Parameter optimization method for pot insulator curing process based on NSGA-II and RBF neural network

Abstract

The present invention discloses a method for optimizing parameters during the curing process of a pot-type insulator based on the NSGA-II and RBF neural networks. The method comprises the following steps: establishing a pot-type insulator curing simulation model; obtaining simulation data of the pot-type insulator curing simulation model through simulation software, and randomly dividing the simulation data into a training set and a test set; training the RBF neural network using the training set, inputting the test set into the trained test RBF neural network for testing, and completing the training when the prediction results meet the error requirements; performing multi-objective optimization on the model parameters using the NSGA-II algorithm and the trained RBF neural network to obtain a Pareto front solution set; and calculating and screening the Pareto front solution set using the TOPSIS method to obtain the optimal solution, thereby completing the parameter optimization. The method for optimizing parameters during the curing process of a pot-type insulator based on the NSGA-II and RBF neural networks reduces the residual stress of the pot-type insulator, while also reducing production costs, improving the overall performance of the insulator, and maximizing economic benefits.

Description

Technical Field

[0001] The invention belongs to the technical field of model parameter optimization and relates to a method for optimizing parameters of a pot-type insulator curing process based on NSGA-II and RBF neural network. Background Art

[0002] Pot insulators are essential components of power equipment, widely used in the insulation systems of high-voltage transmission lines and substations. Their primary function is to provide electrical insulation between the conductive parts and the ground, ensuring the safe and reliable operation of the power system. The mechanical properties of insulators directly impact the stability and safety of power equipment. For example, insufficient mechanical strength can lead to equipment failure or even downtime, impacting the normal operation of the power system. Residual stress generated during the curing process of pot insulators can degrade mechanical properties. Therefore, during the design and manufacturing of insulators, it is necessary to optimize the residual stress during the curing process to improve their overall performance. Considering production costs and economic benefits, multi-objective optimization is crucial to balance the minimization of residual stress and the control of production costs.

[0003] Traditional methods for optimizing the curing process of pot insulators typically rely on laboratory experiments. While these experiments can provide direct performance data, they are costly, time-consuming, and unable to systematically explore multiple parameter combinations. Furthermore, while finite element optimization methods can provide more accurate simulation and analysis, they are computationally complex and require significant computing resources.

[0004] In summary, the existing technology has the problems of high cost and complex calculation in the optimization method of the pot insulator curing process. Summary of the Invention

[0005] The purpose of the present invention is to provide a parameter optimization method for a pot-type insulator curing process based on NSGA-II and RBF neural network, which solves the problems of high cost and complex calculation of the pot-type insulator curing process optimization method in the prior art.

[0006] The technical solution adopted by the present invention is a method for optimizing parameters of the pot insulator curing process based on NSGA-II and RBF neural network, comprising the following steps:

[0007] S1. Establish a basin insulator curing simulation model, assign material properties, and set model parameters;

[0008] S2. obtain simulation data of a basin-type insulator curing simulation model through simulation software, and randomly divide the simulation data into a training set and a test set;

[0009] S3. Use the training set to train the RBF neural network, input the test set into the trained test RBF neural network for testing, and complete the training when the prediction result meets the error requirement; if the test result does not meet the error requirement, continue training the RBF neural network;

[0010] S4. Set the initial parameters and optimization target requirements of the NSGA-II algorithm, perform multi-objective optimization on the model parameters using the NSGA-II algorithm and the trained RBF neural network, and obtain the Pareto frontier solution set;

[0011] S5. The optimal solution is obtained by calculating and screening the Pareto front solution set through the TOPSIS method, and the parameter optimization is completed.

[0012] The present invention is also characterized in that:

[0013] S1 includes the following steps:

[0014] S1.1. Establish a pot insulator curing simulation model in the finite element simulation software, assign material properties to the pot insulator curing simulation model, and set boundary conditions;

[0015] S1.2. Set the oven internal temperature and the ratio W of alumina to epoxy resin in the composite material for the pot insulator curing simulation model in the finite element simulation software.

[0016] The basin insulator curing simulation model is two-dimensionally axially symmetrical, with one end being the central metal insert, the other end and the outside of the model being the metal mold, and the inside of the metal mold being the epoxy resin / alumina composite material used to manufacture the basin insulator.

[0017] The internal temperature of the oven of the pot insulator curing simulation model is set by a piecewise function Internal variables simulate their changing process, piecewise function As shown below:

[0018] ,

[0019] in, represents the time of temperature change inside the oven, t1 represents the time of holding the first stage of the temperature inside the oven, T2 represents the time of holding the second stage of the temperature inside the oven, t3 represents the time of holding the second stage of the temperature inside the oven, k d Indicates the cooling rate inside the oven.

[0020] The model parameters include the first stage holding time t1 of the internal temperature of the oven, the second stage holding time T2 of the internal temperature of the oven, the second stage holding time t3 of the internal temperature of the oven, the cooling rate k of the oven d , the ratio W of alumina to epoxy resin in the composite material;

[0021] The first stage of the oven internal temperature holding time t1 value range is 60-180min, the second stage of the oven internal temperature holding temperature T2 value range is 125-135℃, the second stage of the oven internal temperature holding time t2 value range is 120-240min, the oven internal cooling rate k d The value range is 5-15℃ / h, and the ratio W of alumina to epoxy resin in the composite material ranges from 200% to 300%.

