Resistance thermal drift prediction method based on particle swarm optimization support vector machine

Abstract

The invention relates to a low-voltage high-power three-phase asynchronous induction motor control method, in particular to a resistance thermal drift prediction method based on a particle swarm optimization support vector machine. According to the method, temperature and resistance thermal drift data of different phases of the 18kW induction motor are collected and analyzed, and a particle swarm optimization (PSO) is established to optimize a support vector machine (SVM) model, so that resistance thermal drift of the motor caused by heat energy generation is predicted. Experimental verification shows that the method can effectively predict the thermal drift of the resistance of the induction motor and improve the prediction precision, so that the stability and precision of motor control can be improved, and an effective reference model and a solution are provided for solving the problem of thermal drift of the stator resistance of the motor.

Description

Technical Field:

[0001] The present invention relates to a control method for a low-voltage high-power three-phase asynchronous induction motor, and particularly to a prediction method for resistance thermal drift based on particle swarm optimization support vector machine. Background Art:

[0002] In order to conserve natural resources and promote a future society with net-zero carbon emissions, higher requirements have been put forward for servo motor drive technology. The pursuit of greater power density, torque density, and speed in motor design has led to an increase in the loss density of the motor and the complication of motor thermal management. As the temperature of the motor increases, the stator resistance value changes, reducing the estimation accuracy of the stator flux, and thus causing significant fluctuations in the electromagnetic torque, which will significantly affect the performance of the control system.

[0003] In order to improve the accuracy of motor control, it is necessary to adjust the thermal drift of the motor resistance. Currently, methods for reducing the thermal drift of motor resistance include thermal error prevention and temperature control. However, these methods require changing the motor structure or additionally installing new devices to suppress thermal errors, and there are problems with cost control and installation layout. Compared with the above methods, the thermal error compensation method has obvious advantages. The thermal error compensation method can suppress the influence of motor resistance thermal error on control without changing the hardware structure, and the prediction of resistance thermal error is the basis of this method.

[0004] Currently, certain progress has been made in the research on error and thermal drift prediction using machine learning algorithms. However, the research on specifically predicting the thermal drift of motor resistance using regression models is relatively limited, and the accuracy and flexibility of the prediction algorithm models used in machine learning algorithms directly affect the accuracy of the prediction results of motor resistance thermal drift. Summary of the Invention:

[0005] In view of the above problems, the present invention proposes a prediction method for resistance thermal drift based on particle swarm optimization support vector machine, which uses support vector machine as the basic model for predicting the thermal drift of motor resistance, and uses particle swarm optimization (PSO) as the parallel algorithm of the model, overcoming the problem that the support vector machine cannot find the optimal kernel function and penalty factor.

[0006] To achieve the above object, the present invention includes the following steps:

[0007] Step 1: Build an experimental platform;

[0008] Step 2: Construct a support vector machine prediction model;

[0009] Step 3: Set particle swarm optimization parameters based on the support vector machine prediction model;

[0010] Step 4: PSO_SVM thermal drift modeling;

[0011] Step 5: Evaluate the prediction capabilities of the PSO_SVM model and the SVM model.

[0012] Preferably, step 1 is specifically as follows:

[0013] The experimental test uses a KTY84 / 150 temperature sensor to determine the heat of the motor stator coil. The device for measuring temperature is connected to the driver, and the driver is connected to the upper computer, i.e., the data acquisition system. The upper computer receives and displays the real-time temperature data of the motor stator resistance fed back by the temperature sensor. A milliohm meter is used to test the stator resistance between two phases of the motor (i.e., UV, VW, and UW), and three sets of thermal drift data corresponding to the currently displayed stator temperature are formed.

[0014] Preferably, step 2 is specifically as follows:

[0015] (1) Set the training set. The formula for the training set Q can be expressed as:

[0016] Q = {(t1, d1), (t2, d2), …, (t n , d n )} (1)

[0017] In the formula, t i ∈T = R n , d i ∈D = {1, -1} (i = 1, 2, …, n); where t i represents the feature vector of the i-th sample, R n represents the n-dimensional real number space, d i represents the label of t i , n represents the number of samples in the training set, T represents the feature space, and D represents the label set.

