Method for measuring gas volume fraction of gas-liquid two-phase flow

Abstract

The invention relates to a gas-liquid two-phase flow gas volume fraction measurement method, which comprises the following steps of: acquiring local gas content signals at each position through an array optical fiber probe sensor, measuring by using a flow meter to obtain corresponding standard gas volume fractions, and constructing a sample data set; constructing a BP neural network, and optimizing the weight and threshold of the BP neural network by using a particle swarm optimization algorithm to obtain preset T weak predictors; and combining the T weak predictors according to the following formula to obtain a strong predictor which is used for obtaining a final gas volume fraction predicted value. The optical fiber probe sensor adopted by the invention can accurately detect gas-phase and liquid-phase media in gas-liquid two-phase flow, provides basic data for accurate measurement, optimizes the weight and the threshold value of the BP neural network through the particle swarm optimization algorithm, helps the network to jump out of local optimum, and improves the global search capability of the model, thereby improving the measurement precision, and reducing the measurement cost. According to the AdaBoost algorithm, a plurality of BP neural network weak predictors subjected to PSO optimization are combined into a strong predictor, so that the model prediction precision and stability are greatly improved.

Description

Technical Field

[0001] The invention belongs to the field of measurement technology, and in particular relates to a method for measuring the gas volume fraction of a gas-liquid two-phase flow. Background Art

[0002] Multiphase flow is often encountered in the chemical industry, nuclear reactors, and petroleum industry. As a typical multiphase flow system, gas-liquid two-phase flow has complex fluid dynamics behavior, called flow pattern, due to the existence of complex interface effects and relative motion caused by two dispersed phases with different physical properties. In flow parameter measurement, different flow behaviors will affect the performance of the sensor. A challenging problem in flow parameter measurement is the measurement of gas volume fraction associated with the spatiotemporal structure of the flow pattern.

[0003] Fiber optic probe sensors have become a common tool for measuring gas phase parameters in multiphase flow due to their resistance to electromagnetic interference, ease of array creation, and high sensitivity. A single fiber optic probe sensor can only measure the gas content of a local cross section, so most studies increase the number of measurement points by constructing a fiber optic probe array, and then use the average value of these measurement points to estimate the gas content of the cross section.

[0004] However, the multiphase flow structure has temporal and spatial complexity, and the measurement environment will change dynamically. Especially in annular and stirring flows, there will be a certain degree of error between the measured values ​​at different times and the true values. Simply adding the measured values ​​of each probe and averaging them cannot effectively eliminate this error. At the same time, due to the large gap between the gas-liquid two-phase flow and the difference in inherent properties, slippage will occur between the phases, resulting in a difference between the gas volume fraction (i.e., the ratio of gas flow rate to total flow rate) and the cross-sectional gas content (i.e., the area ratio of the gas phase to the pipe cross section). Therefore, there is a complex nonlinear relationship between the local gas fraction and the gas volume fraction, and it is difficult to directly establish an accurate model between the two. This shows that there are great challenges in relying on a single sensor to achieve accurate measurement of the gas volume fraction. Summary of the invention

[0005] The technology to be solved by the present invention is to overcome the shortcomings of the prior art and provide a method for measuring the gas volume fraction of a gas-liquid two-phase flow with reasonable design and high measurement accuracy.

[0006] The technical solution adopted to solve the above technical problems is: a method for measuring the gas volume fraction of a gas-liquid two-phase flow, comprising the following steps:

[0007] Step 1. The local gas content signal at each position of the cross section is collected by an array optical fiber probe sensor, and the corresponding standard gas volume fraction is measured by a flow meter. The local gas content signal at each position is processed to obtain local gas content data. The collection time is s each time, and the collection is performed N times. The local gas content data at each position collected each time and the corresponding gas volume fraction constitute a sample data, forming a sample data set containing N sample data;

[0008] Step 2. Construct a BP neural network, and use the particle swarm optimization algorithm to optimize the weights and thresholds of the BP neural network to obtain a weak predictor;

[0009] Step 2.1. Combine the weights and thresholds of the BP neural network into particle codes;

[0010] Step 2.2. Randomly generate a particle swarm in the solution space as the initial solution, each particle represents a set of weights and thresholds;

[0011] Step 2.3. Evaluate the performance of each particle through the fitness function, and iteratively update the particle's speed and position according to the evaluation results. During the update, the particle continuously approaches the optimal solution area. When the preset number of iterations is reached or the convergence condition is met, the optimized weight and threshold are obtained, thereby obtaining a weak predictor;