[0022] S2 includes the following steps:

[0023] S2.1. Use simulation software to obtain the curing degree and strain changes of the pot insulator curing simulation model. Record the curing residual strain E at the interface between the pot insulator and the central metal insert at the last moment, the final curing degree α, and the maximum value Δα of the difference between the maximum and minimum internal curing degrees during the pot insulator curing process. max ;

[0024] S2.2, the first stage of the oven internal temperature is maintained for time t1, the second stage of the oven internal temperature is maintained at temperature T2, the second stage of the oven internal temperature is maintained for time t2, the oven internal temperature cooling rate k d , the ratio of alumina to epoxy resin in the composite material W, the curing residual strain E, the final curing degree α, and the maximum value Δα of the difference between the maximum and minimum internal curing degrees during the curing process of the pot insulator max A set of simulation data is obtained by combining;

[0025] S2.3, change the first stage holding time t1 of the internal temperature of the oven, the second stage holding time T2 of the internal temperature of the oven, the second stage holding time t2 of the internal temperature of the oven, and the cooling rate k of the oven d , the ratio W of alumina to epoxy resin in the composite material is set, repeating steps S2.1-S2.3 and setting the number of repetitions;

[0026] S2.4. Normalize the simulation data and randomly divide it into training and test sets;

[0027] The calculation formula for normalization is as follows:

[0028] ,

[0029] in, is the normalized simulation data, n is the original simulation data, n min is the minimum value of the original simulation data, n max is the maximum value of the original simulation data.

[0030] S3 includes the following steps:

[0031] S3.1. Set the expansion rate of the RBF neural network and train the RBF neural network using the training set.

[0032] S3.2. Test the RBF neural network using the test set. When the prediction results of the RBF neural network meet the error requirements, the training is completed. If the prediction results of the RBF neural network do not meet the error requirements, repeat the training process.

[0033] The network structure of RBF neural network includes input layer, hidden layer and output layer. The input vector x=[t1,T2,t2,k d ,W], the output vector y=[E,α,Δα max ];

[0034] The error function of the RBF neural network is the root mean square error function. The calculation formula of the root mean square error function is as follows:

[0035] ,

[0036] Among them, RMSE represents the error value of the prediction result, n is the number of training times of the RBF neural network, is the true value in the simulation data, is the predicted value obtained by RBF neural network.

[0037] S4 includes the following steps:

[0038] S4.1. Set the initial parameters and optimization target requirements of the NSGA-II algorithm. The optimization target requirement is that the optimization result satisfies the curing degree α not less than 0.99;

[0039] Initial parameters include the initial population size, number of iterations, crossover probability, and mutation probability;

[0040] S4.2. The model parameters are optimized by multi-objective optimization using the NSGA-II algorithm and the trained RBF neural network to obtain the Pareto frontier solution set.

[0041] The optimization objectives of the multi-objective optimization are the curing residual strain E, the maximum value Δα of the difference between the maximum and minimum internal curing degree during the curing process of the pot insulator, and the max and economic factors Q;

[0042] The calculation formula of economic factor Q is as follows:

[0043] ,

[0044] Where W represents the ratio of alumina to epoxy resin in the composite material, t1 represents the first stage holding time of the internal temperature of the oven, T2 represents the second stage holding time of the internal temperature of the oven, t2 represents the second stage holding time of the internal temperature of the oven, k d Indicates the cooling rate inside the oven.

[0045] S5 includes the following steps:

[0046] S5.1. Set the curing residual strain E and the maximum value Δα of the difference between the maximum and minimum internal curing degree of the pot insulator during the curing process. max and the weight parameter of economic factor Q in the TOPSIS method;

[0047] S5.2. After calculating the Pareto front solution set using the TOPSIS method, the ranking results of the multi-objective optimization results of the pot insulator are obtained. The combination ranked first is taken as the optimal solution, and the parameter optimization is completed.

[0048] The beneficial effects of the present invention are as follows: the optimization method proposed in the present invention combines the non-dominated sorting genetic algorithm-II (NSGA-II) and the radial basis function (RBF) neural network, reduces the computational cost, reduces the residual stress of the pot insulator, and also reduces the production cost, improves the overall performance of the insulator, and maximizes the economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flow chart of a method for optimizing parameters during the curing process of a pot-type insulator based on NSGA-II and RBF neural network according to the present invention;

[0050] Figure 2 This is a schematic diagram of a curing simulation model of a pot-type insulator in the present invention;

[0051] Figure 3 1 is a schematic diagram of simulation results of a basin-type insulator curing simulation model according to an embodiment of the present invention;

[0052] Figure 4 3 is a comparison diagram of the predicted value and the actual value of the curing residual strain in the RBF neural network in an embodiment of the present invention;

[0053] Figure 5 3 is a comparison chart of the predicted value and the actual value of the final curing degree in the RBF neural network in an embodiment of the present invention;

[0054] Figure 6 is a comparison diagram of the predicted value and the true value of the maximum value of the difference between the maximum value and the minimum value of the internal curing degree during the curing process of the pot-type insulator in the RBF neural network in an embodiment of the present invention;

[0055] Figure 7This is a ranking diagram of multi-objective optimization results in an embodiment of the present invention;

[0056] Figure 8 3 is a comparison chart of data before and after multi-objective optimization in an embodiment of the present invention.

