Nuclear accident inversion method based on improved extreme learning machine
By improving the extreme learning machine method, combining long-term memory networks and optimization algorithms, a nuclear accident inversion model is constructed, which solves the problems of weak analysis capabilities and low data processing efficiency in complex situations in the existing technology, and achieves a fast and accurate nuclear accident The release rate prediction of the leaked source term improves the robustness and prediction accuracy of the model.
Patent Information
- Application Number
- CN202411012652.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-26
- Publication Date
- 2024-12-17
AI Technical Summary
The existing nuclear accident inversion methods are weak in complex situations, and have high requirements for data accuracy, are easily affected by errors, and are sensitive to parameter selection and slow to process large-scale data, making it difficult to quickly and accurately predict the source of nuclear accident leakage. release rate.
The improved extreme learning machine method is adopted, combined with long and short-term memory networks for data preprocessing and feature extraction, and the extreme learning machine neural network is optimized using sparrow optimization algorithm and cosine algorithm, and the C-loss loss function and genetic algorithm are introduced to build a nuclear accident inversion model. , able to quickly and accurately predict the release rate of nuclear accident leakage sources.
Improve the efficiency and accuracy of the inversion model, adapt to the prediction of complex environments, reduce the inherent complexity of the model, prevent overfitting, improve the prediction accuracy and speed, overcome the local optimal problem, and enhance the robustness of the model. .
Smart Images
Figure CN119150657A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of nuclear accident source term inversion, and in particular to a nuclear accident inversion method based on an improved extreme learning machine. Background Art
[0002] When a nuclear accident occurs, it is extremely important to quickly and accurately judge and analyze the operating conditions of the nuclear power plant, conduct consequence assessments, and implement emergency protection measures. Rapidly and accurately estimating the released source terms is an urgent problem to be solved in the early stages of nuclear emergency response. Currently, there are two main methods for estimating accident source terms: one is to determine the source terms based on forward modeling of plant operating data, including nuclear power plant operating data, reactor building status monitoring data, and readings of related instruments, but there may be situations such as unknown degree of core damage and damage to equipment instruments that affect reliability and accuracy; the other is to estimate the source terms based on radioactive data monitored by off-site air dose detection points. Higher accuracy and faster speed are what technicians in the field hope to overcome.
[0003] At present, the commonly used nuclear accident inversion methods include least squares method, data assimilation method, optimization algorithm, and neural network. Among the common inversion methods, the least squares method mainly analyzes single variables in linear systems. Its application is relatively simple, but its ability to analyze complex situations is weak and it has high requirements for data accuracy. The data assimilation method uses the cost function to quantitatively represent the difference between theoretical values and observed values, and solves the data assimilation problem by solving extreme values. It is mainly based on linear models and has high requirements for the error of observed data. Once there is a large error, the result will be greatly affected. The optimization algorithm can easily fall into local optimality. Machine learning trains models through a large amount of data, does not need to find mathematical relationships between data, can quickly perform inversion, and has strong application value for source term estimation.
[0004] The Chinese patent "CN115455808 A method for inverting nuclear accident release categories based on support vector machines" provides a method for inverting nuclear accident release categories based on support vector machines. This patent estimates the release rates of different radioactive nuclides under different nuclear accident release categories, uses support vector machines to analyze environmental gamma dose rate monitoring data, and quickly inverts nuclear accident release categories. However, support vector machines are sensitive to parameter and kernel function selection, and are slow to process large-scale data sets. Summary of the invention
[0005] In view of the shortcomings of the prior art, the present invention provides a nuclear accident inversion method based on an improved extreme learning machine. According to real-time measured data, the release rates of 14 radioactive source nuclides (I-131, Xe-133, Cs-137, Kr-88, Sr-91, Te-132, Mo-99, Ba-140, La-140, Ce-144, Sb-129, Ru-106, Y-91, Zr-95) of nuclear accident leakage sources are quickly and accurately predicted. At the same time, the changes in complex meteorological conditions are taken into account, providing a reference and basis for subsequent consequence evaluation and implementation of emergency measures.
