Sea wave height prediction method and system based on two-dimensional learnable wavelet transform

Abstract

The application relates to the technical field of marine prediction, and discloses a sea wave height prediction method and system based on a two-dimensional learnable wavelet transform, which comprises the following steps: S1, extracting a global frequency feature: performing a Fourier transform operation on input sea wave height data to extract a global frequency feature; S2, extracting a local space-time comprehensive feature; and S3, gate fusion: constructing multiple gate mechanisms, dynamically fusing a residual feature obtained by connecting residuals of the global frequency feature, the local space-time comprehensive feature and the input sea wave height data, respectively calculating fusion weights between the features, weighting and fusing the features, generating unified fusion features, and mapping to obtain finally predicted sea wave height data; the global frequency feature and the local space-time feature are effectively integrated through the gate mechanism, low-frequency swell and high-frequency wind wave features in the sea wave are accurately distinguished, and the precise prediction capability for extreme changes of the sea wave height is significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of marine prediction technology, and specifically relates to a method and system for predicting ocean wave height based on two-dimensional learnable wavelet transform. Background Technology

[0002] Ocean wave heights are random, so accurate wave height prediction can provide accurate information for optimizing wave fields, which is of great significance for protecting the safety of nearshore areas. Accurate wave height prediction can help people understand sea conditions in a timely manner, take preventive measures, reduce disaster risks, and ensure the safety of maritime activities.

[0003] Traditional methods rely on Fourier transform to extract frequency information of ocean waves. However, Fourier transform assumes that the signal is globally stationary, which has significant limitations when processing non-stationary dynamic ocean wave signals. This method struggles to capture local spatiotemporal variation features, leading to the loss of crucial details about ocean waves, especially the manifestation of local events or abrupt changes within a short period. This restricts the comprehensive analysis and accurate modeling of the complex spatiotemporal characteristics of ocean waves.

[0004] While the widely used wavelet transform has some ability to extract local time-frequency features, its core mechanism is based on fixed filters and lacks learning capabilities. This approach often exhibits insufficient adaptability when processing diverse and complex ocean wave signals, limiting the model's accurate modeling of key local features.

[0005] Ocean wave signals can be divided into two categories: low-frequency swells and high-frequency wind waves. Swells are usually caused by distant storms or other weather factors, exhibiting low-frequency, long-period fluctuations; while wind waves are caused by local wind forces, having a higher frequency and shorter period, exhibiting faster fluctuations. Due to the frequency difference between swells and wind waves, traditional methods often fail to effectively separate these two types of wave characteristics, instead treating them together, leading to limitations in capturing local features and accurately modeling wave height prediction. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art. The present invention provides a method and system for predicting ocean wave height based on two-dimensional learnable wavelet transform. By dynamically fusing global frequency features extracted by Fourier transform with local spatiotemporal features such as swell and wind waves extracted by wavelet transform through a gating mechanism, and using an adaptive learnable filter to accurately distinguish between low-frequency swell and high-frequency wind waves, the prediction ability of complex spatiotemporal characteristics and extreme changes of ocean waves is significantly improved.

[0007] To achieve the above objectives, the first aspect of this invention provides a method for predicting ocean wave height based on two-dimensional learnable wavelet transform, comprising the following steps:

[0008] S1. Extract global frequency features:

[0009] Perform a Fourier transform operation on the input wave height data to extract global frequency features;

[0010] S2. Extraction of local spatiotemporal integrated features based on two-dimensional learnable wavelet transform:

[0011] The input wave height data is reshaped into two different dimensions: spatiotemporal features and spatial wave height features. For the spatiotemporal features and spatial wave height features, multiple learnable filters are constructed to extract swell features, wind wave features, spatial variation features, and local spatial variation features. For the multiple features extracted by the learnable filters, a set of two-dimensional learnable wavelet filter kernels is constructed to perform wavelet decomposition to obtain multi-scale frequency features. The inverse two-dimensional learnable wavelet filter kernel is used to reconstruct the data to obtain local spatiotemporal comprehensive features that simultaneously integrate the time and spatial dimensions.

[0012] S3, Gated Fusion:

[0013] Multiple gating mechanisms are constructed to dynamically fuse global frequency features, local spatiotemporal integrated features, and residual features obtained by residual connection of input wave height data. The fusion weights between each feature are calculated separately, and the features are weighted and fused to generate a unified fused feature, which is then mapped to obtain the final predicted wave height data.

[0014] Furthermore, the construction of multiple learnable filters to extract surge features, wind and wave features, spatial variation features, and local spatial variation features includes:

[0015] Constructing a learnable spatiotemporal low-pass filter to capture large-scale variation trends of ocean waves and obtain swell characteristics. ;

[0016] A learnable spatiotemporal high-pass filter is constructed to capture high-frequency variations in ocean waves, thereby obtaining wind and wave characteristics. ;

[0017] A learnable spatial low-pass filter is constructed to capture the stationary features with longer time periods in ocean wave signals, thereby obtaining the spatial variation characteristics of ocean waves on a large scale after processing. ;

[0018] A learnable spatial high-pass filter is constructed to extract high-frequency components with short time periods from ocean wave signals, thereby obtaining the local spatial variation characteristics of ocean waves at a small scale after processing. .

