Wind wave relationship analysis method and system based on a lag response model

Abstract

The application provides a wind wave relationship analysis method and system based on a lag response model, relates to the field of marine weather forecasting, and comprises grouping historical wind wave data according to wind direction and wind speed intervals, calculating the lag duration of each group, and establishing a regression equation to construct multiple lag response models. When forecasting, the wave height forecast value is calculated after the lag translation according to the forecast wind speed matching model. The method improves the accuracy of wave height forecasting by precisely modeling the wind wave lag response relationship.

Description

Technical Field

[0001] This invention relates to marine meteorological forecasting technology, and more particularly to a method and system for analyzing wind-wave relationships based on a hysteresis response model. Background Technology

[0002] Accurate analysis of wind-wave relationships is crucial in fields such as marine engineering, weather forecasting, and maritime safety. Wind is the primary driving force behind wave generation, and a significant statistical correlation exists between wind speed and wave height. However, because it takes time for wind energy to travel to the sea surface and form waves, there is a time lag between wind speed changes and wave height responses. Therefore, establishing wind-wave forecasting models that can characterize this lag relationship is of practical significance for improving the accuracy of wave forecasts.

[0003] The conventional approach to analyzing wind-wave relationships and constructing forecasting models is typically based on statistical analysis of historical observation data. A widely adopted method is to establish a direct empirical regression relationship between wind speed and wave height, for example, by fitting a formula in the form of a power function. This method is relatively simple to operate, but it neglects the significant impact of wind direction on wave propagation and growth, and does not consider the differences in wind-wave response mechanisms under different wind speed conditions. A more refined approach involves introducing the concept of time lag. By calculating the correlation coefficient between wind speed and wave height sequences at different time offsets, a global or wind-direction-specific average lag time can be determined. This allows for time-shifting of the wind speed data before building a regression model.

[0004] These existing conventional methods have significant shortcomings. The main problem lies in their oversimplification of the wind-wave relationship, failing to fully consider its dynamic and conditionally dependent nature. Specifically, the wind-wave response lag time is not fixed; it is complexly influenced by various factors such as wind direction, wind speed, sea topography, and initial sea state. Existing methods, whether using a fixed lag time or calculating a single lag value based on all wind direction data, struggle to accurately reflect this spatiotemporal variation. This leads to significantly increased forecast errors when applying models for wave height forecasting, especially when wind direction is variable or wind speed ranges are wide, resulting in insufficient model adaptability and robustness. Another shortcoming is the insufficient resolution and specificity of the models. Conventional methods often establish single regression relationships under global or coarse-grained conditions, failing to perform hierarchical modeling for different wind speed levels. In reality, under low, medium, and high wind speeds, the wind-wave growth mechanism differs from the saturation state, and the statistical relationships between them exhibit nonlinear differences. Using a uniform model format can smooth out these key features, thereby affecting the accuracy of forecasts in specific wind speed ranges, especially under extreme wind conditions. Summary of the Invention

[0005] This invention provides a method and system for analyzing wind-wave relationships based on a hysteresis response model, which can solve the problems in the prior art.

[0006] A first aspect of this invention provides a method for analyzing wind-wave relationships based on a hysteresis response model, comprising: Based on wind direction, historical wind speed data and historical wave height data are divided into multiple wind direction group datasets. For each wind direction group dataset, the correlation coefficient between historical wind speed data and historical wave height data at different time offsets is calculated, and the time offset corresponding to the maximum correlation coefficient is taken as the lag time. Multiple wind speed ranges are set, and the historical wind speed data and historical wave height data in each wind direction group dataset are divided into multiple wind speed hierarchical datasets according to the wind speed range. For each wind speed stratified dataset, the historical wind speed data is shifted according to the corresponding lag duration to obtain the effective wind speed data. A regression equation is established based on the effective wind speed data and historical wave height data. The lag duration, wind speed range and regression equation are combined to form a lag response model, resulting in multiple lag response models. Obtain forecast wind speed data, match the corresponding lag response model based on the forecast wind speed data, shift the forecast wind speed data according to the lag time in the matched lag response model to obtain the forecast effective wind speed data, and substitute the forecast effective wind speed data into the matched lag response model to calculate the wave height forecast value.

[0007] Based on wind direction, historical wind speed and wave height data are divided into multiple wind direction group datasets. For each wind direction group dataset, the correlation coefficient between historical wind speed and historical wave height data at different time offsets is calculated. The time offset corresponding to the maximum correlation coefficient is taken as the lag duration. Obtain the prevailing wind direction distribution information of the sea area, determine the wind direction division angle corresponding to each wind direction based on the prevailing wind direction distribution information of the sea area, divide the wind direction range into multiple wind direction intervals based on the wind direction division angles, and classify historical wind speed data and historical wave height data into the corresponding wind direction grouping datasets based on the wind direction intervals to obtain multiple wind direction grouping datasets. Obtain the data time span of each wind direction group dataset, set the time offset search range based on the data time span, and generate multiple candidate time offsets within the time offset search range; The historical wind speed data in the wind direction grouping dataset is shifted according to each candidate time offset to obtain the shifted wind speed data. The correlation coefficient between the shifted wind speed data and the historical wave height data in the wind direction grouping dataset is calculated to obtain multiple correlation coefficients corresponding to multiple candidate time offsets. A correlation coefficient curve is constructed by combining multiple candidate time offsets with multiple correlation coefficients. The correlation coefficient curve is then smoothed to obtain a smoothed correlation coefficient curve. The maximum correlation coefficient is identified from the smoothed correlation coefficient curve, and the time offset corresponding to the maximum correlation coefficient is taken as the lag duration.

[0008] Multiple wind speed ranges are defined, and the historical wind speed data and historical wave height data in each wind direction group dataset are divided into multiple hierarchical wind speed datasets based on the wind speed ranges, including: For each wind direction group dataset, obtain the wind speed value distribution of historical wind speed data in the wind direction group dataset, calculate multiple quantile values ​​based on the wind speed value distribution, use the multiple quantile values ​​as the boundary for dividing the wind speed interval, and set multiple wind speed intervals based on the boundary for dividing the wind speed interval. Iterate through each historical wind speed data point in the wind direction grouping dataset, extract the wind speed value and data time, determine the wind speed interval to which the wind speed value belongs, extract the corresponding wave height value from the historical wave height data based on the data time, and classify the wind speed value and wave height value into the wind speed stratified dataset corresponding to the wind speed interval to obtain multiple wind speed stratified datasets.

[0009] For each stratified wind speed dataset, historical wind speed data is shifted according to the corresponding lag duration to obtain effective wind speed data. A regression equation is established based on the effective wind speed data and historical wave height data. The lag duration, wind speed range, and regression equation are combined to form a lag response model, resulting in multiple lag response models, including: For each wind speed stratified dataset, the timestamps of the historical wind speed data in the wind speed stratified dataset are shifted backward according to the lag time. The historical wind speed data and historical wave height data are then rematched based on the shifted timestamps to obtain the effective wind speed data. Linear fitting is performed on the effective wind speed data and historical wave height data to obtain an initial fitted line. The residual value of each data point of the effective wind speed data and the initial fitted line is calculated. The residual threshold is calculated based on the sample correlation coefficient between the effective wind speed data and the historical wave height data. Data points with residual values ​​exceeding the residual threshold are removed to obtain the filtered effective wind speed data and historical wave height data. The selected effective wind speed data and historical wave height data are curve fitted to obtain the fitted curve. The rate of change of curvature of the fitted curve is calculated, and the regression equation type is selected from the preset regression equation type library according to the rate of change of curvature. Identify the location of the parameter to be determined in the regression equation type, substitute the filtered effective wind speed data as the independent variable and the corresponding historical wave height data as the dependent variable into the regression equation type to establish the target equation system, solve the target equation system to obtain the parameter value, and substitute the parameter value into the location of the parameter to be determined to obtain the regression equation. Wind speed intervals corresponding to the stratified wind speed datasets are extracted, and lag duration, wind speed intervals, and regression equations are combined to form lag response models, resulting in multiple lag response models.

