JPH0683795A - Recognition or diagnosis method - Google Patents

Abstract

(57) [Summary] [Objective] To provide a highly efficient recognition and diagnosis method by analytically obtaining the configuration and coupling coefficient of a neural network. [Structure] For example, except the output layer, the output is always 1 at the bottom.
Then, a neuron for threshold correction is provided. The number of intermediate layers is two or less, and is input after the total is calculated for each case. For each output of the output layer, the relationship between the input sum and the teacher data in each case is tabulated in the descending order of the input sum, and the value of the teacher data having the maximum sum and the number of changes of the teacher data are focused. Based on these, the configuration of the neural network (the number of intermediate layers and the number of neurons thereof) can be determined, and each coupling coefficient can be analytically calculated using the table. When the number of changes in the teacher data is odd, some do not pass through the second intermediate layer. [Effect] The calculation time can be shortened, and reliable diagnosis can be performed regardless of the scale.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a recognition or diagnosis method, and more particularly to a present use method utilizing past operation information of various components of a power circuit such as a GIS (Gas Insulated Switchgear) and a transformer. The present invention mainly relates to a recognition or diagnosis method that uses a neural network to diagnose whether or not there is an abnormality in a state.

[0002]

2. Description of the Related Art Conventionally, as disclosed in, for example, Japanese Patent Application Laid-Open No. 2-297074, a method of diagnosing an abnormality of equipment using a neural network has been proposed. The method is to input the state of various equipments to the input layer of the neural network having a multi-layered structure in advance for learning, and when new states of various equipments are input, the equipments are to be learned based on the previous learning result. Is determined to be normal, and when it is determined to be abnormal, the cause thereof is estimated.

Further, in Japanese Patent Laid-Open No. 2-272326, a detailed description is given regarding mechanical vibration, acoustic vibration, electric vibration, etc. of a rotating machine. Furthermore, JP-A 2-1
In 00757, a learning method for a parallel neural network is proposed. Among them, the back propagation method is becoming effective as a learning method. In this conventional method, only the point of minimizing the error is found, and once it falls to the local minimum, the learning does not proceed. A flaw is pointed out. As an improvement plan, there has been proposed a plan to improve learning efficiency and accuracy by connecting one or more neural networks in parallel and sequentially learning.

[0004]

FIG. 2 shows an example of a conventional neural network. An intermediate layer of an arbitrary number of layers is provided between the input layer and the output layer (illustration is a single layer example). In the input layer, X ₁ , X ₂ , X ₃ ...
... _Xn is input. In FIG. 2, besides that, 1 is always input as one of the inputs for adjusting the output from the neuron. Weights (coupling coefficients) W ₁ , W ₂ , W for these inputs
A value obtained by multiplying ₃ ... W _n and W _{n + 1} is, for example, an input U ₁ to the first neuron in the intermediate layer. The output from the neuron is V ₁ . U ₁ and V ₁ are calculated as described in Table 1, for example.

[0005]

[Table 1]

Similar calculation formulas hold for inputs and outputs of other middle layer neurons and output layer neurons. In particular, only one of the intermediate layers (the one hatched at the bottom in the figure) is coupled only to the input 1 for output adjustment, and the coupling coefficient is given in advance so that the output becomes 1. There is.

In such a conventional neural network, an operation called learning is indispensable. Learning means that when a certain input data is input, the coupling coefficient between the neurons is changed so that the calculated value approximated to the data called the predetermined teacher data corresponding to the input data is output from the output layer. It means to obtain iterative calculation.
For example, it means that 0.5 times the sum of squares of the difference between the teacher data and the calculation output is taken as an error, and the calculation for correcting the coupling coefficient little by little is repeated to reduce this error. If learning progresses satisfactorily, the error will be small, but in some cases, this error will not be small, and even if learning is performed many times, the calculation output may not be obtained with sufficient accuracy. In some cases, it is said that the local minimum has fallen. In this case, no matter how many times learning is performed, it is not possible to escape from the minimum value, and an absolutely appropriate coupling coefficient cannot be obtained. Even if the calculated output converges to a desired value, depending on the size of the neural network and the training data, learning may be performed many times.
It may take a very long time (eg, several hours or more).

Further, in the conventional neural network, cut-and-try is required to determine the optimum number of intermediate layers and the number of neurons, which is inefficient and has been desired to be improved.

It is an object of the present invention to provide a recognition or diagnosis method capable of obtaining a coupling coefficient accurately and easily in a system such as a neural network.

Another object of the present invention is to provide a recognition or diagnosis method capable of easily determining the appropriate number of intermediate layers of a neural network and the number of neurons thereof.

[0011]

In order to achieve the above object, the present invention analytically finds the coupling coefficient of each neuron from input data and teacher data.

