Sea wave height prediction method and system based on hybrid quadratic decomposition

Abstract

The invention provides a sea wave height prediction method and system based on hybrid quadratic decomposition, and relates to the technical field of sea wave height prediction, and the method comprises the steps: obtaining to-be-predicted original wave height data; performing primary decomposition on the original wave height data to obtain an intrinsic mode function and a residual term; calculating a sample entropy of the intrinsic mode function; according to the size of the sample entropy, classifying the intrinsic mode function to obtain a reconstructed mode component; performing secondary decomposition on the high-frequency components through a VMD algorithm to generate sub-sequence components; establishing a periodic sensing time deep learning model; and inputting the subsequence component, the intermediate-frequency component and the low-frequency component into a periodic sensing time deep learning model, and outputting a sea wave height prediction result.

Description

Technical Field

[0001] This invention relates to the field of ocean wave height prediction technology, and in particular to a wave height prediction method and system based on hybrid quadratic decomposition. Background Technology

[0002] Hybrid quadratic decomposition is a mathematical signal processing technique. Its purpose is to break down complex signals, such as time-series data of ocean wave heights, into multiple components. "Quadratic" typically refers to splitting the data into multiple frequency components to analyze different signal characteristics. Ocean wave height prediction refers to predicting the wave height in the ocean using certain techniques. Hybrid quadratic decomposition-based wave height prediction methods utilize this technique to decompose ocean wave height data multiple times, extracting different frequency components, and then using these components to predict future wave height changes.

[0003] Ocean waves are periodic fluctuations on the ocean surface caused by natural forces such as wind, tides, and earthquakes. As one of the core parameters in 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 wave height prediction is of great significance for ensuring the safety of maritime activities and safeguarding national maritime rights.

[0004] However, while existing wave height prediction methods have made significant progress, they also have certain limitations. Numerical simulation methods rely on high-performance computing and have long computation times, which limits their application in emergency scenarios, especially when real-time prediction is required. Furthermore, numerical models have limited ability to handle complex nonlinear and non-stationary wave characteristics. Classical time series analysis methods struggle to cope with the nonlinear and non-stationary characteristics of wave height, thus failing to 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 typically rely on large amounts of training data and computational resources, and may suffer from overfitting or insufficient generalization in complex marine environments. In addition, while models based on Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) can effectively handle nonlinear and non-stationary data, they still face challenges in data decomposition accuracy, noise handling, and model optimization. In summary, existing prediction methods still have certain limitations when handling complex wave height data, resulting in long computation times, difficulty in meeting the real-time prediction needs of emergency scenarios, reduced prediction accuracy, and further contributing to overfitting or poor generalization. Summary of the Invention

[0005] In view of the shortcomings of the prior art, the purpose of this invention is to provide a wave height prediction method based on hybrid quadratic decomposition, which can solve the technical problems that existing prediction methods still have certain limitations when processing complex wave height data, resulting in long calculation time, difficulty in meeting the real-time prediction needs in emergency scenarios, reduced prediction accuracy, and further causing overfitting or poor generalization ability.

[0006] A first aspect of this invention proposes a wave height prediction method based on hybrid quadratic decomposition, comprising: S1: Obtain the raw wave height data to be predicted; S2: Perform initial decomposition on the original wave height data to obtain the intrinsic mode functions and residual terms; S3: Calculate the sample entropy of the intrinsic mode function; S4: Based on the magnitude of the sample entropy, classify the intrinsic mode functions to obtain reconstructed mode components, wherein the reconstructed mode components include: high-frequency components, mid-frequency components and low-frequency components; S5: The high-frequency components are decomposed in two stages using the VMD algorithm to generate subsequence components; S6: Establish a periodic-aware time-deep learning model; S7: Input the subsequence component, the mid-frequency component, and the low-frequency component into the periodic sensing time deep learning model, and output the wave height prediction result.

