JPH0675935A - Multivariable system construction method and its device - Google Patents

Abstract

PURPOSE:To decide the number of units in an intermediate layer without depending on experience and to obtain a multilayered perceptron with high versatility in a neural network using the multilayered perceptron. CONSTITUTION:The input/output sample 20 of an unknown system is divided into a learning sample 21 and an evaluation sample 22, and the multilayered perceptron 10 is caused to execute learning by using the input sample of the learning sample 21. Then, the input samples of the learning sample 21 and the evaluation sample 22 are inputted to the multilayered perceptron 10 after learning and respective operation results are obtained. The square average of the operation results and a difference between the output samples of the learning sample 21 and the evaluation sample 22 are compared, and it is detected that overlearning occurs in the multilayered perceptron 10. When overlearning is detected, one unit 130 in the intermediate layer 13 is removed, and the multilayered perceptron 10 is caused to execute learning by the learning sample 21. The learning and the detection of overlearning are repeated until overlearning is not detected.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for constructing a multivariable system, and more particularly to a method and an apparatus for constructing a multivariable system using a perceptron.

[0002]

2. Description of the Related Art As a method of identifying an input / output relationship of a system (an unknown system) whose input / output functional relationship is unknown, a method using a multi-layer perceptron and learning by an error back propagation method has been conventionally known. .

The multi-layer perceptron is a network in which a large number of unit units each having multiple inputs and one output are connected in layers by links for transmitting signals. A coefficient called a weight that represents the strength of the connection is defined for each link.

Each unit receives as input the output of several other units coupled to the input by the link times the weight of the link. The inputs received are added and the sum of the inputs is calculated. The output of the unit is determined according to the sum of this input and the input / output function of the unit. This output is transmitted to the next unit unit through the output side link.

In the multi-layer perceptron, there is no link or feedback link between unit units in the same layer, and the signal flow is from the input layer side to the intermediate layer → ... → The output layer side to the output layer side. One way. The multi-layer perceptron is used for the purpose of estimating the functional relationship between the input and output of an unknown system by the above operation.

Learning to adjust the weights of the multi-layer perceptron as described above by using a signal called a teacher signal so that the input / output relationship of an unknown system can be estimated is called learning. The teacher signal used for this learning samples and uses actual input / output data of an unknown system for estimating the input / output relationship.

[0007]

Conventionally, since the method of identifying the input / output relation of an unknown system using the multilayer perceptron is performed as described above, there are the following problems. If more unit units of the middle layer are prepared than necessary, or if the number of samples of the input / output values of the unknown system is small with respect to the number of couplings of each layer, the number of weights to be adjusted by learning is It is too large for the number of samples of unknown system input / output values.

Therefore, the error is excessively reduced with respect to the input / output samples used for learning, and the identified function becomes excessively complicated. As a result, when an output value corresponding to an input value other than the input sample to the unknown system is to be estimated using the identified function, a phenomenon that a completely invalid estimated value is output occurs. was there. This phenomenon is called overlearning.

In order to prevent this over-learning, it is necessary to make the number of unit units in the intermediate layer appropriate, reduce the coupling between units included in each layer, and reduce the weight which is a parameter of this coupling. However, there have been many empirical methods for determining the number of units in the middle layer of the multi-layer perceptron (methods for constructing a multivariable system), and there has been a problem that it is difficult to obtain an appropriate number of unit units.

The present invention has been made in view of the above-mentioned problems, and can appropriately determine the number of unit units of the intermediate layer of the multilayer perceptron regardless of experience, and has good generalization. An object of the present invention is to provide a multivariable system configuration method and its apparatus.

[0011]

In order to achieve the above-mentioned object, the multivariable system configuration method of the present invention performs a first operation on one independent signal input, and outputs a plurality of operation processing results. To perform a second operation on these operation results, output a plurality of operation processing results, perform a third operation on the second operation results, and output a plurality of operation processing results A multi-layer perceptron is used, a learning sample and an evaluation sample are applied as independent input signals to each of a plurality of nodes in the multi-layer perceptron, and the sample from the sample applying means and the calculation from the multi-layer perceptron are performed. When the result is input to detect over-learning in the intermediate processing means in the multi-layer perceptron, and when over-learning is detected, the second operator in the intermediate node of the intermediate processing means is detected. Correct the reduce the predetermined intermediate node for learning and evaluation.