[0010] An initial fitted line is obtained by linearly fitting the effective wind speed data and historical wave height data. The residual values ​​of each data point of the effective wind speed data and the initial fitted line are calculated, including: Calculate the distribution dispersion of effective wind speed data and historical wave height data, determine the sampling adjustment coefficient based on the distribution dispersion, and adjust the sampling density of effective wind speed data and historical wave height data based on the sampling adjustment coefficient to obtain the sampled and adjusted effective wind speed data and sampled and adjusted historical wave height data. A linear fitting operation is performed on the sampled and adjusted effective wind speed data and the sampled and adjusted historical wave height data. The parameters of the fitted line are determined by minimizing the sum of squared vertical distances between the sampled and adjusted effective wind speed data and the sampled and adjusted historical wave height data. An initial fitted line is established based on the fitted line parameters. Substitute the sampled and adjusted effective wind speed data into the initial fitted line to calculate the fitted wave height value. Calculate the absolute value of the difference between the sampled and adjusted historical wave height data and the fitted wave height value to obtain the residual value between each data point of the effective wind speed data and the initial fitted line.

[0011] Obtain forecast wind speed data, match the corresponding lag response model based on the forecast wind speed data, shift the forecast wind speed data according to the lag duration in the matched lag response model to obtain the effective forecast wind speed data, and substitute the effective forecast wind speed data into the matched lag response model to calculate the wave height forecast value, including: Obtain forecast wind speed data, extract wind direction information and wind speed value from the forecast wind speed data, determine the wind direction interval to which the forecast wind speed data belongs based on the wind direction information, determine the wind speed interval to which the forecast wind speed data belongs based on the wind speed value, and retrieve the matching hysteresis response model from multiple hysteresis response models based on the wind direction interval and wind speed interval. Extract the regression equation type identifier from the matched hysteresis response model, set the applicable boundary conditions for the forecast wind speed data based on the regression equation type identifier, verify the applicable boundary conditions for the forecast wind speed data, and obtain the verified forecast wind speed data. Extract the lag duration from the matched lag response model, shift the forecast timestamp of the verified forecast wind speed data backward according to the lag duration, and convert the verified forecast wind speed data into valid forecast wind speed data based on the shifted forecast timestamp. The regression equation is extracted from the matched hysteresis response model, and the predicted effective wind speed data is substituted into the regression equation to calculate the wave height forecast value.

[0012] The regression equation type identifier is extracted from the matched hysteresis response model. Based on the regression equation type identifier, applicable boundary conditions for the forecast wind speed data are set. The applicable boundary conditions are then validated on the forecast wind speed data, resulting in validated forecast wind speed data including: Extract the regression equation type identifier and regression equation parameters from the matched hysteresis response model, determine the domain characteristics of the regression equation based on the regression equation type identifier, calculate the effective input interval of the regression equation based on the domain characteristics and regression equation parameters, and set the effective input interval as the applicable boundary conditions for the forecast wind speed data. The fault tolerance range is calculated based on the applicable boundary conditions. The extended boundary conditions are obtained by superimposing the applicable boundary conditions and the fault tolerance range. A hierarchical verification rule is established based on the applicable boundary conditions and the extended boundary conditions. Obtain the wind speed values ​​from the forecast wind speed data, determine the positional relationship between the wind speed values ​​and the applicable boundary conditions and extended boundary conditions according to the graded verification rules, and obtain the positional relationship judgment result. Based on the location relationship, when the wind speed value is within the applicable boundary conditions, the forecast wind speed data is retained; when the wind speed value is within the extended boundary conditions but exceeds the applicable boundary conditions, the wind speed value is corrected to the boundary value of the applicable boundary conditions; when the wind speed value exceeds the extended boundary conditions, the forecast wind speed data is discarded, and the verified forecast wind speed data is obtained.

[0013] A second aspect of the present invention provides a wind-wave relationship analysis system based on a hysteresis response model, comprising: The wind direction grouping unit is used to divide historical wind speed data and historical wave height data into multiple wind direction grouping datasets according to wind direction. For each wind direction grouping dataset, the correlation coefficient between historical wind speed data and historical wave height data at different time offsets is calculated, and the time offset corresponding to the maximum correlation coefficient is used as the lag time. The wind speed stratification unit is used to set multiple wind speed intervals and divide the historical wind speed data and historical wave height data in each wind direction group dataset into multiple wind speed stratification datasets according to the wind speed intervals. The model building unit is used to shift the historical wind speed data according to the corresponding lag duration for each wind speed stratified dataset to obtain effective wind speed data. Based on the effective wind speed data and historical wave height data, a regression equation is established. The lag duration, wind speed range and regression equation are combined to form a lag response model, resulting in multiple lag response models. The forecast calculation unit is used to acquire forecast wind speed data, match the corresponding lag response model according to the forecast wind speed data, shift the forecast wind speed data according to the lag time in the matched lag response model to obtain the forecast effective wind speed data, and substitute the forecast effective wind speed data into the matched lag response model to calculate the wave height forecast value.

[0014] A third aspect of the present invention provides an electronic device, comprising: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0015] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0016] In this embodiment, by considering the modulating effect of wind direction on the wind-wave relationship, historical data is grouped by wind direction, effectively distinguishing the differences in the physical mechanisms between wind speed and wave height under different wind directions. This avoids the problem of insufficient adaptability of a single model under different wind directions, making model construction more targeted. For each wind direction group, by calculating the correlation coefficient at different time offsets and determining the lag time corresponding to the maximum correlation coefficient, the physical delay process of wind speed change being transmitted to wave height response is accurately captured, solving the instantaneous relationship modeling error caused by ignoring the lag effect in traditional methods. This avoids the defect of insufficient fitting of a single regression equation across the entire wind speed range, making the established regression equation more consistent with actual physical laws within its respective wind speed range. In practical forecasting applications, this method can automatically match the best-fitting lag response model based on the forecast wind speed and perform corresponding wind speed time shifts and wave height calculations, thereby more realistically reconstructing the dynamic process from wind field to wave field in terms of mechanism. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the wind-wave relationship analysis method based on the hysteresis response model according to an embodiment of the present invention. Figure 2 This is a flowchart illustrating the construction process of a hysteresis response model based on data filtering and dynamic model selection in an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] The technical solution of the present invention will be described in detail below with reference to specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0020] Figure 1 This is a flowchart illustrating the wind-wave relationship analysis method based on a hysteresis response model according to an embodiment of the present invention. Figure 1 As shown, the method includes: Based on wind direction, historical wind speed data and historical wave height data are divided into multiple wind direction group datasets. For each wind direction group dataset, the correlation coefficient between historical wind speed data and historical wave height data at different time offsets is calculated, and the time offset corresponding to the maximum correlation coefficient is taken as the lag time. Multiple wind speed ranges are set, and the historical wind speed data and historical wave height data in each wind direction group dataset are divided into multiple wind speed hierarchical datasets according to the wind speed range. For each wind speed stratified dataset, the historical wind speed data is shifted according to the corresponding lag duration to obtain the effective wind speed data. A regression equation is established based on the effective wind speed data and historical wave height data. The lag duration, wind speed range and regression equation are combined to form a lag response model, resulting in multiple lag response models. Obtain forecast wind speed data, match the corresponding lag response model based on the forecast wind speed data, shift the forecast wind speed data according to the lag time in the matched lag response model to obtain the forecast effective wind speed data, and substitute the forecast effective wind speed data into the matched lag response model to calculate the wave height forecast value.

