Medium and long term significant wave height prediction method based on multivariable mode decomposition

Abstract

The invention relates to a medium and long term significant wave height prediction method based on multivariable modal decomposition. The method comprises the following steps: screening variables related to significant wave height by using a Pearson's correlation coefficient method; multivariable empirical mode decomposition is carried out, and then a permutation entropy method is used to carry out high and low frequency grouping on the decomposed intrinsic mode function; constructing a data set for the grouped data by adopting a sliding window algorithm; constructing a dual-channel deep learning model; and inputting the test set into a trained dual-channel deep learning model, obtaining prediction results of the intrinsic mode functions IMF, and summing all the prediction results of the intrinsic mode functions IMF to obtain a final significant wave height prediction value. The two-channel deep learning model based on multivariable empirical mode decomposition can effectively capture the mutual influence between the significant wave height data and other variables, solves the problem that the mutual relation between the variables is ignored in a traditional method, and remarkably improves the prediction precision of the medium and long term significant wave height.

Description

Technical Field

[0001] This invention relates to the fields of artificial intelligence and time series prediction technology, specifically to a method for predicting medium- and long-term effective wave height based on multivariate mode decomposition. Background Technology

[0002] With the escalating global energy crisis and the increasing severity of the greenhouse effect, promoting the development of renewable energy has become a crucial issue in global environmental protection and energy transition. Wave energy, as a clean and sustainable energy source, is increasingly seen as an important energy choice due to its high energy density and widespread distribution. Significant wave height, as a key wave parameter, directly affects the generation and conversion efficiency of wave energy. Therefore, accurate prediction of medium- and long-term significant wave height is of great practical significance for marine energy development and related engineering applications. However, due to the nonlinearity and non-stationarity of significant wave height data, traditional numerical models and single deep learning models struggle to achieve sufficiently high accuracy in medium- and long-term predictions.

[0003] Most existing methods for predicting medium- and long-term significant wave heights employ hybrid models combining deep learning and decomposition algorithms. However, these hybrid models only decompose and predict a single significant wave height. In multivariate decomposition, methods such as Recursive Quantization Analysis (RQA) and Refined Composite Multiscale Entropy (RCMSE) are commonly used to reconstruct the decomposed subsequences. However, these methods fail to adequately consider the interactions between variables, resulting in the model's inability to effectively capture the complex relationships between multiple variables. Furthermore, using these techniques significantly increases computational complexity, thus affecting model efficiency and practical feasibility. Moreover, the multiple intrinsic mode functions (IMFs) obtained after decomposition are not always applicable to a single deep learning model, further limiting the improvement of prediction accuracy. Summary of the Invention

[0004] The technical problem of this invention is that existing medium- and long-term effective wave height prediction methods fail to fully consider the complex relationships between variables in multivariate modeling, have high computational complexity, and the decomposition results are not well adapted to the prediction model.

[0005] The purpose of this invention is to solve the above problems and propose a method for predicting medium- and long-term effective wave height based on multivariate mode decomposition, comprising the following steps: S1: Collect historical standard meteorological data, preprocess the data, and then use the Pearson correlation coefficient method to screen out variables related to effective wave height; S2: Normalize the selected variables and perform multivariate empirical mode decomposition. Then, use the permutation entropy method to group the decomposed intrinsic mode functions into high- and low-frequency groups. S3: Use the sliding window algorithm to construct a dataset based on the proportions of the grouped data; S4: Construct a dual-channel deep learning model and train the model using the training set; S5: Input the test set into the trained dual-channel deep learning model, obtain the prediction results of the intrinsic mode functions (IMFs), and sum the prediction results of all IMFs to obtain the final effective wave height prediction value.

[0006] Furthermore, in step S1, the variables include significant wave height, wind direction, wind speed, peak gust speed, dominant wave period, average wave period, dominant wave direction, sea level pressure, air temperature, and sea surface temperature.

[0007] Preferably, in step S1, the data is preprocessed, and outlier removal and data alignment are performed on the collected meteorological data.