Further, the intermediate node in the intermediate processing means has one stage, a weight is used for the second operation, and the learning / evaluation means adjusts the weight when overlearning is detected. Characterize.

Further, the learning / evaluation means detects the difference between the sample and the calculation result of the multi-layer perceptron, or detects it as overlearning when the sum of squares of the difference is equal to or larger than the correction value.

Further, the learning / evaluation means is characterized by causing a maximum error when overlearning is detected.

Further, an input processing means having a plurality of input nodes for performing a first calculation on one independent signal input and outputting a plurality of calculation processing results, and a plurality of input nodes in the input processing means. From a plurality of intermediate nodes in the intermediate processing means having a plurality of at least one intermediate node for outputting a plurality of arithmetic processing results and outputting a plurality of arithmetic processing results A multilayer perceptron having an output processing means having a plurality of output nodes for inputting a plurality of arithmetic processing results and performing a third arithmetic operation and outputting one output signal, each of the plurality of nodes in the multilayer perceptron In addition, sample applying means for applying the learning sample and the evaluation sample as independent input signals, the sample from the sample applying means, and the multilayer parser. When the over-learning in the intermediate processing means in the multi-layer perceptron is detected by inputting the operation result from the thoron, and when the over-learning is detected, the second operation means in the intermediate node of the intermediate processing means is modified to a predetermined intermediate node. And learning / evaluation means for reducing

Further, the intermediate node in the intermediate processing means has one stage, weights are used for the second operation, and the learning / evaluation means adjusts the weights when overlearning is detected. Characterize.

Further, the learning / evaluation means detects the difference between the sample and the calculation result of the multi-layer perceptron, or detects it as overlearning when the sum of squares of the difference is equal to or larger than the correction value.

Further, the learning / evaluation means is characterized by causing a maximum error when overlearning is detected.

[0019]

First, the samples of input / output values of the unknown system are classified into learning input / output samples and evaluation input / output samples. Regarding the multi-layer perceptron trained on this learning input / output sample, the multi-layer perceptron is compared by comparing the output when the learning input sample and the evaluation input sample are input and the error of the corresponding output sample. Detect the occurrence of over-learning in.

When the occurrence of overlearning is detected, the number of unit units in the intermediate layer is reduced, and the multilayer perceptron is made to perform learning again on the input / output samples for learning. The learning during the over-training and the operation of reducing the number of unit units and the detection of the occurrence of the over-learning are repeated until the error of the output sample with respect to the evaluation input sample becomes smaller than the error of the output sample with respect to the learning input sample. By doing so, an appropriate number of unit units in the intermediate layer is obtained.

[0021]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A multivariable system (neural network) construction method and apparatus of the present invention will be described below. FIG. 1 is a diagram showing a configuration of a multilayer perceptron 10 applied to a multivariable system configuration method of the present invention. Figure 1
1, the multilayer perceptron 10 is composed of an input layer 11, an intermediate layer 13, and an output layer 15, and the respective layers have a coupling relationship as shown in FIG. 1 (a coupling 12 between the input layer and the intermediate layer, and a coupling between the intermediate layer and the output layer). A three-layer perceptron with a bond 14). Input layer 11, middle layer 13, and output layer 15
Are k, m, and n unit units (nodes) 110a to 110k, 130a to 130m, and 150, respectively.
It is a hierarchy composed of a to 150n.

Here, the number of unit units 110 included in the input layer 11 is the number of input variables of the unknown function for identification, and the number of unit units 150 included in the output layer 15 is the number of output variables. The initial number of the unit units 130 included in the mid layer 13 is arbitrary. Also, unit unit 1
10a to 110k, 130a to 130m, 150a to 1
50n is configured by software on a computer (not shown).

The operation of the multi-layer perceptron 10 will be described below. The input layer 11 and the intermediate layer 13 have a coupling relationship as indicated by an arrow of the coupling 12 of the input layer and the intermediate layer,
The intermediate layer 13 and the output layer 15 have a coupling relationship as indicated by an arrow of the coupling 14 between the intermediate layer and the output layer.