[0018] (2) First, determine the kernel function G(t i , t j ) and the optimal penalty factor parameter C. The kernel function G(t i , t j ) is used to calculate the inner product of samples in the high-dimensional space, and the optimal penalty factor parameter C controls the tolerance of the model to misclassifications; then, establish an optimization problem, that is, solve the minimum value a * of formula (2), where

[0019]

[0020] The constraint conditions are as follows:

[0021]

[0022] In the formula, ai Denote the Lagrange multipliers corresponding to each sample. This is a problem of optimizing a quadratic function under inequality constraints, which has a unique solution, and only a part of the \(a\) in the solution i is non - zero. These non - zero \(a\)'s i corresponding samples are the support vectors.

[0023] (3) Select the positive components of the minimum \(a\) * within the range of \(0\lt a\) i * \(\lt C\), and calculate the threshold \(b\) using Equation (4) * .

[0024]

[0025] (4) Use the obtained \(a\) * and \(b\) * to construct the decision function, which can be expressed as:

[0026]

[0027] In the present invention, the kernel function of the decision function adopts the radial basis kernel function \(G(t,t i ) and its formula is expressed as:

[0028] G(t,t i ) = exp(-γ||t - t i || 2 ), γ > 0 (6)

[0029] Where: sgn represents the sign function, which returns the sign (positive, negative or zero) of a number; the radial basis kernel function \(G(t,t i ) is used to calculate the similarity between input data points. γ is a parameter in the radial basis kernel function, which controls the width of the function and thus affects the smoothness of the decision boundary. \(t\) is the newly input sample.

[0030] (5) Build a support vector machine model based on the decision function.

[0031] Preferably, the specific steps of step 3 are as follows:

[0032] (1) Establish a group of particles, each particle representing a parameter combination (penalty factor \(c\) and kernel function \(g\)) of the SVM, and assign a random position and velocity to each particle.

[0033] (2) Calculate the fitness value of each particle.

[0034] (3) Compare the current position of each particle with its best position in history. If the current position is superior, update its historical best position. If it is not superior, adjust the position and velocity of the particle according to formulas (7) and (8).

[0035]

[0036] Where m = 1, 2, …, n, where n is the total number of particles in the particle swarm. represents the velocity of particle m at the (k + 1)-th iteration, represents the velocity of particle m at the k-th iteration. c1 and c2 are learning factors, and they are usually equal. rand() is a random number between 0 and 1. and represent the individual historical best position and the global historical best position of particle m at the k-th iteration, respectively. represents the current position of particle m at the (k + 1)-th iteration, represents the current position of particle m at the k-th iteration. v max represents v m 's maximum value, and v max > 0. Impose velocity boundary condition restrictions on the particle. If v m > v max , then execute v m = v max ;

[0037] (4) Repeat steps (2)-(4) until the stopping condition is met.

[0038] Preferably, step 4 specifically is:

[0039] (1) Collect the motor resistance data corresponding to different temperatures of the UV phase, UW phase, and VW phase. Select the resistance data between the UV and UW phases as the training set data, and retrieve and normalize the data.

[0040] (2) Construct a particle swarm optimization model according to the training set data and set the relevant parameters. Through cross-validation, select the value ranges of the penalty factor c and the kernel function g.

[0041] (3) Use the mean square error MSE as the fitness function, as shown in formula (9).

[0042]

[0043] Where m represents the number of training set data samples, d i and are the true resistance value and the predicted resistance value of the PSO_SVM, respectively.

[0044] (4) Use the training set data to train the PSO_SVM model, calculate the fitness function MSE, and save the optimal values of the penalty factor c and the kernel function g, denoted as c_best and g_best.

[0045] (5) Compare the values of c_best and g_best with the current position of the particle. If the fitness function value on the particle information is smaller, then update the values of the penalty factor c and the kernel function g on the particle to the optimal values.

[0046] (6) If the optimal value of the fitness function reaches the required accuracy, or the number of iterations reaches the limit, then go to (7). Otherwise, return to step (5).

[0047] (7) Stop the iteration, and record c_best and g_best respectively as the best penalty factor and the best kernel function.

[0048] (8) Establish a PSO_SVM thermal drift model according to the best penalty factor and the best kernel function in step (7).

[0049] Preferably, step 5 is specifically as follows:

[0050] (1) Use the motor resistance data corresponding to different temperatures of the VW phase collected in step 4 as the test set data, retrieve and normalize the data.