[0008] Preferably, in step S1, the Pearson correlation coefficient method is used to screen out variables with significant wave height correlation, and the calculation formula is: ; In the formula, This represents the Pearson correlation coefficient. and They represent variables respectively. and No. Data from one sample, and They represent variables respectively. and The average value, This represents the number of samples for the variable.

[0009] Preferably, step S1 further includes setting a correlation threshold, comparing the Pearson correlation coefficient with the correlation threshold, and selecting the significant wave height SWH, wind speed WSPD, peak gust wind speed GST, and mean wave period APD.

[0010] Furthermore, in step S2, the selected variables are normalized by performing Min-Max normalization on the time series data of the selected variables and mapping them to the 0-1 interval. The calculation formula is as follows: ; In the formula, Represents the original data. Represents normalized data. and These represent the maximum and minimum values ​​in the original data, respectively.

[0011] Preferably, in step S2, multivariate empirical mode decomposition (MEMD) involves expanding the local mean of the variable time series using MEMD by projecting it onto the hypersphere along multiple directions, thereby obtaining multiple eigenmode functions (IMFs) of equal number. The formula for calculating the local mean of the multivariate time series is as follows: ; In the formula, Represents the local mean. Indicates the number of multiple variables. Represents the direction vector The multidimensional envelope of the projection.

[0012] In step S4, a dual-channel deep learning model is used, including a WaveNet sub-model and a Long Short-Term Memory (LSTM) sub-model.

[0013] Furthermore, the WaveNet sub-model, used to train high-frequency intrinsic mode functions, includes the following steps: 1) Set the input to a time series Based on previously input samples, predict the distribution of each sample, and its conditional probability function expression is: ; In the formula, Indicates the sample index. This represents a sample of the current time series. Indicates the characteristic length of the previous sample; 2) The expression for the gated structure is: ; In the formula, and These represent the input and output feature maps of the gated structure, respectively. This represents a trainable convolutional filter. Represents the convolution operator. This represents an element-wise multiplication operator. Indicates the level index. and These represent filters and gates, respectively.

[0014] Preferably, the Long Short-Term Memory (LSTM) sub-model is used to train low-frequency intrinsic mode functions. Specifically, it involves adding unit structures to the LSTM sub-model, as expressed in the following expression: ; ; ; In the formula, , , These represent the input, forget, and output gates, respectively. express Input data at any time, This indicates the output of the previous unit. and These represent the weights and biases corresponding to each gate, respectively. This represents the sigmoid function.

[0015] Compared with the prior art, the beneficial effects of the present invention include: 1) The dual-channel deep learning model based on multivariate empirical mode decomposition proposed in this invention can effectively capture the interaction between effective wave height data and other variables, thereby solving the problem of ignoring the relationship between variables in traditional methods and significantly improving the prediction accuracy of medium- and long-term effective wave height.

[0016] 2) The multivariate empirical mode decomposition method proposed in this invention decomposes the time series data of multiple variables in a unified manner, so that the number of final IMFs remains consistent. This avoids the use of complex grouping methods, thereby reducing computational complexity and improving the computational efficiency and feasibility of the model in practical applications.

[0017] 3) The dual-channel deep learning model proposed in this invention divides the IMF after MEMD into high-frequency and low-frequency components, and uses the WaveNet model to process the high-frequency IMF and the LSTM model to process the low-frequency IMF. This can better capture high-frequency fluctuations and low-frequency trends respectively, effectively alleviate the impact of high-frequency IMF on the model, and further improve the prediction accuracy of medium- and long-term effective wave height. Attached Figure Description

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0019] Figure 1 This is a schematic diagram of the process for predicting the medium- and long-term effective wave height based on multivariate mode decomposition according to an embodiment of the present invention. Figure 2 This is a graph showing the calculation of the Pearson correlation coefficient in an embodiment of the present invention. Figure 3 This is a MEMD diagram of an embodiment of the present invention; Figure 4 This is a calculation diagram of the PE method according to an embodiment of the present invention; Figure 5 This is a structural diagram of an LSTM cell according to an embodiment of the present invention; Figure 6 This is a scatter plot comparing the predicted and actual long-term effective wave heights at 6h, 12h, and 24h in an embodiment of the present invention. Detailed Implementation

[0020] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0021] like Figure 1 As shown, a method for predicting medium- to long-term effective wave height based on multivariate mode decomposition includes the following steps: S1: Collect historical standard meteorological data, preprocess the data, and then use the Pearson correlation coefficient method to screen out variables related to effective wave height.

