Signal prediction method based on IVMD-EMD fusion feature and LSTM network

Abstract

The invention relates to the technical field of quasi-periodic non-stationary signal prediction, in particular to a signal prediction method based on IVMD-EMD fusion features and an LSTM network. Comprising the following steps: S1, preprocessing data by averaging adjacent data and deleting repeated data; s2, performing primary decomposition on the data by using CEEMDAN, and calculating a sample entropy of an intrinsic mode component obtained by decomposition; s3, according to the sample entropy, integrating the sample entropy into three integrated intrinsic mode functions, and respectively inputting a low-frequency component Co-IMF2 and a trend component Co-IMF3 in the three integrated intrinsic mode functions into a network structure of the single-variable long-short-term memory network; s4, performing secondary decomposition on the high-frequency component Co-IMF1 by using improved variational mode decomposition which combines a multi-scale sample entropy, an energy loss coefficient, a frequency extreme point and an adjacent mode main frequency interval to realize optimization of a preset mode number K, and inputting an IMF component obtained by decomposition into a multivariable LSTM network structure; and S5, integrating the component prediction results to obtain a final prediction result.

Description

Technical Field

[0001] The present invention relates to the technical field of quasi-periodic non-stationary signal prediction, and in particular to a signal prediction method based on IVMD-EMD fusion features and LSTM network. Background Art

[0002] Quasi-periodic non-stationary signals refer to signals that have approximately periodic characteristics, but this periodicity is not strictly fixed. In addition, the statistical characteristics of the signal also change over time, showing non-stationarity. Many signals in real life, such as biomedical signals, economic and financial data, and agricultural and livestock price data, are such signals. Analyzing historical data, mining its complex relationship patterns, and accurately predicting future data are of great significance in many fields.

[0003] However, due to the unique complexity of quasi-periodic non-stationary signals, it is difficult to directly apply traditional methods to extract stable features from the signal for prediction, and it becomes particularly difficult to establish an accurate mathematical model to describe the dynamic changes of the signal. At present, scholars at home and abroad have explored many different prediction methods, covering statistical analysis models, econometric models, machine learning algorithms, etc. Among them, the methods of neural networks and machine learning models have broken through the limitations of traditional data characteristics due to their strong adaptability and nonlinear mapping capabilities. They can capture historical data fluctuations more finely and perform well in processing complex quasi-periodic non-stationary signals. However, due to the complex signal characteristics, the performance of a single prediction method is often not ideal. The combined prediction method that integrates multiple strategies combines the advantages of multiple prediction methods and further improves the stability and accuracy of the prediction model. It is currently a hot research topic in this direction.

[0004] After searching, the patent number "CN202211139921.7" disclosed in "Prediction method for hemispherical resonant gyroscope stability period based on time series-entropy RBF neural network of CEEMDAN" includes steps 1: collecting gyroscope output signal data; 2: decomposing to obtain IMF component signal and residual signal; 3: testing the stability of IMF component signal; 4: establishing an ARMA prediction model for IMF component signal that meets the stability; 5: establishing an entropy RBF neural network prediction model for IMF component signal that does not meet the stability; 6: establishing a gyroscope output prediction model and verifying the accuracy of the model, which effectively improves the accuracy of gyroscope output prediction; 7: when the gyroscope output prediction value is within the stable range, the gyroscope output is continuously predicted by rolling forward in time; when the output prediction value exceeds the stable range for the first time, the gyroscope stability period is obtained;

[0005] This method has the following defects:

[0006] (1) The performance of RBF neural network for highly complex and nonlinear systems may not be as good as other more complex neural network structures, resulting in low model accuracy;

[0007] (2) During the training process, the RBF neural network needs to calculate the distance from each sample point to the center, which leads to high computational complexity. Especially when processing large-scale data, the training time may be long.

