CN112231987B - Ionosphere forecasting method based on VMD and Elman neural network - Google Patents

Ionosphere forecasting method based on VMD and Elman neural network Download PDF

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CN112231987B
CN112231987B CN202011218421.3A CN202011218421A CN112231987B CN 112231987 B CN112231987 B CN 112231987B CN 202011218421 A CN202011218421 A CN 202011218421A CN 112231987 B CN112231987 B CN 112231987B
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汤俊
高鑫
李垠健
李长春
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East China Jiaotong University
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Abstract

The invention discloses an ionosphere prediction method based on a VMD (vector mode decomposition) and an Elman neural network, which is used for ionosphere TEC prediction modeling by combining a variational modal decomposition method and the Elman neural network. The invention utilizes the combination of Variational Modal Decomposition (VMD) and Elman neural network to carry out ionized layer TEC forecasting modeling. In consideration of the characteristics of nonlinearity, non-stationarity and the like of the ionized layer TEC sequence, the VMD algorithm can effectively reduce the complexity of the original sequence and does not generate modal aliasing phenomenon when the pretreatment is carried out on the TEC original sequence. Compared with a common EMD algorithm, the VMD can effectively avoid the occurrence of modal aliasing in the data preprocessing process, and the filtering and noise reduction performance is better. The invention introduces a VMD method to decompose the ionized layer TEC sequence to obtain a corresponding intrinsic mode component (IMF) and provide a high-quality input value for a subsequent prediction model.

Description

Ionosphere forecasting method based on VMD and Elman neural network
Technical Field
The invention relates to an ionosphere technology, in particular to an ionosphere forecasting method based on a VMD and Elman neural network.
Background
Currently, the ionosphere, which is an important component of the near-earth space environment, has a significant impact on the accuracy and real-time performance of navigation positioning systems and radio communications. Total Electronic Content (TEC) of the ionized layer is an important parameter of the ionized layer, and accurate prediction of the total electronic content can effectively avoid influence of the ionized layer on life of people. To search for a high-precision ionized layer TEC forecasting model, domestic and foreign scholars carry out extensive research and obtain certain achievements. The ionized layer has spatial-temporal disorder, randomness and nonlinearity, and if an inherent model is selected to forecast the electron content of the ionized layer, the obtained TEC precision cannot meet the application requirement, so that domestic and foreign scholars develop extensive research and obtain some achievements. The prediction of the ionized layer TEC is carried out by utilizing a time sequence model, and experiments show that the time sequence model is simple in structure and the prediction precision of the TEC is improved. In recent years, a neural network is widely applied in many fields as a typical nonlinear model, Li Hui et al predict 12 TEC values in a target day by using the neural network model, and experimental results show that the neural network model can better reflect the periodic and disturbance change characteristics of the TEC value of an ionized layer. The short-term prediction of TEC is carried out by establishing a time sequence and a BP (back propagation) neural network combination model by Lujianhua and the like, and the result shows that the prediction precision of the combination model is obviously improved compared with that of a single time sequence model. However, more and more researches show that the BP neural network has a slow learning speed and a low model stability, and is only a conventional static model. In order to further preprocess the original TEC data, so that the model has higher data quality during input, a scholars proposes a model combining Empirical Mode Decomposition (EMD) and time series to predict the TEC value; and predicting by combining Empirical Mode Decomposition (EMD) and an autoregressive neural network. The research results show that the prediction precision of the TEC has a remarkable improvement effect after the pretreatment is carried out on the original ionized layer TEC data. However, the EMD algorithm has the phenomenon of modal aliasing, which causes inaccurate signal decomposition, thereby affecting the TEC value prediction precision.