[0019] Furthermore, for each of the extracted features, two sets of two-dimensional learnable wavelet filter kernels are constructed. Wavelet decomposition is performed using these two-dimensional learnable wavelet filter kernels to obtain multi-scale frequency features, including:

[0020] Construct a two-dimensional learnable wavelet spatiotemporal filter kernel, wherein the two-dimensional learnable wavelet spatiotemporal filter kernel is composed of a spatiotemporal low-frequency filter. Spatiotemporal vertical high-frequency filter Spatiotemporal high-frequency filter and spatiotemporal high frequency filters It is formed by aggregation;

[0021] The spatiotemporal low-frequency filter Spatiotemporal vertical high-frequency filter Spatiotemporal high-frequency filter and spatiotemporal high frequency filters These are used to extract spatiotemporal low-frequency information, spatiotemporal vertical high-frequency information, spatiotemporal horizontal high-frequency information, and spatiotemporal high-frequency information, respectively, as follows:

[0022] The spatiotemporal low-frequency filter Low-frequency filtering is performed in both the horizontal and vertical directions;

[0023] The spatiotemporal vertical high-frequency filter The spatiotemporal horizontal high-frequency filter performs low-frequency filtering in the horizontal direction and high-frequency filtering in the vertical direction. Low-frequency filtering occurs in the vertical direction, while high-frequency filtering occurs in the horizontal direction.

[0024] The spatiotemporal high frequency filter High-frequency filtering is performed in both the horizontal and vertical directions;

[0025] Constructing a spatial two-dimensional learnable wavelet filter kernel Processing spatial features, the spatial two-dimensional learnable wavelet filter kernel Space low-frequency filter Space vertical high frequency filter Horizontal high-frequency filter and space high frequency filters It is formed by aggregation.

[0026] Furthermore, the fusion weights are calculated and expressed as:

[0027] ;

[0028] ;

[0029] ;

[0030] in, Represents global frequency characteristics. Represents the spatiotemporal integrated characteristics, Representing residual characteristics, The fusion weights, obtained by concatenating global frequency features and spatiotemporal integrated features and inputting them into the gating network, are used to control the spatiotemporal integrated features. Contribution The fusion weights, obtained by concatenating the global frequency features and residual features and inputting them into the gating network, are used to control the contribution of the global frequency features. The fusion weights, obtained by concatenating the spatiotemporal integrated features and residual features and inputting them into the gating network, are used to control the contribution of the residual features. , , These are the weight matrices for each gated network. It is a bias term. This indicates the concatenation of two features. Indicates the activation function;

[0031] By performing element-wise multiplication and weighted fusion of each feature, the final fused feature is obtained, represented as:

[0032] ;

[0033] in, This indicates a weighted operation. This indicates the fusion feature.

[0034] To achieve the above objectives, a second aspect of the present invention provides a wave height prediction system based on two-dimensional learnable wavelet transform, the wave height prediction system comprising:

[0035] The global frequency information feature extraction module is used to extract global frequency features: it performs a Fourier transform operation on the input wave height data to extract global frequency features.

[0036] The local spatiotemporal comprehensive feature extraction module includes a local spatiotemporal information extraction module and a local spatial information extraction module, which are used to extract local spatiotemporal comprehensive features: the input wave height data is reshaped into two different dimensions of spatiotemporal features and spatial wave height features. For the spatiotemporal features and spatial wave height features, multiple learnable filters are constructed to extract swell features, wind wave features, spatial variation features and local spatial variation features. For the extracted features, a set of two-dimensional learnable wavelet filter kernels are constructed to perform wavelet decomposition to obtain multi-scale frequency features. The inverse two-dimensional learnable wavelet filter kernel designed in conjunction with the two-dimensional learnable wavelet filter kernel is used for reconstruction to obtain local spatiotemporal comprehensive features that simultaneously integrate the time dimension and the spatial dimension.

[0037] The gated fusion module is used for gated fusion: it constructs multiple gated mechanisms to dynamically fuse global frequency features, local spatiotemporal integrated features and residual features obtained by residual connection of input ocean wave height data, calculates the fusion weight between each feature, performs weighted fusion of each feature, generates a unified fusion feature, and maps it to obtain the final predicted ocean wave height data.

[0038] By adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art:

[0039] This invention employs a gating mechanism to effectively integrate global frequency features and local spatiotemporal features. It combines global frequency features extracted by Fourier transform with local low-frequency and high-frequency information extracted by wavelet transform. The gating mechanism dynamically adjusts the contributions of both, ensuring accurate capture of local details and changes while simultaneously capturing global patterns, thereby improving the characterization of complex spatiotemporal characteristics of ocean waves. Through dynamic weight adjustment, this invention achieves the organic fusion of different features, preserving the overall pattern information of global frequency features while capturing detailed changes in local spatiotemporal features, thus significantly improving the accuracy of predicting extreme wave height variations.

[0040] This invention can simultaneously capture the temporal dynamics and spatial local structure of ocean wave signals. Unlike traditional wavelet transform methods, the filter in this invention can adaptively adjust its response characteristics during training, accurately distinguishing between low-frequency swells and high-frequency wind waves. By differentiating between low-frequency swells and high-frequency wind waves, it can more accurately capture the local abrupt changes and multi-scale features of ocean waves. This separation strategy overcomes the limitations of Fourier transform in processing non-stationary signals, and through a specifically designed processing framework, it makes the feature extraction of low-frequency swells and high-frequency wind waves independent of each other, effectively improving the model's ability to process multi-scale, multi-frequency signals and enhancing its ability to express and predict complex ocean wave features.

[0041] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0042] The accompanying drawings, as part of this invention, are provided to further illustrate the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention, but do not constitute an undue limitation thereof. Clearly, the drawings described below are merely some embodiments; those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0043] In the attached diagram:

[0044] Figure 1 This is a flowchart illustrating the wave height prediction method in this specific embodiment;

[0045] Figure 2 This is a diagram illustrating the architecture of the wave height prediction model in this specific implementation.