[0008] The patent number "202311581023.1" discloses the "Wind power probability prediction method and system based on diffusion model and non-stationary signal enhancement". First, based on the special imaging mechanism of infrared images, an improved CLBP feature - MSF-CLBP is extracted for the target in the infrared scene to express texture information, and an improved local HOG feature - HOG-FV is used to express shape information to discover effective features in the target; secondly, for the two heterogeneous features extracted above, a series fusion method is used for feature fusion, so that the description of the target feature information is more objective and comprehensive. Finally, a classifier that integrates multi-core classification and the TrAdaBoost transfer learning framework is designed, which effectively solves the problem of lack of labeled infrared sample images, and at the same time enhances the distinguishability of the data to be classified to obtain better recognition effects;

[0009] This method has the following defects:

[0010] (1) Diffusion models and non-stationary signal enhancement methods greatly increase the complexity of the model and are slow to process large-scale data;

[0011] (2) HOG’s expression of shape information has limited impact on target feature mining. Summary of the invention

[0012] The purpose of the present invention is to combine signal decomposition technology with deep neural networks, and design a combined prediction model based on complete ensemble empirical mode decomposition, improved variational mode decomposition and long short-term memory network (CEEMDAN-IVMD-LSTM) to achieve accurate prediction of quasi-periodic non-stationary signals according to the complex characteristics of quasi-periodic non-stationary signals.

[0013] To achieve the above object, the present invention provides a signal prediction method based on IVMD-EMD fusion features and LSTM network, comprising the following steps:

[0014] S1: Preprocess the data by averaging adjacent data and removing duplicate data;

[0015] S2: Use CEEMDAN to decompose the data once and calculate the sample entropy of the intrinsic mode function (IMF) obtained by decomposition;

[0016] S3: According to the sample entropy, it is integrated into three integrated intrinsic mode functions (Co-IMF), and the low-frequency component Co-IMF2 and the trend component Co-IMF3 are respectively input into the network structure of the univariate long short-term memory network (Long Short-Term Memory, LSTM);

[0017] S4: The high-frequency component Co-IMF1 is decomposed twice using the improved variational mode decomposition (IVMD) that combines multi-scale sample entropy (SE), energy loss coefficient, frequency extreme point and adjacent modal main frequency interval to achieve the optimization of the preset modal number K, and then the IMF components obtained by the decomposition are input into the multivariate LSTM network structure;

[0018] S5: Integrate the prediction results of each component to obtain the final prediction result.

[0019] The original data set may have missing data values, anomalies, etc. due to errors in the collection process, equipment failures, human input errors, or data transmission problems. Therefore, the data set needs to be preprocessed and analyzed to improve the integrity, accuracy, and reliability of the data. The missing values ​​are processed by averaging adjacent data and outliers are removed. The Augmented Dickey-Fuller (ADF) test is further used to test the stationarity of the data, and the Ljung-Box test is used to test the autocorrelation of the data to analyze whether the input time series is non-stationary and whether it contains strong autocorrelated noise.

[0020] Preferably, the formula for the first decomposition in S2 is:

[0021]

[0022] Where x(t) is the input of the time series, n is the number of IMF components obtained by decomposition, and r(t) is the residual component.

[0023] The EMD algorithm can decompose the signal according to the time characteristics of the data itself without defining any basis functions in advance. Due to this feature, it shows significant superiority in processing non-stationary and nonlinear data. EMD can decompose a time series into multiple IMF components and a residual component that reflects the trend of the signal, as described in equation (1). Each IMF represents a narrowband signal with a specific vibration frequency range and modulation amplitude, reflecting the characteristics of the original series at different time scales.

[0024] Each IMF component satisfies the following two conditions:

[0025] (1) In the entire sequence range, the number of local extreme points and zero-crossing points should be consistent, or the difference should not exceed 1;

[0026] (2) At any time, the average value of the upper envelope formed by the local maximum value of the sequence and the average value of the lower envelope formed by the local minimum value must be zero.

[0027] Although EMD performs well in processing nonlinear and non-stationary signals, it still has some inherent problems, such as mode mixing. Mode mixing means that an IMF contains multiple components of different time scales, or similar time scale components are scattered in different IMFs, which makes it impossible to completely distinguish different frequency bands of the signal, thus greatly affecting the signal decomposition performance.