In the prior art:
in the data preprocessing method, the Empirical Mode Decomposition (EMD) algorithm essentially smoothes a signal, which results in gradually decomposing fluctuations or trends in the signal at different scales to generate a series of data sequences with different characteristic scales, each sequence representing an Intrinsic Mode Function (IMF) and satisfying the following two conditions: the number of local extrema is equal to the number of zero crossing points or the difference is at most 1; the mean value of the upper envelope line and the lower envelope line of any point on the data, which is determined by a local extremum, is zero. These two conditions actually represent a wave pattern, most of the time series of packetsThe EMD comprises a plurality of fluctuation modes, so that the EMD decomposes a signal into a series of IMFs with characteristic scales increasing from minimum to maximum and a trend term margin through a screening process on the basis of defining an eigenmode sequence. By EMD algorithm, raw input signal
Figure DEST_PATH_IMAGE001
Is decomposed into
Figure 99765DEST_PATH_IMAGE002
A basic component
Figure DEST_PATH_IMAGE003
And 1 residual component
Figure 65447DEST_PATH_IMAGE004
And can be represented by formula (1):
Figure DEST_PATH_IMAGE005
(1)
in the existing neural network prediction model of the ionosphere, the BP neural network is widely applied. The basic idea of the BP algorithm is that the whole learning process consists of two processes of forward propagation of signals and backward propagation of errors. When the forward propagation is carried out, the input parameters are imported from the input layer, and are transmitted to the output layer part after being processed by the hidden layer, and if the actual output result and the expected output result do not accord with the expected requirement, the error backward propagation stage is carried out. The error back propagation is to reversely propagate the output result error to the input layer by layer through the hidden layer in a certain form, and distribute the error to all processing units of each layer, thereby obtaining the error signal of each layer unit, and the error signal is used as the basis for correcting each unit. The weight adjustment process of each layer of signal forward propagation and error backward propagation is performed circularly. This process is continued until the error in the network output is reduced to an acceptable level or until a preset number of learning is performed.
The simple mathematical description of the BP algorithm is:
first, the network initializes and sets an error function
Figure 325658DEST_PATH_IMAGE006
Giving a calculation accuracy value
Figure DEST_PATH_IMAGE007
And a maximum number of learning times M;
step two, randomly selecting k input samples and corresponding expected outputs;
Figure 718593DEST_PATH_IMAGE008
(2)
thirdly, calculating the input and output of each neuron of the hidden layer
Figure DEST_PATH_IMAGE009
(3)
Fourthly, calculating partial derivatives of the error function to each neuron of the output layer by utilizing the expected output and the actual output of the network
Figure 821679DEST_PATH_IMAGE010
；
Figure DEST_PATH_IMAGE011
(4)
The fifth step, using the connection weight from the hidden layer to the output layer, the output layer
Figure 591052DEST_PATH_IMAGE010
Calculating partial derivative of error function to each neuron of hidden layer according to output of hidden layer
Figure 299245DEST_PATH_IMAGE012
；
Figure DEST_PATH_IMAGE013
(5)
Sixth, using neurons of the output layer
Figure 131590DEST_PATH_IMAGE014
Correcting the connection weight value by the output value of each neuron of the hidden layer
Figure DEST_PATH_IMAGE015
Figure 190813DEST_PATH_IMAGE016
(6)
Seventh, using neurons of the hidden layer
Figure DEST_PATH_IMAGE017
And the input correction connection weight of each neuron of the input layer
Figure 232718DEST_PATH_IMAGE018
Figure DEST_PATH_IMAGE019
(7)
Eighth, calculating a global error
Figure 326576DEST_PATH_IMAGE020
(8)
And step nine, finishing the algorithm when the error reaches the preset precision or the learning times is more than the set maximum times.
In the aspect of data preprocessing, in the process of decomposing a signal, due to intermittent components in the signal, the second-order filter network characteristics of the EMD are compromised, and the problem of modal aliasing is caused in the conventional EMD algorithm. When the phenomenon occurs, the intrinsic formula component of the IMF obtained by decomposition loses its own physical characteristics, so that different physical processes are expressed in the same IMF component, even a false IMF component appears, and the accuracy of EMD decomposition is influenced. Therefore, in order to improve the quality of raw data preprocessing, the invention introduces a Variational Modal Decomposition (VMD) algorithm to carry out preprocessing analysis on the raw TEC sequence, and the processed data is used as the input quantity of a subsequent prediction model.