That is, the present invention provides a threshold correction neuron that always outputs 1 in a region other than the output layer in a recognition or diagnosis method using a neural network having an input layer, an intermediate layer and an output layer. Is provided for each case, the sum is calculated for the input data for each case, and for each output of the output layer, in order of the size of each sum of the input data, it is created together with the corresponding teacher data. A number of neurons equal to the number of changes N of N are sequentially arranged according to the above table as the first intermediate layer, and when N is an odd number, (N-1) / 2 neurons are used as the second intermediate layer. The output of the first intermediate layer is sequentially input by two, and each output of the second intermediate layer is output together with the remaining one output of the first intermediate layer. In the input and also the Is an even number, N / 2 neurons are arranged as the second intermediate layer, and two outputs of the first intermediate layer are sequentially input to each of the second intermediate layers. The output is used as an input of the output layer, the teacher data corresponding to the case where the total sum of the input data in the table is the maximum, the total sum of the input data before and after the change of the teacher data, and the teacher data are combined to combine the respective parts. It is characterized in that the coefficient is analytically obtained.

[0013]

(1) When the analytical method is used as in the present invention, iterative learning, which has been necessary in the past, becomes unnecessary. The optimal number of intermediate layers of the neural network and the number of neurons thereof can be determined in advance. Further, the problem of local minimum value unlike the conventional case does not occur. Therefore, the time from the input of data to the diagnosis using the neural network can be shortened. Since this method can be applied regardless of the number of input data or the number of cases, the coupling coefficient between each neuron of a large-scale neural network can be reliably obtained in a short time.

(2) It is possible to greatly reduce the learning time by using iterative learning, which also uses an analytical method.

(3) The present invention can be applied to a method other than a neural network, and even in this case, efficient recognition and diagnosis are possible.

(4) Since the number of calculations is significantly reduced, for example, even an economical book type personal computer or the like may be recognized and diagnosed by the method of the present invention depending on its memory capacity.

[0017]

In the following description of the embodiments of the present invention, it is assumed that the input is an arbitrary numerical value of 0 to 1 and the teacher data is 0 or 1. When there are multiple outputs, each of the outputs is handled as follows.

First, the coupling coefficients W ₁ , W ₂ , and
It has been found that most of W ₃ ... W _n are equal to each other as shown in the following equation, although there are extremely rare exceptions. (Exceptions are mentioned _{later.) W 1 = W 2 =} W 3 ··· = W n ······ ( number 1) the weight W _{n + 1} to the input 1 for threshold modification, Generally, it takes a different value.

Considering (Equation 1), the coupling coefficient may be multiplied after the total of the inputs is calculated for each case. Therefore, the total sum of inputs is calculated for each case, and as shown in Table 2, for example, they are rearranged in the descending order of the total sum and displayed together with the corresponding teacher data.

[0020]

[Table 2]

As a result of various examinations after making such an arrangement, the sum of the inputs is the maximum (displayed as S ₁ ).
It was found that it is necessary to change the way of handling when obtaining the coupling coefficient and the like depending on whether the teacher data of 0 is 0 or 1. Here, first, the case where the teacher data corresponding to S ₁ is 0 will be described.

For convenience of description, a simple example will be described. Figure 3
Is the vertical axis of S ₁ , S ₂ , S ₃ , ..., S _n in Table 2,
The teacher data is displayed on the horizontal axis, and an example in which the teacher data changes only once is shown. Although FIG. 3 shows the case where the teacher data changes at the boundary between S ₁ and S ₂ , it may naturally change at other places. When this simple change is generated, the neural network does not need any intermediate layer, and a simple one as shown in FIG. 4 may be used. The coupling coefficients W _a and W _b of the neural network are obtained as follows.

Focusing on the change in the teacher data in Table ₂ , using the input sums immediately before and after the boundary where the teacher data shown by the dotted line in the table changes, that is, S ₁ and S ₂ , the following (Equation 2) , (Equation 3) Creates a binary simultaneous linear equation.

S ₁ · W _{a + 1} · W _b = −10 (Equation 2) S ₂ · W _{a + 1} · W _b = 10 (Equation 3) The value on the left side is , The input of Case 1'and Case 2'to the output layer, and the value on the right side is the output calculated in Table 1 is practically 0.
Alternatively, the input value is such that a value that can be regarded as 1 is obtained. In the case of (-10, 1 / (1 + exp (-(-1
0))) ≈ 0, and if 10 then 1 / (1 + exp
(-(10))) ≈1. ) When this simultaneous equation is solved, S ₁ −S ₂ ≠ 0, and W _a = −20 / (S ₁ −S ₂ ) ... (Equation 4) W _b = 10 + 20S ₂ / (S ₁ − S ₂ ) ... (Equation 5) Since W _a has a negative value and W _b has a positive value, the following inequality holds if S ′ is smaller than S ₂ .