[0007] A second aspect of the present invention provides a wave height prediction system based on hybrid quadratic decomposition, comprising: a processor and a memory; The memory stores a program or instruction that can run on a processor, and when the program or instruction is executed by the processor, it implements the steps of the wave height prediction method based on hybrid quadratic decomposition as described in the first aspect.

[0008] A third aspect of the present invention provides a readable storage medium on which a program or instructions are stored, which, when executed by a processor, implement the steps of the wave height prediction method based on hybrid quadratic decomposition as described in the first aspect.

[0009] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least: 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. Attached Figure Description

[0010] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts. Obviously, the drawings described below are merely some embodiments of the present invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.

[0011] Figure 1 This is a flowchart illustrating a wave height prediction method based on hybrid quadratic decomposition provided in an embodiment of the present invention. Figure 2 This is a schematic diagram of the structure of a wave height prediction system based on hybrid secondary decomposition provided in an embodiment of the present invention. Detailed Implementation

[0012] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. It should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0013] The wave height prediction method based on hybrid quadratic decomposition provided by the present invention will be described in detail below with reference to the accompanying drawings, through specific embodiments and application scenarios.

[0014] Reference manual attached Figure 1The diagram shows a flowchart of a wave height prediction method based on hybrid quadratic decomposition provided by an embodiment of the present invention.

[0015] This invention provides a method for predicting ocean wave height based on hybrid quadratic decomposition, which may include the following steps: S1: Obtain the raw wave height data to be predicted.

[0016] Raw wave height data typically comes from ocean observation stations, buoys, remote sensing satellites, or other oceanographic measurement tools, and includes the actual wave height values ​​at a specific moment or over a certain period. By obtaining accurate wave height data, we can reflect the true state of the current marine environment and provide accurate and practical information for subsequent analysis and processing.

[0017] S2: Perform initial decomposition on the original wave height data to obtain the intrinsic mode functions and residual terms.

[0018] Specifically, the original wave height data is initially decomposed using the CEEMDAN algorithm to obtain the intrinsic mode functions and residual terms.

[0019] The CEEMDAN algorithm (Complete Ensemble Empirical Mode Decomposition with Adaptive Noise) is an improved Empirical Mode Decomposition (EMD) algorithm that decomposes non-stationary and nonlinear signals by adding adaptive noise. The Intrinsic Mode Functions (IMFs) are signal components obtained through the CEEMDAN algorithm, reflecting the intrinsic characteristics of the signal at different scales. The residual terms represent the parts of the signal that cannot be further decomposed, typically low-frequency trend components.

[0020] It should be noted that the CEEMDAN algorithm is used to initially decompose the raw wave height data, breaking down the complex wave height signal into multiple intrinsic mode functions (IMFs) and residual terms. The advantage of this process is its ability to effectively handle nonlinear and non-stationary data, common characteristics of wave height data. Through decomposition, CEEMDAN can extract different frequency components from the signal, providing more accurate features for subsequent analysis. Its adaptive noise handling capability significantly improves the robustness of the decomposition, reduces noise interference, and ensures the accuracy of the decomposition results.

[0021] In one possible implementation, the initial decomposition of the raw wave height data using the CEEMDAN algorithm specifically includes: White noise is added to the original wave height data using the CEEMDAN algorithm to generate a noise sequence: ; 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. ρ i ( ) indicates the first i Standard Gaussian white noise, n Indicates the sequence length.

[0022] Perform EMD decomposition on the noisy sequence until the residual signal meets the stopping criterion, generating the eigenmode function and residual terms: ; 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.

[0023] 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.

[0024] S3: Calculate the sample entropy of the intrinsic mode functions.

[0025] Sample entropy, proposed by Alcaraz and Rieta, is a signal processing algorithm that measures the complexity of a research object based on the probability of new patterns emerging in a signal, thus serving as a metric for evaluating the complexity of a time series. The more complex the time series, the higher its sample entropy value. A smaller sample entropy value indicates a more regular and stable data series, while a larger value indicates a more complex and irregular data series.

