A Nonlinear System Identification Method for T-S Fuzzy Model Based on Interval Type-2 Fuzzy

Abstract

The present invention discloses a method for identifying a nonlinear system of a T-S fuzzy model based on interval type-2 fuzzy, which relates to the technical field of automatic control. The method for identifying a nonlinear system of a T-S fuzzy model identifies the antecedent parameters of the nonlinear system by using interval type-2 fuzzy C-means clustering, identifies the consequent parameters of the nonlinear system by using the least square algorithm, and inputs the condition parameters of the nonlinear system collected in real time into the T-S fuzzy model for determining the antecedent parameters and the consequent parameters, so as to predict the estimated value of the decision variable of the nonlinear system. The method for identifying a nonlinear system of a T-S fuzzy model in the present invention greatly improves the identification accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of automatic control, and particularly to a method for identifying a nonlinear system of a T-S fuzzy model based on interval type-2 fuzzy. Background Art

[0002] The identification of nonlinear systems has always been a research hotspot in the field of control. Since fuzzy systems have been proven to be able to approximate nonlinear systems with arbitrary accuracy, they are widely used in the identification of nonlinear systems, and the most widely used is the T-S fuzzy model. The identification of the T-S fuzzy model is divided into parameter identification and structure identification, and structure identification plays a major role. In structure identification, the key step is the division of the fuzzy space. The methods for dividing the fuzzy space mainly include: fuzzy grid method, fuzzy clustering algorithm, fuzzy tree method, etc. Fuzzy clustering is simple to implement and has a relatively high identification accuracy, and is widely used. For example, Fuzzy C-Means (FCM) clustering, Gustafson-Kessel (G-K) clustering, subtractive clustering, etc. are widely used in the identification of the T-S fuzzy model.

[0003] Generally, the determination of fuzzy membership function values, also known as type-1 fuzzy sets, does not match the uncertainty of the actual system. By extending the type-1 fuzzy set, a type-2 fuzzy set is obtained, and its membership degree consists of a primary membership degree and a secondary membership degree, which can exactly make up for the deficiencies of the type-1 fuzzy set. Summary of the Invention

[0004] In view of this, the present invention provides a method for identifying a nonlinear system of a T-S fuzzy model based on interval type-2 fuzzy. By using interval type-2 fuzzy C-means clustering to identify the antecedent parameters of the nonlinear system and using the least squares algorithm to identify the consequent parameters of the nonlinear system, the identification accuracy of the nonlinear system identification method of the present invention is greatly improved.

[0005] To achieve the above object, the present invention adopts the following technical solutions: A method for identifying a nonlinear system of a T-S fuzzy model based on interval type-2 fuzzy, comprising the following steps:

[0006] Step 1: Collect historical data (x k , y) of the nonlinear system, set the number of clustering centers c of the T-S fuzzy model, and initialize the clustering centers The initial iteration number r = 0, the maximum iteration number I max , where x k is the k-th conditional parameter, and y is the decision variable;

[0007] Step 2: Input the conditional parameters in the historical data into the T-S fuzzy model, obtain the Euclidean distance from the conditional parameters to the clustering centers, and calculate the upper limit and lower limit of the membership degree of each conditional parameter belonging to a certain clustering center;

[0008] Step 3: Calculate the upper limit of the corresponding clustering center according to the upper limit of the membership degree of the conditional parameter, calculate the lower limit of the corresponding clustering center according to the lower limit of the membership degree of the conditional parameter, and take the average value of the upper limit and the lower limit of the corresponding clustering center as the clustering center for the next iteration;

[0009] Step 4: Increment the iteration count by 1, and repeat Steps 2 - 3 until the Euclidean distance between the clustering center for the next iteration and the current clustering center is less than the threshold or the iteration count is greater than the maximum iteration count. Take the clustering center for the next iteration as the antecedent parameter of the T - S fuzzy model;

[0010] Step 5: Calculate the contribution degree of each conditional parameter to the T - S fuzzy model at a certain clustering center through the upper limit and the lower limit of the membership degree corresponding to the clustering center for the next iteration. After normalization and combined with the least - squares algorithm, determine the consequent parameter of the T - S fuzzy model;

[0011] Step 6: Collect the conditional parameters of the nonlinear system in real - time, input them into the T - S fuzzy model with the determined antecedent and consequent parameters, and predict the estimated value of the decision variable of the nonlinear system.

