A multi-step significant wave height prediction method based on variational mode decomposition and adaptive frequency allocation gated sequence LSTM

Abstract

The application discloses a multi-step significant wave height prediction method based on variational mode decomposition and adaptive frequency allocation gated sequence LSTM. The method pre-processes the significant wave height sequence in time sequence and respectively performs variational mode decomposition, maps the mode to a high-frequency branch, a medium-frequency branch and a low-frequency branch through an adaptive frequency allocation module, generates a future guide hidden state by a multi-branch sequence LSTM coding and decoding, and combines branch energy to output a multi-step significant wave height prediction value through a gated timing adjustment module. The application improves the prediction accuracy and stability of a non-stationary sea wave sequence at a medium-long prediction step.

Description

Technical Field

[0001] This invention relates to the fields of time series forecasting and intelligent marine environment forecasting, and in particular to a multi-step effective wave height prediction method based on variational mode decomposition and adaptive frequency allocation gated sequence LSTM. Background Technology

[0002] Significant wave height is one of the important parameters characterizing sea state and is widely used in scenarios such as maritime traffic control, port operations, offshore engineering, marine resource development, and marine disaster early warning. Significant wave height time series usually exhibit strong nonlinearity, non-stationarity, and multi-scale fluctuation characteristics. Its changes are influenced by factors such as wind field, ocean current, topography, seasonal wave conditions, and extreme weather. Therefore, phase lag and error accumulation are prone to occur in multi-step forecast tasks such as 12-hour, 24-hour, 36-hour, and 48-hour forecasts.

[0003] Traditional numerical wave models can describe wave propagation and evolution based on physical equations, but these methods rely on high-quality boundary conditions, complex parameter settings, and high computational resources, making them difficult to apply at low cost in engineering deployment scenarios that require rapid rolling updates. Statistical prediction models and single machine learning models, while computationally simple, are not well-suited to non-stationary fluctuations, multi-frequency coupling, and the accumulation of prediction errors over medium to long step sizes.

[0004] In recent years, VMD-LSTM, EMD-LSTM, CNN-LSTM, and other decomposition-prediction combination models have been used for significant wave height and similar time series prediction tasks. These methods typically decompose the original sequence into several modes, then predict each mode separately and superimpose the results, which can reduce the complexity of the original sequence to some extent. However, the organization of mode-to-frequency branches in existing technologies often relies on mode indices, fixed thresholds, or manual experience, making it difficult to adapt to the drift of the center frequencies of intrinsic mode components under different sea areas, seasons, and sea states.

[0005] On the other hand, existing multimodal prediction methods typically use conventional LSTM or direct mapping to output future values, without fully separating the historical encoding and future decoding processes. The multi-scale fusion stage often employs simple superposition, static weighting, or a single attention mechanism, failing to dynamically assess the importance of different frequency scales by combining branch hidden states and current frequency band energy. When sea state changes abruptly or the forecast step size increases, these methods are prone to problems such as imbalanced frequency band contributions, cross-scale interference, and decreased forecast stability. Summary of the Invention

[0006] (a) Technical problems to be solved

[0007] The purpose of this invention is to provide a multi-step effective wave height prediction method based on variational mode decomposition and adaptive frequency allocation gated sequence LSTM, so as to solve the problems of rigid frequency band organization, insufficient time series representation, coarse cross-scale fusion, information leakage risk, and accumulation of prediction errors in medium and long step lengths in existing effective wave height prediction methods.

[0008] (II) Technical Solution

[0009] This invention comprises the following five steps:

[0010] Step 1: Segmented VMD decomposition and IMF input tensor construction.

[0011] Variational mode decomposition is performed on the divided training time period, validation time period and test time period respectively, decomposing the non-stationary effective wave height sequence into multiple band-limited intrinsic mode components, and stacking multiple IMF components within the historical window into the input tensor Z.

[0012] Step 2: Adaptive frequency soft allocation and branch input generation.

[0013] For each intrinsic mode component, its spectral centroid is calculated and a spectral prior score is obtained. At the same time, a learnable descriptor is set for each intrinsic mode component, and a learning assignment score is obtained by mapping through a multilayer perceptron. The spectral prior score and the learning assignment score are fused to generate a soft assignment matrix, and high-frequency, mid-frequency and low-frequency weighted inputs are constructed accordingly.

[0014] Step 3: Modeling multi-branch sequence LSTM encoding and decoding.

[0015] The high-frequency, mid-frequency, and low-frequency weighted inputs are fed into the corresponding sequence LSTM branches, the encoder reads the historical window and generates the coded final state, and the decoder generates the future guided hidden state oriented towards the target prediction step size.

[0016] Step 4: Gated fusion and multi-scale representation generation.