[0022] The variables include significant wave height (SWH), wind direction (WDIR), wind speed (WSPD), peak gust wind speed (GST), dominant wave period (DPD), mean wave period (APD), dominant wave direction (MWD), sea level pressure (PRES), air temperature (ATMP), and sea surface temperature (WTMP).

[0023] Data preprocessing includes outlier removal and data alignment of the collected meteorological data.

[0024] The variables with significant wave height correlation were screened using the Pearson correlation coefficient method, and the calculation formula is as follows: ; In the formula, This represents the Pearson correlation coefficient. and They represent variables respectively. and No. Data from one sample, and They represent variables respectively. and The average value, This represents the number of samples for the variable.

[0025] A correlation threshold was set, and the Pearson correlation coefficient was compared with the correlation threshold. Four variables were selected: significant wave height (SWH), wind speed (WSPD), peak gust wind speed (GST), and mean wave period (APD).

[0026] S2: Normalize the selected variables and perform multivariate empirical mode decomposition. Then, use the permutation entropy method to group the decomposed intrinsic mode functions into high- and low-frequency groups.

[0027] The selected variables are normalized by performing Min-Max normalization on their time series data and mapping it to the 0-1 interval. The calculation formula is as follows: ; In the formula, Represents the original data. Represents normalized data. and These represent the maximum and minimum values ​​in the original data, respectively.

[0028] Multivariate empirical mode decomposition (MEMD) is used to extend the local mean of a variable time series by projecting it onto a hypersphere along multiple directions, thereby obtaining multiple eigenmode functions (IMFs) of the same number. Specifically, MEMD is used to decompose the normalized four-variable time series data, resulting in four IMFs of equal quantity. For univariate time series... The formula for calculating empirical mode decomposition is: ; In the formula, Indicates the first One IMF, Indicates residual signal, This indicates the number of IMFs in the final decomposition.

[0029] MEMD extends the calculation of the local mean of a multivariate time series by projecting it onto the hypersphere along multiple directions; the formula for calculating the local mean of a multivariate time series is: ; In the formula, Represents the local mean. Indicates the number of multiple variables. Represents the direction vector The multidimensional envelope of the projection.

[0030] The results of MEMD are as follows: Figure 3 As shown, the number of IMFs decomposed for each variable is consistent.

[0031] Use PE to group the decomposed IMFs into high- and low-frequency groups: set each IMF after univariate decomposition to a length of [value missing]. time series ,right Reconstruct the matrix to obtain the matrix. The calculation formula is: ; ; In the formula, Indicates the embedding dimension. Indicates the delay time.

[0032] The permutation entropy is calculated using the following formula: ; In the formula, Represents the permutation entropy. Representation matrix The OK.

[0033] Extending this approach, permutation entropy is calculated for all selected variables, and the permutation entropy of their corresponding IMFs is averaged. Based on a set correlation threshold, high-frequency IMFs and low-frequency IMFs are grouped. The specific calculation is as follows: Figure 4 As shown.

[0034] S3: Use the sliding window algorithm to construct a dataset based on the proportions of the grouped data.

[0035] Specifically, all IMF time series data were divided into training, validation, and test sets in a 3:1:1 ratio.

[0036] S4: Build a dual-channel deep learning model and train the model using the training set.

[0037] A dual-channel deep learning model, including a WaveNet sub-model and a Long Short-Term Memory (LSTM) sub-model.