[0012] Furthermore, the Euclidean distance is obtained as follows:

[0013]

[0014] where is the i - th distance center in the r - th iteration, M is the number of each conditional parameter, l is the index of M, x kl is the k - th conditional parameter under the l - th working condition, is the corresponding l - th dimensional value in

[0015] Furthermore, the calculation process of the upper limit of the membership degree of the conditional parameter belonging to a certain clustering center is as follows:

[0016]

[0017] The calculation process of the lower limit of the membership degree of the conditional parameter belonging to a certain clustering center is as follows:

[0018]

[0019] where i is the index of the clustering center, m1 is the first weighting exponent, and m2 is the second weighting exponent.

[0020] Furthermore, the calculation process of the upper limit of the clustering center is as follows:

[0021]

[0022] The lower limit of the center of the clustering The calculation process is as follows:

[0023]

[0024] where N is the number of conditional parameters and m is the parameter characterizing the degree of fuzzification.

[0025] Furthermore, the contribution degree ω of each conditional parameter to the T-S fuzzy model at a certain clustering center ik The calculation process is as follows:

[0026]

[0027] where is the upper limit of the membership degree of the k-th conditional parameter belonging to the i-th clustering center, is the lower limit of the membership degree of the k-th conditional parameter belonging to the i-th clustering center.

[0028] Furthermore, the normalization process of the contribution degree of each conditional parameter to the T-S fuzzy model at a certain clustering center in step 5 is as follows:

[0029]

[0030] where is the normalized value of the contribution degree of the k-th conditional parameter at the i-th clustering center, and ω ik is the contribution degree of the k-th conditional parameter at the i-th clustering center.

[0031] Furthermore, the consequent parameter matrix P * is:

[0032] P * =(X T ×X) -1 ×X T ×Y

[0033] where Y is the matrix composed of decision variables, X is the matrix composed of , x kl is the k-th conditional parameter under the l-th working condition, is the normalized value of the contribution degree of the k-th conditional parameter at the i-th clustering center.

[0034] Compared with the prior art, the present invention has the following beneficial effects: The non-linear system identification method based on the interval type-2 fuzzy T-S fuzzy model of the present invention aims at the problem that it is difficult to establish an accurate mathematical model for non-linear objects. It uses the T-S fuzzy model to fit the non-linear system and can fit the non-linear system with relatively high accuracy. At the same time, due to the defect that the traditional type-1 fuzzy T-S fuzzy model cannot handle the uncertainties of the actual system, the interval type-2 T-S fuzzy model is used to improve the accuracy of clustering and classification. Description of the Drawings

[0035] Figure 1 It is a comparison chart of the predicted output and the actual output curves of the main steam temperature system of a 1000MW thermal power unit using the identification method of the present invention;

[0036] Figure 2 It is a curve graph of the predicted output error of the main steam temperature system of a 1000MW thermal power unit using the identification method of the present invention. Detailed Embodiments

[0037] The technical solution of the present invention will be further explained below with reference to the accompanying drawings.

[0038] The present invention provides a non-linear system identification method based on the interval type-2 fuzzy T-S fuzzy model, including the following steps:

[0039] Step 1: Collect the historical data (x k , y) of the non-linear system, set the number c of clustering centers of the T-S fuzzy model, and initialize the clustering centers The initial iteration number r = 0, the maximum iteration number I max , where x k is the k-th conditional parameter, each conditional parameter contains data under multiple different working conditions, and y is the decision variable; in the present invention, the number of clustering centers is generally set to 2-6, which can basically meet the modeling and control of industrial processes. If the number of clustering centers is too large, the calculation is complex and the identification accuracy will not be significantly improved.

[0040] Step 2: Input the conditional parameters in the historical data into the T-S fuzzy model to obtain the Euclidean distance from the conditional parameters to the clustering centers Calculate the upper limit of the membership degree and the lower limit of the membership degree of each conditional parameter belonging to a certain clustering center, so as to improve the classification accuracy.