[0028] Preferably, the CEEMDAN signal decomposition step in S2 is:

[0029] S2.1: Add N Gaussian white noises to the original signal y(t) to construct a total of N preprocessed sequences yn(t) (n=1, 2, ..., N)

[0030] y n (t) = y(t) + ε 0 δ n (t)#(2)

[0031] where ε 0 is the weight coefficient of Gaussian white noise, δ n is the Gaussian white noise processed for the nth time;

[0032] S2.2: For all y n (t) Perform EMD decomposition to obtain the first IMF component, take its mean as the first IMF component, and update the residual at the same time;

[0033] S2.3: Similarly, the residual r 1(t) Add Gaussian white noise to construct new N preprocessed sequences, continue to perform EMD decomposition on them, calculate their mean to obtain the second IMF component, and update the residual, where Ej(·) represents the jth IMF component after the sequence is decomposed by EMD. By further analogy, the formula for the residual in the mth stage is:

[0034] r m (t) = r m-1 (t)-IMF m (t)#(3)

[0035] S2.4: R m (t)+ε m E m (δ n (t)) Perform N times of EMD decomposition to obtain the m+1th IMF sequence;

[0036] S2.5: Repeat the above steps until the decomposition stops after reaching the set stop threshold. Finally, the expression of y(t) after CEEMDAN decomposition is:

[0037]

[0038] CEEMDAN is derived from the empirical mode decomposition algorithm and is an improved method for the modal aliasing problem generated during the EMD decomposition process. CEEMDAN adds a limited amount of adaptive Gaussian white noise sequence to the original signal and the residual of each level to obtain multiple groups of disturbance signals for multiple decompositions, and averages the modes to obtain more accurate and stable results.

[0039] Preferably, the intrinsic modal component IMF of the variational modal decomposition in S2 is defined as amplitude-frequency modulation (AM-FM) expressed as:

[0040]

[0041] Where t represents time is the instantaneous phase, A k (t) is the envelope amplitude of the IMF component, ω k (t) is the instantaneous frequency.

[0042] VMD is a signal decomposition method based on variational mode. It decomposes the signal into a series of modal components with different center frequencies and certain bandwidths by finding the optimal solution to the variational problem. Different from the EMD algorithm, VMD is based on a certain mathematical foundation. It converts the cyclic iterative decomposition process of the signal into the framework of the variational problem and realizes the adaptive decomposition of the signal by finding the optimal solution of the constrained variational problem model.

[0043] Preferably, the calculation formula of the S2 sample entropy is:

[0044]

[0045] Where τ is the scale factor;

[0046] By By calculating the sample entropy value, we can get the multi-scale sample entropy of the time series:

[0047]

[0048] Among them, E SE is the sample entropy.

[0049] The present invention proposes to make corresponding improvements based on the standard VMD algorithm from the aspects of time domain and frequency domain:

[0050] Multi-scale sample entropy MSE. The entropy value reflects the degree of disorder (i.e., complexity) of the time series. In the process of VMD decomposition, the modal component or residual sample entropy (SE) under different modal numbers is often used as a criterion for decomposition quality. However, since sample entropy can only analyze data at a single time scale, it ignores the behavior of data at other scales, which limits its effectiveness in processing nonlinear and non-stationary signals. MSE performs a series of coarse-graining processes on the original signal, enabling it to analyze the complexity of the signal at multiple scales.

[0051] Preferably, the ratio of the energy of the decomposition residual to the energy of the original signal is:

[0052]

[0053] where u k represents the kth IMF component, ∑u k Represents the reconstructed signal. The larger the e is, the more information is lost during the signal decomposition process.

[0054] There will be some energy loss in the decomposition process of VMD, that is, the reconstructed IMF components after decomposition cannot be completely equal to the original signal. Therefore, the energy loss coefficient is considered as one of the evaluation indicators.

[0055] Preferably, the K value algorithm steps in S4 are as follows:

[0056] ①, the initial modal number range is selected as K[2, 10], the step size is 1, and other parameters including penalty factor α and bandwidth τ take the default values ​​α=2000 and T=0 respectively;

[0057] ② Perform VMD decomposition on the signal with the set K value and obtain 10 IMFs respectively j Sequence, and then calculate the multi-scale sample entropy of the corresponding residual term And select the three IMFs with the smallest entropy value K j ;

[0058] ③、For the IMF selected in ② j Reconstruct and calculate the energy loss coefficient e respectively, and select IMF′ with e less than the threshold value of 0.01 j ;

[0059] ④、Then calculate the selected IMF′ j The sample entropy value of Select The maximum amount is Then separately ask The maximum extreme point Pf;

[0060] ⑤. Determine P f Is it from the noise component? If it is from the noise component, return to ④ and select The second largest component; otherwise, the filtered The main frequency interval of each adjacent component is averaged and obtained

[0061]

[0062] ⑥Comparison The largest The corresponding K value is the optimal mode number K best ; If there are multiple identical largest values, compare the sample entropy of the residual term obtained in ②, and the K value corresponding to the smallest sequence is the optimal modal number K best .