[0046] Figure 3 This is a comparison chart of the predicted RMSE of different methods in this specific implementation.

[0047] Figure 4 This is a comparison chart of the predicted MAE of different methods in this specific implementation;

[0048] Figure 5 This is a comparison chart of the predicted R² of different methods in this specific embodiment;

[0049] Figure 6 This is a comparison chart of RMSE of different methods in 2-meter wave height prediction in this specific embodiment;

[0050] Figure 7 This is a comparison chart of RMSE of different methods in 4-meter wave height prediction in this specific embodiment;

[0051] Figure 8 This is a comparison chart of RMSE of different methods in 8-meter wave height prediction in this specific embodiment;

[0052] Figure 9 This is a schematic diagram of the wave height prediction system in this specific embodiment. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0054] Please see Figure 1 and Figure 2 This invention provides a method for predicting ocean wave height based on two-dimensional learnable wavelet transform, comprising the following steps:

[0055] S1. Extract global frequency features:

[0056] Perform a Fourier transform operation on the input wave height data to extract global frequency features;

[0057] S2. Extraction of local spatiotemporal integrated features based on two-dimensional learnable wavelet transform:

[0058] The input wave height data is reshaped into two different dimensions: spatiotemporal features and spatial wave height features. For the spatiotemporal features and spatial wave height features, multiple learnable filters are constructed to extract swell features, wind wave features, spatial variation features, and local spatial variation features. For the extracted features, a set of two-dimensional learnable wavelet filter kernels are constructed to perform wavelet decomposition to obtain multi-scale frequency features. The inverse two-dimensional learnable wavelet filter kernel designed in conjunction with the two-dimensional learnable wavelet filter kernel is used for reconstruction to obtain local spatiotemporal comprehensive features that simultaneously integrate the time and spatial dimensions.

[0059] S3, Gated Fusion:

[0060] Multiple gating mechanisms are constructed to dynamically fuse global frequency features, local spatiotemporal integrated features, and residual features obtained by residual connection of input wave height data. The fusion weights between each feature are calculated separately, and the features are weighted and fused to generate a unified fused feature, which is then mapped to obtain the final predicted wave height data.

[0061] It should be noted that the execution entity of the prediction method in this embodiment is a wave height prediction device based on two-dimensional learnable wavelet transform. This device can be an electronic device, a component in an electronic device, an integrated circuit, or a chip. The electronic device can be a mobile electronic device or a non-mobile electronic device. For example, mobile electronic devices can be mobile phones, tablets, laptops, PDAs, in-vehicle electronic devices, wearable devices, etc., while non-mobile electronic devices can be servers and personal computers, etc. This invention does not impose specific limitations. The following description uses a server as the execution entity to illustrate the wave height prediction method based on two-dimensional learnable wavelet transform in this embodiment.

[0062] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of the present invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0063] like Figure 2As shown, this embodiment also provides a wave height prediction model based on two-dimensional learnable wavelet transform, used to implement the wave height prediction method based on two-dimensional learnable wavelet transform as described above. This prediction model includes a global frequency information extraction module, a local spatiotemporal comprehensive feature extraction module, and a gated fusion module. The global frequency information extraction module performs Fourier transform and inverse transform on the input data to generate global frequency features K; the local spatiotemporal comprehensive feature extraction module includes a local spatiotemporal information extraction module and a local spatial information extraction module, which extracts and reconstructs multi-scale features through two-dimensional learnable wavelet transform to generate local spatiotemporal comprehensive features O; the gated fusion module calculates the dynamic fusion weights between K, O, and residual features P to generate fusion features Q and map them to the final prediction result.

[0064] Please see Figure 1 and Figure 2 The specific implementation methods for each step are as follows:

[0065] S1. Extract global frequency features: Perform a Fourier transform operation on the input wave height data to extract global frequency features, which represent the overall trend and periodic pattern of wave changes.

[0066] Specifically, the effective wave height data with dimensions M×N×T at n time points are named As input to the model, frequency information from global regions is extracted and fused. The specific calculation process is as follows:

[0067] ;

[0068] ;

[0069] ;

[0070] in, It is a frequency domain weight tensor. This represents the original input feature map at time step t. This represents the frequency domain representation after the two-dimensional Fourier transform. This indicates that a learnable frequency domain weight tensor is applied to the frequency domain representation. , and Let represent the Fourier transform and the inverse Fourier transform, respectively, and K represent the global frequency characteristic;

[0071] S2. Extraction of local spatiotemporal integrated features based on two-dimensional learnable wavelet transform:

[0072] The input wave height data A is processed by a reshape layer to obtain spatiotemporal features C with dimensions T×L and spatial wave height features D with dimensions M×N. The reshape layer is used to change the dimensions of the data, but does not change the content of the data, represented as follows:

[0073] ;

[0074] ;

[0075] To analyze the signal more accurately, four learnable filters are constructed to extract different features of C and D in the two dimensions respectively. Among them, the spatial low-pass filter captures the stationary features of the signal with a longer time period, reflecting the macro trend of the waves; the spatial high-pass filter extracts the high-frequency components of the signal with a shorter time period, reflecting the rapid changes of the waves; the spatiotemporal low-pass filter combines time and space information to smooth the relationship between time and space, capturing the overall trend of change in the signal; and the spatiotemporal high-pass filter extracts short-term high-frequency features through time and space information, capturing local abrupt changes in the signal.

