JP4851396B2 - Parameter identification apparatus and program thereof - Google Patents

Description

  The present invention performs a simulation using a nonlinear physical model, compares the output with the output to be optimized, and repeatedly corrects the parameters of the physical model based on the comparison result, thereby asymptotically bringing each parameter to a true value. It relates to the identification of parameters to be performed.

  Conventionally, simulation using a model has been performed, and for this purpose, a model in accordance with the actual situation is required. For this reason, it is necessary to determine the specifications of the model, and the specifications of the model are identified from experimental data. In this case, a process for determining whether the identification has been performed with high accuracy is required.

In the field of statistics, the problem of “multicollinearity” is known as a case where counting cannot be accurately identified when the input / output relationship is recently identified by a linear function. This is because, for example, when the time series data (y, u1, u2) is used to identify the coefficients (a1, a2) of the formula (1), the strong correlation between the time series data (u1, u2). If there is, the coefficient (a1, a2) cannot be correctly identified.
y = a ₁ · u ₁ + a ₂ · u ₂

  Here, the strength of the correlation can be examined using the correlation coefficient, and the correlation coefficient indicates that the correlation is stronger as the correlation coefficient is closer to 1 or -1. Such a point is described in Non-Patent Document 1.

  Patent Document 1 proposes a method for diagnosing an abnormal state of a target facility or product process and improving the abnormal state. Here, the abnormal state identifies the relationship between the state of the target facility (= explanatory variable, corresponding to u1 and u2 in equation (1)) and the abnormal state (= target variable, corresponding to y in equation (1)). In this case, there is a problem that the identification accuracy deteriorates if identification including unnecessary explanatory variables is performed. Therefore, in Patent Document 1, factor analysis (calculation of F value or t value) of the influence of the explanatory variable on the objective variable is performed, and the unnecessary explanatory variable is discarded.

JP 2000-315111 A Tanaka Yutaka, Wakimoto Kazumasa (1985): Multivariate Statistical Analysis, Modern Mathematics Company

  Here, Non-Patent Document 1 determines whether identification can be performed on the premise that a plurality of input time-series data (u1, u2) exist for a linear model. Therefore, the nonlinear model cannot be applied when a plurality of time series data does not exist.

  In addition, as in Non-Patent Document 1, Patent Document 1 has a problem of selecting an explanatory variable with high identification accuracy from multi-input explanatory variables (u1, u2,...), And such a premise does not apply. It cannot be applied to.

  The present invention performs a simulation using a nonlinear physical model, compares the output with the output to be optimized, and repeatedly corrects the parameters of the physical model based on the comparison result, thereby asymptotically bringing each parameter to a true value. This is a parameter identification device to be used, and the amount of change in the output evaluation function value between all parameters is compared with the amount of change in the output evaluation function value when the parameter is changed. When there is a strong correlation combination, it is determined that the output of the physical model or the optimization target does not contain sufficient information for asymptotically bringing the physical parameter to the true value.

  Further, it is preferable that the change amount of the output evaluation function is an influence of a parameter change on an error between the output of the physical model and the output to be optimized.

  The change amount of the output evaluation function is a gradient vector for each parameter change with respect to a sum of squares of errors between the output of the physical model and the output to be optimized, and a correlation coefficient between the gradient vectors of the parameters is obtained. Is preferred.

  In addition, when it is determined that it is not sufficient, it is preferable to change the physical parameters to be identified, reduce the number of parameters, or change the output data to be optimized used for identification.

  Furthermore, the present invention relates to a program that causes a computer to execute the above processing by being executed in the above apparatus.

  Thus, according to the present invention, it can be determined from the output state whether the parameter can converge to the true value. In addition, it is possible to specify which parameter set is used in the determination.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

  FIG. 2 shows a schematic configuration of a hydraulic system to be identified in the present embodiment. An automatic transmission is connected to the engine, and the rotation of the engine output shaft is changed by this automatic transmission and transmitted to the tire. The automatic transmission receives a hydraulic pressure and performs a shift operation. For example, when the shift timing comes according to the running state of the vehicle, an ECU (electronic control unit) detects this, supplies a current according to the shift command to the hydraulic control circuit, and in the hydraulic control circuit automatic transmission The shift operation is performed by controlling the hydraulic pressure to the clutch pack.