S ′ · W _{a + 1} · W _b > 10 (Equation 6) Therefore, the output of S ₃ or less in FIG. 3 is closer to 1 than that of S ₂ and practically 1 A value that can be regarded as It can be seen that a set of simultaneous equations such as (Equation 2) and (Equation 3) corresponds to one change of the teacher data.

Next, consider the case where the teacher data starts from 0 and then returns to 0 again through 1 as shown by the broken line 50 in FIG.
This is the case where the teacher data changes twice. The polygonal line 51 and the polygonal line 52 can be generated almost in the same manner as in the case of FIG. Only when both of the broken line 51 and the broken line 52 are 1, the output needs to be 1. Therefore, it is understood that both of them should be connected to the AND circuit in the end. The output of the AND circuit becomes 1 only when the input from both is 1 and the polygonal line 53 is obtained, which coincides with the polygonal line 50.

This neural network is shown in FIG. In this case, the coupling coefficients of the input layer and the intermediate layer are obtained by solving twice the simultaneous equations similar to (Equation 2) and (Equation 3) immediately before and after the change of the teacher data, respectively. In this case, the case where the teacher data changes from 0 to 1 and the case where the teacher data changes from 1 to 0 after that will also be considered.

The neuron hatched at the bottom of the intermediate layer is for threshold correction, and if the coupling coefficient between the input layer and the intermediate layer is designated as shown in FIG. It becomes 1. Further, the coefficient of the coupling (AND circuit) between the intermediate layer and the output layer can be easily obtained by the same method, and may be 20, 20, and −30 as shown in FIG. 6, for example. -30 is for changing the threshold value. Figure 6
The display of (OR) and (-10) shown at the same time will be described later.

Next, consider the case where the teacher data changes three times as indicated by the broken line 70 in FIG. First, since the broken line 71 and the broken line 72 can be generated by the same method as described above, these A
ND is taken to generate a broken line 73. Next, if the polygonal line 74 is generated in the same manner as the polygonal line 71 and the like, and the polygonal lines 73 and 74 are connected by an OR circuit, the output becomes 1 when at least one of them is 1, so the polygonal line 75 is obtained. . This corresponds to the polygonal line 70.

This neural network is shown in FIG. Also in this case, the hatched neuron at the bottom of the intermediate layer is for threshold value correction, and its output is always 1. The third output from the top of the first intermediate layer is directly input to the output layer without passing through the AND circuit.

Further, the coupling coefficient of the OR circuit can be easily obtained by the same method, and at least one of the inputs to the output layer is 1.
In this case, as shown in FIG. 7, for example, 20, 20 and −10 may be output so that 1 can be output. -10 is for changing the threshold value. (OR) and (-
10) and (AND) and (-30) of the output layer will be described later.

Table 3 is obtained by continuing the same analysis while increasing the number of changes of the teacher data.

[0033]

[Table 3]

Table 3 shows that the number of changes in the teacher data is from 1 to 7, the general number n ₁ is the number n ₂ of neurons in the first intermediate layer, the number n _{3 of} AND circuits in the second intermediate layer, and The number n _{4 of} OR circuits to be the output layer is shown (however, in the intermediate layer, a threshold value correcting neuron is considered separately). As shown in the table, the number of neurons in the first intermediate layer matches the number of changes n ₁ of the teacher data. However, when the number of changes n ₁ of the teacher data is 1, the neuron of the first intermediate layer is the neuron of the output layer itself, and when the number of changes n ₁ of the teacher data is 2, the second intermediate layer The layer neurons are the output layer neurons. Regarding these, considering the calculation method of the coupling coefficient, etc., rather than expressing that there is no intermediate layer, it is more convenient to think in this way regarding the number 1 shown in brackets in Table 3. As described above, when there are multiple outputs from the output layer, the calculation method described above is repeated. According to this analysis, it has become clear that at most two intermediate layers may be considered.

If the above is described more generally for the case where the number of changes in the teacher data is relatively large, the configuration of the neural network of the present invention is as shown in FIG. When the number of changes of the teacher data is odd, as shown by the dotted line, the one directly input from the first intermediate layer to the output layer and not passing through the second intermediate layer appears. The coupling coefficient of each part is obtained as described above.

Next, for example, as shown in Table 4, a case will be described in which the teacher data corresponding to the maximum input sum S ₁ is 1.

[0037]

[Table 4]

FIG. 9 shows an example in which the teacher data changes once. Although FIG. 9 shows an example in which the teacher data changes between S ₁ and S ₂ , in general, it may change in another place. The neural network in this case does not need an intermediate layer and may be the same as that in FIG. 4, but the coupling coefficient is different. The coupling coefficient is obtained by constructing the simultaneous equations similar to (Equation 2) and (Equation 3), but the sign of the right side is changed so that the output becomes 1,0.