[0041] In the present invention, the process of obtaining the Euclidean distance is as follows:

[0042]

[0043] Among them, is the i-th distance center in the r-th iteration, M is the number of each condition parameter, l is the index of M, and x kl is the k-th condition parameter under the l-th working condition, is the corresponding l-th dimensional value in

[0044] The upper limit of the membership degree of the condition parameter belonging to a certain clustering center in the present invention is calculated as follows:

[0045]

[0046] The lower limit of the membership degree of the condition parameter belonging to a certain clustering center in the present invention is calculated as follows:

[0047]

[0048] wherein, i is the index of the clustering center, m1 is the first weighting exponent, and m2 is the second weighting exponent.

[0049] Step 3: Calculate the upper limit of the corresponding clustering center according to the upper limit of the membership degree of the condition parameter, calculate the lower limit of the corresponding clustering center according to the lower limit of the membership degree of the condition parameter, and take the average value of the upper limit and the lower limit of the corresponding clustering center as the clustering center for the next iteration; Since the interval type-2 fuzzy C-means clustering adopts 2 weighting exponents, therefore, each weighting exponent corresponds to a clustering center, determine the upper and lower limits of the clustering center according to the upper and lower limits of the membership degree respectively, and take their average value as the clustering center for the next step of iteration.

[0050] The upper limit of the clustering center in the present invention is calculated as follows:

[0051]

[0052] The lower limit of the center of the clustering in the present invention is calculated as follows:

[0053]

[0054] wherein, N is the number of condition parameters, and m is the parameter characterizing the degree of fuzzification.

[0055] Step 4: Add 1 to the number of iterations, and repeat Steps 2-3 until the Euclidean distance between the clustering center for the next time and the current clustering center is less than the threshold or the number of iterations is greater than the maximum number of iterations, and take the clustering center for the next time as the antecedent parameter of the T-S fuzzy model;

[0056] Step 5: Calculate the contribution degree of each condition parameter to the T-S fuzzy model at a certain clustering center through the upper limit and lower limit of membership degree corresponding to the next clustering center. After normalization and combined with the least squares algorithm, determine the consequent parameters of the T-S fuzzy model. In the present invention, the least squares method is used to find the best function matching of data by minimizing the sum of squares of errors. The least squares method can simply obtain unknown data, and make the sum of squares of errors between the obtained data and the actual data the smallest, and is easy to implement.

[0057] In the present invention, the contribution degree ω of each condition parameter to the T-S fuzzy model at a certain clustering center ik is calculated as follows:

[0058]

[0059] where is the upper limit of membership degree of the k-th condition parameter belonging to the i-th clustering center, is the lower limit of membership degree of the k-th condition parameter belonging to the i-th clustering center.

[0060] The normalization process of the contribution degree of each condition parameter to the T-S fuzzy model at a certain clustering center in the present invention is as follows:

[0061]

[0062] where is the normalized value of the contribution degree of the k-th condition parameter at the i-th clustering center.

[0063] The consequent parameter matrix P * in the present invention is:

[0064] P * =(X T ×X) -1 ×X T ×Y

[0065] where Y is the matrix composed of decision variables, and X is the matrix composed of , that is:

[0066]

[0067] Step 6: Collect the condition parameters of the nonlinear system in real time, input them into the T-S fuzzy model with the antecedent parameters and consequent parameters determined, and predict the estimated value of the decision variable of the nonlinear system.

[0068] Apply the non-linear system identification method of the interval type-2 fuzzy T-S fuzzy model of the present invention to identify the main steam temperature in the main steam temperature system of a 1000MW thermal power unit. The conditional parameters collected in the main steam temperature system of a 1000MW thermal power unit include: coal feeding amount, main feed water amount, and the decision variable is the main steam temperature. Input the conditional parameters into the T-S fuzzy model to identify the antecedent parameters of the main steam temperature system of a 1000MW thermal power unit. Combine the antecedent parameters with the least squares algorithm to identify the consequent parameters of the main steam temperature system of a 1000MW thermal power unit, and use the real-time collected conditional parameters as the input of the T-S fuzzy model for determining the antecedent parameters and consequent parameters, and predict the estimated value of the main steam temperature of the main steam temperature system of a 1000MW thermal power unit, such as Figure 1 is a comparison chart of the predicted output and the actual output curves. It can be seen that the predicted output curve basically coincides with the actual output curve, indicating that the identification accuracy of the identification method of the present invention is high; such as Figure 2 is the predicted output error curve chart of the main steam temperature system of a 000MW thermal power unit using the identification method of the present invention. It can be seen that the absolute value of the error of the estimated value of the main steam temperature is within 10°C, indicating that the accuracy rate of the identification method of the present invention is high.