[0021] Based on wind direction, historical wind speed and wave height data are divided into multiple wind direction group datasets. For each wind direction group dataset, the correlation coefficient between historical wind speed and historical wave height data at different time offsets is calculated. The time offset corresponding to the maximum correlation coefficient is taken as the lag duration. Obtain the prevailing wind direction distribution information of the sea area, determine the wind direction division angle corresponding to each wind direction based on the prevailing wind direction distribution information of the sea area, divide the wind direction range into multiple wind direction intervals based on the wind direction division angles, and classify historical wind speed data and historical wave height data into the corresponding wind direction grouping datasets based on the wind direction intervals to obtain multiple wind direction grouping datasets. Obtain the data time span of each wind direction group dataset, set the time offset search range based on the data time span, and generate multiple candidate time offsets within the time offset search range; The historical wind speed data in the wind direction grouping dataset is shifted according to each candidate time offset to obtain the shifted wind speed data. The correlation coefficient between the shifted wind speed data and the historical wave height data in the wind direction grouping dataset is calculated to obtain multiple correlation coefficients corresponding to multiple candidate time offsets. A correlation coefficient curve is constructed by combining multiple candidate time offsets with multiple correlation coefficients. The correlation coefficient curve is then smoothed to obtain a smoothed correlation coefficient curve. The maximum correlation coefficient is identified from the smoothed correlation coefficient curve, and the time offset corresponding to the maximum correlation coefficient is taken as the lag duration.

[0022] After acquiring historical wind speed and wave height data, the precision of wind direction classification is determined by analyzing the prevailing wind direction distribution information in the sea area. This information includes the frequency of wind directions in different directions and their contribution to wave generation. When a wind direction occurs frequently and has a significant impact on wave height, a smaller wind direction classification angle is set for that direction, such as 15 degrees or 22.5 degrees, to capture subtle changes in the wind-wave relationship under that wind direction. For wind directions that occur less frequently or have a weaker impact, a larger wind direction classification angle, such as 45 degrees, can be set. Using this adaptive classification strategy, the 360-degree wind direction range is divided into 8, 12, or 16 wind direction intervals. Each historical wind speed and wave height data point includes a timestamp and wind direction information. Based on the wind direction value in the data, the wind direction interval to which it belongs is determined. Wind speed and wave height data within the same wind direction interval are then grouped to form corresponding wind direction group datasets.

[0023] For each wind direction group dataset, its data time span is calculated, which is the time difference between the earliest and latest timestamps in the dataset. Ocean waves respond to wind with a physical lag, typically ranging from minutes to hours. A time offset search range is set based on the data time span, with the lower limit usually set to 0 hours and the upper limit determined according to the sea area characteristics and the data time span, generally set to 6 to 24 hours. Within the search range, candidate time offsets are generated at fixed time intervals, which can be set to 10 minutes, 30 minutes, or 1 hour, generating a candidate time offset sequence.

[0024] The historical wind speed data in the wind direction grouping dataset is time-shifted according to each candidate time offset. Specifically, the timestamp of the wind speed data is shifted forward by the corresponding candidate time offset value, causing a displacement of the wind speed data on the time axis. After shifting, the shifted wind speed data is paired with the original historical wave height data at the same timestamp, and the Pearson correlation coefficient between the two is calculated. The correlation coefficient r is calculated using the following formula: , where x i For the translated wind speed data, y i The data consists of historical wave heights. All candidate time offsets are iterated through to obtain a one-to-one correlation coefficient sequence.

[0025] A correlation coefficient curve is constructed with the candidate time offsets on the horizontal axis and the correlation coefficients on the vertical axis. Due to noise interference in the measured data, the original correlation coefficient curve may exhibit local fluctuations. The correlation coefficient curve is smoothed using a moving average method or Gaussian smoothing filter. The filter window width is determined based on the density of the candidate time offsets, typically taking 3 to 5 data points. After smoothing, a smoothed correlation coefficient curve is obtained, with a clearer trend. The point with the largest correlation coefficient value is identified in the smoothed correlation coefficient curve; the time offset corresponding to this point is the lag time for that wind direction group dataset. The lag time reflects the time delay characteristic from wind speed change to wave height response under that wind direction condition, providing a time registration benchmark for subsequent regression equation establishment.

[0026] Multiple wind speed ranges are defined, and the historical wind speed data and historical wave height data in each wind direction group dataset are divided into multiple hierarchical wind speed datasets based on the wind speed ranges, including: For each wind direction group dataset, obtain the wind speed value distribution of historical wind speed data in the wind direction group dataset, calculate multiple quantile values ​​based on the wind speed value distribution, use the multiple quantile values ​​as the boundary for dividing the wind speed interval, and set multiple wind speed intervals based on the boundary for dividing the wind speed interval. Iterate through each historical wind speed data point in the wind direction grouping dataset, extract the wind speed value and data time, determine the wind speed interval to which the wind speed value belongs, extract the corresponding wave height value from the historical wave height data based on the data time, and classify the wind speed value and wave height value into the wind speed stratified dataset corresponding to the wind speed interval to obtain multiple wind speed stratified datasets.

[0027] In practice, the first step is to obtain historical wind speed and wave height data for the target sea area. Historical wind speed data includes wind direction, wind speed value, and data time; historical wave height data includes wave height value and data time. This data can be obtained through ocean buoys, radar observation stations, or satellite remote sensing.

[0028] After acquiring the data, the historical wind speed data is first grouped according to wind direction. Wind direction can be divided according to the traditional eight directions (east, west, south, north, northeast, southeast, northwest, southwest) or sixteen directions. For example, for the eight-direction division, wind directions from 0° to 45° can be classified as northeast winds, wind directions from 45° to 90° as east winds, and so on. In this way, the historical wind speed data is divided into multiple wind direction group datasets.

[0029] Taking a year's observation data of a certain sea area as an example, assuming an eight-directional division, the wind speed data of this sea area is divided into eight wind direction groups: northeast, east, southeast, south, southwest, west, northwest, and north. Among them, there are 3650 data entries for the east wind direction, which include information such as wind speed value, wind direction angle, and observation time.

[0030] For each wind direction group dataset, it is necessary to analyze the distribution characteristics of wind speed values ​​under that wind direction in order to reasonably define wind speed intervals. Here, the quantile method is used to divide the wind speed intervals. First, the probability distribution of the wind speed data is calculated, and then multiple quantiles are determined as the boundaries for dividing the wind speed intervals.

[0031] The quantile calculation method is as follows: Arrange all wind speed values ​​in the wind direction grouping dataset in ascending order. Let the total data volume be n. To calculate the p-quantile (0≤p≤1), the position corresponding to this quantile is n×p. If n×p is not an integer, take the value of the nearest integer position; if n×p is an integer, take the average of the values ​​at that position and the next position.