Next, FIG. 10 shows a case where the teacher data changes twice, as shown by the broken line 100. First, the polygonal line 101 and the polygonal line 102 can be generated by the same method as that described above. Therefore, a method of synthesizing the polygonal line 100 by using this is devised. At least one of the broken line 101 and the broken line 102 is 1
At the time of, 1 may be output. After all, both should be connected by the OR circuit. The neural network in this case is almost the same as that in FIG. 6, but the coupling coefficient for threshold value correction is changed from −30 to, for example, −10 so that the output layer functions as an OR circuit rather than an AND circuit. To do.

Next, FIG. 11 shows a case where the teacher data changes three times, as indicated by the broken line 110. Also in this case, the polygonal line 111 and the polygonal line 112 are generated by the same method as described above, and the OR of the polygonal line 111 and the polygonal line 112 is obtained to obtain the polygonal line 113. Next, the polygonal line 114 is generated in the same manner as the polygonal line 111. Finally, if the broken line 113 and the broken line 114 are connected by an AND circuit,
A fold line 115 is obtained. This corresponds to the polygonal line 110.
The neural network in this case is almost the same as that shown in FIG. 8, except that an OR circuit is arranged in the second intermediate layer and the output layer functions as an AND circuit so that the coupling coefficient for each threshold correction is adjusted. To change.

Next, Table 5 is obtained by summarizing the results of analysis by increasing the number of changes of the teacher data.

[0042]

[Table 5]

Table 5 shows that the number of changes in the teacher data is 1 to 7
Up to and including the general number n ₅ , the number n ₆ of neurons in the first intermediate layer, the number n _{7 of} OR circuits that is the number of neurons in the second intermediate layer, and the number n _{8 of} AND circuits as output layers are shown. As in the case of Table 3, regarding the intermediate layer, the neuron for threshold value correction is separately considered, and the numeral 1 displayed in parentheses also serves as the output of the output layer. Comparing Tables 3 and 5 shows that AND and OR are interchanged. Also in this case, the maximum number of intermediate layers may be two.

If the above is described more generally for the case where the number of changes of the teacher data is relatively large, the configuration of the neural network becomes similar to that of FIG. When the number of changes in the teacher data is an odd number, in this case also, as shown by the dotted line, the data directly input from the first intermediate layer to the output layer and not passing through the second intermediate layer appears. However, the second intermediate layer is an OR circuit and the output layer is an AND circuit. The calculation method of the coupling coefficient of each part is almost the same as the above case.

When the output layer has a plurality of outputs, the analysis is repeated for each output according to the procedure described above. In addition, when each output is obtained, if the boundary line of the teacher data change shown in Table 2 or Table 4 is common, a part of the neural network can be shared. The overall configuration may be simple.

Further, in (Equation 4) and (Equation 5), S ₁ and S ₂
When Eq. Is equal, the denominator of these mathematical expressions becomes zero, which is inconvenient. In such a case, the inputs are not simply added, but are multiplied by a number Ki that is not 1 obtained by, for example, a random number, and then added. That is, ΣKiXi is obtained and they are shown in Table 2 and Table 4
Of _{S 1, S 2, S 3} , treated in the same manner as · · · S _n. This way, unless the inputs in multiple cases are exactly the same,
The denominators of (Equation 4) and (Equation 5) almost never become zero. If the denominators of (Equation 4) and (Equation 5) are still zero, the operation of obtaining another random number can be repeated again. Further, as is apparent from the above description, the problem that the denominator of the mathematical expressions such as (Equation 4) and (Equation 5) becomes zero is that S ₁ and S ₂ are equal, and Only when the teacher data corresponding to them differ. S ₁ and S ₂
, But if the teacher data corresponding to them are equal, they are not used in the calculation of the coupling coefficient.
It doesn't matter.

Therefore, in a more general expression, there is no simple ΣXi in Tables 2 and 4, etc., and ΣKiXi is obtained by using the numerical value Ki obtained as a random number or the like, and the calculation proceeds as described above. Good. In this case, the weight for each input is KiWi.

It is assumed that S ₁ ′ and S ₃ ′ are equal and the teacher data corresponding to them are equal. In this case, it is assumed that there is a total sum S ₂ ′ of inputs which is equal to the case where the order of magnitude is between S ₁ ′ and S ₃ ′ and the teacher data is S ₁ ′ and S ₃ ′. In this case, as is apparent from the above calculation method, since there is no change in the teacher data among the three teacher data, S ₂ ′ is not used for calculating the coupling coefficient. Therefore, it can be seen that data such as S ₂ ′ does not exist as diagnostic data or is worth adding. You can remove it to save memory. When the newly added teacher data changes the boundary of the change of the teacher data, it is worth adding.

According to the above-mentioned embodiment of the present invention, the following effects can be obtained.

(1) Iterative learning, which was necessary in the past, is no longer necessary.

(2) Since the number of intermediate layers, the number of neurons required there, and the coupling coefficient of each part can be analytically determined, efficient diagnosis can be performed in a short time.