[0051] (2) Use the SVM model constructed in step 2 to predict the resistance of the test set data, and save the resistance prediction value.

[0052] (3) Use the PSO_SVM thermal drift model established in step 4 to predict the resistance of the test set data, and save the resistance prediction value.

[0053] (4) Compare the resistance prediction values and the true resistance values of PSO_SVM and SVM, and then use four indicators, namely the coefficient of determination (R 2 ), the mean absolute error (MAE), the mean square error (MSE), and the RMSE (root mean square error), to evaluate the performance of the two models.

[0054] Through the comparison of the experimental results, it can be obtained that a prediction method for resistance thermal drift based on particle swarm optimization support vector machine can effectively predict the motor resistance thermal drift, verifying the effectiveness of the present invention.

[0055] The beneficial effects of the present invention are:

[0056] 1. The present invention is a prediction method based on support vector machine, which performs well in analyzing and predicting small sample and non-linear data, and effectively solves the problem of small sample size.

[0057] 2. The PSO_SVM model established by the present invention is significantly superior to the SVM model in terms of fitting accuracy and prediction accuracy, has high accuracy and good robustness, and provides a reference model and solution for the problem of thermal drift of the motor stator resistance. Description of the Drawings:

[0058] Figure 1 It is the overall flowchart proposed by the present invention;

[0059] Figure 2 It is the experimental platform built by the present invention;

[0060] Figure 3 It is the data graph of the thermal drift of the motor resistance in Step 1 of the present invention;

[0061] Figure 4 It is the SVM architecture diagram in Step 2 of the present invention;

[0062] Figure 5 It is the PSO_SVM regression prediction flowchart in Step 4 of the present invention;

[0063] Figure 6 It is the prediction result graph of the SVM model in Step 5 of the present invention ((a) Comparison graph of the prediction results of the training set; (b) Comparison graph of the prediction results of the test set);

[0064] Figure 7 It is the prediction result graph of the PSO_SVM model in Step 5 of the present invention ((a) Comparison of the prediction results of the training set; (b) Comparison graph of the prediction results of the test set);

[0065] Figure 8 It is the comparison and evaluation result graph of each index of the SVM model and PSO_SVM in Step 5 of the present invention. Detailed Embodiment:

[0066] The following further details a prediction method for thermal drift of resistance based on particle swarm optimization support vector machine proposed by the present invention in conjunction with the drawings and specific embodiments. According to the following description and the claims, the advantages and features of the present invention will be clearer. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0067] To achieve the above object of the claims, the present invention includes the following steps:

[0068] Step 1: Build an experimental platform;

[0069] Step 2: Construct a support vector machine prediction model;

[0070] Step 3: Set parameters for particle swarm optimization based on the support vector machine prediction model;

[0071] Step 4: Establish PSO_SVM thermal drift modeling;

[0072] Step 5: Evaluate the prediction capabilities of the PSO_SVM model and the SVM model.

[0073] Preferably, step 1 specifically is:

[0074] An experimental test uses a KTY84 / 150 temperature sensor to determine the heat of the motor stator coil. The experimental platform is as Figure 2 shown: The device for measuring temperature is connected to the driver, and the driver is connected to the upper computer, i.e., the data acquisition system; the upper computer receives and displays the real-time temperature data of the motor stator resistance feedback by the temperature sensor; the oscilloscope is used to record the voltage and current data during motor operation. The milliohm meter is used to test the stator resistance between two phases of the motor (i.e., UV, VW, and UW), and form three groups of thermal drift data corresponding to the currently displayed stator temperature, as Figure 3 shown.

[0075] Preferably, step 2 specifically is:

[0076] (1) Set the training set. The formula for the training set Q can be expressed as:

[0077] Q = {(t1, d1), (t2, d2), …, (t n , d n )} (1)

[0078] In the formula, t i ∈T = R n , d i ∈D = {1, -1} (i = 1, 2, …, n); where t i represents the feature vector of the i-th sample, R n represents the n-dimensional real number space, d i represents the label of t i , n represents the number of samples in the training set, T represents the feature space, and D represents the label set.