[0038] The WaveNet sub-model is used to train high-frequency intrinsic mode functions. The specific process is as follows: the time series is passed through a causal layer and several residual blocks, and then processed by activation functions and normalized exponential functions to output the results; the residual blocks contain extended convolutional neural networks, gating structures, and residual modules. Specifically, it includes: 1) Set the input to a time series Based on previously input samples, predict the distribution of each sample, and its conditional probability function expression is: ; In the formula, Indicates the sample index. This represents a sample of the current time series. Indicates the characteristic length of the previous sample; 2) The expression for the gated structure is: ; In the formula, and These represent the input and output feature maps of the gated structure, respectively. This represents a trainable convolutional filter. Represents the convolution operator. This represents an element-wise multiplication operator. Indicates the level index. and These represent filters and gates, respectively.

[0039] A Long Short-Term Memory (LSTM) sub-model is used to train low-frequency intrinsic mode functions; such as... Figure 5 As shown, an LSTM cell structure consists of a cell, an input gate, an output gate, and a forget gate. The cell structure stores these values ​​as memory at different time intervals, while the gates regulate the features entering and leaving the cell structure.

[0040] The formula for calculating each variable of the flow in the LSTM cell structure is: Specifically, this involves adding unit structures to the LSTM sub-model of the Long Short-Term Memory network, expressed as follows: ; ; ; ; ; ; In the formula, , , These represent the input, forget, and output gates, respectively. yes Input data at any time, It is the output of the previous LSTM unit. and These are the weights and biases corresponding to each gate. and express The old element structure state and the candidate element structure state at time 1. and These represent the hyperbolic tangent and sigmoid functions, respectively.

[0041] High-frequency IMFs are input into the WaveNet model for training, while low-frequency IMFs are input into the Long Short-Term Memory (LSTM) network model for training. The validation set is used to provide feedback during training, thereby optimizing the model's performance and preventing overfitting.

[0042] S5: Input the test set into the trained dual-channel deep learning model, obtain the prediction results of the intrinsic mode functions (IMFs), and sum the prediction results of all IMFs to obtain the final effective wave height prediction value.

[0043] To verify the effectiveness of the method of the present invention for medium- and long-term effective wave height prediction, such as... Figure 6As shown, the predicted significant wave height values ​​for the next 6 hours, 12 hours, and 24 hours using the test set are compared with the actual significant wave height values. Model performance is evaluated using root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and correlation coefficient (R). Lower values ​​for RMSE, MAE, and MAPE indicate better model performance; a higher R value indicates better model performance.

[0044] The formula for calculating performance indicators is: ; ; ; ; In the formula, and They represent variables respectively. and No. Data from one sample, and They represent variables respectively. and The average value, This represents the number of samples for the variable.

[0045] This method compares the evaluation results with those of the single-model LSTM method and the MEMD+LSTM method. The comparison results are shown in Table 1. Table 1

[0046] The test set of this invention yielded the following results for RMSE, MAE, MAPE, and R at 6h, 12h, and 24h: 0.089, 0.113, 0.147; 0.065, 0.083, 0.099; 0.042, 0.053, 0.060; 0.989, 0.984, 0.968. The results show that the model of this invention significantly outperforms the single-model LSTM method in predicting medium- and long-term effective wave heights, and is slightly better than the MEMD+LSTM method.

[0047] Experimental results show that this invention can not only effectively capture the interaction between significant wave height data and other variables, but also better handle the IMF generated by the decomposition algorithm, proving the effectiveness of the improved method presented in this paper. By combining the advantages of existing algorithms, this ensemble model significantly improves the prediction accuracy of medium- and long-term significant wave heights, providing reliable technical support for practical applications.

[0048] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The scope of protection of the present invention should be the technical solution described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A method for predicting medium- and long-term effective wave height based on multivariate mode decomposition, characterized in that, Includes the following steps: S1: Collect historical standard meteorological data, preprocess the data, and then use the Pearson correlation coefficient method to screen out variables related to effective wave height; S2: Normalize the selected variables and perform multivariate empirical mode decomposition. Then, use the permutation entropy method to group the decomposed intrinsic mode functions into high- and low-frequency groups. S3: Use the sliding window algorithm to construct a dataset based on the proportions of the grouped data; S4: Construct a dual-channel deep learning model and train the model using the training set; S5: Input the test set into the trained dual-channel deep learning model, obtain the prediction results of the intrinsic mode functions (IMFs), and sum the prediction results of all IMFs to obtain the final effective wave height prediction value.