(3) It has been clarified that the number of intermediate layers may be up to two.

(4) Since the coupling coefficient of each part can be easily obtained analytically, it can be applied to a large-scale one having a lot of input data and output data.

(5) Since the conventional iterative learning is no longer necessary, a more economical computer can be used for recognition and diagnosis.

(6) When input data is to be added in order to improve the accuracy of diagnosis, it can be determined from the input data and the teacher data whether or not it is worth adding, and if it is not worthwhile, the addition is made. Can be stopped and the memory can be used effectively.

Next, another embodiment of the present invention will be described.

In (Equation 2) and (Equation 3), the example in which 0 or 1 is approximately output from the neuron has been described, but by the conversion as shown in FIG. With ε as a positive number close to zero, various calculations are performed in the interval of ε and (1-ε), and at the final output stage, it is also partially performed to return to the number of 0 and 1 again. If this is applied to the right side of (Equation 2) and (Equation 3), S ₁ · W _{a + 1} · W _b = log (ε / (1-ε)) ···, where log is the natural logarithm. ··· (Equation 2 ′) S ₂ · W _{a + 1} · W _b = −log (ε / (1-ε)) ··· (Equation 3 ′) In the method of treating the output of Table 1 with 0 and 1 in practice, an error due to approximation calculation is partially included, but in this embodiment, there is no such error, which is convenient.

Next, still another embodiment of the present invention will be described.
In this embodiment, the input data is first subjected to an input number conversion operation so that the number of cases is equal to the number of input data per case, and then used for the neural network. By performing such a conversion, it becomes possible to easily handle many cases by simultaneous equations, as will be shown later. FIG. 13 is an example in which the number of inputs after conversion of the number of inputs is smaller than the original number. The example of FIG. 13 is applied when the number of inputs per case is larger than the number of cases. In this case, the number of input data is converted so as to be exactly the same as the number of cases by an appropriate calculation.
The appropriate operation is, for example, as shown in FIG. 13, a sum (or an operation in which a difference, a product, or a division is also combined) of a plurality of input data in the same case is taken and the result is converted. It can be considered as input data.

FIG. 14 is an example in which the input number conversion calculation is performed by the neural network itself. By selecting the connection between the input layer and the intermediate layer as shown in the figure, the total number of outputs from the intermediate layer is calculated as the original value. The number of cases can be reduced to match the number of cases.

Further, as a method of increasing the number of converted inputs rather than the number of original input data, as shown in FIG. 15, an appropriate numerical value is calculated from the original input by using, for example, an exponential function or a sine function. Calculate and use.

FIG. 16 shows an example in which the input after the calculation for increasing the number of inputs is applied to the neural network and four cases are handled. Exclusive OR (Exclusive OR (also abbreviated as XOR)) using FIG. 15 and FIG.
An example applied to the operation called is shown in more detail.

In the XOR operation, as shown in Table 6, there are four possible cases for two inputs X ₁ and X ₂ .

[0063]

[Table 6]

Therefore, the input number conversion operation is performed so that the number of cases and the number of inputs are equal, and as shown in the same table, there are inputs of y ₁ , y ₂ , y ₃ and y _4. I reckon. Here, y ₁ and y ₂ are inputs X ₁ and X ₂ , respectively, and y ₃ and y ₄ are calculated by the following equations as exponential functions using X ₁ and X ₂ , respectively.

Y ₃ = exp (− (X ₁ + X ₂ )) ··· (Equation 6) y ₄ = exp (−0.5 (X ₁ + X ₂ )) ··· (Equation 7) For this input, as shown in Table 6, 0, 1, 1 and 0
Consider to output. Considering the neural network in FIG. 16, the following simultaneous equations are obtained for each case.

Here, the numerical values on the right side are the calculation formulas for the outputs of Table 1, and -10 and 10 were selected from the viewpoint of inputs that can approximately output 0 or 1.

1.000000 · W ₁ + 1.00000 · W ₂ ＋ 0.135335 · W ₃ ＋ 0.367879 · W ₄ = −10
・ ・ (Equation 8) 1.000000 ・ W ₁ ＋0.000000 ・ W ₂ ＋0.367879 ・ W ₃ ＋0.606531 ・ W ₄ = 10 ・ ・ (Equation 9) 0.000000 ・ W ₁ +1.00000 ・ W ₂ ＋0.367879 ・W ₃ ＋0.606531 ・ W ₄ ＝ 10 ・ (Equation 10) 0.000000 ・ W ₁ ＋0.000000 ・ W ₂ ＋1.000000 ・ W ₃ ＋1.000000 ・ W ₄ ＝ -10 ・ (Equation 11) If this is solved, The following values are obtained as the coupling coefficient.