[0057] In the figure, 1. Metal mold; 2. Epoxy resin / alumina composite material; 3. Center metal insert. DETAILED DESCRIPTION

[0058] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0059] Parameter optimization method for pot insulator curing process based on NSGA-II and RBF neural network, such as Figure 1 As shown, the following steps are included:

[0060] S1. Establish a basin insulator curing simulation model, assign material properties, and set model parameters;

[0061] S1.1. Establish a pot insulator curing simulation model in the finite element simulation software, assign material properties to the pot insulator curing simulation model, and set boundary conditions;

[0062] S1.2. Set the oven internal temperature and the ratio W of alumina to epoxy resin in the composite material for the pot insulator curing simulation model in the finite element simulation software;

[0063] The internal temperature of the oven of the pot insulator curing simulation model is set by a piecewise function Internal variables simulate their changing process, piecewise function As shown below:

[0064] ,

[0065] in, represents the time of temperature change inside the oven, t1 represents the time of holding the first stage of the temperature inside the oven, T2 represents the time of holding the second stage of the temperature inside the oven, t3 represents the time of holding the second stage of the temperature inside the oven, k d Indicates the cooling rate inside the oven;

[0066] like Figure 2 As shown in FIG, the insulator curing simulation model is two-dimensionally symmetrical, with a central metal insert 3 at one end, a metal mold 1 at the other end and the outside of the model, and an epoxy resin / alumina composite material 2 for manufacturing pot-type insulators inside the metal mold 1; the model parameters include the first stage holding time t1 of the oven internal temperature, the second stage holding time T2 of the oven internal temperature, the second stage holding time t3 of the oven internal temperature, and the cooling rate k inside the oven. d, the ratio of alumina to epoxy resin in the composite material W; the first stage holding time t1 of the oven internal temperature is in the range of 60-180min, the second stage holding temperature T2 of the oven internal temperature is in the range of 125-135℃, the second stage holding time t2 of the oven internal temperature is in the range of 120-240min, and the cooling rate k inside the oven d The value range is 5-15℃ / h, and the ratio W of alumina to epoxy resin in the composite material ranges from 200% to 300%;

[0067] S2. obtain simulation data of a basin-type insulator curing simulation model through simulation software, and randomly divide the simulation data into a training set and a test set;

[0068] S2.1. Use simulation software to obtain the curing degree and strain changes of the basin insulator curing simulation model. Record the curing residual strain E at the interface between the basin insulator and the central metal insert 3 at the last moment, the final curing degree α, and the maximum value Δα of the difference between the maximum and minimum internal curing degrees during the basin insulator curing process. max ;

[0069] S2.2, the first stage of the oven internal temperature is maintained for time t1, the second stage of the oven internal temperature is maintained at temperature T2, the second stage of the oven internal temperature is maintained for time t2, the oven internal temperature cooling rate k d , the ratio of alumina to epoxy resin in the composite material W, the curing residual strain E, the final curing degree α, and the maximum value Δα of the difference between the maximum and minimum internal curing degrees during the curing process of the pot insulator max A set of simulation data is obtained by combining;

[0070] S2.3, change the first stage holding time t1 of the internal temperature of the oven, the second stage holding time T2 of the internal temperature of the oven, the second stage holding time t2 of the internal temperature of the oven, and the cooling rate k of the oven d , the ratio W of alumina to epoxy resin in the composite material is set, repeating steps S2.1-S2.3 and setting the number of repetitions;

[0071] S2.4. Normalize the simulation data and randomly divide it into training and test sets;

[0072] The calculation formula for normalization is as follows:

[0073] ,

[0074] in, is the normalized simulation data, n is the original simulation data, n min is the minimum value of the original simulation data,n max is the maximum value of the original simulation data;

[0075] S3. Use the training set to train the RBF neural network, input the test set into the trained test RBF neural network for testing, and complete the training when the prediction result meets the error requirement; if the test result does not meet the error requirement, continue training the RBF neural network;

[0076] S3.1. Set the expansion rate of the RBF neural network and train the RBF neural network using the training set.

[0077] S3.2. Test the RBF neural network using the test set. When the prediction results of the RBF neural network meet the error requirements, the training is completed. If the prediction results of the RBF neural network do not meet the error requirements, repeat the training process.