In an ionosphere prediction model, a traditional BP neural network model performs data calculation based on the principle of a gradient descent function (gradient device). During data training, the method is easy to make the model fall into a dead loop of a local minimum value, so as to avoid a real optimal value. On the other hand, the BP neural network is structurally set as an input layer, a hidden layer and an output layer, although the hidden layer is connected with the input layer and the output layer in the training process, single neurons contained in each hidden layer are independent from each other, and information feedback is not formed among the neurons. This lack of intra-layer information feedback further reduces the data processing capacity of the network structure. In order to establish a high-precision ionized layer TEC forecasting model and fully consider the characteristics of nonlinearity, non-stationarity and the like of a TEC value sequence by considering the defects of the forecasting model, the invention utilizes the Elman neural network to carry out forecasting modeling on the ionized layer TEC.
Disclosure of Invention
The invention mainly aims to provide an ionosphere prediction method based on a VMD (virtual machine model) and an Elman neural network, and the ionosphere TEC prediction model is improved from the aspects of improving data preprocessing quality and optimizing the internal structure of the model.
The technical scheme adopted by the invention is as follows: an ionosphere prediction method based on VMD and Elman neural networks utilizes a variational modal decomposition method and an Elman neural network to carry out ionosphere TEC prediction modeling, and specifically comprises the following steps:
step 1, carrying out original TEC sequence on ionized layer
Figure 654789DEST_PATH_IMAGE021
Fourier spectrum analysis is carried out, and the amplitude-frequency characteristic of the TEC is analyzed to judge that the TEC original sequence contains several frequency components, so that the decomposition mode number of the subsequent VMD algorithm is determined
Figure 670150DEST_PATH_IMAGE022
；
Step 2, utilizing the decomposition modal number obtained by the analysis in the step 1
Figure 374801DEST_PATH_IMAGE022
VMD decomposition is carried out on the original TEC sequence to respectively obtain a plurality of intrinsic mode components
Figure 792007DEST_PATH_IMAGE023
These components are ordered in order from low frequency to high frequency;
step 3, the eigenmode component obtained in the step 2 is processed
Figure 291121DEST_PATH_IMAGE023
As an input layer of the Elman neural network, the number of hidden layer nodes is set through an empirical formula, and the setting of the number of hidden layer nodes refers to the following two empirical formulas:
Figure 793778DEST_PATH_IMAGE024
(9)
in the formula (I), the compound is shown in the specification,
Figure 770961DEST_PATH_IMAGE025
number of nodes of hidden layer;
Figure 308253DEST_PATH_IMAGE026
number of nodes of input layer;
Figure 978269DEST_PATH_IMAGE027
number of output layer nodes;
Figure 230871DEST_PATH_IMAGE028
a constant between;
step 4, the Elman neural network trains and models the input data and further outputs corresponding prediction components
Figure DEST_PATH_IMAGE029
And finally, summing and reconstructing the predicted IMF components to obtain a predicted ionized layer TEC value, wherein the predicted ionized layer TEC value is represented by the formula (10):
Figure 418270DEST_PATH_IMAGE030
(10)。
further, the VMD algorithm comprises:
the VMD algorithm first pairs the parameters
Figure DEST_PATH_IMAGE031
Initializing, and setting the iteration number n as 1; are respectively paired by the formula (11)
Figure 341226DEST_PATH_IMAGE032
Carrying out iterative updating; updating Lagrange penalty operators according to the formula (11); judging whether an iteration stopping condition is met or not according to the formula (12), if so, stopping iteration, and outputting a result, otherwise, adding 1 to the iteration number n, returning to an iteration formula, and performing re-iteration on the parameters; finally according to given decomposition mode number
Figure DEST_PATH_IMAGE033
Obtaining a corresponding modal subsequence IMF;
Figure 588668DEST_PATH_IMAGE034
(11)
Figure DEST_PATH_IMAGE035
(12)
Figure 862655DEST_PATH_IMAGE036
(13)
in the formula
Figure DEST_PATH_IMAGE037
Represents K components;
Figure 853744DEST_PATH_IMAGE038
representing the center frequency of each component;
Figure DEST_PATH_IMAGE039
a transfer function of the center frequency of the corresponding component;
Figure 631207DEST_PATH_IMAGE040
is a penalty operator;
Figure 518392DEST_PATH_IMAGE041
updating the parameters;
Figure 341991DEST_PATH_IMAGE042
a desired minimum error;
Figure 620262DEST_PATH_IMAGE043
is a secondary penalty factor coefficient.
