A method for constructing a hydrological time series prediction model based on IVMD-LSTM-EBLS

Abstract

The present invention discloses a method for constructing a hydrological time series prediction model based on IVMD-LSTM-EBLS, which predicts future hydrological conditions based on historical precipitation and runoff changes. The method comprises: obtaining hydrological time series data in historical records; decomposing and reconstructing the time series using IVMD according to the changes in the time series in the historical records; establishing a new feature set based on the reconstructed hydrological time series; extracting feature data of the new feature set using LSTM; using EBLS to perform linear transformation on the extracted feature data to generate mapping features, further extract deep feature information and calculate the final weight. The present invention can effectively improve the prediction accuracy of time series data, and at the same time improve prediction efficiency and resource utilization.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydrological prediction, and in particular relates to a method for constructing a hydrological time series prediction model based on deep learning. Background Art

[0002] Hydrological prediction provides a scientific basis for the prevention and dispatch of hydrological conditions. Hydrological time series is an orderly and discrete collection of hydrological elements collected according to time changes. It is highly dependent on the temporal sequence of values ​​and has the characteristics of nonlinearity, mutation, and multiple noise. Therefore, the prediction effect of models based on traditional machine learning and statistics is often unsatisfactory, and the theory and method of high-precision prediction are increasingly valued.

[0003] Long and Short-term Memory (LSTM) networks have obvious advantages in processing data with long time steps and nonlinear sequences, and have achieved excellent results in time prediction. However, due to the influence of deep structures, hydrological time prediction models based on LSTM generally have the disadvantage of being easily trapped in local optimality. This is mainly due to the need to cyclically adjust weights during LSTM training. Therefore, a single model cannot fully capture the nonlinear characteristics of runoff sequences. Research results show that hybrid models help improve prediction accuracy.

[0004] Variational Mode Decomposition (VMD) can effectively reduce the problem of center frequency aliasing and make the data more stable. The multiple groups of modal data formed by decomposition can enable multiple feature extractions of small sample data sets according to frequency levels. However, traditional VMD decomposition puts all modes into model training, and the loss value deviation of irrelevant modal data is amplified after model training, affecting the calculation of the final weight value and threshold.

[0005] The Broad Learning System (BLS) can directly calculate weights and has the advantage of being able to learn deep important features directly from training data, solving the defect that pure deep learning combination models are prone to falling into local optimality; however, the weights of the input layer and feature nodes in BLS, as well as the weights from feature nodes to enhancement nodes, are initially generated randomly. For different learning tasks, the generation of weights is completely independent of the samples, and this method lacks explainability. Summary of the invention

[0006] Purpose of the invention: In view of the problems of multiple noises and non-stationarity in hydrological time series prediction, which lead to deviations in prediction results, the present invention proposes a method for constructing a hydrological time series prediction model based on IVMD-LSTM-EBLS. The improved IVMD (Improved Variational Mode Decomposition, IVMD) decomposition module makes the decomposed sub-signals more stable, which is more conducive to feature extraction by the model. At the same time, combined with EBLS (Enhanced Broad Learning System, EBLS), the relationship between the model and the original data is enhanced to solve the gradient explosion phenomenon.

[0007] Technical solution: To achieve the purpose of the present invention, the technical solution adopted by the present invention is:

[0008] A method for constructing a hydrological time series prediction model based on IVMD-LSTM-EBLS includes the following steps:

[0009] Step 1: Data preparation: Obtain hydrological time series data from historical records and determine the training set and test set;

[0010] Step 2: Use IVMD to decompose and reconstruct the original hydrological time series of the training set: the center frequency method and Pearson correlation coefficient method are used to determine the decomposition mode number K; the residual index minimization criterion is used to determine the step length τ;

[0011] Step 3, data reconstruction: The one-dimensional modal component IMF data after IVMD decomposition is superimposed and reconstructed into three-dimensional data including time step, number of samples and number of features, which is used as the first-layer input data of the two-layer LSTM model;

[0012] Step 4: Use a two-layer LSTM model to extract features from the reconstructed three-dimensional data. Add a Dropout layer after each LSTM layer to obtain preliminary hydrological time series data features.

[0013] Step 5: Use EBLS to perform deep feature extraction on the data features obtained in step 4 to complete the construction of the prediction model, and use the training set to train the prediction model to obtain the final weight value and threshold of the prediction model;

[0014] Step 6: Input the test set into the trained prediction model to verify the feasibility of the method and the performance of the proposed model.

