A sea wave height prediction method and system based on mixed quadratic decomposition

Abstract

The application provides a sea wave height prediction method and system based on mixed secondary decomposition, and relates to the technical field of sea wave height prediction. The method comprises the following steps: obtaining original wave height data to be predicted; performing primary decomposition on the original wave height data to obtain an intrinsic mode function and a residual term; calculating the sample entropy of the intrinsic mode function; classifying the intrinsic mode function according to the size of the sample entropy to obtain a reconstructed modal component; performing secondary decomposition on the high-frequency component through a VMD algorithm to generate a subsequence component; establishing a cycle-aware time deep learning model; inputting the subsequence component, the medium-frequency component and the low-frequency component into the cycle-aware time deep learning model to output a sea wave height prediction result.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ocean wave height prediction, in particular to a wave height prediction method and system based on hybrid second decomposition. BACKGROUND

[0002] Hybrid second decomposition is a mathematical signal processing technique. The purpose of hybrid second decomposition is to split complex signals, such as time series data of sea wave height, into multiple components through decomposition techniques. "Second" usually refers to splitting data into multiple frequency components in order to analyze different characteristics of the signal. Wave height prediction refers to predicting the wave height in the ocean through certain technical means. The wave height prediction method based on hybrid second decomposition refers to using hybrid second decomposition to decompose wave height data multiple times, extracting different frequency components in the data, and then using these components to predict future wave height changes.

[0003] Sea waves are periodic fluctuations on the ocean surface caused by natural forces such as wind, tides, and earthquakes. As one of the core parameters of coastal and marine engineering design, wave height not only directly affects the stability of various marine engineering structures, but also relates to the safety and efficiency of offshore operations. Accurate prediction of wave height is of great significance to ensuring the safety of offshore activities and protecting national maritime rights and interests.

[0004] However, although the existing wave height prediction methods have made significant progress, they also have certain limitations. Numerical simulation methods rely on high-performance computing and have a long calculation time, which limits their application in emergency scenarios, especially in real-time prediction situations. In addition, numerical models have limited ability to handle complex nonlinear and non-stationary wave fluctuation characteristics. Classic time series analysis methods are difficult to deal with the nonlinear and non-stationary characteristics of wave height, so they cannot accurately predict the complex dynamics of waves. Machine learning and deep learning methods perform well in handling nonlinear and time-dependent problems, but these methods usually rely on a large amount of training data and computing resources, and may have overfitting or insufficient generalization ability in complex marine environments. In addition, models based on empirical mode decomposition (EMD) and variational mode decomposition (VMD) can effectively handle nonlinear and non-stationary data, but still face challenges in data decomposition accuracy, noise processing, and model optimization. In summary, existing prediction methods still have certain limitations in dealing with complex wave height data, resulting in long calculation time, difficulty in meeting real-time prediction requirements in emergency scenarios, reducing prediction accuracy, and further causing overfitting or poor generalization ability. SUMMARY

[0005] In view of the above prior art deficiencies, the purpose of the embodiments of the present application is to provide a sea wave height prediction method based on mixed secondary decomposition, which can solve the technical problems that the existing prediction methods still have certain limitations when processing complex sea wave height data, resulting in long calculation time, difficulty in meeting the real-time prediction demand in emergency scenarios, reducing the prediction accuracy, and further causing overfitting or poor generalization ability.

[0006] In a first aspect, the embodiments of the present application provide a sea wave height prediction method based on mixed secondary decomposition, comprising:

[0007] S1: obtaining original wave height data to be predicted;

[0008] S2: performing primary decomposition on the original wave height data to obtain an intrinsic mode function and a residual term;

[0009] S3: calculating the sample entropy of the intrinsic mode function;

[0010] S4: classifying the intrinsic mode function according to the size of the sample entropy to obtain a reconstructed modal component, wherein the reconstructed modal component includes a high-frequency component, a medium-frequency component, and a low-frequency component;

[0011] S5: performing secondary decomposition on the high-frequency component through a VMD algorithm to generate a subsequence component;

[0012] S6: establishing a cycle-aware temporal deep learning model;

[0013] S7: inputting the subsequence component, the medium-frequency component, and the low-frequency component into the cycle-aware temporal deep learning model to output a sea wave height prediction result.

[0014] In a second aspect, the embodiments of the present application provide a sea wave height prediction system based on mixed secondary decomposition, comprising: a processor and a memory;

[0015] The memory stores programs or instructions executable on the processor, and the programs or instructions are executed by the processor to implement the steps of the sea wave height prediction method based on mixed secondary decomposition of the first aspect.

[0016] In a third aspect, the embodiments of the present application provide a readable storage medium, and the readable storage medium stores programs or instructions, and the programs or instructions are executed by the processor to implement the steps of the sea wave height prediction method based on mixed secondary decomposition of the first aspect.