[0006] The technical solution of the present invention is:
[0007] A nuclear accident inversion method based on an improved extreme learning machine comprises the following steps:
[0008] S1. Acquire several groups of nuclear accident measurement data, each group of nuclear accident measurement data includes m related features; the related features are nuclear power plant related information, air dose rate time series at different distances, and meteorological data time series;
[0009] S2. Processing the acquired nuclear accident measurement data to obtain processed nuclear accident measurement data;
[0010] The data processing method is specifically as follows: missing data and abnormal data in the air dose rate time series and the meteorological data time series at different distances are screened and deleted, and then the air dose rate time series and the meteorological data time series at different distances are input into the long short-term memory network for preliminary feature extraction and preliminary prediction of the release rate of the radioactive source nuclides of the nuclear accident leakage source item to obtain the prediction result, and at the same time, the air dose rate time series and the meteorological data time series after the missing data and the abnormal data are deleted are processed in the form of a window and split into a plurality of data features;
[0011] S3, dividing the processed nuclear accident measurement data into a training set and a test set according to a set ratio;
[0012] S4, establishing an extreme learning machine neural network and optimizing the extreme learning machine neural network using a training set and an improved sparrow optimization algorithm, and using the optimized extreme learning machine neural network as a nuclear accident inversion model;
[0013] S4.1: Establish an extreme learning machine neural network and set the parameters of the extreme learning machine neural network; the extreme learning machine neural network includes an input layer, a hidden layer and an output layer, the input of the input layer is the prediction result obtained by the long short-term memory network and the data features obtained by splitting, and the output of the output layer is the release rate of the radioactive nuclides of the nuclear accident leakage source item; the parameters of the extreme learning machine neural network are the number of nodes in the input layer, the number of nodes in the hidden layer and the number of nodes in the output layer;
[0014] S4.2: Improve the structure of the extreme learning machine neural network to obtain an improved extreme learning machine neural network;
[0015] The output layer in the improved extreme learning machine neural network not only uses the output matrix of the hidden layer, but also obtains the input of the input layer to calculate the output weight, and at the same time, the C-loss loss function is used to improve the output weight of the extreme learning machine neural network;
[0016] The input of the output layer node of the improved extreme learning machine neural network is:
[0017] H'=[P;H]
[0018] Among them, H' is the input of the output layer node, P is the input of the input layer node, and H is the output of the hidden layer node;
[0019]
[0020] Among them, lc(e i ) is the C-loss loss function, e i is the error between the predicted value and the actual value, σ is the square root of the variance;
[0021] S4.3: setting the number of individuals in the sparrow optimization algorithm population and initializing the individuals in the sparrow optimization algorithm population; the individuals represent the input layer weights and biases of the extreme learning machine neural network;
[0022] The specific method for initializing individuals in the sparrow optimization algorithm is:
[0023] First determine the group space:
[0024] Z=L+R*(UL)
[0025] Among them, Z is the group space, L is the lower bound of the group space, U is the upper bound of the group space, and R represents a randomly generated number in [0,1];
[0026] S4.4: using the individuals in the sparrow optimization algorithm population as training parameters of the extreme learning machine neural network, and obtaining a plurality of extreme learning machine neural networks with different training parameters; the training parameters are the input layer weights and biases;
[0027] S4.5: Input the training set into the extreme learning machine neural network corresponding to each individual, calculate the mean absolute error, and use it as the fitness of the individual in the sparrow optimization algorithm population;
[0028]
[0029] Among them, RMAE is the mean absolute error, N is the number of training set samples, and y l is the predicted output of the lth training sample, is the actual output of the lth training sample;
[0030] S4.6: Select the individual with the largest fitness as the current global optimal individual;
[0031] S4.7: Perform population exploration, introduce the sine-cosine algorithm improvement into the position update formula of the producer of the sparrow optimization algorithm, and update the position of individuals in the population;
[0032] The iterative update formula of the individual position is:
[0033]
[0034] r1=α(1-t / T max )
[0035] r2=r3=2π*rand; r4=rand
[0036] Among them, x i (t+1) is the position of the i-th individual in the t+1-th iteration, t is the number of iterations, x i (t) is the position of the i-th individual in the t-th iteration, x best (t) is the current position of the global optimal individual, r1 is the search step, r2 r3 r4 are all random numbers that obey uniform distribution, and rand is a random value between 0 and 1;
[0037] S4.8: Select the individual with the largest fitness as the global optimal individual of this iteration and compare it with the current global optimal individual. If the fitness of the global optimal individual of this iteration is larger, then the global optimal individual of this iteration is updated to the current global optimal individual, otherwise it remains unchanged;
[0038] S4.9: Determine whether the global optimal individual has not changed within the set number of iterations. If so, execute S4.10, otherwise execute S4.11;
[0039] S4.10: Sort the individuals in the current population according to their fitness, and use genetic algorithms to perform mutation crossover on individuals whose fitness is less than the set threshold;
[0040] S4.11: Determine whether the current number of iterations reaches the set number of iterations. If so, output the current global optimal individual and execute S4.12. Otherwise, increase the number of iterations by 1 and execute S4.7.