[0012] Step 3. Use the AdaBoost algorithm to train the weak predictor to obtain a strong predictor;

[0013] Step 3.1. Randomly select m sample data from the sample data set as the training set;

[0014] Step 3.2. Assign the same initial weight to each sample data in the training set, and these weights are used in the subsequent weighted training process;

[0015] Step 3.3. In each round of training, the weak predictor is trained using the current sample weights to generate the weak predictor for this round, the classification error rate of the weak predictor for this round on the training set is determined, and the weight of the prediction sequence of the weak predictor for this round is obtained based on the classification error rate;

[0016] Step 3.4. Update the sample weights for the next round of training based on the prediction results of the weak learner in this round and the weights of the prediction sequence; increase the weights of the samples that are misclassified, and reduce the weights of the samples that are correctly classified. The updated weights are normalized to ensure that the sum of all sample weights is 1;

[0017] Step 3.5. After the preset T rounds of training, generate T weak predictors;

[0018] Step 4. Combine T weak predictors according to the following formula to obtain a strong predictor to obtain the final gas volume fraction prediction value,

[0019]

[0020] Where F(x) is the predicted value of the final gas volume fraction obtained for the input local gas content x at each location, and f t (x) is the predicted value of the gas volume fraction of the local gas content x at each input position by the weak predictor in the tth round, α t is the weight of the prediction sequence of the weak predictor in round t.

[0021] Preferably, the method for obtaining local gas content data by processing the local gas content signal at each position in step 1 is:

[0022] Step 1.1. First, perform photoelectric conversion and analog-to-digital conversion on the reflected light signal of the array optical fiber probe sensor to obtain a digital signal;

[0023] Step 1.2. Convert the digital signal into a binary rectangular wave signal by using a dynamic threshold adjustment method;

[0024] Step 1.2.1. Set two adjustable parameters, namely the maximum value a max and the minimum value a min , and give them two initial values ​​respectively;

[0025] Step 1.2.2. The current sampled signal amplitude a n The signal amplitude a sampled before n-1 For comparison, a n >a n-1 , then a max Update to a n , indicating that the current sampling signal amplitude is greater than the previous sampling signal amplitude, and the signal is close to the range of the gas phase signal, so the maximum value is updated; a n <a n-1 , then a min Update to a n , indicating that the current sampling signal amplitude is smaller than the previous sampling signal amplitude, and the signal is close to the range of the water phase signal, so the minimum value is updated; a n =a n-1 , then keep a max and a min The original state remains unchanged;

[0026] Step 1.2.3. Determine the true value of the current sampling point according to the following formula (1) (2):

[0027] a n >a min +y (1)

[0028] a n <amax -y (2)

[0029] Where y is a variable that depends on the signal noise and is adjusted according to the noise level of the actual signal to ensure effective conversion of the signal;

[0030] If equation (1) is true, the output is 1, indicating that the signal at the current sampling point is close to the gas phase signal;

[0031] If equation (2) is true, the output is 0, indicating that the signal at the current sampling point is close to the water phase signal;

[0032] If neither equation (1) nor (2) is satisfied, the output of this sampling point is the same as the previous sampling point, maintaining the continuity of the signal;

[0033] Step 1.2.3. Determine the local gas content based on the binary rectangular wave signal;

[0034] The total amount of data collected at the position j of the optical fiber probe sensor array within the acquisition time s is N tj , where the number of data outputted as 1 is N gj , represents the gas phase signal, and the local gas content x at the position j of the fiber probe of the array fiber probe sensor j for:

[0035]

[0036] Where R is the total number of probes.

[0037] Preferably, the BP neural network includes an input layer, a hidden layer, and an output layer, and the neuron set of the input layer is: x=(x 1 ,x 2 ,…,x j ,…,x R ), R is the number of neurons in the input layer, 1≤j≤R, x j represents the local gas content at the position j of the optical fiber probe;

[0038] The number of neurons a in the hidden layer is determined according to the following formula:

[0039]

[0040] Where l is the number of neurons in the output layer, and b is an integer between 0 and 10, which is used to adjust the complexity of the model;

[0041] The number of neurons in the output layer is l=1, and the neurons in the output layer represent the gas volume fraction of the gas-liquid two-phase flow.