[0069] The above is only the preferred implementation manner of the present invention. The protection scope of the present invention is not limited to the above implementation manner. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims

1. A method for identifying a nonlinear system of a T-S fuzzy model based on interval type-2 fuzzy, characterized in that, It includes the following steps: Step 1, collect historical data of the non-linear system ( x k , y ), set the number of clustering centers c of the T-S fuzzy model, initialize the clustering centers , the initial number of iterations r = 0, the maximum number of iterations I max , where x k is the k-th conditional parameter, y is the decision variable; Step 2: Input the conditional parameters in the historical data into the T-S fuzzy model, obtain the Euclidean distance from the conditional parameters to the cluster centers, and calculate the upper limit and lower limit of the membership degree of each conditional parameter belonging to a certain cluster center; Step 3: Calculate the upper limit of the corresponding cluster center according to the upper limit of the membership degree of the conditional parameter, calculate the lower limit of the corresponding cluster center according to the lower limit of the membership degree of the conditional parameter, and take the average value of the upper limit and lower limit of the corresponding cluster center as the cluster center for the next iteration; Step 4: Add 1 to the number of iterations, and repeat Steps 2-3 until the Euclidean distance between the cluster center for the next time and the current cluster center is less than the threshold or the number of iterations is greater than the maximum number of iterations, and take the cluster center for the next time as the antecedent parameters of the T-S fuzzy model; Step 5: Calculate the contribution degree of each conditional parameter to the T-S fuzzy model at a certain cluster center through the upper limit and lower limit of the membership degree corresponding to the cluster center for the next time. After normalization, combined with the least squares algorithm, determine the consequent parameters of the T-S fuzzy model; Step 6: Real-time collect the conditional parameters of the nonlinear system, input them into the T-S fuzzy model with the determined antecedent parameters and consequent parameters, and predict the estimated value of the decision variable of the nonlinear system.

2. The method for identifying a nonlinear system based on an interval type-2 fuzzy T-S fuzzy model according to claim 1, characterized in that, The Euclidean distance is obtained as follows: Among them, is the r th distance center under the i th iteration, M is the number of each conditional parameter, l is M 's index, is the l th k-th conditional parameter under the th working condition, is the corresponding l th dimensional value in 3. The method for identifying a nonlinear system based on an interval type-2 fuzzy T-S fuzzy model according to claim 2, characterized in that The upper limit of the membership degree of the said conditional parameter belonging to a certain cluster center The calculation process is as follows: The membership degree lower limit of the said conditional parameter belonging to a certain clustering center The calculation process is as follows: Among them, i is the index of the clustering center, m1 is the first weighting exponent, and m2 is the second weighting exponent.

4. The method for identifying a nonlinear system based on an interval type-2 fuzzy T-S fuzzy model according to claim 3, characterized in that, The upper limit of the clustering center The calculation process is as follows: The lower limit of the center of the clustering The calculation process is as follows: where N is the number of conditional parameters, m is a parameter for characterizing the degree of fuzzification.

5. The method for identifying a nonlinear system based on an interval type-2 fuzzy T-S fuzzy model according to claim 1, characterized in that The contribution degree of each conditional parameter to the T-S fuzzy model at a certain clustering center The calculation process is as follows: Among them, is the upper limit of the membership degree of the k th conditional parameter belonging to the i th cluster center, and k is the lower limit of the membership degree of the i th conditional parameter belonging to the th cluster center.

6. The method for identifying a nonlinear system based on an interval type-2 fuzzy T-S fuzzy model according to claim 1, wherein The normalization process of the contribution degree of each conditional parameter to the T-S fuzzy model at a certain cluster center in Step 5 is as follows: Among them, is the normalized contribution value of the k th conditional parameter to the i th cluster center, and k is the contribution of the i th conditional parameter to the th cluster center.

7. The method for identifying a nonlinear system of the interval type-2 fuzzy-based T-S fuzzy model according to claim 1, wherein Consequent parameter matrix is as follows: Among them, Y is a matrix composed of decision variables, X is a matrix composed of , is the l th condition parameter under the k th working condition, is the normalized contribution value of the k th condition parameter to the i th clustering center.

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