A method for solving PID index by using variant differential evolution-radial basis neural network

Abstract

The application discloses a PID index solving method of a variant differential evolution-radial basis neural network, twice value extraction and mutation operators are introduced in the mutation stage of a mutation differential evolution (MDE) algorithm, so that dominant individuals participate in the competition of the next generation, local optimum is avoided, and the global search capability is improved; in a radial basis neural (RBF) network, an exponential smoothing factor is combined with a conjugate gradient method, and an adaptive step length is adopted to control data fluctuation in an iteration process. The mutation differential evolution (MDE) algorithm obtains a dominant population, the optimized radial basis neural (RBF) network is used to identify system loop information, online adjustment of PID parameters is realized, and through three industrial control models, the effect of the disclosed method is verified by comparing and analyzing a standard PID and RBF-PID control.

Description

Technical Field

[0001] This invention belongs to the field of fast problem solving in artificial intelligence algorithms, specifically an evaluation method for achieving fast convergence of hybrid algorithms to solve problems. Background Technology

[0002] As artificial intelligence algorithms continue to develop, their applications are becoming more and more widespread. However, the shortcomings of traditional PID controllers are obvious: the closed-loop dynamic regulation quality is too sensitive to changes in PID gain; PID directly takes the error as the correction amount for the next moment, which often makes the initial control force too large and causes the system to overshoot. Summary of the Invention

[0003] The purpose of this invention is to solve the technical problems of traditional PID controllers, which are difficult to achieve fast adjustment effectively and have large overshoot and long duration.

[0004] This invention provides a method for solving the PID index of a mutation differential evolution-radial basis neural network, comprising the following steps:

[0005] S1, the specific implementation of the differential evolution algorithm involves using a DE / best / 1 / bin control strategy to update and mutate individuals, generating a perturbation vector from a random integer. Select the smaller value from the two random selections in the generated random array;

[0006] S2, for the first Generation population and its variant intermediates Perform cross-operations between individuals;

[0007] S3. A greedy algorithm is used on the individuals obtained after crossover. If the crossover individual is better, the crossover individual is entered into the next generation; otherwise, the original individual is copied to the next generation.

[0008] S4, Mutation Differential Evolution Algorithm: To avoid the search getting trapped in local optima, a random factor is added to the DE / best / 1 / bin control strategy and a minimum value is generated by comparison, which improves the algorithm's convergence speed, accuracy and global search capability;

[0009] S5, using the conjugate gradient method to target the node centers of hidden layer neurons. Base width Connection weights between hidden layers and output layers The three parameters are adjusted, and the maximum number of iterations (IMAX) and the loop stopping condition are set.

[0010] S6, Radial Basis Interaction Neural Network: Based on the original conjugate gradient descent method, a smoothing factor is introduced in the search direction according to the idea of ​​exponential smoothing prediction algorithm. The two items are superimposed in the search direction. And the weight is less than or equal to 1;

[0011] S7 uses an adaptive control rule to control the learning efficiency of gradient descent, with the gradient between two adjacent iterations... When the signs are consistent, it means that the correction direction is consistent with the expectation, thus improving the learning efficiency of the parameters; otherwise, the learning efficiency is reduced, and the correction result of the previous step is discarded; when the gradient is 0, the current step size is maintained.

[0012] S8, PID controller section: The radial basis function neural network is combined with PID control, and the PID controller adopts an incremental structure.

[0013] Preferably, the mutation differential evolution algorithm obtains an intermediate population through mutation and crossover operations, and then applies it to the competition between offspring and parents to obtain a new generation of population. It continuously searches in the solution space and iterates to the optimal solution, that is, it initializes the population, iterates and updates, and checks the stopping condition to search for the optimal solution of the objective function.

[0014] Preferably, in step S4, the globality and fast convergence of the mutation differential evolution algorithm are analyzed and verified using the CEC2005 test function set.

[0015] Preferably, in S6, for the radial basis neural network portion, when the number of iterations... Smoothing factor Determined by the Polak-Ribiere formula.

[0016] Preferably, in step S8, for the PID controller section, an error square function is introduced as a performance index function; the difference between the system's input and output is used as a correction amount for the neural network weights; and simultaneously, the deviation integral function is used to solve for the PID index of the hybrid algorithm of the differential evolution and radial basis neural network.