Further, the spatial expression of the nonlinear state of the Elman neural network is:
Figure 845707DEST_PATH_IMAGE044
(14)
in the formula:
Figure 169372DEST_PATH_IMAGE045
is the time;
Figure 621213DEST_PATH_IMAGE046
respectively representing a 1-dimensional output node vector, an m-dimensional hidden layer node unit vector, an n-dimensional input vector and an m-dimensional feedback state vector;
Figure 547581DEST_PATH_IMAGE047
respectively representing connection weight matrixes from a hidden layer to an output layer, from an input layer to the hidden layer and from a receiving layer to the hidden layer;
Figure 768478DEST_PATH_IMAGE048
respectively representing the threshold values of the input layer and the hidden layer;
suppose that
Figure 387678DEST_PATH_IMAGE049
The actual output of the step system is
Figure 61236DEST_PATH_IMAGE050
Then the objective function of the Elman network can be expressed as:
Figure 260136DEST_PATH_IMAGE051
(15)
according to a gradient descent algorithm, respectively calculating
Figure 601119DEST_PATH_IMAGE052
The partial derivative of the weights is taken to be 0, so the algorithm of Elman is:
Figure 391220DEST_PATH_IMAGE053
(16)
Figure 286495DEST_PATH_IMAGE054
(17)
Figure 820245DEST_PATH_IMAGE055
(18)
Figure 750154DEST_PATH_IMAGE056
(19)
in the formula:
Figure 445578DEST_PATH_IMAGE057
correction quantity of three connection weight values;
Figure 90798DEST_PATH_IMAGE058
is an input layer vector;
Figure 162660DEST_PATH_IMAGE059
is the state vector of the hidden layer;
Figure 947076DEST_PATH_IMAGE060
the transfer function derivatives for the hidden layer and the output layer, respectively;
Figure 78980DEST_PATH_IMAGE061
iteration coefficients are weights;
Figure 948847DEST_PATH_IMAGE062
the learning step size of (2).
The invention has the advantages that:
the invention utilizes a Variable Mode Decomposition (VMD) algorithm to preprocess the original TEC sequence, thereby effectively reducing the complexity of the original TEC sequence and avoiding the occurrence of mode aliasing. And finally, performing summation reconstruction on the corresponding IMF components obtained through prediction to obtain a final TEC prediction value. Compared with other models, the method fully considers the characteristics of nonlinearity, non-stationarity and the like of the ionized layer TEC sequence, improves the preprocessing quality of the original data by utilizing the VMD algorithm, introduces the Elman neural network, improves the defects of the traditional BP neural network, and provides a new method for ionized layer TEC modeling research.
The method has important application value in the ionized layer TEC anomaly monitoring aspect, and the ionized layer has a plurality of adverse effects besides beneficial effects on human life. For example, when the ionosphere is severely disturbed, the satellite and ground communication equipment can be interrupted, the spacecraft can be out of order or damaged, the long-distance oil and gas pipelines and the high-voltage transmission network can be damaged, and the like. In addition, relevant researches show that when natural disasters such as earthquakes occur, the ionized layer TEC can also generate corresponding disturbance, so that the ionosphere abnormal disturbance is predicted and monitored, and the method is the final embodiment of the method in practical application.