[0017] The technical scheme provided by the embodiments of the present application has at least the following beneficial effects:

[0018] In the embodiment of the present application, by acquiring the original wave height data to be predicted, the original wave height data is firstly decomposed to obtain the intrinsic mode function and the residual term, then the sample entropy of the intrinsic mode function is calculated, the intrinsic mode function is classified according to the size of the sample entropy, and the reconstructed modal component is obtained, so as to ensure the accurate separation of different frequency components. Through the VMD algorithm, the high-frequency component is secondarily decomposed to generate a subsequence component, and according to the subsequence component, the medium-frequency component and the low-frequency component, a cycle perception time deep learning model is established, finally, the subsequence component, the medium-frequency component and the low-frequency component are input into the cycle perception time deep learning model, and the sea wave height prediction result is output, which overcomes the limitations of the traditional method, improves the prediction accuracy, enhances the practicability and accuracy of the model, reduces the calculation time, meets the real-time prediction demand in the emergency scene, improves the generalization ability of the model, and has important application value for offshore operation, shipping safety and marine disaster warning. BRIEF DESCRIPTION OF DRAWINGS

[0019] The accompanying drawings are included to provide a further understanding of the embodiments of the present application, and are incorporated herein and constitute a part of the detailed description. It should be apparent that the drawings described are only a few embodiments of the present application. Therefore, the accompanying drawings should not be used to limit the scope of the present application.

[0020] Figure 1 is a flowchart of a sea wave height prediction method based on hybrid secondary decomposition provided by an embodiment of the present application;

[0021] Figure 2 is a structural schematic diagram of a sea wave height prediction system based on hybrid secondary decomposition provided by an embodiment of the present application. DETAILED DESCRIPTION

[0022] In order for those skilled in the art to better understand the technical solutions in the embodiments of the present application, the technical solutions of the present application will be described in detail below with reference to the drawings. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. It should be understood that these descriptions are only exemplary, and are not used to limit the scope of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor should be within the scope of protection of the present application.

[0023] The sea wave height prediction method based on hybrid secondary decomposition provided by the embodiments of the present application will be described in detail below with reference to the drawings and specific embodiments and application scenarios.

[0024] Reference is made to the accompanying drawings Figure 1Fig. 1 shows a flowchart of a method for predicting sea wave height based on hybrid quadratic decomposition according to an embodiment of the present application.

[0025] The method for predicting sea wave height based on hybrid quadratic decomposition according to an embodiment of the present application can comprise the following steps:

[0026] S1: Obtain original wave height data to be predicted.

[0027] The original wave height data is usually obtained from ocean observation stations, buoys, remote sensing satellites or other ocean measurement tools, and contains the actual wave height values of the sea wave at a certain time or within a certain time period. By obtaining real sea wave height data, the real situation of the current marine environment can be reflected, providing accurate and practical information for subsequent analysis and processing.

[0028] S2: Perform primary decomposition on the original wave height data to obtain intrinsic mode functions and residual terms.

[0029] Specifically, the CEEMDAN algorithm is used to perform primary decomposition on the original wave height data to obtain intrinsic mode functions and residual terms.

[0030] The CEEMDAN algorithm (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) is an improved EMD algorithm that decomposes non-stationary and nonlinear signals by adding adaptive noise to the signal. The intrinsic mode function (IMF) is a signal component obtained by CEEMDAN algorithm decomposition, which reflects the intrinsic characteristics of the signal at different scales. The residual term represents the part of the signal that cannot be further decomposed, which is usually the low-frequency trend component.

[0031] It should be noted that the CEEMDAN algorithm is used to perform primary decomposition on the original wave height data, which decomposes the complex sea wave height signal into multiple intrinsic mode functions (IMF) and residual terms. The advantage of this process is that it can effectively handle nonlinear and non-stationary data, which is a common characteristic of sea wave height data. Through decomposition, CEEMDAN can extract different frequency components in the signal, providing more accurate features for subsequent analysis. Its adaptive noise processing capability greatly improves the robustness of decomposition, reduces noise interference, and ensures the accuracy of the decomposition results.

[0032] In one possible implementation, the primary decomposition of the original wave height data by the CEEMDAN algorithm specifically includes:

[0033] White noise is added to the original wave height data using the CEEMDAN algorithm to generate a noise sequence:

[0034] ;

[0035] in, Indicates the first i The signal sequence after adding noise. , N This represents the total amount of Gaussian white noise. This represents the original wave height data. This represents the amplitude control coefficient for white noise. p i ( ) indicates the first i Standard Gaussian white noise, n Indicates the sequence length.