[0078] The network structure of RBF neural network includes input layer, hidden layer and output layer. The input vector x=[t1,T2,t2,k d ,W], the output vector y=[E,α,Δα max ];

[0079] The error function of the RBF neural network is the root mean square error (RMSE) function. The calculation formula of the root mean square error function is as follows:

[0080] ,

[0081] Among them, RMSE represents the error value of the prediction result, n is the number of training times of the RBF neural network, is the true value in the simulation data, is the predicted value obtained by RBF neural network;

[0082] S4. Set the initial parameters and optimization target requirements of the NSGA-II algorithm, perform multi-objective optimization on the model parameters using the NSGA-II algorithm and the trained RBF neural network, and obtain the Pareto frontier solution set;

[0083] S4.1. Set the initial parameters and optimization target requirements of the NSGA-II algorithm. The optimization target requirement is that the optimization result satisfies the curing degree α not less than 0.99;

[0084] Initial parameters include the initial population size, number of iterations, crossover probability, and mutation probability;

[0085] S4.2. Multi-objective optimization of model parameters is performed using the NSGA-II algorithm and the trained RBF neural network to obtain the Pareto frontier solution set;

[0086] The optimization objectives of the multi-objective optimization are the curing residual strain E, the maximum value Δα of the difference between the maximum and minimum internal curing degree during the curing process of the pot insulator, and the max and economic factors Q;

[0087] The calculation formula of economic factor Q is as follows:

[0088] ,

[0089] Where W represents the ratio of alumina to epoxy resin in the composite material, t1 represents the first stage holding time of the internal temperature of the oven, T2 represents the second stage holding time of the internal temperature of the oven, t2 represents the second stage holding time of the internal temperature of the oven, k d Indicates the cooling rate inside the oven;

[0090] S5. Set the weight parameters of the TOPSIS method, and use the TOPSIS method to calculate and screen the Pareto frontier solution set to obtain the optimal solution, and the parameter optimization is completed;

[0091] S5.1. Set the curing residual strain E and the maximum value Δα of the difference between the maximum and minimum internal curing degree of the pot insulator during the curing process. max and the weight parameter of economic factor Q in the TOPSIS method;

[0092] S5.2. After calculating the Pareto front solution set using the TOPSIS method, the ranking results of the multi-objective optimization results of the pot insulator are obtained. The combination ranked first is taken as the optimal solution, and the parameter optimization is completed.

[0093] Example 1

[0094] This embodiment proposes a parameter optimization method for the pot insulator curing process based on NSGA-II and RBF neural network, such as Figure 1 As shown, the following steps are included:

[0095] S1. Establish a basin insulator curing simulation model, assign material properties, and set model parameters;

[0096] The curing simulation model of the pot-type insulator is two-dimensionally symmetrical, with a central metal insert 3 at one end, a metal mold 1 at the other end and the outside of the model, and an epoxy resin / alumina composite material 2 for manufacturing pot-type insulators inside the metal mold 1; the model parameters include the first stage holding time t1 of the oven internal temperature, the second stage holding time T2 of the oven internal temperature, the second stage holding time t3 of the oven internal temperature, and the cooling rate k inside the oven. d, the ratio of alumina to epoxy resin in the composite material W; the first stage holding time t1 of the oven internal temperature is 120min, the second stage holding time T2 of the oven internal temperature is 130℃, the second stage holding time t2 of the oven internal temperature is 180min, and the cooling rate k inside the oven d The value is 10℃ / h, and the ratio W of alumina to epoxy resin in the composite material is 250%;

[0097] S1.1. Establish a pot insulator curing simulation model in the finite element simulation software, assign material properties to the pot insulator curing simulation model, and set boundary conditions;

[0098] S1.2. Set the oven internal temperature and the ratio W of alumina to epoxy resin in the composite material for the pot insulator curing simulation model in the finite element simulation software;

[0099] The internal temperature of the oven of the pot insulator curing simulation model is set by a piecewise function Internal variables simulate their changing process, piecewise function As shown below:

[0100] ,

[0101] in, represents the time of temperature change inside the oven, t1 represents the time of holding the first stage of the temperature inside the oven, T2 represents the time of holding the second stage of the temperature inside the oven, t3 represents the time of holding the second stage of the temperature inside the oven, k d Indicates the cooling rate inside the oven;

[0102] S2. obtain simulation data of a basin-type insulator curing simulation model through simulation software, and randomly divide the simulation data into a training set and a test set;

[0103] S3. Use the training set to train the RBF neural network, input the test set into the trained test RBF neural network for testing, and complete the training when the prediction result meets the error requirement; if the test result does not meet the error requirement, continue training the RBF neural network;

[0104] The error function of the RBF neural network is the root mean square error (RMSE) function;

[0105] S4. Set the initial parameters and optimization target requirements of the NSGA-II algorithm, perform multi-objective optimization on the model parameters using the NSGA-II algorithm and the trained RBF neural network, and obtain the Pareto frontier solution set;

[0106] The optimization objectives of the multi-objective optimization are the curing residual strain E, the maximum value Δα of the difference between the maximum and minimum internal curing degree during the curing process of the pot insulator, and the max and economic factors Q;

[0107] S5. The optimal solution is obtained by calculating and screening the Pareto front solution set through the TOPSIS method, and the parameter optimization is completed.

