Power load prediction method based on VMD algorithm and improved TimesNet

Abstract

The invention discloses a power load prediction method based on a VMD algorithm and an improved TimesNet, and the method comprises the steps: carrying out the normalization processing of collected power load data, decomposing the data into modal components of different frequencies through employing the VMD algorithm, taking an envelope entropy as a target function of an MPA algorithm, and carrying out the calculation of the model, and optimizing the decomposition number and penalty factor of the modal component by using an MPA optimization algorithm to obtain an optimized modal component, inputting the optimized modal component into an improved TimesNet model for training, and adding the obtained prediction results of the modal components to obtain a power load prediction result. The characteristics of nonlinearity, non-stationarity and periodicity of the power load data are considered, the improved TimesNet network is utilized to perform multi-periodicity modeling based on the load data, a one-dimensional time sequence is expanded into a two-dimensional space, the characteristics in the period and during the period are fully extracted, and the power load is accurately predicted.

Description

Technical Field

[0001] The invention relates to the technical field of photovoltaic power generation prediction, and in particular to an intelligent prediction method for power load. Background Art

[0002] As the basis of power system dispatch, power load forecasting not only plays an important role in the operation and dispatch of power systems, but also directly affects the safety and reliability of power system operation and the quality of electricity consumption. Accurate power load forecasting has been an important research topic in recent years. At present, the methods of power load forecasting can be divided into traditional forecasting methods based on statistical analysis and methods based on deep neural networks. However, these forecasting methods do not fully consider the nonlinearity, non-stationarity, and periodicity of power load data. The single forecasting model structure itself has limitations and it is difficult to achieve ideal forecasting results. Summary of the invention

[0003] The purpose of the present invention is to provide a power load forecasting method based on a variational mode decomposition algorithm (VMD) and an improved TimesNet to address the above problems. The power load data is decomposed into multiple smooth subsequences using VMD, and the parameters of the VMD algorithm are optimized using a marine predator algorithm (MPA). The improved TimesNet network is used to model the multi-periodicity of electronic load data, expand the one-dimensional time series into a two-dimensional space, fully extract its intra-cycle and inter-cycle features, and accurately predict the power load.

[0004] The technical solution of the present invention is a power load forecasting method based on VMD algorithm and improved TimesNet, and the method comprises the following steps: S1, collecting power load data to obtain a data set D1, and normalizing the data set D1 to obtain a data set D2; S2, using VMD algorithm to decompose the load data of data set D2 into modal components of different frequencies; S3, taking the envelope entropy as the objective function of MPA, using MPA to optimize the decomposition number and penalty factor of the modal components to obtain the optimal number of modal components; S4, decomposing the load data of the data set D2 according to the optimal number of modal components obtained in step S3 to obtain optimized modal components, and further dividing them into a training set and a test set, inputting the training set into the improved TimesNet model for training, and extracting the multi-periodic characteristics of the power load; S5. Input the test set into the trained improved TimesNet model, add the prediction results of each modal component, and obtain the power load prediction result.

[0005] Furthermore, the dataset D1 is normalized in step S1 to obtain the dataset D2, which is expressed as follows: ; In the formula, y i represents the normalized data, x i Represents the original data of power load, x max and x min Represent the maximum and minimum values ​​in data set D1 respectively.

[0006] The optimized VMD algorithm includes: (1) Construct a variational constraint model, expressed as: ; Where u1,u2, ,u k are the k modal components obtained by decomposition, w1, w2, ,w k is the center frequency of each mode, It means the partial derivative of the function with respect to time t, represents the unit impulse function; ; Where, f represents the original load data; (2) By introducing the quadratic penalty term α and the Lagrange multiplier λ, and augmenting the Lagrangian function L, the constrained problem is transformed into an unconstrained variational problem, expressed as: ； In the formula, α represents the quadratic penalty term, λ represents the Lagrange multiplier, L represents the augmented Lagrangian function; (3) Use the alternating direction multiplier algorithm to perform a series of iterations to find the optimal solution, expressed as: ; ; ; In the formula, τ represents the noise tolerance, , , They are , , Fourier transform of for Fourier transform of (4) The convergence condition calculation formula is: ; In the formula, Represents an arbitrarily small positive number.