  Here, the hydraulic system of the automatic transmission has a hydraulic pump driven by an engine, and oil from the hydraulic pump is supplied to the hydraulic line. A hydraulic pressure adjusting valve is provided near the hydraulic pump in the hydraulic line, and thereby the line pressure (original pressure) in the hydraulic line is controlled to a predetermined value. A linear solenoid valve is provided in the hydraulic line, and the supply of the line pressure of the hydraulic line to the clutch pack is controlled. Note that an orifice is provided in the flow path from the linear solenoid valve to the clutch pack to limit the supply of hydraulic pressure to the clutch pack. The clutch pack controls the engagement / release of the input side disk and the output side disk by moving the piston against the spring pressure by hydraulic pressure. For example, when shifting from the first speed to the second speed, the first-speed output disk originally engaged with the input-side disk is released, and the second-speed output disk is engaged.

  Considering such a hydraulic system to be controlled, the input is a hydraulic pressure command value, and the output is the hydraulic pressure supplied to the clutch pack.

  In FIG. 3, the outline | summary of the identification method of this embodiment is shown. It shows that the parameters (i) to (iv) in the detailed hydraulic model are identified based on the error between the hydraulic system output of the actual machine and the model output. In this example, the parameters are (i) the time constant of the hydraulic system, (ii) the position where the clutch pack is clogged, (iii) the clutch operating load, and (iv) the hydraulic dead zone width. The oil pressure command value is supplied to the oil pressure detailed model. This hydraulic detail model is composed of a design condition model and a characteristic variation model. Then, by inputting the hydraulic pressure command value, the hydraulic pressure supplied to the clutch pack is output from the detailed hydraulic model. The hydraulic pressure command value is also supplied to the actual hydraulic system to measure the hydraulic pressure that is actually output. The output of this actual machine is the output to be optimized. Then, the error between the two is calculated and supplied to the identification (optimization) method. In the identification method, the characteristic parameter of the characteristic variation model in the hydraulic detail model is changed according to the error, and new parameters for parameters (i) to (iv) are set in the characteristic variation model. As a result, the next hydraulic detail model is set and the operation of obtaining this output is repeated.

  FIG. 4A shows a block diagram of the hydraulic system. First, a shift command is supplied to the ECU. The ECU supplies a signal for operating the linear solenoid valve in response to the shift command. Actually, both a release signal for the linear solenoid valve of the release hydraulic line and an engagement signal for the linear solenoid valve of the engagement hydraulic line are both used. As a result, the oil accompanying the operation of the linear solenoid valve is supplied to the orifice flow path to the clutch pack, and the clutch pressure is determined. Note that the flow rate of the orifice channel is q, the clutch piston stroke in the clutch pack is xc, the clutch area Ac, and the clutch pressure Pc.

  FIG. 4B shows the specifications of the hydraulic system to be identified. When a shift command is input, the ECU generates a delay with respect to this command. In this example, the delay is expressed by 1 / (T · s + 1), where T is a time constant, which is the parameter (i). Further, the linear solenoid valve has a dead zone until the operation starts, and this is the parameter (iv).

Orifice, the flow rate qc is determined by _{qc = C 0 · Ac√ {2} (Pl-Pc) / ρ}. Here, Pl is the upstream pressure of the orifice, Pc is the clutch pack side pressure, ρ is the density of the oil, and C ₀ is a constant relating to the viscosity (opening ratio, Reynolds number) of the oil.

  In the clutch pack, the clutch piston stroke xc and the clutch pressure PC are expressed as xc = ∫qcdt / Ac, Pc = Kc · xc / Ac. Kc is a constant. Furthermore, the operation of the clutch pack is greatly affected by the clogging of the pack. Therefore, the pack clogging position is set to xc_max, and the clutch pressure at that position is set to Pc_max. Therefore, at the pack clogging position, xc = xc_max, Pc = Kc · xc_max / Ac = PC_max.

  Next, parameter identification in the present embodiment will be described with reference to the flowcharts of FIGS. 1A and 1B. In the description, the output of the hydraulic detail model in which the values of the parameters (i) to (iv) are appropriately changed is used instead of the output data of the actual machine.