[0017] Calculate the energy descriptor at the last moment of each frequency branch, concatenate the branch's future guided hidden state with the corresponding energy descriptor, and input it into the gating timing adjustment module to generate dynamic fusion weights, thereby obtaining the fusion timing representation.

[0018] Step 5: Multi-step effective wave height output and statistical analysis of results.

[0019] The time series representation is input into the prediction mapping layer, and the effective wave height prediction result under the target prediction step size is output. During the training process, the mean absolute error, root mean square error, or a weighted combination of the two are used as loss functions to optimize the parameters of adaptive frequency allocation AFA, multi-branch sequence LSTM, GT gated time series network and prediction mapping layer.

[0020] (III) Beneficial Effects

[0021] The advantages of this invention are as follows: Compared with the prior art, this invention has at least the following effects: First, it reduces the non-stationary complexity of the original effective wave height sequence through variational mode decomposition; second, it avoids information loss caused by fixed mode grouping by soft mapping the intrinsic mode components to high-frequency, mid-frequency, and low-frequency branches through an adaptive frequency allocation mechanism; third, it enhances the future guidance representation capability under medium- and long-term forecast step sizes by separating historical encoding and future decoding through a multi-branch sequence LSTM encoding and decoding structure; fourth, it improves robustness under sea state changes by dynamically fusing multi-scale information through a gated timing adjustment module in conjunction with branch hidden states and frequency band energy; and fifth, it reduces the risk of future information leakage by performing VMD separately after dividing the time. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the overall prediction model structure proposed in this invention, which shows that the effective wave height data is decomposed into multiple components by VMD, and then distributed to high-frequency, mid-frequency and low-frequency branches by the AFA adaptive frequency allocation module. Finally, the prediction result is output through the sequence LSTM and gated timing adjustment module.

[0023] Figure 2 This is a flowchart of the AFA adaptive frequency allocation module in this invention; it shows the process of IMF component sequence input, IMF embedding representation extraction, spectral feature calculation, Gaussian prior construction, Softmax normalization allocation, and high-frequency, mid-frequency, and low-frequency component group output.

[0024] Figure 3 This is a flowchart of the GT gating timing adjustment module in this invention; it shows the process of obtaining high-frequency, mid-frequency and low-frequency component groups and residual reference terms, calculating timing gating coefficients, correcting residuals, generating fusion weights and weighted fusion output.

[0025] Figure 4 The scatter plots show the distribution of measured and predicted significant wave heights at site 41004 with prediction steps of 12, 24, 36, and 48 hours; they also show the distribution of the ideal line, the fitted line, and the validation samples.

[0026] Figure 5 The graph shows a time series comparison of measured and predicted values ​​for station 41004 at prediction step lengths of 12 hours, 24 hours, 36 hours, and 48 hours, illustrating the tracking effect of the model of this invention on the trend of effective wave height variation under different prediction step lengths. Detailed Implementation

[0027] To make the objectives, technical solutions, and beneficial effects of the present invention clearer, the specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0028] Reference Figures 1 to 5 This invention provides a multi-step effective wave height prediction method and system based on variational mode decomposition and adaptive frequency allocation gated sequence LSTM, and its specific implementation steps are as follows.

[0029] Step 1: Segmented VMD decomposition and IMF input tensor construction.

[0030] To reduce the impact of the non-stationarity of the effective wave height sequence on the prediction model, variational mode decomposition is performed on the original sequence within the training interval, and the resulting K IMF components are used as the basic input for subsequent frequency assignment. The decomposition result can be expressed as:

[0031]

[0032] in, This represents the original significant wave height time series to be decomposed. This represents the k-th eigenmode component obtained from VMD decomposition. This represents the total number of IMF modes obtained from the decomposition. This represents the residual terms not characterized by each modal component; k is the modal index, ranging from 1 to K. VMD achieves adaptive decomposition by minimizing the bandwidth of each modal component, and its optimization objective is:

[0033]

[0034] in, This represents the k-th modal component to be solved. This represents the center angular frequency of the k-th modal component; Represents the Dirac function, Represents the imaginary unit. Pi This represents the convolution operation. This represents taking the partial derivative with respect to time t; This represents the complex exponential term used to demodulate the k-th modal component to the baseband. Represents the L2 norm. The constraints are used to ensure that all modal components, after reconstruction, are consistent with the original sequence. During the alternating optimization process, the modal components and center frequencies are updated according to the following formulas:

[0035]

[0036] in, This represents the frequency domain representation of the k-th modal component obtained in the (n+1)-th iteration. Represents frequency variables; Represents the original effective wave height sequence The frequency domain representation, The frequency domain representation of the i-th modal component; The frequency domain representation of the Lagrange multiplier, The variable represents the VMD bandwidth penalty factor, and n represents the number of alternating optimization iterations. The center frequency of the k-th modal component is updated by the following formula:

