A method, medium, and system for ocean digital twinning sea wave spectrum parameter calculation

Abstract

The application provides a method, medium and system for ocean digital twinning sea wave spectrum parameter calculation, and belongs to the technical field of electric digital data processing. The application obtains and pre-processes original sea wave spectrum data, selects Jonswap frequency sea wave spectrum as a theoretical model, establishes a multi-index fitting criterion, optimizes and solves a peak rise factor parameter, performs statistical analysis according to effective wave height period levels, distinguishes typhoon and non-typhoon working condition sea wave spectrum characteristics, calculates wave amplitude wave numbers and random phases to construct a wave surface height model, and finally forms a sea wave spectrum parameter database. The technical problem that sea wave spectrum parameters are difficult to accurately describe and calculate in an ocean digital twinning system is solved, and the extreme sea condition simulation capability is particularly optimized, thereby providing technical support for high-precision sea wave field simulation of the ocean digital twinning system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of digital data processing, and particularly relates to a method, medium and system for ocean digital twinning sea wave spectrum parameter calculation. BACKGROUND

[0002] As a virtual reproduction of the physical ocean environment, the ocean digital twinning system is widely used in the fields of ocean engineering design, ocean disaster warning and ship navigation safety. Traditional ocean digital twinning technology usually uses a theoretical sea wave spectrum model to simulate the sea wave field. Commonly used models include the P-M spectrum and the Jonswap spectrum. These models achieve a simplified description of the sea wave field through a small number of parameters such as significant wave height and spectral peak period. However, there are significant differences between the theoretical sea wave spectrum model and the actual sea wave spectrum, especially in terms of morphological characteristics.

[0003] Currently, sea wave spectrum parameter calculation mainly uses a fixed parameter method or a simple regression method. The fixed parameter method uses an empirical constant as the peak enhancement factor, which cannot adapt to the dynamic changes of the sea wave spectrum under different sea areas and weather conditions. The simple regression method considers the influence of the marine environment, but ignores the complexity and spatiotemporal variability of the sea wave spectrum shape, resulting in insufficient fitting accuracy. Especially under extreme weather conditions such as typhoons, the morphological characteristics of the sea wave spectrum change significantly, and existing methods are difficult to accurately depict.

[0004] Due to the insufficient accuracy of sea wave spectrum parameter calculation, existing ocean digital twinning systems have low simulation accuracy and poor adaptability in sea wave field reproduction, which cannot meet the needs of high-precision ocean digital twinning applications, especially in terms of simulation accuracy under multi-temporal and spatial scales and extreme sea conditions. This has become a key technical problem that limits the development and application of ocean digital twinning technology. That is, there is a technical problem in the existing technology that the sea wave spectrum parameters in the ocean digital twinning system are difficult to accurately describe and calculate. SUMMARY

[0005] Therefore, the present application provides a method, medium and system for ocean digital twinning sea wave spectrum parameter calculation, which can solve the technical problem of the existing technology that the sea wave spectrum parameters in the ocean digital twinning system are difficult to accurately describe and calculate.

[0006] The application is implemented in the following manner: a method for ocean digital twinning sea wave spectrum parameter calculation is provided in the first aspect of the application, comprising: obtaining original sea wave spectrum data and performing preprocessing; selecting Jonswap frequency sea wave spectrum as a theoretical frequency sea wave spectrum; establishing a fitting criterion to evaluate the degree of conformity between the fitted frequency sea wave spectrum and the original frequency sea wave spectrum; constructing a frequency sea wave spectrum formula according to the significant wave height and the spectral peak period, and solving the optimal fitting peak elevation factor by a numerical optimization method; classifying and calculating the statistical characteristics of the peak elevation factor according to the significant wave height period level; distinguishing the typhoon sea wave spectrum from the non-typhoon sea wave spectrum through spatial and temporal matching of the typhoon wave; constructing a wave face height model based on the fitted frequency sea wave spectrum to calculate wave parameters; and generating a sea wave spectrum parameter database.

[0007] In the step of obtaining original sea wave spectrum data and performing preprocessing, the direction sea wave spectrum is directionally integrated to obtain the frequency sea wave spectrum, and the one-dimensional frequency sea wave spectrum with a frequency component quantity exceeding 25 is subjected to frequency interpolation, so as to ensure that the total energy difference before and after frequency interpolation is not greater than 0.1 square meters per second.

[0008] The direction sea wave spectrum refers to the energy distribution of the sea wave spectrum at different frequencies and different directions, and is expressed as , wherein is the frequency, is the direction; the frequency sea wave spectrum refers to the energy distribution of the sea wave spectrum at different frequencies, and is obtained by integrating the direction sea wave spectrum in the range of 0 to , and is expressed as .

[0009] The frequency component refers to a frequency discrete point for describing the frequency sea wave spectrum, and the original frequency sea wave spectrum is resampled to 25 frequency components with a frequency interval of ; the total energy refers to the zero-order spectral distance of the frequency sea wave spectrum, and the calculation formula is .

[0010] In the step of establishing a fitting criterion, the fitting criterion comprises the spectral peak absolute error, the zero-order spectral distance error and the spectral value root mean square error; the spectral peak absolute error refers to the absolute value of the spectral peak value difference between the fitted frequency sea wave spectrum and the original frequency sea wave spectrum, and the calculation formula is .

[0011] The zero-order spectral distance error refers to the absolute value of the zero-order spectral distance difference between the fitted frequency sea wave spectrum and the original frequency sea wave spectrum, and the calculation formula is ; the spectral value root mean square error refers to the root mean square of the spectral value difference between the fitted frequency sea wave spectrum and the original frequency sea wave spectrum at all frequency points, and the calculation formula is .

[0012] Wherein, in the step of selecting Jonswap frequency wave spectrum as the theoretical frequency wave spectrum, a sea wave development energy balance equation is further introduced for physical mechanism analysis, and the fitting accuracy of the peak elevation factor is improved.

[0013] Wherein, in the step of solving the optimal fitting peak elevation factor, a pre-trained sea wave spectrum parameter intelligent prediction network WaveSpecNet model is further established, and the peak elevation factor prediction accuracy and calculation efficiency are improved through multi-modal data fusion.

[0014] Wherein, the gradient descent method is to calculate the gradient of the objective function to the peak elevation factor, and update the peak elevation factor parameter according to the learning rate iteration, until the objective function converges or reaches the maximum iteration number, and the gradient calculation formula is , wherein , and the parameter update formula is , wherein is the learning rate, and the value is 0.01. The numerical optimization method includes an array search method or a gradient descent method; the array search method refers to discretizing the peak elevation factor in the range of 1 to 7 with a step length of 0.01 to form a peak elevation factor array with a dimension of 661, substituting the peak elevation factor into the theoretical frequency wave spectrum formula in turn, calculating the error with the original frequency wave spectrum, and selecting the peak elevation factor value with the minimum error.

[0015] Wherein, the sea wave development energy balance equation is used to describe the evolution process and energy transfer mechanism of the frequency wave spectrum in space and time; the sea wave development energy balance equation considers physical processes such as wind energy input, nonlinear interaction between waves, white wave dissipation and bottom friction dissipation, and inputs include average wind speed, wind direction, wind duration, water depth and effective wave height, and outputs are the space-time evolution characteristics of the frequency wave spectrum and the dynamic adjustment value of the peak elevation factor.

[0016] Wherein, the WaveSpecNet model is a deep neural network based on an encoder-decoder architecture; the encoder part of the WaveSpecNet model adopts a multi-head self-attention mechanism to process multi-source space-time data, including original frequency wave spectrum data, meteorological data and terrain data; the decoder part adopts a sparse attention mechanism to fuse different modal features, and outputs the peak elevation factor value and the peak elevation factor uncertainty estimate.

[0017] The second aspect of the present application provides a computer readable storage medium, the computer readable storage medium stores program instructions, the program instructions are run in the computer, and are used for executing the above-mentioned method for calculating the sea wave spectrum parameter of the ocean digital twin.

[0018] The third aspect of the present application provides a system for ocean digital twinning sea wave spectrum parameter calculation, comprising the computer readable storage medium described above, the system is any one of a computer, a server, and a single chip microcomputer, the computer readable storage medium is arranged in the system, and the system is provided with a microprocessor for executing program instructions stored in the computer readable storage medium.

[0019] The present application realizes accurate calculation and classified management of the peak enhancement factor by establishing a multi-step fitting optimization process between the original sea wave spectrum data and the theoretical frequency sea wave spectrum. The method uses a multi-index fitting criterion combining the absolute error of the spectrum peak value, the zero-order spectral distance error, and the root mean square error of the spectrum value to ensure the accuracy of the whole spectrum segment in the fitting process. The present application solves the problem of insufficient accuracy caused by fixed parameters or simple regression in traditional methods, and solves the optimal fitting peak enhancement factor by using array search method or gradient descent method, establishes peak enhancement factor statistical characteristic analysis for different effective wave height period levels, and realizes the sea wave spectrum parameter distinction of typhoon and non-typhoon working conditions combined with typhoon data. Especially for extreme sea conditions, this method can provide more actual peak enhancement factor values, which significantly improves the simulation accuracy. By constructing the sea wave spectrum parameter database and the wave surface height model, high-precision digital twinning simulation of the sea wave field is realized, and the technical problem of difficult accurate description and calculation of sea wave spectrum parameters is solved. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 The flowchart of the method of the present application.

[0021] Figure 2 The sea wave surface distribution generated in Example 2.

[0022] Figure 3 The typhoon and non-typhoon working condition distinction diagram in Example 2, wherein the light yellow circles represent the typhoon influence range (radius 200 km), and the red plus signs inside the circles represent the points affected by the typhoon. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0024] As shown in Figure 1 , it is a flowchart of the method for sea wave spectrum parameter calculation in ocean digital twinning provided by the first aspect of the present application, and the method comprises the following steps:

[0025] S01, obtain the original sea wave spectrum data, directionally integrate the directional sea wave spectrum to obtain the frequency sea wave spectrum, and frequency interpolate the one-dimensional frequency sea wave spectrum with a frequency group number exceeding 25 to ensure that the total energy difference before and after frequency interpolation is not greater than 0.1 square meters per second;

[0026] S02, select Jonswap frequency sea wave spectrum as the theoretical frequency sea wave spectrum, use the known significant wave height and spectral peak period to construct the frequency sea wave spectrum formula, and determine the peak enhancement factor as the fitting parameter;

[0027] S03, establish a fitting criterion including the absolute error of the spectral peak value, the error of the zero-order spectral distance, and the root mean square error of the spectral value, for evaluating the degree of conformity between the fitted frequency sea wave spectrum and the original frequency sea wave spectrum;

[0028] S04, substitute the initial guess value of the significant wave height, the spectral peak period, and the peak enhancement factor into the theoretical frequency sea wave spectrum formula to preliminarily fit the theoretical frequency sea wave spectrum and the original frequency sea wave spectrum;

[0029] S05, solve the optimal fitting peak enhancement factor based on array search method or gradient descent method, and select the peak enhancement factor value that minimizes the fitting criterion error as the optimal fitting parameter of the sea wave spectrum;

[0030] S06, classify according to the effective wave height period level of the sea wave data, calculate the mean value, standard deviation, and 95% confidence interval of the peak enhancement factor value for each effective wave height period level, and make a scatter plot of the peak enhancement factor value;

[0031] S07, perform spatio-temporal matching of typhoon waves through the tropical cyclone best path data set, identify the sea wave spectrum of points within 200 kilometers from the typhoon center during the occurrence of a typhoon as the typhoon sea wave spectrum, and distinguish the sea wave spectrum parameters corresponding to the typhoon sea wave spectrum and the non-typhoon sea wave spectrum;

[0032] S08, calculate the fitted frequency sea wave spectrum using the matched peak enhancement factor value, calculate the wave amplitude, wave number, and wave random phase based on the fitted frequency sea wave spectrum, and finally construct a wave height model to complete the sea wave digital twin simulation;

[0033] S09, generate a sea wave spectrum parameter database according to the fitted peak enhancement factor parameters under multiple spatio-temporal conditions, provide real-time peak enhancement factor parameter support for the marine digital twin system, and realize high-precision sea wave simulation.