[0063] VMD decomposition determines the optimal solution through cyclic iterative updates, thereby obtaining the limited bandwidth and center frequency of the IMF modal components, and adaptively separating the signal frequency domain information. An obvious feature of VMD is that the number of modes can be specified by setting the K value. If the K value is too small, multiple frequency components may be merged into one mode, thereby losing some important information of the signal. If the K value is too large, noise or non-main components may be extracted as independent modes. If the K value is selected appropriately, modal aliasing can be greatly avoided.

[0064] MSE can be used to evaluate the complexity of each mode obtained by VMD decomposition at different time scales. MSE is extremely sensitive to noise and its values ​​are significantly different for signals of different complexity. Using MSE can help us judge the quality of VMD decomposition and then select the K value.

[0065] From the frequency domain perspective, the ideal situation after the signal is decomposed by VMD should be that each IMF component has its own clearly defined frequency center and there is no aliasing with other IMF components. Therefore, we believe that the clarity and separation of the frequency domain maximum can be used as an indicator of modal purity, and the frequency domain maximum of each IMF component represents the most significant frequency feature of the IMF component. Therefore, if there is only one significant extreme point in the frequency domain of the IMF component, it means that no modal aliasing occurs inside it, and the IMF component is a completely decomposed IMF; on the contrary, if the frequency domain maxima of multiple IMF components are close to or overlap each other, it indicates that modal aliasing occurs, indicating that the signal has not been completely decomposed.

[0066] The above indicators are all indicators for detecting under-decomposition of VMD. Over-decomposition can also lead to the appearance of false components or pure noise components. At this time, the main frequencies of adjacent IMF components are highly similar in the frequency domain. Therefore, by checking the distance between the main frequencies of adjacent IMF components, it can be determined whether there is over-decomposition.

[0067] The LSTM neural network prediction model is:

[0068] LSTM essentially expands the memory of the Recurrent Neural Network (RNN), enabling it to maintain and learn long-term dependencies of inputs. Compared with other neural networks, LSTM is more efficient and stable when processing long sequence data.

[0069] The structure consists of an input layer, an LSTM layer, a random dropout layer (Dropout layer), and a fully connected layer (Dense layer). The None in the input layer indicates that the sample of the input data can be arbitrary during model training and prediction. 30 is the set time step, indicating that the data is associated with the 30 previous data of the data. 3 is the number of features, indicating that there are 3 features at each time step. The LSTM layer is usually set to less than 4 layers and the number of units is set to less than 200. The main reason is that too many layers or units will greatly increase the time complexity, while the improvement of prediction accuracy is limited. The Dropout layer is used to prevent the model from relying on noise or specific features in the training data, thereby reducing overfitting and improving the generalization ability of the model. The main function of the Dense layer is to further process and transform the features extracted by LSTM to obtain the final output result.

[0070] The Tanh function is selected as the activation function inside the LSTM layer, and the optimizer selects the Adam optimizer with mean square error (MSE) as the loss. The Tanh activation function maps the input value to between -1 and 1, and its shape is an S-shaped curve. Since the output value is centered at 0, this helps reduce the offset phenomenon during training and further improves the convergence speed of the model.

[0071]

[0072] f′(x)=1-Tanh 2 x#(10).

[0073] Hybrid prediction model integrating decomposition algorithm and neural network:

[0074] The proposed hybrid prediction model of fusion decomposition algorithm and neural network is divided into signal decomposition part and two basic prediction model parts, namely single variable prediction model and multivariate prediction model. Among them, the single variable prediction model refers to inputting each Co-IMF into the LSTM neural network prediction model to obtain the prediction results of each single variable. The multivariate prediction model takes multiple Co-IMFs as feature vectors and inputs them into the LSTM neural network prediction model.