[0037]

[0038] in, This represents the center frequency of the k-th mode after the (n+1)-th iteration update. Let represent the energy density of the k-th modal component at frequency ω. The numerator is used to calculate the energy-weighted frequency sum, and the denominator is used to calculate the total spectral energy of that modal component. After combining each IMF component according to a time window, the input tensor is constructed as follows:

[0039]

[0040] in, This represents the model input tensor obtained by stacking K IMF components according to time windows; Indicates the number of samples in the batch. Indicates the length of the input time window. represents the number of IMF components, to These represent the 1st to the Kth IMF components, respectively.

[0041] Step 2: Adaptive frequency allocation soft allocation and branch input generation.

[0042] Reference Figure 2 For each IMF component, the spectral energy center is calculated, and prior distance constraints for high, mid, and low frequencies are introduced to allow each IMF component to enter different frequency band branches via soft allocation. The spectral energy center of the k-th IMF component is:

[0043]

[0044] in, This represents the spectral energy center of the k-th IMF component. This represents the j-th discrete frequency point. Indicates the k-th IMF component at frequency Spectral values ​​at that location This indicates the energy intensity at that frequency point. This indicates a small positive number to prevent the denominator from being zero. After normalizing the frequency characteristics, the frequency band... Establish Gaussian prior scores:

[0045]

[0046] in, This indicates that the k-th IMF component belongs to the frequency band. The frequency prior score, This represents the energy center of the normalized spectrum. Indicates frequency band The central prior, δ, represents the width of the Gaussian prior. The formula represents the frequency band category, with H, M, and L representing the high-frequency, mid-frequency, and low-frequency branches, respectively. This formula characterizes the fit of the IMF components to each frequency band by measuring the distance between the spectrum center and the frequency band center. Simultaneously, a data-driven allocation score for IMF embedding is generated using a multilayer perceptron.

[0047]

[0048] in, The representation is given by the MLP based on the k-th IMF embedding. The output data drives the assignment of score vectors. This indicates that the vector is in the frequency band. The amount on, This represents the embedding representation of the k-th IMF component, and MLP represents a multilayer perceptron. This represents the combined allocation score after fusing data-driven scores and frequency priors. This represents the temperature coefficient of the AFA module. The weighting coefficients represent the frequency prior scores. This represents the corresponding Gaussian prior score.

[0049]

[0050] in, This indicates that the k-th IMF component is assigned to the frequency band. Soft allocation weights, Represents an exponential function. This represents the frequency band index traversed during Softmax normalization. This represents the sum of the scores allocated to the three branches: high frequency, mid frequency, and low frequency. This indicates that the sum of the weights allocated to the same IMF component across the three frequency bands is 1. The input tensor is then weighted according to this weight to obtain the three frequency band branch inputs:

[0051]

[0052] in, Indicates input to frequency band The weighted feature tensor of the branch, This represents the input tensor composed of all IMF components. Indicates frequency band The corresponding soft-assigned weight vector, where ⊙ represents element-wise multiplication. This indicates that three branch inputs—high frequency, medium frequency, and low frequency—are generated respectively.

[0053] Step 3: Modeling multi-branch sequence LSTM encoding and decoding.

[0054] The three frequency band branches are input into their respective sequence LSTM encoder-decoder networks to obtain temporal dependency features at different frequency scales. For any frequency band branch, the gating update process of the LSTM unit is as follows:

[0055]

[0056] in, , and Let these represent the input gate, forget gate, and output gate of the LSTM at time t, respectively. This represents the Sigmoid activation function; , and These represent the weight matrices for the input gate, forget gate, and output gate, respectively. , and These represent the corresponding bias vectors; This represents the input features of the frequency band branch at time t. This indicates the hidden state at the previous moment. This represents the input vector after concatenating the two.

[0057]

[0058] in, This represents the candidate memory unit at time t. This represents the hyperbolic tangent activation function. and These represent the weight matrix and bias vector of the candidate memory unit, respectively; This represents the memory unit at time t. This represents the memory unit from the previous moment. Let represent the hidden state at time t. This indicates element-wise multiplication; this set of formulas controls the retention of historical information, the writing of current information, and the output of hidden states through forget gates, input gates, and output gates. The encoder's end state serves as the decoder's initial state, yielding the branch prediction representation at the target step size:

[0059]

[0060] in, and They represent frequency bands respectively. The initial hidden state and initial memory unit of the branch decoder. and They represent frequency bands respectively. The hidden state and memory unit output by the branch encoder at the end L of the window; Indicates decoder, Indicates encoder, Indicates frequency band Decoding representation of the branch at prediction step size τ Indicates frequency band The corresponding decoder, This represents the initial input to the decoder.