[0042] Preferably, the method for iteratively updating the speed and position of the particle according to the evaluation result in step 2.3 is:

[0043]

[0044] In the formula, is the velocity of the dth dimension of the ith particle at the k+1th iteration, w is the inertia weight, which is used to control the attenuation of the particle velocity. is the velocity of the dth dimension of the ith particle at the kth iteration, c 1 and c 2 is the learning factor, which is used to control the speed at which particles move to the individual optimal position and the global optimal position. and is the random number at the kth iteration, used to increase the randomness of particle movement. is the individual optimal position of the dth dimension of the ith particle at the kth iteration, is the global optimal position of the dth dimension of the ith particle at the kth iteration, is the position of the dth dimension of the ith particle at the kth iteration, is the position of the dth dimension of the ith particle at the k+1th iteration.

[0045] The beneficial effects of the present invention are as follows:

[0046] The fiber optic probe sensor used in the present invention has the characteristics of high sensitivity and anti-electromagnetic interference, can accurately detect the gas and liquid media in the gas-liquid two-phase flow, and provide basic data for precise measurement. The particle swarm optimization (PSO) algorithm is used to optimize the weights and thresholds of the BP neural network, helping the network to jump out of the local optimum and enhance the global search capability of the model, thereby improving the measurement accuracy. The AdaBoost algorithm combines multiple PSO-optimized BP neural network weak predictors into a strong predictor, further improving the prediction accuracy and stability of the model.

[0047] The present invention uses optical fiber probe sensors to collect data, which can adapt to complex gas-liquid two-phase flow patterns such as bubbly flow and slug flow, ensure stable measurement under different flow conditions, and can increase the number of optical fiber probes as needed to further optimize the algorithm model to adapt to different measurement requirements and complex environments, thus having extremely high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a principle block diagram of the gas volume fraction measurement method of the gas-liquid two-phase flow of the present invention.

[0049] Figure 2 This is the planar position distribution diagram of the optical fiber probes of the array optical fiber probe sensor in the experiment.

[0050] Figure 3 Schematic diagram of the comparison between the measured and predicted gas volume fractions in the experiment.

[0051] Figure 4 It is a schematic diagram of the relative error results of the SVM model and the PSO-BP-AdaBoost model of the present invention.

[0052] Figure 5 It is a schematic diagram of the relative error results of the BP neural network and the PSO-BP-AdaBoost model of the present invention.

[0053] Figure 6 It is a schematic diagram of the relative error results of the PSO-BP neural network and the PSO-BP-AdaBoost model of the present invention.

[0054] Figure 7 This is a comparison chart of the error indicators of the PSO-BP-AdaBoost model of the present invention and the existing model. DETAILED DESCRIPTION

[0055] The present invention will be further described in detail below in conjunction with the accompanying drawings and examples, but the present invention is not limited to the following embodiments.

[0056] Example

[0057] exist Figure 1 In this embodiment, a method for measuring the gas volume fraction of a gas-liquid two-phase flow comprises the following steps:

[0058] Step 1. The local gas content signal at each position of the cross section is collected by an array optical fiber probe sensor, and the corresponding standard gas volume fraction is measured by a flow meter. The local gas content signal at each position is processed to obtain local gas content data. The collection time is s each time, and the collection is performed N times. The local gas content data at each position collected each time and the corresponding measured gas volume fraction constitute a sample data, forming a sample data set containing N sample data;

[0059] The method for processing the local gas content signal at each position to obtain the local gas content data is as follows:

[0060] Step 1.1. First, perform photoelectric conversion and analog-to-digital conversion on the reflected light signal of the array optical fiber probe sensor to obtain a digital signal;

[0061] Step 1.2. Convert the digital signal into a binary rectangular wave signal by using a dynamic threshold adjustment method;

[0062] Step 1.2.1. Set two adjustable parameters, namely the maximum value a max and the minimum value a min, and give them two initial values ​​respectively;

[0063] Step 1.2.2. The current sampled signal amplitude a n The signal amplitude a sampled before n-1 For comparison, a n >a n-1 , then a max Update to a n , indicating that the current sampling signal amplitude is greater than the previous sampling signal amplitude, and the signal is close to the range of the gas phase signal, so the maximum value is updated; a n <a n-1 , then a min Update to a n , indicating that the current sampling signal amplitude is smaller than the previous sampling signal amplitude, and the signal is close to the range of the water phase signal, so the minimum value is updated; a n =a n-1 , then keep a max and a min The original state remains unchanged;