W ₁ = −21.426952 (Equation 12) W ₂ = −21.426952 (Equation 13) W ₃ = −157.100139 (Equation 14) ) W ₄ = + 147.100139 (Equation 15) When the left side of each equation is calculated by substituting these values for verification, it matches the right side. Therefore, according to Table 1, FIG.
The output of 6 is approximately 0, 1, 1 and 0, which matches the output of XOR shown in Table 6.

As described above, in the method of performing the input number conversion operation, the number of input data per case at least after conversion can be made equal to the number of cases in any case. In combination with simultaneous linear equations, there is an effect that recognition and diagnosis can be easily performed.

Next, the same problem is solved in Tables 1 to 5, FIGS.
Solving with the general solution method described using (1), when arranged in descending order of the sum of the two inputs,
It becomes 1, 1 and 0.

(2) The teacher data corresponding to each of them is 0, 1, 1 and 0. (It starts from 0.) (3) The number of changes of teacher data is the following two times (0
→ 1, 1 → 0).

(4) Therefore, according to the construction method of the neural network, from Table 3, the number of neurons in the first intermediate layer is two except for the threshold correction, and an AND circuit for connecting them as neurons in the second intermediate layer. Is one. A
The output from the ND is the final output as it is. OR
No circuit is needed.

(5) The coupling coefficient of each part is, for example, as shown in FIG.
As shown in 7.

As in the embodiment shown in FIG. 1 and the like, in the method of always using the input 1 for the threshold value correction, the total number of inputs is taken and the number of inputs is set to 1, and then the input number conversion operation is performed. Can also be regarded as a special case in which the total sum of inputs and the total sum are divided by themselves and 1 is output as a standardized value.

Another embodiment of the present invention will be described. The present invention can also be applied to recognition and diagnosis that are not called neural networks. That is, if the number of inputs in each case is equal to the number of cases, or if converted so, the right side of the simultaneous equations should be set directly equal to the case number without being input to the next neuron. You can also In this case, although different from the neural network, since the case number can be directly calculated by calculation when the input is determined, there is an effect that it can be easily used for various kinds of recognition and diagnosis.

A further different embodiment of the present invention will be described. In the present embodiment, after the configuration of the neural network such as the number of layers of the intermediate layer and the number of neurons thereof is determined by the above-described method, further considering the condition that some coupling coefficients are equal to each other, if necessary. Then, back propagation learning is repeated as in the conventional case.

According to this method, not only the number of intermediate layers and the number of neurons are clarified, but also the number of coupling coefficients to be learned can be significantly reduced, so that the learning time can be shortened. In particular, if the user already has a program for back propagation learning, the program can be easily modified, the advantages of the present invention can be incorporated, and various conventional functions can be used.

By the various methods described above, the state equivalent to the completion of learning by the conventional iterative method can be efficiently realized. Therefore, if any of the input data used for these calculations is used, a calculated value that is exactly equal to or extremely close to the predetermined teacher data is output. If you handle a large number of cases in advance as described above, you can obtain output that is similar to the case of similar input even for those that have never been input, so it can be used for various recognition and diagnosis. it can. Next, a comparison between the result calculated by the method of the present invention and the result calculated by the conventional back propagation learning rule will be described. The comparison was performed based on the data obtained by measuring the GIS corona noise by a well-known method and performing frequency analysis on the data stored in the flexible disk to read out a typical value.

Table 7 shows the conventional back propagation learning rule.
A neural network as shown in was used. Sample G
For the purpose of discriminating the structure of IS, the number of outputs from the output layer was three. We aim to discriminate up to 8 (= 2 * 2 * 2) types.

[0080]

[Table 7]

Table 8 is designated as three desirable outputs (teaching data) in each case.

[0082]

[Table 8]

Tables 9 and 10 show examples of outputs calculated by the back propagation learning rule in the conventional method.

[0084]

[Table 9]

[0085]

[Table 10]

As a method of counting the number of times of learning, here, the state in which each case is learned once and all the cases are cycled is counted as once. Table 9 shows that the number of learnings is 400 and 8
The number of times of learning is 1200, and Table 10 shows the case of learning 1200 times. The calculated output should ideally match Table 8, but in this case it does not match completely. At least, when expecting 0 as an output, it is difficult to allow a value of 0.5 or more. Similarly, if one expects an output of 1, a number less than 0.5 is unacceptable. In this way, values that are difficult to tolerate are underlined. It can be seen that the number of underlined numbers decreases to 7, 3, and 2 as the number of learning increases to 400, 800, and 1200, and the calculation accuracy increases. The sum of the time required for the calculation and the error in each case at the time when the calculation was terminated is also shown. In this example, 12
It can be seen that the learning of 00 times requires more than 5 hours and 20 minutes, and that the error decreases gradually when the number of times of learning increases to some extent. In this example, when the backpropagation learning rule is used for calculation, the learning count and total error are also calculated by the CRT (Cathode Ray Tub).
Calculation is in progress while displaying in e). According to the display, the total error did not monotonically decrease with respect to the number of times of learning, and it seemed that it had become small to some extent, but suddenly it became large, but the overall tendency gradually decreased. Generally speaking, even in the state of Table 10, it is considered that the calculation accuracy is still insufficient, and further learning is required.