[0076] Specifically, through a recursive process, the surge characteristics after processing by a learnable spatiotemporal low-pass filter can be obtained. Capturing large-scale changes in ocean waves, wind and wave characteristics processed by a learnable spatiotemporal high-pass filter. To capture the high-frequency changes in ocean waves and highlight the rapid fluctuations under the influence of local wind forces, it is represented as:

[0077] ;

[0078] ;

[0079] ;

[0080] ;

[0081] in, express Surge characteristics at different scales express Wave characteristics at this scale The scale is represented by 2p, which represents the position of the wavelet transform, equivalent to downsampling with a step size of 2. Represents the translation and scaling of a learnable spatiotemporal low-pass filter. Represents the translation and scaling of a learnable spatiotemporal high-pass filter. and The approximation coefficients of spatiotemporal data C based on the scaling function φ and the detail coefficients based on the wavelet function ψ are represented by the constructed learnable spatiotemporal low-pass filter.

[0082] Specifically, through a recursive process, the spatial variation characteristics of ocean waves at a large scale after processing by a learnable spatial low-pass filter can be obtained. Local spatial variation characteristics of ocean waves at a small scale after processing with a learnable spatial high-pass filter , represented as:

[0083] ;

[0084] ;

[0085] ;

[0086] ;

[0087] in, express Spatial variation characteristics at different scales express Local spatial variation characteristics at a certain scale This represents the translation and scaling of a learnable spatial low-pass filter. This represents the translation and scaling of a learnable spatial high-pass filter. and The approximation coefficients of the spatial wave height feature D based on the scaling function φ and the detail coefficients based on the wavelet function ψ are represented by the constructed learnable spatial low-pass filter.

[0088] Specifically, these spatial variation features (DL), local spatial variation features (DH), wind and wave features (CH), and swell features (CL) are combined with supervision of swell and wind and wave data, and loss is calculated using real data values. Finally, they are summed to obtain the first loss function. After all samples in a batch have been predicted and the loss calculated, the batch size is defined as m. The final loss value is obtained using the following formula. Perform backpropagation to update model parameters, the first loss function. Represented as:

[0089] ;

[0090] in, Let be the predicted value of the physical field of the swell spacetime wave height at the next moment in the i-th sample. This represents the true value of the physical field of the surge spacetime wave height at the next moment in the i-th sample; Let be the predicted value of the physical field of the wind and wave spacetime wave height at the next moment in the i-th sample. This represents the true value of the physical field of wind and wave spatial wave height at the next moment in the i-th sample. Let be the predicted value of the physical field of the surge wave height at the next moment in the i-th sample. This represents the true value of the physical field of the surge wave height in the next moment of the i-th sample. Let be the predicted value of the physical field of wind and wave spatial wave height at the next moment in the i-th sample. Let be the true value of the physical field of wind and wave spatial wave height in the i-th sample at the next moment.

[0091] In practical applications, a spatiotemporal low-frequency filter is constructed. Spatiotemporal vertical high-frequency filter Spatiotemporal high-frequency filter and spatiotemporal high frequency filters Spatiotemporal low-frequency information LLC, spatiotemporal vertical high-frequency information LHC, spatiotemporal horizontal high-frequency information HLC, and spatiotemporal high-frequency information HHC are extracted respectively.

[0092] Specifically, spatiotemporal low-frequency filter Extracting low-frequency spatiotemporal information from ocean wave signals involves simultaneously applying low-frequency filters in both the horizontal and vertical directions. This process preserves the smooth portions and overall trend of the wave signal. Since swells are generated by distant storms, they typically exhibit large-scale, low-frequency fluctuations. Therefore, low-frequency filters... This helps to better understand the overall propagation characteristics of low-frequency surges, and is represented as:

[0093] ;

[0094] in, This indicates that low-frequency filtering is performed in the horizontal direction. This indicates that low-frequency filtering is performed in the vertical direction.

[0095] Specifically, wave variations are mainly influenced by horizontal and vertical wind fields, thus requiring analysis of signals from both directions. Since wind waves are caused by localized wind forces and have a higher frequency, they typically exhibit finer, shorter-period fluctuations. Therefore, a spatiotemporal vertical high-frequency filter is first designed. It captures the vertical details of ocean wave signals by performing low-frequency filtering in the horizontal direction and high-frequency filtering in the vertical direction. Spatiotemporal Vertical High-Frequency Filter This can help extract the vertical characteristics of wind and waves, capturing rapid changes and disturbances in the vertical direction. Similarly, it can be used to design spatiotemporal horizontal high-frequency filters. By using low-frequency filtering in the vertical direction and high-frequency filtering in the horizontal direction, the high-frequency components of wind and waves in the horizontal direction can be extracted, thus revealing the rapid changes in wind and waves on the horizontal plane, as shown below:

[0096] ;

[0097] ;

[0098] in, This indicates that low-frequency filtering is performed in the horizontal direction. This indicates that high-frequency filtering is performed in the vertical direction. This indicates that high-frequency filtering is performed in the horizontal direction. This indicates that low-frequency filtering is performed in the vertical direction.

[0099] Specifically, designing a spatiotemporal high-frequency filter This involves performing high-frequency filtering in both the horizontal and vertical directions to extract the highest-frequency details from the signal, including rapid changes and subtle disturbances in the wind and waves, thereby obtaining accurate information on local abrupt changes, represented as:

[0100] ;

[0101] in, This indicates that high-frequency filtering is performed in the horizontal direction. This indicates that high-frequency filtering is performed in the vertical direction.