[0064] Step 1.2.3. Determine the true value of the current sampling point according to the following formula (1) (2):

[0065] a n >a min +y (1)

[0066] a n max -y (2)

[0067] Where y is a variable that depends on the signal noise and is adjusted according to the noise level of the actual signal to ensure effective conversion of the signal;

[0068] If equation (1) is true, the output is 1, indicating that the signal at the current sampling point is close to the gas phase signal;

[0069] If equation (2) is true, the output is 0, indicating that the signal at the current sampling point is close to the water phase signal;

[0070] If neither equation (1) nor (2) is satisfied, the output of this sampling point is the same as the previous sampling point, maintaining the continuity of the signal;

[0071] Step 1.2.3. Determine the local gas content based on the binary rectangular wave signal;

[0072] The total amount of data collected at the position j of the optical fiber probe sensor array within the acquisition time s is N tj , where the number of data outputted as 1 is N gj , represents the gas phase signal, and the local gas content x at the position j of the fiber probe of the array fiber probe sensor​j for:

[0073]

[0074] Wherein, R is the total number of optical fiber probes in the array optical fiber probe sensor.

[0075] Step 2. Construct a BP neural network, and use the particle swarm optimization algorithm to optimize the weights and thresholds of the BP neural network to obtain a weak predictor;

[0076] The BP neural network includes an input layer, a hidden layer, and an output layer. The neuron set of the input layer is: x=(x 1 ,x 2 ,…,x j ,…,x R ), R is the number of neurons in the input layer, i.e., the total number of fiber probes in the array fiber probe sensor, 1≤j≤R, x j represents the local gas content at the position j of the optical fiber probe;

[0077] The number of neurons a in the hidden layer is determined by the following formula:

[0078]

[0079] Where l is the number of neurons in the output layer, and b is an integer between 0 and 10, which is used to adjust the complexity of the model;

[0080] The number of neurons in the output layer is l=1, and the neurons in the output layer represent the gas volume fraction of the gas-liquid two-phase flow.

[0081] Step 2.1. Combine the weights and thresholds of the BP neural network into particle codes;

[0082] Step 2.2. Randomly generate a particle swarm in the solution space as the initial solution, each particle represents a set of weights and thresholds;

[0083] Step 2.3. Evaluate the performance of each particle through the fitness function, and iteratively update the particle's speed and position according to the evaluation results as follows:

[0084]

[0085] In the formula, is the velocity of the dth dimension of the ith particle at the k+1th iteration, w is the inertia weight, which is used to control the attenuation of the particle velocity. is the velocity of the dth dimension of the ith particle at the kth iteration, c 1 and c 2 is the learning factor, which is used to control the speed at which particles move to the individual optimal position and the global optimal position. and is the random number at the kth iteration, used to increase the randomness of particle movement. is the individual optimal position of the dth dimension of the ith particle at the kth iteration, is the global optimal position of the dth dimension of the ith particle at the kth iteration, is the position of the dth dimension of the ith particle at the kth iteration, is the position of the dth dimension of the ith particle at the k+1th iteration.

[0086] During the update, particles continuously approach the optimal solution region. When the preset number of iterations is reached or the convergence condition is met, the optimized weights and thresholds are obtained, thereby obtaining a weak predictor.

[0087] Step 3. Use the AdaBoost algorithm to train the weak predictor to obtain a strong predictor;

[0088] Step 3.1. Randomly select m sample data from the sample data set obtained in step 1 as the training set;

[0089] Step 3.2. Assign the same initial weight to each sample data in the training set. The initial weight is These weights are used in the subsequent weighted training process;

[0090] Step 3.3. In each round of training, the weak predictor is trained using the current sample weights to generate the weak predictor for this round, the classification error rate of the weak predictor for this round on the training set is determined, and the weight of the prediction sequence of the weak predictor for this round is obtained based on the classification error rate;

[0091] Step 3.4. Update the sample weights for the next round of training based on the prediction results of the weak learner in this round and the weights of the prediction sequence; increase the weights of the samples that are misclassified, and reduce the weights of the samples that are correctly classified. The updated weights are normalized to ensure that the sum of all sample weights is 1;

[0092] Step 3.5. After the preset T rounds of training, generate T weak predictors;

[0093] Step 4. Combine T weak predictors according to the following formula to obtain a strong predictor to obtain the final gas volume fraction prediction value,

[0094]

[0095] Where F(x) is the predicted value of the final gas volume fraction obtained for the input local gas content x at each location, and f t (x) is the predicted value of the gas volume fraction of the local gas content x at each input position by the weak predictor in the tth round, αt is the weight of the prediction sequence of the weak predictor in round t.