[0108] Example 2

[0109] This embodiment proposes a parameter optimization method for the pot insulator curing process based on NSGA-II and RBF neural network, such as Figure 1 As shown, the following steps are included:

[0110] S1. Establish a basin insulator curing simulation model, assign material properties, and set model parameters;

[0111] The curing simulation model of the pot-type insulator is two-dimensionally symmetrical, with a central metal insert 3 at one end, a metal mold 1 at the other end and the outside of the model, and an epoxy resin / alumina composite material 2 for manufacturing pot-type insulators inside the metal mold 1; the model parameters include the first stage holding time t1 of the oven internal temperature, the second stage holding time T2 of the oven internal temperature, the second stage holding time t3 of the oven internal temperature, and the cooling rate k inside the oven. d , the ratio of alumina to epoxy resin in the composite material W; the first stage holding time t1 of the oven internal temperature is 180min, the second stage holding time T2 of the oven internal temperature is 135℃, the second stage holding time t2 of the oven internal temperature is 240min, and the cooling rate k inside the oven d The value is 15℃ / h, and the ratio W of alumina to epoxy resin in the composite material is 300%;

[0112] S1.1. Establish a pot insulator curing simulation model in the finite element simulation software, assign material properties to the pot insulator curing simulation model, and set boundary conditions;

[0113] S1.2. Set the oven internal temperature and the ratio W of alumina to epoxy resin in the composite material for the pot insulator curing simulation model in the finite element simulation software;

[0114] The internal temperature of the oven of the pot insulator curing simulation model is set by a piecewise function Internal variables simulate their changing process, piecewise function As shown below:

[0115] ,

[0116] in, represents the time of temperature change inside the oven, t1 represents the time of holding the first stage of the temperature inside the oven, T2 represents the time of holding the second stage of the temperature inside the oven, t3 represents the time of holding the second stage of the temperature inside the oven, k d Indicates the cooling rate inside the oven;

[0117] S2. obtain simulation data of a basin-type insulator curing simulation model through simulation software, and randomly divide the simulation data into a training set and a test set;

[0118] S3. Use the training set to train the RBF neural network, input the test set into the trained test RBF neural network for testing, and complete the training when the prediction result meets the error requirement; if the test result does not meet the error requirement, continue training the RBF neural network;

[0119] The error function of the RBF neural network is the root mean square error (RMSE) function;

[0120] S4. Set the initial parameters and optimization target requirements of the NSGA-II algorithm, perform multi-objective optimization on the model parameters using the NSGA-II algorithm and the trained RBF neural network, and obtain the Pareto frontier solution set;

[0121] S5. The optimal solution is obtained by calculating and screening the Pareto front solution set through the TOPSIS method, and the parameter optimization is completed.

[0122] Example 3

[0123] This embodiment proposes a parameter optimization method for the pot insulator curing process based on NSGA-II and RBF neural network, such as Figure 1 As shown, the following steps are included:

[0124] S1. Establish a basin insulator curing simulation model, assign material properties, and set model parameters;

[0125] The curing simulation model of the pot-type insulator is two-dimensionally symmetrical, with a central metal insert 3 at one end, a metal mold 1 at the other end and the outside of the model, and an epoxy resin / alumina composite material 2 for manufacturing pot-type insulators inside the metal mold 1; the model parameters include the first stage holding time t1 of the oven internal temperature, the second stage holding time T2 of the oven internal temperature, the second stage holding time t3 of the oven internal temperature, and the cooling rate k inside the oven. d , the ratio of alumina to epoxy resin in the composite material W; the first stage holding time t1 of the oven internal temperature is 60min, the second stage holding time T2 of the oven internal temperature is 125℃, the second stage holding time t2 of the oven internal temperature is 120min, and the cooling rate k inside the oven dThe value is 5°C / h, and the ratio W of alumina to epoxy resin in the composite material is 200%;

[0126] S1.1. Establish a pot insulator curing simulation model in the finite element simulation software, assign material properties to the pot insulator curing simulation model, and set boundary conditions;

[0127] S1.2. Set the oven internal temperature and the ratio W of alumina to epoxy resin in the composite material for the pot insulator curing simulation model in the finite element simulation software;

[0128] The internal temperature of the oven of the pot insulator curing simulation model is set by a piecewise function Internal variables simulate their changing process, piecewise function As shown below:

[0129] ,

[0130] in, represents the time of temperature change inside the oven, t1 represents the time of holding the first stage of the temperature inside the oven, T2 represents the time of holding the second stage of the temperature inside the oven, t3 represents the time of holding the second stage of the temperature inside the oven, k d Indicates the cooling rate inside the oven;

[0131] S2. obtain simulation data of a basin-type insulator curing simulation model through simulation software, and randomly divide the simulation data into a training set and a test set;

[0132] S2.1. Use simulation software to obtain the curing degree and strain changes of the basin insulator curing simulation model. Record the curing residual strain E at the interface between the basin insulator and the central metal insert 3 at the last moment, the final curing degree α, and the maximum value Δα of the difference between the maximum and minimum internal curing degrees during the basin insulator curing process. max ;

[0133] S2.2, the first stage of the oven internal temperature is maintained for time t1, the second stage of the oven internal temperature is maintained at temperature T2, the second stage of the oven internal temperature is maintained for time t2, the oven internal temperature cooling rate k d , the ratio of alumina to epoxy resin in the composite material W, the curing residual strain E, the final curing degree α, and the maximum value Δα of the difference between the maximum and minimum internal curing degrees during the curing process of the pot insulator max A set of simulation data is obtained by combining;