[0034] The directional sea wave spectrum refers to the energy distribution of the sea wave spectrum at different frequencies and different directions, and is expressed as wherein is the frequency, is the direction.

[0035] The frequency wave spectrum refers to energy distribution of the wave spectrum at different frequencies, is obtained by integrating the directional wave spectrum in the range of 0 to 2π, and is expressed as , which is used to represent the distribution characteristics of the wave energy at different frequencies.

[0036] The frequency component refers to a frequency discrete point for describing the frequency wave spectrum, and the original frequency wave spectrum is resampled to 25 frequency components , and the frequency interval is .

[0037] The total energy refers to a zero-order spectral distance of the frequency wave spectrum, and the calculation formula is The difference between the total energy of the original frequency wave spectrum and the interpolated frequency wave spectrum is not greater than 0.1 square meters per second.

[0038] The Jonswap frequency wave spectrum is a classical frequency wave spectrum of a wave theory, and the calculation formula is , wherein , is an effective wave height, is a spectral peak period, is a frequency, is a peak enhancement factor, is a dimensionless spectral width parameter.

[0039] The peak enhancement factor refers to a parameter in the Jonswap frequency wave spectrum formula that affects the spectral shape , and the value range is 1 to 7. It is a key parameter for reflecting the spectral shape characteristics of the frequency wave spectrum, and the optimal value is determined by fitting.

[0040] The spectral peak period refers to a period corresponding to the maximum energy density in the frequency wave spectrum, and is one of the key characteristic parameters of the wave spectrum.

[0041] The effective wave height refers to an average value of the highest 1 / 3 wave height, and is related to the zero-order spectral distance of the frequency wave spectrum. The calculation formula is .

[0042] The spectral peak absolute error refers to an absolute value of the spectral peak difference between the fitted frequency wave spectrum and the original frequency wave spectrum. The calculation formula is , which is used to evaluate the fitting accuracy of the maximum energy in the wave group.

[0043] The zero-order spectral distance error refers to an absolute value of the zero-order spectral distance difference between the fitted frequency wave spectrum and the original frequency wave spectrum. The calculation formula is The zero-order spectral distance is calculated by integrating the frequency wave spectrum with respect to the frequency, and reflects the overall energy of the wave.

[0044] Wherein, the spectral value root mean square error refers to the root mean square of the spectral value difference between the fitted frequency wave spectrum and the original frequency wave spectrum at all frequency points, and the calculation formula is , which reflects the overall fitting degree of the frequency wave spectrum.

[0045] Wherein, the initial guess value of the peak enhancement factor is set to 3.3, which is the starting value of the peak enhancement factor parameter optimization.

[0046] Wherein, the array search method refers to discretizing the peak enhancement factor in the range of 1 to 7 with a step of 0.01 to form a peak enhancement factor array with a dimension of 661, which is substituted into the theoretical frequency wave spectrum formula in turn to calculate the error with the original frequency wave spectrum, and the peak enhancement factor value with the smallest error is selected.

[0047] Wherein, the gradient descent method is to calculate the gradient of the objective function with respect to the peak enhancement factor, and update the peak enhancement factor parameter according to the learning rate until the objective function converges or the maximum iteration number is reached. The gradient calculation formula is , wherein , and the parameter update formula is , wherein is the learning rate, which is 0.01.

[0048] Wherein, the effective wave height period level refers to dividing the effective wave height into intervals in the range of 0 to 12 meters with a step of 0.5 meters, and dividing the period into intervals in the range of 2 to 20 seconds with a step of 1 second, forming a two-dimensional grid classification.

[0049] Wherein, the peak enhancement factor value mean refers to the arithmetic mean of all peak enhancement factor values within a certain effective wave height period level, and the calculation formula is , wherein , , is the wave height, is the period, is the number of qualified samples.

[0050] Wherein, the peak enhancement factor standard deviation refers to the square root of the mean of the sum of squares of the difference between all peak enhancement factor values and the peak enhancement factor value mean within a certain effective wave height period level, and the calculation formula is .

[0051] Wherein, the peak enhancement factor 95% confidence interval refers to the peak enhancement factor value mean plus or minus 1.96 times the standard error, wherein the standard error calculation formula is , is the peak enhancement factor standard deviation, is the sample number.

[0052] The peak enhancement factor value scatter plot refers to a wave height-period joint distribution table, with the period range of 2-20 seconds as the horizontal axis and the significant wave height range of 0-12 meters as the vertical axis. The table content is the average peak enhancement factor value in the corresponding significant wave height period range.

[0053] The tropical cyclone optimal path data set refers to a time series data set recording the center position, intensity, moving speed and direction of a tropical cyclone.

[0054] The typhoon sea wave spectrum refers to the sea wave spectrum occurring during a severe tropical storm and higher-level typhoon, and within 200 kilometers from the typhoon center.

[0055] The wave amplitude is a parameter calculated according to the frequency sea wave spectrum, and the calculation formula is wherein is the spectral density at frequency , and is the frequency interval.

[0056] The wave number is the spatial frequency of the wave, which is calculated through the dispersion relationship between the angular frequency and the wave number, and the dispersion relationship formula is wherein is the angular frequency, is the acceleration of gravity, which is 9.8 meters per square second, is the water depth, is the wave number.

[0057] The wave random phase is a parameter randomly generated from a uniform distribution , which is used to simulate the randomness of the wave.

[0058] The wave surface height model is a mathematical model of sea surface fluctuation constructed by superimposing multiple simple harmonic waves, and the calculation formula is wherein is the wave amplitude, is the wave number, is the angular frequency, is the wave random phase, is the spatial position, is the time.

[0059] Optionally, a sea wave development energy balance equation is introduced for the frequency wave spectrum fitting process in step S02 to perform physical mechanism analysis and improve the fitting accuracy of the peak enhancement factor. The sea wave development energy balance equation is used to describe the evolution process and energy transfer mechanism of the frequency wave spectrum in space and time, and considers physical processes such as wind energy input, nonlinear interaction between waves, white wave dissipation and bottom friction dissipation. The input includes average wind speed, wind direction, wind duration, water depth and effective wave height, and the output is the space-time evolution characteristics of the frequency wave spectrum and the dynamic adjustment value of the peak enhancement factor. The sea wave development energy balance equation regards the frequency wave spectrum as the distribution of the energy density function in the frequency domain and the direction domain, analyzes the energy input, nonlinear interaction between waves and energy dissipation in the wind wave interaction, and establishes the coupling relationship between the frequency wave spectrum and the external wind field, so that the fitting of the peak enhancement factor has stronger physical significance. The sea wave development energy balance equation can be expressed as the rate of change of the energy density function with respect to time being equal to the sum of the source terms, and the dynamic response mechanism of the peak enhancement factor value changing with the wind field condition can be obtained by solving the sea wave development energy balance equation, thereby improving the accuracy of the peak enhancement factor in extreme sea conditions. At the same time, the sea wave development energy balance equation also considers the influence of the shallow water effect on the peak enhancement factor, and modifies the peak enhancement factor under different water depth conditions, so that the digital twin simulation also has high accuracy in the nearshore sea area.

[0060] Optionally, a pre-trained WaveSpecNet model is established for steps S05 and S06 to improve the prediction accuracy and computational efficiency of the peak enhancement factor through multi-modal data fusion. The specific structure of the WaveSpecNet model is a deep neural network based on an encoder-decoder architecture. The encoder part uses a multi-head self-attention mechanism to process multi-source spatio-temporal data, including original frequency wave spectrum data, meteorological data, and terrain data. The decoder part uses a sparse attention mechanism to fuse different modal features and outputs the peak enhancement factor value and the peak enhancement factor uncertainty estimate. The sparse attention mechanism parameters in the WaveSpecNet model are determined by a difference contribution vector calculation function, which is constructed based on the wind wave area development theory and takes into account the physical contribution of wind speed, wind area length, and wind duration to the formation of the frequency wave spectrum. The difference contribution vector calculation function inputs five parameters: wind speed, wind area length, wind duration, water depth, and significant wave height, and outputs a vector representing the contribution degree of different parameters to the formation of the frequency wave spectrum. The difference contribution vector is compared with a preset difference contribution standard vector to adjust the sparse attention weight according to the similarity. The training data set of the WaveSpecNet model is established by collecting multi-year multi-site original frequency wave spectrum observation data and corresponding meteorological conditions and terrain conditions, performing spatio-temporal alignment and scale normalization on the original frequency wave spectrum data, dividing the data into layers according to the typhoon wave spectrum and non-typhoon wave spectrum working conditions, constructing a labeled data set containing input features and target peak enhancement factor values, enhancing the time series characteristics of the data set using the sliding time window method, and dividing the training set, validation set, and test set through cross-validation method. The training steps of the WaveSpecNet model include first performing self-supervised pre-training on a large-scale frequency wave spectrum data set to learn the internal relationship between the peak enhancement factor and the meteorological environment, then fine-tuning using the labeled data set to optimize the prediction performance of the WaveSpecNet model in the measured sea area, and adjusting the sparse attention parameters by incorporating the output of the difference contribution vector calculation function during the training process to make the WaveSpecNet model pay more attention to feature combinations with significant physical meaning. An uncertainty estimation module is introduced to quantify the confidence of the peak enhancement factor value prediction. Finally, the WaveSpecNet model parameters are continuously updated through online learning mechanism to adapt to the dynamic changes of the marine environment.

[0061] The specific implementation of the above steps is described in detail below.

[0062] The specific implementation of step S01 is to preprocess the original wave spectrum data to ensure that the data used in the subsequent fitting process has sufficient quality. First, the original directional wave spectrum data is obtained from the wave observation station or buoy system , the one-dimensional frequency wave spectrum is obtained by integrating the directional wave spectrum in the range of 0 to 2π direction using the numerical integration method . For the one-dimensional frequency wave spectrum with more than 25 frequency components, the frequency points are resampled using the cubic spline interpolation algorithm to resample the original irregular frequency discrete points into 25 equi-proportional frequency discrete points. Before and after interpolation, the zero-order spectral distance of the frequency wave spectrum, i.e., the total energy , is calculated by the trapezoidal integration method to ensure that the difference in total energy before and after interpolation is not greater than 0.1 square meters per second. If the interpolation result exceeds the threshold, the frequency interpolation is re-performed by adjusting the tension coefficient of the cubic spline interpolation until the energy conservation constraint is met. The purpose of this step is to ensure the establishment of the standardized format of the wave spectrum data, reduce the computational load caused by too many data components in the subsequent fitting process, and at the same time maintain the energy characteristics of the wave.

