JP4577239B2 - Method and apparatus for determining Wiebe function parameters - Google Patents

Description

  The present invention relates to a method and apparatus for determining a Wiebe function parameter, and in particular, determination of a Wiebe function parameter suitable for determining a parameter value of a Wiebe function for modeling heat generation in a cylinder of an internal combustion engine. The present invention relates to a method and a determination device.

  Conventionally, attempts have been made to model heat generation in a cylinder of an internal combustion engine using a Wiebe function. According to the Wiebe function, it is possible to calculate a heat generation rate, a combustion rate, and the like for each crank angle. Then, if values such as the heat generation rate for each crank angle are known, the in-cylinder pressure and the indicated torque can be calculated. Therefore, if the heat generation in the cylinder can be accurately modeled by the Wiebe function, the Wiebe function can be effectively used in fields such as the development of the internal combustion engine and the control of the internal combustion engine.

  In order to accurately simulate the heat generation in the cylinder using the Wiebe function, it is necessary to accurately determine the values of some parameters included in the Wiebe function according to the model of the target internal combustion engine. The values of these parameters also vary depending on operating conditions such as air-fuel ratio, engine speed, load factor, and ignition timing.

  Japanese Patent Application Laid-Open No. 2004-332659 discloses a technique for controlling the ignition timing in the vicinity of MBT (Minimum advance for the Best Torque) using a Wiebe function. According to this publication, in the MBT of the same engine, the shape (waveform) of the heat generation rate is the same regardless of the length of the combustion period, and the crank angle and the combustion rate when the heat generation rate is maximized are also constant. It is assumed that Then, among the Wiebe function parameters, the shape parameter m related to the heat release rate shape is set as a constant, and these values are obtained by experiments (see paragraph number 0030 of the above publication). The parameter “n” in the above publication corresponds to “m” in this specification.

JP 2004-332659 A

  However, the above publication does not disclose any specific method for determining the shape parameter m and other Wiebe function parameters based on experimental data. Further, according to the knowledge of the present inventor, even in the MBT of the same engine, the value of the shape parameter m varies depending on operating conditions and is not constant. Further, in a modern engine in which various controls are performed, it is not always necessary to match the ignition timing with MBT. For this reason, there is also a request for estimating a torque or the like under an ignition timing other than MBT, and for that purpose, it is necessary to grasp the change tendency of the value of the Wiebe function parameter due to the change of the ignition timing.

  Thus, in order to actually use the Wiebe function for control of an internal combustion engine, etc., the Wiebe function parameters are accurately determined under various operating conditions, and how their values change according to the operating conditions. It is necessary to grasp exactly. However, the actual situation is that a method for accurately determining the Wiebe function parameter has not been established.

  The present invention has been made to solve the above-described problems. Determination of a Wiebe function parameter that can accurately determine a parameter of a Wiebe function for modeling heat generation in a cylinder of an internal combustion engine. It is an object to provide a method and a determination device.

In order to achieve the above object, a first invention is a method for determining a Wiebe function parameter,
A method for determining a value of at least one parameter of a Wiebe function for modeling heat generation due to combustion in a cylinder of an internal combustion engine, comprising:
For the internal combustion engine, an in-cylinder pressure measuring step for measuring an in-cylinder pressure for each crank angle in a section including at least a combustion period;
A model in-cylinder pressure calculating step for calculating a heat generation rate by a Wiebe function in which a provisional value is substituted for a parameter to be determined, and calculating a model in-cylinder pressure for each crank angle during the combustion period based on the heat generation rate;
An error evaluation value calculating step for calculating an error evaluation value representing the magnitude of an error of the model cylinder pressure with respect to the actual cylinder pressure measured in the cylinder pressure measuring step;
With
The model in-cylinder pressure calculation step and the error evaluation value calculation step are repeated by changing the provisional value, and the provisional value when the error evaluation value is minimized is set as a definite value of the parameter to be determined. It is characterized by.

The second invention is the first invention, wherein
In the model in-cylinder pressure calculating step, the model in-cylinder pressure is calculated so that the model in-cylinder pressure at the heat generation start point coincides with the actual in-cylinder pressure measured in the in-cylinder pressure measuring step.

The third invention is the first or second invention, wherein
The parameters to be determined include the shape parameter m, the combustion period θ _p [degCA], the efficiency k in which the amount of heat of the fuel supplied into the cylinder is converted into the amount of heat generated in the cylinder, the ignition timing, and the Wiebe It includes at least one of a heat generation start point deviation amount θ _b [degCA] representing a deviation amount from the heat generation start point of the function.

According to a fourth invention, in any one of the first to third inventions,
Calculating the actual heat generation rate based on the actual in-cylinder pressure measured in the in-cylinder pressure measuring step;
An initial provisional value calculating step for calculating an initial value of the provisional value based on the actual heat generation rate;
Is further provided.

The fifth invention is a Wiebe function parameter determination device,
An apparatus for determining a value of at least one parameter of a Wiebe function for modeling heat generation due to combustion in a cylinder of an internal combustion engine,
For the internal combustion engine, in-cylinder pressure measuring means for measuring the in-cylinder pressure for each crank angle in a section including at least a combustion period;
A model in-cylinder pressure calculating means for calculating a heat generation rate by a Wiebe function in which a provisional value is substituted for a parameter to be determined, and calculating a model in-cylinder pressure for each crank angle during the combustion period based on the heat generation rate;
Error evaluation value calculation means for calculating an error evaluation value representing the magnitude of the error in the model cylinder pressure with respect to the actual cylinder pressure measured by the cylinder pressure measurement means;
The provisional value is changed, the model in-cylinder pressure is calculated by the model in-cylinder pressure calculating unit, and the error evaluation value is calculated by the error evaluation value calculating unit, and the error evaluation value is minimized. Fixed value acquisition means for acquiring a provisional value as a fixed value of the parameter to be determined;
It is characterized by providing.

According to a sixth invention, in any one of the first to fourth inventions,
When the Wiebe function is expressed by the following formula (I) (where, Q is the calorific value [J] in the cylinder, Q _total is the calorific value [J] of fuel supplied into the cylinder, θ wherein the elapsed crank angle after the heat generation starting [deg CA], theta _p combustion period [deg CA], m is the shape parameter, k represents efficiency, respectively), the shape parameter m in the parameter to be the determining,
As a step of obtaining an initial provisional value of the shape parameter m,
Calculating an actual heat generation rate for each crank angle based on the actual in-cylinder pressure measured in the in-cylinder pressure measuring step;
Calculating an actual combustion rate α at a crank angle at which the actual heat generation rate is maximized;
Calculating an initial provisional value of the shape parameter m according to the following equation (II) or an equivalent equation based on the actual combustion ratio α;
Is further provided.