[0075] The sample entropy of the IMF components obtained after CEEMDAN decomposition is calculated separately to group them into three Co-IMF components. Then, the low-frequency component Co-IMF2 and the trend component Co-IMF3 are normalized and input into the univariate prediction model respectively. In the test data set experiment, multiple evaluation indicators perform well, especially for the prediction of medium-frequency time series. However, due to its high complexity and great volatility, the prediction results directly input into the univariate prediction model are poor in accuracy. Therefore, it is necessary to use IVMD to perform secondary decomposition of the high-frequency component Co-IMF1 to improve the prediction accuracy. At the same time, in order to reduce the time cost, each IMF component obtained after IVMD decomposition is selected as a feature input into the multivariate prediction model. The prediction results obtained are input into the multivariate prediction model together with the prediction results obtained by the Co-IMF2 and Co-IMF3 univariate prediction models as feature vectors to obtain the final prediction results.

[0076] The beneficial effects of the present invention are:

[0077] When in use, the present invention utilizes a signal decomposition algorithm to fuse a deep neural network to solve the prediction problem of quasi-periodic non-stationary signals. The signal decomposition algorithm can decompose the time series signal into multiple sub-signals in different frequency domains, which can fully highlight the characteristics of different frequency bands of the signal and mine key information such as the trend, periodicity, and noise of the time series signal changes. The deep learning model captures the complex nonlinear relationship between these factors, and combines them as a combined prediction model, thereby effectively improving the prediction accuracy and generalization ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0079] Figure 1 It is the prediction flow chart of CEEMDAN-IVMD-LSTM hybrid model;

[0080] Figure 2 It is the CEEMDAN decomposition flow chart;

[0081] Figure 3 It is the flow chart of IVMD decomposition algorithm;

[0082] Figure 4 It is a flowchart of the LSTM neural network structure;

[0083] Figure 5 It is the prediction model flow chart of CEEMDAN-IVMD-LSTM hybrid model;

[0084] Figure 6 This is the price data prediction result chart of the CEEMDAN-IVMD-LSTM hybrid model. DETAILED DESCRIPTION

[0085] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, and preferably the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0086] In the description of the present invention, it should be understood that the terms "length", "width", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, in the description of the present invention, "multiple" means two or more, unless otherwise clearly and specifically defined.

[0087] See also Figures 1 to 6 The present invention provides a signal prediction method based on IVMD-EMD fusion features and LSTM network, comprising the following steps:

[0088] S1: Preprocess the data by averaging adjacent data and removing duplicate data;

[0089] S2: Use CEEMDAN to decompose the data once and calculate the sample entropy of the intrinsic mode function (IMF) obtained by decomposition;

[0090] S3: According to the sample entropy, it is integrated into three integrated intrinsic mode functions (Co-IMF), and the low-frequency component Co-IMF2 and the trend component Co-IMF3 are respectively input into the network structure of the univariate long short-term memory network (Long Short-Term Memory, LSTM);

[0091] S4: The high-frequency component Co-IMF1 is decomposed twice using the improved variational mode decomposition (IVMD) that combines multi-scale sample entropy (SE), energy loss coefficient, frequency extreme point and adjacent modal main frequency interval to achieve the optimization of the preset modal number K, and then the IMF components obtained by the decomposition are input into the multivariate LSTM network structure;

[0092] S5: Integrate the prediction results of each component to obtain the final prediction result.

[0093] The formula for one decomposition in S2 is:

[0094]

[0095] Where x(t) is the input of the time series, n is the number of IMF components obtained by decomposition, and r(t) is the residual component.

[0096] The CEEMDAN signal decomposition steps in S2 are:

[0097] S2.1: Add N Gaussian white noises to the original signal y(t) to construct a total of N preprocessed sequences yn(t) (n=1, 2, ..., N)

[0098] y n (t) = y(t) + ε 0 δ n (t)#(2)

[0099] where ε 0 is the weight coefficient of Gaussian white noise, δ n is the Gaussian white noise processed for the nth time;

[0100] S2.2: For all y n (t) Perform EMD decomposition to obtain the first IMF component, take its mean as the first IMF component, and update the residual at the same time;

[0101] S2.3: Similarly, the residual r 1 (t) Add Gaussian white noise to construct new N preprocessed sequences, continue to perform EMD decomposition on them, calculate their mean to obtain the second IMF component, and update the residual, where Ej(·) represents the jth IMF component after the sequence is decomposed by EMD. By further analogy, the formula for the residual in the mth stage is:

[0102] r m (t) = r m-1 (t)-IMF m (t)#(3)

[0103] S2.4: R m (t)+ε m E m (δ n (t)) Perform N times of EMD decomposition to obtain the m+1th IMF sequence;

[0104] S2.5: Repeat the above steps until the decomposition stops after reaching the set stop threshold. Finally, the expression of y(t) after CEEMDAN decomposition is:

[0105]

[0106] The intrinsic modal component IMF of the variational modal decomposition in S2 is defined as amplitude-frequency modulation (AM-FM) expressed as:

[0107]

[0108] Where t represents time is the instantaneous phase, A k (t) is the envelope amplitude of the IMF component, ω k (t) is the instantaneous frequency.

[0109] The calculation formula of the S2 sample entropy is:

[0110]

[0111] Where T is the scale factor;

[0112] By all T By calculating the sample entropy value, we can get the multi-scale sample entropy of the time series:

[0113]

[0114] Among them, E SE is the sample entropy.

[0115] The ratio of the energy of the decomposition residual to the energy of the original signal is:

[0116]

[0117] where u k represents the kth IMF component, ∑u k Represents the reconstructed signal. The larger the e is, the more information is lost during the signal decomposition process.

[0118] The steps of the K value algorithm in S4 are as follows:

[0119] ①, the initial modal number range is selected as K[2, 10], the step size is 1, and other parameters including penalty factor α and bandwidth τ take the default values ​​α=2000 and T=0 respectively;

[0120] ② Perform VMD decomposition on the signal with the set K value and obtain 10 IMFs respectively j Sequence, and then calculate the multi-scale sample entropy of the corresponding residual term And select the three IMFs with the smallest entropy value K j ;

[0121] ③、For the IMF selected in ② j Reconstruct and calculate the energy loss coefficient e respectively, and select IMF′ with e less than the threshold value of 0.01 j ;

[0122] ④、Then calculate the selected IMF′ j The sample entropy value of Select The maximum amount is Then separately ask The maximum extreme point Pf;

[0123] ⑤. Determine P f Is it from the noise component? If it is from the noise component, return to ④ and select The second largest component; otherwise, the filtered The main frequency interval of each adjacent component is averaged and obtained

[0124]

[0125] ⑥Comparison The largest The corresponding K value is the optimal mode number K best ; If there are multiple identical largest values, compare the sample entropy of the residual term obtained in ②, and the K value corresponding to the smallest sequence is the optimal modal number K best . Specific embodiment one:

[0127] In this embodiment:

[0128] First, the signal is decomposed once using Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) to obtain the intrinsic mode functions (IMFs) containing different frequency components. Then, the IMFs are integrated into three new conformity-intrinsic mode functions (Co-IMFs) using sample entropy: a high-frequency sequence Co-IMF1 with high complexity, a low-frequency sequence Co-IMF2 with moderate complexity, and a trend sequence Co-IMF3 with low complexity. The low-frequency component Co-IMF2 and the trend component Co-IMF3 are input into the long short-term memory (LSTM) univariate prediction model, and the high-frequency intrinsic mode component Co-IMF1 is decomposed twice using Improved Variational Mode Decomposition (IVMD). The IMF components obtained after the secondary decomposition are input into the LSTM multivariate prediction model as features. Finally, the Co-IMF components are integrated and input into the LSTM multivariate prediction model again to obtain the final prediction result.

[0129] Table 1 CEEMDAN-IVMD-LSTM hybrid prediction model indicators

[0130]

[0131]

[0132] What is disclosed above is only a preferred embodiment of the present invention, and it certainly cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of the above embodiment and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A signal prediction method based on IVMD-EMD fusion features and LSTM network, characterized in that: The following steps are involved: S1: Preprocess the data by averaging adjacent data and removing duplicate data; S2: Use CEEMDAN to decompose the data once and calculate the sample entropy of the intrinsic mode function (IMF) obtained by decomposition; S3: According to the sample entropy, it is integrated into three integrated intrinsic mode functions (Co-IMF), and the low-frequency component Co-IMF2 and the trend component Co-IMF3 are respectively input into the network structure of the univariate long short-term memory network (Long Short-Term Memory, LSTM); S4: The high-frequency component Co-IMFl is decomposed twice using the improved variational mode decomposition (IVMD) that combines multi-scale sample entropy (SE), energy loss coefficient, frequency extreme point and adjacent modal main frequency interval to achieve the optimization of the preset modal number K, and then the IMF components obtained by the decomposition are input into the multivariate LSTM network structure; S5: Integrate the prediction results of each component to obtain the final prediction result.