  First, in step 1, initial (nominal) values [a (1) b (1) c (1) d (1)] of model parameters to be identified (optimized) are determined. This nominal value is preferably set to a value that is normally considered to be correct. In this example, the hydraulic system specifications to be identified are indicated by broken-line circles in FIG. 4B.

  In steps 2 and 3, the model is simulated, and an error between the model output and the actual machine output is obtained as shown in FIG. In the present embodiment, the sum of squares of this error is used as an evaluation value, and this is calculated according to formula (1) or formula (2). Expression (1) is a case of a continuous system of analog data, and Expression (2) is a case of a discrete system using sampling data. In the case of a continuous system, it is a value obtained by integrating the square of the error of the output hydraulic pressure Pc from time t = 0 to tf, and in the case of a discrete system, it is 1 / N of the square sum of the errors of N samples. .

  Subsequently, in step 4, if the error (evaluation value: sum of squares of error) in equation (1) or equation (2) is within a threshold, the target output is obtained and the identification step is terminated.

If NO in step 4, that is, if the error (evaluation value) is larger than the threshold value, the process proceeds to step 5 to set a new parameter obtained by appropriately shifting the initial value of the model parameter (formula (3)).
[a (1) b (1) c (1) ...] = [a (1) + δ ₁ b (1) + δ ₂ c (1) + δ ₃ ...] (3)

  In step 6, model simulation is performed in the same manner as in step 2 using the parameters of equation (3). In step 7, an error (evaluation value) is calculated again using equation (1) or equation (2). It is determined whether (evaluation value) is within a threshold value. If the determination in step 8 is within the threshold value, the identification step ends. On the other hand, if it is determined in step 8 that the error (evaluation value) is larger than the threshold value, the process proceeds to step 9.

  In step 9, a gradient vector is calculated from the factor effect of each parameter. For this purpose, first, with respect to the four parameters (i) to (iv) shown in FIGS. 3 and 4B, combinations of two levels (two values for one parameter) as shown in Table 1, Sixteen patterns are prepared, and error sums of squares J1 to J16 are calculated for each combination.

  As shown in Table 2, the factor effect (average value for each level) is calculated for each parameter level (2 levels) from the obtained error.

That is, J _a (1) is the average value (evaluation value) of the square sum of errors when the parameter (hydraulic system time constant) is a (1) (level 1), and J _a (2) is the parameter ( This is an average value of the sum of squares of errors when the hydraulic system time constant) is a (2) (level 2). Similarly, Jb (1), Jb (2), Jc (1), Jc (2), Jd (1), Jd (2) are average values of the evaluation values at the levels 1 and 2 for each parameter. . Therefore, Table 2 shows the effect of each parameter on the level 1 and 2 changes.

  From the factor effects in Table 2, the gradient vector [Sa (1) Sb (1) Sc (1) Sd (1)] of the entire parameter defined by Expression (4) is obtained. That is, each element of the gradient vector is an output gradient with respect to levels 1 and 2 of one parameter.

  In step 10, the parameter correction amount is calculated based on the gradient vector S (i). Here, i indicates the number of calculations, and the above levels 1 and 2 represent those used for the first and second calculations, i = 3 in the third calculation, and level 1 I = 2 and level 2 is i = 3.

  The next model parameter is calculated by equation (5) using the scalar value k.

  In this way, the next parameter is determined by adding the correction amount corresponding to the evaluation value for each parameter. When the next parameter is determined, the process returns to step 6 and the same steps are repeated until the error becomes equal to or less than the threshold value.

  In this way, it is possible to identify a parameter (= hydraulic specification) whose error is equal to or less than a predetermined value.

"Check Physical Parameters"
Next, a process for determining whether or not the target physical parameter is appropriate for the identification of such hydraulic parameters will be described with reference to FIG. 1B.

  The physical parameter is repeatedly identified by the process of FIG. 1A described above. First, it is determined whether the number of repetitions n is equal to or greater than a predetermined number of times n_min (step 11). If this determination result is NO, the process ends (no process for determining whether it is appropriate).

  If the determination in step 11 is Yes, the correlation coefficient γ between the gradient vectors is calculated (step 12).