[0061] Step 4: Gated fusion and multi-scale representation generation.

[0062] Reference Figure 3 To fully utilize the complementary information from different frequency band branches, a GT-gated timing adjustment module is constructed, and the fusion weights are adaptively determined based on the branch prediction representation and branch energy descriptor. The energy descriptors for each frequency band branch are:

[0063]

[0064] in, Indicates frequency band The energy descriptor of the branch, Indicates frequency band Branch feature dimension Indicates the feature dimension index. Indicates frequency band The branch occurs at point T at the end of the time window. The eigenvalues ​​are used to summarize the overall energy intensity of each frequency band branch at the end of the current window. The predicted representations of each branch are concatenated with the energy descriptor to form the gated input vector:

[0065]

[0066] in, This represents the input vector of the GT gated network. , and Let represent the decoding representations of the high-frequency, mid-frequency, and low-frequency branches at the prediction step size τ, respectively. , and The first three terms represent the energy descriptors for the high-frequency, mid-frequency, and low-frequency branches, respectively; the square brackets indicate vector concatenation operations.

[0067] The fusion weights of the three branches are calculated using a gated network:

[0068]

[0069] in, This represents the fusion weight vector output by the GT gated network. Represents the normalized exponential function, and This represents the weight matrix of a two-layer gating network. and This represents the corresponding bias vector. This represents a hyperbolic tangent nonlinear mapping. This represents the gated input vector obtained by concatenating the branch decoding representation and the energy descriptor.

[0070] The predicted representations of the three frequency bands are weighted and fused according to the fusion weights to obtain the final multi-scale representation and prediction results:

[0071]

[0072] in, This represents the multi-scale representation after weighted fusion of three frequency band branches. , and These represent the fusion weights for high-frequency, mid-frequency, and low-frequency branches, respectively. , and These represent the decoding representations of the corresponding branches at the prediction step size τ; Indicates the first The final predicted value of the effective wave height at any given time. Indicates the predicted mapping layer weights. This indicates the bias of the prediction mapping layer.

[0073] Step 5: Multi-step effective wave height output and statistical analysis of results.

[0074] During training, the learning rate, hidden layer dimensions, branch network parameters, and gating parameters are adjusted using a validation set, and multi-step prediction accuracy is evaluated using a test set. To simultaneously constrain the mean absolute error and root mean square error, the model's training loss function is:

[0075]

[0076] in, This represents the model training loss function. This represents the weighting coefficient between the mean absolute error term and the root mean square error term. This represents the number of training samples, and i represents the sample index. This represents the model prediction value for the i-th sample. This represents the actual observed value of the i-th sample. The loss function simultaneously constrains the average bias and the larger error, enabling the model to maintain stable error control capabilities during multi-step predictions. Once training is complete, inputting the historical sequence of effective wave heights up to the time before the prediction point into the trained model will output effective wave height predictions for target step lengths such as 12 hours, 24 hours, 36 hours, and 48 hours.

[0077] The method of this invention achieves superior overall prediction performance at all prediction step lengths. In 12-hour prediction, the RMSE, MAE, MAPE, R, and R² scores of the method of this invention are reduced by 9.0%, 10.2%, and 11.8% respectively compared to the best-performing comparative model VMD-DLT at that step length.

[0078] As the prediction step size increases from 12 hours to 48 hours, the prediction difficulty of each model gradually increases, but the method of this invention still maintains a stable advantage. Its RMSE in 24-hour, 36-hour, and 48-hour predictions is lower than that of other comparative models; in the 48-hour prediction, the R² of the method of this invention still reaches 0.8775, indicating that it still has good correlation preservation ability under longer prediction step sizes.

[0079] Experimental results show that the method of the present invention can simultaneously take into account both short-term prediction accuracy and medium- to long-term prediction stability, and has strong multi-step prediction adaptability for effective wave height sequences that are nonlinear, non-stationary, and have multi-frequency coupling characteristics.

[0080] Example

[0081] The effects of the present invention are further illustrated by the following data:

[0082] In this embodiment, the hourly significant wave height sequence of the 41004 ocean buoy station is used as the sample data. The data of this station comes from the NDBC buoy observation sequence. Training samples and test samples are established by dividing the data in chronological order. The specific dataset information is shown in Table 1.

[0083] Table 1. Description of the significant wave height dataset for station 41004

[0084] Data site NDBC Buoy Site 41004 Spatial location 32.50°N, 79.10°W Observation time range 2015.01.01-2020.12.31 Total number of samples 52608 Number of training samples 42086 Number of test samples 10522 Division method Based on chronological order, the first 80% is used for model training, and the last 20% is used for model testing.