[0017] The present invention has the following advantages over the prior art:

[0018] This invention discloses a PID control based on the Mutant Differential Evolution-Radial Basis Function (MDE-RBF) method. In the mutation phase of the MDE algorithm, two rounds of sampling and mutation operators are introduced to obtain dominant individuals to participate in the next generation of competition, avoiding getting trapped in local optima and improving global search capability. In the RBF network, an exponential smoothing factor combined with the conjugate gradient method is used, and an adaptive step size is employed to control data fluctuations during the iteration process. The MDE algorithm obtains the dominant population, and the optimized RBF network identifies system loop information to achieve online adjustment of PID parameters. This solves the problem that the closed-loop dynamic control quality is too sensitive to changes in PID gain. Directly using the error as the correction amount for the next step often results in excessive initial control force and overshoot. This invention offers the advantages of fast and accurate adjustment with short time requirements and high efficiency. Attached Figure Description

[0019] Figure 1 This is a general flowchart of the present invention;

[0020] Figure 2 This invention demonstrates a comparison of the fitness function of the mutation differential evolution algorithm with that of the differential evolution algorithm. Line graph;

[0021] Figure 3 This invention presents the improved RBF-PID_G neural network response diagram.

[0022] Figure 4 This invention demonstrates the use of the MDE-RBF hybrid algorithm to solve PID control. , , Iterative graph;

[0023] Figure 5 This invention uses the optimal , , Time object , and The response diagram. Detailed Implementation

[0024] To enable those skilled in the art to better understand the solution method of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] Please refer to the accompanying drawings. This invention is a method for solving the PID index of a mutation differential evolution-radial basis neural network, comprising the following steps:

[0026] Step one: In the differential evolution algorithm, the DE / best / 1 / bin control strategy is used to update and mutate individuals, generating a random integer perturbation vector. Choose the smaller of the two generated random arrays; that is, the two random arrays are... and ,Right now;

[0027] Formula 1

[0028] Formula 2

[0029] Step two, for the first Generation population and its variant intermediates The expression for performing crossover operations between individuals is as follows;

[0030] Formula 3

[0031] In Formula 3, The crossover probability is [0 1]. for random integers

[0032] Step 3: Apply a greedy algorithm to the individuals obtained after crossover. Crossover individuals are preferred to enter the next generation; otherwise, the original individuals are copied to the next generation. The expression is as follows:

[0033] Formula 4

[0034] Step 4: To avoid the search getting stuck in local optima, a random factor is added to the DE / best / 1 / bin control strategy, and a minimum value is generated by comparison. This improves the algorithm's convergence speed, accuracy, and global search capability. The expression is as follows:

[0035] Formula 5

[0036] Formula 5: Let be a random vector over an interval, with a length equal to the number of variables; It represents the upper and lower bounds of the objective function.

[0037] Step 5: Use the CEC2005 test function to test various indicators of the Mutation Differential Evolution Algorithm, and compare it with the Standard Differential Evolution Algorithm. The results are shown in the table below.

[0038] Formula Six

[0039] Formula 7

[0040] Formula 8

[0041] Formula Nine

[0042] For the standard differential evolution (DE) algorithm and the mutation differential evolution (MDE) algorithm, the initial population NP is set to 50, 80, and 100 respectively, the function is set to 10 dimensions, and 1000, 2000, and 3000 iterations are performed or the termination threshold is less than 1000. The iteration stops, the scaling factor of the test algorithm is set to 0.5, the crossover probability is set to 0.1, each function is solved independently 30 times, and the optimal value is taken as the result and filled into the table. The function was tested, and the results are as follows:

[0043] Step 5: Use the conjugate gradient method to analyze the node centers of the hidden layer neurons. Base width Connection weights between hidden layers and output layers The three parameters are adjusted, and the maximum number of iterations (IMAX) and the loop stopping condition are set.

[0044] Step six: Based on the original conjugate gradient descent method, a smoothing factor is introduced in the search direction according to the idea of ​​exponential smoothing prediction algorithm. The two items are superimposed in the search direction. And the weights are less than or equal to 1. The new gradient search calculation direction is as follows:

[0045] ( Formula 10

[0046] In Equation 10: when the number of iterations... Smoothing factor Determined by the Polak-Ribiere formula:

[0047] ( Formula Eleven

[0048] Step 7: Use adaptive control rules to control the learning efficiency of gradient descent, increasing the parameters in... Learning efficiency per session:

[0049] ( Formula Twelve

[0050] In formula twelve: To correct the multiplier, When the gradients of two adjacent iterations in the formula are... When the signs are consistent, it means that the correction direction is consistent with the expectation, thus improving the learning efficiency of the parameters; otherwise, the learning efficiency is reduced and the correction result of the previous step is discarded; when the gradient is 0, the current step size is maintained.