[0015] Furthermore, the process of decomposing and reconstructing the original hydrological time series using IVMD in step 2 is:

[0016] S2.1. Use VMD to decompose the original hydrological time series into K modes, obtain the central frequency value of each IMF, analyze the central frequency, and determine the final K value;

[0017] S2.2, introduce the residual index method to determine the update step size τ; when the residual index REI value is the smallest, the current τ value is used to perform VMD decomposition to obtain the modal decomposition signals, which are superimposed and reconstructed to be closest to the original hydrological time series;

[0018] Set the initial value range of τ to [0,1], the step size to 0.01, perform several VMD decompositions on the original hydrological time series with the determined K value, calculate the REI value corresponding to the current τ value, and obtain the value of τ when REI reaches the minimum value;

[0019] S2.3. Using the Pearson correlation coefficient method, the K IMFs are analyzed with the original hydrological time series by Pearson correlation coefficient. The IMF with the smallest correlation is excluded, and the remaining IMFs are reorganized to obtain new time series data.

[0020] Furthermore, the process of deep feature extraction using EBLS is as follows:

[0021] S3.1. The feature information data extracted by the first two layers of LSTM is used as BLS input data; the weight between the input vector transmitted by LSTM and the output gate is used as the initial weight of BLS to perform linear transformation to generate mapping features;

[0022] S3.2, generating a plurality of mapping nodes by mapping features;

[0023] S3.3, performing linear transformation on the mapping nodes to generate enhanced nodes;

[0024] S3.4, the mapping node and the enhancement node calculate the weight value by matrix inversion; the weight value obtained by matrix inversion is corrected in combination with the weight value and threshold of the input gate and the forget gate in the BLS memory unit to obtain the final weight value and threshold.

[0025] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0026] In the simulation analysis, it was found that the coupling superposition of LSTM and BLS models was still affected by the deep structure, resulting in the problem of gradient explosion. The present invention introduces EBLS (enhanced BLS) to improve LSTM for hydrological time series prediction. The improved IVMD decomposition module makes the decomposed sub-signals more stable, which is more conducive to feature extraction by the model. At the same time, combined with EBLS, the relationship between the model and the original data is enhanced to solve the problem of gradient explosion.

[0027] In terms of computational efficiency, IVMD removes the influence of honor mode on the model, and combines the advantages of EBLS fast calculation to further improve the computational efficiency of the model. The model of the present invention not only has obvious advantages in the accuracy of predicted values, the efficiency of the model and the computational efficiency, but also has applicability to different types of small sample data sets of hydrological time series data, further improving the prediction accuracy of drastic changes in runoff under extreme weather conditions, with extremely high credibility, and can provide guiding prevention and scheduling suggestions for real hydrological conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is the overall flow chart of the prediction model of the present invention;

[0029] Figure 2 It is the EBLS structure diagram of the prediction model of the present invention;

[0030] Figure 3 It is the IVMD decomposition result diagram of the present invention for data set I;

[0031] Figure 4 It is the IVMD decomposition result diagram of the present invention for data set II;

[0032] Figure 5 is a comparison chart of the prediction results of the model of the present invention for data set I;

[0033] Figure 6 It is a comparison chart of the prediction results of the model of the present invention for data set II. DETAILED DESCRIPTION

[0034] The technical solution of the present invention is described in detail below with reference to the accompanying drawings.

[0035] The technical solution adopted by the present invention is: a hydrological time series prediction model based on IVMD-LSTM-EBLS is as follows Figure 1 As shown in Figure 2, predicting future hydrological conditions based on historical precipitation and runoff changes includes the following steps:

[0036] Step 1: Data preparation: Take the hydrological time series data from historical records and determine the training set and test set.

[0037] Step 2: Use IVMD to process the original hydrological time series of the training set: the center frequency method and Pearson correlation coefficient method are used to determine the decomposition mode number K; the residual index minimization criterion is used to determine the tau value.

[0038] The improvements of IVMD compared to VMD are: first, the optimal K value is selected; second, the optimal update step size is selected; third, the modal components with the lowest correlation are excluded, and only the modal components with high correlation are selected for model training. Since VMD decomposes the modal number K and the update step size τ, it has a great impact on the model training results and noise reduction. Therefore, the center frequency method is used to locate the K value. The specific steps are as follows:

[0039] (1) VMD is used to decompose the original signal (original hydrological time series) K times, K = 2, 3, ..., n, to obtain one-dimensional modal component (Intrinsic Mode Functions, IMF) data, and the central frequency of each mode at each decomposition is derived.