[0032] Taking easterly wind speed data as an example, assuming there are 3650 records with wind speeds ranging from 0.5 m / s to 15.3 m / s. To divide the wind speed into intervals, we can calculate the values ​​of five quantile points: 0.1, 0.3, 0.5, 0.7, and 0.9. The calculated quantile points are 2.3 m / s, 4.6 m / s, 6.8 m / s, 9.1 m / s, and 12.5 m / s. Based on these quantile points, we can divide the wind speed into six intervals: [0, 2.3), [2.3, 4.6), [4.6, 6.8), [6.8, 9.1), [9.1, 12.5), and [12.5, ∞).

[0033] After completing the wind speed interval division, it is necessary to traverse each historical wind speed data in the wind direction grouping dataset, determine the wind speed interval to which it belongs, and assign the corresponding wind speed value and the wave height value at the corresponding time to the corresponding wind speed stratification dataset.

[0034] The specific operation process is as follows: For each wind speed record in the wind direction grouping dataset, extract its wind speed value and data time. Determine which wind speed interval the wind speed value belongs to; for example, a wind speed value of 5.7 m / s belongs to the interval [4.6, 6.8). Then, based on the timestamp of the wind speed record, find the corresponding wave height value from the historical wave height data. It should be noted that because wind and waves have a delayed response, a certain time delay can be added to the wind speed record time before searching for the wave height value. For example, if the wind and wave delayed response time is 2 hours, then the wave height value should be searched for 2 hours after the wind speed record time.

[0035] Paired wind speed and wave height values ​​are assigned to hierarchical datasets corresponding to the wind speed intervals. After traversing all data, multiple hierarchical wind speed datasets corresponding to the wind speed intervals are obtained.

[0036] Continuing with the example of easterly winds, let's assume that by traversing the data, we obtain stratified wind speed datasets corresponding to six wind speed intervals. The stratified wind speed dataset for the interval [4.6, 6.8) contains 730 data sets, each containing a wind speed value and a corresponding wave height value. For example, in a certain record, the wind speed value is 5.7 m / s, and the corresponding wave height value is 1.2 m.

[0037] For each generated wind speed stratified dataset, statistical characteristics such as mean wind speed, mean wave height, standard deviation, and correlation coefficient can be further calculated to analyze the wind-wave relationship characteristics in different wind speed ranges. For example, for the wind speed stratified dataset in the range [4.6, 6.8), the calculated mean wind speed is 5.5 m / s, the mean wave height is 1.1 m, and the correlation coefficient between wind speed and wave height is 0.75.

[0038] This method allows for detailed analysis of wind-wave relationships under different wind directions and speed ranges, providing data support for marine environmental research, shipping safety, and offshore engineering. Furthermore, by considering the hysteresis response characteristics of wind and waves, this analytical method can more accurately reflect the dynamic relationship between wind speed and wave height.

[0039] like Figure 2 The diagram shows the flowchart for constructing a hysteresis response model based on data filtering and dynamic model selection in this embodiment.

[0040] For each stratified wind speed dataset, historical wind speed data is shifted according to the corresponding lag duration to obtain effective wind speed data. A regression equation is established based on the effective wind speed data and historical wave height data. The lag duration, wind speed range, and regression equation are combined to form a lag response model, resulting in multiple lag response models, including: For each wind speed stratified dataset, the timestamps of the historical wind speed data in the wind speed stratified dataset are shifted backward according to the lag time. The historical wind speed data and historical wave height data are then rematched based on the shifted timestamps to obtain the effective wind speed data. Linear fitting is performed on the effective wind speed data and historical wave height data to obtain an initial fitted line. The residual value of each data point of the effective wind speed data and the initial fitted line is calculated. The residual threshold is calculated based on the sample correlation coefficient between the effective wind speed data and the historical wave height data. Data points with residual values ​​exceeding the residual threshold are removed to obtain the filtered effective wind speed data and historical wave height data. The selected effective wind speed data and historical wave height data are curve fitted to obtain the fitted curve. The rate of change of curvature of the fitted curve is calculated, and the regression equation type is selected from the preset regression equation type library according to the rate of change of curvature. Identify the location of the parameter to be determined in the regression equation type, substitute the filtered effective wind speed data as the independent variable and the corresponding historical wave height data as the dependent variable into the regression equation type to establish the target equation system, solve the target equation system to obtain the parameter value, and substitute the parameter value into the location of the parameter to be determined to obtain the regression equation. Wind speed intervals corresponding to the stratified wind speed datasets are extracted, and lag duration, wind speed intervals, and regression equations are combined to form lag response models, resulting in multiple lag response models.

[0041] For each wind speed stratified dataset, a time shift operation needs to be performed to account for the lag response characteristics of wind and waves. The timestamps of historical wind speed data in the wind speed stratified dataset are shifted backward according to the lag duration corresponding to the wind direction group, achieving time alignment between wind speed and wave height data. For example, if the lag duration for an easterly wind in a certain sea area is 3 hours, the timestamp of the wind speed record at 10:00 on May 10, 2022 in the wind speed stratified dataset will be shifted backward by 3 hours, adjusted to 13:00 on May 10, 2022. Based on the shifted timestamp, the wave height value at the matching time is searched from the historical wave height data, forming a pairing set of valid wind speed data and historical wave height data. For the wind speed stratified dataset in the northeast wind [4.6, 6.8) m / s wind speed range, containing 650 original records, after time shift matching, 620 sets of valid paired data are obtained.

[0042] After obtaining valid paired data, preliminary fitting and outlier removal are performed. Linear fitting is performed between the valid wind speed data and historical wave height data to obtain an initial fitted line of the form H = a × V + b, where H represents wave height, V represents wind speed, and a and b are fitting parameters. For the northeast wind [4.6, 6.8) m / s wind speed range, the initial fitting yields a fitted line of H = 0.21 × V + 0.05. The difference between the actual wave height and the predicted wave height of the fitted line for each data point is calculated, i.e., the residual value. A residual threshold is calculated based on the data characteristics, set to 2.5 times the standard deviation. Here, the standard deviation refers to the standard deviation of the residuals across all data points. Taking the northeast wind [4.6, 6.8) m / s wind speed range as an example, the residual standard deviation is 0.092 m, and the calculated residual threshold is 0.23 m. Data points with residual values ​​exceeding the threshold are removed, resulting in a filtered valid dataset. For the northeast wind speed range of [4.6, 6.8) m / s, 42 out of 620 data sets had residuals exceeding the threshold. After removing these, 578 valid data sets were retained.

[0043] Curve fitting was performed on the selected valid data to determine the most suitable type of regression equation. Cubic spline interpolation was used to initially fit the data points, resulting in a fitted curve. The curvature of the fitted curve at different wind speeds was calculated, and the rate of change of curvature was analyzed. The curvature calculation formula is k = |f''(x)| / (1 + f'(x)). 2 )(3 / 2) , where f'(x) and f''(x) are the first and second derivatives of the curve at x, respectively. The rate of change of curvature is defined as the percentage change in curvature between adjacent wind speed points. For northeasterly winds in the range of [4.6, 6.8) m / s, the average rate of change of curvature is calculated to be 8.5% within the range of wind speed from 4.6 m / s to 6.8 m / s.

[0044] Select an appropriate regression equation type from a pre-defined regression equation type library based on the rate of change of curvature. The regression equation type library includes linear equations H=a×V+b and quadratic equations H=a×V. 2 +b×V+c, power function equation H=a×V b The exponential equation H = a × e (b×V) When the average rate of change of curvature is less than 5%, a linear equation is chosen; when the average rate of change of curvature is between 5% and 15% and shows a monotonically increasing trend, a quadratic equation is chosen; when the average rate of change of curvature is between 5% and 15% and shows a non-monotonic change, a power function equation is chosen; when the average rate of change of curvature is greater than 15%, an exponential equation is chosen. For the northeast wind [4.6, 6.8) m / s wind speed range, the average rate of change of curvature is 8.5% and shows a monotonically increasing trend, so the quadratic equation H=a×V is chosen. 2 +b×V+c is used as the regression equation type.

