TWI439952B - Method for neuro-fuzzy system modeling - Google Patents

Description

Fuzzy neural system construction method

The invention relates to a system construction method, in particular to a fuzzy neural system construction method.

The Neuro-Fuzzy System is a common machine learning system. A fuzzy rule base is defined by a training data, and a set of approximate functions is found for the fuzzy rule base by a function approximation method, so that the approximation function can interpret the limited sampling of the training data, and according to different The input value produces a corresponding output value. When the approximate function of the fuzzy rule base is found, the approximation function can be applied to engineering fields such as automatic control or system judgment, so that the operation mode of the system can be closer to the user's requirements.

Generally, when constructing the fuzzy neurological system, it is mainly divided into two learning parts, namely, structure identification and parameter identification. The architecture identification mainly defines an initial system model for the training data, and defines the system. After the model, the parameter is identified and reused by a learning algorithm to fine-tune the fuzzy-like nervous system. Therefore, for the fuzzy-like nervous system, since the architecture identification can determine the initial model of the system, when the initial model is poorly constructed, the effect of the parameter identification is also affected.

For the part of architecture identification, the conventional knowledge is mostly based on clustering. The training data is divided into several clusters by clustering, wherein each cluster can be represented as a fuzzy rule, and the fuzzy rule rule is composed of a fuzzy rule base, and then the fuzzy rule base constructs an initial neural network. . For the fuzzy rule contained in the fuzzy rule base, the more common one is the TSK type (Takagi-Sugeno-Kang type), wherein the j-th fuzzy now can be defined as follows:

Where x _i : the i- th system input variable, y : system output variable, A _j,i : fuzzy attribution function, c _j,i : coefficient, n : input dimension.

However, when the fuzzy-like neural system is used for architecture identification, for the coefficient c _j,i in the fuzzy rule, c _j,0 can only be obtained first _, and the remaining coefficients are obtained by parameter identification. As a result, in the learning phase of architecture identification, it is easy to produce poor learning effects, resulting in a large gap between the approximation function of the fuzzy neurological system and the original function of the learning material.

The main object of the present invention is to provide a system construction method which can construct a fuzzy-like nervous system closer to the original function.

In order to achieve the foregoing object, the technical means used in the present invention include:

A fuzzy neural system construction method comprises: a main program for defining a fuzzy rule base, wherein a learning data is grouped to define a fuzzy rule base of the learning data, the definition fuzzy rule library main program system comprises: a subroutine (a): from the learning material, reading a set of unprocessed corresponding data, and executing the subroutine (b); subroutine (b): determining whether there is any fuzzy rule in the fuzzy rule base, if If there is no fuzzy rule, the subroutine (c) is executed; if there is at least one fuzzy rule, the subroutine (e) is executed; the subroutine (c): the corresponding data is defined by the function approximation method, and the fuzzy rule is defined, and Executing subroutine (d); subroutine (d): judging whether there is unprocessed corresponding data in the learning material, and if there is no unprocessed corresponding data, the main program of the definition fuzzy rule base is completed, If there is unprocessed corresponding data, execute subroutine (e); subroutine (e): find the corresponding data and one of the fuzzy rules, input attribution value and an output difference value, and determine the input attribution value Outputting the difference value, whether to pass a home threshold value and a difference threshold value respectively, if not, executing the subroutine (c), if yes, grouping the corresponding data into the fuzzy rule having the largest input attribution value And updating the fuzzy rule coefficient, and executing the subroutine (d); and establishing a class-like neural network main program, constructing a fuzzy class neural based on the fuzzy rule base in the main program of the definition fuzzy rule base network.

The fuzzy neural system construction method of the present invention, wherein the subroutine (e) comprises: step (i): respectively calculating an input attribute value of the corresponding data and each of the fuzzy rules by an input attribution formula, and when each input When the attribution value is less than a home threshold, the subroutine (c) is executed. When at least one input attribution value is greater than or equal to the home threshold, a step (ii) is performed; step (ii): an output The difference formula respectively calculates an output difference value of the corresponding data and each of the fuzzy rules, and when each of the output difference values is greater than the difference threshold, the subroutine (c) is executed, when at least one output difference value is less than or equal to When the difference threshold is used, a step (iii) is performed; step (iii): comparing the input data of the corresponding data with each of the fuzzy rules, and grouping the corresponding data into a fuzzy rule having a maximum input attribution value, and Step (iv) is performed; and step (iv): the fuzzy rule coefficient after regrouping is updated, and the subroutine (d) is executed.

The fuzzy neural system construction method of the present invention, wherein the formula of the input attribution value is:

among them ( t ) represents the t-th input vector, m and σ are parameters of the attribution value function G , respectively, representing the mean and standard deviation.