[0007] Optimized, in step S3, calculating the target function envelope entropy includes the following steps: (1) Calculate the envelope, the expression is: ; Where H represents the Hilbert transform, and α(i) represents the input data set x(i) (i=1,2, ,m) The envelope signal sequence obtained after Hilbert transform, m Indicates the number of data samples in the dataset; (2) Normalization processing, the expression is: ; Where P j represents the envelope signal of α(j) after normalization; (3) Calculate the envelope entropy, the expression is: ; In the formula, Represents the envelope entropy of the signal; Indicates P j Find the base 10 logarithm; Furthermore, the MPA optimization algorithm is used to optimize the decomposition number and penalty factor of the modal component, including the following steps: (1) Initialize the parameters of the marine predator optimization algorithm, including the population size n, dimension d, and maximum number of iterations; (2) Initialize the population, set the range of k and α, and use the envelope entropy as the fitness function of VMD; (3) Preliminarily calculate the fitness of all populations based on the initial parameters and find the position of the initial population with the smallest fitness value; (4) Update the population position through the three optimization stages of the marine predator optimization algorithm: exploration stage, transition stage, and development stage, continuously iterate, recalculate the fitness, and select the minimum fitness value to determine the optimal population position; (5) If the current number of iterations reaches the set maximum value, the iteration ends and the optimal hyperparameter decomposition number and penalty factor of variational mode decomposition VMD are obtained; otherwise, the above iterative process is repeated until the current number of iterations reaches the set threshold; (6) Output the optimal parameters k and α, and use VMD with the optimal parameters to decompose the original signal into k modal components.

[0008] The optimized,MPA algorithm includes the following steps: (1) MPA initializes the element X in the prey matrix Prey according to the population size n and dimension d ij Construct the n×d dimensional matrix Prey: ； ； Where X max and X min are the upper and lower limits of the variable respectively, and rand is a uniform random function ranging from 0 to 1.

[0009] (2) Construct the elite matrix Elite, which consists of the individuals with the best fitness in the matrix Prey Copy n times to form: ； The MPA optimization process simulates the life activities of predators and preys while considering different speed ratios. It is divided into three stages according to the relationship between the number of iterations Iter and the maximum number of iterations Max_Iter: Phase 1: Exploration phase, when Iter< When Max_Iter, it is a high rate ratio, the prey moves faster than the predator, and the predator adopts a static strategy, and the expression is: ； ； In the formula, represents the predator’s step vector, represents the position vector of the prey, is a random number vector based on a normal distribution, representing Brownian motion, Indicates that the corresponding elements are multiplied one by one, Multiplying with Prey simulates the movement of prey. P is a constant with a value of 0.5. .

[0010] Phase 2: Transition phase, when Max_Iter <Iter< At Max_Iter, the rate ratio is the same, and the prey and predator have the same speed.

[0011] For the first half of the population: ； ； In the formula, is a random number vector based on Lévy distribution, representing the Lévy motion, Multiplying by Prey simulates the Lévy motion of prey, where .

[0012] For the second half of the population: ； ； in is an adaptive parameter that controls the predator's movement step size, Multiplying with the matrix Elite simulates the predator Brownian motion, .

[0013] Phase 3: Development phase, when Iter> At Max_Iter, it is a low rate ratio, and the predator moves faster than the prey. The mathematical expression of this process is: ； ； in Multiply with Elite to simulate Predator Lévy movement.