[0045] After determining the type of regression equation, the location of the parameters to be solved in the equation is identified and the parameters are solved. The selected effective wind speed data is used as the independent variable, and the corresponding historical wave height data is used as the dependent variable. These are substituted into the regression equation type to establish a system of equations. The least squares method is used to solve for the parameter values ​​in the system of equations. For the northeast wind [4.6, 6.8) m / s wind speed range, the quadratic equation H = a × V is selected. 2 The regression equation, H = 0.03 × V + c, is obtained using the least squares method, yielding parameter values ​​a = 0.03, b = 0.12, and c = -0.15. 2 +0.12×V-0.15. The coefficient of determination R² is used to assess the quality of fit of the regression equation. 2 A value of 0.86 indicates a good fit.

[0046] When forming the lag response model, wind direction and wind speed range information corresponding to the stratified wind speed dataset are extracted and combined with the lag duration and regression equation. Taking the northeast wind [4.6, 6.8) m / s wind speed range as an example, the corresponding lag duration is 3 hours, and the regression equation is H=0.03×V 2 +0.12×V-0.15, combined to form a hysteresis response model: {Wind direction: Northeast, Wind speed range: [4.6, 6.8) m / s, Lag time: 3 hours, Regression equation: H=0.03×V}2 +0.12×V-0.15}. Following the same method, corresponding hysteresis response models are established for each wind speed range under each wind direction, ultimately forming a set of hysteresis response models covering multiple wind directions and wind speed conditions.

[0047] In this embodiment, differentiated regression equations are established based on different wind directions and speeds, enabling a more accurate description of the nonlinear relationship between wind speed and wave height. Outlier identification and removal techniques improve the model's robustness and reliability. Curvature change rate analysis is used to determine the optimal regression equation type, enhancing the model's adaptability. An automatic solution and evaluation mechanism for model parameters ensures the scientific validity of the prediction results.

[0048] An initial fitted line is obtained by linearly fitting the effective wind speed data and historical wave height data. The residual values ​​of each data point of the effective wind speed data and the initial fitted line are calculated, including: Calculate the distribution dispersion of effective wind speed data and historical wave height data, determine the sampling adjustment coefficient based on the distribution dispersion, and adjust the sampling density of effective wind speed data and historical wave height data based on the sampling adjustment coefficient to obtain the sampled and adjusted effective wind speed data and sampled and adjusted historical wave height data. A linear fitting operation is performed on the sampled and adjusted effective wind speed data and the sampled and adjusted historical wave height data. The parameters of the fitted line are determined by minimizing the sum of squared vertical distances between the sampled and adjusted effective wind speed data and the sampled and adjusted historical wave height data. An initial fitted line is established based on the fitted line parameters. Substitute the sampled and adjusted effective wind speed data into the initial fitted line to calculate the fitted wave height value. Calculate the absolute value of the difference between the sampled and adjusted historical wave height data and the fitted wave height value to obtain the residual value between each data point of the effective wind speed data and the initial fitted line.

[0049] After obtaining valid wind speed data for a specific stratified wind speed dataset, it is necessary to establish a regression equation between this dataset and the corresponding historical wave height data. Since the sampling density of the original data may vary across different wind speed ranges, direct fitting could lead to densely populated areas having an excessive impact on the regression results. Therefore, a sampling density adjustment method based on distribution dispersion is introduced.

[0050] Before establishing regression equations for effective wind speed data and historical wave height data, it is necessary to calculate the data distribution dispersion for sampling adjustment. Distribution dispersion reflects the uniformity of data distribution within the wind speed range, and is quantified by calculating the coefficient of variation of the number of data points under different wind speed values. Taking the northeast wind direction [5.0, 7.5) m / s wind speed range as an example, the wind speed range is divided into 5 sub-intervals: [5.0, 5.5), [5.5, 6.0), [6.0, 6.5), [6.5, 7.0), and [7.0, 7.5) m / s. The number of data points in each sub-interval is 68, 125, 210, 98, and 43, respectively. The calculated average number of data points is 108.8, the standard deviation is 64.7, and the coefficient of variation is 0.59. The larger the coefficient of variation, the more uneven the data distribution, and the greater the necessity for sampling adjustment.

[0051] The sampling adjustment coefficient is determined based on the calculated distribution dispersion. The sampling adjustment coefficient is directly proportional to the distribution dispersion, and its calculation formula is: Sampling adjustment coefficient = Basic adjustment factor × (1 + Coefficient of variation), where the basic adjustment factor is set to 0.5. For the northeast wind direction [5.0, 7.5) m / s wind speed range, the calculated sampling adjustment coefficient is 0.5 × (1 + 0.59) = 0.795. The sampling adjustment coefficient is used to balance the influence weights of data within different sub-intervals, ensuring that the data for each wind speed segment has relatively balanced representativeness during the fitting process.

[0052] The density of effective wind speed data is adjusted based on a sampling adjustment factor. For sub-intervals with more data points than the average, downsampling is performed proportionally; for sub-intervals with fewer data points than the average, all data points are retained. The downsampling ratio is calculated as: Retention Ratio = Average / (Number of Data Points in Current Sub-interval × Sampling Adjustment Factor). For the sub-interval [6.0, 6.5) m / s, the number of data points is 210, and the retention ratio is calculated as 108.8 / (210 × 0.795) = 0.65, meaning that approximately 210 × 0.65 ≈ 137 data points are randomly selected from this sub-interval and retained. For the sub-intervals [5.0, 5.5), [6.5, 7.0), and [7.0, 7.5) m / s, the number of data points are 68, 98, and 43 respectively, all lower than the average of 108.8, therefore all data points are retained. For the sub-interval [5.5, 6.0) m / s, the number of data points is 125, slightly higher than the average. The retention ratio is calculated to be 108.8 / (125×0.795)=1.09, which is greater than 1. Therefore, all data points are retained. After sampling adjustment, the dataset with 68+125+137+98+43=471 data points is obtained.

[0053] A linear fitting operation is performed on the sampled and adjusted effective wind speed data and historical wave height data. The linear fitting is based on the least squares method, determining the parameters of the fitted line by minimizing the sum of squared vertical distances from all data points in the sampled and adjusted dataset to the fitted line. Let the equation of the fitted line be H = aV + b, where H represents wave height, V represents wind speed, and a and b are the parameters to be determined. According to the least squares method, the formulas for calculating parameters a and b are: a = (n∑ViHi - ∑Vi∑Hi) / (n∑Vi 2 -(∑Vi) 2 ), b=(∑Hi-a∑Vi) / n, where n is the total number of data points, and Vi and Hi are the wind speed and wave height values ​​of the i-th data point, respectively. For the dataset after sampling and adjustment of the northeast wind direction [5.0, 7.5) m / s wind speed interval, we calculate a=0.237, b=-0.315, therefore the initial fitted straight line equation is H=0.237V-0.315.