[0085] In this embodiment, the complete model adopts a VMD-AFA-SeqLSTM-GT structure; where VMD is used to extract multi-scale fluctuation components, the AFA adaptive frequency allocation module is used to adaptively generate soft allocation inputs for high-frequency, mid-frequency and low-frequency branches, the SeqLSTM (Sequence LSTM) is used for encoding and decoding prediction of each frequency branch, and the GT gated timing adjustment module is used to fuse the future guided hidden states of multiple branches and generate the final prediction value.

[0086] Step 1: Segmented VMD decomposition and IMF input tensor construction.

[0087] Variational mode decomposition (VMD) is performed on the divided training, validation, and testing time periods to decompose the non-stationary effective wave height sequence into multiple band-limited intrinsic mode components (IMFs). Multiple IMFs within the historical window are then stacked into an input tensor Z0. In this embodiment, the data from station 41004 is divided into training, validation, and testing sets in chronological order, with a preferred ratio of 7:1:2. The sampling interval is 1 hour, and missing values ​​are imputed using linear time interpolation followed by normalization. The VMD mode number K is set to 8, the penalty factor α to 2000, the noise tolerance parameter τ to 0, the DC component parameter DC to 0, the initialization method init to 1, the convergence threshold ε to 1e-7, and the maximum number of iterations to 500. The historical input window length L is 72 hours, and samples are constructed for four prediction step sizes: 12 hours, 24 hours, 36 hours, and 48 hours. Therefore, the size of the IMF input tensor Z0 for a single sample can be expressed as L×K. This segmented processing method ensures that the decomposition of the test segment relies only on the data available for the test segment, thus preventing future sample information from leaking into the training phase through the decomposition process.

[0088] Step 2: Adaptive frequency soft allocation and branch input generation.

[0089] For each intrinsic mode component (IMF), its spectral centroid is calculated and a spectral prior score is obtained. Simultaneously, a learnable descriptor is set for each IMF, and a learning assignment score is obtained through multilayer perceptron mapping. The spectral prior score and the learning assignment score are fused to generate a soft assignment matrix, which is used to construct high-frequency, mid-frequency, and low-frequency weighted inputs. In this embodiment, the spectral centroid of each IMF is first normalized to the [0,1] interval, and the three reference frequency centers for high-frequency, mid-frequency, and low-frequency are set to 1, 0.5, and 0, respectively. The spectral prior uses a Gaussian distance function, with a prior smoothing coefficient σ of 0.15. The learnable descriptor dimension d is 16, the descriptor mapping network adopts a two-layer fully connected structure with a hidden layer dimension of 32, and the activation function is ReLU. The assignment temperature parameter T is 1.0, and the spectral prior intensity λ is 0.5. After softmax normalization, a K×3 soft allocation matrix is ​​obtained, in which the sum of the weights of each IMF for the three branches of high frequency, mid frequency and low frequency is 1, and three branch weighted inputs with the same length L as the history window are generated accordingly.

[0090] Step 3: Modeling multi-branch sequence LSTM encoding and decoding.

[0091] The high-frequency, mid-frequency, and low-frequency weighted inputs are fed into the corresponding sequence LSTM branches. The encoder reads the historical window and generates the encoded final state, while the decoder generates the future-oriented guided hidden state for the target prediction step size, thus representing short-period fluctuations, mesoscale changes, and low-frequency trend terms, respectively. In this embodiment, the high-frequency, mid-frequency, and low-frequency branches all adopt an encoder-decoder sequence LSTM structure, and the parameters of each branch are independent. Both the encoder and decoder are set to 2-layer LSTMs, with a hidden state dimension of 64, and the unit state dimension is the same as the hidden state dimension. The LSTM input dimension is determined by the IMF feature dimension after weighting the corresponding branch, and the dropout is set to 0.2. The decoder uses the learnable start vector as its first input and is initialized with the encoder's final state. For 12-hour, 24-hour, 36-hour, and 48-hour prediction tasks, the decoding lengths are 12, 24, 36, and 48, respectively. Finally, the future-oriented hidden state corresponding to the target prediction step size is selected for subsequent gating fusion.

[0092] Step 4: Gated fusion and multi-scale representation generation.