[0014] In addition, eddies and fish gatherings will change the behavior of predators. Predators have the probability to jump in space and jump out of FADs to find another environment where prey is distributed. The mathematical expression is: ； Where FADs = 0.2 is a constant, which represents the probability of predator space jump. is a randomly generated binary vector containing an array of 0 and 1. If the array is less than 0.2, the array is 0. If the array is greater than 0.2, the array is 1. r is a uniform random number in the range [0,1]. r1 and r2 are two random subscripts of Prey.

[0015] The current solution is continuously updated through the above process until the algorithm termination condition is met and the optimal solution is obtained.

[0016] Furthermore, the improved TimesNet network of step S4 is composed of multiple stacked TimesBlocks in a residual connection manner, and the processing process of each TimesBlock on the input signal data is: (1) For a one-dimensional time series X 1D Perform Fast Fourier Transform FFT to analyze the spectrum: ； In the formula, , Represents the real number space, where T is the time length, C is the channel dimension, A represents the calculation of the average amplitude of different frequencies, FFT represents the fast Fourier transform of the one-dimensional time series to the frequency domain, Amp represents the amplitude calculated from the time series converted to the frequency domain, and Avg represents the average amplitude.

[0017] (2) Take the k frequencies corresponding to the largest amplitude and record them from large to small as f1, ,f k , corresponding to the period p1,┄,p k for: ； (3) Fold the one-dimensional time series based on the selected period and reconstruct the one-dimensional time series into a two-dimensional tensor , the expression is: ； Where Padding represents the zero-padding function of the time series, and Reshape represents the reconstruction of a one-dimensional sequence into a two-dimensional tensor. .

[0018] (4) Extracting time series features using 2D convolutional network Inception Block , the expression is: ； In the formula, Represents the time series characteristics, A function representing the 2D convolutional network Inception module; (5) Reconstruct the extracted time series features back into one-dimensional space, expressed as: ； Where Trunc represents the zero removal function of the time series, express Convert from a 2D tensor to a 1D sequence.

[0019] (6) The k one-dimensional representations are weighted and summed according to the strength of their corresponding frequencies to complete information aggregation and obtain the final output of TimesBlock , the expression is: ； ； Where Softmax is the activation function.

[0020] Furthermore, in step S4, the improved TimesNet model is an improvement on the two-dimensional temporal feature extraction network Inception Block. It uses serially connected n×1 and 1×n convolutions to replace the original n×n convolution, which can reduce the number of parameters and computational complexity while maintaining good performance.

[0021] Compared with the prior art, the beneficial effects of the present invention include: 1) The present invention fully considers the nonlinearity, non-stationarity and periodicity of power load data, decomposes the load data into multiple relatively gentle subsequences by using VMD, and optimizes the key parameters of VMD by using the MPA optimization algorithm. Then, the improved TimesNet network is used to model the multi-periodicity of load data, and the one-dimensional time series is extended to the two-dimensional space, so as to fully extract its intra-cycle and inter-cycle characteristics, and effectively improve the accuracy of power load forecasting. 2) The present invention uses VMD to decompose the power load data into modal components of different frequencies, thereby reducing the non-stationarity of nonlinear data; 3) The present invention uses the MPA optimization algorithm to optimize the decomposition number k and penalty factor α of VMD, avoiding the influence of the subjectivity of manual parameter selection and improving the decomposition effect of power load data; 4) The present invention uses an improved TimesNet network to extract the multi-periodic characteristics of power load data to achieve more accurate prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0023] Figure 1 A schematic diagram of a method for predicting power load according to an embodiment of the present invention; Figure 2 The improved embodiment of the present invention TimesNet Network structure diagram; Figure 3 is the original power load sequence and MPA-VMD Exploded view; Figure 4A comparison diagram of a predicted load curve and a real load curve according to an embodiment of the present invention; Figure 5 For the embodiment of the present invention TimesNet With improved TimesNet Prediction error comparison chart of ; Figure 6 For the embodiment of the present invention FEDformer Comparison chart of prediction errors with the model of the present invention. DETAILED DESCRIPTION