[0096] experiment

[0097] In order to verify the beneficial effects of the present invention, the inventors adopted the technical solution of Example 1 (hereinafter referred to as PSO-BP-AdaBoost model) to conduct a gas volume fraction measurement experiment of a gas-liquid two-phase flow:

[0098] The total number R of optical fiber probes in the array optical fiber probe sensor of this experiment is 7. Figure 2 The voltage responses of 7 optical fiber probes were recorded using a data acquisition card at a sampling frequency of 2kHz, and the corresponding standard gas volume fraction was measured using a flow meter. Each acquisition lasted for 5 seconds, and 480 acquisitions were made. After processing, 480 sets of local gas content data at 7 positions were obtained. The local gas content data at 7 positions collected each time and the corresponding measured gas volume fraction constituted a sample data, forming a total of 480 sample data. The sample data were divided into a training set (including 440 sample data) and a test set (including 40 sample data).

[0099] After training the PSO-BP-AdaBoost model using the training set, 40 samples in the test set are used to verify the effectiveness of the trained model. Figure 3 , comparing the measured gas volume fraction and the predicted gas volume fraction. It can be seen from the figure that the predicted value of the present invention is highly close to the measured value, and the data points overlap well with each other.

[0100] The relative errors of the prediction results of the present invention (hereinafter referred to as PSO-BP-AdaBoost model) and the existing models, namely support vector machine (SVM), BP neural network, and PSO-BP neural network, are compared. Figure 4 , Figure 5 , Figure 6 , wherein the relative error of the PSO-BP-AdaBoost model of the present invention is 0.14%, that of SVM is 4.37%, that of BP neural network is 4.14%, and that of PSO-BP neural network is 1.09%. The relative error of the present invention is at the lowest level and has good robustness.

[0101] The performance of the present invention is compared with that of the existing model, and the four indicators are: mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and maximum error (ME). MAE, RMSE, and MAPE all reflect the deviation between the model prediction and the actual situation. The smaller the value, the closer the model prediction is to the true value, and the better the performance of the model. ME is the maximum absolute value of the difference between the predicted value and the actual value, reflecting the error degree of the model in the worst case. Comparison data such as Figure 7,It can be seen that the present invention outperforms the other three models in key evaluation indicators, such as MAE, RMSE, MAPE and ME, ,showing significant advantages.

Claims

1. A method for measuring gas volume fraction of gas-liquid two-phase flow, characterized in that: The following steps are involved: Step 1. The local gas content signal at each position of the cross section is collected by an array optical fiber probe sensor, and the corresponding standard gas volume fraction is measured by a flow meter. The local gas content signal at each position is processed to obtain local gas content data. The collection time is s each time, and the collection is performed N times. The local gas content data at each position collected each time and the corresponding gas volume fraction constitute a sample data, forming a sample data set containing N sample data; Step 2. Construct a BP neural network, and use the particle swarm optimization algorithm to optimize the weights and thresholds of the BP neural network to obtain a weak predictor; Step 2.

1. Combine the weights and thresholds of the BP neural network into particle codes; Step 2.

2. Randomly generate a particle swarm in the solution space as the initial solution, each particle represents a set of weights and thresholds; Step 2.

3. Evaluate the performance of each particle through the fitness function, and iteratively update the particle's speed and position according to the evaluation results. During the update, the particle continuously approaches the optimal solution area. When the preset number of iterations is reached or the convergence condition is met, the optimized weight and threshold are obtained, thereby obtaining a weak predictor; Step 3. Use the AdaBoost algorithm to train the weak predictors to obtain T preset weak predictors; Step 3.

1. Randomly select m sample data from the sample data set as the training set; Step 3.

2. Assign the same initial weight to each sample data in the training set, and these weights are used in the subsequent weighted training process; Step 3.

3. In each round of training, the weak predictor is trained using the current sample weights to generate the weak predictor for this round, the classification error rate of the weak predictor for this round on the training set is determined, and the weight of the prediction sequence of the weak predictor for this round is obtained based on the classification error rate; Step 3.