The invention utilizes the combination of Variational Modal Decomposition (VMD) and Elman neural network to carry out ionized layer TEC forecasting modeling. In consideration of the characteristics of nonlinearity, non-stationarity and the like of the ionized layer TEC sequence, the VMD algorithm can effectively reduce the complexity of the original sequence and does not generate the modal aliasing phenomenon when the pretreatment is carried out on the TEC original sequence. Compared with a common EMD algorithm, the VMD can effectively avoid the occurrence of modal aliasing in the data preprocessing process, and the filtering and noise reduction performance is better. The invention introduces a VMD method to decompose the ionized layer TEC sequence to obtain a corresponding intrinsic mode component (IMF) and provide a high-quality input value for a subsequent prediction model. In consideration of the defects of the traditional BP neural network, the invention utilizes the Elman neural network as an ionized layer TEC prediction model. The Elman recurrent neural network is a typical dynamic neural network, and has the function of mapping dynamic characteristics through an internal storage state on the basis of the basic structure of the BP artificial neural network, so that a network system has the capability of adapting to time-varying characteristics. Compared with the BP neural network, the Elman neural network is additionally provided with a reception layer besides an input layer, a hidden layer and an output layer. The Elman neural network is characterized in that the output of the hidden layer is self-connected to the input of the hidden layer through the delay and storage of the receiving layer, and the mode enables the Elman neural network to have higher sensitivity to the data of the historical state, improves the capability of the network for processing dynamic data and meets the required precision requirement.
In addition to the objects, features and advantages described above, other objects, features and advantages of the present invention are also provided. The present invention will be described in further detail below with reference to the drawings.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the invention and, together with the description, serve to explain the invention and not to limit the invention.
FIG. 1 is a trend graph of the variation of the 30-day ionized layer TEC original sequence of the present invention;
FIG. 2 is a diagram of 5 IMF components of the present invention after decomposition by the VMD algorithm;
FIG. 3 is a diagram of the present invention using Elman neural using IMF components as input values to the neural network
Different IMF components and actual components obtained by network model prediction are compared;
FIG. 4 is the Elman neural network prediction of the invention obtained after IMF components are summed and reconstructed
And (4) comparing the predicted value and the actual value of the ionized layer TEC.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
An ionosphere prediction method based on VMD and Elman neural networks utilizes a variational modal decomposition method and an Elman neural network to carry out ionosphere TEC prediction modeling, and specifically comprises the following steps:
step 1, carrying out original TEC sequence on ionized layer
Figure 824399DEST_PATH_IMAGE021
Fourier spectrum analysis is carried out, and the TEC original sequence is judged to contain a plurality of frequency components by analyzing the amplitude-frequency characteristics of the TEC original sequence, so that the decomposition mode number of the subsequent VMD algorithm is determined
Figure 728901DEST_PATH_IMAGE022
；
Step 2, utilizing the decomposition modal number obtained by the analysis in the step 1
Figure 766127DEST_PATH_IMAGE022
VMD decomposition is carried out on the original TEC sequence to respectively obtain a plurality of intrinsic mode components
Figure 388870DEST_PATH_IMAGE023
These components are ordered in order from low frequency to high frequency;
in the step (3), the step (B),the eigenmode components obtained in the step 2
Figure 802534DEST_PATH_IMAGE023
As an input layer of the Elman neural network, the number of hidden layer nodes is set through an empirical formula, and the setting of the number of hidden layer nodes refers to the following two empirical formulas:
Figure 561542DEST_PATH_IMAGE024
(9)
in the formula (I), the compound is shown in the specification,
Figure 769670DEST_PATH_IMAGE025
number of hidden layer nodes;
Figure 614129DEST_PATH_IMAGE026
the number of nodes of an input layer;
Figure 831484DEST_PATH_IMAGE027
number of output layer nodes;
Figure 179419DEST_PATH_IMAGE028
a constant between;
and 4, the Elman neural network trains and models the input data, the specific input layer of the neural network is K IMF components preprocessed by the VMD algorithm, namely K input layer nodes, the original data is subjected to noise reduction processing by the VMD decomposition algorithm, the Elman performs model training by the data subjected to noise reduction processing, the precision and the calculation efficiency of the model are further improved, and compared with the traditional BP neural network, the Elman adds feedback links among hidden layers, so that the Elman neural network has a dynamic memory function and is more sensitive to the historical state and real-time change of the input information. Outputting corresponding K prediction components by an output layer after model training
Figure 89607DEST_PATH_IMAGE063
Finally, the predicted IMF component is subjected to summation reconstruction to obtain the predicted ionized layer TECThe value, as shown in equation (10):
Figure 424292DEST_PATH_IMAGE030
(10)。
the invention utilizes a Variable Mode Decomposition (VMD) algorithm to preprocess the original TEC sequence, thereby effectively reducing the complexity of the original TEC sequence and avoiding the occurrence of mode aliasing. And finally, performing summation reconstruction on the corresponding IMF components obtained through prediction to obtain a final TEC prediction value. Compared with other models, the method fully considers the characteristics of nonlinearity, non-stationarity and the like of the ionized layer TEC sequence, improves the preprocessing quality of the original data by utilizing the VMD algorithm, introduces the Elman neural network, improves the defects of the traditional BP neural network, and provides a new method for ionized layer TEC modeling research.