[0024] like Figure 1 As shown, the power load forecasting method based on VMD algorithm and improved TimesNet includes the following steps: S1: Collect power load data to obtain data set D1, and normalize data set D1 to obtain data set D2; S2: Decompose the load data D2 into modal components of different frequencies using the VMD algorithm; S3: Taking the envelope entropy as the fitness function of the MPA algorithm, the MPA optimization algorithm is used to optimize the decomposition number and penalty factor of the modal component; S4: optimally decompose the power load data according to the decomposition number obtained in step S3 to obtain optimized modal components, divide them into a training set and a test set, input the training set into the improved TimesNet model for training, and extract the multi-periodic characteristics of the power load; S5: Input the test set into the trained improved TimesNet model to obtain the power load forecasting results.

[0025] Furthermore, the dataset D1 is normalized in step S1 to obtain the dataset D2, which is expressed as follows: ; In the formula, y i represents the normalized data, x i Represents the original data of power load, x max and x min Represent the maximum and minimum values ​​in data set D1 respectively.

[0026] In step S2, the VMD algorithm includes: (1) Constructing a variational constraint model ; In the formula, u k is the decomposed modal component, w k is the center frequency of the mode, Represents a function of time t Find the partial derivative, represents the unit impulse function, k represents the decomposition number, j represents an imaginary unit; (2) By introducing the quadratic penalty term α and the Lagrange multiplier λ, and augmenting the Lagrangian function L, the constrained problem is transformed into an unconstrained variational problem, expressed as: ； In the formula, α represents the quadratic penalty term, λ represents the Lagrange multiplier, L represents the augmented Lagrangian function; (3) Use the alternating direction multiplier algorithm to perform a series of iterations to find the optimal solution, expressed as: ; ; ; In the formula, τ represents the noise tolerance, , , They are , , Fourier transform of for Fourier transform of (4) Convergence condition, expressed as: ; In the formula, Represents an arbitrarily small positive number.

[0027] Furthermore, the MPA optimization algorithm is used to optimize the decomposition number and penalty factor of the modal component, including the following steps: (1) Initialize the MPA algorithm parameters, including the population size n, dimension d, maximum number of iterations Max_Iter, etc.; (2) Initialize the population, set the range of k and α, and use the envelope entropy as the fitness function of VMD; (3) Preliminarily calculate the fitness of all populations based on the initial parameters and find the position of the initial population with the smallest fitness value; (4) Update the population position through the three optimization stages of the MPA algorithm, continuously iterate, recalculate the fitness, and select the minimum fitness value to determine the optimal population position; (5) If the current number of iterations Iter reaches the set maximum value Max_Iter, the iteration ends and the optimal hyperparameters k and α of variational mode decomposition VMD are obtained; otherwise, the above iteration process is repeated, Iter = Iter + 1, until the current number of iterations reaches the set threshold; (6) Output the optimal parameters k and α, and use VMD with the optimal parameters to decompose the original signal into k modal components.

[0028] In step S3, the objective function envelope entropy includes the following steps: (1) Calculation envelope ; Where H represents the Hilbert transform, α(i) represents the input data set x(i), i=1,2, ,m, envelope signal sequence obtained after Hilbert transform; m Indicates the number of data samples in the dataset; (2) Normalization ; Where P j represents the envelope signal of α(j) after normalization; (3) Calculation of envelope entropy ; In the formula, Represents the envelope entropy of the signal; Indicates P j Find the base 10 logarithm; In an embodiment, the MPA algorithm comprises the following steps: (1) MPA initializes the element X in the prey matrix Prey according to the population size n and dimension d ij Construct the n×d dimensional matrix Prey: ； ； Where X max and X min are the upper and lower limits of the variable, respectively, and rand is a uniform random function ranging from 0 to 1. (2) Construct the elite matrix Elite, which consists of the individuals with the best fitness in Prey Copy n times to form: ； In the embodiment, the MPA optimization process simultaneously simulates the life activities of the predator and the prey while considering different speed ratios, and is divided into three stages according to the relationship between the number of iterations Iter and the maximum number of iterations Max_Iter: Phase 1: Exploration phase, when Iter< When Max_Iter, it is a high rate ratio, the prey moves faster than the predator, and the predator adopts a static strategy, and the expression is: ； ； In the formula, is a random number vector based on a normal distribution, representing Brownian motion, Indicates that the corresponding elements are multiplied one by one, Multiplying with Prey simulates the movement of prey. P is a constant with a value of 0.5. .