The fuzzy neural system construction method of the present invention, wherein the formula of the output difference is:

Where b ( t ) is ( t ) the desired output corresponding to it. The fuzzy neural system construction method of the present invention, wherein the function approximation method of the subroutine (c) is a recursive singular value decomposition method.

The above and other objects, features and advantages of the present invention will become more <RTIgt;

Referring to FIG. 1, the fuzzy neural system construction method of the present invention comprises a definition fuzzy rule base program S1 and a built-up neural network main program S2, and at least one computer is used to execute the fuzzy type nervous system. The arithmetic processor that constructs the method.

The definition fuzzy rule base main program S1 groups a learning material to define a fuzzy rule base of the learning material. The learning material includes an array corresponding data, and each corresponding data has a corresponding input value and an output value. The corresponding data of the array can be divided into several data clusters by clustering, and each data cluster has a fuzzy rule, and a function approximation method is used to obtain an approximation function of the fuzzy rule, and then the fuzzy representative of each cluster is represented. The rules make up the fuzzy rule base. After the establishment of the fuzzy rule base, the establishment of the neural network main program S2 is performed to determine an initial system model of the fuzzy neural system. As shown in Figure 2, the definition fuzzy rule base main program S1 contains the following subroutines:

The subroutine S11 reads a set of unprocessed corresponding data from the learning material, and executes the subroutine S12. In order to make the explanation of the present invention more detailed, the following is a mathematical equation to explain the operation process. In this embodiment, the corresponding data read by the learning material can be expressed as:

The b(t) of the corresponding data represents the expected output value of the t-th pen, ( t ) represents the t-th pen containing input vectors of n dimensions.

The subroutine S12 determines whether there is any fuzzy rule in the fuzzy rule base. If there is no fuzzy rule, the subroutine S13 is executed; if there is at least one fuzzy rule, the subroutine S15 is executed. In the present embodiment, in the initial state, the fuzzy rule base does not have any fuzzy rules, so after the judgment of the subroutine 12, the subroutine S13 is first executed.

The subroutine S13 defines the fuzzy rule by the function approximation method, and executes the subroutine S14. The function approximation method is not limited herein. Preferably, in this embodiment, a recursive Singular Value Decomposition (RSVD) is used to find the optimal solution of the corresponding data, and a Fuzzy rules. The data corresponding to the t-th pen as in equation (1), and transmitted through the decomposition of singular values obtained recursively article of a j-th fuzzy rule, the fuzzy rule article j can be expressed as:

Wherein, the coefficients such as C _{j , 0} , C _{j , 1 ,} etc. can be obtained by the function approximation method in the subroutine S13.

The subroutine S14 determines whether there is any unprocessed corresponding data in the learning material. If there is no unprocessed corresponding data, it means that the definition fuzzy rule base main program S1 is completed, and the establishment class is executed. The neural network main program S2; if there is the unprocessed corresponding data, the subroutine S11 is executed, and a set of unprocessed corresponding data is read again. In this embodiment, the learning material still has the unprocessed corresponding data, so the subroutine S14 will execute the subroutine S11 again, and after reading another corresponding data, since the fuzzy rule base has at least one Since the rule is fuzzy, the subroutine S15 is executed after the judgment of the subroutine S12.

The subroutine S15 is configured to determine the input attribution value and an output difference value of the corresponding data and each of the fuzzy rules, and determine whether the input attribution value and the output difference value respectively pass a belonging threshold and a difference threshold. If not, the subroutine S13 is executed; if there is a pass, the corresponding data is grouped to the fuzzy rule having the largest input attribution value, the fuzzy rule coefficient is updated, and the subroutine S14 is executed. More specifically, as shown in FIG. 3, the subroutine S15 includes the following steps:

Step S151, the input attribution value G of each corresponding fuzzy rule is calculated by an input attribution formula, and when each of the input attribution values G is less than a home threshold value ρ ^I , the subroutine S13 is executed to execute the subroutine S13. Forming a new cluster, and defining a new fuzzy rule by using a function approximation method; when at least one input attribution value G is greater than or equal to the home threshold value ρ ^I , performing a step S152 to proceed to the next step Judge. More specifically, in this embodiment, a corresponding data is read as described in equation (1), and the input attribution value G is compared with the j-th fuzzy rule (2). The formula of the input attribution value G is as follows Shown as follows:

Where m and σ are the mean and standard deviation parameters of the input attribution function G , respectively. When the corresponding data is the equation (1) ( ( t ), b ( t )), this ( t ) substituting the input attribution formula to obtain an input attribution value G _j ( ( t )). The hometh threshold ρ ^I is not limited herein, and may be set to 0.01 as in the embodiment. When the input attribution value G _j ( And the attribution threshold ρ ^I has the following characteristics:

That is to say, the corresponding data has a large input similarity with the fuzzy rule.