[0036] Perform EMD decomposition on the noisy sequence until the residual signal meets the stopping criterion, generating the eigenmode function and residual terms:

[0037] ;

[0038] in, Indicates the first m One IMF component, , T This represents the total number of IMF components. Indicates the first p One residual term, Indicates the first EMD m -1 component, Indicates the first q -1 stage residuals Indicates the first q White noise coefficients in the -1 stage. Indicates the first T One IMF component.

[0039] In this embodiment of the invention, CEEMDAN, derived from EMD, can adaptively decompose data according to the characteristics of the signal itself. For signals such as ocean wave height data, which have multi-scale, nonlinear, and non-stationary characteristics, CEEMDAN can automatically identify and extract the fluctuation components at different time scales, thereby better capturing the local features and global trends of the data. Compared with EMD, CEEMDAN introduces adaptive white noise and ensemble averaging techniques, enhancing the noise robustness of the sequence and making the decomposed subsequences more suitable for modeling and prediction.

[0040] S3: Calculate the sample entropy of the intrinsic mode functions.

[0041] where the sample entropy is a signal processing algorithm proposed by Alcaraz and Rieta, which measures the complexity of the research object according to the probability of generating new patterns in the signal, and uses it as a measure of the complexity of time series. The more complex the time series is, the larger the sample entropy value of the sequence will be. The smaller the value of sample entropy, the more regular and stable the data sequence is. The larger the value, the more complex and irregular the data sequence is.

[0042] It should be noted that in the prediction of sea wave height, sample entropy is used to evaluate the complexity of each intrinsic mode function (IMF). By calculating the sample entropy of the intrinsic mode function, the complexity of each mode can be quantified. This process helps to identify components with high complexity in the signal and provides a deeper understanding of sea wave height data. Through the evaluation of sample entropy, mode functions with high prediction potential can be screened out, avoiding the influence of redundant modal components on subsequent analysis.

[0043] In one possible implementation, the calculation formula of sample entropy is specifically:

[0044] ;

[0045] wherein, SampEn ( a , r , d ) represents the sample entropy, a represents the dimension of the constructed vector, r represents the tolerance, d represents the total number of data points, ln represents the natural logarithm function, represents the probability of matching r data points between two sequences under the tolerance a , a +1 represents the dimension of the constructed vector, represents the probability of matching r +1 data points between two sequences under the tolerance a , represents the matching condition of the a +1th point pair when the vector dimension is s +1, , represents the matching condition of the a th point pair when the vector dimension is v , .

[0046] It should be noted that sample entropy can reflect the nonlinear characteristics of wave height data, help better identify dynamic change patterns in the data, enhance the adaptability of the model to complex wave phenomena, and thus improve the accuracy and reliability of the prediction.

[0047] S4: classifying the intrinsic mode functions according to the size of the sample entropy to obtain reconstructed modal components, wherein the reconstructed modal components include high-frequency components, medium-frequency components and low-frequency components.

[0048] Specifically, the intrinsic mode functions are classified by a K-means clustering algorithm to obtain the reconstructed modal components.

[0049] The K-means clustering algorithm is a common unsupervised learning algorithm, which is usually used for clustering analysis of data. The algorithm divides the data into K clusters so that the data points in the same cluster are as similar as possible, and the data points between different clusters are quite different. The algorithm updates the cluster centroids iteratively until the cluster assignments no longer change. The reconstructed modal components refer to the combination (reconstruction) of intrinsic mode functions belonging to the same category to generate more representative signal components.

[0050] The high-frequency component refers to a signal feature with fast changes and short periods, which is often related to sudden changes and small-scale disturbances in waves. The medium-frequency component represents a part with moderate periods and relatively stable changes, which may reflect conventional wave fluctuations. The low-frequency component is usually the trend item or long-term change part of the signal, reflecting the overall trend or slow change component of the wave height.

[0051] It should be noted that the classification of intrinsic mode functions by the K-means clustering algorithm can clearly distinguish different frequency components (such as high-frequency, medium-frequency and low-frequency) in the sea wave height signal. This classification can effectively avoid confusion between frequency components, allowing each component to be processed individually, thereby improving the accuracy and effectiveness of subsequent analysis.

[0052] In one possible implementation, classifying the intrinsic mode functions by the K-means clustering algorithm specifically includes:

[0053] Initializing a preset number of centroids by the K-means clustering algorithm.

[0054] In the K-means clustering algorithm, the centroid is the center point of each cluster, representing the mean position of all data points in the cluster. The update of the centroid is a key step in the K-means algorithm, which optimizes the cluster assignments through continuous iteration.

[0055] Calculating the distance between the sample entropy and the centroid until the objective function value of the K-means clustering algorithm is less than the preset objective function value, and outputting the classification result.

[0056] The skilled person in the art can set the size of the preset objective function value according to the actual situation, and the present application does not make any limitation.