[0063] The specific implementation of step S02 is to determine the theoretical frequency wave spectrum model and the parameters to be fitted. The Jonswap frequency wave spectrum is selected as the theoretical frequency wave spectrum, which is a modification of the Pierson-Moskowitz spectrum and is suitable for describing the wind wave developed under the condition of limited wind area and limited wind time. The frequency wave spectrum formula is constructed using the known significant wave height and spectral peak period , where is a normalization coefficient, is a dimensionless spectral width parameter, when , when , . The peak enhancement factor is determined as the parameter to be fitted, which reflects the sharpness of the peak region of the frequency wave spectrum and is a key parameter for describing the shape of the wave spectrum. The purpose of this step is to establish a theoretical model framework to lay a foundation for subsequent parameter optimization.

[0064] The specific implementation of step S03 is to establish a fitting criterion for evaluating the degree of conformity between the fitted frequency wave spectrum and the original frequency wave spectrum. First, the spectral peak absolute error is defined to evaluate the fitting accuracy of the maximum energy in the wave group, where and are the spectral values of the fitted frequency wave spectrum and the original frequency wave spectrum at the spectral peak frequency, respectively. Second, the zero-order spectral distance error is defined to evaluate the difference in total energy between the fitted frequency wave spectrum and the original frequency wave spectrum, where and are the zero-order spectral distances of the fitted frequency wave spectrum and the original frequency wave spectrum, respectively, which are calculated by the trapezoidal integration method. Finally, the root mean square error of the spectral value ​, to evaluate the overall fitting degree of the frequency wave spectrum in the full frequency range, where is the number of frequency discrete points, and are the spectral values of the fitted frequency wave spectrum and the original frequency wave spectrum at the th frequency point, respectively. The three criteria established in this step evaluate the fitting effect from the peak accuracy, energy conservation and overall shape, respectively, to ensure the comprehensiveness and accuracy of the fitting results.

[0065] The specific implementation of step S04 is to substitute the initial guess values of the significant wave height, spectral peak period and peak enhancement factor into the theoretical frequency wave spectrum formula to perform preliminary fitting of the theoretical frequency wave spectrum and the original frequency wave spectrum. First, the significant wave height and the spectral peak period are extracted from the original frequency wave spectrum data, where the significant wave height is calculated by the zeroth-order spectral distance, i.e. , and the spectral peak period is obtained by finding the frequency corresponding to the maximum energy density in the frequency wave spectrum and taking the reciprocal, i.e. . Then, the peak enhancement factor initial guess value is set to 3.3, which is determined according to the statistical average value of the North Sea wave observation data and is suitable for initial fitting in most sea areas. Substituting these three parameters into the Jonswap frequency wave spectrum formula, the preliminary fitted frequency wave spectrum is calculated. The initial fitting error is calculated using the fitting criteria defined in step S03 as the benchmark value for subsequent optimization. The purpose of this step is to provide a reasonable initial estimate of the peak enhancement factor, providing a starting point for subsequent parameter optimization.

[0066] The specific implementation of step S05 is to solve the optimal fitting peak enhancement factor based on an optimization algorithm. First, using the array search method, the peak enhancement factor is discretized in the range of 1 to 7 with a step of 0.01 to form a peak enhancement factor array with a dimension of 661. For each peak enhancement factor value in the array, substitute it into the Jonswap frequency wave spectrum formula to calculate the fitted frequency wave spectrum, and use the fitting criteria established in step S03 to calculate the fitting error. To consider the three fitting criteria comprehensively, introduce the weighted error function , where the weight coefficients , , are determined according to the actual needs of marine engineering, with more emphasis on peak accuracy and energy conservation. Select the peak enhancement factor value that minimizes the weighted error function as the optimal fitting result. For scenarios with limited computing resources or high real-time requirements, the gradient descent method can be used instead of the array search method to approach the optimal solution iteratively. The gradient of the objective function with respect to the peak enhancement factor is calculated using numerical differentiation, and the gradient calculation formula is , where . The parameter update formula is where the learning rate The convergence condition is set as the absolute value of gradient less than 0.001 or the maximum iteration number 100. The purpose of this step is to find the peak enhancement factor value that makes the fitted frequency wave spectrum most close to the original frequency wave spectrum by optimization algorithm.

[0067] The specific implementation of step S06 is to perform statistical analysis according to the classification of the wave data in the effective wave height period level. First, the effective wave height is divided into intervals in the range of 0 to 12 meters with a step of 0.5 meters, forming 24 wave height levels; the period is divided into intervals in the range of 2 to 20 seconds with a step of 1 second, forming 18 period levels. The combination of the two forms 24x18=432 effective wave height period level grids. For each grid unit, collect all the peak enhancement factor samples belonging to the grid, and the sample number is usually tens to hundreds. For the grid units with sample number greater than 5, calculate the peak enhancement factor value mean where , , is the wave height, is the period, is the number of qualified samples. Calculate the peak enhancement factor standard deviation to represent the dispersion degree of the peak enhancement factor in this level. Calculate the peak enhancement factor 95% confidence interval, and the upper and lower limits of the confidence interval are Finally, make a peak enhancement factor value scatter plot, with period as the horizontal axis and effective wave height as the vertical axis, using the wave height period joint distribution table form, and the table content is the peak enhancement factor value mean in the corresponding effective wave height period range. The purpose of this step is to establish the correlation model of the peak enhancement factor and the effective wave height and period, and to provide a scientific basis for the selection of wave spectrum parameters under different sea conditions.

[0068] The specific implementation method of step S07 is to divide the wave spectrum into two working conditions: typhoon wave spectrum and non-typhoon wave spectrum through the typhoon wave spatiotemporal matching process. First, obtain the tropical cyclone optimal path data set, which contains information such as the center position, time, intensity, moving speed and direction of the tropical cyclone. For each wave spectrum observation data, record its observation time and geographical location. Use the spatiotemporal matching algorithm to calculate the distance between each wave spectrum observation point and the nearest typhoon center at the same time. Time matching uses linear interpolation to interpolate the typhoon position data at 6-hour intervals to 1-hour intervals to ensure that the time matching accuracy is not less than 1 hour. The spatial distance calculation uses the spherical distance formula to calculate the great circle distance based on the longitude and latitude of the two points. The wave spectrum within 200 kilometers from the typhoon center is identified as the typhoon wave spectrum, and the rest is identified as the non-typhoon wave spectrum. For the typhoon wave spectrum and the non-typhoon wave spectrum, the peak rise factor statistical model in step S06 is established respectively to obtain the peak rise factor distribution law under the two working conditions. The purpose of this step is to distinguish the wave spectrum characteristics under different wind and wave generation mechanisms and improve the accuracy of wave simulation under special weather conditions.

[0069] The specific implementation method of step S08 is to use the matched peak rise factor value to calculate the fitting frequency wave spectrum, and calculate the wave parameters based on the fitting frequency wave spectrum to construct a wave surface height model. First, according to the effective wave height, spectrum peak period and working conditions of the observation point, the corresponding peak rise factor value is queried from the statistical model established in steps S06 and S07. Substitute the effective wave height, spectrum peak period and the peak rise factor obtained by the query into the Jonswap frequency wave spectrum formula to calculate the fitting frequency wave spectrum. The wave amplitude is calculated based on the fitting frequency wave spectrum, and the calculation formula is ,in Frequency The spectral density at is the frequency interval. Calculate the wave number by solving the dispersion relation equation Get, among them is the angular frequency, is the acceleration due to gravity, For water depth, is the wave number. The nonlinear equation is solved using the bisection method, and the initial search interval is , the convergence accuracy is set to Generate waves with random phases, from a uniform distribution Finally, the wave height model is constructed. ,in is the wave amplitude, is the wave number, is the angular frequency, is the random phase of the wave, is the spatial position, The purpose of this step is to convert the optimized frequency wave spectrum parameters into a time-domain wave surface model to realize the digital twin simulation of the ocean surface.

[0070] The specific implementation method of step S09 is to generate a wave spectrum parameter database based on the fitted peak rise factor parameters under multiple spatiotemporal conditions. First, wave observation data from major ocean areas around the world are collected, covering different latitudes, seasons and meteorological conditions. The collected wave spectrum data are gridded according to the geographical location, with a grid resolution of 1 degree × 1 degree. For each grid cell, the methods of steps S01 to S07 are applied to extract the statistical characteristics of the peak rise factor, including the monthly average, seasonal variation trend and extreme value distribution. A spatiotemporal database of peak rise factor parameters is constructed, and the database index structure adopts a quadtree method to support fast retrieval by geographical location and time. A database update mechanism is established to automatically update the peak rise factor statistical parameters of the corresponding grid cell whenever there is new wave observation data. A database interface protocol is designed to support real-time query of peak rise factor parameters by the ocean digital twin system, with an interface response time of no more than 100 milliseconds. The purpose of this step is to systematize and structure the discrete wave spectrum parameter optimization results to form a continuously updated parameter library, provide real-time and accurate peak rise factor parameter support for the ocean digital twin system, and achieve high-precision wave simulation.

[0071] Optionally, for the frequency wave spectrum fitting process in step S02, the wave development energy balance equation is introduced to perform physical mechanism analysis to improve the fitting accuracy of the peak rise factor. First, a wave development energy balance equation model is established. The model uses the frequency wave spectrum as the state variable to describe the evolution process of the frequency wave spectrum in time and space and the energy transfer mechanism. The model input parameters include average wind speed, wind direction, wind duration, water depth and effective wave height. The energy balance equation is solved by numerical integration method to obtain the spatiotemporal evolution characteristics of the frequency wave spectrum. The wave development energy balance equation considers four key physical processes: wind energy input, nonlinear interaction between waves, whitecap dissipation and bottom friction dissipation. The wind energy input source term adopts the Miles mechanism formula to describe the energy transfer between the wind field and the wave surface; the nonlinear interaction source term between waves adopts the discrete interaction approximation method, considering the four-wave resonance interaction; the whitecap dissipation source term adopts the saturation spectrum theory and is related to the wave steepness; the bottom friction dissipation source term adopts an empirical formula and is related to the water depth and track speed. The wave development energy balance equation establishes the coupling relationship between the frequency wave spectrum and the external wind field, and can dynamically calculate the theoretical value of the peak rise factor under different wind field conditions. For extreme sea conditions, a parameterized adjustment method is adopted. When the wind speed exceeds 25 meters per second, the peak rise factor is dynamically adjusted according to the ratio of wind speed to wave age, which improves the accuracy of the peak rise factor under extreme sea conditions. At the same time, considering the influence of shallow water effect on the peak rise factor, the relative water depth parameter is introduced. ,when At the same time, the peak enhancement factor is corrected according to the empirical formula, so that the digital twin simulation also has high precision in the nearshore sea area. This optimization step changes the determination of the peak enhancement factor from pure statistical fitting to a parameterization method based on physical mechanisms, enhancing the adaptability and reliability of the model in complex sea conditions.

