umlaut over (φ)})=rK·sin φ+rK·{dot over (φ)}2·cos φrK/2λPl·sin(2·φ)+rK·{dot over (φ)}2·λPl·cos(2·φ)

Assuming a constant mean speed nmot, the relationship for the piston acceleration becomes simpler:
{umlaut over (S)}red(φ,{dot over (φ)})=rK·{dot over (φ)}2·(cos φ+λpl·cos(2φ))  (16)

The assumption leads to an error that can be disregarded. The influence of the angular acceleration results in a negligible deviation over the entire characteristic map.
β(φ)=arcsin(λpl·sin φ)  (16.5)

Push rod ratio
λPl=rK/lPl(17)
Pcyl=Pcyl(18)

Reference to ambient pressure
P0=Pamb(19)
or as also used in the following the reference to crankcase pressure
P0=PCrkc=Pamb−DPS(20)
wherein DPS stands for the negative pressure (pressure difference) in the intake manifold.

The frictional torque from equation (13) can be represented in different ways. Either a model can be introduced which reflects measured data for a specific operating point of the diagnosis. A target-oriented approach here would be a functional linking of the term with the speed, the load and the oil temperature.

In the following, however, it is assumed that the diagnosis is carried out at fixed, steady-state load points. This means that the frictional torque for this load point can be assumed to be invariable.
{tilde over (M)}R=const.  (21)

The same approach is also used for the proportional moment due to rotational inertia and the mass moment of inertia.
M=const.  (22)
J=const.  (23)

A suitable choice of diagnostic constants at the steady-state operating point allows easy application of the parameters in retrospect.

Solving equation (13) according to the gas moment gives:
=J·{dot over (ω)}++

After inserting the relationships from equations (21) to (23), the following simplification with the application constant K_RM can be concluded:
=J·ω+KRM(24)
Application of the Diagnosis:

FIG.3shows the detail X fromFIG.2, i.e. the development in the speed101over the crank angle KW during the diagnosis time window112with the measuring points P1and P2in the compression of cylinder Z1. Pressure p1prevails in the cylinder at point P1, and pressure p2at point P2.

The gradient of the angular velocity from equation (14) is expanded. The speed to be determined must be averaged here, and constants are marked again.

ω˙≈(π3⁢0)2·nmot_·Δ⁢nmotΔφ(25)ω˙≈(π3⁢0)2·nmot2+nmot12·nmot2-nmot1φ2-φ1ω˙≈12·(π3⁢0)2·nmot22-nmot12φ2-φ1ω.≈Kω·nmot2-nmot12φ2-φ1

The term for the tangential moment from equation (15) is expanded in the following by the relationships from equations (16) to (20), and constants are marked.

M~tan=[⁠(p1+p2-2·pamb+2·DPS)2·AK-mosc·s¨(φ)]·rK·sin⁡(φ+β)cos⁢β(25.5)M~tan=[(p1+p2-2·pamb+2·DPS)2·AK-mosc·s¨(φ)]·KK
with a kinematic constant for the steady-state point in which the diagnosis takes place

KK=rK·sin⁡(φ+β)cos⁢β(26)

After inserting equations (26) and (25) into equation (24), resolving according to the cylinder pressures, and amalgamating all constants, the following is given:

[(p1+p2-2·pamb+2·DPS)2·AK-mosc·s¨(φ)]·KK=J·Kω·nmot22-nmot12φ2-φ1+κRM(27)p1+p22=J·KωKK·AK·nmot22-nmot12φ2-φ1+KRMKK·AK+mosc·s¨(φ)AK+pamb-DPSp1+p22=K1·nmot22-nmot12φ2-φ1+K2+mosc·s¨(φ)AK+pamb-DPS

All pressure variables and speeds in equation (27) can be measured at the times P1and P2for the conditions of the constants shown. A suitable indexing measurement technique, known per se, resolves the necessary physical quantities based on the crank angle or at least averaged over several operating cycles. In addition or as an alternative to the indexing measurement technique, data from a suitable operating model, for example the motor control system, can be used. The kinematic constant KKcan be tabulated and used in dependence on the piston position.