[0026] It's important to note that in wave height prediction, sample entropy is used to assess the complexity of each intrinsic mode function (IMF). By calculating the sample entropy of the IMFs, the complexity of each mode can be quantified. This process helps identify components with higher complexity in the signal, providing a deeper understanding of the wave height data. Through the evaluation of sample entropy, mode functions with high predictive potential can be selected, avoiding redundant mode components from affecting subsequent analysis.

[0027] In one possible implementation, the formula for calculating sample entropy is as follows: ; in, SampEn ( a , r , d ) represents sample entropy, a Indicates the dimension of the constructed vector. r Indicates tolerance. d This represents the total number of data points. ln Represents the natural logarithm function. Indicates tolerance r Below, the two sequences match. a The probability of each data point a +1 indicates the dimension of the constructed vector. Indicates tolerance r Below, the two sequences match. a The probability of adding 1 data point The vector dimension is a +1 hour s The matching status of point pairs. , The vector dimension is a Time v The matching situation of each pair of points. .

[0028] It should be noted that sample entropy can reflect the nonlinear characteristics of wave height data, helping to better identify dynamic change patterns in the data, enhance the model's adaptability to complex wave phenomena, and thus improve the accuracy and reliability of predictions.

[0029] S4: Based on the magnitude of the sample entropy, the intrinsic mode functions are classified to obtain the reconstructed mode components, which include: high-frequency components, mid-frequency components and low-frequency components.

[0030] Specifically, the intrinsic mode functions are classified using the K-means clustering algorithm to obtain the reconstructed mode components.

[0031] K-means clustering is a common unsupervised learning algorithm typically used for data clustering analysis. This algorithm divides data into K clusters, ensuring that data points within the same cluster are as similar as possible, while data points between different clusters are significantly different. The algorithm iteratively updates the centroids of the clusters until the cluster assignments no longer change. Modal component reconstruction refers to combining (reconstructing) eigenmode functions belonging to the same category to generate more representative signal components.

[0032] High-frequency components represent signal characteristics that change rapidly and have short periods, often associated with sudden changes and small-scale disturbances in waves. Mid-frequency components represent the portion with moderate periods and relatively stable changes, potentially reflecting regular wave fluctuations. Low-frequency components typically represent the trend term or long-term variation of the signal, reflecting the overall trend of wave height or slowly changing components.

[0033] It should be noted that classifying intrinsic mode functions using the K-means clustering algorithm can clearly distinguish different frequency components (such as high-frequency, mid-frequency, and low-frequency) in ocean wave height signals. This classification effectively avoids confusion between frequency components, allowing each component to be processed independently, thereby improving the accuracy and effectiveness of subsequent analysis.

[0034] In one possible implementation, classifying intrinsic mode functions using the K-means clustering algorithm specifically includes: A preset number of centroids are initialized using the K-means clustering algorithm.

[0035] In the K-means clustering algorithm, the centroid is the center point of each cluster, representing the mean position of all data points within that cluster. Updating the centroid is a crucial step in the K-means algorithm, iteratively optimizing the cluster assignment.

[0036] Calculate 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 then output the classification result.

[0037] Those skilled in the art can set the value of the preset objective function according to the actual situation, and the present invention does not impose any limitations.

[0038] The specific formula for calculating the objective function value is as follows: ; 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.

[0039] 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.

[0040] S5: The high-frequency components are decomposed in two stages using the VMD algorithm to generate subsequence components.

[0041] 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.

[0042] 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.

[0043] In one possible implementation, S5 specifically includes: S501: Decompose the high-frequency components into a predetermined number of sub-components to construct a variational problem: ; in, express t The first moment k Subsequences, Indicates the first k The 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.

[0044] 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.

[0045] S502: By introducing a quadratic penalty factor and a Lagrange penalty operator, an unconstrained objective function for the variational problem is constructed: ; 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 λ 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.

[0046] 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.

[0047] S503: Solve the unconstrained objective function using the alternating direction multiplier method to generate subsequence components.