[0072] This optimization step fundamentally enhances the physical basis of sea wave spectrum parameter fitting by introducing the sea wave development energy balance equation for physical mechanism analysis. The optimization establishes a dynamic coupling relationship between the frequency sea wave spectrum and the external wind field conditions, so that the determination of the peak enhancement factor is no longer dependent on numerical fitting, but incorporates the comprehensive influence of wind energy input, nonlinear interaction between waves, white wave dissipation, and bottom friction dissipation. This parameter adjustment mechanism based on physical mechanisms can capture the evolution characteristics of the sea wave spectrum under the driving of the wind field, and is more accurate in predicting the morphological changes of the sea wave spectrum under extreme sea conditions. At the same time, the optimization also considers the influence of water depth on wave propagation characteristics, and solves the problem of precision decline in traditional methods in complex terrain sea areas near the shore through a shallow water effect correction mechanism, so that the sea wave spectrum parameter calculation maintains high accuracy under different water depth conditions, thereby expanding the applicability of digital twin technology in the entire sea area.

[0073] Optionally, for steps S05 and S06, a pre-trained sea wave spectrum parameter intelligent prediction network, namely WaveSpecNet model, is established to improve the prediction accuracy and calculation efficiency of peak elevation factor through multi-modal data fusion. The WaveSpecNet model is designed based on an encoder-decoder architecture. The encoder part uses a multi-head self-attention mechanism to process multi-source spatio-temporal data, including original frequency sea wave spectrum data, meteorological data and terrain data. The encoder consists of 3 layers of multi-head attention layers, each layer containing 8 attention heads, with a hidden layer dimension of 512. The decoder part uses a sparse attention mechanism to fuse different modal features, consisting of 2 layers of sparse attention layers and 3 layers of feedforward neural networks, outputting the peak elevation factor value and its uncertainty estimate. The sparse attention mechanism parameters in the WaveSpecNet model are determined by a difference contribution vector calculation function, which is constructed based on the sea wave wind area development theory, considering the physical contribution of wind speed, wind area length and wind duration to the formation of frequency sea wave spectrum. The difference contribution vector calculation function inputs five parameters: wind speed, wind area length, wind duration, water depth and significant wave height, and outputs a vector representing the contribution degree of different parameters to the formation of frequency sea wave spectrum. The vector is compared with a preset difference contribution standard vector in terms of cosine similarity, with a similarity threshold of 0.85, and the sparse attention weight is adjusted according to the similarity. The WaveSpecNet model training data set contains multi-year multi-site original frequency sea wave spectrum observation data and corresponding meteorological conditions and terrain conditions, with a total of more than 1 million data. The sliding time window method is used to enhance the time series characteristics of the data set, with a window size of 24 hours and a step size of 6 hours. The five-fold cross-validation method is used to divide the training set, validation set and test set in the ratio of 8:1:1. In the training process, first, the mask autoencoder method is used to learn the internal structural features of the frequency sea wave spectrum based on a large-scale frequency sea wave spectrum data set for self-supervised pre-training, and then the labeled data set is used for supervised fine-tuning to optimize the prediction performance of the model in the measured sea area. In the training, an adaptive learning rate strategy is used, with an initial learning rate of 0.001, and every 30 training periods, the learning rate is decayed to 0.1 times of the original. An uncertainty estimation module is introduced to quantify the confidence of peak elevation factor value prediction based on the ensemble learning method, providing risk assessment basis for the digital twin system. This optimization step combines deep learning technology with ocean physical mechanism, significantly improving the accuracy of peak elevation factor prediction is the water depth, is the wave number.

[0074] wherein the wave random phase is a parameter randomly generated from a uniform distribution to simulate the randomness of the wave.

[0075] wherein the wave surface height model is a mathematical model of sea surface undulation constructed by superimposing multiple simple harmonic waves, and the calculation formula is wherein is the wave amplitude, is a wave number, is an angular frequency, is a random phase of the wave, is a spatial position, is a time.

[0076] Optionally, a sea wave development energy balance equation is introduced for the frequency sea wave spectrum fitting process in step S02 to perform physical mechanism analysis and improve the fitting accuracy of the peak enhancement factor. The sea wave development energy balance equation is used to describe the evolution process and energy transfer mechanism of the frequency sea wave spectrum in space and time, and considers physical processes such as wind energy input, nonlinear interaction between waves, white wave dissipation, and bottom friction dissipation. The input includes average wind speed, wind direction, wind duration, water depth, and effective wave height, and the output is the spatiotemporal evolution characteristics of the frequency sea wave spectrum and the dynamic adjustment value of the peak enhancement factor. The sea wave development energy balance equation regards the frequency sea wave spectrum as the distribution of the energy density function in the frequency domain and the direction domain, analyzes the energy input, nonlinear interaction between waves, and energy dissipation in the wind wave interaction, establishes the coupling relationship between the frequency sea wave spectrum and the external wind field, and makes the fitting of the peak enhancement factor have stronger physical significance. The sea wave development energy balance equation can be expressed as the rate of change of the energy density function with respect to time being equal to the sum of the source terms, and the dynamic response mechanism of the peak enhancement factor value changing with the wind field condition can be obtained by solving the sea wave development energy balance equation, thereby improving the accuracy of the peak enhancement factor under extreme sea conditions. At the same time, the sea wave development energy balance equation also considers the influence of the shallow water effect on the peak enhancement factor, and corrects the peak enhancement factor under different water depth conditions, so that the digital twin simulation also has high accuracy in the nearshore sea area.

[0077] Optionally, a pre-trained WaveSpecNet model is established for steps S05 and S06 to improve the prediction accuracy and computational efficiency of the peak enhancement factor through multi-modal data fusion. The specific structure of the WaveSpecNet model is a deep neural network based on an encoder-decoder architecture. The encoder part uses a multi-head self-attention mechanism to process multi-source spatio-temporal data, including original frequency wave spectrum data, meteorological data, and terrain data. The decoder part uses a sparse attention mechanism to fuse different modal features and outputs the peak enhancement factor value and the peak enhancement factor uncertainty estimate. The sparse attention mechanism parameters in the WaveSpecNet model are determined by a difference contribution vector calculation function, which is constructed based on the wind wave area development theory and takes into account the physical contribution of wind speed, wind area length, and wind duration to the formation of the frequency wave spectrum. The difference contribution vector calculation function inputs five parameters: wind speed, wind area length, wind duration, water depth, and significant wave height, and outputs a vector representing the contribution degree of different parameters to the formation of the frequency wave spectrum. The difference contribution vector is compared with a preset difference contribution standard vector to adjust the sparse attention weight according to the similarity. The training data set of the WaveSpecNet model is established by collecting multi-year multi-site original frequency wave spectrum observation data and corresponding meteorological conditions and terrain conditions, performing spatio-temporal alignment and scale normalization on the original frequency wave spectrum data, dividing the data into layers according to the typhoon wave spectrum and non-typhoon wave spectrum working conditions, constructing a labeled data set containing input features and target peak enhancement factor values, enhancing the time series characteristics of the data set using the sliding time window method, and dividing the training set, validation set, and test set through cross-validation method. The training steps of the WaveSpecNet model include first performing self-supervised pre-training on a large-scale frequency wave spectrum data set to learn the internal relationship between the peak enhancement factor and the meteorological environment, then fine-tuning using the labeled data set to optimize the prediction performance of the WaveSpecNet model in the measured sea area, and adjusting the sparse attention parameters by incorporating the output of the difference contribution vector calculation function during the training process to make the WaveSpecNet model pay more attention to feature combinations with significant physical meaning. An uncertainty estimation module is introduced to quantify the confidence of the peak enhancement factor value prediction. Finally, the WaveSpecNet model parameters are continuously updated through online learning mechanism to adapt to the dynamic changes of the marine environment.

[0078] The specific implementation of the above steps is described in detail below.

[0079] The specific implementation of step S01 is to preprocess the original wave spectrum data to ensure that the data used in the subsequent fitting process has sufficient quality. First, the original directional wave spectrum data is obtained from the wave observation station or buoy system , the one-dimensional frequency wave spectrum is obtained by integrating the directional wave spectrum in the range of 0 to 2π direction using the numerical integration method . For the one-dimensional frequency wave spectrum with more than 25 frequency components, the frequency points are resampled using the cubic spline interpolation algorithm to resample the original irregular frequency discrete points into 25 equi-proportional frequency discrete points. Before and after interpolation, the zero-order spectral distance of the frequency wave spectrum, i.e., the total energy , is calculated by the trapezoidal integration method to ensure that the difference in total energy before and after interpolation is not greater than 0.1 square meters per second. If the interpolation result exceeds the threshold, the frequency interpolation is re-performed by adjusting the tension coefficient of the cubic spline interpolation until the energy conservation constraint is met. The purpose of this step is to ensure the establishment of the standardized format of the wave spectrum data, reduce the computational load caused by too many data components in the subsequent fitting process, and at the same time maintain the energy characteristics of the wave.

[0080] The specific implementation of step S02 is to determine the theoretical frequency wave spectrum model and the parameters to be fitted. The Jonswap frequency wave spectrum is selected as the theoretical frequency wave spectrum, which is a modification of the Pierson-Moskowitz spectrum and is suitable for describing the wind wave developed under the condition of limited wind area and limited wind time. The frequency wave spectrum formula is constructed using the known significant wave height and spectral peak period , wherein , is a normalized coefficient, is a dimensionless spectral width parameter, when , when , when . The peak enhancement factor is determined as the parameter to be fitted, which reflects the sharpness of the peak region of the frequency wave spectrum and is a key parameter for describing the shape of the wave spectrum. The purpose of this step is to establish a theoretical model framework to lay a foundation for subsequent parameter optimization.

[0081] The specific implementation of step S03 is to establish a fitting criterion for evaluating the degree of conformity between the fitted frequency wave spectrum and the original frequency wave spectrum. First, the spectral peak absolute error is defined to evaluate the fitting accuracy of the maximum energy in the wave group, wherein and are the spectral values of the fitted frequency wave spectrum and the original frequency wave spectrum at the spectral peak frequency, respectively. Second, the zero-order spectral distance error is defined to evaluate the difference in total energy between the fitted frequency wave spectrum and the original frequency wave spectrum, wherein and are the zero-order spectral distances of the fitted frequency wave spectrum and the original frequency wave spectrum, respectively, which are calculated by the trapezoidal integration method. Finally, the root mean square error of the spectral value , to evaluate the overall fitting degree of the frequency wave spectrum in the full frequency range, where is the number of frequency discrete points, and are the spectral values of the fitted frequency wave spectrum and the original frequency wave spectrum at the th frequency point, respectively. The three criteria established in this step evaluate the fitting effect from the peak accuracy, energy conservation and overall shape, respectively, to ensure the comprehensiveness and accuracy of the fitting results.

[0082] The specific implementation of step S04 is to substitute the initial guess values of the significant wave height, spectral peak period and peak enhancement factor into the theoretical frequency wave spectrum formula to perform preliminary fitting of the theoretical frequency wave spectrum and the original frequency wave spectrum. First, the significant wave height and the spectral peak period are extracted from the original frequency wave spectrum data, where the significant wave height is calculated by the zeroth-order spectral distance, i.e. , and the spectral peak period is obtained by finding the frequency corresponding to the maximum energy density in the frequency wave spectrum and taking the reciprocal, i.e. . Then, the peak enhancement factor initial guess value is set to 3.3, which is determined according to the statistical average value of the North Sea wave observation data and is suitable for initial fitting in most sea areas. Substituting these three parameters into the Jonswap frequency wave spectrum formula, the preliminary fitted frequency wave spectrum is calculated. The initial fitting error is calculated using the fitting criteria defined in step S03 as the benchmark value for subsequent optimization. The purpose of this step is to provide a reasonable initial estimate of the peak enhancement factor, providing a starting point for subsequent parameter optimization.