The influence of the speed nmotrelated to the oscillatory masses can, for example, be calculated in real time or stored on the control unit in the form of a lookup table of a suitably stored operating model with respect to speed and load.

The reduced piston acceleration (cf. in particular equation (16)) can be formulated for the two discrete points:

s¨red(φ,φ˙)=rK·[π30⁢nmot1+nmot2)2]2·[cos⁡(φ1+φ22)+cos⁡(φ1+φ2)](27.5)

The constants K1and K2can be determined on the basis of reference measurements (motor function and load change OK, respectively).

After determining the application constants K1and K2, equation (27) can be used to determine the diagnostic cylinder pressure from the speed change in the compression:

p¯cyl,diag=K1·nmot22-nmot12φ2-φ1+K2+mosc·s¨red(φ,nmot)AK+pamb-DPS(28)

The diagnostic cylinder pressurepcyl,diagis an indicator of the pressure curve during the compression stroke of the cylinder.

In this way, the diagnostic cylinder pressurepcyl,diag=pcyl, diag, 660-690can be determined for the diagnosis time window112of the diagnosed cylinder Z at the time interval t12=t[P1; P2] in driving operation.

This calculation of the diagnostic cylinder pressure pcyl, diag, 660-690in the calculated operating cycle for the calculated cylinder is used to estimate the simplified cylinder load parameter rf* in the next operating cycle according to equation (12).

The fresh-air mass parameter rf can then also be determined from this, if necessary, in dependence on the steady-state cylinder load parameter rfSBdetermined for steady-state operation and/or an offset prediction rfOFFSETderived from this. Weightings with which the simplified fresh-air mass parameter rf*, the steady-state fresh-air mass parameter rfSBand/or the offset prediction rfOFFSETare included in the calculation of rf for transient operating states TB are in themselves dependent on the degree of transience and/or other expert considerations considered on their own.

Feedforward control of the fuel injection quantity into the cylinder Z1then takes place in the exemplary embodiment for an operating cycle on the basis of the value of the fresh-air mass parameter rf determined for the previous operating cycle.

LIST OF REFERENCE SIGNS

1Internal combustion engine2Control means4Computing unit6Detection unit for the speed of the crankshaft7Cylinder pressure detection unit9Intake system10Torque curve of the internal combustion engine over an engine cycle12Low-torque ranges14Predetermined limit for relevant torque contribution16Cylinder temperature detection unit18Lambda sensor150Graph showing development in the speed101Speed curve112Diagnosis time window113Diagnosis time point200Engine control unit202Memory204Diagnostic component of an engine control unit206Control component of an engine control unit208Offboard diagnostic computerKT Crank driveKW Crank angleLStStoichiometric fuel-air ratio, fuel-specificmfuelFuel mass in the cylindermairAir mass in the cylindermresidual gasResidual gas mass in the cylindermtotGas mass in the cylinderM Torque of a cylinder inFIG.1n Speedp* Cylinder pressure at time of diagnosisPcyl,diagPressure index, here diagnostic cylinder pressureP Measurement time points at the beginning and end of the diagnosis time windowp0Atmospheric pressure under standard conditions (1013 hPa)R ideal gas constantrf Fresh-air mass parameter; relative air charge of the cylinder in %.rf* Simplified cylinder load parameterrfSBSteady-state cylinder load parameterrfOffsetOffset predictionSB Steady-state operationτ Time interval in the diagnosis time windowT* Temperature of the gas mixture in the cylinder at time of diagnosisT0Ambient temperature under standard conditions (293K)TB Transient operationV* Cylinder volume at time of diagnosisVmaxmaximum cylinder volume at bottom dead center of crankshaftxrg Residual gas fractionZ CylinderZZP Ignition timing point of a cylinderλCombustion air ratio