[0134] S2.3, change the first stage holding time t1 of the internal temperature of the oven, the second stage holding time T2 of the internal temperature of the oven, the second stage holding time t2 of the internal temperature of the oven, and the cooling rate k of the oven d, the ratio W of alumina to epoxy resin in the composite material is set, repeating steps S2.1-S2.3 and setting the number of repetitions;

[0135] S2.4. Normalize the simulation data and randomly divide it into training and test sets;

[0136] S3. Use the training set to train the RBF neural network, input the test set into the trained test RBF neural network for testing, and complete the training when the prediction result meets the error requirement; if the test result does not meet the error requirement, continue training the RBF neural network;

[0137] S4. Set the initial parameters and optimization target requirements of the NSGA-II algorithm, perform multi-objective optimization on the model parameters using the NSGA-II algorithm and the trained RBF neural network, and obtain the Pareto frontier solution set;

[0138] S5. The optimal solution is obtained by calculating and screening the Pareto front solution set through the TOPSIS method, and the parameter optimization is completed;

[0139] S5.1. Set the curing residual strain E and the maximum value Δα of the difference between the maximum and minimum internal curing degree of the pot insulator during the curing process. max and the weight parameter of economic factor Q in the TOPSIS method;

[0140] S5.2. After calculating the Pareto front solution set using the TOPSIS method, the ranking results of the multi-objective optimization results of the pot insulator are obtained. The combination ranked first is taken as the optimal solution, and the parameter optimization is completed.

[0141] Example 4

[0142] This embodiment proposes a parameter optimization method for the pot insulator curing process based on NSGA-II and RBF neural network, such as Figure 1 As shown, the following steps are included:

[0143] S1. Establish a basin insulator curing simulation model, assign material properties, and set model parameters;

[0144] The curing simulation model of the pot-type insulator is two-dimensionally symmetrical, with a central metal insert 3 at one end, a metal mold 1 at the other end and the outside of the model, and an epoxy resin / alumina composite material 2 for manufacturing pot-type insulators inside the metal mold 1; the model parameters include the first stage holding time t1 of the oven internal temperature, the second stage holding time T2 of the oven internal temperature, the second stage holding time t3 of the oven internal temperature, and the cooling rate k inside the oven. d, the ratio of alumina to epoxy resin in the composite material W; the first stage holding time t1 of the oven internal temperature is 60min, the second stage holding time T2 of the oven internal temperature is 130℃, the second stage holding time t2 of the oven internal temperature is 120min, and the cooling rate k inside the oven d The value is 10℃ / h, and the ratio W of alumina to epoxy resin in the composite material is 300%;

[0145] S1.1. Establish a pot insulator curing simulation model in the finite element simulation software, assign material properties to the pot insulator curing simulation model, and set boundary conditions;

[0146] S1.2. Set the oven internal temperature and the ratio W of alumina to epoxy resin in the composite material for the pot insulator curing simulation model in the finite element simulation software;

[0147] The internal temperature of the oven of the pot insulator curing simulation model is set by a piecewise function Internal variables simulate their changing process, piecewise function As shown below:

[0148] ,

[0149] in, represents the time of temperature change inside the oven, t1 represents the time of holding the first stage of the temperature inside the oven, T2 represents the time of holding the second stage of the temperature inside the oven, t3 represents the time of holding the second stage of the temperature inside the oven, k d Indicates the cooling rate inside the oven;

[0150] S2. The simulation data of the basin insulator solidification simulation model is obtained through simulation software. The simulation results are as follows: Figure 3 As shown, the simulation data is randomly divided into training set and test set;

[0151] S2.1. Use simulation software to obtain the curing degree and strain changes of the basin insulator curing simulation model. Record the curing residual strain E at the interface between the basin insulator and the central metal insert 3 at the last moment, the final curing degree α, and the maximum value Δα of the difference between the maximum and minimum internal curing degrees during the basin insulator curing process. max ;

[0152] S2.2, the first stage of the oven internal temperature is maintained for time t1, the second stage of the oven internal temperature is maintained at temperature T2, the second stage of the oven internal temperature is maintained for time t2, the oven internal temperature cooling rate k d , the ratio of alumina to epoxy resin in the composite material W, the curing residual strain E, the final curing degree α, and the maximum value Δα of the difference between the maximum and minimum internal curing degrees during the curing process of the pot insulatormax A set of simulation data is obtained by combining;

[0153] S2.3, change the first stage holding time t1 of the internal temperature of the oven, the second stage holding time T2 of the internal temperature of the oven, the second stage holding time t2 of the internal temperature of the oven, and the cooling rate k of the oven d , the ratio W of alumina to epoxy resin in the composite material is set, repeating steps S2.1-S2.3 and setting the number of repetitions;

[0154] S2.4. Normalize the simulation data and randomly divide it into training and test sets;

[0155] S3. Use the training set to train the RBF neural network, input the test set into the trained test RBF neural network for testing, and complete the training when the prediction result meets the error requirement; if the test result does not meet the error requirement, continue training the RBF neural network;

[0156] like Figure 4 As shown in the figure, it is a comparison diagram between the predicted value and the true value of the curing residual strain in the RBF neural network, as shown in Figure 5 As shown in the figure, the comparison between the predicted value and the true value of the final curing degree in the RBF neural network is as follows: Figure 6 As shown in the figure, the comparison between the predicted value and the true value of the maximum value of the difference between the maximum value and the minimum value of the internal curing degree of the pot insulator in the curing process of the RBF neural network is shown. It can be seen from the figure that the error between the predicted value and the true value is small;

[0157] S3.1. Set the expansion rate of the RBF neural network and train the RBF neural network using the training set.