[0093] The energy descriptors at the last moment of each frequency branch are calculated. The future-oriented hidden state of each branch is concatenated with the corresponding energy descriptor and then input into the gating time series adjustment module to generate dynamic fusion weights, thereby obtaining the fused time series representation. In this embodiment, the energy descriptors of each branch are calculated using the mean square energy of the branch inputs within 6 hours near the end of the historical window, and then normalized within the batch. The gating input of each branch is formed by concatenating a 64-dimensional future-oriented hidden state with a 1-dimensional energy descriptor. The GT gating network uses a two-layer perceptron. The first layer has a dimension of 32 and an activation function of tanh. The second layer outputs three gating scores and generates dynamic fusion weights for the high-frequency, mid-frequency, and low-frequency branches through softmax. The fused time series representation has a dimension of 64, and the sum of the gating weights is 1. This process enables the model to adaptively emphasize the dominant frequency band and suppress interference from weaker contributing frequency bands when sea state changes.

[0094] Step 5: Multi-step effective wave height output and statistical analysis of results.

[0095] The time-series representation is input into the prediction mapping layer, and the output is the effective wave height prediction result at the target prediction step size. During training, the mean absolute error, root mean square error, or a weighted combination of the two are used as loss functions to optimize the parameters of the adaptive frequency allocation AFA, multi-branch sequence LSTM, GT-gated time-series network, and prediction mapping layer. In this embodiment, the prediction mapping layer consists of a 64-dimensional input, a 32-dimensional hidden layer, and a 1-dimensional output layer, with ReLU as the activation function of the hidden layer. The output value is denormalized to obtain the effective wave height prediction value in meters. The Adam optimizer is used for training, with an initial learning rate of 0.001, a weight decay of 1e-5, a batch size of 64, and a maximum number of training epochs of 200. Early stopping is triggered when the validation set RMSE does not decrease for 20 consecutive epochs. The loss function is a combination of 0.5×MAE + 0.5×RMSE. The corresponding prediction head is trained for the four prediction step sizes of 12 hours, 24 hours, 36 hours, and 48 hours, or a multi-step output head is set on the basis of a shared feature layer.

[0096] Statistical and comparative analyses were conducted on the multi-step prediction results for 12-hour, 24-hour, 36-hour, and 48-hour periods to evaluate the model's error control and correlation preservation capabilities at short-term, medium-term, and longer prediction step lengths. In this embodiment, the evaluation metrics for the test set include RMSE, MAE, MAPE, correlation coefficient R, and coefficient of determination R²; RMSE and MAE are both in meters, and MAPE is expressed in decimal form.

[0097] Combination Figure 4 and Figure 5 It can be seen that the predicted and measured values ​​maintain a high degree of consistency in the main fluctuation range, and most of the scatter points are distributed near the ideal line, effectively tracking the main peaks and trend changes in the time series. When the prediction step size increases, the error in the peak range is amplified, but this invention reduces the non-stationarity of the original sequence through VMD, improves the efficiency of frequency scale feature utilization through the AFA adaptive frequency allocation module, and enhances the medium- and long-term time series representation and error adjustment capabilities through sequence LSTM and GT, thus mitigating the accumulation of errors in multi-step prediction.

[0098] The innovation of this invention is reflected in the following aspects:

[0099] This invention addresses the problems of strong nonlinearity, non-stationarity, multi-scale fluctuations, and easy accumulation of medium- and long-term prediction errors in significant wave height sequences under complex and changing marine environmental conditions. It proposes a multi-step significant wave height prediction method and system based on variational mode decomposition and adaptive frequency allocation gated sequence LSTM, namely the VMD-AFA-SeqLSTM-GT prediction model. This method first uses VMD to decompose the original significant wave height time series, dividing the complex non-stationary sequence into multiple IMF components with different frequency characteristics, thereby reducing the fluctuation complexity of the original sequence and enhancing the expression of local frequency features. Then, through the AFA adaptive frequency allocation module, the modal components are softly allocated to high-frequency, mid-frequency, and low-frequency branches according to the spectral energy center, frequency prior score, and data-driven allocation score of each IMF component, avoiding information loss caused by fixed frequency band division. Next, the multi-branch sequence LSTM encoding and decoding structure is used to extract the time-dependent features at different frequency scales, improving the model's ability to express short-term drastic fluctuations and medium- to long-term trend changes. Finally, the GT-gated time series adjustment module fuses the prediction representations and energy description information of different frequency branches, adaptively generating fusion weights to obtain the final multi-step significant wave height prediction result.