[0057] The calculation formula of the objective function value is specifically:

[0058] ;

[0059] in, E This represents the objective function of the k-means algorithm. Indicates the first b Clusters, x This represents a sample point in the dataset. Indicates the first b The centroid of a cluster, , w Indicates the number of clusters.

[0060] It's important to note that the unsupervised nature of the K-means algorithm allows it to automatically identify patterns in signals without prior knowledge of the data's structure. Furthermore, the introduction of sample entropy helps prioritize modes based on complexity, ensuring that important components are accurately extracted. This approach improves data processing efficiency and quality, providing clearer and more precise input for subsequent prediction steps.

[0061] S5: The high-frequency components are decomposed in two stages using the VMD algorithm to generate subsequence components.

[0062] The VMD algorithm is a signal decomposition method used to break down a signal into multiple sub-signals with different frequency characteristics. It extracts different patterns of the signal step by step by minimizing a variational objective function. Subsequence components refer to the multiple sub-sequences into which the signal is decomposed in the VMD algorithm; these sub-sequences reflect the signal's variation characteristics within different frequency ranges. Each subsequence component corresponds to a specific frequency component.

[0063] It should be noted that using the VMD algorithm to further decompose high-frequency components can effectively extract different frequency components from the signal into independent subsequence components. This process not only improves the accuracy of signal decomposition but also enables clearer identification of different frequency features in ocean wave height data. Compared with traditional decomposition methods, VMD avoids mode aliasing, ensuring that each component is independent and clear.

[0064] In one possible implementation, S5 specifically includes:

[0065] S501: Decompose the high-frequency components into a predetermined number of sub-components to construct a variational problem:

[0066] ;

[0067] in, express t The first moment k Subsequences Indicates the first kThe subsequence of the first subsequence t The instantaneous amplitude at time t, where cos represents the cosine function. Indicates the first t The phase of a moment.

[0068] Specifically, variational problems typically refer to solving an optimization problem to obtain a certain ideal solution, usually by minimizing (or maximizing) an objective function. In signal decomposition, the goal of variational problems is to accurately decompose the signal by optimizing the objective function, so that the decomposed sub-signals (or sub-components) can most accurately reflect the different frequency characteristics of the original signal.

[0069] S502: By introducing a quadratic penalty factor and a Lagrange penalty operator, an unconstrained objective function for the variational problem is constructed:

[0070] ;

[0071] in, L Represents an unconstrained objective function. u k Indicates the first k Subsequences w k Indicates the first k The center frequency of each subsequence l This indicates that the Lagrange penalty operator, α Represents the regularization parameter. The sign for differentiation is given. express t The Dirac function at time t, j Represents the imaginary unit. express t The signal of the moment, express t Lagrange penalty operator for time.

[0072] Specifically, a quadratic penalty factor and a Lagrange penalty operator are introduced to construct a Lagrange augmented function, transforming the constrained variational problem into an unconstrained variational problem. The quadratic penalty factor ensures the accuracy of the reconstructed signal even under the influence of independent and identically distributed Gaussian noise. The Lagrange multiplier guarantees the rigor of the process.

[0073] S503: Solve the unconstrained objective function using the alternating direction multiplier method to generate subsequence components.

[0074] Among them, the alternating direction multiplier method (Alternating Direction Method of Multipliers, ADMM) is an algorithm for solving convex optimization problems, especially suitable for optimization problems with constraints. Its basic idea is to decompose the original optimization problem into several sub-problems that are easier to solve, and solve these sub-problems step by step through iteration.

[0075] It should be noted that VMD can more accurately control the decomposition process by minimizing the variational objective function, especially when dealing with complex, non-stationary signals, it can provide more stable decomposition results. Through this refined decomposition, the subsequent deep learning model provides more accurate and differentiated signal components, thereby improving the prediction accuracy and stability.

[0076] In one possible implementation, S503 specifically includes:

[0077] S5031: initialize each sub-component, center frequency and Lagrange penalty operator.

[0078] Among them, the Lagrange penalty operator is a mathematical tool used to constrain the objective function. In the optimization process of VMD, the Lagrange penalty factor is used to ensure that the constraint conditions in the decomposition process are met.

[0079] S5032: update the sub-component, center frequency and Lagrange penalty operator respectively to minimize the unconstrained objective function:

[0080] ;

[0081] Among them, denotes the frequency domain component of the n th sub-modal at the e th iteration, w denotes the frequency (integral variable), denotes the frequency component of the original signal, denotes the frequency domain component of the n th sub-modal at the e th iteration, , F denotes the total number of sub-modalities, denotes the representation of the Lagrange penalty operator on the center frequency domain, denotes the center frequency of the n th sub-modal at the e th iteration, denotes the Lagrange penalty operator corresponding to the n th sub-modal at the e th iteration, denotes then In the next iteration, the representation in the frequency domain of the corresponding Lagrange multiplier.