  That is, the gradient vector [Sa (1) Sb (1) Sc (1) Sd (1) in the equation (4) is used as the amount of change in the output evaluation function value (for example, the sum of squared errors) when each parameter is changed. ], The correlation coefficient between the gradient vectors is obtained as in mp expression (6) in FIG. 1B. Note that, in Equation (6), the correlation coefficient between the two parameters is shown. However, as shown in FIG. 1B, the correlation coefficients between all the parameters are calculated and calculated.

Next, the value of the total correlation coefficient γ _{i, j} is compared with a threshold value of γ (for example, a threshold value 0.9 which is considered to be a strong correlation above it) (step 13). If this determination is NO, there is no problem parameter, and the process ends.

  On the other hand, if the determination in step 13 is Yes, it is determined that the identification accuracy is poor (step 14). In this case, either (i) change of identification parameters, (ii) reduction of the number of identification parameters, or (iii) change of actual machine output data used for identification is performed. The countermeasures (i) to (iii) are performed in consideration of parameters that are considered to be correlated. For example, if (i) (ii), one of the two parameters having a high correlation is changed or deleted. In the case of (iii), the actual machine output data is changed so that the two parameters having a high correlation take into account the characteristics of the two parameters.

"Specific examples of successful identification"
First, the case where the specification value of the hydraulic system can be identified with high accuracy is shown. FIG. 6 shows a comparison of the time response waveforms of the model and the actual machine before and after the identification, and FIG. 7 shows a search history of the sum of squares of the identification parameter and the error. It can be seen that the model and the actual machine almost coincide, and the identification parameter converges to a true value after about 15 searches.

  At this time, the gradient vector [Sa (1) Sb (1) Sc (1) Sd (1) in Expression (4) is used as the amount of change in the output evaluation function value (for example, the sum of squares of errors) when each parameter is changed. )], The correlation coefficient between the gradient vectors is obtained as in the above-described equation (6).

  Table 3 shows the correlation coefficients for the parameters thus obtained.

  Since the correlation coefficient between any gradient vectors is not close to 1 or −1 (the absolute value of the correlation coefficient is less than about 0.9), it can be determined that the identification has been performed with high accuracy. In FIG. 7, since a model whose true value is known for verification is identified as a target, it can be determined whether or not it has converged to the true value.

  Next, two examples of cases where identification is not successful are shown.

“If identification does not work, 1”
In this example, in FIG. 3 and FIG. 4B, “hydraulic dead zone width” among the four identification parameters is changed to “hydraulic response dead time”.

  FIG. 8 shows a comparison of the time response waveforms of the model and the actual machine before and after identification, and FIG. As can be seen from FIG. 8, the hydraulic output of the model and the actual machine are almost the same. However, as can be seen from FIG. 9, the identification parameter does not converge to the true value.

  At this time, Table 4 shows the result of the correlation coefficient between the gradient vectors of Equation (4) obtained by Equation (6).

  Since the correlation coefficient between the gradient vector (hydraulic system time constant) and (dead time) is close to 0.97 and 1, it can be seen that the two parameters have the same effect on the sum of squares of error (evaluation function) Therefore, it can be determined that the identification has not been performed with high accuracy.

"If the identification is not successful 2"
In this example, the case where the parameter “orifice flow coefficient” is simultaneously identified in addition to the four identification parameters in FIGS. 3 and 4B will be considered.

  FIG. 10 shows a comparison of the time response waveforms of the model and the actual machine before and after identification, and FIG. 11 shows a search history of the sum of squares of the identification parameter and error. In this example, the identification parameter does not converge to the true value even though the output waveforms of the model and the actual machine are almost the same.

  Table 5 shows the result of the correlation coefficient between the gradient vectors of equation (4) obtained by equation (6) at this time.

  The correlation coefficient between the gradient vector (pack clogging position) and (orifice flow coefficient) is close to -0.99 and -1. Therefore, it can be seen that the two parameters have the same effect on the sum of squared errors (evaluation function), and therefore it can be determined that the identification has not been performed with high accuracy.

"Problem of identification parameter not converging to true value"
Finally, what kind of problem occurs when the identification parameter does not converge to the true value will be described.

  Table 6 is an example of the result of identifying the parameters with the same problem setting as in FIGS.