4. Update the sample weights for the next round of training based on the prediction results of the weak learner in this round and the weights of the prediction sequence; increase the weights of the samples that are misclassified, and reduce the weights of the samples that are correctly classified. The updated weights are normalized to ensure that the sum of all sample weights is 1; Step 3.

5. After the preset T rounds of training, generate T weak predictors; Step 4. Combine T weak predictors according to the following formula to obtain a strong predictor to obtain the final gas volume fraction prediction value, Where F(x) is the predicted value of the final gas volume fraction obtained for the input local gas content x at each location, and f t (x) is the predicted value of the gas volume fraction of the local gas content x at each input position by the weak predictor in the tth round, α t is the weight of the prediction sequence of the weak predictor in round t.

2. The method for measuring the gas volume fraction of a gas-liquid two-phase flow according to claim 1, characterized in that: The method for obtaining local gas content data by processing the local gas content signals at various positions in step 1 is: Step 1.

1. First, perform photoelectric conversion and analog-to-digital conversion on the reflected light signal of the array optical fiber probe sensor to obtain a digital signal; Step 1.

2. Convert the digital signal into a binary rectangular wave signal by using a dynamic threshold adjustment method; Step 1.2.

1. Set two adjustable parameters, namely the maximum value a max and the minimum value a min , and give them two initial values ​​respectively; Step 1.2.

2. The current sampled signal amplitude a n The signal amplitude a sampled before n-1 For comparison, a n >a n-1 , then a max Update to a n , indicating that the current sampling signal amplitude is greater than the previous sampling signal amplitude, and the signal is close to the range of the gas phase signal, so the maximum value is updated; a n <a n-1 , then a min Update to a n , indicating that the current sampling signal amplitude is smaller than the previous sampling signal amplitude, and the signal is close to the range of the water phase signal, so the minimum value is updated; a n =a n-1 , then keep a max and a min The original state remains unchanged; Step 1.2.

3. Determine the true value of the current sampling point according to the following formula (1) (2): to n >a min +y (1) to n max -and (2)​ Where y is a variable that depends on the signal noise and is adjusted according to the noise level of the actual signal to ensure effective conversion of the signal; If equation (1) is true, the output is 1, indicating that the signal at the current sampling point is close to the gas phase signal; If equation (2) is true, the output is 0, indicating that the signal at the current sampling point is close to the water phase signal; If neither equation (1) nor (2) is satisfied, the output of this sampling point is the same as the previous sampling point, maintaining the continuity of the signal; Step 1.2.

3. Determine the local gas content based on the binary rectangular wave signal; The total amount of data collected at the position j of the optical fiber probe sensor array within the acquisition time s is N tj , where the number of data outputted as 1 is N gj , represents the gas phase signal, and the local gas content x at the position j of the fiber probe of the array fiber probe sensor j for: Where R is the total number of probes.

3. The method for measuring gas volume fraction of gas-liquid two-phase flow according to claim 1, characterized in that: The BP neural network includes an input layer, a hidden layer, and an output layer. The neuron set of the input layer is: x = (x1, x2, ..., x j ,…,x R ), R is the number of neurons in the input layer, 1≤j≤R, x j represents the local gas content at the position j of the optical fiber probe; The number of neurons a in the hidden layer is determined according to the following formula: Where l is the number of neurons in the output layer, and b is an integer between 0 and 10, which is used to adjust the complexity of the model; The number of neurons in the output layer is l=1, and the neurons in the output layer represent the gas volume fraction of the gas-liquid two-phase flow.

4. The method for measuring gas volume fraction of gas-liquid two-phase flow according to claim 1, characterized in that: The method for iteratively updating the particle speed and position according to the evaluation results in step 2.3 is: In the formula, is the velocity of the dth dimension of the ith particle at the k+1th iteration, w is the inertia weight, which is used to control the attenuation of the particle velocity. is the velocity of the dth dimension of the ith particle at the kth iteration, c1 and c2 are learning factors used to control the speed at which the particle moves to the individual optimal position and the global optimal position, and is the random number at the kth iteration, used to increase the randomness of particle movement. is the individual optimal position of the dth dimension of the ith particle at the kth iteration, is the global optimal position of the dth dimension of the ith particle at the kth iteration, is the position of the dth dimension of the ith particle at the kth iteration, is the position of the dth dimension of the ith particle at the k+1th iteration.

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