[0048] The Alternating Direction Method of Multipliers (ADMM) is an algorithm for solving convex optimization problems, particularly suitable for constrained optimization problems. Its basic idea is to decompose the original optimization problem into several easier-to-solve subproblems and solve these subproblems iteratively.

[0049] It's worth noting that VMD, by minimizing the variational objective function, allows for more precise control over the decomposition process, especially when dealing with complex, non-stationary signals, providing more stable decomposition results. This refined decomposition provides subsequent deep learning models with more accurate and discriminative signal components, thereby improving prediction accuracy and stability.

[0050] In one possible implementation, S503 specifically includes: S5031: Initialize each sub-component, center frequency, and Lagrange penalty operator.

[0051] The Lagrange penalty operator is a mathematical tool used to constrain the objective function. In the VMD optimization process, the Lagrange penalty factor is used to ensure that the constraints in the decomposition process are satisfied.

[0052] S5032: With the objective of minimizing the unconstrained objective function, update the sub-components, center frequencies, and Lagrange penalty operators respectively: ; in, Indicates the first n At the +1st iteration, the... e Frequency domain components of each submode, ω Represents frequency (integral variable). Represents the frequency components of the original signal. Indicates the first n During the nth iteration, the 1st e Frequency domain components of each submode, , F This represents the total number of submodes. This represents the Lagrange penalty operator in the central frequency domain. Indicates the first n At the +1st iteration, the... e The center frequency of each sub-mode Indicates the first n At the +1st iteration, the... e Lagrange penalty operator corresponding to each submodal Indicates the first n The frequency domain representation of the corresponding Lagrange penalty operator at the next iteration.

[0053] S5033: Stop updating when the error accuracy is less than the preset error accuracy, and output the final sub-component and the center frequency corresponding to the final sub-component.

[0054] Those skilled in the art can set the preset error accuracy according to the actual situation, and the present invention does not limit it.

[0055] S5034: Determine the subsequence components based on the final sub-components and the center frequency.

[0056] It should be noted that the Alternating Direction Multiplier Method (ADMM) is a powerful optimization algorithm suitable for solving constrained convex optimization problems. It decomposes complex optimization problems into easily solvable subproblems by introducing Lagrange multipliers, and gradually approximates the optimal solution to the original problem by alternately updating the solutions of each subproblem. ADMM is widely used in many practical applications due to its efficiency and flexibility.

[0057] S6: Establish a periodic-aware time-deep learning model.

[0058] In one possible implementation, the periodic-aware time-deep learning model includes: a period segmentation module, a hybrid predictor module, and an ensemble aggregator module.

[0059] Among them, the periodic-aware time-series deep learning model is a deep learning model specifically designed for processing time-series data. It has periodic awareness capabilities, enabling it to identify and utilize periodic patterns in time series data. In ocean wave height prediction, periodic features typically reflect the regular fluctuations of ocean waves (such as tides, seasonal variations, etc.), and the periodic awareness module helps the model consider these periodic changes during prediction.

[0060] The period segmentation module is used to divide time series data into periodic segments. By periodically segmenting the signal, the model can identify and extract different periodic features in the time series, thereby improving the accuracy of predictions.

[0061] The hybrid predictor module combines multiple prediction methods, typically a combination of different deep learning algorithms, and is able to process different types of features and data, outputting more accurate prediction results.

[0062] The ensemble module is responsible for combining and integrating multiple prediction results to form the final prediction output. The ensemble method can reduce the bias of a single model and improve the stability and accuracy of predictions by combining the prediction results of multiple models.

[0063] It's worth noting that the period segmentation module effectively divides the time series into different periods, helping the model identify the periodic changes in waves and ensuring that these natural patterns are considered during the prediction process. The hybrid predictor module combines multiple deep learning methods to handle different features in the data, thereby improving the model's flexibility and adaptability. The ensemble aggregator module further improves prediction stability and reduces the errors that might occur with a single model by integrating the prediction results from multiple models.