Step S152, respectively, calculating an output difference value D of the corresponding data and each of the fuzzy rules by an output difference formula, and when each of the output difference values D is greater than the difference threshold value ρ ^O , executing subroutine S13 to Forming a new cluster, and defining a new fuzzy rule by using the function approximation method; when at least one output difference value is less than or equal to the difference threshold value ρ ^O , performing a step S153 to perform the next judgment . More specifically, in this embodiment, a corresponding data is read as described in equation (1), and the output difference value is compared with the j-th fuzzy rule (2), and the output difference value d _j ( t ) The formula is as follows:

The difference threshold ρ ^O is not limited herein, and may be set to 0.1 as in the embodiment. And when the output difference value d _j (t) and the attribution threshold ρ ^O have the following characteristics:

d _j (t) ρ ^o (6)

That is to say, the corresponding data has a large output similarity with the fuzzy rule.

Step S153, comparing the corresponding data with the input attribution value G of each of the fuzzy rules, and grouping the corresponding data into the fuzzy rule having the largest input attribution value G , and executing step S154. In the step S153, since the corresponding data has passed the judgment of the step S151 and the step S152, it indicates that the corresponding data has a high degree of similarity with the number fuzzy rule, so the corresponding data can be grouped to have the maximum input at this time. The fuzzy rule of the attribution value is assumed to be the j ^* th strip, and step S154 is performed.

In step S154, the coefficient of the j ^* th fuzzy rule after regrouping is updated, and the subroutine S14 is executed. Since the corresponding data has been grouped into the fuzzy rule, in order for the fuzzy rule to interpret the input and output states of the corresponding data, the average value of the fuzzy rule must be updated. And a standard deviation And then update the coefficient of the fuzzy rule, the formula of the update coefficient is as follows:

among them The number of materials originally included in the j ^* fuzzy rule. In addition, The coefficients can be obtained by a function approximation method. Preferably, as in the present embodiment, a recursive singular value decomposition method is utilized.

After the update, the subroutine S14 is executed to determine whether there is any unprocessed corresponding data in the learning material. If there is no unprocessed corresponding data, it means that the definition fuzzy rule base main program S1 is completed. And enter the establishment of the neural network main program S2.

The main neural network main program S2 is constructed based on the fuzzy rule base in the fuzzy rule base step S1, and a fuzzy neural network is constructed. The fuzzy-like neural architecture is not limited herein. As shown in FIG. 4, it is preferable to have an input layer 1, a fuzzification layer 2, and a regular layer as in this embodiment. Rule layer 3, a normalization layer 4, a Consequent layer 5, and an output layer 6.

The input layer 1 is composed of n nodes corresponding to the dimension n of the learning material, and the corresponding output of the input layer 1 is expressed as follows:

The fuzzification layer 2 is composed of J clusters, each cluster includes n nodes of the input layer, so that there are J×n nodes to form the fuzzification layer, and the corresponding output of the number of nodes of the fuzzification layer 2 As follows:

Where m _ij and σ _ij are respectively defined as the mean and standard deviation of the fuzzy rule, and J nodes represent J rules.

The rule layer 3 is composed of n nodes, and the product of each dimension in each data is also referred to as the starting strength corresponding to the data. The corresponding output of the node of the rule layer 3 is as follows:

The normalization layer 4 receives the activation strength of each fuzzy rule corresponding to the rule layer 3, and performs normalization calculation. The corresponding output of the number of nodes of the normalization layer 4 is as follows:

The splicing layer 5 receives the startup intensity after the normalization layer 4 is normalized, and combines the corresponding data dimensions to calculate an output result corresponding to each rule of each data. The corresponding output of the number of nodes of the connection layer 5 is as follows:

The output layer 6 mainly outputs the output value y corresponding to x . The corresponding output of the number of nodes of the output layer 6 is as follows:

When the establishment of the neural network main program S2 is completed, a fuzzy neural network can be established. The establishment of the conventional fuzzy rules can only obtain a part of the coefficients in the initial stage, and further derive other coefficients in the later stage. In the process of defining the fuzzy rule base step S1 of the present invention, in the process of grouping, that is, continuously optimizing all the coefficients of the fuzzy rule, the fuzzy-like nervous system of the present invention can obtain an approximation closer to the original function. function.