[0158] S3.2. Test the RBF neural network using the test set. When the prediction results of the RBF neural network meet the error requirements, the training is completed. If the prediction results of the RBF neural network do not meet the error requirements, repeat the training process.

[0159] The network structure of RBF neural network includes input layer, hidden layer and output layer. The input vector x=[t1,T2,t2,k d ,W], the output vector y=[E,α,Δα max ];

[0160] The error function of the RBF neural network is the root mean square error (RMSE) function;

[0161] S4. Set the initial parameters and optimization target requirements of the NSGA-II algorithm, perform multi-objective optimization on the model parameters using the NSGA-II algorithm and the trained RBF neural network, and obtain the Pareto frontier solution set;

[0162] The optimization objectives of the multi-objective optimization are the curing residual strain E, the maximum value Δα of the difference between the maximum and minimum internal curing degree during the curing process of the pot insulator, and the max and economic factors Q;

[0163] S4.1. Set the initial parameters and optimization target requirements of the NSGA-II algorithm. The optimization target requirement is that the optimization result satisfies the curing degree α not less than 0.99;

[0164] Initial parameters include the initial population size, number of iterations, crossover probability, and mutation probability;

[0165] S4.2. Multi-objective optimization of model parameters is performed using the NSGA-II algorithm and the trained RBF neural network to obtain the Pareto frontier solution set;

[0166] S5. The optimal solution is obtained by calculating and screening the Pareto front solution set through the TOPSIS method, and the parameter optimization is completed;

[0167] S5.1. Set the curing residual strain E and the maximum value Δα of the difference between the maximum and minimum internal curing degree of the pot insulator during the curing process. max and the weight parameter of economic factor Q in the TOPSIS method;

[0168] S5.2. The Pareto front solution set is calculated by TOPSIS method and the following is obtained: Figure 7 The ranking results of the multi-objective optimization results of the pot insulator are shown. The combination ranked first is taken as the optimal solution, and the parameter optimization is completed.

[0169] like Figure 8 As shown in the figure, after the model parameters are optimized by the optimization method of the present invention, the maximum value Δα of the difference between the maximum and minimum values of the curing residual strain E and the internal curing degree of the pot insulator during the curing process is max And the improvement ratio of economic factor Q.

[0170] NSGA-II is an effective multi-objective optimization algorithm. RBF neural networks are used to establish fast prediction models, which not only improves optimization efficiency but also reduces computational costs in practical applications. The purpose of introducing RBF neural networks is to enable rapid prediction and evaluation of complex optimization problems at a lower computational cost. Compared with traditional methods, this significantly reduces the demand for computing resources and the optimization cycle, making the optimization process more efficient and enabling rapid application in actual production, thereby improving the economic and practicality of insulator production.

Claims

1. A parameter optimization method for pot insulator curing process based on NSGA-II and RBF neural network, characterized in that: The following steps are involved: S1. Establish a basin insulator curing simulation model, assign material properties, and set model parameters; S1.

1. Establish a pot insulator curing simulation model in the finite element simulation software, assign material properties to the pot insulator curing simulation model, and set boundary conditions; S1.

2. Set the oven internal temperature and the ratio W of alumina to epoxy resin in the composite material for the pot insulator curing simulation model in the finite element simulation software; The internal temperature of the oven of the pot insulator curing simulation model is set by a piecewise function The internal variable simulates its change process, the piecewise function As shown below: in, represents the time of temperature change inside the oven, t1 represents the time of holding the first stage of the temperature inside the oven, T2 represents the time of holding the second stage of the temperature inside the oven, t3 represents the time of holding the second stage of the temperature inside the oven, k d Indicates the cooling rate inside the oven; The model parameters include the first stage holding time t1 of the internal temperature of the oven, the second stage holding time t2 of the internal temperature of the oven, the second stage holding time t3 of the internal temperature of the oven, the cooling rate k d , the ratio W of alumina to epoxy resin in the composite material; The first stage of the oven internal temperature holding time t1 is in the range of 60-180min, the second stage of the oven internal temperature holding temperature T2 is in the range of 125-135℃, the second stage of the oven internal temperature holding time t2 is in the range of 120-240min, and the oven internal cooling rate k d The value range is 5-15°C / h, and the ratio W of aluminum oxide to epoxy resin in the composite material ranges from 200% to 300%; S2. obtain simulation data of a basin-type insulator curing simulation model through simulation software, and randomly divide the simulation data into a training set and a test set; S3. Use the training set to train the RBF neural network, input the test set into the trained RBF neural network for testing, and the training is completed when the prediction result meets the error requirement; if the prediction result does not meet the error requirement, continue to train the RBF neural network; S4. Set the initial parameters and optimization target requirements of the NSGA-II algorithm, perform multi-objective optimization on the model parameters using the NSGA-II algorithm and the trained RBF neural network, and obtain the Pareto frontier solution set; S5. The optimal solution is obtained by calculating and screening the Pareto front solution set through the TOPSIS method, and the parameter optimization is completed.