[0064] In one possible implementation, the period segmentation module is used to segment the subsequence components, the intermediate frequency components, and the low frequency components.

[0065] The segmentation process performed by the periodic segmentation module specifically includes: The time-domain signal is converted into a frequency-domain signal by using the Fast Fourier Transform.

[0066] The Fast Fourier Transform (FFT) is an efficient algorithm for the Fourier Transform, used to convert time-domain signals into frequency-domain signals. The Fourier Transform is a mathematical transformation that converts a signal from the time domain (describing how the signal changes over time) to the frequency domain (describing the signal's components at different frequencies).

[0067] Select a preset number of dominant frequency components from the frequency domain signal to generate the frequency characteristics of the dominant period.

[0068] The value of the dominant period is obtained by taking the reciprocal of the dominant frequency component: ; in, Indicates the amplitude corresponding to the sequence. n It is the sequence length. AMP This indicates the operation for extracting the amplitude value. X This represents a subsequence of the input. FFT Represents the Fast Fourier Transform. arg This indicates that the frequency corresponding to the maximum amplitude has been returned. Indicates in Before being selected The largest frequency, Indicates the first h Larger frequencies correspond to longer period lengths. n Indicates the sequence length. f h Indicates the first h High frequency.

[0069] Based on the value of the dominant period, the subsequence components, mid-frequency components, and low-frequency components are segmented to generate multiple patches.

[0070] Specifically, in order to enhance the predictive model’s sensitivity to the periodicity of the data, the input sequence is divided into several patches according to the calculated period length.

[0071] The individual patches are arranged and integrated in the order of segmentation into a two-dimensional tensor for time series prediction: ; in, Indicates the first h Large frequencies correspond to 2D tensor data. reshape (.) indicates a rearrangement operation. Representing a two-dimensional tensor The row number, i.e., the first row h Larger frequencies correspond to longer period lengths. Representing a two-dimensional tensor The number of columns.

[0072] A two-dimensional tensor is a matrix formed by arranging multiple signal features (patches) in chronological order. In machine learning and deep learning, two-dimensional tensors are often used to represent and process time series data, allowing the model to consider information from different time points and different features simultaneously.

[0073] It should be noted that segmenting the subsequence components, mid-frequency components, and low-frequency components using the periodic segmentation module, generating multiple patches, and finally integrating them into a two-dimensional tensor helps improve the accuracy and efficiency of time series prediction. First, the Fast Fourier Transform (FFT) converts the time-domain signal into a frequency-domain signal, accurately capturing the periodic components and frequency characteristics of the signal. Selecting the dominant frequency component and calculating the dominant period helps to clarify the main fluctuation period of the signal, making the segmented patches more representative. Reasonably segmenting the signal according to its periodic characteristics and organizing it into a two-dimensional tensor format not only preserves the time-frequency information of the time series but also provides high-quality input data for deep learning models.

[0074] In one possible implementation, the hybrid predictor module uses the encoder structure of a Transformer as a framework. The hybrid predictor module processes the two-dimensional tensor output by the period segmentation module. The processing specifically includes: By calculating attention scores row-by-row on a two-dimensional tensor, short-term dependency features, i.e., short-term attention scores, are extracted: ; in, Indicates the first 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.

[0075] Specifically, short-term dependency characteristics reflect the changing trends or local patterns of data within a shorter time window.

[0076] By calculating attention scores column-wise on a two-dimensional tensor, long-term dependency features, i.e., long-term attention scores, are extracted: ; 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.

[0077] 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.

[0078] Based on the variation patterns among the patches in the two-dimensional tensor, global variation features, i.e., global attention scores, are extracted: ; in, A inter This represents the global attention matrix, i.e., the global attention score. Q inter Represents the query matrix. K inter Represents the key matrix. V inter Represents a value matrix, d m This represents the scaling factor.