The operation of the unit unit 130i (i = 1, 2, ... M) included in the intermediate layer 13 will be described. The unit unit 130i includes the unit unit 110j and the unit unit 130 in the output Y _j of the unit unit 110j (j = 1, 2, ..., K) included in the input layer 11.
A numerical value representing the coupling strength of i, the sum of the values obtained by multiplying the weights W _ij are input, and a certain nonlinear function f is applied to the input.
The value Y _i subjected to is output. That is, the unit unit 13
The output Y _j 0 of the output Y _i and basic unit 110,

[Equation 1] The relationship is established.

A unit unit 130 included in the intermediate layer 13
The same relationship holds between i and the unit unit 150 _h included in the output layer 15. That is, the unit unit 150
The output Y _{h of h} (h = 1, 2, ..., N) and the output Y _i of the unit unit 130 are:

[Equation 2] The relationship is established. Here, the function g is a non-linear function corresponding to the above-mentioned function f, and usually g = f. Also, W
_hi is a numerical value representing the strength of the bond corresponding to the weight W _ij .

When a sufficient number of samples of combinations of input values and output values of an unknown system exist, the multilayer perceptron 10 described above is input with the samples of the input values of the unknown system, and the multilayer perceptron 10 corresponding to the input values is input. an output of comparing the samples of the output values of the corresponding unknown system, adjusting the weight W _ij and the weight W _ij as the value of the sample of the output and the output value of the unknown system of the multi-layer perceptron 10 matches (Hereafter, this is called learning). By repeating this operation a sufficient number of times, the multilayer perceptron 10 identifies the input / output relationship of the unknown system.

In the form of a multilayer perceptron 10,
For perceptrons with three or more layers, if the number of unit units in the middle layer (layers other than the input layer and output layer in a multilayer perceptron of three or more layers) is sufficiently large, the input / output of any unknown system It is known that the functional relation of can be approximated with arbitrary accuracy.

As a method for causing the multilayer perceptron 10 to perform the learning, a method called an error back propagation method is known to be effective. Backpropagation method is a method that minimizes the sum of squares of the errors in the output Z _p of the p-th output sample Z _p 'and multilayer perceptron 10 of the unknown system. The sum of the squared errors is a loss function E. The loss function E is

[Equation 3] However, in (Equation 3), w is the number of input samples.
It can be expressed as.

[0029] Each weight W _hi, each weight in each gradient (gradient) direction about W _ij W _hi, to modify the W _ij. This method corresponds to the steepest descent method. That is,
Weights W _hi and W _hi before learning and weights W _hi 'and W _ij ' after learning are

[Equation 4]

[Equation 5] and,

[Equation 6]

[Equation 7] It becomes a relationship like.

FIG. 2 is a learning / evaluation software 1 for implementing the multivariable system configuration method and apparatus of the present invention.
It is a figure which shows the structure of. In FIG. 2, the multilayer perceptron 10 is a three-layer perceptron. The learning / evaluation unit 30 is a unit that adjusts the weights W _hi and W _ij of the coupling of each layer.

Input / output value sample (input / output sample) 2
0 is sample data of (u + v) sets of input values given to an unknown system (not shown) and output values of the unknown system corresponding thereto. The learning sample 21 is sample data of input values and output values of u (u = integer) set used for learning of the multilayer perceptron 10 among the input / output samples 20. The evaluation sample 22 is sample data of v (v = integer) sets of input values and output values used for evaluation of the multilayer perceptron 10 among the input / output samples 20. The learning sample 21 and the evaluation sample 22 are obtained by dividing the input / output sample 20 into two so that the contents of both sample data are not biased. The above-mentioned respective parts shown in FIG. 2 exist in the form of software or data on a computer (not shown).

The operation of the learning / evaluation software 1 will be described below. First, the learning / evaluation unit 30 obtains the input / output sample 20 from an unknown system. Of the input / output samples 20, the input sample I of the learning sample 21
_21p (p = 1,2, ... u) with multi-layer perceptron 1
0 to obtain the calculation result output Z _20p 'in the multilayer perceptron 10. This is done for all input samples I _21p . Here, the calculation performed in each unit of the multilayer perceptron 10 is the same as that described above.

Next, the learning / evaluation unit 30 learns the multilayer perceptron 10 based on the output sample Z _21p of the input / output sample 20 and the calculation result Z _21p ′. That is, the weights W _hi and W _ij are replaced with the weights W _hi 'and W _ij to adjust the weights. That is, the loss function E is

[Equation 8] And the weights W _hi and W _ij are calculated according to (Equation 4), (Equation 5), (Equation 6), and (Equation 7). However, i = 1, 2 ,. ． ． m j = 1, 2 ,. ． ． kh = 1, 2 ,. ． ． n.