[0029] Phase 2: Transition phase, when Max_Iter <Iter< At Max_Iter, the rate ratio is the same, and the prey and predator have the same speed.

[0030] For the first half of the population: ； ； In the formula, is a random number vector based on Lévy distribution, representing the Lévy motion, Multiplying by Prey simulates the Lévy motion of prey, where .

[0031] For the second half of the population: ； ； in is an adaptive parameter that controls the predator's movement step size, Multiplying with Elite simulates the predator Brownian motion, .

[0032] Phase 3: Development phase, when Iter> At Max_Iter, it is a low rate ratio, and the predator moves faster than the prey. The mathematical expression of this process is: ； ； in Multiply with Elite to simulate Predator Lévy movement.

[0033] In addition, eddies and fish gatherings will change the behavior of predators. Predators have the probability to jump in space and jump out of FADs to find another environment where prey is distributed. The mathematical expression is: ； Where FADs=0.2 is a constant, which indicates the probability of predator space jump. is a randomly generated binary vector containing an array of 0 and 1. If the array is less than 0.2, the array is 0. If the array is greater than 0.2, the array is 1. r is a uniform random number in the range [0,1]. r1 and r2 are two random subscripts of Prey.

[0034] The current solution is continuously updated through the above process until the algorithm termination condition is met and the optimal solution is obtained.

[0035] like Figure 2 As shown, the improved TimesNet network of step S4 is composed of multiple stacked TimesBlocks in a residual connection manner, including the following steps: (1) For a one-dimensional time series X 1D Perform Fast Fourier Transform FFT to analyze the spectrum: ； In the formula, , Represents the real number space, where T is the time length, C is the channel dimension, A represents the calculation of the average amplitude of different frequencies, FFT represents the fast Fourier transform of the one-dimensional time series to the frequency domain, Amp represents the amplitude calculated from the time series converted to the frequency domain, and Avg represents the average amplitude.

[0036] (2) Take the k frequencies corresponding to the largest amplitude and record them from large to small as f1, ,f k , corresponding to the period p1,┄,p k for: ； In the formula, the frequency from large to small is recorded as f 1 , ,f k , the corresponding frequency period is recorded from large to small as p 1,┄,p k ； (3) Fold the one-dimensional time series based on the selected period and reconstruct the one-dimensional time series into a two-dimensional tensor , the expression is: ； In the formula, Represents a two-dimensional tensor, Padding represents the zero-padding function of the time series, and Reshape represents the reconstruction of a one-dimensional sequence into a two-dimensional tensor. ; (4) Extracting time series features using 2D convolutional network Inception Block , where the expression is:

[0037] In the formula, Represents the time series characteristics, A function representing the 2D convolutional network Inception module; (5) Reconstruct the extracted time series features back into one-dimensional space, expressed as: ； In the formula, Trunc means removing the 0 added by the Padding operation. express Convert from a 2D tensor to a 1D sequence.

[0038] (6) The k one-dimensional representations are weighted and summed according to the strength of their corresponding frequencies to complete information aggregation and obtain the final output of TimesBlock , the expression is: ； ； Where Softmax is the activation function, Represents the output prediction result, Represents the weighted summation of frequencies.