[0079] (2) First, determine the kernel function G(t i , t j ) and the optimal penalty factor parameter C. The kernel function G(t i , t j ) is used to calculate the inner product of samples in the high-dimensional space, and the optimal penalty factor parameter C controls the tolerance of the model to misclassification; then establish an optimization problem, that is, solve the minimum value a * of formula (2), where

[0080]

[0081] The constraints are as follows:

[0082]

[0083] where a i represents the Lagrange multiplier corresponding to each sample. This is a problem of optimizing a quadratic function under inequality constraints, and there is a unique solution. Only a part of the a i in the solution is non-zero. These non-zero a i corresponding samples are the support vectors.

[0084] (3) Select the positive components of the minimum value of a * within the range of 0 < a i * < C, and use Equation (4) to calculate the threshold b * .

[0085]

[0086] (4) Use the obtained a * and b * to construct a decision function, which can be expressed as:

[0087]

[0088] In the present invention, the kernel function of the decision function adopts a radial basis kernel function G(t, t i ), and its formula is expressed as:

[0089] G(t, t i ) = exp(-γ||t - t i || 2 ), γ > 0 (6)

[0090] where: sgn represents the sign function, which returns the sign (positive, negative, or zero) of a number; the radial basis kernel function G(t, t i ) is used to calculate the similarity between input data points. γ is a parameter in the radial basis kernel function, which controls the width of the function and thus affects the smoothness of the decision boundary. t is the newly input sample.

[0091] (5) Based on the decision function, construct a support vector machine model, and the process is as Figure 4 shown.

[0092] Preferably, step 3 is specifically:

[0093] (1) Each particle represents a parameter combination (penalty factor c and kernel function g) of the SVM, and a random position and velocity are assigned to each particle.

[0094] (2) Calculate the fitness value of each particle.

[0095] (3) Compare the current position of each particle with its historical best position. If the current position is superior, update its historical best position; if the result is not satisfactory, adjust the position and velocity of the particle according to formulas (7) and (8).

[0096]

[0097] In the formula, m = 1, 2, …, n, where n is the total number of particles in the particle swarm; represents the velocity of particle m at the (k + 1)-th iteration, represents the velocity of particle m at the k-th iteration; c1 and c2 are learning factors, and they are usually equal; rand() is a random number between 0 and 1; and respectively represent the individual historical optimal position and the global historical optimal position of particle m at the k-th iteration; represents the current position of particle m at the (k + 1)-th iteration, represents the current position of particle m at the k-th iteration; v max represents m the maximum value of v max and v m > 0. The velocity boundary condition of the particle is restricted. If v max > v m is satisfied, then v max = v

[0098] (4) Repeat steps (2)-(4) until the stopping condition is met. The stopping condition is that the set maximum number of iterations is reached or the optimal value of the fitness function reaches the required accuracy.

[0099] Preferably, step 4 is specifically:

[0100] (1) Use a temperature sensor and a megohmmeter to collect the temperature and the corresponding resistance data of the UV phase, UW phase, and VW phase during the operation of the stator winding of an 18 kW three-phase asynchronous induction motor. The motor resistance data corresponding to different temperatures of the UV phase and UW phase collected are used as training set data, and the data is retrieved and normalized.

[0101] (2) Construct a particle swarm optimization model based on the training set data and set relevant parameters. Through cross-validation, select the value ranges of the penalty factor c and the kernel function g to reduce the risk of overfitting.

[0102] (3) Use the mean square error MSE as the fitness function, as shown in formula (9).

[0103]

[0104] Where m represents the number of training set data samples, and d i and are the true resistance value and the predicted resistance value of PSO_SVM respectively

[0105] (4) Use the training set data to train PSO_SVM, calculate the fitness function MSE and save the optimal values of the penalty factor c and the kernel function g, c_best and g_best.

[0106] (5) Compare the two optimal values c_best and g_best saved in the previous step with the current position of the particle. If the fitness function value on the particle information is smaller, update the values of the penalty factor c and the kernel function g on the particle to the optimal values.

[0107] (6) If the optimal value of the fitness function reaches the stop condition, go to step (7); otherwise, return to step (5).

[0108] (7) Stop the iteration and record c_best and g_best respectively as the best penalty factor and the best kernel function.

[0109] (8) Establish a PSO_SVM thermal drift model according to the best penalty factor and the best kernel function in step (7), and the process is as Figure 5 shown.