The seventh invention is the sixth invention, wherein
The parameter to be determined further includes the combustion period θ _p ,
As a step of _obtaining an initial provisional value of the combustion period θ _p ,
Obtaining an integral value of the actual heat generation rate as a total calorific value kQ _total ;
When the maximum value of the actual heat generation rate is β, based on the actual heat generation rate maximum value β, the total calorific value kQ _total , the initial provisional value of the shape parameter m, and a predetermined constant a. Calculating an initial provisional value of the combustion period θ _p according to the following formula (III) or an equivalent formula:
Is further provided.

The eighth invention is the seventh invention, wherein
When the ignition timing of the internal combustion engine is SA [degBTDC], and the amount of deviation between the ignition timing SA and the heat generation start point of the Wiebe function is the heat generation start point deviation amount θ _b [degCA], the parameter to be determined further comprising the heat generation start point deviation amount theta _b, the
As a step of _obtaining an initial provisional value of the heat generation start point deviation amount θb,
When the crank angle when the actual heat generation rate becomes maximum is θ _ATDC ^* [degATDC], the crank angle θ _ATDC ^* , the ignition timing SA, the initial provisional value of the shape parameter m, and the the initial provisional value of the combustion period theta _p, based on the predetermined constant a, the following (IV) and (V) type or in accordance with any equivalent expressions, the heat generation start point deviation amount theta _b initial provisional value of The method further includes the step of calculating.

According to a ninth invention, in any of the sixth to eighth inventions,
The parameter to be determined further includes the efficiency k;
As a step of obtaining an initial provisional value of the efficiency k,
Obtaining an integral value of the actual heat generation rate as a total calorific value kQ _total ;
_Obtaining a value of the amount of heat Q _total of the fuel supplied into the cylinder;
Dividing the _total calorific value kQ _total by the value of Q _total to calculate an initial provisional value of the efficiency k;
Is further provided.

  According to the first aspect, the value of the Wiebe function parameter can be determined so that the error between the actual in-cylinder pressure and the model in-cylinder pressure calculated based on the Wiebe function is as small as possible. Therefore, according to the first aspect of the invention, in predicting the in-cylinder pressure and torque of the internal combustion engine using the Wiebe function model, the dependence of the Wiebe function parameter on the internal combustion engine model and the relationship between the operating condition and the Wiebe function parameter. Can be accurately grasped. As a result, the in-cylinder pressure and torque of the internal combustion engine can be accurately predicted using the Wiebe function model.

  According to the second invention, in the process of determining the Wiebe function parameter, the model in-cylinder pressure can be calculated so that the model in-cylinder pressure at the heat generation start point coincides with the actual in-cylinder pressure. Thereby, the value of the Wiebe function parameter can be determined with higher accuracy.

According to the third invention, as the Wiebe function parameters, the shape parameter m, the combustion period θ _p [degCA], and the efficiency k at which the amount of heat of the fuel supplied into the cylinder is converted into the amount of heat generated in the cylinder. And at least one of the heat generation start point deviation amount θ _b [degCA] representing the deviation amount between the ignition timing and the heat generation start point of the Wiebe function can be determined with high accuracy.

  According to the fourth aspect of the invention, the initial value of the provisional value of the Wiebe function parameter used in the process of determining the Wiebe function parameter can be accurately calculated based on the actual heat generation rate. For this reason, it is possible to easily find a definite value (adapted value) of the Wiebe function parameter that minimizes the error evaluation value, and the calculation load can be reduced.

  According to the fifth aspect, the value of the Wiebe function parameter can be determined so that the error between the actual in-cylinder pressure and the model in-cylinder pressure calculated based on the Wiebe function is as small as possible. Therefore, according to the fifth aspect of the invention, in predicting the in-cylinder pressure and torque of the internal combustion engine using the Wiebe function model, the dependency of the Wiebe function parameter on the model of the internal combustion engine and the relationship between the operating condition and the Wiebe function parameter. Can be accurately grasped. As a result, the in-cylinder pressure and torque of the internal combustion engine can be accurately predicted using the Wiebe function model.

  According to the sixth aspect, the initial provisional value of the shape parameter m, which is one of the Wiebe function parameters, can be calculated with high accuracy. For this reason, when searching for the final definite value of the shape parameter m, an accurate initial provisional value can be used as a starting point. Therefore, the final definite value can be easily found, and the calculation load can be reduced.

According to the seventh aspect, it is possible to accurately calculate the one initial provisional value of the combustion period theta _p is the Wiebe function parameters. Therefore, in order to explore the final determined value of the combustion period theta _p, it can be a starting point an accurate initial provisional. Therefore, the final definite value can be easily found, and the calculation load can be reduced.

According to the eighth aspect, it is possible to accurately calculate the initial provisional value of the heat start point deviation amount theta _b is one of the Wiebe function parameters. Therefore, in order to explore the final determined value of the heat generation starting point deviation amount theta _b, it can be a starting point an accurate initial provisional. Therefore, the final definite value can be easily found, and the calculation load can be reduced.

  According to the ninth aspect, the initial provisional value of efficiency k, which is one of the Wiebe function parameters, can be calculated with high accuracy. For this reason, when searching for a final definite value of the efficiency k, an accurate initial provisional value can be used as a starting point. Therefore, the final definite value can be easily found, and the calculation load can be reduced.

Embodiment 1 FIG.
[Description of system configuration]
FIG. 1 is a diagram for explaining a system configuration used in Embodiment 1 of the present invention. As shown in FIG. 1, the system of this embodiment includes a spark ignition type internal combustion engine 10. Each cylinder of the internal combustion engine 10 is provided with an intake valve 14, an exhaust valve 16 and a spark plug 30.

  The internal combustion engine 10 is provided with a crank angle sensor 12 that detects the rotational position (crank angle) of the crankshaft. The crank angle sensor 12 is a sensor that reverses the Hi output and the Lo output each time the crankshaft rotates by a predetermined rotation angle. According to the output of the crank angle sensor 12, the engine speed NE can also be detected.