[0082] S5033: Stop updating until the error precision is less than the preset error precision, and output the final sub-component and the center frequency corresponding to the final sub-component.

[0083] Wherein, the size of the preset error precision can be set by the person skilled in the art according to the actual situation, and the present application is not limited.

[0084] S5034: Determine the sub-sequence component according to the final sub-component and the center frequency.

[0085] It should be noted that the alternating direction multiplier method is a powerful optimization algorithm suitable for solving convex optimization problems with constraints. It introduces Lagrange multipliers to decompose complex optimization problems into easy-to-solve sub-problems, and gradually approaches the optimal solution of the original problem by alternately updating the solutions of each sub-problem. ADMM is widely used in many practical applications due to its efficiency and flexibility.

[0086] S6: Establish a periodic perception time deep learning model.

[0087] In one possible implementation, the periodic perception time deep learning model includes a periodic segmentation module, a hybrid predictor module, and an integrated aggregator module.

[0088] Wherein, the periodic perception time deep learning model is a deep learning model specifically designed to process time series data, with periodic perception function, capable of identifying and utilizing periodic patterns in time series. In sea wave height prediction, periodic features usually reflect the regular fluctuations of sea waves (such as diurnal tide, seasonal changes, etc.), and the periodic perception module helps the model consider these periodic changes when predicting.

[0089] Wherein, the periodic segmentation module is used for periodic division of time series data. By periodically dividing the signal, the model can identify and extract different periodic features in the time series, thereby improving the accuracy of prediction.

[0090] Wherein, the hybrid predictor module combines multiple prediction methods, usually a combination of different deep learning algorithms, capable of processing different types of features and data, and outputting more accurate prediction results.

[0091] Wherein, the integrated aggregator module is responsible for combining and integrating multiple prediction results to form the final prediction output. The integrated method can reduce the bias of a single model by combining the prediction results of multiple models, improving the stability and accuracy of prediction.

[0092] It is worth noting that the cycle segmentation module helps the model identify the periodic changes of waves by effectively dividing the time series into different cycles, ensuring that the model considers these natural laws during the prediction process. The hybrid predictor module combines multiple deep learning methods, enabling it to handle different features in the data, thus improving the model's flexibility and adaptability. The integrated aggregator module further improves the stability of the prediction by integrating the prediction results of multiple models, reducing the errors that may occur with a single model.

[0093] In one possible implementation, the cycle segmentation module is configured to segment the subsequence component, the medium frequency component, and the low frequency component.

[0094] The process of segmentation performed by the cycle segmentation module specifically includes:

[0095] The time-domain signal is converted into a frequency-domain signal through a fast Fourier transform.

[0096] The fast Fourier transform is an efficient algorithm for Fourier transform, which is used to convert time-domain signals into frequency-domain signals. Fourier transform is a mathematical transformation that can convert signals from time domain (describing the way signals change over time) to frequency domain (describing the composition of signals at different frequencies).

[0097] A preset number of dominant frequency components are selected from the frequency-domain signal to generate frequency features of the dominant cycle.

[0098] The value of the dominant cycle is obtained by taking the inverse of the dominant frequency component:

[0099] ;

[0100] wherein, represents the amplitude corresponding to the sequence, n is the sequence length, AMP represents the extraction operation on the amplitude value, X represents the input subsequence, FFT represents the fast Fourier transform, arg represents the frequency corresponding to the maximum amplitude, represents the first largest frequencies are selected in , represents the period length corresponding to the h largest frequency, n represents the sequence length, f h represents the h largest frequency.

[0101] According to the value of the dominant cycle, the subsequence component, the medium frequency component, and the low frequency component are segmented respectively to generate a plurality of patches.

[0102] Specifically, to enhance the sensitivity of the prediction model to the periodicity of the data, the input sequence is divided into several patches according to the calculated period length.

[0103] Each patch is arranged and integrated according to the division order into a two-dimensional tensor for time series prediction:

[0104] ;

[0105] wherein, represents the 2-dimensional tensor data corresponding to the largest frequency, h (.) represents a rearrangement operation, reshape represents the number of rows of the two-dimensional tensor , i.e. the period length corresponding to the largest frequency, represents the number of columns of the two-dimensional tensor h .

[0106] wherein, the two-dimensional tensor is a matrix formed by arranging multiple signal features (patches) in time order, in machine learning and deep learning, the two-dimensional tensor is usually used to represent and process time series data, so that the model can consider the information of different time points and different features at the same time.

[0107] It should be noted that the subsequence component, the intermediate frequency component and the low frequency component are divided by the period division module, and a plurality of patches are generated, and finally integrated into a two-dimensional tensor, which helps to improve the accuracy and efficiency of time series prediction. First, the fast Fourier transform (FFT) converts the time domain signal into the frequency domain signal, which can accurately capture the periodic components and frequency characteristics of the signal. Selecting the dominant frequency component and calculating the value of the dominant period helps to clearly define the main fluctuation period of the signal, so that the divided patches are more representative. Reasonably dividing the signal according to the periodic characteristics and organizing it into a two-dimensional tensor format not only retains the time-frequency information of the time series, but also provides high-quality input data for deep learning models.