[0083] The specific implementation of step S05 is to solve the optimal fitting peak enhancement factor based on an optimization algorithm. First, using the array search method, the peak enhancement factor is discretized in the range of 1 to 7 with a step of 0.01 to form a peak enhancement factor array with a dimension of 661. For each peak enhancement factor value in the array, substitute it into the Jonswap frequency wave spectrum formula to calculate the fitted frequency wave spectrum, and use the fitting criteria established in step S03 to calculate the fitting error. To consider the three fitting criteria comprehensively, introduce the weighted error function , where the weight coefficients , , are determined according to the actual needs of marine engineering, with more emphasis on peak accuracy and energy conservation. Select the peak enhancement factor value that minimizes the weighted error function as the optimal fitting result. For scenarios with limited computing resources or high real-time requirements, the gradient descent method can be used instead of the array search method to approach the optimal solution iteratively. The gradient of the objective function with respect to the peak enhancement factor is calculated using numerical differentiation, and the gradient calculation formula is , where . The parameter update formula is where the learning rate The convergence condition is set as the absolute value of gradient less than 0.001 or the maximum iteration number 100. The purpose of this step is to find the peak enhancement factor value that makes the fitted frequency wave spectrum most close to the original frequency wave spectrum by optimization algorithm.

[0084] The specific implementation of step S06 is to perform statistical analysis according to the classification of the wave data in the effective wave height period level. First, the effective wave height is divided into intervals in the range of 0 to 12 meters with a step of 0.5 meters, forming 24 wave height levels; the period is divided into intervals in the range of 2 to 20 seconds with a step of 1 second, forming 18 period levels. The combination of the two forms 24x18=432 effective wave height period level grids. For each grid unit, collect all the peak enhancement factor samples belonging to the grid, and the sample number is usually tens to hundreds. For the grid units with sample number greater than 5, calculate the peak enhancement factor value mean where , , is the wave height, is the period, is the number of qualified samples. Calculate the peak enhancement factor standard deviation to represent the dispersion degree of the peak enhancement factor in this level. Calculate the peak enhancement factor 95% confidence interval, and the upper and lower limits of the confidence interval are Finally, make a peak enhancement factor value scatter plot, with period as the horizontal axis and effective wave height as the vertical axis, using the wave height period joint distribution table form, and the table content is the peak enhancement factor value mean in the corresponding effective wave height period range. The purpose of this step is to establish the correlation model of the peak enhancement factor and the effective wave height and period, and to provide a scientific basis for the selection of wave spectrum parameters under different sea conditions.

[0085] The specific implementation of step S07 is to divide the sea wave spectrum into typhoon sea wave spectrum and non-typhoon sea wave spectrum through a typhoon wave space-time matching process. First, the tropical cyclone best path data set is obtained, which contains the center position, time, intensity, moving speed and direction of the tropical cyclone. For each sea wave spectrum observation data, the observation time and geographical position are recorded. The space-time matching algorithm is used to calculate the distance between each sea wave spectrum observation point and the nearest typhoon center at the same time. The linear interpolation method is used to interpolate the typhoon position data at 6-hour intervals to 1-hour intervals to ensure that the time matching accuracy is not less than 1 hour. The spherical distance formula is used to calculate the great circle distance according to the latitude and longitude of the two points. The sea wave spectrum within 200 kilometers from the typhoon center is identified as the typhoon sea wave spectrum, and the rest is identified as the non-typhoon sea wave spectrum. The peak elevation factor statistical model in step S06 is established for the typhoon sea wave spectrum and the non-typhoon sea wave spectrum, respectively, to obtain the peak elevation factor distribution law under the two working conditions. The purpose of this step is to distinguish the characteristics of the sea wave spectrum under different wind wave generation mechanisms and improve the accuracy of sea wave simulation under special weather conditions.

[0086] The specific implementation of step S08 is to calculate the fitted frequency sea wave spectrum using the matched peak elevation factor value, and to calculate the wave parameter based on the fitted frequency sea wave spectrum to construct the wave surface height model. First, the peak elevation factor value is queried from the statistical model established in steps S06 and S07 according to the significant wave height, spectral peak period and the working condition of the observation point. The significant wave height, spectral peak period and the queried peak elevation factor are substituted into the Jonswap frequency sea wave spectrum formula to calculate the fitted frequency sea wave spectrum. The wave amplitude is calculated based on the fitted frequency sea wave spectrum, and the calculation formula is wherein is the spectral density at frequency , and is the frequency interval. The wave number is calculated by solving the dispersion relation equation , wherein is the angular frequency, is the gravitational acceleration, is the water depth, is the wave number. The bisection method is used to solve the nonlinear equation, and the initial search interval is , and the convergence accuracy is set to . The wave random phase is generated by randomly sampling from the uniform distribution . Finally, the wave surface height model is constructed as , wherein is the wave amplitude, is the wave number, is the angular frequency, is the wave random phase, is the spatial position, The purpose of this step is to convert the optimized frequency wave spectrum parameters into a time-domain wave surface model to realize the digital twin simulation of the ocean surface.

[0087] The specific implementation method of step S09 is to generate a wave spectrum parameter database based on the fitted peak rise factor parameters under multiple spatiotemporal conditions. First, wave observation data from major ocean areas around the world are collected, covering different latitudes, seasons and meteorological conditions. The collected wave spectrum data are gridded according to the geographical location, with a grid resolution of 1 degree × 1 degree. For each grid cell, the methods of steps S01 to S07 are applied to extract the statistical characteristics of the peak rise factor, including the monthly average, seasonal variation trend and extreme value distribution. A spatiotemporal database of peak rise factor parameters is constructed, and the database index structure adopts a quadtree method to support fast retrieval by geographical location and time. A database update mechanism is established to automatically update the peak rise factor statistical parameters of the corresponding grid cell whenever there is new wave observation data. A database interface protocol is designed to support real-time query of peak rise factor parameters by the ocean digital twin system, with an interface response time of no more than 100 milliseconds. The purpose of this step is to systematize and structure the discrete wave spectrum parameter optimization results to form a continuously updated parameter library, provide real-time and accurate peak rise factor parameter support for the ocean digital twin system, and achieve high-precision wave simulation.

[0088] Optionally, for the frequency wave spectrum fitting process in step S02, the wave development energy balance equation is introduced to perform physical mechanism analysis to improve the fitting accuracy of the peak rise factor. First, a wave development energy balance equation model is established. The model uses the frequency wave spectrum as the state variable to describe the evolution process of the frequency wave spectrum in time and space and the energy transfer mechanism. The model input parameters include average wind speed, wind direction, wind duration, water depth and effective wave height. The energy balance equation is solved by numerical integration method to obtain the spatiotemporal evolution characteristics of the frequency wave spectrum. The wave development energy balance equation considers four key physical processes: wind energy input, nonlinear interaction between waves, whitecap dissipation and bottom friction dissipation. The wind energy input source term adopts the Miles mechanism formula to describe the energy transfer between the wind field and the wave surface; the nonlinear interaction source term between waves adopts the discrete interaction approximation method, considering the four-wave resonance interaction; the whitecap dissipation source term adopts the saturation spectrum theory and is related to the wave steepness; the bottom friction dissipation source term adopts an empirical formula and is related to the water depth and track speed. The wave development energy balance equation establishes the coupling relationship between the frequency wave spectrum and the external wind field, and can dynamically calculate the theoretical value of the peak rise factor under different wind field conditions. For extreme sea conditions, a parameterized adjustment method is adopted. When the wind speed exceeds 25 meters per second, the peak rise factor is dynamically adjusted according to the ratio of wind speed to wave age, which improves the accuracy of the peak rise factor under extreme sea conditions. At the same time, considering the influence of shallow water effect on the peak rise factor, the relative water depth parameter is introduced. ,when When performing the peak rise factor analysis, the peak rise factor is modified according to an empirical formula, ensuring that the digital twin simulation also has high accuracy in nearshore waters. This optimization step transforms the determination of the peak rise factor from a purely statistical fit to a parameterized method based on physical mechanisms, enhancing the model's adaptability and reliability in complex sea conditions.

[0089] This optimization step fundamentally strengthens the physical basis of wave spectrum parameter fitting by introducing the wave development energy balance equation for physical mechanism analysis. The optimization establishes a dynamic coupling relationship between the frequency wave spectrum and the external wind field conditions, so that the determination of the peak rise factor no longer relies solely on numerical fitting, but incorporates the comprehensive influence of physical processes such as wind energy input, nonlinear interaction between waves, whitecap dissipation and bottom friction dissipation. This parameter adjustment mechanism based on physical mechanisms can capture the evolution characteristics of the wave spectrum driven by the wind field, especially for more accurate prediction of the changes in the wave spectrum morphology under extreme sea conditions. At the same time, the optimization also takes into account the influence of water depth on wave propagation characteristics. Through the shallow water effect correction mechanism, it solves the problem of reduced accuracy of traditional methods in complex nearshore terrain areas, so that the calculation of wave spectrum parameters maintains a high degree of accuracy under different water depth conditions, thereby expanding the applicability of digital twin technology in the entire sea area.

[0090] Optionally, for steps S05 and S06, a pre-trained sea wave spectrum parameter intelligent prediction network, namely WaveSpecNet model, is established to improve the prediction accuracy and calculation efficiency of peak enhancement factor through multi-modal data fusion. The WaveSpecNet model is based on an encoder-decoder architecture design. The encoder part uses a multi-head self-attention mechanism to process multi-source spatio-temporal data, including original frequency sea wave spectrum data, meteorological data and terrain data. The encoder consists of 3 layers of multi-head attention layers, each layer containing 8 attention heads, with a hidden layer dimension of 512. The decoder part uses a sparse attention mechanism to fuse different modal features, consisting of 2 layers of sparse attention layers and 3 layers of feedforward neural networks, outputting the peak enhancement factor value and its uncertainty estimate. The sparse attention mechanism parameters in the WaveSpecNet model are determined by a difference contribution vector calculation function, which is based on the sea wave wind area development theory and considers the physical contribution of wind speed, wind area length and wind duration to the formation of frequency sea wave spectrum. The difference contribution vector calculation function inputs five parameters: wind speed, wind area length, wind duration, water depth and significant wave height, and outputs a vector representing the contribution degree of different parameters to the formation of frequency sea wave spectrum. The vector is compared with a preset difference contribution standard vector in terms of cosine similarity, with a similarity threshold of 0.85, and the sparse attention weight is adjusted according to the similarity. The WaveSpecNet model training data set contains multi-year multi-site original frequency sea wave spectrum observation data and corresponding meteorological conditions and terrain conditions, with a total amount of more than 1 million. The sliding time window method is used to enhance the time series characteristics of the data set, with a window size of 24 hours and a step size of 6 hours. The five-fold cross-validation method is used to divide the training set, validation set and test set in the ratio of 8:1:1. The training process first performs self-supervised pre-training on the large-scale frequency sea wave spectrum data set, using the mask autoencoder method to learn the internal structural features of the frequency sea wave spectrum, and then uses the labeled data set for supervised fine-tuning to optimize the prediction performance of the model in the measured sea area. The adaptive learning rate strategy is used during training, with an initial learning rate of 0.001, and every 30 training periods the learning rate is decayed to 0.1 times the original value. An uncertainty estimation module is introduced to quantify the confidence of peak enhancement factor value prediction based on ensemble learning method, providing risk assessment basis for digital twin system. This optimization step combines deep learning technology with ocean physical mechanism, significantly improving the accuracy of peak enhancement factor prediction. The calculation formula of the equi-frequency point is:

[0091] ;

[0092] wherein, is the th frequency point, takes a value from 1 to 25; is the minimum frequency point, usually taking a value of 0.03 hertz; The maximum frequency point is usually 0.5 Hz. The zero-order spectral width of the frequency wave spectrum before and after interpolation is calculated by the trapezoidal integral method, that is, the total energy , and the calculation formula is:

[0093] ;

[0094] The discrete form is:

[0095] ;

[0096] In the formula, is the number of frequency discrete points; is the th frequency discrete point; is the frequency interval, and the calculation method is For the boundary points, take and . Ensure that the total energy difference before and after interpolation is not greater than 0.1 square meters per second, that is:

[0097] ;

[0098] In the formula, is the zero-order spectral width of the original frequency wave spectrum; is the zero-order spectral width of the frequency wave spectrum after interpolation. If the interpolation result exceeds the threshold value, the tension coefficient of the cubic spline interpolation is adjusted to re-perform frequency interpolation, the initial value of which is 0.5, the adjustment range is 0.1 to 0.9, and the adjustment step is 0.1 each time, until the energy conservation constraint is met.