In order to verify the fuzzy neurological system construction method of the present invention, the approximation function is closer to the original function, and the following special type-2 Takagi-Sugeno-Kang fuzzy logic modeling using subtractive clustering (hereinafter referred to as document 1) A neuro-fuzzy system modeling with self-constructing rule generation and hybrid SVD-based learning (hereinafter referred to as Document 2) published by S.-J. Lee et al. is compared with the present invention. The original function of the experiment is as follows:

The learning material has 121 corresponding data, the attribution threshold ρ ^{I is} set to 0.01, and the difference threshold ρ ^{O is} set to 0.1. A performance criterion (root mean square error, RMSE) is used as the performance evaluation method. The performance indicators are as follows:

Where q(t) is the desired output, and y(t) is the actual output. When the difference between the expected output and the actual output is smaller, it means that the approximate function of the architecture identification is closer to the original function. The comparison between the present invention and literature 1 and document 2 is shown in Table 1:

It can be seen from Table 1 that the fuzzy-like nervous system construction method of the present invention has a small error between the approximation function and the original function, and is closer to the original function than the literature 1 and the literature 2.

The fuzzy neural system construction method of the present invention can optimize parameters in the grouping process, and has the effect of making the approximate function of the nervous system closer to the original function.

While the invention has been described in connection with the preferred embodiments described above, it is not intended to limit the scope of the invention. The technical scope of the invention is protected, and therefore the scope of the invention is defined by the scope of the appended claims.

[this invention]

1. . . Input layer

2. . . Fuzzy layer

3. . . Rule layer

4. . . Normalization layer

5. . . Conclusion layer

6. . . Output layer

S1. . . Define the fuzzy rule base main program

S2. . . Establish a neural network main program

Figure 1: The construction of the nervous system of the present invention.

Figure 2: The present invention defines the main procedure steps of the fuzzy rule base.

Figure 3: The present invention defines the main procedure steps of the fuzzy rule base.

Figure 4: The fuzzy neural network architecture of the present invention.

S1. . . Define the fuzzy rule base main program

S2. . . Establish a neural network main program

Claims (5)

A fuzzy neural system construction method comprises: a main program for defining a fuzzy rule base, wherein a learning data is grouped to define a fuzzy rule base of the learning data, the definition fuzzy rule library main program system comprises: a subroutine (a): from the learning material, reading a set of unprocessed corresponding data, and executing the subroutine (b); subroutine (b): determining whether there is any fuzzy rule in the fuzzy rule base, if If there is no fuzzy rule, the subroutine (c) is executed; if there is at least one fuzzy rule, the subroutine (e) is executed; the subroutine (c): the corresponding data is defined by a function approximation method, And executing the subroutine (d); the subroutine (d): determining whether the corresponding data in the learning material is unprocessed, and if there is no unprocessed corresponding data, the main program of the definition fuzzy rule base is completed. If there is unprocessed corresponding data, execute subroutine (e); subroutine (e): find the corresponding data and one of the fuzzy rules, input attribution value and an output difference value, and determine the input Attribution And outputting the difference value, whether to pass a belonging threshold and a difference threshold respectively, if not, executing the subroutine (c), if yes, grouping the corresponding data into the fuzzy with the largest input attribution value Rule, then update the fuzzy rule coefficient, and execute the subroutine (d); and establish a class-like neural network main program, based on the fuzzy rule base in the main program of the definition fuzzy rule base, construct a fuzzy class Neural network. According to the method for constructing a fuzzy nervous system according to claim 1, wherein the subroutine (e) comprises: step (i): respectively calculating an input attribute of the corresponding data and each fuzzy rule by an input attribution formula a value, and when each of the input attribution values is less than a home threshold, the subroutine (c) is executed, and when at least one input attribution value is greater than or equal to the home threshold, a step (ii) is performed; (ii): calculating an output difference value of the corresponding data and each of the fuzzy rules by an output difference formula, and when each of the output difference values is greater than the difference threshold, executing the subroutine (c), when at least When an output difference value is less than or equal to the difference threshold value, a step (iii) is performed; step (iii): comparing the corresponding data with the input attribution value of each of the fuzzy rules, and grouping the corresponding data to have the largest input The fuzzy rule of the attribution value, and performing step (iv); and step (iv): updating the fuzzy rule coefficient after regrouping, and executing the subroutine (d). According to the fuzzy neural system construction method described in claim 2, wherein the formula of the input attribution value is: Where m and σ are the mean and standard deviation of the attribution function G , respectively. According to the fuzzy neural system construction method described in claim 2, wherein the formula of the output difference value is: According to the fuzzy neural system construction method described in claim 1, wherein the function approximation method of the subroutine (c) is a recursive singular value decomposition method.