  The internal combustion engine 10 incorporates an in-cylinder pressure sensor 18. The in-cylinder pressure sensor 18 can detect the pressure generated in the cylinder (combustion chamber).

  A surge tank 20 is provided in the intake passage 19 of the internal combustion engine 10. The surge tank 20 is provided with an intake pressure sensor 21 for detecting the internal pressure, that is, the intake pipe pressure. In addition, an air flow meter 22 that detects an intake air amount GA flowing through the inside of the intake passage 19 is disposed. According to the output of the intake pressure sensor 21, the load factor KL [%] of the internal combustion engine 10 can be acquired. The load factor KL may be calculated based on the intake air amount GA and the engine speed NE.

  A throttle valve 24 is disposed downstream of the air flow meter 22. In the vicinity of the throttle valve 24, a throttle opening sensor 26 for detecting the throttle opening TA is assembled.

  An injector 28 for injecting fuel such as gasoline is disposed at the intake port of the internal combustion engine 10. The internal combustion engine in the present invention is not limited to such a port injection type internal combustion engine, but is an in-cylinder direct injection type internal combustion engine or an internal combustion engine that uses both port injection and in-cylinder injection. May be.

  An air-fuel ratio sensor 33 for detecting the air-fuel ratio of the exhaust gas is installed in the exhaust passage 32 of the internal combustion engine 10. A catalyst 34 for purifying exhaust gas is incorporated in the exhaust passage 32.

  The system of this embodiment includes an ECU (Electronic Control Unit) 50 as a control device. Sensor signals are supplied to the ECU 50 from the various sensors described above. The ECU 50 can control various actuators such as the throttle valve 24, the injector 28, and the spark plug 30 based on those sensor signals. Further, the ECU 50 can perform Wiebe function parameter determination processing, which will be described later, based on sensor signals from the crank angle sensor 12, the in-cylinder pressure sensor 18, and the like.

(Wiebe function)
The Wiebe function of the present embodiment is expressed by the following formula (1) or the following formula (2).

The meaning of each symbol in the above formulas (1) and (2) is as follows.
Q: Calorific value in the cylinder of the internal combustion engine 10 [J]
Q _total : calorific value of fuel supplied to the cylinder [J]
θ: Elapsed crank angle after start of heat generation [degCA]
θ _p : Combustion period [degCA]
m: shape parameter k: efficiency

The above equation (1) is a Wiebe function for calculating the heat generation rate dQ / dθ. Q / kQ _{total on} the left side of the equation (2) represents a combustion ratio as will be described later. That is, the above equation (2) is a Wiebe function for calculating the combustion ratio Q / kQ _total .

  2A is a graph in which the horizontal axis represents the crank angle and the vertical axis represents the heat generation rate, and FIG. 2B is a graph in which the horizontal axis represents the crank angle and the vertical axis represents the in-cylinder pressure. . In FIG. 2, a thin line is a measured value in an actual machine, and a thick line is a value calculated based on the Wiebe function. Note that FIG. 2A and FIG. 2B are separate graphs, and the horizontal axis position and scale representing the crank angle do not match.

  In the system shown in FIG. 1, the in-cylinder pressure of the actual machine as shown by the thin line in FIG. 2B can be measured for each crank angle by the in-cylinder pressure sensor 18. In the following description, this measured value is referred to as “actual cylinder pressure”. As will be described later, the heat generation rate for each crank angle can be calculated from the actual in-cylinder pressure using an energy conservation law equation. This is the heat generation rate of the actual machine indicated by a thin line in FIG. In the following description, the heat generation rate calculated from the actual in-cylinder pressure is referred to as “actual heat generation rate”.

  On the other hand, from the Wiebe function of the above equation (1), the heat generation rate for each crank angle as shown by the thick line in FIG. 2A can be calculated. Then, from the heat generation rate calculated by the Wiebe function (hereinafter referred to as “model heat generation rate”), the in-cylinder pressure for each crank angle can be calculated using an energy conservation law equation. This is the in-cylinder pressure indicated by the thick line in FIG. In the following description, the in-cylinder pressure thus calculated based on the Wiebe function is referred to as “model in-cylinder pressure”.

Hereinafter, each parameter of the Wiebe function will be described.
(Combustion period θ _p )
As shown in FIG. 2A, the combustion period θ _p has a physical meaning as a period in which the generation of heat due to combustion continues, that is, a period from the start to the end of combustion expressed by a crank angle. ing. In the Wiebe function of the above equations (1) and (2), the point of θ = 0 means a heat generation start point (combustion start point) as described later, and these Wiebe functions are 0 ≦ θ ≦ θ. It is defined in the range of _p .

(Shape parameter m)
The shape parameter m is a parameter greatly related to the shape of the model heat generation rate dQ / dθ in the graph as shown in FIG. 2A, and is particularly a parameter greatly related to the crank angle at which the heat generation rate takes the maximum value. is there.

(Heat generation start point deviation amount θ _b )
As shown in FIG. 2A, in the Wiebe function expressed by the above equation (1), the model heat generation rate dQ / dθ = 0 when θ = 0, and from the point when θ exceeds 0. dQ / dθ> 0 and heat generation starts. That is, in the Wiebe function of the present embodiment, θ = 0 is a heat generation start point (combustion start point), and θ represents an elapsed crank angle after the start of heat generation (after the start of combustion).

According to the knowledge of the present inventor, when the heat generation start point of the Wiebe function is made to coincide with the actual ignition timing SA, the waveform of the model heat generation rate by the Wiebe function is accurately matched to the waveform of the actual heat generation rate. I can't. Therefore, in this embodiment, the heat generation start point (θ = 0) of the Wiebe function is set to be different from the actual ignition timing SA. Then, it was decided to introduce represents a shift amount of both the heat generation start point deviation amount theta _b, this as a parameter of the Wiebe function. That is, the heat generation start point deviation amount θ _b [degCA] is a parameter that represents a deviation amount between the heat generation start point of the Wiebe function and the ignition timing SA by a crank angle (see FIG. 2A). Hereinafter, in the present embodiment, the case of using the Wiebe function such (1), the heat generation starting point deviation amount theta _b min shifted reference point a point from the ignition timing SA (theta = 0) as the (1) The formula etc. shall be applied.