Next, using the same input data, the calculation results obtained by the method of FIG. 1 and FIG. 12 of the present invention are shown in Table 11.
Shown in.

[0088]

[Table 11]

As is clear from this table, the calculation output was completely in agreement with the training data shown in Table 8 in the case of rounding to the fourth decimal place. The time required to calculate the coupling coefficient was about 0.84 seconds. In the method according to the invention,
The calculation time is very short because it is calculated analytically and there is no iterative calculation to converge the numerical values.

The effects of the above-described embodiments of the present invention can be summarized as follows.

(1) The number of intermediate layers of the neural network and the number of neurons thereof can be determined from the input data and the teacher data, and the coupling coefficient of each part can be calculated analytically. Therefore, the conventional iterative learning of back propagation that requires a long time is not required, and there is an effect that the time from data input to recognition and diagnosis can be shortened.

(2) Conventionally, it took some time to cut and try to select the number of intermediate layers and the number of neurons, but that time is no longer necessary. This has the effect that the calculation can proceed efficiently.

(3) A lot of input data and teacher data,
This has the effect of being applicable to large-scale neural networks.

(4) When the input data is added together with the teacher data, it can be judged whether or not it is worth adding, and if it is judged as useless, the addition is canceled to save the memory of the computer. The effect is that you can.

(5) Since iterative learning is not necessary, there is a possibility that even a more economical computer, such as a book type personal computer, can calculate the coupling coefficient between neurons and perform diagnosis.

(6) If the above-described findings obtained by the present invention are used in combination with a conventional back-propagation type neural network that requires iterative learning, the number of intermediate layers and the number of neurons thereof will be clarified. In addition, since the relationship between the coupling coefficients of each part has been clarified, the number of coupling coefficients that actually require learning is very small. It has the effect of being convenient because the functions of the program can be used.

In the above description, the description has been made mainly of software, but it is naturally possible to realize it as hardware having a similar function. The fields to which the present invention can be applied include not only various engineering fields but also biotechnology and medical fields, as well as recognition and diagnosis of various physical, chemical and biological phenomena, agriculture and forestry, education,
It can also be used for recognition and diagnosis in various fields such as economy.

[0098]

According to the present invention, in a system such as a neural network, the coupling coefficient can be accurately calculated,
It can also be easily obtained.

Further, according to the present invention, it is possible to easily determine the appropriate number of intermediate layers of the neural network and the number of neurons thereof.

[Brief description of drawings]

FIG. 1 is a diagram showing a configuration of a neural network which is an embodiment of the present invention.

FIG. 2 is a diagram showing an example of a conventional neural network.

FIG. 3 is a diagram showing a relationship between a total sum of input data for each case and teacher data, and is a diagram showing an example in which the teacher data changes once.

FIG. 4 is a diagram showing an example of the configuration of the neural network of the present invention in the case where there is one change in teacher data.

FIG. 5 is a diagram showing the relationship between the total sum of input data in each case and teacher data, showing an example in which the teacher data changes twice and a method of synthesizing the same.

FIG. 6 is a diagram showing an example of the configuration of the neural network of the present invention when the change in the teacher data is twice.

FIG. 7 is a diagram showing the relationship between the total sum of input data in each case and teacher data, showing an example in which the teacher data changes three times and a method of synthesizing the same.

FIG. 8 is a diagram showing an example of the configuration of the neural network of the present invention when the teacher data changes three times.

FIG. 9 is a diagram showing a relationship between the total sum of input data in each case and teacher data, and is a diagram (No. 2) showing another example in which the teacher data changes once.

FIG. 10 is a diagram showing the relationship between the total sum of input data for each case and teacher data, and is a diagram (No. 2) showing another example in which the teacher data changes twice and its synthesis method.

FIG. 11 is a diagram showing the relationship between the total sum of input data in each case and teacher data, and is a diagram (No. 2) showing another example in which the teacher data changes three times and its synthesis method.

FIG. 12 is a diagram showing an example of conversion between a value during calculation and input / output.

FIG. 13 is a diagram showing an example of calculation for reducing the number of inputs.

FIG. 14 is a diagram showing an example of converting the number of inputs by the neural network itself.

FIG. 15 is a diagram showing an example of calculation for increasing the number of inputs.

FIG. 16 is a diagram showing an example of inputs and outputs after the number of inputs is increased.

FIG. 17 is a diagram showing an example of a neural network that realizes XOR.