[0110] Preferably, step 5 is specifically as follows:

[0111] (1) Use the motor resistance data corresponding to different temperatures of the VW phase collected in step 4 as the test set data, retrieve and normalize the data.

[0112] (2) Use the SVM model constructed in step 2 to predict the resistance of the test set data, and save the predicted resistance value to obtain the Figure 6 prediction result graph of the SVM model as shown.

[0113] (3) Use the PSO_SVM thermal drift model established in step 4 to predict the resistance of the test set data, and save the predicted resistance value to obtain the Figure 7 prediction result graph of the PSO_SVM model as shown.

[0114] (4) Compare the predicted resistance values of PSO_SVM and SVM with the true resistance value measured by collection, and from Figure 6 and Figure 7The prediction error range of the SVM model can be calculated from the data of the medium model prediction curve to be approximately 0 - 1.058, while the prediction error range of the PSO_SVM model is 0 - 0.711. By comparing the prediction error ranges, it can be seen that the prediction result accuracy of the PSO_SVM model is higher. Then, use the four indicators of the coefficient of determination (R 2 ), mean absolute error (MAE), mean square error (MSE), and RMSE (root mean square error) to further evaluate the performance of the two models. From the Figure 8 situation, it can be seen that the MAE values of the models are 0.283 and 0.102 respectively, and the RMSE55 values are 0.321 and 0.183 respectively. The R 2 values are 0.912 and 0.984 respectively. In turn: Through data comparison, the R 2 of the PSO-optimized SVM has increased by 0.072, and the MAE and RMSE have decreased by 0.181 and 0.138 respectively. In summary, the PSO-optimized SVM machine learning algorithm provides a predicted value closer to the actual measured value in the prediction of motor resistance thermal drift, significantly improving the accuracy of the SVM prediction model.

[0115] In summary, the prediction method of resistance thermal drift based on particle swarm optimization support vector machine proposed by the present invention can effectively predict the motor resistance thermal drift, which verifies the effectiveness of the present invention. The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments. Even if various changes are made to the present invention, if these changes fall within the scope of the claims of the present invention and its equivalent technologies, they still fall within the protection scope of the present invention.

Claims

1. A prediction method for the thermal drift of resistors based on particle swarm optimization support vector machine, characterized in that, It includes the following steps: Step 1: Build an experimental platform; Step 2: Construct a support vector machine prediction model; Step 3: Set parameters for particle swarm optimization based on the support vector machine prediction model; Step 4: Conduct PSO_SVM thermal drift modeling; Step 5: Evaluate the prediction capabilities of the PSO_SVM model and the SVM model.

2. The method according to claim 1, wherein , Step 1 includes: In the experimental test, a KTY84 / 150 temperature sensor is used to determine the heat of the motor stator coil. The device for measuring temperature is connected to the driver, and the driver is connected to the upper computer, i.e., the data acquisition system; the upper computer receives and displays the real-time temperature data of the motor stator resistance fed back by the temperature sensor; an oscilloscope is used to record the voltage and current data during motor operation; a milliohm meter is used to test the stator resistance between every two phases of the motor and form three groups of thermal drift data corresponding to the currently displayed stator temperature.

3. The method according to claim 1, wherein , Step 2 includes: Step 2.1: Set the training set. The formula for the training set Q can be expressed as: Q = {(t1, d1), (t2, d2), …, (t n , d n )} (1) where t i ∈T = R n , d i ∈D = {1, -1} (i = 1, 2, …, n); where t i represents the feature vector of the i-th sample, R n represents the n-dimensional real number space, d i represents the label of t i , n represents the number of samples in the training set, T represents the feature space, and D represents the label set; Step 2.2: First, determine the kernel function G(t i , t j ), and the optimal penalty factor parameter C. The kernel function G(t i , t j ) is used to calculate the inner product of samples in the high-dimensional space, while the optimal penalty factor parameter C controls the tolerance of the model to misclassifications. Then, establish an optimization problem, that is, solve for the minimum value a of formula (2) * , where The constraint conditions are as follows: where a i represents the Lagrange multiplier corresponding to each sample. This is a problem of optimizing a quadratic function under inequality constraints, and there is a unique solution. Only a part of a i is non-zero. These non-zero a i corresponding samples are the support vectors; Step 2.3: Select the positive components of the minimum value a * within the range where these components are in 0 < a i * < C, and calculate the threshold b using Equation (4) * ; Step 2.4: Use the obtained a * and b * to construct a decision function, which can be expressed as: The kernel function of the decision function adopts the radial basis kernel function G(t, t i ), and its formula is expressed as: G(t,t i ) = exp(-γ||t - t i || 2 ), γ > 0 (6) In the formula: sgn represents the sign function, which returns the sign of a number, i.e., positive, negative, or zero; the radial basis kernel function G(t, t i ) is used to calculate the similarity between input data points. γ is a parameter in the radial basis kernel function that controls the width of the function and thus affects the smoothness of the decision boundary. t is the newly input sample; Step 2.5: Construct a support vector machine model based on the decision function.