[0108] In one possible implementation, the hybrid predictor module uses the encoder structure of the Transformer as the framework, and the hybrid predictor module is used to process the two-dimensional tensor output by the period division module, and the processing process specifically includes:

[0109] By calculating the attention score of the two-dimensional tensor by row, the short-term dependence feature, i.e. the short-term attention score, is extracted:

[0110] ;

[0111] wherein, represents the 2-dimensional tensor data corresponding to the largest frequency, j ​​The attention matrix for each patch, where softmax represents the activation function. Indicates the first j The query matrix for each patch Indicates the first j The key matrix of each patch, T Indicates transpose. d m Indicates the scaling factor. Indicates the first j The value matrix of each patch M Indicates the total number of patches. A intra This represents the short-term attention score.

[0112] Specifically, short-term dependency characteristics reflect the changing trends or local patterns of data within a shorter time window.

[0113] By calculating attention scores column-wise on a two-dimensional tensor, long-term dependency features, i.e., long-term attention scores, are extracted:

[0114] ;

[0115] in, Indicates the first c Attention matrix for each phase, Indicates the first c A query matrix for each phase. Indicates the first c A bond matrix with phases, Indicates the first c A matrix of values ​​for each phase, P This represents the total number of phases. Concat This indicates a splicing operation. A phase This represents the final attention matrix, i.e., the long-term attention score.

[0116] Specifically, long-term dependency characteristics typically refer to the relationship between current data and data from a longer historical period. For example, in wave height prediction, the current wave height may not only be related to the wave height in the last few minutes, but also to the fluctuations several hours or days ago.

[0117] Based on the variation patterns among the patches in the two-dimensional tensor, global variation features, i.e., global attention scores, are extracted:

[0118] ;

[0119] in, A inter This represents the global attention matrix, i.e., the global attention score. Q inter Represents the query matrix.K inter denotes a key matrix, V inter denotes a value matrix, d m denotes a scaling factor.

[0120] In particular, the global variation features can capture macro patterns exhibited by the data throughout the time series, such as seasonal variations in sea wave height, long-term climate changes, etc. These features are not confined to short-term local dependencies, but rather focus on overall trends or periodic changes throughout the time series.

[0121] The short-term attention scores, the long-term attention scores, and the global attention scores are combined by concatenation and dimension reduction operations to generate hybrid attention results:

[0122] ;

[0123] wherein, A denotes a hybrid attention result, Flatten denotes a dimension reduction operation, A intra denotes a short-term attention score, A phase denotes a long-term attention score, A inter denotes a global attention score.

[0124] The individual hybrid attention results are concatenated in series, and the series concatenation result is mapped to obtain a sequence prediction result:

[0125] ;

[0126] wherein, denotes a final feature matrix, denotes an th two-dimensional tensor, denotes a sequence prediction result, Linear denotes a linear layer.

[0127] It should be noted that by calculating the attention scores row-wise and column-wise, the model can effectively capture different time scales and patterns in the signal. The short-term dependency features help to capture immediate, rapidly changing trends. The long-term dependency features help to reveal long-term trends in the signal. The global variation features can capture the overall fluctuation pattern of the signal. This hierarchical feature extraction approach enables the model to comprehensively understand the multi-dimensional structure of the data, thereby improving the accuracy and robustness of the prediction.

[0128] In one possible implementation, the aggregator module is configured to output the prediction result.

[0129] The specific formula for calculating the prediction result is as follows:

[0130] ;

[0131] in, Indicates the prediction result. Indicates the first k Prediction results for each subsequence, Indicates the first k The weights of each subsequence, , Q This represents the total number of subsequences.

[0132] S7: Input the subsequence components, mid-frequency components, and low-frequency components into the periodic-aware time-deep learning model and output the wave height prediction results.

[0133] Among them, the wave height prediction result is the wave height prediction result after being processed by the periodic time-aware deep learning model.

[0134] It's important to note that inputting multiple frequency components of the signal (such as high-frequency, mid-frequency, and low-frequency components) into the periodic-aware time-series deep learning model allows for the full utilization of the features of different frequency components to achieve accurate wave height prediction. By processing these components separately, the model can capture wave characteristics at different scales, resulting in more accurate predictions. Furthermore, the periodic-aware module enables the model to pay particular attention to periodic changes in the signal, improving its ability to capture long-term fluctuations and seasonal trends. Ultimately, by integrating the features of these multi-frequency components, the model can discover patterns in complex time-series data and provide high-precision prediction results.