  FIG. 12 shows the result of simulation using the same current command as identified by applying the identification parameters shown in Table 6. Although the identified parameter value is different from the true value, the time series waveform of the hydraulic pressure is almost the same in the model as the actual machine.

  However, when a simulation is performed using a current command different from that at the time of identification, the time series waveform of the model deviates from the waveform corresponding to the actual machine as shown in FIG. As described above, when the identification parameter does not converge to the true value, it can be seen that there is a problem that the parameter is not properly set, and only a simulation under a specific condition can be handled.

"Effects of this embodiment"
As described above, in this embodiment, in order to quantitatively evaluate the strength of correlation between parameters, which is the cause of deterioration of identification accuracy, an evaluation function value (for example, error) of the output when each identification parameter is changed. We focused on the amount of change in the sum of squares). When this change amount has the same tendency in each parameter (high correlation), it is determined that identification cannot be performed properly. This is because it is considered that the identification tendency becomes worse as the parameters tend to have the same tendency (the correlation is larger) (the correlation is stronger) and the two cannot be distinguished and identified.

  Therefore, according to this embodiment, it can be determined whether the identification parameter can converge to a true value. Further, it can be understood why the set of identification parameters does not converge to the true value based on which correlation is large. That is, if a set of parameters has the same effect on the evaluation function value (for example, the sum of squares of errors), the identification parameter cannot converge to a true value, but the set of parameters that cause this can be specified. Therefore, it is possible to perform appropriate identification work by changing the identification parameters according to the determination result or reducing the number of identification parameters.

It is a flowchart which shows the process of parameter identification. It is a flowchart which shows the process of a parameter check. It is a figure which shows the outline | summary of a hydraulic control system. It is a figure which shows the outline | summary of the identification method of a parameter. It is a block diagram of a hydraulic system. It is a figure which shows the item of the hydraulic system to identify. It is a figure which shows the example of the simulation result of a model. Identification result 1: It is a figure which shows a time series waveform. Identification result 2: It is a figure which shows the square sum of a parameter value and an error. Identification result 1: It is a figure which shows a time series waveform. Identification result 2: It is a figure which shows the square sum of a parameter value and an error. Identification result 1: It is a figure which shows a time series waveform. Identification result 2: It is a figure which shows the square sum of a parameter value and an error. It is a figure which shows the result at the time of using the same current command pattern as the time of identification. It is a figure which shows the result at the time of using the electric current command pattern equal to the time of identification.

Claims (5)

A parameter that makes each parameter asymptotic to a true value by performing a simulation using a nonlinear physical model, comparing the output with the output of the optimization target, and repeatedly correcting the parameters of the physical model based on the comparison result The identification device of
Regarding the amount of change in the output evaluation function value when the parameter is changed, determine whether there is a combination of strong correlations for the amount of change in the output evaluation function value between all parameters,
An apparatus for identifying a parameter, characterized in that when there is a strong correlation combination, it is determined that the physical model or the output of the optimization target does not contain sufficient information to make the physical parameter asymptotic to a true value. The parameter identification device according to claim 1,
The parameter identification apparatus characterized in that the change amount of the output evaluation function is an influence of a parameter change on an error between the output of the physical model and the output of the optimization target. The parameter identification device according to claim 2,
The amount of change in the output evaluation function is a gradient vector for each parameter change with respect to the sum of squares of the error between the output of the physical model and the output to be optimized, and the correlation coefficient between the gradient vectors of the parameters is obtained. Feature identification device. In the parameter identification device according to any one of claims 1 to 3,
An apparatus for identifying a parameter, characterized in that when it is determined that the physical parameter to be identified is changed, the number of parameters is reduced, or output data to be optimized used for identification is changed. A parameter that makes each parameter asymptotic to a true value by performing a simulation using a nonlinear physical model, comparing the output with the output of the optimization target, and repeatedly correcting the parameters of the physical model based on the comparison result A parameter identification program for causing a computer to execute the identification process of
For the amount of change in the output evaluation function value when each parameter is changed, comparing the amount of change in each parameter to determine whether there is a strong correlation combination between both parameters,
Determining that the output of the physical model or optimization target does not contain sufficient information to make the physical parameter asymptotic to a true value when there is a strong correlation combination;
Is a parameter identification program characterized by causing a computer to execute.