4. The method according to claim 1, wherein , Step 3 includes: Step 3.1: Each particle represents a parameter combination of the SVM, i.e., the penalty factor c and the kernel function g. Assign a random position and velocity to each particle; Step 3.2: Calculate the fitness value of each particle; Step 3.3: Compare the current position of each particle with its historical best position. If the current position is superior, update its historical best position; otherwise, adjust the position and velocity of the particle according to formulas (7) and (8); where \(m = 1, 2, \ldots, n\), and \(n\) is the total number of particles in the particle swarm; represents the velocity of particle \(m\) at the \((k + 1)\)-th iteration, represents the velocity of particle \(m\) at the \(k\)-th iteration; \(c_1\) and \(c_2\) are learning factors, and they are usually equal; \(rand()\) is a random number between 0 and 1; and respectively represent the individual historical best position and the global historical best position of particle \(m\) at the \(k\)-th iteration; represents the current position of particle \(m\) at the \((k + 1)\)-th iteration, represents the current position of particle \(m\) at the \(k\)-th iteration; \(v\) max represents m the maximum value of \(v\), and \(v\) max > 0. Velocity boundary condition restrictions are imposed on the particles. If \(v\) m > \(v\) max , then execute \(v\) m = \(v\) max ; Step 3.4: Repeat steps 3.2 - 3.4 until the stop condition is met. The stop condition is reaching the set maximum number of iterations or the optimal value of the fitness function reaching the required accuracy.

5. The method according to claim 1, characterized in that , Step 4 includes: Step 4.1: Experimentally collect the motor resistance data corresponding to different temperatures of the UV phase, UW phase, and VW phase of an 18kW induction motor. Select the resistance data between the UV and UW phases as the training set data, retrieve and normalize the data; Step 4.2: Construct a particle swarm optimization model based on the training set data and set relevant parameters. Through cross-validation, select the value ranges of the penalty factor c and the kernel function g to reduce the risk of overfitting; Step 4.3: Use the mean square error MSE as the fitness function, as shown in formula (9): where m represents the number of training set data samples, and d i and are the true resistance value and the predicted resistance value of PSO_SVM, respectively; Step 4.4: Train the PSO_SVM model using the training set data, calculate the fitness function, and save the optimal values of the penalty factor c and the kernel function g, denoted as c_best and g_best; Step 4.5: Compare the optimal values c_best and g_best saved in the previous step with the current position of the particle. If the fitness function value on the particle information is smaller, update the values of the penalty factor c and the kernel function g on the particle to the optimal values; Step 4.6: If the optimal value of the fitness function reaches the stop condition, go to step (7); otherwise, return to step 4.5; Step 4.7: Stop the iteration and record c_best and g_best respectively as the best penalty factor and the best kernel function; Step 4.8: Establish a PSO_SVM thermal drift model based on the optimal penalty factor and optimal kernel function in Step 4.

7.

6. The method according to claim 1, wherein , Step 5 includes: Step 5.1: Select the motor resistance data at different temperatures with different VW phases described in claim 4 for the test set data, retrieve and normalize the data; Step 5.2: Use the SVM model constructed in Step 2 to predict the resistance of the test set data and save the predicted resistance values; Step 5.3: Use the PSO_SVM thermal drift model described in Step 4 to predict the resistance of the test set data and save the predicted resistance values; Step 5.4: Compare the resistance prediction values of PSO_SVM and SVM with the true resistance values measured by acquisition, and use the coefficient of determination R 2 , mean absolute error MAE, mean square error MSE, and root mean square error RMSE to evaluate the performance of the two models.

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