Next, the learning / evaluation unit 30 adds an evaluation sample 22 to the multilayer perceptron 10 after the above learning.
Input the input sample I _22p of Multilayer Perceptron 1
The calculation result Z _22p 'at 0 is obtained. This is performed for all input samples of the evaluation sample 22.

The learning / evaluation unit 30 calculates the _root mean square E ₂₂ of each of the calculation results Z _22p 'and the output sample Z _22p of the evaluation sample 22. That is,

[Equation 9] Is calculated.

Similarly, the learning / evaluation unit 30 inputs the input sample I _21p of the learning sample 21 to the multilayer perceptron 10 again, and squares the calculation result Z _21p ′ and the output sample Z _21p of the learning sample 21. Calculate the average E ₂₁ . That is,

[Equation 10] Is calculated.

The learning / evaluation unit 30 detects the occurrence of over-learning in the multilayer perceptron 10 based on the above two root mean squares E ₂₁ and E ₂₂ . That is, if the root mean square E ₂₂ is larger than E ₂₁ (E ₂₂ > E ₂₁ ), it is determined that overlearning has occurred. Also here 2
Multiply the average E ₂₂ is E ₂₁ and the equivalent or a small value, (E ₂₂ ≦
If it is E ₂₁ ), it is judged that over-learning has not occurred,
The process ends.

If it is determined that over-learning is occurring,
The unit unit 130i of the intermediate layer 13 is reduced by one. It is arbitrary which unit unit 130i is removed, but here, for example, the unit unit 130i having the largest subscript is removed.
Shall be removed from. That is, the unit unit 130
When i is reduced, unit units 130m, 130m-
1, 130 m-2 ,. ． ． Are removed in order.

Next, the learning / evaluation unit 30 uses the learning sample 21 to perform the learning of the multilayer perceptron 10 again. The learning procedure of the multilayer perceptron 10 is the same as the above-mentioned procedure. After the learning of the multi-layer perceptron 10, the learning / evaluation unit 30 detects over-learning of the multi-layer perceptron 10 again. If overlearning is detected, learn /
The evaluation unit 30 performs a procedure of reducing the unit unit 130i. The learning / evaluation unit 30 repeats the procedure of detecting over-learning and reducing the unit unit 130i until no over-learning is detected. This completes the learning of the multilayer perceptron 10, that is, the optimization of the weights W _hi and W _ij .

In this embodiment, as the over-learning detection condition, the values of the root mean squares E ₂₁ and E ₂₂ are compared, and the root mean square E
_Although it is determined that overlearning has occurred when ₂₁ is larger than E ₂₂ , the determination condition is not limited to this. For example, the quotient obtained by dividing the mean square E ₂₁ by E ₂₂ is in a certain range, for example, 1.3 to
The determination condition may be 0.7. Further, when the error when the evaluation sample 22 is used becomes too large as compared with the error when the learning sample 21 is used, the unit unit 130i may be increased again. Further, the numerical value used for the over-learning determination is not limited to the root mean square, and may be, for example, the average of absolute values.

FIG. 3 shows the learning / evaluation software 1 described above.
3 is a flowchart showing the operation of FIG. In FIG. 3, in step 00 (S00), the learning / evaluation unit 30 obtains the input / output sample 20 from an unknown system. In step 01 (S01), the learning / evaluation unit 30 sets the input / output sample 20 to the learning sample 21 and the evaluation sample 22.
Divide into two. In step 02 (S02), the learning / evaluation unit 30 uses the learning sample 21 to learn the multilayer perceptron 10.

In step 03 (S03), learning /
The evaluation unit 30 uses the learning sample 21 and the evaluation sample 22, and calculates the root mean square of each of them. In step 04 (S04), the learning / evaluation unit 3
For 0, overlearning is detected from the root mean square value obtained in S03. If overlearning is detected, the process proceeds to S05, and if overlearning is not detected, the process ends. Step 0
5 (S04), the learning / evaluation unit 30 determines that the middle class 13
One unit unit 130i of is removed.