[Explanation of symbols]

X ₁ , X ₂ , X ₃ , X ₄ , X ₅ , X _n ... Input, W ₁ , W ₂ ,
W ₃ , W ₄ , W _a , W _b ... Coupling coefficient, U ₁ ... Input to first intermediate layer, V ₁ ... Output from first intermediate layer, S ₁ , S ₂ , S ₃ , S
₄ , S ₅ , S _n ... Input sum of each case, y ₁ , y ₂ , y ₃ ,
y ₄ Input (after input number conversion calculation).

Claims (10)

[Claims] 1. A recognition or diagnosis method using a neural network having an input layer, an intermediate layer, and an output layer, wherein a threshold correction neuron that always outputs 1 is provided in each of the output layers other than the output layer. , The sum of the input data for each case is calculated, and is created for each output of the output layer in the order of the size of each sum of the input data together with the corresponding teacher data. And the number of neurons is sequentially arranged according to the above table as a first intermediate layer, and when the N is an odd number, the second intermediate layer is (N-
1) / 2 neurons are arranged so that two outputs of the first intermediate layer are sequentially input, and each output of the second intermediate layer is converted into a remainder of the output of the first intermediate layer. With one
In the input of the output layer, and when the N is an even number, as the second intermediate layer,
By arranging N / 2 neurons, two outputs of the first intermediate layer are sequentially input, and each output of the second intermediate layer is made an input of the output layer. Recognition or diagnosis characterized by analytically obtaining the coupling coefficient of each part by focusing on the teacher data corresponding to the case where the sum of the data is maximum, the sum of the input data before and after the change of the teacher data, and the teacher data Method. 2. The recognition or diagnosis method according to claim 1, wherein instead of summing the input data of each case, the sum is calculated after multiplying each input by an arbitrary number Ki which is not all equal. A recognition or diagnosis method characterized by the above. 3. The recognition or diagnosis method according to claim 1, wherein when the teacher data corresponding to the case where the total sum of the input data in the table is maximum is 0, the second intermediate layer is A recognition or diagnosis method, wherein a coupling coefficient is selected so that the output layer functions as an OR circuit as an AND circuit. 4. The recognition or diagnosis method according to claim 1 or 2, wherein when the teacher data corresponding to the case where the sum of the input data in the table is maximum is 1, the second intermediate layer is A recognition or diagnosis method characterized in that, as an OR circuit, the output layer selects a coupling coefficient so as to function as an AND circuit. 5. The recognition or diagnosis method according to claim 1, wherein a back propagation iterative learning method is used to calculate a coupling coefficient of a part of the neural network. 6. The number of input data per case is made equal to the number of cases, simultaneous equations are created for each case using a calculation formula of inputs to neurons, and the coupling coefficient is calculated by solving this simultaneous equation. A recognizing or diagnosing method characterized by using the neural network based on the coupling coefficient obtained. 7. The recognition or diagnosis method according to claim 6, wherein a case number of input data is used as a value corresponding to an input to a neuron in the calculation formula, and simultaneous equations are used instead of the neural network. A recognition or diagnosis method characterized in that a case number or the like of input data can be identified by solving. 8. A recognition or diagnosis method using a neural network having at least an input layer and an output layer, wherein a threshold correction neuron that always outputs 1 is provided in each of the output layers other than the output layer. The sum is calculated for the input data for each case, the cases are arranged for each output of the output layer in the order of the size of the sum of the input data, and the number N of changes of the corresponding teacher data is calculated. An equal number of neurons are arranged as the first intermediate layer, and when the N is an odd number, the second intermediate layer is (N-
1) / 2 neurons are arranged, two outputs of the first intermediate layer are input, and each output of the second intermediate layer is converted into the remaining one output of the first intermediate layer. A recognition or diagnosis method characterized in that it is used as an input to the output layer together with the individual. 9. A recognition or diagnosis method using a neural network having at least an input layer and an output layer, wherein a threshold correction neuron that always outputs 1 is provided in each of the output layers except for the output layer. The sum is calculated for the input data for each case, the cases are arranged for each output of the output layer in the order of the size of the sum of the input data, and the number N of changes of the corresponding teacher data is calculated. An equal number of neurons are arranged as the first intermediate layer, and when the N is an even number, N / 2 is set as the second intermediate layer.
Recognition or diagnosis, in which each neuron is arranged, two outputs of the first intermediate layer are input, and each output of the second intermediate layer is used as an input of the output layer. Method. 10. A recognition or diagnosis method using a neural network having at least an input layer and an output layer, wherein a threshold correction neuron that always outputs 1 is provided in each of the output layers other than the output layer. The sum is calculated for the input data for each case, and for each output of the output layer, in the order of the size of each sum of the input data, it is drawn together with the corresponding teacher data, and the sum of the input data in the table is the maximum case. A recognition or diagnosis method characterized in that the coupling coefficient of each part is analytically obtained by focusing on the teacher data corresponding to, the sum of the input data before and after the teacher data changes, and the teacher data.