(Efficiency k)
In the above formulas (1) and (2), the heat quantity Q _total of the fuel supplied into the cylinder can be calculated by multiplying the fuel quantity supplied into the cylinder by the lower heating value of the fuel. The lower heating value is a physical property value called a true heating value. The lower calorific value is the amount of heat generated when a unit amount of fuel is completely burned, minus the amount of heat (latent heat) required to evaporate the moisture contained in the fuel and the moisture generated by the combustion. means. In the system shown in FIG. 1, the value of Q _total can be calculated based on the fuel injection amount from the injector 28 on the assumption that the lower heating value of the fuel is known. Alternatively, Q _total can also be calculated from the air-fuel ratio A / F and the in-cylinder air amount (load factor KL).

Combustion in an internal combustion engine usually involves some heat loss due to a cooling loss, unburned fuel, and the like. For this reason, it is practically impossible for all the amount of heat Q _{total of} the fuel supplied into the cylinder to be directly converted into the amount of heat generated Q in the cylinder. In this embodiment, the efficiency k is introduced as a parameter for reflecting this in the Wiebe function. That is, the efficiency k has a physical meaning as an efficiency in which the heat quantity Q _{total of} the fuel supplied into the cylinder is converted into the heat generation quantity Q, and is a number in a range of 0 <k <1.

When the efficiency k is used, the total calorific value in the cylinder can be expressed as kQ _total obtained by multiplying Q _total by k. The total calorific value kQ _total corresponds to the area surrounded by the thin line indicating the actual heat generation rate and the straight line of dQ / dθ = 0 on the graph in FIG. That is, the value of the _total calorific value kQ _total can be calculated by integrating the actual heat generation rate. The value of efficiency k can be obtained by dividing the total calorific value kQ _total thus calculated by Q _total calculated by the above-described method.

Since the total calorific value is expressed as kQ _total as described above, the combustion ratio at a certain crank angle θ is expressed as a ratio Q / kQ _total between the calorific value Q up to the crank angle θ and the total calorific value kQ _total. be able to. This combustion ratio Q / kQ _total is expressed by the above equation (2) according to the Wiebe function. When the equation (2) is differentiated by θ, the equation (1) is obtained. That is, the above equation (2) is equivalent to the above equation (1).

(Parameter a)
From the original definition of the combustion rate, the value of the combustion rate should be 100%, ie 1 at the end of combustion. On the other hand, the Wiebe function does not have a combustion ratio value of 1 at the end of combustion due to its nature. That is, in the Wiebe function, the combustion rate at the combustion end, by substituting theta = theta _p in equation (2) is represented by the following formula.
Q / kQ _total (at the end of combustion) = 1−exp (−a)

As in the above equation, the value of the combustion ratio Q / kQ _total at the end of combustion on the Wiebe function is represented only by the parameter a. Therefore, if the value {1-exp (−a)} of the above equation is set equal to a predetermined value close to 1, the value of a can be determined. For example, if {1-exp (−a)} = 0.999, a≈6.9 is obtained. Therefore, in the following description, the parameter a is treated as a constant 6.9. However, the present invention is not limited to the case where the parameter a is handled as a constant, and the value of a may be determined together with other parameters by a method described later.

[Features of Embodiment 1]
In the present embodiment, since the parameter a is treated as a constant, there are four Wiebe function parameters to be determined: a shape parameter m, an efficiency k, a heat generation start point deviation amount θ _b , and a combustion period θ _p . Hereinafter, in order to facilitate understanding of the operation and effect of the Wiebe function parameter determination method of the present embodiment, first, a method of a comparative example will be described.

(Method for determining Wiebe function parameters of comparative example)
As a comparative example, the Wiebe function parameters m, k, θ _b are set so that the error evaluation value indicating the magnitude of the error between the actual heat generation rate and the model heat generation rate as shown in FIG. , Θ _p can be optimized. For example, when the least square method is used, the sum of squares of errors (deviations) between the actual heat generation rate and the model heat generation rate for each crank angle is used as the error evaluation value. Then, the error evaluation value is considered as a multivariable function having m, k, θ _b , and θ _p as variables, and the error evaluation value is obtained by changing each value of m, k, θ _b , and θ _p little by little. Are repeatedly calculated to find a set of Wiebe function parameters m, k, θ _b and θ _p that minimize the error evaluation value, and determine these values as final values.

According to the method of the comparative example, the error between the actual heat generation rate and the model heat generation rate can be minimized. However, the shape (waveform) of the actual heat generation rate and the shape (waveform) of the model heat generation rate do not completely match. Therefore, when the model in-cylinder pressure is calculated using the values of the Wiebe function parameters m, k, θ _b , θ _p determined by the method of the comparative example, as shown in FIG. It is easy for a situation that the error of the above does not become sufficiently small.

  By the way, in utilizing the Wiebe function in the development stage of the internal combustion engine 10 or the control device for the internal combustion engine 10, it is often required to accurately predict the in-cylinder pressure and torque of the internal combustion engine 10. If the in-cylinder pressure of the internal combustion engine 10 can be accurately predicted, the torque of the internal combustion engine 10 can be accurately predicted. Therefore, when considering the actual usage of the Wiebe function, rather than minimizing the error between the actual heat generation rate and the model heat generation rate, the error between the actual cylinder pressure and the model cylinder pressure should be minimized. It is more reasonable to determine the Wiebe function parameters.

(Wiebe function parameter determination method of this embodiment)
Therefore, in this embodiment, the values of the Wiebe function parameters m, k, θ _b , and θ _p are optimized so that the error evaluation value indicating the magnitude of the error between the actual in-cylinder pressure and the model in-cylinder pressure is minimized. I decided to make it. This error evaluation value is, for example, the sum of squares of errors (deviations) between the actual cylinder pressure and the model cylinder pressure for each crank angle. Then, the error evaluation value is considered as a multivariable function having m, k, θ _b , and θ _p as variables, and the error evaluation value is changed while gradually changing the values of m, k, θ _b , and θ _p. Are repeatedly calculated to find a set of Wiebe function parameters m, k, θ _b , θ _p that minimizes the error evaluation value.

In order to calculate the error evaluation value between the actual in-cylinder pressure and the model in-cylinder pressure, first, a temporary value (provisional value) is substituted into the Wiebe function parameters m, k, θ _b , θ _p (1 It is necessary to calculate the model in-cylinder pressure using the Wiebe function. Then, Wiebe function parameter m that minimizes the error evaluation value, k, theta _b, to find the fitness value of theta _p, until it finds such a fitness _{value, m, k, θ b,} θ p It is necessary to repeat the model in-cylinder pressure calculation process and the error evaluation value calculation process while gradually changing the provisional value.