[0040] (2) Analyze the center frequency and determine the final K value: When the mode selection value is small, VMD is equivalent to an adaptive filter, which causes important information in the signal to be filtered out, affecting the subsequent model prediction accuracy; when the mode selection value is large, the center frequencies of adjacent modal components will be close to each other, resulting in passband overlap or additional noise, thereby causing over-decomposition.

[0041] (3) The residual error index method is introduced to determine the update step size τ. The value of the residual error index (REI) is directly related to the value of τ. When the REI value is the smallest, the superposition and reconstruction of the modal decomposition signals obtained by VMD decomposition using the current value of τ is closest to the original signal.

[0042] Set the initial value range of τ to [0,1], with a step size of 0.01, and continuously perform VMD decomposition on the original signal with the determined K value, and calculate the REI value corresponding to the current τ value. Visualize the results and get the value of τ when REI reaches the minimum value. REI is calculated as follows:

[0043]

[0044] Where K represents the number of decomposed modes, N is the length of the decomposed signal, is the kth modal component after decomposition of the ith signal, f i is the original signal of the i-th signal. After determining the optimal decomposition mode number K and the update step length τ, IVMD is used to determine the decomposition subsequences for data sets I and II as follows Figure 3 , 4 shown.

[0045] Finally, the Pearson correlation coefficient method is used to perform correlation analysis on the center frequencies of the final K modes and the original signal, and the IMF with the smallest correlation is excluded. The remaining IMFs are reorganized to obtain new time series data. The Pearson correlation coefficient method is shown in the following formula:

[0046]

[0047] Where Pearson represents the Pearson correlation coefficient, x i is the modal component signal, is the mean value of the modal component signal data, y i is the original signal, is the mean value of the original signal data.

[0048] Under the condition that the null hypothesis is true, that is, under the premise that there is no correlation between the two variables, the probability value (P value) of the correlation between the two variables is calculated: if the P value is very small, it means that the probability that the two variables are not correlated is very small; conversely, the probability that there is a correlation is very small. It is usually necessary to consider the size of the correlation coefficient under the premise of meeting the P value requirements. The correlation strength between variables is usually judged according to the following correlation coefficient value range: 0.8-1.0, extremely strong correlation; 0.6-0.8, strong correlation; 0.4-0.6, medium strength correlation; 0.2-0.4, weak correlation; 0.00-0.2, extremely weak correlation or no correlation. The correlation analysis of the IVMD decomposed mode and the original hydrological time series data is performed, and the calculation results are shown in Tables 1 and 2.

[0049] Table 1 Correlation coefficients between decomposed modes and original data (data set I)

[0050] IMF0 IMF1 IMF2 IMF3 IMF4 IMF5 P-value 17.5170 2.3231 455.17 5.4268 68.9763 1.5232 Correlation coefficient 0.4135 0.6259 0.4845 0.7851 0.8503 0.8360

[0051] For data set I, the correlation coefficient of IMF4 is 0.8503, and the correlation coefficient of IMF5 is 0.8360, which are extremely correlated with the original data; the correlation coefficient of IMF1 is 0.6259, and the correlation coefficient of IMF3 is 0.7851, which are strongly correlated with the original data; the correlation coefficient of IMF0 is 0.4135, and the correlation coefficient of IMF2 is 0.4845, which are moderately correlated with the original data. Combined with the size of the P value, it can be seen that although IMF4 has an extremely strong correlation with the original data, and IMF0 and IMF2 have a moderate correlation with the original data, their P values ​​are too large, and the probability of correlation is very small. Therefore, for data set I, IMF1, IMF3 and IMF5 are selected as the main training modes.

[0052] Table 2 Correlation coefficients between decomposed modes and original data (data set II)

[0053] IMF0 IMF1 IMF2 IMF3 IMF4 P-value 16.7243 2.3545 6.4569 1.4141 136.1080 Correlation coefficient 0.3502 0.6272 0.7206 0.8413 0.7643

[0054] For data set II, the correlation coefficient of IMF3 is 0.8413, which has a very strong correlation with the original data; the correlation coefficient of IMF1 is 0.6272, the correlation coefficient of IMF2 is 0.7206, and the correlation coefficient of IMF4 is 0.7643, which has a strong correlation with the original data; the correlation coefficient of IMF0 is 0.3502, which has a weak correlation with the original data. Combined with the size of the P value, it can be seen that although IMF4 has a strong correlation with the original data, its P value is too large, and the probability of correlation is very small, while IMF0 itself has a weak correlation with the original data. Therefore, for data set II, IMF1, IMF2 and IMF3 are selected as the main training modes.

[0055] Step 3: Data reconstruction: The one-dimensional IMF data after IVMD decomposition is superimposed and reconstructed into three-dimensional data including time steps, number of samples and number of features, which is used as the first-layer input data of the two-layer LSTM model.