[0054] The effective wind speed data after sampling adjustment is substituted into the initial fitted line to calculate the fitted wave height value. Taking the i-th data point in the sampled and adjusted dataset as an example, its wind speed value Vi is 6.2 m / s. Substituting it into the fitted line equation H = 0.237V - 0.315, the fitted wave height value Hi' is calculated to be 0.237 × 6.2 - 0.315 = 1.154 m. The absolute value of the difference between the actual wave height Hi and the fitted wave height value Hi' at this data point, |Hi - Hi'|, is calculated to obtain the residual value for this data point. Assuming the actual wave height Hi at this data point is 1.28 m, the residual value is |1.28 - 1.154| = 0.126 m. The above calculation process is repeated for all 471 data points in the sampled and adjusted dataset to obtain 471 residual values, forming a residual value set.

[0055] The residual value set is used for subsequent outlier identification and removal. A reasonable residual threshold is set by calculating the mean and standard deviation of the residual values. For the northeast wind direction [5.0, 7.5) m / s wind speed range, the mean residual value is 0.087 m and the standard deviation is 0.062 m. The residual threshold is set to the mean plus 2.5 times the standard deviation, i.e., 0.087 + 2.5 × 0.062 = 0.242 m. The residual value of each data point is checked; if it exceeds the threshold of 0.242 m, it is determined to be an outlier and removed. After checking, 38 data points in the sampled and adjusted dataset had residual values ​​exceeding the threshold. After removing these outliers, 433 valid data points are retained for subsequent curve fitting and regression equation establishment.

[0056] By introducing a sampling adjustment method based on distribution dispersion, combined with residual analysis and outlier removal techniques, this approach significantly improves the accuracy and robustness of the wind-wave relationship regression model. Sampling density adjustment ensures that data from different wind speed ranges are represented evenly, avoiding excessive influence of high-density areas on the fitting results. Residual analysis effectively identifies and removes outliers that do not conform to the overall distribution pattern, thus improving data quality.

[0057] Obtain forecast wind speed data, match the corresponding lag response model based on the forecast wind speed data, shift the forecast wind speed data according to the lag duration in the matched lag response model to obtain the effective forecast wind speed data, and substitute the effective forecast wind speed data into the matched lag response model to calculate the wave height forecast value, including: Obtain forecast wind speed data, extract wind direction information and wind speed value from the forecast wind speed data, determine the wind direction interval to which the forecast wind speed data belongs based on the wind direction information, determine the wind speed interval to which the forecast wind speed data belongs based on the wind speed value, and retrieve the matching hysteresis response model from multiple hysteresis response models based on the wind direction interval and wind speed interval. Extract the regression equation type identifier from the matched hysteresis response model, set the applicable boundary conditions for the forecast wind speed data based on the regression equation type identifier, verify the applicable boundary conditions for the forecast wind speed data, and obtain the verified forecast wind speed data. Extract the lag duration from the matched lag response model, shift the forecast timestamp of the verified forecast wind speed data backward according to the lag duration, and convert the verified forecast wind speed data into valid forecast wind speed data based on the shifted forecast timestamp. The regression equation is extracted from the matched hysteresis response model, and the predicted effective wind speed data is substituted into the regression equation to calculate the wave height forecast value.

[0058] In practical applications, forecast wind speed data is acquired from meteorological observation stations or numerical weather prediction systems. This data includes wind direction angles and wind speed values ​​for future moments. Wind direction information, typically expressed as an angle (e.g., 270 degrees for westerly winds), is extracted from the forecast wind speed data. This wind direction angle is compared to pre-defined wind direction intervals. Assuming wind directions are grouped into eight directions—north, northeast, east, southeast, south, southwest, westerly, and northwest—each corresponding to a 45-degree range, the wind direction interval is determined by which range the wind direction angle falls into. Simultaneously, the forecast wind speed value, for example, 8.5 meters per second, is extracted. Based on a pre-defined wind speed interval division scheme (e.g., 0-5 m / s, 5-10 m / s, 10-15 m / s), the wind speed value is determined to belong to the 5-10 m / s interval. Based on the defined wind direction and wind speed ranges, a dual search is performed on multiple stored hysteresis response models. Each hysteresis response model is associated with a specific wind direction identifier and wind speed range identifier. The corresponding hysteresis response model is found by matching these two identifiers.

[0059] After retrieving a matching lag response model, the regression equation type identifier is extracted from the model. Common regression equation types include linear regression, quadratic polynomial regression, or exponential regression. Different regression equation types correspond to different applicable boundary conditions. For example, a linear regression equation may require wind speed data not to exceed a certain threshold to ensure a linear relationship. If the regression equation is of the form H = a·V + b, then the upper limit of wind speed is set as the upper bound of that wind speed range; for quadratic polynomial regression H = a·V... 2 +b·V+c requires verification that the wind speed is within the data range used in modeling. When validating the boundary conditions of the forecast wind speed data, check whether the wind speed value exceeds the effective range of the regression equation. If it does, perform boundary truncation to limit the excess part to the boundary value. If it meets the conditions, it is directly used as the validated forecast wind speed data.

[0060] The lag duration parameter, expressed in hours, is extracted from the matched lag response model. This parameter represents the time delay between wind speed change and wave height response. Assuming the extracted lag duration is 3 hours, the forecast timestamp of the validated forecast wind speed data is obtained, for example, the wind speed forecast corresponds to 12:00 on January 15, 2024. Shifting the lag duration backward implies that the wave height response occurs after the wind speed action; therefore, the forecast timestamp is shifted 3 hours backward from 12:00 to 15:00. Based on the shifted timestamp, the original forecast wind speed data is re-marked as the valid forecast wind speed data corresponding to 15:00, indicating that the wind speed value had a valid impact on wave height at 15:00. This time shift operation ensures that the time correspondence between wind speed and wave height conforms to the physical lag law.

[0061] The coefficients of the regression equation, such as coefficients a and b in a linear regression equation, are extracted from the matched hysteresis response model. The predicted effective wind speed data is substituted into the regression equation as an independent variable, and numerical calculations are performed to obtain the predicted wave height. If the regression equation is H = 0.32·V + 0.15, and the predicted effective wind speed is 8.5 meters per second, then the predicted wave height is calculated to be 0.32 × 8.5 + 0.15 = 2.87 meters. This predicted wave height corresponds to the shifted prediction timestamp, i.e., the wave height prediction result at 15:00. Through this complete process of matching retrieval, boundary verification, time shifting, and equation calculation, accurate wave height prediction based on the hysteresis response model is achieved, ensuring that the prediction results fully consider the physical hysteresis characteristics and nonlinear response relationship between wind and waves.

[0062] The regression equation type identifier is extracted from the matched hysteresis response model. Based on the regression equation type identifier, applicable boundary conditions for the forecast wind speed data are set. The applicable boundary conditions are then validated on the forecast wind speed data, resulting in validated forecast wind speed data including: Extract the regression equation type identifier and regression equation parameters from the matched hysteresis response model, determine the domain characteristics of the regression equation based on the regression equation type identifier, calculate the effective input interval of the regression equation based on the domain characteristics and regression equation parameters, and set the effective input interval as the applicable boundary conditions for the forecast wind speed data. The fault tolerance range is calculated based on the applicable boundary conditions. The extended boundary conditions are obtained by superimposing the applicable boundary conditions and the fault tolerance range. A hierarchical verification rule is established based on the applicable boundary conditions and the extended boundary conditions. Obtain the wind speed values ​​from the forecast wind speed data, determine the positional relationship between the wind speed values ​​and the applicable boundary conditions and extended boundary conditions according to the graded verification rules, and obtain the positional relationship judgment result. Based on the location relationship, when the wind speed value is within the applicable boundary conditions, the forecast wind speed data is retained; when the wind speed value is within the extended boundary conditions but exceeds the applicable boundary conditions, the wind speed value is corrected to the boundary value of the applicable boundary conditions; when the wind speed value exceeds the extended boundary conditions, the forecast wind speed data is discarded, and the verified forecast wind speed data is obtained.