In the case of performing such processing, from the viewpoint of reducing the calculation load required to find the final conforming value, initial values of the temporary values of the Wiebe function parameters m, k, θ _b , θ _p (hereinafter referred to as “initial values”). It is important that the “provisional value” is an accurate value as close as possible to the final conforming value. Therefore, in this embodiment, the initial provisional values of the Wiebe function parameters m, k, θ _b , and θ _p are calculated with high accuracy based on the actual heat generation rate. Hereinafter, a method for calculating initial provisional values of the Wiebe function parameters m, k, θ _b , and θ _p in the present embodiment will be described.

(Calculation method of initial provisional value of shape parameter m)
The initial provisional value of the shape parameter m can be calculated by paying attention to the combustion rate when the heat generation rate becomes maximum. FIG. 3 is a graph of the model heat release rate calculated by the Wiebe function. The combustion rate when the model heat generation rate is maximized is the total area (the area up to the crank angle at which the model heat generation rate is maximized among the areas enclosed by the model heat generation rate graph of FIG. It is calculated as a value divided by the hatched portion in FIG.

In order to calculate this value, first, the above formula (1) is differentiated by θ, and d ² Q / dθ ² = 0, so that the crank angle θ _{* at} which the model heat generation rate dQ / dθ is maximized is obtained. Ask. By performing the following expression expansion, an expression representing the crank angle θ _* is obtained.

By substituting the crank angle θ _* represented by the above equation (3) into the above equation (2), the combustion rate at the crank angle θ _* at which the model heat generation rate dQ / dθ is maximized is as follows (4) It can be expressed by a formula.

  As shown in the above equation (4), the combustion ratio at the crank angle at which the model heat generation rate is maximum is expressed by a function of only the shape parameter m. Therefore, the actual measurement value corresponding to this, that is, the combustion ratio at the crank angle at which the actual heat generation rate is maximum is obtained, and if the value is equal to the right side of the above equation (4), m can be calculated. it can.

Here, the combustion ratio at the crank angle at which the actual heat generation rate is maximized (hereinafter referred to as “actual combustion ratio”) is α. In the present embodiment, the initial provisional value of the shape parameter m can be calculated by the following equation (5) by setting the actual combustion ratio α equal to the right side of the above equation (4).

(Calculation method of initial provisional value of combustion period θ _p )
By substituting the crank angle θ _* expressed by the above equation (3) into the above equation (1), the maximum value of the model heat generation rate (dQ / dθ) _max can be expressed by the following equation (6). .

Therefore, when the maximum value of the actual heat generation rate is β, the following equation is obtained by setting the maximum value β equal to the lower stage of the above equation (6).

In the right side of the above equation (7), the part other than a / θ _pm ^{+ 1} is represented only by the total calorific value kQ _total and the shape parameter m. As described above, the value of the _total heat generation amount kQ _total can be calculated by integrating the actual heat generation rate. The initial provisional value of m can be calculated by the above equation (5). Therefore, the value of a / θ _pm ^{+ 1} can be calculated by substituting these values and the actual heat generation rate maximum value β into the above equation (7). In the present embodiment, as described above, a = 6.9. Therefore, if the value of a / θ _pm ^{+ 1} can be calculated, the value of the combustion period θ _p can be calculated. In the present embodiment, it was decided to the value calculated as above to the initial provisional value of the combustion period theta _p.

(Method of calculating the initial provisional value of the heat start point deviation amount theta _b)
In the present embodiment, the model heat generation rate is calculated and a position of maximum, by actual heat release rate to match the position of the maximum, the initial provisional value of the heat start point deviation amount theta _b. That is, when the crank angle based on the compression top dead center when the actual heat generation rate is maximum is θ _ATDC ^* [degATDC], the position of the crank angle θ _{* at which} the model heat generation rate is maximum is θ _ATDC ^* To match.

As can be seen with reference to FIG. 3, when the ignition timing is SA [degBTDC] and the positions of θ _* and θ _ATDC ^* coincide with each other, between SA, θ _ATDC ^* , θ _b , and θ _* , The following equation (9) holds. Further, the above expression (3) can be modified as the following expression (8).

According to the above equation (8), the crank angle θ _* can be calculated based on the previously calculated value of m and the value of a / θ _pm ^{+ 1} . The calculated and its theta _*, and the ignition timing SA, by the theta _ATDC ^* and derived from the real heat release rate data are substituted into Equation (9), the initial provisional value of the heat start point deviation amount theta _b can do.

With the above method, the initial provisional values of the Wiebe function parameters m, θ _p , and θ _b can be calculated with high accuracy. Note that the initial provisional value of the efficiency k is calculated by the method described above at the place where the efficiency k is described. By the way, the Wiebe function of the above equation (1) can be modified as the following equation.

According to the above equation (10), it can be seen that if the values of m, k, a / θ _pm ^{+ 1} , and θ _b are determined, the Wiebe function can be specifically described. In this embodiment, as described above, a is treated as a constant and four of m, k, θ _p , and θ _b are used as Wiebe function parameters, but the combination of Wiebe function parameters is not limited to this. For example, by using the Wiebe function in the form of the above equation (10), without determining individual values of a and θ _p , both are combined with a / θ _pm ^{+ 1} , and m _{, k, a / θ p m} + 1, four values of theta _b may be handled as Wiebe function parameters.

[Specific Processing in Embodiment 1]
FIG. 4 is a flowchart of a routine executed by the ECU 50 in the present embodiment in order to calculate the initial provisional value of the Wiebe function parameter based on the principle described above. FIG. 5 is a diagram showing the relationship between the actual heat generation rate and the actual in-cylinder pressure.

According to the routine shown in FIG. 4, first, during the operation of the internal combustion engine 10, based on the outputs of the crank angle sensor 12 and the in-cylinder pressure sensor 18, the actual in-cylinder pressure P _data [ Pa] is measured (step 100). In this step 100, the interval of the crank angle for measuring the actual cylinder pressure P _data may be not particularly limited, for example, 1degCA interval. Further, the actual in-cylinder pressure P _data need not be measured over the entire crank angle range, and may be measured in a range including at least the actual combustion period.