[0102] High-frequency characteristics of spatiotemporal wind and waves can be achieved by using different filters. Low-frequency characteristics of spatiotemporal surges After feature extraction, different filters are aggregated to obtain the final spatiotemporal two-dimensional learnable wavelet filter kernel. , Wavelet transforms were performed using spatiotemporal two-dimensional learnable wavelet filter kernels to obtain features. , , represented as:

[0103] ;

[0104] ;

[0105] ;

[0106] in, This represents a spatiotemporal two-dimensional learnable wavelet filter kernel. Indicates aggregation operation, This indicates low-frequency characteristics Input wavelet filter kernel Then, the multi-subband wavelet decomposition results were obtained. Indicates high-frequency features Input wavelet filter kernel Then, the multi-subband wavelet decomposition results were obtained.

[0107] Then, the features were verified using spatiotemporal inverse two-dimensional learnable wavelet filters. and Perform inverse wavelet transform and then sum and fuse the results to obtain the reconstructed features. The inverse wavelet kernel inference process is similar to that of a two-dimensional learnable wavelet filter kernel. It can also be constructed using spatiotemporal high-frequency filters and spatiotemporal low-frequency filters, and then the features of the inverse wavelet transform can be obtained. Finally, convolution operations are used. Resize the image to its original size. , represented as:

[0108] ;

[0109] ;

[0110] in, This represents the spatiotemporal inverse two-dimensional learnable wavelet filter kernel. Representation of features and The features are obtained by adding and fusing the features after processing by the inverse two-dimensional learnable wavelet filter kernel in spacetime.

[0111] Similarly, construct a spatial low-frequency filter. Space vertical high frequency filter Horizontal high-frequency filter and space high frequency filters Spatial low-frequency feature (LLD), spatial vertical high-frequency feature (LHD), spatial horizontal high-frequency feature (HLD), and spatiotemporal high-frequency feature (HHD) are extracted respectively. Specifically, this is represented as follows:

[0112] ;

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] in, This indicates that low-frequency filtering is performed in the horizontal direction to extract the low-frequency components of spatial features; This indicates that low-frequency filtering is performed in the vertical direction. This indicates that high-frequency filtering is performed in the vertical direction. This indicates that high-frequency filtering is performed in the horizontal direction to extract the high-frequency components of spatial features;

[0118] Subsequently, the spatial low-frequency characteristics High-frequency characteristics of space Input spatial two-dimensional learnable wavelet filter kernels respectively Wavelet decomposition is performed to obtain sub-band features. , Then, spatial inverse two-dimensional learnable wavelet filter kernels are used respectively. right , Perform an inverse transformation and then add and fuse the results to obtain the reconstructed features. Finally, through convolutional layers Restored to the original scale, spatial branch output features are obtained. , represented as:

[0119] ;

[0120] ;

[0121] ;

[0122] ;

[0123] The input A is processed through a tensor dimension reshape layer to obtain a feature D with dimension M×N. Then, through the wavelet transform, inverse wavelet transform, and convolution operations described above, spatial features are obtained. .

[0124] Finally, feature E and spatial features are fused. This yields the spatiotemporal integrated feature O. Feature E provides rich spatiotemporal dynamic information, while spatial features... This captures the details of the local spatial structure. Therefore, the spatiotemporal integrated feature O not only integrates temporal features but also spatial features, thus more comprehensively representing the complex characteristics of ocean waves. The feature fusion is represented as:

[0125] .

[0126] S3, Gated Fusion:

[0127] Finally, multiple gating mechanisms are constructed to dynamically fuse global frequency features, local spatiotemporal integrated features, and residual features obtained by residual connection of input wave height data. The fusion weights between each feature are calculated separately, and the features are weighted and fused to generate a unified fused feature, which is then mapped to obtain the final predicted wave height data.

[0128] The fusion weights are calculated and expressed as follows:

[0129] ;

[0130] ;

[0131] ;

[0132] in, Represents global frequency characteristics. Represents the spatiotemporal integrated characteristics, Representing residual characteristics, The fusion weights, obtained by concatenating global frequency features and spatiotemporal integrated features and inputting them into the gating network, are used to control the spatiotemporal integrated features. Contribution The fusion weights, obtained by concatenating the global frequency features and residual features and inputting them into the gating network, are used to control the contribution of the global frequency features. The fusion weights, obtained by concatenating the spatiotemporal integrated features and residual features and inputting them into the gating network, are used to control the contribution of the residual features. , , These are the weight matrices for each gated network. It is a bias term. This indicates the concatenation of two features. Indicates the activation function;

[0133] By performing element-wise multiplication and weighted fusion of each feature, the final fused feature is obtained, represented as:

[0134] ;

[0135] in, This indicates a weighted operation. This indicates the fusion feature.

[0136] In practical applications, wavelet errors mainly arise from aliasing between high-frequency and low-frequency filters during decomposition and reconstruction, leading to the loss of some signal features. Therefore, a loss function is designed based on the perfect reconstruction theorem as a second loss function, ensuring that the original signal can be accurately reconstructed after wavelet decomposition and reconstruction.

[0137] This section derives the perfect reconstruction theorem. For ease of calculation, we first perform a Z-transform on the signal. The Z-transform converts the discrete-time signal... A complex function mapped onto the complex plane is expressed as:

[0138] ;

[0139] Where z is a complex number, Represents the time index of a discrete-time signal. Represents a spatiotemporal feature sequence;

[0140] Using the principle of the perfect reconstruction theorem, for Downsampling followed by upsampling ensures no information loss; firstly, the data is processed by downsampling and then upsampling back. Downsampling is performed, represented as:

[0141] ;

[0142] ;

[0143] in, and These represent the information after downsampling through spatiotemporal low-pass filtering and spatiotemporal high-pass filtering, respectively. Represent and z-transform;

[0144] Then, by upsampling it again and combining the above two equations, we can express it as follows:

[0145]

[0146]

[0147] ;

[0148] HBC and LBC respectively represent and Inverse transform of c and These represent the spatiotemporal low-pass reconstruction filter and the spatiotemporal high-pass reconstruction filter, respectively.