[0100] In summary, the VMD-AFA-SeqLSTM-GT hybrid prediction model proposed in this invention overcomes the problems of traditional single prediction models failing to fully characterize the non-stationarity of effective wave height, multi-frequency coupling, and accumulation of multi-step prediction errors. Compared with traditional LSTM, decomposed LSTM, and fixed-band combination prediction methods, this invention can reduce the complexity of the original sequence through VMD, achieve adaptive frequency assignment of different IMF components through the AFA adaptive frequency allocation module, capture the long-term and short-term temporal dependencies in different frequency branches through SeqLSTM (Sequence LSTM), and dynamically coordinate the contributions of high-frequency, mid-frequency, and low-frequency branches to the final prediction result through the GT gated fusion mechanism. Therefore, this invention has strong nonlinear modeling capabilities, multi-scale feature fusion capabilities, and medium- to long-term multi-step prediction stability, effectively improving the effective wave height prediction accuracy at prediction step sizes of 12 hours, 24 hours, 36 hours, and 48 hours, providing reliable data support for applications such as maritime traffic scheduling, marine engineering construction, port operations, marine disaster early warning, and marine resource development.

[0101] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-step effective wave height prediction method based on variational mode decomposition and adaptive frequency allocation gated sequence LSTM, characterized in that, Including the following steps: Step 1: Segmented VMD decomposition and IMF input tensor construction: Use the VMD decomposition module to perform variational mode decomposition on the original effective wave height sequence to obtain multiple IMF components with different center frequencies, and stack the IMF components according to the sliding window to form an IMF input tensor; Step 2: Adaptive Frequency Soft Assignment and Branch Input Generation: The adaptive frequency assignment module calculates the spectral energy center, frequency prior score, and data-driven assignment score for each IMF component. The data-driven assignment score and frequency prior score are fused and normalized to obtain the soft assignment weights for each IMF component to the high-frequency, mid-frequency, and low-frequency branches. The IMF input tensor is then weighted according to these soft assignment weights to obtain the high-frequency, mid-frequency, and low-frequency branch inputs, respectively. The specific steps are as follows: (1) Calculate the spectral energy center for the kth IMF component. The formula for representing the dominant frequency position of the IMF component is as follows: In the formula, This represents the spectral energy center of the k-th IMF component. This represents the j-th discrete frequency point. This represents the spectral value of the k-th IMF component at that frequency point. This indicates a small positive number that prevents the denominator from being zero; (2) After normalizing the spectral energy center, compare it with the reference centers of high frequency, mid frequency, and low frequency respectively to construct the Gaussian frequency prior score for each frequency band. The calculation formula is as follows: In the formula, This indicates that the k-th IMF component belongs to the frequency band. The frequency prior score, The normalized value is used to characterize the frequency position of the IMF. Indicates frequency band The central prior, Indicates the prior width. Including high frequency (H), mid frequency (M), and low frequency (L); (3) Input the learnable embedding representation of the k-th IMF component into the multilayer perceptron to obtain the data-driven allocation score, and fuse it with the frequency prior score to obtain the comprehensive allocation score. The calculation formula is as follows: In the formula, This indicates that the score vector is assigned based on data. This represents the embedding representation of the k-th IMF component. Indicates the distribution temperature coefficient. This represents the frequency prior strength coefficient; this fusion method utilizes both data learning information and spectrum prior information simultaneously. (4) Perform Softmax normalization on the overall allocation score to obtain the soft allocation weights for the same IMF component belonging to the high-frequency, mid-frequency, and low-frequency branches, respectively, with the sum of the weights on the three frequency bands being 1. The calculation formula is as follows: In the formula, This indicates that the k-th IMF component is assigned to the frequency band. Soft allocation weights, This represents the frequency band index traversed during Softmax normalization; Soft allocation avoids fixed grouping based solely on modality number; (5) Finally, the IMF input tensor is weighted according to the soft-assignment weights to obtain the high-frequency branch input, mid-frequency branch input, and low-frequency branch input, respectively. The calculation formula is as follows: In the formula, This represents the input tensor composed of all IMF components. Indicates frequency band Weighted input, This indicates element-wise multiplication. Step 3: Multi-branch sequence LSTM encoding and decoding modeling: The sequence LSTM module is used to receive high-frequency, mid-frequency and low-frequency branch inputs. The encoder extracts the hidden states of the historical window and the decoder generates the future guided decoding representation under the target prediction step size. Step 4: Gated fusion and multi-scale representation generation: The gated adjustment and multi-scale fusion module is used to calculate the fusion weights based on the future-oriented decoding representations of each frequency branch and the energy descriptors at the last time step, so as to obtain the weighted fusion prediction results. Step 5: Multi-step effective wave height output and statistical analysis of results: Based on the weighted fusion prediction results, generate the effective wave height prediction value under the target prediction step size, and compare the predicted value with the measured value. Statistical RMSE, MAE, MAPE, R and R² are used as evaluation indicators to evaluate the multi-step prediction accuracy, trend consistency and prediction stability of the model.

2. The multi-step effective wave height prediction method according to claim 1, characterized in that: In step 1, the VMD decomposition module is used to decompose the non-stationary effective wave height sequence into several IMF components with different center frequencies.