Next, the actual heat generation rate for each crank angle is calculated by the following method based on the actual in-cylinder pressure P _data for each crank angle measured in step 100 (step 102). Here, the energy conservation law in terms of thermodynamics is expressed by the following equation using the heat generation rate dQ / dθ, the in-cylinder pressure P, the in-cylinder volume V [m ³ ], and the crank angle θ. The crank angle θ here represents an absolute crank angle based on the top dead center, unlike θ in the Wiebe function such as the above equation (1).

In the above equation (11), κ is a specific heat ratio, which is a known value determined based on the composition of the combustion gas. The in-cylinder volume V and the rate of change dV / dθ are geometrically determined values according to the crank angle θ. Therefore, by substituting these known values and the value of the actual in-cylinder pressure P _data for each crank angle measured in the above step 100 into the above equation (11), each crank angle as shown in FIG. The actual heat generation rate can be calculated.

Next, the total heat generation amount kQ _total is calculated based on the actual heat generation rate calculated in step 102 (step 104). Specifically, the total heat generation amount kQ _total is calculated by integrating (integrating) the actual heat generation rate for each crank angle calculated in step 102.

Next, an initial provisional value of efficiency k is calculated (step 106). Specifically, first, the heat quantity Q _{total of} the fuel supplied into the cylinder is calculated based on the fuel injection quantity from the injector 28 and the like. Then, the initial provisional value of efficiency k is calculated by dividing the total calorific value kQ _total calculated in step 104 by this Q _total .

Next, by finding the maximum value of the actual heat generation rates for each crank angle calculated in step 102 and the crank angle at that time, the actual heat generation rate maximum value β and the crank angle θ _ATDC ^{* at} that time are obtained ^. Are acquired (step 108).

Next, the actual combustion ratio α at the crank angle θ _ATDC ^* at which the actual heat generation rate is maximized is calculated (step 110). Specifically, the value obtained by integrating (integrating) the actual heat generation rate for each crank angle calculated in step 102 up to the crank angle θ _ATDC ^* is divided by the _total calorific value kQ _total calculated in step 104. Thus, the actual combustion ratio α is calculated.

  Next, an initial provisional value of the shape parameter m is calculated (step 112). Specifically, the initial provisional value of m is calculated by substituting the actual combustion ratio α calculated in step 110 into the above equation (5).

Then, the initial provisional value is calculated combustion period theta _p (step 114). Specifically, first, the total calorific value kQ _total calculated in step 104, the actual heat generation rate maximum value β acquired in step 108, and the initial provisional value of the shape parameter m calculated in step 112 are described. By substituting the value into the above equation (7), a / θ _pm ^{+ 1} is calculated. Thereafter, the value of the calculated a / θ _{p m} ^{+ 1,} and a = 6.9, by using the initial provisional value of the shape parameter m, the initial provisional value of the combustion period theta _p is calculated.

Finally, the initial provisional value of the heat start point deviation amount theta _b is calculated (step 116). Specifically, the ignition timing SA set by the ECU 50, the crank angle θ _ATDC ^* at which the actual heat generation rate obtained in step 108 is maximized, and the initial values of the shape parameter m calculated in step 112 above. and provisional value, and a / θ _{p m} ^{+ 1} calculated in step 114 by substituting the above (8) and (9), the initial provisional value of the heat start point deviation amount theta _b is calculated The

When the initial provisional values of the wiebe function parameters m, k, θ _p , θ _b are obtained by the routine of FIG. 4 described above, next, m, k, θ _p are processed by the processing of the routine shown in FIG. , the process of obtaining the final fit values of theta _b (determined value) is performed. FIG. 6 is a flowchart of a routine executed by the ECU 50 in the present embodiment in order to obtain a definite value of the Wiebe function parameter.

According to the routine shown in FIG 6, first, the Wiebe function of equation (1), the model heat release rate dQ / d [theta] is calculated for each crank angle during the combustion period theta _p (step 120). In this calculation, provisional values are assigned to the Wiebe function parameters m, k, θ _p , and θ _b , respectively. Hereinafter, a provisional value [m k θ _p θ _b ] of a set of Wiebe function parameters is represented by a symbol x. That is, x = [m k θ _p θ _b ]. When the process of step 120 is executed first, the initial provisional value calculated by the routine process shown in FIG. 4 is used as the provisional value x.

Next, based on the model heat release rate dQ / dθ for each crank angle calculated in step 120 and the above equation (11), the model in-cylinder pressure P _{model for} each crank angle as shown by the broken line in FIG. Is calculated (step 122). Specifically, the differential equation of the in-cylinder pressure P is generated by setting the value of the model heat generation rate dQ / dθ calculated at step 120 equal to the right side of the equation (11). A value obtained by approximately solving the differential equation by numerical calculation by the ECU 50 is set as a model in-cylinder pressure P _model . In this calculation process, since κ, V, and dV / dθ are known values as described above, values stored in advance in the ECU 50 may be used.

In the process of step 122, when calculating the model in-cylinder pressure P _model by solving the differential equation of the in-cylinder pressure P, it is necessary to determine an initial value (initial condition). That is, it is necessary to determine the value of the model cylinder pressure P _model at the heat generation start point (combustion start point) that is the start point of the Wiebe function. In the present embodiment, as shown in FIG. 5, the initial value of the model cylinder pressure P _{model is} the value at the corresponding crank angle of the actual cylinder pressure P _data measured in step 100 of the routine of FIG. We read and decided to use the value. The heat generation starting point, since the change with heat generation starting point deviation amount theta _b, the value to be read as the initial value of the model cylinder pressure P _model in accordance with the provisional value of the heat start point deviation amount theta _b change To do. According to such processing, the actual in-cylinder pressure P _data and the model in-cylinder pressure P _model can always be made to coincide with each other at the heat generation start point. Therefore, in adapting the model in-cylinder pressure P _model to the actual in-cylinder pressure P _data. Is reasonable.

Once the model in-cylinder pressure P _model has been calculated by the processing in step 122, next, the magnitude of the error between the actual in-cylinder pressure P _data measured in step 100 of the routine of FIG. 4 and the model in-cylinder pressure P _model is represented. An error evaluation value Error (x) serving as an index is calculated. The error evaluation value Error (x), in the present embodiment, which is calculated as the square sum of errors (deviation) between the actual cylinder pressure P _data and the model cylinder pressure P _model for each crank angle during the combustion period theta _p However, it may be calculated by another calculation method.