[0099] The specific implementation of step S02 is to determine the theoretical frequency wave spectrum model and the parameters to be fitted. The Jonswap frequency wave spectrum is selected as the theoretical frequency wave spectrum, which is a modification of the Pierson-Moskowitz spectrum and is suitable for describing the wind wave developed under the condition of limited wind area and limited wind time. The frequency wave spectrum formula is constructed using the known significant wave height and spectral peak period

[0100] ;

[0101] In the formula, is the normalization coefficient, and the calculation formula is:

[0102] ;

[0103] is the significant wave height, in meters; is the spectral peak period, in seconds; is the frequency, in hertz; is the peak enhancement factor, which is in the range of 1 to 7; is the non-dimensional spectral width parameter, when where is the spectral peak frequency. The peak enhancement factor is determined as a fitting parameter, which reflects the sharpness of the peak region of the frequency wave spectrum and is a key parameter to describe the shape of the frequency wave spectrum. The larger the peak enhancement factor, the sharper the peak region of the frequency wave spectrum, and the higher the energy concentration; the smaller the peak enhancement factor, the flatter the peak region of the frequency wave spectrum, and the more uniform the energy distribution. In the Jonswap frequency wave spectrum model, when , the model degenerates into the Pierson-Moskowitz spectrum, which is applicable to fully developed wind waves; when , the model can describe the characteristics of developing wind waves.

[0104] The specific implementation of step S03 is to establish a fitting criterion for evaluating the degree of coincidence between the fitted frequency wave spectrum and the original frequency wave spectrum. First, define the spectral peak absolute error , the calculation formula is:

[0105] ;

[0106] In the formula, is the spectral value of the fitted frequency wave spectrum at the spectral peak frequency; is the spectral value of the original frequency wave spectrum at the spectral peak frequency. The spectral peak absolute error is used to evaluate the fitting accuracy of the maximum energy in the wave group, and its threshold is usually set to 10% of the original spectral peak value, i.e. . Secondly, define the zero-order spectral distance error , the calculation formula is:

[0107] ;

[0108] In the formula, is the zero-order spectral distance of the fitted frequency wave spectrum; is the zero-order spectral distance of the original frequency wave spectrum. The zero-order spectral distance is calculated by the trapezoidal integral method, and the formula is:

[0109] ;

[0110] ;

[0111] The zero-order spectral distance error is used to evaluate the total energy difference between the fitted frequency wave spectrum and the original frequency wave spectrum, and its threshold is usually set to 0.1 square meters per second, i.e. . Finally, define the root mean square error of spectral value​​​ , the calculation formula is:

[0112] ;

[0113] Where, is the number of frequency discrete points; To fit the frequency wave spectrum in Spectral value at frequency point; The original frequency wave spectrum is The spectrum value at each frequency point. The root mean square error of the spectrum value is used to evaluate the overall fitting degree of the frequency wave spectrum in the full frequency band, and its threshold is usually set at 20% of the root mean square value of the original frequency wave spectrum, that is, .

[0114] The specific implementation of step S04 is to substitute the initial guess values ​​of significant wave height, spectrum peak period and peak rise factor into the theoretical frequency wave spectrum formula, and perform preliminary fitting between the theoretical frequency wave spectrum and the original frequency wave spectrum. First, extract the significant wave height from the original frequency wave spectrum data. Sum spectrum peak period , the effective wave height is calculated by the zero-order spectrum distance, and the calculation formula is:

[0115] ;

[0116] The peak period is obtained by finding the frequency corresponding to the maximum energy density in the frequency wave spectrum and taking the inverse. The calculation formula is:

[0117] ;

[0118] Where, is the spectrum peak frequency. Then the peak rise factor is initially guessed to be 3.3. This value is determined based on the statistical average of the North Sea wave observation data and is suitable for the initial fitting of most sea areas. Substituting these three parameters into the Jonswap frequency wave spectrum formula, the preliminary fitting frequency wave spectrum is calculated:

[0119] ;

[0120] Where, is the initial guess value of the peak rise factor. Use the fitting criterion defined in step S03 to calculate the initial fitting error and calculate the absolute error of the spectrum peak value respectively. , zero-order spectral distance error RMS error of the sum spectrum , as the benchmark value for subsequent optimization.

[0121] The specific implementation of step S05 is to solve the optimal fitting peak raising factor based on the array search method or the gradient descent method. First, the array search method is used to discretize the peak raising factor in the range of 1 to 7 with a step size of 0.01 to form a peak raising factor array with a dimension of 601:

[0122] ;

[0123] Where, is the array index, ranging from 1 to 601; For the For each peak-raising factor value in the array, substitute the Jonswap frequency wave spectrum formula to calculate the fitted frequency wave spectrum:

[0124] ;

[0125] Where, To correspond to The normalization coefficient is calculated as follows:

[0126] .

[0127] The fitting error is calculated using the fitting criterion established in step S03, and a weighted error function is introduced. , the calculation formula is:

[0128] ;

[0129] Where, 、 and Use The absolute error of the spectrum peak, the zero-order spectrum distance error and the root mean square error of the spectrum value during fitting; 、 and is the weight coefficient, usually taken as 、 and , these weight coefficients are determined according to the actual needs of marine engineering, and more emphasis is placed on peak accuracy and energy conservation. The smallest peak elevation factor value is taken as the best fitting result:

[0130] .

[0131] For scenarios with limited computing resources or high real-time requirements, the gradient descent method can be used instead of the array search method to approximate the optimal solution through iteration. The gradient of the objective function with respect to the peak rise factor is calculated using numerical differentiation. The gradient calculation formula is:

[0132] ;

[0133] wherein, is the step size for gradient calculation. The parameter update formula is:

[0134] ;

[0135] wherein, is the peak elevation factor value of the th iteration; is the peak elevation factor value of the th iteration; is the learning rate, taking a value of 0.01; is the gradient of the objective function at the th iteration. The convergence condition is set as the absolute value of the gradient being less than 0.001 or reaching the maximum number of iterations of 100 times, i.e.

[0136] or .

[0137] The specific implementation of step S06 is to perform classified statistical analysis according to the effective wave height period level of the sea wave data. First, the effective wave height is divided into intervals in the range of 0 to 12 meters at a step size of 0.5 meters, forming 24 wave height levels; the period is divided into intervals in the range of 2 to 20 seconds at a step size of 1 second, forming 18 period levels. The combination of the two forms 24x18=432 effective wave height period level grids. For each grid unit , all the peak elevation factor samples belonging to the grid are collected, and the sample collection condition is:

[0138] and ;

[0139] wherein, is the effective wave height of the th sample; is the spectral peak period of the th sample; is the grid center effective wave height value; is the grid center spectral peak period value. For the grid unit with a sample number greater than 5, the peak elevation factor value mean is calculated, and the calculation formula is:

[0140] ;

[0141] wherein, is the sample number in the grid unit ; is the peak elevation factor value of the th sample. The peak elevation factor standard deviation , the calculation formula is:

[0142] ;

[0143] The peak elevation factor 95% confidence interval is calculated, and the upper and lower limits of the confidence interval are calculated as follows:

[0144] ;

[0145] In the formula, is the standard error. Finally, a peak elevation factor value scatter plot is made with the period as the horizontal axis and the significant wave height as the vertical axis, using a wave height period joint distribution table form, and the table content is the peak elevation factor value mean in the corresponding significant wave height period range.

[0146] The specific implementation of step S07 is to divide the sea wave spectrum into typhoon sea wave spectrum and non-typhoon sea wave spectrum through a typhoon wave space-time matching process. First, the tropical cyclone best path data set is obtained, which includes the center position, time, intensity, moving speed and direction of the tropical cyclone and other information. For each sea wave spectrum observation data, record its observation time and geographical position , wherein is the longitude, is the latitude. Using a space-time matching algorithm, the distance between each sea wave spectrum observation point and the nearest typhoon center at the same time is calculated. The linear interpolation method is used to interpolate the typhoon position data at 6-hour intervals to 1-hour intervals, and the interpolation formula is as follows:

[0147] ;

[0148] ;

[0149] In the formula, and are the longitudes and latitudes of the typhoon center at time ; and are the left and right boundary times of the interpolation interval, respectively, satisfying ; , , and are the longitudes and latitudes of the typhoon center at time and . The spatial distance is calculated using the spherical distance formula, which calculates the great circle distance according to the longitude and latitude of two points:

[0150] ;

[0151] In the formula, is the radius of the earth, which is 6371 kilometers; and are the latitude and longitude of the wave spectrum observation point, respectively, in radians; and are the latitude and longitude of the typhoon center, in radians. The wave spectrum within 200 kilometers from the typhoon center is identified as the typhoon wave spectrum, that is, The peak rise factor statistical model in step S06 is established for the typhoon wave spectrum and the non-typhoon wave spectrum respectively, and the peak rise factor distribution law under the two working conditions is obtained.

[0152] The specific implementation of step S08 is to calculate the fitting frequency wave spectrum using the peak rise factor value after matching, and calculate the wave parameters based on the fitting frequency wave spectrum to construct the wave surface height model. , spectral peak period and its corresponding working conditions, query the corresponding peak rise factor value from the statistical model established in steps S06 and S07 Substitute the significant wave height, spectrum peak period and peak rise factor obtained from the query into the Jonswap frequency wave spectrum formula to calculate the fitted frequency wave spectrum Calculate wave amplitude based on the fitted frequency wave spectrum , the calculation formula is:

[0153] ;

[0154] Where, Frequency The wave amplitude at Frequency spectral density at ; is the frequency interval. Calculate the wave number , by solving the dispersion relation equation we get:

[0155] ;

[0156] Where, is the angular frequency; is the acceleration due to gravity, which is 9.8 meters per second squared; is the water depth in meters; is the wave number in radians per meter. The nonlinear equation is solved using the bisection method, and the initial search interval is , the convergence accuracy is set to The binary iteration formula is:

[0157] ;

[0158] Where, For the the wave number estimation value of the (n-1)th iteration; the wave number estimation value of the (n-1)th iteration; the wave number estimation value of the (n-1)th iteration; and are the lower and upper bounds of the current iteration interval, respectively. The iteration termination condition is:

[0159] or .