[0056] Step 4: Use a two-layer LSTM model to extract features from the reconstructed three-dimensional data: Add a Dropout layer after each LSTM layer to prevent overfitting and obtain preliminary hydrological time series data features.

[0057] Step 5: EBLS (enhanced BLS) deep feature extraction completes the construction of the prediction model, and uses the training set to train the prediction model to obtain the final weight value and threshold of the prediction model.

[0058] In BLS, the weights of the input layer and feature nodes, as well as the weights from feature nodes to enhancement nodes, are initially generated randomly. For different learning tasks, the generation of weights is completely independent of the samples, so this method lacks interpretability.

[0059] In order to seek a way to interpret the weights and enhance the learning ability of BLS weights, this model proposes an enhanced BLS. The EBLS structure is shown in the figure Figure 2 As shown. Combining the advantages of BLS fast calculation, the output gate of the last layer LSTM in the deep network structure is replaced, and the weight value between the input vector and the output gate in LSTM is used as the initial weight of BLS for linear transformation to generate mapping features. Multiple mapping nodes are generated through mapping features, and the mapping nodes are linearly transformed to generate enhanced nodes. The mapping nodes and enhanced nodes calculate the weight values ​​through matrix inversion, and the weight values ​​between the input vector and the forget gate and input gate in the memory unit are directly calculated to obtain the final weight value. The calculation method is as follows:

[0060] Z i =φ(XW xoi +β xoi ),i=1,…,n

[0061] Among them, Zi is the final weight value, φ is the activation function, X is the input vector, W xoi , β xoi is the weight value and threshold between the input vector and the output gate in the LSTM model, and n is the number of windows of the feature node.

[0062] Since the initial weights of the BLS model are randomly generated, this randomness is completely independent of the training samples, and the generated weight values ​​have nothing to do with the training samples. If the generated weight values ​​have large deviations, it will usually increase the calculation time of the model and even have a significant impact on the final prediction results. The introduction of the EBLS model effectively reduces the impact of the initial weights randomly generated by the BLS model on the prediction results, and further improves the model's operational efficiency.

[0063] Step 6: Finally, the test set is input into the trained prediction model to verify the feasibility of the method and the performance of the proposed model.

[0064] In order to verify the effectiveness of the model proposed in the present invention, the present invention uses the root mean square error (RMSE), mean absolute error (MAE) and certainty coefficient (NS) as evaluation indicators, and the calculation formula is as follows:

[0065]

[0066] Among them, y i Indicates the actual value, represents the predicted value, Represents the mean of the true values.

[0067] In order to verify the effectiveness and applicability of each module of the model of the present invention, two data sets, monthly precipitation data and monthly runoff data, are used to analyze and compare the new model proposed in the present invention with VMD-CNN-LSTM and VMD-LSTM-BLS. RMSE, MAE and NS are used as reference indicators. The experimental results are shown in Table 3.

[0068] Table 3 Comparison of evaluation indicators between the proposed model and the ablation model at different prediction lengths

[0069]

[0070] Comparing the evaluation indicators in Table 3, it can be seen that for dataset I, the new model reduces RMSE by about 44.68% and 10.11% compared with VMD-CNN-LSTM and VMD-LSTM-BLS models in the case of a one-month time step; reduces MAE by about 50.81% and 13.38%; and improves NSE by about 15.30% and 1.61%. In the case of a three-month time step, RMSE is reduced by about 46.85% and 6.04%; MAE is reduced by about 49.85% and 16.35%; NSE is improved by about 17.88% and 2.69%. In the case of a six-month time step, RMSE is reduced by about 27.44% and 6.03%; MAE is reduced by about 31.59% and 5.83%; NSE is improved by about 12.33% and 1.82%. The comparison of the prediction results of dataset I is shown in the figure below. Figure 5 As shown. For Dataset II, when the time step is 1 month in advance, the combined model proposed by the present invention reduces RMSE by about 67.31% and 36.23% compared with the VMD-CNN-LSTM and VMD-LSTM-BLS models; reduces MAE by about 61.98% and 31.95%; and improves NSE by about 28.36% and 4.95%. When the time step is 3 days in advance, RMSE is reduced by about 45.44% and 7.73%; MAE is reduced by about 44.35% and 12.62%; and NSE is improved by about 23.43% and 1.73%. When the time step is 6 days in advance, RMSE is reduced by about 38.36% and 3.62%; MAE is reduced by about 32.08% and 4.58%; and NSE is improved by about 22.55% and 1.02%. The comparison of prediction results of Dataset II is shown in the figure below. Figure 6 shown.