2. The method for optimizing parameters of pot-type insulator curing process based on NSGA-II and RBF neural network according to claim 1, characterized in that: The basin-type insulator curing simulation model is two-dimensionally axially symmetrical, with one end being a central metal insert (3), the other end and the outside of the model being a metal mold (1), and the inside of the metal mold (1) being an epoxy resin / alumina composite material (2) for manufacturing the basin-type insulator.

3. The method for optimizing parameters of the pot insulator curing process based on NSGA-II and RBF neural network according to claim 2, characterized in that: The S2 comprises the following steps: S2.

1. The curing degree and strain change of the basin insulator curing simulation model are simulated by simulation software, and the curing residual strain E at the interface between the basin insulator and the central metal insert (3) at the last moment, the final curing degree α, and the maximum value Δα of the difference between the maximum and minimum internal curing degrees during the curing process of the basin insulator are recorded. max ; S2.2, the first stage of the oven internal temperature is maintained for time t1, the second stage of the oven internal temperature is maintained at temperature T2, the second stage of the oven internal temperature is maintained for time t2, the oven internal temperature cooling rate k d , the ratio of alumina to epoxy resin in the composite material W, the curing residual strain E, the final curing degree α, and the maximum value Δα of the difference between the maximum and minimum internal curing degrees during the curing process of the pot insulator max A set of simulation data is obtained by combining; S2.3, change the first stage holding time t1 of the internal temperature of the oven, the second stage holding time T2 of the internal temperature of the oven, the second stage holding time t2 of the internal temperature of the oven, and the cooling rate k of the oven d , the ratio W of alumina to epoxy resin in the composite material is set, repeating steps S2.1-S2.3 and setting the number of repetitions; S2.

4. Normalize the simulation data and randomly divide it into training set and test set; The calculation formula for the normalization process is as follows: in, is the normalized simulation data, n is the original simulation data, n min is the minimum value of the original simulation data, n max is the maximum value of the original simulation data.

4. The method for optimizing parameters of the pot insulator curing process based on NSGA-II and RBF neural network according to claim 3, characterized in that: The S3 includes the following steps: S3.

1. Set the expansion rate of the RBF neural network and train the RBF neural network using the training set. S3.

2. Test the RBF neural network using the test set. When the prediction results of the RBF neural network meet the error requirements, the training is completed. If the prediction results of the RBF neural network do not meet the error requirements, repeat the training process. The network structure of the RBF neural network includes an input layer, a hidden layer and an output layer. The input vector x of the input layer is [t1, T2, t2, k d ,W], the output vector y=[E,α,Δα max ]; The error function of the RBF neural network is the root mean square error function, and the calculation formula of the root mean square error function is as follows: ， Among them, RMSE represents the error value of the prediction result, m is the number of training times of the RBF neural network, is the true value in the simulation data, is the predicted value obtained by RBF neural network.

5. The method for optimizing parameters of the pot insulator curing process based on NSGA-II and RBF neural network according to claim 4, characterized in that: The S4 comprises the following steps: S4.

1. Set the initial parameters and optimization target requirements of the NSGA-II algorithm. The optimization target requirement is that the optimization result satisfies the final curing degree α not less than 0.99; The initial parameters include the initialization population size, the number of iterations, the crossover probability and the mutation probability; S4.

2. The model parameters are optimized by multi-objective optimization using the NSGA-II algorithm and the trained RBF neural network to obtain the Pareto frontier solution set.

6. The method for optimizing parameters of the pot insulator curing process based on NSGA-II and RBF neural network according to claim 5, characterized in that: The optimization objectives of the multi-objective optimization are the curing residual strain E, the maximum value Δα of the difference between the maximum and minimum values of the internal curing degree during the curing process of the pot insulator, and the maximum value of the curing residual strain E. max and economic factors Q; The calculation formula of the economic factor Q is as follows: Where W represents the ratio of alumina to epoxy resin in the composite material, t1 represents the first stage holding time of the internal temperature of the oven, T2 represents the second stage holding time of the internal temperature of the oven, t2 represents the second stage holding time of the internal temperature of the oven, k d Indicates the cooling rate inside the oven.

7. The method for optimizing parameters of the pot insulator curing process based on NSGA-II and RBF neural network according to claim 6, characterized in that: The S5 comprises the following steps: S5.

1. Set the curing residual strain E and the maximum value Δα of the difference between the maximum and minimum internal curing degree of the pot insulator during the curing process. max and the weight parameter of economic factor Q in the TOPSIS method; S5.

2. After calculating the Pareto front solution set using the TOPSIS method, the ranking results of the multi-objective optimization results of the pot insulator are obtained. The combination ranked first is taken as the optimal solution, and the parameter optimization is completed.

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