[0149] here To eliminate the aliasing phenomenon mentioned above, let:

[0150] ;

[0151] ;

[0152] That is, it satisfies the perfect reconstruction theorem;

[0153] Similarly, in spatial branches, in order to ensure that no information is lost after the spatial features are decomposed and reconstructed, constraints need to be designed based on the perfect reconstruction theorem.

[0154] First, let the Z-transform of the spatial signal be:

[0155] ;

[0156] in It represents a spatial signal sequence.

[0157] Under the spatial branch, the signal is downsampled to obtain:

[0158] ;

[0159] ;

[0160] in, and These represent the information after downsampling through spatial low-pass filtering and spatial high-pass filtering, respectively; They represent , Z-transform.

[0161] Then it is upsampled and reconstructed to obtain:

[0162] ;

[0163] To eliminate aliasing terms The following conditions must be met for a perfect refactoring:

[0164] ;

[0165] ;

[0166] Therefore, we can conclude that:

[0167] ;

[0168] That is, the spatial branches also satisfy the perfect reconstruction theorem, thus ensuring that key information is not lost during the decomposition and reconstruction process.

[0169] Therefore, the definition It consists of two parts, represented as:

[0170] + ;

[0171] in, It is the length of the learnable wavelet filter. It is an index variable for traversing the positions of the filter coefficients. This indicates that low-frequency filtering is performed in the horizontal direction to extract the low-frequency components of the input signal; This indicates that high-frequency filtering is performed in the horizontal direction to extract the high-frequency components of the input signal; This represents a spatiotemporal low-pass reconstruction filter, and... Pairing is used to reconstruct low-frequency components; This represents a spatiotemporal high-pass reconstruction filter, and... Pairing is used to reconstruct high-frequency components; This indicates that low-frequency filtering is performed in the horizontal direction to extract the low-frequency components of spatial features; This indicates that high-frequency filtering is performed in the horizontal direction to extract the high-frequency components of spatial features; This indicates a spatial low-pass reconstruction filter, and Pairing is used to reconstruct the low-frequency components of space; This represents a spatial high-pass reconstruction filter, and... Pairing is used to reconstruct spatial high-frequency components.

[0172] Comparative experiment:

[0173] To verify the technical effectiveness of the proposed method in the significant wave height prediction task, this embodiment selects historical oceanographic data of the coastal waters of Country C as the input dataset. The data time range is from January 1, 2013 to December 31, 2022, with a spatial resolution of 0.5°×0.5°. The data source is the ERA5 reanalysis dataset, which includes hourly 10-meter height wind speed (u component, v component) and significant wave height (SWH) data for each day.

[0174] To train the prediction model, this embodiment divides all samples into three sets: 80% training set, 10% validation set, and 10% test set. The input data includes wind speed and wave height data from the past 10 hours. The model task is to predict wave height changes in the next 1 hour, 6 hours, and 12 hours, aiming to cover various scenarios from short-term nowcasting to medium- and long-term trend prediction.

[0175] The model performance was evaluated using commonly used metrics in ocean wave modeling: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Determination (R²). RMSE measures the standard deviation between predicted and actual values; a smaller value indicates lower error. MAE measures the average magnitude of the error between predicted and actual values. R² represents the model's ability to explain the variation in real data; a value closer to 1 indicates a better fit. Furthermore, to further analyze the model's adaptability under different sea state levels, this embodiment conducted a stratified evaluation based on the magnitude of the significant wave height, selecting typical wave height levels: 2m (low to medium wave height), 4m (medium to high wave height), and 8m (extremely high wave height), corresponding to different intensities of ocean states, to examine the model's robustness and generalization ability under multi-scale wave conditions.

[0176] It should be noted that the formulas for calculating RMSE, MAE, and R² are as follows:

[0177] ;

[0178] ;

[0179] ;

[0180] in, Represents the total number of samples. Indicates the first Index of prediction points, This represents the true value of that point. This represents the model's prediction.

[0181] The experiments in this embodiment were conducted on a single NVIDIA Titan RTX GPU, using the Adam optimizer to train the network for 300 epochs with a minimum batch size of 64. During training, the learning rate was adjusted to 1e-4.

[0182] Using the trained model for prediction, we can see that the predicted value and the true value remain within a very small range. The prediction loss, i.e., the RMSE loss, is as follows: Figure 3 As shown.

[0183] To demonstrate the effectiveness of the proposed solution, this embodiment also selected Convolutional Long Short-Term Memory (CONV-LSTM), Vision Transformer-Residual Multi-kernel Pooling (VIT-RMP), and Federated learning-Attention-based Long Short-Term Memory-Temporal Convolutional Network (FEDAL-TCN) for comparative experiments with the method proposed in this invention. Detailed experimental results are shown in Tables 1-6 below, which relate to RMSE, MAE, and... Comparison of 2m, 4m and 8m wave heights.