[0071] Combining Table 3 and the relevant provisions of the Hydrological Information Forecast Specification, it can be seen that the NSE index of VMD-CNN-LSTM reaches above 0.7396, and the highest can reach 0.7796, and the prediction accuracy reaches the Class B standard; the NSE index of VMD-LSTM-BLS is up to 0.9165, and the prediction result is the Class A standard; the IVMD-LSTM-EBLS model proposed in the present invention has a simulation result of the NSE evaluation index of the precipitation data of month I in the dataset of 0.8629, and the NSE value reaches 0.9326 in the case of one month in advance. The prediction accuracy is of Class A standard, with the highest credibility. In terms of monthly runoff of dataset II, the highest NSE value of VMD-CNN-LSTM is 0.6824, reaching Class C standard. The highest NSE index of VMD-LSTM-BLS is 0.9165, and the prediction result is of Class A standard. The simulation result of the NSE rating index of the IVMD-LSTM-EBLS model proposed in the present invention reaches above 0.8671. When the prediction length is 1 day in advance, the NSE index can reach 0.9660. The prediction accuracy is of Class A standard, with the highest credibility standard.

[0072] Although the above embodiments describe the present invention in detail, in the specific implementation process, the details can still be supplemented and replaced by equivalents according to actual operations. It should be pointed out that the technical solutions after the details of the claims of the present invention are supplemented and replaced by equivalents are all regarded as the protection scope of the present invention.

Claims

1. A method for constructing a hydrological time series prediction model based on IVMD-LSTM-EBLS, characterized in that: The method comprises the following steps: Step 1: Data preparation: Obtain hydrological time series data from historical records and determine the training set and test set; Step 2: Use IVMD to decompose and reconstruct the original hydrological time series of the training set: the center frequency method and Pearson correlation coefficient method are used to determine the decomposition mode number K; the residual index minimization criterion is used to determine the step length τ; S2.

1. Use VMD to decompose the original hydrological time series into K modes, obtain the central frequency value of each IMF, analyze the central frequency, and determine the final K value; S2.2, introduce the residual index method to determine the update step size τ; when the residual index REI value is the smallest, the current τ value is used to perform VMD decomposition to obtain the modal decomposition signals, which are superimposed and reconstructed to be closest to the original hydrological time series; Set the initial value range of τ to [0,1], the step size to 0.01, perform several VMD decompositions on the original hydrological time series with the determined K value, calculate the REI value corresponding to the current τ value, and obtain the value of τ when REI reaches the minimum value; REI is calculated as follows: Where K represents the number of decomposed modes, N is the length of the decomposed signal, is the kth modal component after decomposition of the ith signal, f i is the original signal of the i-th signal; S2.3, using the Pearson correlation coefficient method, perform Pearson correlation coefficient analysis on K IMFs and the original hydrological time series, exclude the IMF with the smallest correlation, and reorganize the remaining IMFs to obtain new time series data; Step 3, data reconstruction: The one-dimensional modal component IMF data after IVMD decomposition is superimposed and reconstructed into three-dimensional data including time step, number of samples and number of features, which is used as the first-layer input data of the two-layer LSTM model; Step 4: Use a two-layer LSTM model to extract features from the reconstructed three-dimensional data. Add a Dropout layer after each LSTM layer to obtain preliminary hydrological time series data features. Step 5: Use EBLS to perform deep feature extraction on the data features obtained in step 4 to complete the construction of the prediction model, and use the training set to train the prediction model to obtain the final weight value and threshold of the prediction model; The process of deep feature extraction using EBLS is: The feature information data extracted by the first two layers of LSTM is used as BLS input data; the weight between the input vector transmitted by LSTM and the output gate is used as the initial weight of BLS for linear transformation to generate mapping features; Generate multiple mapping nodes by mapping features; perform linear transformation on the mapping nodes to generate enhanced nodes; The mapping nodes and enhancement nodes calculate weight values ​​by matrix inversion; the weight values ​​obtained by matrix inversion are corrected by combining the weight values ​​and thresholds of the input gate and forget gate in the BLS memory unit to obtain the final weight value and threshold; The calculation method is as follows: Z i =φ(XW xoi +β xoi ),i=1,…,n Among them, Z i is the final weight value, φ is the activation function, X is the input vector, W xoi , β xoi is the weight value and threshold between the input vector and the output gate in the LSTM model, and n is the number of windows of the feature node; Step 6: Input the test set into the trained prediction model to verify the feasibility of the method and the performance of the proposed model.

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