3. The multi-step effective wave height prediction method according to claim 1, characterized in that: In step 3, the sequence LSTM module is used to receive high-frequency, intermediate-frequency, and low-frequency branch inputs. The specific steps are as follows: Constructing LSTM units: LSTM is a temporal neural network structure improved on the basis of recurrent neural networks (RNN). Its unit structure includes an input gate, a forget gate, and an output gate. The forget gate is used to selectively discard or retain historical information in the memory unit of the previous time step, the input gate is used to control the degree to which the current input features are written into the memory unit, and the output gate is used to generate the current hidden state based on the current memory state. Constructing a Seq2Seq structure: The Seq2Seq structure includes an encoder and a decoder. The encoder is used to read continuous temporal features within the historical input window. The decoder uses the hidden state at the end of the encoding and the memory state as the initial state, and combines the initial input to generate a decoded representation for future prediction steps step by step. The sequence LSTM prediction branches are formed by embedding LSTM units into a Seq2Seq encoder-decoder structure, and include high-frequency sequence LSTM branches, mid-frequency sequence LSTM branches, and low-frequency sequence LSTM branches. Each branch receives high-frequency, mid-frequency, and low-frequency weighted feature sequences output by the adaptive frequency allocation module, and each branch has the same structure and independent parameters. The high-frequency sequence LSTM branch is used to learn short-period fluctuation features, the mid-frequency sequence LSTM branch is used to learn mesoscale variation features, and the low-frequency sequence LSTM branch is used to learn long-term trend features. Each branch outputs a decoded representation at the corresponding prediction step size and passes it to the gating adjustment and multi-scale fusion module.

4. The multi-step effective wave height prediction method according to claim 1, characterized in that: In step 4, the gating adjustment and multi-scale fusion module is used to dynamically adjust the contribution of each frequency band based on the branch decoding representation and frequency band energy. The specific steps are as follows: First, the energy descriptors for the high-frequency, mid-frequency, and low-frequency branches at the end of the historical window are calculated to characterize the overall energy intensity of each frequency band branch within the current window. The calculation formula is as follows: In the formula, Indicates frequency band The energy descriptor of the branch, This indicates the feature dimension of this branch. Indicates frequency band The branch is located at the j-th eigenvalue at the end of the time window, T. Next, the decoded representations of the high-frequency, mid-frequency, and low-frequency branches at the target prediction step size τ are concatenated with the corresponding energy descriptors to form the input vector of the gated network, the expression of which is: In the formula, This represents the input vector of the gating network. , and Let represent the decoding representations of the high-frequency, mid-frequency, and low-frequency branches at the prediction step size τ, respectively. , and These represent the energy descriptors for the corresponding branches; Next, the input vector of the gated network is sequentially fed into the nonlinear mapping layer and the Softmax normalization layer to obtain the fusion weights of the high-frequency, mid-frequency, and low-frequency branches, the expression of which is: In the formula, Represents the fusion weight vector. and This represents the weight matrix of the gated network. and This represents the bias vector, and the softmax function is used to normalize the fusion weights of each branch. Finally, the decoded representations of the three frequency band branches are weighted and summed according to the fusion weights to obtain a multi-scale fused representation, which is then output by the prediction mapping layer. The expression for the predicted effective wave height at time t is: In the formula, This represents a multi-scale fusion representation. , and These represent the fusion weights of the three frequency band branches, Indicates the first Predicted effective wave height at time 10:00 and These represent the prediction mapping layer weights and biases, respectively.

5. The multi-step effective wave height prediction method according to claim 1, characterized in that: In step 5, the prediction output and evaluation criteria module is used to output multi-step effective wave height prediction values ​​and generate evaluation criteria data. The specific steps are as follows: During training, a weighted combination of the mean absolute error term and the root mean square error term is used as the training loss function to optimize the parameters of the adaptive frequency allocation module, the sequence LSTM module, the gating and multi-scale fusion module, and the prediction mapping layer. After training, the effective wave height historical sequence before the time to be predicted is input into the trained model, and the effective wave height prediction value of at least one target step size in the next 12 hours, 24 hours, 36 hours and 48 hours is output. During the testing phase, predicted and measured values ​​were recorded one by one according to the prediction standard data, and RMSE, MAE, MAPE, R and R² indices were calculated respectively. Among them, RMSE is used to evaluate the degree of penalty for large errors, MAE is used to evaluate the mean absolute deviation, MAPE is used to evaluate the relative error, and R and R² are used to evaluate the consistency between the prediction results and the actual effective wave height change trend. The evaluation results under different prediction step sizes are output as model performance indicators, which are used to evaluate the multi-step effective wave height prediction method in terms of point prediction error, trend correlation and multi-step prediction stability.

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