[0079] Specifically, global change characteristics can capture the macroscopic patterns exhibited by data throughout the entire time series, such as seasonal variations in ocean wave height and long-term climate change. These characteristics are not limited to short-term local dependencies, but rather focus on the overall trend or periodic changes of the entire time series.

[0080] By concatenating and reducing dimensions, the short-term attention score, long-term attention score, and global attention score are merged to generate a hybrid attention result: ; in, A This indicates the results of mixed attention. Flatten This indicates a dimensionality reduction operation. A intra Indicates short-term attention score, A phase Indicates long-term attention score, A inter This represents the global attention score.

[0081] The results of the various hybrid attention operations are concatenated and then mapped to obtain the sequence prediction result. ; in, Represents the final characteristic matrix. Indicates the first A two-dimensional tensor This indicates the sequence prediction result. Linear This indicates a linear layer.

[0082] It's important to note that by calculating attention scores for each row and column of data, the model effectively captures different time scales and patterns in the signal. Short-term dependency features help capture immediate, rapidly changing trends. Long-term dependency features help reveal the long-term trend of the signal. Global change 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 predictions.

[0083] In one possible implementation, the aggregator module is used to output the prediction results.

[0084] The specific formula for calculating the prediction result is as follows: ; 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.

[0085] 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.

[0086] Among them, the wave height prediction result is the wave height prediction result after being processed by the periodic time-aware deep learning model.

[0087] 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.

[0088] The beneficial effects brought about by the technical solution provided by the embodiment of the present invention include at least: 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.

[0089] Reference manual attached Figure 2 The diagram shows a schematic representation of a wave height prediction system based on hybrid quadratic decomposition provided in an embodiment of the present invention.

[0090] This invention provides a wave height prediction system 20 based on hybrid quadratic decomposition, comprising: a processor 201 and a memory 202; The memory 202 stores programs or instructions that can run on the processor 201. When the program or instructions are executed by the processor 201, they implement the steps of the above-mentioned wave height prediction method based on hybrid quadratic decomposition and achieve the same technical effect. To avoid repetition, the present invention will not repeat the above-mentioned steps.

[0091] It should be understood that the processor 201 in this embodiment of the invention may be a central processing unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor.

[0092] It should also be understood that the memory 202 in the embodiments of the present invention can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDR SDRAM), enhanced synchronous DRAM (ESDRAM), synchronous linked DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0093] The above embodiments can be implemented, in whole or in part, by software, hardware (such as circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the flow or function according to the embodiments of the present invention is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. Computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., infrared, wireless, microwave, etc.) means. A computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more sets of available media. Available media can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., DVDs), or semiconductor media. Semiconductor media can be solid-state drives.

[0094] It should be understood that, in various embodiments of the present invention, the order of the above-mentioned process numbers does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0095] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0096] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices, apparatuses, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0097] In the embodiments provided by this invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0098] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0099] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0100] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0101] This invention provides a readable storage medium that stores a program or instructions on the medium. When the program or instructions are executed by a processor, they implement the steps of the above-described method for predicting ocean wave height based on hybrid quadratic decomposition and achieve the same technical effect. To avoid repetition, this invention will not elaborate further.

[0102] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the embodiments of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the protection scope of the present invention.

Claims

1. A wave height prediction method based on hybrid quadratic decomposition, characterized in that, include: S1: Obtain the raw wave height data to be predicted; S2: Perform initial decomposition on the original wave height data to obtain the intrinsic mode functions and residual terms; S3: Calculate the sample entropy of the intrinsic mode function; S4: Based on the magnitude of the sample entropy, classify the intrinsic mode functions to obtain reconstructed mode components, wherein the reconstructed mode components include: high-frequency components, mid-frequency components and low-frequency components; S5: The high-frequency components are decomposed in two stages using the VMD algorithm to generate subsequence components; S6: Establish a periodic-aware time-deep learning model; The periodic-aware time-deep learning model includes: a period segmentation module, a hybrid predictor module, and an ensemble aggregator module. S7: Input the subsequence component, the mid-frequency component, and the low-frequency component into the periodic sensing time deep learning model, and output the wave height prediction result.