[0041] S4.12: applying the training parameters corresponding to the output global optimal individual and the weights of the output layer calculated when applying the training parameters to the improved extreme learning machine neural network to obtain the final nuclear accident inversion model;
[0042] S5: Input the test set into the final nuclear accident inversion model and output the release rate of the radioactive source nuclides in the nuclear accident leakage source term.
[0043] Compared with the prior art, the beneficial effects of the present invention are:
[0044] The present invention screens the collected nuclear accident comprehensive data for missing and abnormal data, and inputs the time series data in the nuclear accident comprehensive data into a long short-term memory network (LSTM) for preliminary prediction and window feature extraction processing. As a feedforward neural network, the extreme learning machine provides a flexible framework that does not have strong requirements on the distribution of inputs or the regularity of input-output mapping, does not need to find mathematical relationships between data, and has good generalization performance. It can quickly perform inversion and can adapt to predictions in complex environments, solving the shortcomings of the least squares method in terms of its weak ability to analyze complex situations; the present invention improves the efficiency and accuracy of the inversion model by improving the extreme learning machine, combines the sparrow optimization algorithm with the extreme learning machine, and globally optimizes the weight matrix and bias vector of the extreme learning machine to solve the shortcomings of random non-optimal parameters of the extreme learning machine. At the same time, the traditional sparrow optimization algorithm is prone to fall into local optimality in the later stage. Therefore, in the method of the present invention, the sine-cosine algorithm and the variation crossover of the genetic algorithm are introduced into the sparrow optimization algorithm to overcome the above shortcomings; the input layer information is introduced into the output layer of the extreme learning machine and the C-loss loss function is referenced to improve the structure, thereby improving the model robustness, reducing the intrinsic complexity of the extreme learning machine model, preventing overfitting, improving the quality of the model, and improving the model prediction accuracy and speed. BRIEF DESCRIPTION OF THE DRAWINGS
[0045] Figure 1 It is a flow chart of a nuclear accident inversion method based on an improved extreme learning machine in an embodiment of the present invention;
[0046] Figure 2 This is a flow chart of model training in an embodiment of the present invention;
[0047] Figure 3 It is a box plot of the predicted release rate and actual value of 14 radioactive source nuclides in the test training in the embodiment of the present invention;
[0048] Among them, (a) is a box plot comparison of the predicted release rate of I-131 radioactive nuclides and the actual value; (b) is a box plot comparison of the predicted release rate of Xe-133 radioactive nuclides and the actual value; (c) is a box plot comparison of the predicted release rate of Cs-137 radioactive nuclides and the actual value; (d) is a box plot comparison of the predicted release rate of Kr-88 radioactive nuclides and the actual value; (e) is a box plot comparison of the predicted release rate of Sr-91 radioactive nuclides and the actual value; (f) is a box plot comparison of the predicted release rate of Te-132 radioactive nuclides and the actual value; (g) is a box plot comparison of the predicted release rate of Mo-99 radioactive nuclides and the actual value; (h) is a box plot comparison of the predicted release rate of Ba-140 radioactive nuclide and the actual value; (i) is a box plot comparison of the predicted release rate of La-140 radioactive nuclide and the actual value; (j) is a box plot comparison of the predicted release rate of Ce-144 radioactive nuclide and the actual value; (k) is a box plot comparison of the predicted release rate of Sb-129 radioactive nuclide and the actual value; (l) is a box plot comparison of the predicted release rate of Ru-106 radioactive nuclide and the actual value; (m) is a box plot comparison of the predicted release rate of Y-91 radioactive nuclide and the actual value; (n) is a box plot comparison of the predicted release rate of Zr-9514 radioactive nuclide and the actual value. DETAILED DESCRIPTION
[0049] The present invention is described in detail below with reference to the accompanying drawings and embodiments.