[0039] Furthermore, in step S4, the improved TimesNet model is an improvement on the two-dimensional temporal feature extraction network Inception Block. It uses serially connected n×1 and 1×n convolutions to replace the original n×n convolution, which can reduce the number of parameters and computational complexity while maintaining good performance.

[0040] In this embodiment, Inception Block is a parallel convolutional neural network, which contains four branches, namely, 1x1 convolution alone as a branch, 1x1 convolution, 1x3 convolution and 3x1 convolution in series as a branch, 1x1 convolution, 1x5 convolution and 5x1 convolution in series as a branch, and the maximum pooling layer and 1x1 convolution in series as a branch. Finally, the feature maps output by each branch are spliced ​​together in the depth direction to form the final output of Inception Block. This multi-branch structure using different convolution kernel sizes or pooling operations enables Inception Block to learn features of different sparse scales while maintaining high accuracy.

[0041] Algorithm analysis: The power load data of the present invention comes from the power load data of a certain area in Hubei Province from October 1 to December 31, 2022, and is sampled every 15 minutes. The obtained power load data is decomposed using the VMD algorithm optimized by the MPA algorithm, such as Figure 3 The power load forecasting result obtained by using the method proposed in the present invention is as follows Figure 4 As shown, its mean absolute percentage error is 4.02%.

[0042] In order to verify the effectiveness of the MPA-VMD decomposition proposed in the present invention, the prediction results of the present invention are compared with the prediction results obtained without MPA-VMD decomposition, and the prediction error is obtained by subtracting the true value from the predicted value. The comparison results between the two are as follows: Figure 5 As shown in Figure 2, the average absolute percentage error is reduced from 6.23% to 4.02%. In order to verify the prediction accuracy of the present invention, the prediction results of the present invention and the FEDformer model are compared, as shown in Figure 2. Figure 6 As shown, compared with the FEDformer model, the average absolute percentage error of the present invention is reduced from 8.63% to 4.02%. In summary, the present invention effectively improves the accuracy and precision of power load forecasting.

Claims

1. The power load forecasting method based on VMD algorithm and improved TimesNet is characterized by: The following steps are involved: S1, collecting power load data to obtain a data set D1, and normalizing the data set D1 to obtain a data set D2; S2, using VMD algorithm to decompose the load data of data set D2 into modal components of different frequencies; S3, using the envelope entropy as the objective function of the marine predator optimization algorithm, and using the marine predator optimization algorithm to optimize the decomposition number and penalty factor of the modal components to obtain the optimal number of modal components; S4, decomposing the load data of the data set D2 according to the optimal number of modal components obtained in step S3 to obtain optimized modal components, and further dividing them into a training set and a test set, inputting the training set into the improved TimesNet model for training, and extracting the multi-periodic characteristics of the power load; S5. Input the test set into the trained improved TimesNet model, add the prediction results of each modal component, and obtain the power load prediction result.

2. The power load forecasting method based on VMD algorithm and improved TimesNet according to claim 1 is characterized in that: In step S1, the calculation formula for normalizing the data set D1 is: ； In the formula, y i represents the normalized data, x i Represents the original data of power load, x max and x min Represent the maximum and minimum values ​​in data set D1 respectively.

3. The power load forecasting method based on VMD algorithm and improved TimesNet according to claim 1 or 2, characterized in that: In step S2, the VMD algorithm specifically includes: (1) Construct a variational constraint model, expressed as: ； In the formula, u k is the decomposed modal component, w k is the center frequency of the mode, Represents a function of time t Find the partial derivative, represents the unit impulse function, k represents the decomposition number, j represents an imaginary unit; (2) By introducing the quadratic penalty term and Lagrange multiplier, the constraints are transformed into unconstrained variational conditions by augmenting the Lagrangian function, expressed as: ； In the formula, α represents the quadratic penalty term, λ represents the Lagrange multiplier, L represents the augmented Lagrangian function; (3) Use the alternating direction multiplier algorithm to iteratively find the optimal solution, the expression is: ； ； ； In the formula, τ represents the noise tolerance, , , They are , , Fourier transform of for Fourier transform of (4) The convergence condition expression is: ； In the formula, Represents an arbitrarily small positive number.