The error evaluation value Error (x) can be considered as a function of a set of provisional values x = [m k θ _p θ _b ] assigned to the Wiebe function in step 120. For this reason, it is possible to find a set of provisional values x such that the error evaluation value Error (x) is minimized by the same concept as that for obtaining the minimum value of a multivariable function. That is, for each of the set of provisional values x = [m k θ _p θ _b ], the process of steps 120 to 124 is repeated while changing the values little by little before and after the initial provisional value, and the error evaluation value Error A set of provisional values x = [m k that minimizes the error evaluation value Error (x) is calculated by calculating (x) and finding a provisional value that minimizes the error evaluation value Error (x). [theta] _{p [} theta] _b ] can be found.

In step 126, based on the above concept, it is determined whether or not a set of provisional values x = [m k θ _p θ _b ] that minimizes the error evaluation value Error (x) has been found. . If it is determined that such a set of provisional values x has not been found, the set of provisional values x = [m k θ _p θ _b ] is further changed (step 128). Using the set x = [m k θ _p θ _b ], the processing of steps 120 to 124 is executed again.

In this way, by repeating the processing of the loop passing through the step 128, a set of provisional values x = [m k θ _p θ _b ] that minimizes the error evaluation value Error (x) is found. be able to. If such a provisional value x = [m k θ _p θ _b ] is found and the determination in step 126 is affirmed, then the found set of provisional values x = [m k θ _p θ _b ], that is, a set of provisional values x = [m k θ _p θ _b ] that minimizes the error evaluation value Error (x) is a definite value of the Wiebe function parameters m, k, θ _p , θ _b . (Step 130).

As described above, according to the routine of FIG. 6, the values of the Wiebe function parameters m, k, θ _p , θ _b are set so that the error between the actual in-cylinder pressure P _data and the model in-cylinder pressure P _model is minimized. Can be determined. Accordingly, it is possible to reliably prevent a large error from occurring between the actual cylinder pressure and the model cylinder pressure as shown in FIG. Therefore, according to the present invention, the Wiebe function parameter can be determined so that the actual in-cylinder pressure and torque of the internal combustion engine 10 can be accurately predicted by the Wiebe function model.

  Further, in the present embodiment, the initial provisional value of the Wiebe function parameter is calculated based on the actual heat generation rate by the processing of the routine of FIG. 4, thereby obtaining an accurate initial value close to the final conforming value (determined value). Provisional values can be obtained. For this reason, when searching for a suitable value of the Wiebe function parameter by the processing of the routine of FIG. 6, it is possible to use the initial provisional value with high accuracy as a starting point, so that the suitable value can be easily found and calculated. The load can be reduced.

  Here, the present invention has applications as described below. The value of the Wiebe function parameter determined by the routine processing of FIGS. 4 and 6 depends on the operating conditions of the internal combustion engine 10, that is, the ignition timing SA, the engine speed NE, the air-fuel ratio A / F, the load factor KL, and the like. Change. According to the present invention, for example, in the development stage of the control logic of the internal combustion engine 10, each Wiebe function parameter is determined according to the routine shown in FIG. 4 and FIG. It is possible to accurately grasp the relationship between Wiebe function parameters and operating condition parameters such as the ignition timing SA, the engine speed NE, the air-fuel ratio A / F, and the load factor KL. Then, if the relationship grasped in this way is used, the Wiebe function can be accurately determined for any operating condition, and the in-cylinder pressure and torque of the internal combustion engine 10 can be accurately determined using the Wiebe function. Can be predicted.

  When the control logic is examined in the development stage of the internal combustion engine 10, conventionally, it is necessary to actually measure the in-cylinder pressure, torque, and the like under various operating conditions. On the other hand, if the relationship between the value of the Wiebe function parameter and the operating condition is accurately grasped as described above using the present invention, the actual measurement work of the in-cylinder pressure and torque can be replaced with the prediction based on the Wiebe function. Can do. For this reason, the number of measurement points of actual machine data can be greatly reduced, and the development man-hours and development costs can be greatly reduced.

  In addition, the relationship between the value of the Wiebe function parameter and the operating condition obtained as described above can be stored in the vehicle-mounted ECU as a Wiebe function model in the form of a map or an arithmetic expression. By doing so, it is possible to accurately predict the in-cylinder pressure and torque under various operating conditions for the internal combustion engine 10 mounted on the vehicle by simulation using the Wiebe function. If the prediction result is used, the vehicle-mounted ECU can accurately perform various controls such as torque demand control and drivability improvement control.

  It is also possible to cause the vehicle-mounted ECU to execute routines such as those shown in FIGS. Calculating (determining) a Wiebe function parameter by executing a routine as shown in FIG. 4 and FIG. 6 by the in-vehicle ECU, and learning the value of the calculated Wiebe function parameter in relation to the current operating state; Then, the Wiebe function model stored in the in-vehicle ECU can be modified according to the current state of the internal combustion engine 10. That is, the Wiebe function model stored in the in-vehicle ECU can be modified with higher accuracy by reflecting the time-dependent change in characteristics of the internal combustion engine 10 and individual differences.

  As mentioned above, although embodiment of this invention was described, this invention is not limited to embodiment mentioned above. For example, in the above-described embodiment, the initial provisional value of the Wiebe function parameter is calculated on the basis of the actual heat generation rate, but the adaptive value of each parameter is set using a preset initial provisional value as a starting point. You may make it search.

  In the present embodiment, the above-described various formulas are used. However, in the present invention, these formulas need not be completely the same as those described above, and formulas equivalent to them may be used. Good. In the present invention, at least one of the plurality of Wiebe function parameters may be determined by a process as shown in FIG. 6, and the remaining parameters may be determined by other methods.

  In the first embodiment described above, the ECU 50 executes the process of step 100, so that the “in-cylinder pressure measuring means” in the fifth aspect of the invention executes the processes of steps 120 and 122. The “model in-cylinder pressure calculating means” in the fifth invention executes the processing of step 124, so that the “error evaluation value calculating means” in the fifth invention becomes steps 128, 120, 122, 124 and After the process of 126 is repeatedly executed, the “determined value acquisition unit” in the fifth aspect of the present invention is realized by executing the process of step 130 described above.