[0050] A nuclear accident inversion method based on improved extreme learning machine, such as Figure 1 As shown, the following steps are included:
[0051] S1. Acquire several groups of nuclear accident measurement data, each group of nuclear accident measurement data includes m related features; the related features are nuclear power plant related information, air dose rate time series at different distances, and meteorological data time series;
[0052] In this embodiment, each group of nuclear accident measurement data includes 10 related features, among which, nuclear power plant related information: nuclear power plant release height; meteorological data: atmospheric stability, mixing layer height, wind speed, wind direction, and rainfall degree measured every 15 minutes in the previous 2 hours; air dose rate at different distances: air dose rate time series monitored at 1km, 2km, 5km, and 25km distances;
[0053] S2. Processing the acquired nuclear accident measurement data to obtain processed nuclear accident measurement data;
[0054] The data processing method is specifically as follows: missing data and abnormal data in the air dose rate time series and the meteorological data time series at different distances are screened and deleted, and then the air dose rate time series and the meteorological data time series at different distances are input into the long short-term memory network for preliminary feature extraction and preliminary prediction of the release rate of the radioactive source nuclides of the nuclear accident leakage source item to obtain the prediction result, and at the same time, the air dose rate time series and the meteorological data time series after the missing data and the abnormal data are deleted are processed in the form of a window and split into a plurality of data features;
[0055] In this embodiment, after filtering out missing data and abnormal data in the nuclear accident measurement data and deleting them, the long short-term memory network (LSTM) is used to perform preliminary feature extraction and source item information prediction on the wind speed, wind direction, rainfall degree, and air dose rate time series measured every 15 minutes in the previous 2 hours at a distance of 1km, 2km, 5km, and 25km. After the long short-term memory network (LSTM) processes the preliminary prediction, the predicted result is used as the input feature of the extreme learning machine, and the time series data is processed in the form of a window as an input feature, that is, the input related feature becomes 60;
[0056] S3, dividing the processed nuclear accident measurement data into a training set and a test set according to a set ratio;
[0057] In this embodiment, the processed nuclear accident measurement data is divided into a training set and a test set in a ratio of approximately 7:3;
[0058] S4, such as Figure 2 As shown, an extreme learning machine neural network is established and optimized using a training set and an improved sparrow optimization algorithm, and the optimized extreme learning machine neural network is used as a nuclear accident inversion model;
[0059] S4.1: Establish an extreme learning machine neural network and set parameters of the extreme learning machine neural network; the extreme learning machine neural network includes an input layer, a hidden layer and an output layer; the parameters of the extreme learning machine neural network are the number of nodes in the input layer, the number of nodes in the hidden layer and the number of nodes in the output layer;
[0060] In this embodiment, the number of nodes in the input layer is set to 10, the number of nodes in the hidden layer is set to 60, and the number of nodes in the output layer is set to 14;
[0061] S4.2: Improve the structure of the extreme learning machine neural network to obtain an improved extreme learning machine neural network;
[0062] The output layer in the improved extreme learning machine neural network not only uses the output matrix of the hidden layer, but also obtains the input of the input layer to calculate the output weight, and at the same time, the C-loss loss function is used to improve the output weight of the extreme learning machine neural network to improve the robustness;
[0063] The input of the output layer node of the improved extreme learning machine neural network is:
[0064] H'=[P;H]
[0065] Among them, H' is the input of the output layer node, P is the input of the input layer node, and H is the output of the hidden layer node;
[0066]
[0067] Among them, lc(e i ) is the C-loss loss function, e i is the error between the predicted value and the actual value, σ is the square root of the variance;
[0068] S4.3: setting the number of individuals in the sparrow optimization algorithm population and initializing the individuals in the sparrow optimization algorithm population; the individuals represent the input layer weights and biases of the extreme learning machine neural network;
[0069] The specific method for initializing individuals in the sparrow optimization algorithm is:
[0070] First determine the group space:
[0071] Z=L+R*(UL)
[0072] Among them, Z is the group space, L is the lower bound of the group space, U is the upper bound of the group space, and R represents a randomly generated number in [0,1];
[0073] In this implementation, the number of individuals in the population is defined as 40;
[0074] S4.4: using the individuals in the sparrow optimization algorithm population as training parameters of the extreme learning machine neural network, and obtaining a plurality of extreme learning machine neural networks with different training parameters; the training parameters are the input layer weights and biases;