The method has important application value in the ionized layer TEC anomaly monitoring aspect, and the ionized layer has a plurality of adverse effects besides beneficial effects on human life. For example, when the ionosphere is severely disturbed, the satellite and ground communication equipment can be interrupted, the spacecraft can be out of order or damaged, the long-distance oil and gas pipelines and the high-voltage transmission network can be damaged, and the like. In addition, relevant researches show that when natural disasters such as earthquakes occur, the ionized layer TEC can also generate corresponding disturbance, so that the ionosphere abnormal disturbance is predicted and monitored, and the method is the final embodiment of the method in practical application.
Wherein the VMD algorithm comprises:
VMD algorithm first pair parameters
Figure 179758DEST_PATH_IMAGE031
Initializing, and setting the iteration number n as 1; are respectively coupled by the formula (11)
Figure 913359DEST_PATH_IMAGE032
Carrying out iterative updating; updating Lagrange penalty operators according to the formula (11); according to formula (12)Judging whether an iteration stopping condition is met, if so, stopping iteration, outputting a result, otherwise, adding 1 to the iteration number n, returning to an iteration formula, and carrying out re-iteration on the parameters; finally according to given decomposition mode number
Figure 463289DEST_PATH_IMAGE033
Obtaining a corresponding modal subsequence IMF;
Figure 16761DEST_PATH_IMAGE034
(11)
Figure 575918DEST_PATH_IMAGE035
(12)
Figure 429605DEST_PATH_IMAGE036
(13)
in the formula
Figure 416016DEST_PATH_IMAGE037
Represents K components;
Figure 722363DEST_PATH_IMAGE038
representing the center frequency of each component;
Figure 819632DEST_PATH_IMAGE039
a transfer function of the center frequency of the corresponding component;
Figure 262246DEST_PATH_IMAGE040
is a penalty operator;
Figure 419558DEST_PATH_IMAGE041
to update the parameters;
Figure 947622DEST_PATH_IMAGE042
a desired minimum error;
Figure 989527DEST_PATH_IMAGE043
is a secondary penalty factor coefficient.
Wherein, the spatial expression of the nonlinear state of the Elman neural network is as follows:
Figure 676861DEST_PATH_IMAGE044
(14)
in the formula:
Figure 877510DEST_PATH_IMAGE045
is the time;
Figure 17505DEST_PATH_IMAGE046
respectively representing a 1-dimensional output node vector, an m-dimensional hidden layer node unit vector, an n-dimensional input vector and an m-dimensional feedback state vector;
Figure 331943DEST_PATH_IMAGE047
respectively representing the connection weight matrix from the hidden layer to the output layer, from the input layer to the hidden layer and from the receiving layer to the hidden layer;
Figure 873782DEST_PATH_IMAGE048
respectively representing the threshold values of the input layer and the hidden layer;
suppose that
Figure 248263DEST_PATH_IMAGE049
The actual output of the step system is
Figure 875553DEST_PATH_IMAGE050
Then the objective function of the Elman network can be expressed as:
Figure 993682DEST_PATH_IMAGE051
(15)
according to a gradient descent algorithm, respectively calculating
Figure 655608DEST_PATH_IMAGE052
The partial derivative of the weights is taken to be 0, so the algorithm of Elman is:
Figure 466569DEST_PATH_IMAGE053
(16)
Figure 315576DEST_PATH_IMAGE054
(17)
Figure 237396DEST_PATH_IMAGE055
(18)
Figure 753828DEST_PATH_IMAGE056
(19)
in the formula:
Figure 470111DEST_PATH_IMAGE057
correction quantity of three connection weight values;
Figure 806414DEST_PATH_IMAGE058
is an input layer vector;
Figure 266346DEST_PATH_IMAGE059
is the state vector of the hidden layer;
Figure 637284DEST_PATH_IMAGE060
the transfer function derivatives for the hidden layer and the output layer, respectively;
Figure 515680DEST_PATH_IMAGE061
iteration coefficients are weights;
Figure 745804DEST_PATH_IMAGE062
the learning step size of (2).