2. The method for predicting medium- and long-term effective wave height based on multivariate mode decomposition according to claim 1, characterized in that, In step S1, the variables include significant wave height, wind direction, wind speed, peak gust speed, dominant wave period, average wave period, dominant wave direction, sea level pressure, air temperature, and sea surface temperature.

3. The method for predicting medium- and long-term effective wave height based on multivariate mode decomposition according to claim 1, characterized in that, In step S1, the data is preprocessed by removing outliers and aligning the collected meteorological data.

4. The method for predicting medium- and long-term effective wave height based on multivariate mode decomposition according to claim 1, characterized in that, In step S1, the variables related to effective wave height are screened using the Pearson correlation coefficient method, and the calculation formula is as follows: ； In the formula, This represents the Pearson correlation coefficient. and They represent variables respectively. and No. Data from one sample and They represent variables respectively. and The average value, This represents the number of samples for the variable.

5. The method for predicting medium- and long-term effective wave height based on multivariate mode decomposition according to claim 1, characterized in that, Step S1 further includes setting a correlation threshold, comparing the Pearson correlation coefficient with the correlation threshold, and selecting the significant wave height SWH, wind speed WSPD, peak gust wind speed GST, and mean wave period APD.

6. The method for predicting medium- and long-term effective wave height based on multivariate mode decomposition according to claim 1, characterized in that, In step S2, the selected variables are normalized by performing Min-Max normalization on the time series data of the selected variables and mapping it to the 0-1 interval. The calculation formula is as follows: ； In the formula, Represents the original data. Represents normalized data. and These represent the maximum and minimum values ​​in the original data, respectively.

7. The method for predicting medium- and long-term effective wave height based on multivariate mode decomposition according to claim 1, characterized in that, In step S2, the multivariate empirical mode decomposition involves expanding the local mean of the variable time series using multivariate empirical mode decomposition (MEMD). This is achieved by projecting the MEMD values ​​onto a hypersphere along multiple directions, thereby obtaining multiple intrinsic mode functions (IMFs) of equal number. The formula for calculating the local mean of the multivariate time series is as follows: ； In the formula, Represents the local mean. Indicates the number of multiple variables. Represents the direction vector The multidimensional envelope of the projection.

8. The method for predicting medium- and long-term effective wave height based on multivariate mode decomposition according to claim 1, characterized in that, In step S4, the dual-channel deep learning model includes a WaveNet sub-model and a Long Short-Term Memory (LSTM) sub-model.

9. The method for predicting medium- and long-term effective wave height based on multivariate mode decomposition according to claim 8, characterized in that, The WaveNet sub-model, used to train high-frequency intrinsic mode functions, includes: 1) Set the input to a time series Based on previously input samples, predict the distribution of each sample, and its conditional probability function expression is: ； In the formula, Indicates the sample index. This represents a sample of the current time series. Indicates the characteristic length of the previous sample; 2) The expression for the gated structure is: ； In the formula, and These represent the input and output feature maps of the gated structure, respectively. This represents a trainable convolutional filter. Represents the convolution operator. This represents an element-wise multiplication operator. Indicates the level index. and These represent filters and gates, respectively.

10. The method for predicting medium- and long-term effective wave height based on multivariate mode decomposition according to claim 8, characterized in that, The Long Short-Term Memory (LSTM) sub-model is used to train low-frequency intrinsic mode functions. Specifically, it involves adding unit structures to the LSTM sub-model, as expressed in the following expression: ； ； ； In the formula, , , These represent the input, forget, and output gates, respectively. express Input data at any time, This indicates the output of the previous unit. and These represent the weights and biases corresponding to each gate, respectively. This represents the sigmoid function.

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