[0075] S4.5: Input the training set into the extreme learning machine neural network corresponding to each individual, calculate the mean absolute error (RMAE), and use it as the fitness of the individual in the sparrow optimization algorithm population;
[0076]
[0077] Among them, RMAE is the mean absolute error, N is the number of training set samples, and y lis the predicted output of the lth training sample, is the actual output of the lth training sample;
[0078] S4.6: Select the individual with the largest fitness as the current global optimal individual;
[0079] S4.7: Perform population exploration, introduce the sine-cosine algorithm improvement into the producer position update formula of the sparrow optimization algorithm, and update the position of individuals in the population; use the improvement to achieve global exploration and local development of the search space, and the search step length r1 gradually decreases with the increase of the number of iterations, so as to maximize the convergence, that is, continuously optimize the population position through iterative evolution;
[0080] The iterative update formula of the individual position is:
[0081]
[0082] r1=α(1-t / T max )
[0083] r2=r3=2π*rand; r4=rand
[0084] Among them, x i (t+1) is the position of the i-th individual in the t+1-th iteration, t is the number of iterations, x i (t) is the position of the i-th individual in the t-th iteration, x best (t) is the current position of the global optimal individual, r1 is the search step, which gradually decreases with the increase of the number of iterations, r2 r3 r4 are all random numbers that obey uniform distribution, and rand is a random value between 0 and 1;
[0085] S4.8: Select the individual with the largest fitness as the global optimal individual of this iteration and compare it with the current global optimal individual. If the fitness of the global optimal individual of this iteration is larger, then the global optimal individual of this iteration is updated to the current global optimal individual, otherwise it remains unchanged;
[0086] S4.9: Determine whether the global optimal individual has not changed within the set number of iterations, that is, the current search may fall into a local optimum. If so, execute S4.10, otherwise execute S4.11;
[0087] S4.10: Sort the individuals in the current population according to their fitness, and use genetic algorithms to perform mutation crossover on individuals whose fitness is less than the set threshold to escape from the local optimum;
[0088] S4.11: Determine whether the current number of iterations reaches the set number of iterations. If so, output the current global optimal individual and execute S4.12. Otherwise, increase the number of iterations by 1 and execute S4.7.
[0089] S4.12: applying the training parameters corresponding to the output global optimal individual and the weights of the output layer calculated when applying the training parameters to the improved extreme learning machine neural network to obtain the final nuclear accident inversion model;
[0090] S5: Input the test set into the final nuclear accident inversion model, and output the release rates of 14 radioactive source nuclides (I-131, Xe-133, Cs-137, Kr-88, Sr-91, Te-132, Mo-99, Ba-140, La-140, Ce-144, Sb-129, Ru-106, Y-91, Zr-95) of the nuclear accident leakage source. The box plot of the predicted release rates of the 14 radioactive source nuclides and the actual values is shown in the figure below. Figure 3 shown.
Claims
1. A nuclear accident inversion method based on an improved extreme learning machine, characterized in that: The steps include: S1. Acquire several groups of nuclear accident measurement data, each group of nuclear accident measurement data includes m relevant features; S2. Processing the acquired nuclear accident measurement data to obtain processed nuclear accident measurement data; S3, dividing the processed nuclear accident measurement data into a training set and a test set according to a set ratio; S4, establishing an extreme learning machine neural network and optimizing the extreme learning machine neural network using a training set and an improved sparrow optimization algorithm, and using the optimized extreme learning machine neural network as a nuclear accident inversion model; S5: Input the test set into the final nuclear accident inversion model and output the release rate of the radioactive source nuclides in the nuclear accident leakage source term.
2. A nuclear accident inversion method based on an improved extreme learning machine according to claim 1, characterized in that: The relevant features described in S1 are nuclear power plant related information, air dose rate time series at different distances, and meteorological data time series.
3. A nuclear accident inversion method based on an improved extreme learning machine according to claim 2, characterized in that: The data processing method described in S2 is specifically: screening missing data and abnormal data in the air dose rate time series and meteorological data time series at different distances and deleting them, and then inputting the air dose rate time series and meteorological data time series at different distances into the long short-term memory network for preliminary feature extraction and preliminary prediction of the release rate of radioactive nuclides in the nuclear accident leakage source item to obtain the prediction results. At the same time, the air dose rate time series and meteorological data time series after deleting the missing data and abnormal data are processed in a window form and split into several data features.