The invention provides an ionized layer TEC forecasting method based on the combination of a Variational Mode Decomposition (VMD) algorithm and an Elman neural network.
(1) According to the method, a Variational Modal Decomposition (VMD) algorithm is introduced to carry out pretreatment analysis on the ionized layer TEC sequence, and the characteristics of the VMD algorithm are combined, so that the non-stationarity and non-linearity characteristics of the ionized layer TEC sequence can be optimally pretreated by using the VMD algorithm, and low-complexity and high-quality input data are provided for the subsequent establishment of a prediction model.
(2) The invention introduces the Elman neural network to optimize the prediction model in order to solve the defects of the traditional BP neural network in the ionized layer TEC prediction application aspect. The Elman neural network is characterized in that the output of the hidden layer is self-connected to the input of the hidden layer through the delay and storage of the receiving layer, and the mode enables the Elman neural network to have higher sensitivity to the data of the historical state, improves the capability of the network for processing dynamic data and meets the required precision requirement.
And (3) experimental verification:
in the experiment, the ionized layer TEC value of 30 degrees N and 120 degrees E in 2017, which is provided by an IGS center, for 30 days is selected as the original experiment data, and the data decomposition and model prediction work is carried out.
Fig. 1 shows the variation trend of the original sequence of the ionized layer TEC in 30 days, and it can be seen from the figure that the ionized layer TEC shows the characteristics of non-stationarity and non-linearity, so that the VMD algorithm can effectively preprocess the TEC sequence and reduce the complexity of the TEC sequence;
FIG. 2 shows 5 IMF component graphs after VMD algorithm decomposition, and it can be seen from the graphs that the VMD algorithm decomposes an original sequence into stable components from low frequency to high frequency, and provides input values for a subsequent prediction model;
fig. 3 shows a comparison graph of different IMF components and actual components obtained by using the IMF component as an input value of the neural network and predicting by using the Elman neural network model, and it can be seen that the prediction accuracy of the IMF component can be further improved by decomposing the complex TEC sequence;
fig. 4 shows a comparison between an ionized layer TEC predicted value and an actual value obtained by summing and reconstructing an IMF component predicted by an Elman neural network, which can be seen that the combined model provided by the invention can effectively improve the prediction accuracy of the ionized layer TEC, and provide a new approach for ionized layer TEC research.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (3)

1. An ionosphere forecasting method based on a VMD and Elman neural network is characterized in that,
the method for modeling the ionized layer TEC by utilizing the combination of the variational modal decomposition method and the Elman neural network specifically comprises the following steps:
step 1, carrying out original TEC sequence on ionized layer
Figure 794903DEST_PATH_IMAGE002
Fourier spectrum analysis is carried out, and the TEC original sequence is judged to contain a plurality of frequency components by analyzing the amplitude-frequency characteristics of the TEC original sequence, so that the decomposition mode number of the subsequent VMD algorithm is determined
Figure 305519DEST_PATH_IMAGE004
；
Step 2, utilizing the decomposition modal number obtained by the analysis in the step 1
Figure 554097DEST_PATH_IMAGE004
VMD decomposition is carried out on the original TEC sequence to respectively obtain a plurality of intrinsic mode components
Figure DEST_PATH_IMAGE006
These components are ordered in order from low frequency to high frequency;
step 3, the eigenmode component obtained in the step 2 is processed