4. The power load forecasting method based on VMD algorithm and improved TimesNet according to claim 3 is characterized in that: In step S3, the specific process of calculating the envelope entropy of the objective function is: (1) Calculate the envelope using the following formula: ； Where H represents the Hilbert transform, α(i) represents the input data set x(i), i=1,2, ,m, envelope signal sequence obtained after Hilbert transform; m Indicates the number of data samples in the dataset; (2) Normalization processing, the calculation formula is: ； In the formula, P j represents the envelope signal of α(j) after normalization; (3) Calculate the envelope entropy using the following formula: ； In the formula, Represents the envelope entropy of the signal; Indicates P j Find the base 10 logarithm.

5. The power load forecasting method based on VMD algorithm and improved TimesNet according to claim 4 is characterized in that: In step S3, the method of optimizing the decomposition quantity and penalty factor of the modal component by using the marine predator optimization algorithm specifically includes: (1) Initialize the parameters of the marine predator optimization algorithm, including population size, dimension, and maximum number of iterations; (2) Initialize the population, set the decomposition number and penalty factor range, and use the envelope entropy as the fitness function of VMD; (3) Preliminarily calculate the fitness of all populations based on the initial parameters and find the position of the initial population with the smallest fitness value; (4) Update the population position through the three optimization stages of the marine predator optimization algorithm: exploration stage, transition stage, and development stage, continuously iterate, recalculate the fitness, and select the minimum fitness value to determine the optimal population position; (5) If the current number of iterations reaches the set maximum value, the iteration ends and the optimal hyperparameter decomposition number and penalty factor of variational mode decomposition VMD are obtained; otherwise, the above iterative process is repeated until the current number of iterations reaches the set threshold; (6) Output the optimal parameter decomposition number and penalty factor.

6. The power load forecasting method based on VMD algorithm and improved TimesNet according to claim 5 is characterized in that: In step S4, the TimesNet network includes a plurality of stacked TimesBlocks connected in a residual connection manner, and each TimesBlock processes the input signal data as follows: (1) Perform fast Fourier transform analysis on the one-dimensional time series spectrum, the expression is: ； Where, X 1D represents a one-dimensional time series, , represents the real number space, where T Indicates the length of time, C represents the channel dimension, A It means calculating the average amplitude of different frequencies. FFT Indicates that the one-dimensional time series is converted into a frequency domain function by fast Fourier transform. Amp Represents the function of calculating the amplitude of the time series converted to the frequency domain, Avg represents the amplitude averaging function; (2) Take the frequency corresponding to the maximum amplitude and calculate the corresponding period through the frequency. The expression is: ； In the formula, the frequency from large to small is recorded as f 1 , ,f k , the corresponding frequency period is recorded from large to small as p 1 ,┄,p k ； (3) Based on the selected period, the one-dimensional time series is folded and reconstructed into a two-dimensional tensor, which is expressed as: ； In the formula, Represents a two-dimensional tensor, Padding represents the zero-padding function of the time series, and Reshape represents the reconstruction of a one-dimensional sequence into a two-dimensional tensor. ; (4) Use 2D convolutional network to extract temporal features, the expression is: ； In the formula, Represents the time series characteristics, A function representing the 2D convolutional network Inception module; (5) Reconstruct the extracted time series features back into one-dimensional space, expressed as: ； In the formula, Trunc represents the zero removal function of the time series, Represents a two-dimensional tensor The transformed one-dimensional sequence; (6) The obtained one-dimensional representation is weighted and summed according to the intensity of its corresponding frequency to complete information aggregation and obtain the final output , the expression is: ； ； In the formula, Softmax represents the activation function, Represents the output prediction result, Represents the weighted summation of frequencies.

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