[0063] When using matched lag response models for wave height forecasting, the validity of the forecast wind speed data needs to be verified. First, the regression equation type identifier is extracted from the matched lag response model. This identifier includes types such as linear regression, power regression, or logarithmic regression. Simultaneously, the regression equation parameters are extracted, such as the coefficient k and intercept b in the linear regression equation y=kx+b, or the power regression equation y=ax. n The coefficients 'a' and the exponent 'n' in the regression equation are used. The domain characteristics are determined based on the regression equation type identifier; for example, logarithmic regression requires the input variables to be greater than zero, while power regression requires the input variables to be non-zero when the exponent is negative.

[0064] The effective input interval of the regression equation is calculated based on the characteristics of the defined domain and the parameters of the regression equation. Specifically, the minimum and maximum wind speed values ​​are extracted from the historical wind speed stratified dataset and used as the training data range for the regression equation. Considering that the extrapolation error of the regression equation outside the training data range is usually large, the training data range is set as the effective input interval, and this effective input interval is used as the applicable boundary condition for the forecast wind speed data. For example, if the wind speed range corresponding to a certain hysteresis response model is 5 to 12 meters per second, then the lower bound of this applicable boundary condition is 5 meters per second, and the upper bound is 12 meters per second.

[0065] To avoid the complete rejection of forecasted wind speed data due to slight deviations from the applicable boundary conditions, a tolerance range needs to be calculated. The tolerance range is calculated by multiplying the width of the applicable boundary condition interval by a tolerance coefficient, typically between 0.1 and 0.2. For example, if the applicable boundary conditions are 5 to 12 meters per second, the interval width is 7 meters per second, and the tolerance coefficient is 0.15, then the tolerance range is 1.05 meters per second. Extending the tolerance range to both sides of the applicable boundary conditions yields extended boundary conditions; in this example, the extended boundary conditions are 3.95 to 13.05 meters per second.

[0066] A hierarchical verification rule is established based on applicable boundary conditions and extended boundary conditions. The rule includes three judgment levels: when the wind speed value is within the applicable boundary conditions, it is marked as fully applicable; when the wind speed value exceeds the applicable boundary conditions but is within the extended boundary conditions, it is marked as applicable with correction; and when the wind speed value exceeds the extended boundary conditions, it is marked as inapplicable.

[0067] Obtain the predicted wind speed values ​​and compare them with the applicable and extended boundary conditions. Determine the positional relationship of the wind speed values ​​according to the graded verification rules, obtaining the positional relationship judgment result. If the judgment result is fully applicable, the predicted wind speed data is directly retained for subsequent calculations. If the judgment result is correctable and applicable, the wind speed value is corrected to the nearest boundary value of the applicable boundary conditions. For example, if the wind speed value is 12.8 m / s, exceeding the upper limit of 12 m / s but within the extended upper limit of 13.05 m / s, it is corrected to 12 m / s. If the judgment result is inapplicable, the predicted wind speed data is discarded, and the model re-matching process is triggered. After completing the above processing, the verified predicted wind speed data is obtained, ensuring that the wind speed data input to the regression equation is within the effective range and improving the reliability of wave height forecast values.

[0068] A second aspect of the present invention provides a wind-wave relationship analysis system based on a hysteresis response model, the system comprising: The wind direction grouping unit is used to divide historical wind speed data and historical wave height data into multiple wind direction grouping datasets according to wind direction. For each wind direction grouping dataset, the correlation coefficient between historical wind speed data and historical wave height data at different time offsets is calculated, and the time offset corresponding to the maximum correlation coefficient is used as the lag time. The wind speed stratification unit is used to set multiple wind speed intervals and divide the historical wind speed data and historical wave height data in each wind direction group dataset into multiple wind speed stratification datasets according to the wind speed intervals. The model building unit is used to shift the historical wind speed data according to the corresponding lag duration for each wind speed stratified dataset to obtain effective wind speed data. Based on the effective wind speed data and historical wave height data, a regression equation is established. The lag duration, wind speed range and regression equation are combined to form a lag response model, resulting in multiple lag response models. The forecast calculation unit is used to acquire forecast wind speed data, match the corresponding lag response model according to the forecast wind speed data, shift the forecast wind speed data according to the lag time in the matched lag response model to obtain the forecast effective wind speed data, and substitute the forecast effective wind speed data into the matched lag response model to calculate the wave height forecast value.

[0069] A third aspect of the present invention provides an electronic device, comprising: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the aforementioned method.

[0070] A fourth aspect of the present invention provides a computer-readable storage medium having stored thereon computer program instructions that, when executed by a processor, implement the aforementioned method.

[0071] This invention can be a method, apparatus, system, and / or computer program product. The computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of the invention.

[0072] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A wind-wave relationship analysis method based on a hysteresis response model, characterized in that, include: Based on wind direction, historical wind speed data and historical wave height data are divided into multiple wind direction group datasets. For each wind direction group dataset, the correlation coefficient between historical wind speed data and historical wave height data at different time offsets is calculated, and the time offset corresponding to the maximum correlation coefficient is taken as the lag time. Multiple wind speed ranges are set, and the historical wind speed data and historical wave height data in each wind direction group dataset are divided into multiple wind speed hierarchical datasets according to the wind speed range. For each wind speed stratified dataset, the historical wind speed data is shifted according to the corresponding lag duration to obtain the effective wind speed data. A regression equation is established based on the effective wind speed data and historical wave height data. The lag duration, wind speed range and regression equation are combined to form a lag response model, resulting in multiple lag response models. Obtain forecast wind speed data, match the corresponding lag response model based on the forecast wind speed data, shift the forecast wind speed data according to the lag time in the matched lag response model to obtain the forecast effective wind speed data, and substitute the forecast effective wind speed data into the matched lag response model to calculate the wave height forecast value.

2. The method according to claim 1, characterized in that, Based on wind direction, historical wind speed and wave height data are divided into multiple wind direction group datasets. For each wind direction group dataset, the correlation coefficient between historical wind speed and historical wave height data at different time offsets is calculated. The time offset corresponding to the maximum correlation coefficient is taken as the lag duration. Obtain the prevailing wind direction distribution information of the sea area, determine the wind direction division angle corresponding to each wind direction based on the prevailing wind direction distribution information of the sea area, divide the wind direction range into multiple wind direction intervals based on the wind direction division angles, and classify historical wind speed data and historical wave height data into the corresponding wind direction grouping datasets based on the wind direction intervals to obtain multiple wind direction grouping datasets. Obtain the data time span of each wind direction group dataset, set the time offset search range based on the data time span, and generate multiple candidate time offsets within the time offset search range; The historical wind speed data in the wind direction grouping dataset is shifted according to each candidate time offset to obtain the shifted wind speed data. The correlation coefficient between the shifted wind speed data and the historical wave height data in the wind direction grouping dataset is calculated to obtain multiple correlation coefficients corresponding to multiple candidate time offsets. A correlation coefficient curve is constructed by combining multiple candidate time offsets with multiple correlation coefficients. The correlation coefficient curve is then smoothed to obtain a smoothed correlation coefficient curve. The maximum correlation coefficient is identified from the smoothed correlation coefficient curve, and the time offset corresponding to the maximum correlation coefficient is taken as the lag duration.