4. A nuclear accident inversion method based on an improved extreme learning machine according to claim 1, characterized in that: S4 specifically includes the following steps: S4.1: Establish an extreme learning machine neural network and set the parameters of the extreme learning machine neural network; the extreme learning machine neural network includes an input layer, a hidden layer and an output layer, the input of the input layer is the prediction result obtained by the long short-term memory network and the data features obtained by splitting, and the output of the output layer is the release rate of the radioactive nuclides of the nuclear accident leakage source item; the parameters of the extreme learning machine neural network are the number of nodes in the input layer, the number of nodes in the hidden layer and the number of nodes in the output layer; S4.2: Improve the structure of the extreme learning machine neural network to obtain an improved extreme learning machine neural network; The output layer in the improved extreme learning machine neural network not only uses the output matrix of the hidden layer, but also obtains the input of the input layer to calculate the output weight, and at the same time, the C-loss loss function is used to improve the output weight of the extreme learning machine neural network; S4.3: setting the number of individuals in the sparrow optimization algorithm population and initializing the individuals in the sparrow optimization algorithm population; the individuals represent the input layer weights and biases of the extreme learning machine neural network; S4.4: using the individuals in the sparrow optimization algorithm population as training parameters of the extreme learning machine neural network, and obtaining several extreme learning machine neural networks with different training parameters; The training parameters are input layer weights and biases; S4.5: Input the training set into the extreme learning machine neural network corresponding to each individual, calculate the mean absolute error, and use it as the fitness of the individual in the sparrow optimization algorithm population; Among them, RMAE is the mean absolute error, N is the number of training set samples, and y l is the predicted output of the lth training sample, is the actual output of the lth training sample; S4.6: Select the individual with the largest fitness as the current global optimal individual; S4.7: Perform population exploration, introduce the sine-cosine algorithm improvement into the position update formula of the producer of the sparrow optimization algorithm, and update the position of individuals in the population; S4.8: Select the individual with the largest fitness as the global optimal individual of this iteration and compare it with the current global optimal individual. If the fitness of the global optimal individual of this iteration is larger, then the global optimal individual of this iteration is updated to the current global optimal individual, otherwise it remains unchanged; S4.9: Determine whether the global optimal individual has not changed within the set number of iterations. If so, execute S4.10, otherwise execute S4.11; S4.10: Sort the individuals in the current population according to their fitness, and use genetic algorithms to perform mutation crossover on individuals whose fitness is less than the set threshold; S4.11: Determine whether the current number of iterations reaches the set number of iterations. If so, output the current global optimal individual and execute S4.
12. Otherwise, increase the number of iterations by 1 and execute S4.
7. S4.12: Apply the training parameters corresponding to the output global optimal individual and the weights of the output layer calculated when applying the training parameters to the improved extreme learning machine neural network to obtain the final nuclear accident inversion model.
5. A nuclear accident inversion method based on an improved extreme learning machine according to claim 4, characterized in that: The input of the output layer node of the improved extreme learning machine neural network described in S4.2 is: H'=[P;H] Among them, H' is the input of the output layer node, P is the input of the input layer node, and H is the output of the hidden layer node; Among them, lc(e i ) is the C-loss loss function, e i is the error between the predicted value and the actual value, and σ is the square root of the variance.
6. A nuclear accident inversion method based on an improved extreme learning machine according to claim 4, characterized in that: The specific method for initializing individuals in the sparrow optimization algorithm in S4.3 is: First determine the group space: Z=L+R*(UL) Among them, Z is the group space, L is the lower bound of the group space, U is the upper bound of the group space, and R represents a randomly generated number in [0,1].
7. A nuclear accident inversion method based on an improved extreme learning machine according to claim 4, characterized in that: The iterative update formula for the position of an individual in S4.7 is: r1=α(1-t / T max ) r2=r3=2π*rand; r4=rand Among them, x i (t+1) is the position of the i-th individual in the t+1-th iteration, t is the number of iterations, x i (t) is the position of the i-th individual in the t-th iteration, x best (t) is the current position of the global optimal individual, r1 is the search step, r2 r3 r4 are all random numbers that obey a uniform distribution, and rand is a random value between 0 and 1.