[0184] Table 1: Comparison of RMSE between the method proposed in this invention and existing methods

[0185]

[0186] Table 2: Comparison of MAE between the proposed method and existing methods

[0187]

[0188] Table 3: Comparison of the method proposed in this invention with existing methods Comparison

[0189]

[0190] Table 4: Comparison of the method proposed in this invention with existing methods Comparison of wave height RMSE

[0191]

[0192] Table 5: Comparison of the method proposed in this invention with existing methods Comparison of wave height RMSE

[0193]

[0194] Table 6: Comparison of the method proposed in this invention with existing methods Comparison of wave height RMSE

[0195]

[0196] Please see Figure 3 Across all prediction timescales, the method proposed in this invention consistently exhibits the lowest RMSE values, particularly in 1-hour and 6-hour predictions, with RMSEs of 0.02623 and 0.1486 respectively, significantly outperforming CONV-LSTM (0.0321 and 0.1581), VIT-RMP (0.0308 and 0.165), and FEDAL-TCN (0.0337 and 0.1678). This demonstrates that the method proposed in this invention possesses higher accuracy and stronger error control capabilities in short-time effective wave height prediction. The prediction RMSE comparison chart is shown below. Figure 3 As shown.

[0197] Please see Figure 4 Regarding the MAE metric, the method proposed in this invention also performs excellently, with MAE values ​​of 0.0114 and 0.0863 for 1 hour and 6 hours, respectively, both lower than CONV-LSTM (0.0163 and 0.0897), VIT-RMP (0.0156 and 0.0945), and FEDAL-TCN (0.0185 and 0.0936). This further verifies the effectiveness of the proposed method in reducing the average prediction error, demonstrating stability and reliability across different time scales. The MAE prediction comparison chart is shown in Figure 4.

[0198] Please see Figure 5Regarding the R² coefficient of determination, the method proposed in this invention also performs best in 1-hour and 6-hour predictions, reaching 0.9991 and 0.9712 respectively, significantly higher than CONV-LSTM (0.9987 and 0.9707), VIT-RMP (0.9989 and 0.9698), and FEDAL-TCN (0.9989 and 0.9692), demonstrating its stronger explanatory power for observed data variation. Especially in 12-hour predictions, the method proposed in this invention maintains a high R² value of 0.9141, far superior to other methods at this scale, proving its robustness in medium- and long-term prediction tasks. The comparison of prediction R² values ​​is shown in Figure 5.

[0199] Please see Figure 6 , Figure 7 and Figure 8 Under various wave height conditions (2 meters, 4 meters, and 8 meters), the method proposed in this invention also demonstrates excellent predictive performance. In the prediction of a 2-meter wave height, the model's RMSE at 1 hour, 6 hours, and 12 hours are 0.0479, 0.2917, and 0.5325, respectively, significantly outperforming advanced methods such as CONV-LSTM, VIT-RMP, and FEDAL-TCN, demonstrating accurate modeling capabilities under low to medium wave conditions. For a 4-meter wave height, the proposed method's RMSE at the three time scales are 0.0617, 0.4786, and 0.8233, respectively, showing a significant reduction in error compared to the comparison models, indicating stronger stability and adaptability in medium to high wave environments. In the prediction of extreme wave heights above 8 meters, the model still maintains excellent error control capabilities, with RMSEs of 0.0615, 0.2304, and 0.4624, far exceeding other methods, demonstrating higher robustness and reliability in high-risk, violently undulating ocean scenarios. The overall results fully verify the generalization ability of the proposed method under extreme sea conditions, providing strong support for marine disaster early warning and maritime safety applications. Comparison figures for predicting various wave heights are shown below. Figures 6-8 As shown.

[0200] In summary, the method proposed in this invention outperforms existing representative methods in all three evaluation metrics: RMSE, MAE, and R². In particular, it demonstrates higher accuracy and generalization ability in wave height prediction on short timescales, fully proving its potential and advantages in practical applications such as marine forecasting.

[0201] Please see Figure 9 Based on the same inventive concept, a wave height prediction system based on two-dimensional learnable wavelet transform is provided. In specific implementation, a wave height prediction model based on two-dimensional learnable wavelet transform can be adopted, including the following modules:

[0202] The global frequency information feature extraction module is used to extract global frequency features: it performs a Fourier transform operation on the input wave height data to extract global frequency features.

[0203] The local spatiotemporal comprehensive feature extraction module includes a local spatiotemporal information extraction module and a local spatial information extraction module, which are used to extract local spatiotemporal comprehensive features: the input wave height data is reshaped into two different dimensions of spatiotemporal features and spatial wave height features. For the spatiotemporal features and spatial wave height features, multiple learnable filters are constructed to extract swell features, wind wave features, spatial variation features and local spatial variation features. For the extracted features, a set of two-dimensional learnable wavelet filter kernels are constructed to perform wavelet decomposition to obtain multi-scale frequency features. The inverse two-dimensional learnable wavelet filter kernel designed in conjunction with the two-dimensional learnable wavelet filter kernel is used for reconstruction to obtain local spatiotemporal comprehensive features that simultaneously integrate the time dimension and the spatial dimension.

[0204] The gated fusion module is used for gated fusion: it constructs multiple gated mechanisms to dynamically fuse global frequency features, local spatiotemporal integrated features and residual features obtained by residual connection of input ocean wave height data, calculates the fusion weight between each feature, performs weighted fusion of each feature, generates a unified fusion feature, and maps it to obtain the final predicted ocean wave height data.