The results of applying the multivariable system construction method and apparatus of this embodiment to the identification of the input / output relation of an actually unknown system will be described below. Here, an injection molding machine is taken as an example of the unknown system A, and ten kinds of set values given to this machine are used as input values to obtain one kind of output value.

Therefore, the number of unit units 110 included in the input layer 11 of the multilayer perceptron 10 is 10, and the number of unit units 150 included in the output layer 15 is 1. Further, the initial number of the unit units 130 included in the intermediate layer 13 is set to five. By applying the learning / evaluation software 1 to the multilayer perceptron 10, the number of unit units 130 included in the intermediate layer 13 was reduced to three. In addition, as the non-linear functions f and g, sigmoid functions

[Equation 11] However, in (Equation 11), x is a nonlinear function f,

[Equation 12] In the non-linear function g,

[Equation 13] Is.

FIG. 4 shows the multi-layer perceptron 10
It is a figure which shows the result of having identified the input-output relationship of unknown system A, without using learning / evaluation software 1. FIG. 5 shows the learning / evaluation software 1 described in this embodiment.
FIG. 6 is a diagram showing a result of identification of an input / output relationship for an unknown system A by.

The learning / evaluation unit 30 obtained 100 sets of input / output samples 20 for the unknown system A. This 10
Of the 0 sets of input / output samples 20, the evaluation sample 22 was set every 5 samples, and the others were divided into learning samples 21. That is, 100 sets of input / output samples 2
This means that 0 is divided into 80 sets of learning samples 21 and 20 sets of evaluation samples 22.

In FIG. 4, the horizontal axis represents the input / output sample 20.
Output values of unknown system A for input samples of The vertical axis represents the value of the output of the multilayer perceptron 10 with respect to the input sample of the input / output sample 20 in the multilayer perceptron 10 that has been learned by the 80 sets of learning samples 21.

In FIG. 5, the horizontal axis represents the input / output sample 20.
Output values of unknown system A for input samples of The vertical axis represents the multilayer perceptron 10 for the input sample of the input / output sample 20 in the multilayer perceptron 10 to which the learning / evaluation software 1 of this embodiment is applied.
Is the output value of.

In FIGS. 4 and 5, white circles represent the multilayer perceptron 10 for the input sample of the evaluation sample 22.
And the black circles represent the output of the multilayer perceptron 10 with respect to the input sample of the learning sample 21. In addition, the system A in which the multilayer perceptron 10 is correctly unknown
In the case where is identified, each point is placed on the diagonal line shown in the figure. That is, it can be said that a point closer to the diagonal line has a smaller error.

In FIG. 4, the multilayer perceptron 10 is shown.
Since the number of unit units 130 included in the intermediate layer 13 has not decreased, the error of the output of the multilayer perceptron 10 with respect to the input sample of the learning sample 21 is extremely small. However, the output of the multilayer perceptron 10 with respect to the input sample of the evaluation sample 22 has a value that is completely invalid.

In FIG. 5, the error distributions of the output values of the multilayer perceptron 10 with respect to the input samples of the learning sample 21 and the evaluation sample 22 are almost the same. Such a case corresponds to the case where the best unknown system A in the multilayer perceptron 10 is identified. Therefore, the multilayer perceptron 10 at this time can be regarded as an unknown system A optimal model.

The model (multilayer perceptron 10) in which the number of unit units 130i included in the intermediate layer 13 is determined by applying the learning / evaluation software 1 for the multivariable system configuration method and apparatus of the present invention is for an unknown system A. A reasonable output is obtained for the unlearned data (learning sample 21). Therefore, it is expected that the model has a good generalization, which can expect a reasonable output even for unlearned data about other unknown systems.

In the above-mentioned embodiments, the multi-layer perceptron has been described by taking a three-layer multi-layer perceptron as an example, but a multi-variable system configuration of the present invention is similarly applied to a multi-layer perceptron having an intermediate layer, for example. It is possible to apply the method and its apparatus.
Further, the multi-layer perceptron is not limited to being configured as software on the same computer, but for example, is configured by a so-called multiprocessor multivariable system in which each unit is configured on another computer and each computer is connected. May be. The multivariable system configuration method and apparatus of the present invention can take various configurations other than those described above. The embodiments described above are merely examples.