[0135] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0136] In this embodiment of the invention, the original wave height data to be predicted is acquired and initially decomposed to obtain the intrinsic mode functions (EMFs) and residual terms. Then, the sample entropy of the EMFs is calculated, and the EMFs are classified according to the magnitude of the sample entropy to obtain reconstructed mode components, thereby ensuring accurate separation of different frequency components. The VMD algorithm is used to perform a secondary decomposition of the high-frequency components to generate sub-sequence components. Based on the sub-sequence components, mid-frequency components, and low-frequency components, a periodic time-sensing deep learning model is established. Finally, the sub-sequence components, mid-frequency components, and low-frequency components are input into the periodic time-sensing deep learning model to output the wave height prediction result. This method overcomes the limitations of traditional methods, improves prediction accuracy, enhances the practicality and accuracy of the model, reduces computation time, meets the real-time prediction needs in emergency scenarios, and improves the model's generalization ability. It has significant application value for maritime operations, shipping safety, and marine disaster early warning.

[0137] With reference to the accompanying drawings Figure 2 , a structure schematic diagram of a sea wave height prediction system based on hybrid quadratic decomposition provided by an embodiment of the present application is shown.

[0138] An embodiment of the present application provides a sea wave height prediction system 20 based on hybrid quadratic decomposition, comprising a processor 201 and a memory 202.

[0139] The memory 202 stores programs or instructions executable on the processor 201, the programs or instructions are executed by the processor 201 to realize the steps of the sea wave height prediction method based on hybrid quadratic decomposition and achieve the same technical effects, to avoid repetition, the present application will not repeat the present application will not repeat.

[0140] It should be understood that the processor 201 in the embodiment of the present application can be a central processing unit (CPU), and the processor can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), ready programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc.

[0141] It is also to be understood that the memory 202 in embodiments of the present application can be volatile or nonvolatile memory, or can include both volatile and nonvolatile memory. Nonvolatile memory can be read-only memory (ROM), programmable ROM (PROM), erasable PROM (EPROM), electrically EPROM (EEPROM), or flash memory. Volatile memory can be random access memory (RAM), used as external cache. By way of example, and not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous dynamic RAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0142] The above-described embodiments can be implemented in part or in whole through software, hardware (e.g., circuitry), firmware, or any combination thereof. When implemented in software, the above-described embodiments can be implemented in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When loaded and executed by a computer, the computer instructions or computer programs can generate the flow or function according to the embodiments of the present application in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable apparatus. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another computer-readable storage medium, such as from one website site, computer, server, or data center to another website site, computer, server, or data center through a wired (e.g., infrared, wireless, microwave, etc.) manner. The computer-readable storage medium can be any available medium accessible by a computer or a data storage device such as a server, data center, etc. containing a set of one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. The semiconductor medium can be a solid-state disk.

[0143] It should be understood that the size of the sequence number of each process described above does not mean the order of execution, and the execution order of each process should be determined according to its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0144] Those of ordinary skill in the art can realize that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be realized in electronic hardware, or a combination of computer software and electronic hardware. Whether the functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Those of ordinary skill in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0145] Those of ordinary skill in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the above-described devices, apparatuses, and units can refer to the corresponding processes in the foregoing method embodiments, which will not be described here.

[0146] In several embodiments provided by the present application, it should be understood that the disclosed devices, apparatuses and methods can be implemented in other manners. For example, the embodiments of the apparatus described above are merely schematic. For example, the division of the units is only a logical function division. There can be another division manner for the actual implementation. For example, a plurality of units or components can be combined or integrated into another device, or some features can be ignored or not executed. In addition, the displayed or discussed mutual couplings or direct couplings or communication connections can be indirect couplings or communication connections through some interfaces, devices or units, and can be in electrical, mechanical or other forms.

[0147] The units described as separated components can or can not be physically separated, and the components displayed as units can or can not be physical units, i.e., can be located in one place, or can be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purposes of the embodiments of the present application.

[0148] In addition, each functional unit in the various embodiments of the present application can be integrated in one processing unit, or each unit can exist physically as a separate unit, or two or more units can be integrated in one unit.

[0149] If the functions are implemented in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the parts of the technical solutions that make contributions to the prior art, or the parts of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present application. The foregoing storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes.

[0150] The embodiments of the present application provide a readable storage medium, which includes: a program or instructions stored on the readable storage medium, the program or instructions are executed by a processor to implement the steps of the sea wave height prediction method based on mixed quadratic decomposition described above, and the same technical effects can be achieved. To avoid repetition, the present application will not be described again.

[0151] It should be pointed out finally that the above embodiments are only used to illustrate the technical solutions of the embodiments of the present application, but not to limit them. Although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that the technical solutions recorded in the foregoing embodiments can be modified, or some technical features can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application. Any changes or replacements that can be easily thought of by those skilled in the art within the technical scope disclosed by the present application should be covered within the protection scope of the present application.