[0205] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-described technical content to create equivalent embodiments without departing from the scope of the present invention. The implementation schemes in the above embodiments can also be further combined or replaced. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A wave height prediction method based on two-dimensional learnable wavelet transform, characterized in that, Includes the following steps: S1. Extract global frequency features: Perform a Fourier transform operation on the input wave height data to extract global frequency features; S2. Extraction of local spatiotemporal integrated features based on two-dimensional learnable wavelet transform: The input wave height data is reshaped into two different dimensions: spatiotemporal features and spatial wave height features. For the spatiotemporal features and spatial wave height features, multiple learnable filters are constructed to extract swell features, wind wave features, spatial variation features, and local spatial variation features. For the multiple features extracted by the learnable filters, a set of two-dimensional learnable wavelet filter kernels is constructed to perform wavelet decomposition to obtain multi-scale frequency features. The inverse two-dimensional learnable wavelet filter kernel is used to reconstruct the data to obtain local spatiotemporal comprehensive features that simultaneously integrate the time and spatial dimensions. S3, Gated Fusion: Multiple gating mechanisms are constructed to dynamically fuse global frequency features, local spatiotemporal integrated features, and residual features obtained by residual connection of input wave height data. The fusion weights between each feature are calculated separately, and the features are weighted and fused to generate a unified fused feature, which is then mapped to obtain the final predicted wave height data.

2. The method according to claim 1, characterized in that, The construction of multiple learnable filters to extract surge features, wind wave features, spatial variation features, and local spatial variation features includes: Constructing a learnable spatiotemporal low-pass filter to capture large-scale variation trends of ocean waves and obtain swell characteristics. ; A learnable spatiotemporal high-pass filter is constructed to capture high-frequency variations in ocean waves, thereby obtaining wind and wave characteristics. ; A learnable spatial low-pass filter is constructed to capture the stationary features with longer time periods in ocean wave signals, thereby obtaining the spatial variation characteristics of ocean waves on a large scale after processing. ; A learnable spatial high-pass filter is constructed to extract high-frequency components with short time periods from ocean wave signals, thereby obtaining the local spatial variation characteristics of ocean waves at a small scale after processing. .

3. The method according to claim 2, characterized in that, For each of the extracted features, two sets of two-dimensional learnable wavelet filter kernels are constructed. Wavelet decomposition is performed using these kernels to obtain multi-scale frequency features, including: Construct a two-dimensional learnable wavelet spatiotemporal filter kernel, wherein the two-dimensional learnable wavelet spatiotemporal filter kernel is composed of a spatiotemporal low-frequency filter. Spatiotemporal vertical high-frequency filter Spatiotemporal high-frequency filter and spatiotemporal high frequency filters It is formed by aggregation; The spatiotemporal low-frequency filter Spatiotemporal vertical high-frequency filter Spatiotemporal high-frequency filter and spatiotemporal high frequency filters These are used to extract spatiotemporal low-frequency information, spatiotemporal vertical high-frequency information, spatiotemporal horizontal high-frequency information, and spatiotemporal high-frequency information, respectively, as follows: The spatiotemporal low-frequency filter Low-frequency filtering is performed in both the horizontal and vertical directions; The spatiotemporal vertical high-frequency filter The spatiotemporal horizontal high-frequency filter performs low-frequency filtering in the horizontal direction and high-frequency filtering in the vertical direction. Low-frequency filtering occurs in the vertical direction, while high-frequency filtering occurs in the horizontal direction. The spatiotemporal high frequency filter High-frequency filtering is performed in both the horizontal and vertical directions; Constructing a spatial two-dimensional learnable wavelet filter kernel Processing spatial features, the spatial two-dimensional learnable wavelet filter kernel Space low-frequency filter Space vertical high frequency filter Horizontal high-frequency filter and space high frequency filters It is formed by aggregation.

4. The method according to claim 3, characterized in that, The fusion weights are calculated and expressed as follows: ； ； ； in, Represents global frequency characteristics. Represents the spatiotemporal integrated characteristics, Representing residual characteristics, The fusion weights, obtained by concatenating global frequency features and spatiotemporal integrated features and inputting them into the gating network, are used to control the spatiotemporal integrated features. Contribution The fusion weights, obtained by concatenating the global frequency features and residual features and inputting them into the gating network, are used to control the contribution of the global frequency features. The fusion weights, obtained by concatenating the spatiotemporal integrated features and residual features and inputting them into the gating network, are used to control the contribution of the residual features. , , These are the weight matrices for each gated network. It is a bias term. This indicates the concatenation of two features. Indicates the activation function; By performing element-wise multiplication and weighted fusion of each feature, the final fused feature is obtained, represented as: ； in, This indicates a weighted operation. This indicates the fusion feature.

5. A wave height prediction system based on two-dimensional learnable wavelet transform, characterized in that, The wave height prediction system includes: The global frequency information feature extraction module is used to extract global frequency features: it performs a Fourier transform operation on the input wave height data to extract global frequency features. The local spatiotemporal comprehensive feature extraction module includes a local spatiotemporal information extraction module and a local spatial information extraction module, which are used to extract local spatiotemporal comprehensive features: the input wave height data is reshaped into two different dimensions of spatiotemporal features and spatial wave height features. For the spatiotemporal features and spatial wave height features, multiple learnable filters are constructed to extract swell features, wind wave features, spatial variation features and local spatial variation features. For the extracted features, a set of two-dimensional learnable wavelet filter kernels are constructed to perform wavelet decomposition to obtain multi-scale frequency features. The inverse two-dimensional learnable wavelet filter kernel designed in conjunction with the two-dimensional learnable wavelet filter kernel is used for reconstruction to obtain local spatiotemporal comprehensive features that simultaneously integrate the time dimension and the spatial dimension. The gated fusion module is used for gated fusion: it constructs multiple gated mechanisms to dynamically fuse global frequency features, local spatiotemporal integrated features and residual features obtained by residual connection of input ocean wave height data, calculates the fusion weight between each feature, performs weighted fusion of each feature, generates a unified fusion feature, and maps it to obtain the final predicted ocean wave height data.

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