2. The wave height prediction method based on hybrid quadratic decomposition according to claim 1, characterized in that, S5 specifically includes: S501: Decompose the high-frequency component into a predetermined number of sub-components to construct a variational problem; S502: By introducing a quadratic penalty factor and a Lagrange penalty operator, the unconstrained objective function of the variational problem is constructed; S503: Solve the unconstrained objective function using the alternating direction multiplier method to generate the subsequence components.

3. The wave height prediction method based on hybrid quadratic decomposition according to claim 2, characterized in that, S503 specifically includes: S5031: Initialize each sub-component, center frequency, and Lagrange penalty operator; S5032: With the goal of minimizing the unconstrained objective function, update the sub-components, the center frequency, and the Lagrange penalty operator respectively; S5033: Stop updating until the error accuracy is less than the preset error accuracy, and output the final sub-component and the center frequency corresponding to the final sub-component; S5034: Determine the subsequence component based on the final sub-component and the center frequency.

4. The wave height prediction method based on hybrid quadratic decomposition according to claim 1, characterized in that, The period segmentation module is used to segment the subsequence components, the mid-frequency components, and the low-frequency components.

5. The wave height prediction method based on hybrid quadratic decomposition according to claim 4, characterized in that, The process of segmentation performed by the periodic segmentation module specifically includes: The time-domain signal is converted into a frequency-domain signal by using the Fast Fourier Transform. A predetermined number of dominant frequency components are selected from the frequency domain signal to generate the frequency characteristics of the dominant period; The value of the dominant period is obtained by taking the reciprocal of the dominant frequency component; Based on the value of the dominant period, the subsequence component, the mid-frequency component, and the low-frequency component are segmented to generate multiple patches; The patches are arranged and integrated in the order of their segmentation into a two-dimensional tensor for time series prediction.

6. The wave height prediction method based on hybrid quadratic decomposition according to claim 1, characterized in that, The hybrid predictor module uses the encoder structure of a Transformer as its framework. This module processes the two-dimensional tensor output by the period segmentation module. The processing specifically includes: By calculating attention scores row by row on the two-dimensional tensor, short-term dependency features, i.e., short-term attention scores, are extracted. By calculating attention scores column-wise on the two-dimensional tensor, long-term dependency features, i.e., long-term attention scores, are extracted. Based on the variation patterns among the patches in the two-dimensional tensor, global variation features, i.e., global attention scores, are extracted: ； in, A inter This represents the global attention matrix, i.e., the global attention score. Q inter Represents the query matrix. K inter Represents the key matrix, V inter Represents a value matrix, d m The scaling factor is represented by `softmax`, and the activation function is represented by `softmax`. T Indicates transpose; By concatenating and reducing dimensions, the short-term attention score, the long-term attention score, and the global attention score are merged to generate a hybrid attention result: ； in, A This indicates the results of mixed attention. Flatten This indicates a dimensionality reduction operation. A intra Indicates short-term attention score, A phase Indicates long-term attention score, A inter This represents the global attention score; The various hybrid attention results are concatenated and then mapped to obtain the sequence prediction result: ； in, Represents the final characteristic matrix. Indicates the first A two-dimensional tensor This indicates the sequence prediction result. Linear This indicates a linear layer.

7. The wave height prediction method based on hybrid quadratic decomposition according to claim 1, characterized in that, The aggregator module is used to output the prediction results.

8. A wave height prediction system based on hybrid quadratic decomposition, characterized in that, include: Processor and memory; The memory stores programs or instructions that can run on the processor, which, when executed by the processor, implement the steps of the wave height prediction method based on hybrid quadratic decomposition as described in any one of claims 1 to 7.

9. A readable storage medium, characterized in that, The readable storage medium stores a program or instructions that, when executed by a processor, implement the steps of the wave height prediction method based on hybrid quadratic decomposition as described in any one of claims 1 to 7.

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