[0160] generate wave random phase , randomly sampled from a uniform distribution :

[0161] ;

[0162] Finally, construct the wave surface height model, and the calculation formula is:

[0163] ;

[0164] In the formula, is the wave surface height at position and time ; is the number of frequency group components, usually taking a value of 25; is the wave amplitude of the (n-1)th frequency component; is the wave number of the (n-1)th frequency component; is the angular frequency of the (n-1)th frequency component; is the wave random phase of the (n-1)th frequency component; is the spatial position, in meters; is the time, in seconds. The specific implementation of step S09 is to generate a sea wave spectrum parameter database according to the fitting peak elevation factor parameters under multiple space-time conditions. First, collect sea wave observation data of major sea areas around the world, covering different latitudes, seasons, and weather conditions. The collected sea wave spectrum data is processed by gridding according to geographical position, and the grid resolution is 1 degree x 1 degree. For each grid unit , the method of steps S01 to S07 is applied to extract the peak elevation factor statistical characteristics, including the monthly average value , the seasonal variation trend , and the extreme value distribution parameters

[0165] and . The calculation formula of the monthly average value is: ;

[0166] ;

[0167] In the formula,​​​ for grid cell in months number of samples within; for the th sample. Seasonal variation trend is fitted by Fourier series:

[0168] ;

[0169] where, , and are Fourier coefficients, fitted by least square method; is the fundamental frequency, corresponding to four seasons; is the season index, 1 for spring, 2 for summer, 3 for autumn, and 4 for winter. Extreme value distribution is used to describe the maximum value distribution characteristics of peak elevation factor, and the cumulative distribution function is:

[0170] ;

[0171] where, is the location parameter; is the scale parameter; is the shape parameter. These three parameters are estimated by maximum likelihood method:

[0172] ;

[0173] where, is the probability density function of generalized extreme value distribution, and the calculation formula is:

[0174] .

[0175] A spatio-temporal database of peak elevation factor parameters is constructed, and the database index structure uses the quadtree method to support fast retrieval by geographical location and time. The process of constructing a quadtree is to recursively divide the space into four sub-regions, and each leaf node corresponds to a grid cell and its peak elevation factor statistical characteristics. The quadtree node structure is:

[0176] ;

[0177] where, , , and are the longitude and latitude ranges of the region corresponding to the node, respectively; is the list of child nodes, which is empty if it is a leaf node; The peak rise factor statistical characteristics stored for the node are empty if the node is a non-leaf node. The retrieval algorithm starts from the root node, and accesses layer by layer downwards according to the longitude and latitude of the query point until a leaf node is reached or the smallest area node containing the query point is found. The time retrieval is realized by maintaining the peak rise factor statistical characteristics of 12 months in each spatial node, supporting fast query by month. A database update mechanism is established, and the peak rise factor statistical parameters of the corresponding grid cells are automatically updated whenever new wave observation data is available. The update formula adopts the exponential moving average method:

[0178]

[0179] wherein, and are the monthly average values after and before updating respectively; is the peak rise factor value of the new observation sample; is a smoothing coefficient, and the value is 0.1. A database interface protocol is designed to support real-time query of the peak rise factor parameters by the marine digital twin system, and the interface response time is not more than 100 milliseconds. The database interface includes three modes of spatial query, time query and comprehensive query, and the spatial query interface is:

[0180]

[0181] The time query interface is:

[0182]

[0183] The comprehensive query interface is:

[0184]

[0185] wherein, is a sea state working condition, including typhoon and non-typhoon.

[0186] In another specific embodiment of the application, the optimization steps for S02 and S05, S06 are considered and described in detail below.

[0187] The specific embodiment of the optimization step one is directed to the frequency wave spectrum fitting process in step S02, and the sea wave development energy balance equation is introduced for physical mechanism analysis to improve the fitting accuracy of the peak rise factor. First, a sea wave development energy balance equation model is established, which describes the evolution process and energy transfer mechanism of the frequency wave spectrum in space and time. The sea wave development energy balance equation is expressed as:

[0188]

[0189] wherein, is the energy density of the frequency directional wave spectrum, and the unit is square meter second per radian;​​​​​ t is time, in seconds; G is the spatial gradient operator; C is the group velocity vector, in meters per second; Qw is the wind energy input source term; Qnl is the nonlinear wave-wave interaction source term; Qd is the whitecapping dissipation source term; Qb is the bottom friction dissipation source term. The wind energy input source term Qw is given by the Miles mechanism formula:

[0190]

[0191] where, is the exponential growth rate, given by:

[0192]

[0193] where, is the air density, taken as 1.29 kg / m3; is the water density, taken as 1025 kg / m3; is the friction velocity, in meters per second; is the phase speed, given by is the wave propagation direction; is the wind direction. The nonlinear wave-wave interaction source term Qnl is given by the discrete interaction approximation method:

[0194]

[0195] where, and are the energy gain and energy loss terms, respectively, and are calculated using the four-wave interaction model:

[0196]

[0197]

[0198] where, and are the coupling coefficients, taken as 0.25 and 0.75, respectively; is the gravitational acceleration, taken as 9.8 m / s2. The whitecapping dissipation source term Qd is given by the saturated spectrum theory:

[0199]

[0200] where, is the dissipation coefficient, taken as 0.0023; is the wave number, in radians per meter; ​​​​​​​is the water depth, in meters; is the Pierson-Moskowitz balance spectrum value, and the calculation formula is wherein ; is a nonlinear index, and the value is 2. The bottom friction dissipation source term uses an empirical formula:

[0201] ;

[0202] In the formula, is the bottom friction coefficient, and the value is 0.015. According to the solution results of the energy balance equation, the peak elevation factor is established as a function of the dimensionless parameter wave age :

[0203] ;

[0204] In the formula, is the wave age, is the gravitational acceleration, is the spectral peak period, is the wind speed at a height of 10 meters. For shallow water conditions, a relative water depth correction formula is introduced:

[0205] when ;

[0206] In the formula, is the spectral peak wave number, is the water depth, is the relative water depth parameter. This optimization step changes the determination of the peak elevation factor from purely statistical fitting to a parameterization method based on physical mechanisms, enhancing the adaptability of the model in complex sea conditions.

[0207] The specific implementation of the second optimization step is to establish a pre-trained sea wave spectrum parameter intelligent prediction network, namely the WaveSpecNet model, for steps S05 and S06, to improve the peak elevation factor prediction accuracy and calculation efficiency through multi-modal data fusion. The WaveSpecNet model is based on an encoder-decoder architecture design, and the input-output relationship of the model is represented as:

[0208] ;

[0209] In the formula, is the peak elevation factor output value; is the original frequency sea wave spectrum data; is the meteorological data, including wind speed, wind direction, air pressure and other parameters; For terrain data, including water depth, seafloor slope and other parameters. The encoder part adopts a multi-head self-attention mechanism to process multi-source spatio-temporal data, and the attention calculation formula is:

[0210]

[0211] In the formula, and are query matrix, key matrix and value matrix respectively, and the dimensions are and ; is the dimension of the key; and are the number of queries and keys respectively; is the dimension of the value. The multi-head attention mechanism is represented as:

[0212]

[0213] In the formula, ; and are the maximum value distribution characteristics of the peak elevation factor of the th attention mechanism, and the cumulative distribution function is:

[0214]

[0215] In the formula, is the location parameter; is the scale parameter; is the shape parameter. The three parameters are estimated by maximum likelihood method:

[0216]

[0217] In the formula, is the probability density function of the generalized extreme value distribution, and the calculation formula is:

[0218]

[0219] A spatio-temporal database of peak elevation factor parameters is constructed, and the database index structure adopts a quadtree method, which supports fast retrieval by geographical location and time. The process of constructing quadtree is to recursively divide the space into four sub-regions, and each leaf node corresponds to a grid cell and its peak elevation factor statistical characteristics. The quadtree node structure is:

[0220]

[0221] In the formula, ,​​​​​​​​​​ and are the longitude and latitude range of the node corresponding area respectively; is the list of child nodes, empty if it is a leaf node; is the peak enhancement factor statistical feature stored in the node, empty if it is a non-leaf node. The retrieval algorithm starts from the root node and accesses layer by layer downward according to the longitude and latitude of the query point until reaching a leaf node or finding the smallest area node containing the query point. Time retrieval is achieved by maintaining the peak enhancement factor statistical features of 12 months in each spatial node, supporting fast queries by month. A database update mechanism is established, and whenever there is new wave observation data, the peak enhancement factor statistical parameters of the corresponding grid cells are automatically updated. The update formula uses the exponential moving average method:

[0222] ;

[0223] where, and are the monthly average values after and before updating respectively; is the peak enhancement factor value of the new observation sample; is the smoothing coefficient, taking a value of 0.1. A database interface protocol is designed to support real-time query of peak enhancement factor parameters by the marine digital twin system, with an interface response time of no more than 100 milliseconds. The database interface includes three modes of spatial query, time query and comprehensive query, and the spatial query interface is:

[0224] ;

[0225] The time query interface is:

[0226] ;

[0227] The comprehensive query interface is:

[0228] ;

[0229] where, is the sea state working condition, including typhoon and non-typhoon types.

[0230] In another specific embodiment of the present application, the optimization steps for S02 and S05, S06 are considered and described in detail below.

[0231] The specific embodiment of the optimization step one is directed to the frequency wave spectrum fitting process in step S02, and the sea wave development energy balance equation is introduced for physical mechanism analysis to improve the fitting accuracy of the peak enhancement factor. First, a sea wave development energy balance equation model is established, which describes the evolution process and energy transfer mechanism of the frequency wave spectrum in space and time. The sea wave development energy balance equation is expressed as:

[0232] ;

[0233] wherein, is the energy density of the directional wave spectrum in square meter per second per radian; is time in seconds; is the spatial gradient operator; is the group velocity vector in meter per second; is the wind energy input source term; is the wave-wave nonlinear interaction source term; is the whitecapping dissipation source term; is the bottom friction dissipation source term. The wind energy input source term is calculated by the Miles mechanism formula:

[0234] ;

[0235] wherein, is the exponential growth rate, which is calculated by:

[0236] ;

[0237] wherein, is the air density, which is taken as 1.29 kg / m3; is the water density, which is taken as 1025 kg / m3; is the friction velocity in meter per second; is the phase velocity, which is calculated by ; is the wave propagation direction; is the wind direction. The wave-wave nonlinear interaction source term is calculated by the discrete interaction approximation method:

[0238] ;

[0239] wherein, and are the energy gain and energy loss terms, respectively, which are calculated by the four-wave interaction model:

[0240] ;

[0241] ;

[0242] wherein, and are the coupling coefficients, which are taken as 0.25 and 0.75, respectively; is the gravity acceleration, which is taken as 9.8 m / s2. The whitecapping dissipation source term is calculated by the saturation spectrum theory:

[0243] ;

[0244] wherein, is the dissipation coefficient, taking a value of 0.0023; is the wave number, with unit of radian per meter; is the water depth, with unit of meter; is the Pierson-Moskowitz equilibrium spectrum value, with calculation formula of wherein, ; is the nonlinear index, taking a value of 2. The bottom friction dissipation source term adopts an empirical formula:

[0245] ;

[0246] wherein, is the bottom friction coefficient, taking a value of 0.015. According to the solving result of the energy balance equation, the peak elevation factor is established as a function of the dimensionless parameter wave age :

[0247] ;

[0248] wherein, is the wave age, is the gravity acceleration, is the spectral peak period, is the wind speed at a height of 10 meters. For the shallow water condition, a relative water depth correction formula is introduced:

[0249] when ;

[0250] wherein, is the spectral peak wave number, is the water depth, is the relative water depth parameter. This optimization step makes the determination of the peak elevation factor change from pure statistical fitting to a parameterization method based on physical mechanism, enhancing the adaptability of the model in complex sea conditions.