Claims

1. A sea wave height prediction method based on hybrid quadratic decomposition, characterized in that, The method comprises the following steps: S1: obtaining original wave height data to be predicted; S2: performing primary decomposition on the original wave height data to obtain an intrinsic modal function and a residual term; S3: calculating sample entropy of the intrinsic modal function; S4: classifying the intrinsic modal function according to the size of the sample entropy to obtain a reconstructed modal component, wherein the reconstructed modal component comprises a high-frequency component, a medium-frequency component and a low-frequency component; S5: performing secondary decomposition on the high-frequency component through a VMD algorithm to generate a sub-sequence component; S6: establishing a cycle-aware time deep learning model; The cycle-aware time deep learning model comprises a cycle segmentation module, a hybrid predictor module and an integrated aggregator module; The hybrid predictor module takes the encoder structure of the Transformer as a framework, and is used for processing a two-dimensional tensor output by the cycle segmentation module, and the processing process specifically comprises: extracting short-term dependency features, i.e., short-term attention scores, by calculating attention scores of the two-dimensional tensor row by row; extracting long-term dependency features, i.e., long-term attention scores, by calculating attention scores of the two-dimensional tensor column by column; extracting global change features, i.e., global attention scores, according to the change law between each patch in the two-dimensional tensor: ； wherein, A inter denotes the global attention matrix, i.e. the global attention scores, Q inter denotes the query matrix, K inter denotes the key matrix, V inter denotes the value matrix, d m denotes the scaling factor, softmax denotes the activation function, T denotes the transpose; merging the short-term attention scores, the long-term attention scores and the global attention scores through concatenation and dimension reduction operations to generate hybrid attention results: ； wherein, A represents a mixed attention result, Flatten represents a dimension reduction operation, A intra represents a short-term attention score, A phase represents a long-term attention score, A inter represents a global attention score; concatenating the hybrid attention results in series, and mapping the series concatenation result to obtain a sequence prediction result: ； wherein, represents the final feature matrix, represents the first two-dimensional tensor, represents the sequence prediction result, Linear represents the linear layer; S7: inputting the sub-sequence component, the medium-frequency component and the low-frequency component into the cycle-aware time deep learning model to output a sea wave height prediction result.

2. The sea wave height prediction method based on hybrid quadratic decomposition according to claim 1, characterized in that, The S5 specifically comprises: S501: decomposing the high-frequency component into a preset number of sub-components to construct a variational problem; S502: constructing an unconstrained objective function of the variational problem by introducing a quadratic penalty factor and a Lagrange penalty operator; S503: solving the unconstrained objective function through an alternating direction multiplier method to generate the sub-sequence component.

3. The sea wave height prediction method based on hybrid quadratic decomposition according to claim 2, characterized in that, The S503 specifically comprises: S5031: initializing each sub-component, a center frequency and a Lagrange penalty operator; S5032: updating the sub-component, the center frequency and the Lagrange penalty operator respectively to minimize the unconstrained objective function; S5033: stopping updating until the error precision is less than a preset error precision, and outputting a final sub-component and a center frequency corresponding to the final sub-component; S5034: determining the sub-sequence component according to the final sub-component and the center frequency.

4. The sea wave height prediction method based on hybrid quadratic decomposition according to claim 1, characterized in that, The cycle segmentation module is used for segmenting the sub-sequence component, the medium-frequency component and the low-frequency component.

5. The sea wave height prediction method based on hybrid quadratic decomposition according to claim 4, characterized in that, The segmentation process of the cycle segmentation module specifically comprises: converting a time domain signal into a frequency domain signal through fast Fourier transform; selecting a preset number of main frequency components from the frequency domain signal to generate frequency features of dominant cycles; The main frequency component is inverted to obtain a value of the dominant period; According to the value of the dominant period, the sub-sequence component, the intermediate frequency component and the low frequency component are segmented respectively to generate a plurality of patches; The patches are arranged and integrated according to the segmentation order into a two-dimensional tensor for time series prediction.

6. The sea wave height prediction method based on hybrid quadratic decomposition according to claim 1, characterized in that, The aggregator module is configured to output a prediction result.

7. A sea wave height prediction system based on hybrid quadratic decomposition, characterized by, The method comprises: a processor and a memory; The memory stores programs or instructions executable on the processor, and the programs or instructions are executed by the processor to implement the steps of the sea wave height prediction method based on mixed secondary decomposition according to any one of claims 1 to 6.

8. A readable storage medium, characterized by, The programs or instructions are stored on the readable storage medium, and the programs or instructions are executed by the processor to implement the steps of the sea wave height prediction method based on mixed secondary decomposition according to any one of claims 1 to 6.

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