Figure 11624DEST_PATH_IMAGE006
As an input layer of the Elman neural network, the number of nodes of the hidden layer is set through an empirical formula, and the setting reference of the number of the nodes of the hidden layerThe following two empirical formulas:
Figure DEST_PATH_IMAGE008
(9)
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE010
number of nodes of hidden layer;
Figure DEST_PATH_IMAGE012
number of nodes of input layer;
Figure DEST_PATH_IMAGE014
number of output layer nodes;
Figure DEST_PATH_IMAGE016
a constant between;
step 4, the Elman neural network trains and models the input data and further outputs corresponding prediction components
Figure DEST_PATH_IMAGE018
And finally, summing and reconstructing the predicted IMF components to obtain a predicted ionized layer TEC value, wherein the predicted ionized layer TEC value is represented by the formula (10):
Figure DEST_PATH_IMAGE020
(10)。
2. the VMD and Elman neural network-based ionospheric predictor of claim 1
A method, wherein the VMD algorithm comprises:
the VMD algorithm first pairs the parameters
Figure DEST_PATH_IMAGE022
Initializing, and setting the iteration number n as 1; respectively using the formula (11)To pair
Figure DEST_PATH_IMAGE024
Carrying out iterative updating; updating Lagrange penalty operators according to the formula (11); judging whether an iteration stopping condition is met or not according to the formula (12), if so, stopping iteration, and outputting a result, otherwise, adding 1 to the iteration number n, returning to an iteration formula, and performing re-iteration on the parameters; finally according to given decomposition mode number
Figure DEST_PATH_IMAGE026
Obtaining a corresponding modal subsequence IMF;
Figure DEST_PATH_IMAGE028
(11)
Figure DEST_PATH_IMAGE030
(12)
Figure DEST_PATH_IMAGE032
(13)
in the formula
Figure DEST_PATH_IMAGE034
Represents K components;
Figure DEST_PATH_IMAGE036
representing the center frequency of each component;
Figure DEST_PATH_IMAGE038
a transfer function of the center frequency of the corresponding component;
Figure DEST_PATH_IMAGE040
is a penalty operator;
Figure DEST_PATH_IMAGE042
to update the parameters;
Figure DEST_PATH_IMAGE044
a desired minimum error;
Figure DEST_PATH_IMAGE046
is a secondary penalty factor coefficient.
3. The VMD and Elman neural network-based ionospheric predictor of claim 1
The method is characterized in that the spatial expression of the nonlinear state of the Elman neural network is as follows:
Figure DEST_PATH_IMAGE048
(14)
in the formula:
Figure DEST_PATH_IMAGE050
is the time;
Figure DEST_PATH_IMAGE052
respectively representing a 1-dimensional output node vector, an m-dimensional hidden layer node unit vector, an n-dimensional input vector and an m-dimensional feedback state vector;
Figure DEST_PATH_IMAGE054
respectively representing the connection weight matrix from the hidden layer to the output layer, from the input layer to the hidden layer and from the receiving layer to the hidden layer;
Figure DEST_PATH_IMAGE056
respectively representing the threshold values of the input layer and the hidden layer;
suppose that
Figure DEST_PATH_IMAGE058
The actual output of the step system is
Figure DEST_PATH_IMAGE060
Then the objective function of the Elman network can be expressed as:
Figure DEST_PATH_IMAGE062
(15)
according to a gradient descent algorithm, respectively calculating
Figure DEST_PATH_IMAGE064
The partial derivative of the weights is taken to be 0, so the algorithm of Elman is:
Figure DEST_PATH_IMAGE066
(16)
Figure DEST_PATH_IMAGE068
(17)
Figure DEST_PATH_IMAGE070
(18)
Figure DEST_PATH_IMAGE072
(19)
in the formula:
Figure DEST_PATH_IMAGE074
correction quantity of three connection weight values;
Figure DEST_PATH_IMAGE076
is an input layer vector;
Figure DEST_PATH_IMAGE078
is the state vector of the hidden layer;
Figure DEST_PATH_IMAGE080
the transfer function derivatives for the hidden layer and the output layer, respectively;
Figure DEST_PATH_IMAGE082
iteration coefficients are weights;
Figure DEST_PATH_IMAGE084
the learning step size of (2).
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