[0051] Step 8: The radial basis function neural network is combined with PID control, and the corresponding PID controller adopts an incremental structure;

[0052] Step nine: Introduce the MDE-RBF-PID control into a commonly used industrial control model for testing, and optimize the parameters of the control model.

[0053] Formula Thirteen

[0054] Formula Fourteen

[0055] Formula 15

[0056] Step nine involves validating the proposed hybrid algorithm by introducing a deviation function for testing. System parameter optimization employs the MDE-RBF algorithm, using the objective function to solve for the optimal PID control. , and The objective function adopts the following deviation integral function. The range of values ​​for the optimized control parameters is based on the ZN method, with a lower bound of 1E-10 and an upper bound of twice the result of the ZN method.

[0057] Formula Sixteen

[0058] Formula 17

[0059] Formula 18

[0060] In the above formula: This is the simulation end time. The deviation of the system response is equal to the unit step signal input at time 0. With control object output The difference. The algorithm independently optimizes each of the following metrics 10 times, and takes the optimal value as the final result. to The optimization results are shown in the table below:

[0061]

[0062]

[0063]

[0064] The parameters in the table represent the rise time of the simulation system. Adjusting time (Measured at 2%), overshoot steady-state error The table shows that when one metric is optimal, the others are not optimal, but this reflects the effectiveness of the proposed hybrid algorithm in solving PID metrics.

[0065] Of course, the above description is not intended to limit the invention, nor is the invention limited to the examples given above. Any changes, modifications, additions, or substitutions made by those skilled in the art within the scope of the invention should also fall within the protection scope of the invention. The parts of this invention not described in detail are well-known to those skilled in the art.

Claims

1. A method for solving the PID index of a mutation differential evolution-radial basis neural network, characterized in that, Includes the following steps: S1, the specific implementation of the differential evolution algorithm involves using a DE / best / 1 / bin control strategy to update and mutate individuals, generating a perturbation vector from a random integer. Select the smaller value from the two random selections in the generated random array; S2, for the first Generation population and its variant intermediates Perform cross-operations between individuals; S3. A greedy algorithm is used on the individuals obtained after crossover. If the crossover individual is better, the crossover individual is entered into the next generation; otherwise, the original individual is copied to the next generation. S4, Mutation Differential Evolution Algorithm: To avoid the search getting trapped in local optima, a random factor is added to the DE / best / 1 / bin control strategy and a minimum value is generated by comparison, which improves the algorithm's convergence speed, accuracy and global search capability; S5, using the conjugate gradient method to target the node centers of hidden layer neurons. Base width Connection weights between hidden layers and output layers The three parameters are adjusted, and the maximum number of iterations (IMAX) and the loop stopping condition are set. S6, Radial Basis Function Neural Network (RBF) part: Based on the original conjugate gradient descent method, a smoothing factor is introduced in the search direction according to the idea of ​​exponential smoothing prediction algorithm. The two items are superimposed in the search direction. And the weight is less than or equal to 1; when the number of iterations Smoothing factor Determined by the Polak-Ribiere formula; S7 uses an adaptive control rule to control the learning efficiency of gradient descent, with the gradient between two adjacent iterations... When the signs are consistent, it means that the correction direction is consistent with the expectation, thus improving the learning efficiency of the parameters; Conversely, this reduces learning efficiency and discards the results of the previous correction step. When the gradient is 0, maintain the current step size; S8, PID controller section: The radial basis function neural network is combined with PID control, and the PID controller adopts an incremental structure; the error square function is introduced as the performance index function; the difference between the system input and output is used as the correction amount of the neural network weights; at the same time, the deviation integral function is used to solve the PID index of the hybrid algorithm of the differential evolution and radial basis function neural network.

2. The method for solving the PID index of a mutation differential evolution-radial basis neural network according to claim 1, characterized in that, The mutation differential evolution algorithm obtains an intermediate population through mutation and crossover operations, and then applies it to the competition between offspring and parents to obtain a new generation of population. It continuously searches in the solution space and iterates to the optimal solution, that is, it initializes the population, iterates and updates, and checks the stopping condition to search for the optimal solution of the objective function.

3. The method for solving the PID index of a mutation differential evolution-radial basis neural network according to claim 1, characterized in that, In S4, the globality and fast convergence of the mutation differential evolution algorithm are analyzed and verified using the CEC2005 test function set.

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