2. The signal prediction method based on IVMD-EMD fusion features and LSTM network according to claim 1, characterized in that: The formula for the first decomposition in S2 is: Where x(t) is the input of the time series, n is the number of IMF components obtained by decomposition, and r(t) is the residual component.

3. The signal prediction method based on IVMD-EMD fusion features and LSTM network according to claim 1, characterized in that: The CEEMDAN signal decomposition steps in S2 are: S2.1: Add N Gaussian white noises to the original signal y(t) to construct a total of N preprocessed sequences yn(t) (n=1, 2, ..., N) y n (t)=y(t)+ε0δ n (t)#(2) Where ε0 is the weight coefficient of Gaussian white noise, δ n is the Gaussian white noise processed for the nth time; S2.2: For all y n (t) Perform EMD decomposition to obtain the first IMF component, take its mean as the first IMF component, and update the residual at the same time; S2.3: Similarly, the residual r1(t) is added to Gaussian white noise to construct a new N preprocessed sequences, and the EMD decomposition is continued to be performed on it. The mean is calculated to obtain the second IMF component, and the residual is updated, where E j (·) represents the jth IMF component after EMD decomposition of the sequence. By further analogy, the formula for the residual at the mth stage is: r m (t)=r m-1 (t)-IMF m (t)#(3) S2.4: R m (t)+ε m E m (δ n (t)) Perform N times of EMD decomposition to obtain the m+1th IMF sequence; S2.5: Repeat the above steps until the decomposition stops after reaching the set stop threshold. Finally, the expression of y(t) after CEEMDAN decomposition is:

4. The signal prediction method based on IVMD-EMD fusion features and LSTM network according to claim 1, characterized in that: The intrinsic modal component IMF of the variational modal decomposition in S2 is defined as amplitude-frequency modulation (AM-FM) expressed as: Where t represents time is the instantaneous phase, A k (t) is the envelope amplitude of the IMF component, ω k (t) is the instantaneous frequency.

5. The signal prediction method based on IVMD-EMD fusion features and LSTM network as claimed in claim 1, characterized in that: The calculation formula of the S2 sample entropy is: Where τ is the scale factor; By all T By calculating the sample entropy value, we can get the multi-scale sample entropy of the time series: Among them, E SE is the sample entropy.

6. The signal prediction method based on IVMD-EMD fusion features and LSTM network as claimed in claim 3, characterized in that: The ratio of the energy of the decomposition residual to the energy of the original signal is: where u k represents the kth IMF component, ∑u k Represents the reconstructed signal. The larger the e is, the more information is lost during the signal decomposition process.

7. The signal prediction method based on IVMD-EMD fusion features and LSTM network according to claim 1, characterized in that: The steps of the K value algorithm in S4 are as follows: ①, the initial modal number range is selected as K[2, 10], the step size is 1, and other parameters including penalty factor α and bandwidth τ take the default values ​​α=2000 and τ=0 respectively; ② Perform VMD decomposition on the signal with the set K value and obtain 10 IMFs respectively j Sequence, and then calculate the multi-scale sample entropy of the corresponding residual term And select the three IMFs with the smallest entropy value K j ; ③、For the IMF selected in ② j Reconstruct and calculate the energy loss coefficient e respectively, and select IMF′ with e less than the threshold value of 0.01 j ; ④、Then calculate the selected IMF′ j The sample entropy value of Select The maximum amount is Then separately ask The maximum extreme point P f ; ⑤. Determine P f Is it from the noise component? If it is from the noise component, return to ④ and select The second largest component; otherwise, the filtered The main frequency interval of each adjacent component is averaged and obtained ⑥Comparison The largest The corresponding K value is the optimal mode number K best ; If there are multiple identical largest values, compare the sample entropy of the residual term obtained in ②, and the K value corresponding to the smallest sequence is the optimal modal number K best .

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