[0054]

As described above, according to the method and apparatus for constructing a multivariable system of the present invention, it is possible to determine an appropriate number of unit units in the intermediate layer of a multilayer perceptron regardless of experience, and to perform generalization. It is possible to provide a multivariable system configuration method and device having good performance.

[Brief description of drawings]

FIG. 1 is a diagram showing a configuration of a multi-layer perceptron.

FIG. 2 is a diagram showing a configuration of learning / evaluation software that realizes a configuration method of a multivariable system (multivariable system) and an apparatus thereof according to the present invention.

FIG. 3 is a flowchart showing the operation of learning / evaluation software for implementing the multivariable system configuration method and apparatus of the present invention.

FIG. 4 is a diagram showing a result of identifying an input / output relationship of an unknown system by a conventional multi-layer perceptron.

FIG. 5 is a diagram showing a result of identification of input / output relations of an unknown system by a multi-layer perceptron to which learning / evaluation software for realizing the multivariable system configuration method and apparatus of the present invention is applied.

[Explanation of symbols]

 1 ... Learning / evaluation software 10 ... Multi-layer perceptron 11 ... Input layer 12 ... Coupling of input layer and intermediate layer 13 ... Intermediate layer 14 ... Coupling of intermediate layer and output layer 15. ..Output layer 20 ... Input / output sample 21 ... Learning sample 22 ... Evaluation sample 30 ... Learning / evaluation unit

Claims (8)

[Claims] 1. A first operation is performed on one independent signal input, a plurality of operation processing results are output, a second operation is performed on these operation results, and a plurality of operation processing results are obtained. A multi-layer perceptron that outputs and performs a third calculation on the second calculation result and outputs a plurality of calculation processing results is learned as an independent input signal to each of the plurality of nodes in the multi-layer perceptron. The sample for evaluation and the sample for evaluation are applied, and the sample from the sample applying means and the calculation result from the multilayer perceptron are input to detect overlearning in the intermediate processing means in the multilayer perceptron and detect overlearning. In this case, a multivariable system configuration method in which the second computing means in the intermediate node of the intermediate processing means is modified to reduce a predetermined intermediate node for learning and evaluation. . 2. The multivariable system configuration method according to claim 1, wherein the intermediate node in the intermediate processing means has one stage, a weight is used for the second operation, and the learning / evaluation means is not overlearned. A method for constructing a multivariable system, characterized in that the weight is adjusted when detected. 3. The multivariable system configuration method according to claim 1 or 2, wherein the learning / evaluation means corrects a sum of differences between a sample and a calculation result of a multilayer perceptron, or a sum of squares of the differences. A multi-variable system constituent device that detects over-learning when the value is greater than or equal to the value. 4. The multivariable system configuring method according to claim 3, wherein the learning / evaluating means causes a maximum error when overlearning is detected. 5. An input processing means having a plurality of input nodes for performing a first calculation on one independent signal input and outputting a plurality of calculation processing results, and a plurality of input nodes in the input processing means. From a plurality of intermediate nodes in the intermediate processing means having a plurality of at least one intermediate node for outputting a plurality of arithmetic processing results and outputting a plurality of arithmetic processing results A multi-layer perceptron having an output processing means having a plurality of output nodes for inputting a plurality of operation processing results and performing a third operation and outputting one output signal; and each of the plurality of nodes in the multi-layer perceptron. In addition, sample applying means for applying the learning sample and the evaluation sample as independent input signals, the sample from the sample applying means, and the multilayer percept When the over-learning in the intermediate processing means in the multi-layer perceptron is detected by inputting the operation result from the computer, and when the over-learning is detected, the second operation means in the intermediate node of the intermediate processing means is modified and the predetermined intermediate node And a multi-variable system constituent device having learning / evaluation means for reducing. 6. The multivariable system configuration device according to claim 5, wherein the intermediate node in the intermediate processing means is one stage, weight is used for the second operation, and the learning / evaluation means is not overlearned. A multivariable system constituent device, characterized in that the weight is adjusted when detected. 7. The multivariable system configuration apparatus according to claim 5 or 6, wherein the learning / evaluation means corrects a sum of differences between a sample and a calculation result of a multilayer perceptron, or a sum of squares of the differences. A multi-variable system constituent device that detects over-learning when the value is greater than or equal to the value. 8. The multivariable system constituent device according to claim 7, wherein said learning / evaluation means causes a maximum error when overlearning is detected.