3. The method according to claim 1, characterized in that, Multiple wind speed ranges are defined, and the historical wind speed data and historical wave height data in each wind direction group dataset are divided into multiple hierarchical wind speed datasets based on the wind speed ranges, including: For each wind direction group dataset, obtain the wind speed value distribution of historical wind speed data in the wind direction group dataset, calculate multiple quantile values ​​based on the wind speed value distribution, use the multiple quantile values ​​as the boundary for dividing the wind speed interval, and set multiple wind speed intervals based on the boundary for dividing the wind speed interval. Iterate through each historical wind speed data point in the wind direction grouping dataset, extract the wind speed value and data time, determine the wind speed interval to which the wind speed value belongs, extract the corresponding wave height value from the historical wave height data based on the data time, and classify the wind speed value and wave height value into the wind speed stratified dataset corresponding to the wind speed interval to obtain multiple wind speed stratified datasets.

4. The method according to claim 1, characterized in that, For each stratified wind speed dataset, historical wind speed data is shifted according to the corresponding lag duration to obtain effective wind speed data. A regression equation is established based on the effective wind speed data and historical wave height data. The lag duration, wind speed range, and regression equation are combined to form a lag response model, resulting in multiple lag response models, including: For each wind speed stratified dataset, the timestamps of the historical wind speed data in the wind speed stratified dataset are shifted backward according to the lag time. The historical wind speed data and historical wave height data are then rematched based on the shifted timestamps to obtain the effective wind speed data. Linear fitting is performed on the effective wind speed data and historical wave height data to obtain an initial fitted line. The residual value of each data point of the effective wind speed data and the initial fitted line is calculated. The residual threshold is calculated based on the sample correlation coefficient between the effective wind speed data and the historical wave height data. Data points with residual values ​​exceeding the residual threshold are removed to obtain the filtered effective wind speed data and historical wave height data. The selected effective wind speed data and historical wave height data are curve fitted to obtain the fitted curve. The rate of change of curvature of the fitted curve is calculated, and the regression equation type is selected from the preset regression equation type library according to the rate of change of curvature. Identify the location of the parameter to be determined in the regression equation type, substitute the filtered effective wind speed data as the independent variable and the corresponding historical wave height data as the dependent variable into the regression equation type to establish the target equation system, solve the target equation system to obtain the parameter value, and substitute the parameter value into the location of the parameter to be determined to obtain the regression equation. Wind speed intervals corresponding to the stratified wind speed datasets are extracted, and lag duration, wind speed intervals, and regression equations are combined to form lag response models, resulting in multiple lag response models.

5. The method according to claim 4, characterized in that, An initial fitted line is obtained by linearly fitting the effective wind speed data and historical wave height data. The residual values ​​of each data point of the effective wind speed data and the initial fitted line are calculated, including: Calculate the distribution dispersion of effective wind speed data and historical wave height data, determine the sampling adjustment coefficient based on the distribution dispersion, and adjust the sampling density of effective wind speed data and historical wave height data based on the sampling adjustment coefficient to obtain the sampled and adjusted effective wind speed data and sampled and adjusted historical wave height data. A linear fitting operation is performed on the sampled and adjusted effective wind speed data and the sampled and adjusted historical wave height data. The parameters of the fitted line are determined by minimizing the sum of squared vertical distances between the sampled and adjusted effective wind speed data and the sampled and adjusted historical wave height data. An initial fitted line is established based on the fitted line parameters. Substitute the sampled and adjusted effective wind speed data into the initial fitted line to calculate the fitted wave height value. Calculate the absolute value of the difference between the sampled and adjusted historical wave height data and the fitted wave height value to obtain the residual value between each data point of the effective wind speed data and the initial fitted line.

6. The method according to claim 1, characterized in that, Obtain forecast wind speed data, match the corresponding lag response model based on the forecast wind speed data, shift the forecast wind speed data according to the lag duration in the matched lag response model to obtain the effective forecast wind speed data, and substitute the effective forecast wind speed data into the matched lag response model to calculate the wave height forecast value, including: Obtain forecast wind speed data, extract wind direction information and wind speed value from the forecast wind speed data, determine the wind direction interval to which the forecast wind speed data belongs based on the wind direction information, determine the wind speed interval to which the forecast wind speed data belongs based on the wind speed value, and retrieve the matching hysteresis response model from multiple hysteresis response models based on the wind direction interval and wind speed interval. Extract the regression equation type identifier from the matched hysteresis response model, set the applicable boundary conditions for the forecast wind speed data based on the regression equation type identifier, verify the applicable boundary conditions for the forecast wind speed data, and obtain the verified forecast wind speed data. Extract the lag duration from the matched lag response model, shift the forecast timestamp of the verified forecast wind speed data backward according to the lag duration, and convert the verified forecast wind speed data into valid forecast wind speed data based on the shifted forecast timestamp. The regression equation is extracted from the matched hysteresis response model, and the predicted effective wind speed data is substituted into the regression equation to calculate the wave height forecast value.

7. The method according to claim 6, characterized in that, The regression equation type identifier is extracted from the matched hysteresis response model. Based on the regression equation type identifier, applicable boundary conditions for the forecast wind speed data are set. The applicable boundary conditions are then validated on the forecast wind speed data, resulting in validated forecast wind speed data including: Extract the regression equation type identifier and regression equation parameters from the matched hysteresis response model, determine the domain characteristics of the regression equation based on the regression equation type identifier, calculate the effective input interval of the regression equation based on the domain characteristics and regression equation parameters, and set the effective input interval as the applicable boundary conditions for the forecast wind speed data. The fault tolerance range is calculated based on the applicable boundary conditions. The extended boundary conditions are obtained by superimposing the applicable boundary conditions and the fault tolerance range. A hierarchical verification rule is established based on the applicable boundary conditions and the extended boundary conditions. Obtain the wind speed values ​​from the forecast wind speed data, determine the positional relationship between the wind speed values ​​and the applicable boundary conditions and extended boundary conditions according to the graded verification rules, and obtain the positional relationship judgment result. Based on the location relationship, when the wind speed value is within the applicable boundary conditions, the forecast wind speed data is retained; when the wind speed value is within the extended boundary conditions but exceeds the applicable boundary conditions, the wind speed value is corrected to the boundary value of the applicable boundary conditions; when the wind speed value exceeds the extended boundary conditions, the forecast wind speed data is discarded, and the verified forecast wind speed data is obtained.

8. A wind-wave relationship analysis system based on a hysteresis response model, used to implement the method of any one of claims 1-7, characterized in that, include: The wind direction grouping unit is used to divide historical wind speed data and historical wave height data into multiple wind direction grouping datasets according to wind direction. For each wind direction grouping dataset, the correlation coefficient between historical wind speed data and historical wave height data at different time offsets is calculated, and the time offset corresponding to the maximum correlation coefficient is used as the lag time. The wind speed stratification unit is used to set multiple wind speed intervals and divide the historical wind speed data and historical wave height data in each wind direction group dataset into multiple wind speed stratification datasets according to the wind speed intervals. The model building unit is used to shift the historical wind speed data according to the corresponding lag duration for each wind speed stratified dataset to obtain effective wind speed data. Based on the effective wind speed data and historical wave height data, a regression equation is established. The lag duration, wind speed range and regression equation are combined to form a lag response model, resulting in multiple lag response models. The forecast calculation unit is used to acquire forecast wind speed data, match the corresponding lag response model according to the forecast wind speed data, shift the forecast wind speed data according to the lag time in the matched lag response model to obtain the forecast effective wind speed data, and substitute the forecast effective wind speed data into the matched lag response model to calculate the wave height forecast value.

9. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to invoke instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 7.

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