[0251] The specific implementation of the second optimization step is to establish a pre-trained sea wave spectrum parameter intelligent prediction network, namely WaveSpecNet model, for steps S05 and S06, to improve the peak elevation factor prediction accuracy and calculation efficiency through multi-modal data fusion. The WaveSpecNet model is designed based on an encoder-decoder architecture, and the input-output relationship of the model is expressed as:

[0252] ;

[0253] wherein, is the peak elevation factor output value; is the original frequency sea wave spectrum data; Meteorological data, including wind speed, wind direction, air pressure, and other parameters; Topographic data, including water depth, seafloor slope, and other parameters. The encoder part uses a multi-head self-attention mechanism to process multi-source spatio-temporal data. The attention calculation formula is:

[0254]

[0255] In the formula, , and are the query matrix, key matrix, and value matrix, respectively, with dimensions , and ; is the dimension of the key; and are the number of queries and keys, respectively; is the dimension of the value. The multi-head attention mechanism is represented as:

[0256]

[0257] In the formula, ; , and are the mean values of the first attention; is the standard deviation; is the 95% confidence interval. For grid cells with insufficient sample sizes, a physically constrained Bayesian interpolation method is applied to supplement the data. The interpolation formula is: ; In the formula, is the interpolation result; is the mean value of the peak rise factor of the first adjacent grid cell; is the weight coefficient, and the calculation formula is: ; In the formula, is the grid distance; is the smoothing parameter, taking a value of 0.1; and are the wave ages of the adjacent grid and the target grid, respectively; is the attenuation coefficient, taking a value of 0.5. This step establishes a comprehensive correlation between the peak rise factor and the marine environmental parameters through the WaveSpecNet model combined with multi-dimensional classification methods, improving the accuracy of the sea wave spectrum parameters in complex sea conditions.

[0258] ​​For better understanding and implementation of the present application, the following provides an embodiment 2 of a specific application scenario of the present application: when researchers construct a marine digital twin system in a certain sea area, they apply the sea wave spectrum parameter calculation method of the present application to process the measured data. The buoy station in the sea area is often affected by typhoons, and it is of great significance to distinguish and study the characteristics of typhoon sea waves and non-typhoon sea waves. The researchers collected the sea wave data of the station from 2018 to 2022, a total of 36,792 hours of directional wave spectrum records. First, the original directional wave spectrum data is directionally integrated to obtain the frequency wave spectrum, and then the frequency wave spectrum with more than 25 frequency group fractions is resampled by the cubic spline interpolation method to ensure that the total energy difference before and after interpolation does not exceed 0.1 square meters per second.

[0259] The researchers select Jonswap frequency wave spectrum as the theoretical model, extract the significant wave height and the spectral peak period from the original frequency wave spectrum, and set the initial guess value of the peak elevation factor to 3.3 for preliminary fitting. The array search method is used to optimize the peak elevation factor, and by considering the three fitting criteria of spectral peak absolute error, zero-order spectral distance error and root mean square error, the optimal peak elevation factor value is determined. According to the tropical cyclone best track data set, the researchers identify the sea wave spectrum within 200 kilometers of the typhoon center as the typhoon sea wave spectrum, and statistically obtain the mean value of the peak elevation factor of each wave height period level under typhoon conditions, as shown in Table 1:

[0260] Table 1 Mean value of each level γ under typhoon conditions at the point

[0261]

[0262] In the above table, the values in the five columns of HS 1.5, 2.5, 13.5, 14.5 and 15.5 are all 0, which are omitted and not displayed in the table.

[0263] To evaluate the statistical stability of the peak elevation factor, the researchers also calculated the 95% confidence interval of the peak elevation factor value under different wave height period levels, as shown in Table 2:

[0264] Table 2 95% confidence interval range of γ value at each level under typhoon conditions at the point

[0265]

[0266] In the above table, the values in the five columns of HS 1.5, 2.5, 13.5, 14.5 and 15.5 are all 0, which are omitted and not displayed in the table.

[0267] The researchers found that the peak enhancement factor value under typhoon conditions showed a clear regular distribution through comparative analysis. To evaluate the reliability of the statistical results, the researchers further calculated the standard deviation and sample size of each level of gamma value, as shown in Tables 3 and 4, respectively:

[0268] Table 3 Standard deviation of each level of gamma value under typhoon conditions

[0269]

[0270] Table 4 Number of wave spectra of each level under typhoon conditions

[0271]

[0272] From the above data, it can be seen that the peak enhancement factor value under typhoon conditions is mostly distributed between 1.2 and 1.8, which is significantly lower than the commonly used value of 3.3 in the traditional Jonswap model, and shows a certain regularity with the effective wave height and period. The researchers selected a typhoon sea condition with an effective wave height of 4.5 meters and a spectral peak period of 9.5 seconds, and constructed a sea wave spectrum model using the traditional fixed peak enhancement factor value (γ = 3.3) and the optimized peak enhancement factor value (γ = 1.65) of the present invention, respectively, to generate sea wave surface simulation results (as shown in Figure 2 ) and compare them with the measured data, as shown in Table 5:

[0273] Table 5 Comparison of wave surface simulation accuracy under different peak enhancement factors in typhoon sea conditions

[0274]

[0275] The traditional marine digital twin method usually uses a fixed peak enhancement factor value (γ = 3.3) to construct a Jonswap frequency sea wave spectrum model, which cannot adapt to the special form of sea wave spectrum under different sea conditions, especially in typhoon conditions. The present invention establishes a correlation model between the peak enhancement factor and the effective wave height and spectral peak period by systematically analyzing the original frequency sea wave spectrum data, and optimizes the peak enhancement factor by distinguishing between typhoon and non-typhoon conditions (as shown in Figure 3 ). Compared with the traditional method, the present invention improves the spectral peak fitting accuracy by 77.4%, the wave surface correlation by 33.3%, the wave height prediction accuracy by 67.9%, and the maximum wave height prediction accuracy by 71.8% under typhoon sea conditions. The present invention is particularly suitable for digital twin simulation of extreme sea conditions such as typhoons, providing more reliable technical support for marine engineering safety design, offshore platform operation risk assessment, navigation safety warning, etc.

[0276] It should be noted that the variables involved in the present invention are explained in detail as shown in Tables 6, 7, 8, and 9.

[0277] Table 6 Variable explanation table (first part)

[0278]

[0279] Table 7 Variable explanation table (second part)

[0280]

[0281] Table 8 Variable explanation table (third part)

[0282]

[0283] Table 9 Variable explanation table (fourth part)

[0284]

[0285] The above description is merely a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for calculating wave spectrum parameters for ocean digital twins, characterized in that: include: S01. Obtain original wave spectrum data, perform directional integration on the directional wave spectrum to obtain a frequency wave spectrum, and perform frequency interpolation on the one-dimensional frequency wave spectrum with more than 25 frequency components to ensure that the total energy difference before and after the frequency interpolation is no more than 0.1 square meters per second; S02. Select the Jonswap frequency wave spectrum as the theoretical frequency wave spectrum, construct the frequency wave spectrum formula using the known significant wave height and spectrum peak period, and determine the peak rise factor as the parameter to be fitted; S03, establishing fitting criteria, including spectrum peak absolute error, zero-order spectrum distance error and spectrum value root mean square error; S04. Substitute the initial guess values ​​of significant wave height, spectrum peak period, and peak rise factor into the theoretical frequency wave spectrum formula, and perform preliminary fitting between the theoretical frequency wave spectrum and the original frequency wave spectrum; S05, solving the optimal fitting peak rise factor based on an array search method or a gradient descent method, and selecting the peak rise factor value that minimizes the fitting criterion error as the optimal fitting parameter of the wave spectrum; S06. Classify the wave data according to the significant wave height period level, calculate the mean value, standard deviation and 95% confidence interval of the peak rise factor value of each significant wave height period level, and create a scatter plot of the peak rise factor value; S07. Perform spatiotemporal matching of typhoon waves using the tropical cyclone best path dataset, identify the wave spectrum at points within 200 kilometers from the typhoon center during the typhoon as the typhoon wave spectrum, and distinguish the wave spectrum parameters corresponding to the typhoon wave spectrum and the non-typhoon wave spectrum. S08. Calculate the fitted frequency wave spectrum using the matched peak rise factor value, calculate the wave amplitude, wave number, and wave random phase based on the fitted frequency wave spectrum, and finally construct a wave surface height model to complete the wave digital twin simulation; S09. Generate a wave spectrum parameter database based on the fitted peak rise factor parameters under multiple spatiotemporal conditions, provide real-time peak rise factor parameter support for the ocean digital twin system, and achieve high-precision wave simulation.

2. The method according to claim 1, characterized in that The directional wave spectrum refers to the energy distribution of the wave spectrum at different frequencies and directions, and the frequency wave spectrum refers to the energy distribution of the wave spectrum at different frequencies.

3. The method according to claim 2, characterized in that The frequency components refer to discrete frequency points that describe the frequency wave spectrum.

4. The method according to claim 3, characterized in that In the step of establishing the fitting criterion, the fitting criterion includes the spectrum peak absolute error, the zero-order spectrum distance error and the spectrum value root mean square error; the spectrum peak absolute error refers to the absolute value of the spectrum peak difference between the fitting frequency wave spectrum and the original frequency wave spectrum.

5. The method according to claim 4, characterized in that The zero-order spectral distance error refers to the absolute value of the zero-order spectral distance difference between the fitted frequency wave spectrum and the original frequency wave spectrum; the spectral value root mean square error refers to the root mean square of the spectral value difference between the fitted frequency wave spectrum and the original frequency wave spectrum at all frequency points.

6. The method according to claim 5, characterized in that In the step of selecting the Jonswap frequency wave spectrum as the theoretical frequency wave spectrum, the wave development energy balance equation is also introduced to analyze the physical mechanism.

7. The method according to claim 6, characterized in that In the step of solving the optimal fitting peak rise factor, a pre-trained wave spectrum parameter intelligent prediction network WaveSpecNet model is also established.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores program instructions, and when the program instructions are run in a computer, they are used to execute the method for calculating wave spectrum parameters for ocean digital twins according to any one of claims 1 to 7.

9. A system for calculating wave spectrum parameters for ocean digital twins, characterized in that: The system comprises the computer-readable storage medium according to claim 8, wherein the system is any one of a computer, a server, and a single-chip microcomputer, the computer-readable storage medium is arranged in the system, and the system is provided with a microprocessor for executing program instructions stored in the computer-readable storage medium.

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