It is a figure for demonstrating the system configuration | structure of Embodiment 1 of this invention. (A) is a graph in which the horizontal axis represents the crank angle and the vertical axis represents the heat release rate, and (B) is a graph in which the horizontal axis represents the crank angle and the vertical axis represents the in-cylinder pressure. It is a graph of the model heat release rate calculated by the Wiebe function. It is a flowchart of the routine performed in Embodiment 1 of the present invention. It is a figure which shows the relationship between a real heat generation rate and a real cylinder internal pressure. It is a flowchart of the routine performed in Embodiment 1 of the present invention.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10 Internal combustion engine 12 Crank angle sensor 14 Intake valve 16 Exhaust valve 18 In-cylinder pressure sensor 21 Intake pressure sensor 30 Spark plug 33 Air-fuel ratio sensor 34 Catalyst 50 ECU (Electronic Control Unit)

Claims (8)

A method for determining a value of at least one parameter of a Wiebe function for modeling heat generation due to combustion in a cylinder of an internal combustion engine, comprising:
For the internal combustion engine, an in-cylinder pressure measuring step for measuring an in-cylinder pressure for each crank angle in a section including at least a combustion period;
A model in-cylinder pressure calculating step for calculating a heat generation rate by a Wiebe function in which a provisional value is substituted for a parameter to be determined, and calculating a model in-cylinder pressure for each crank angle during the combustion period based on the heat generation rate;
An error evaluation value calculating step for calculating an error evaluation value representing the magnitude of an error of the model cylinder pressure with respect to the actual cylinder pressure measured in the cylinder pressure measuring step;
Calculating the actual heat generation rate based on the actual in-cylinder pressure measured in the in-cylinder pressure measuring step;
An initial provisional value calculating step for calculating an initial value of the provisional value based on the actual heat generation rate;
With
The model in-cylinder pressure calculation step and the error evaluation value calculation step are repeated by changing the provisional value, and the provisional value when the error evaluation value is minimized is set as a definite value of the parameter to be determined. Of determining Wiebe function parameters characterized by   The model in-cylinder pressure is calculated in the model in-cylinder pressure calculating step so that the model in-cylinder pressure at the heat generation start point coincides with the actual in-cylinder pressure measured in the in-cylinder pressure measuring step. How to determine Wiebe function parameters. The parameters to be determined include the shape parameter m, the combustion period θ _p [degCA], the efficiency k in which the amount of heat of the fuel supplied into the cylinder is converted into the amount of heat generated in the cylinder, the ignition timing, and the Wiebe 3. The method for determining a Wiebe function parameter according to claim 1, comprising at least one of a heat generation start point deviation amount θ _b [degCA] representing a deviation amount from a heat generation start point of the function. . An apparatus for determining a value of at least one parameter of a Wiebe function for modeling heat generation due to combustion in a cylinder of an internal combustion engine,
For the internal combustion engine, in-cylinder pressure measuring means for measuring the in-cylinder pressure for each crank angle in a section including at least a combustion period;
A model in-cylinder pressure calculating means for calculating a heat generation rate by a Wiebe function in which a provisional value is substituted for a parameter to be determined, and calculating a model in-cylinder pressure for each crank angle during the combustion period based on the heat generation rate;
Error evaluation value calculation means for calculating an error evaluation value representing the magnitude of the error in the model cylinder pressure with respect to the actual cylinder pressure measured by the cylinder pressure measurement means;
Means for calculating an actual heat generation rate based on the actual in-cylinder pressure measured by the in-cylinder pressure measuring means;
An initial provisional value calculation means for calculating an initial value of the provisional value based on the actual heat generation rate;
The provisional value is changed, the model in-cylinder pressure is calculated by the model in-cylinder pressure calculating unit, and the error evaluation value is calculated by the error evaluation value calculating unit, and the error evaluation value is minimized. Fixed value acquisition means for acquiring a provisional value as a fixed value of the parameter to be determined;
An apparatus for determining Wiebe function parameters, comprising: When the Wiebe function is expressed by the following formula (I) (where, Q is the calorific value [J] in the cylinder, Q _total is the calorific value [J] of fuel supplied into the cylinder, θ wherein the elapsed crank angle after the heat generation starting [deg CA], theta _p combustion period [deg CA], m is the shape parameter, k represents efficiency, respectively), the shape parameter m in the parameter to be the determining,
As a step of obtaining an initial provisional value of the shape parameter m,
Calculating an actual heat generation rate for each crank angle based on the actual in-cylinder pressure measured in the in-cylinder pressure measuring step;
Calculating an actual combustion rate α at a crank angle at which the actual heat generation rate is maximized;
Calculating an initial provisional value of the shape parameter m according to the following equation (II) or an equivalent equation based on the actual combustion ratio α;
The method of determining a Wiebe function parameter according to any one of claims 1 to 3 , further comprising:

The parameter to be determined further includes the combustion period θ _p ,
As a step of _obtaining an initial provisional value of the combustion period θ _p ,
Obtaining an integral value of the actual heat generation rate as a total calorific value kQ _total ;
When the maximum value of the actual heat generation rate is β, based on the actual heat generation rate maximum value β, the total calorific value kQ _total , the initial provisional value of the shape parameter m, and a predetermined constant a. Calculating an initial provisional value of the combustion period θ _p according to the following formula (III) or an equivalent formula:
The Wiebe function parameter determination method according to claim 5 , further comprising:

When the ignition timing of the internal combustion engine is SA [degBTDC], and the amount of deviation between the ignition timing SA and the heat generation start point of the Wiebe function is the heat generation start point deviation amount θ _b [degCA], the parameter to be determined further comprising the heat generation start point deviation amount theta _b, the
As a step of _obtaining an initial provisional value of the heat generation start point deviation amount θb,
When the crank angle when the actual heat generation rate becomes maximum is θ _ATDC ^* [degATDC], the crank angle θ _ATDC ^* , the ignition timing SA, the initial provisional value of the shape parameter m, and the the initial provisional value of the combustion period theta _p, based on the predetermined constant a, the following (IV) and (V) type or in accordance with any equivalent expressions, the heat generation start point deviation amount theta _b initial provisional value of The method of determining a Wiebe function parameter according to claim 6 , further comprising a step of calculating.

The parameter to be determined further includes the efficiency k;
As a step of obtaining an initial provisional value of the efficiency k,
Obtaining an integral value of the actual heat generation rate as a total calorific value kQ _total ;
_Obtaining a value of the amount of heat Q _total of the fuel supplied into the cylinder;
Dividing the _total calorific value kQ _total by the value of Q _total to calculate an initial provisional value of the efficiency k;
The method of determining a Wiebe function parameter according to any one of claims 5 to 7 , further comprising:

Images