Dynamic Copula extreme wave energy prediction method based on wind speed covariable full-link driving

Abstract

The invention provides a dynamic Copula extreme wave energy prediction method based on wind speed covariant full-link driving. The dynamic Copula extreme wave energy prediction method is applied to safety evaluation of ocean engineering and a wave energy power generation system. Firstly, B-spline-logarithmic normal edge distribution with wind speed as a covariable is constructed through data preprocessing, and dynamic changes of wave height and wave period parameters along with the wind speed are described; secondly, selecting an optimal Copula function, coupling a Copula parameter with the wind speed through Logistic mapping, and establishing a dynamic dependency structure model; then, dividing a low wind speed interval, a medium wind speed interval and a high wind speed interval, and verifying the fitting precision of the model in each interval and extreme wave energy over-limit probability prediction performance; and finally, integrating edge distribution and dynamic Copula, and constructing a wind speed driven wave element joint probability prediction model. Compared with a traditional static model, the method can accurately capture the regulation and control effect of the wind speed on the wave height-wave period dependency relationship, remarkably improves the prediction accuracy of an extreme wave energy event, and provides reliable support for ocean engineering safety and wave energy power station operation.

Description

Technical Field

[0001] This invention relates to the fields of marine engineering and renewable energy technology, and more specifically, to a method for probabilistic prediction of extreme wave energy events, particularly a dynamic Copula extreme wave energy prediction method based on wind speed covariate full-link driving. Background Technology

[0002] The global energy structure is transitioning towards cleaner and lower-carbon energy. Wave energy, with its large reserves, high energy density, and strong renewability, has become a highly promising marine renewable energy source. However, the development and utilization of wave energy faces severe challenges: its power output is highly random and intermittent, especially the "extreme wave energy events" caused by extreme sea conditions. Although these events have a low probability of occurrence, they can cause overload impacts on marine engineering structures and threaten the stability of the power grid. Therefore, achieving accurate prediction of the probability of extreme wave energy events is the key to improving the safety of marine engineering and the economics of wave energy systems. Constructing a model that can accurately describe the joint probability distribution between the two key wave elements, wave height (H) and wave period (T), is the core of calculating the probability of extreme wave conditions. Although Copula theory is widely used, existing technical solutions have the following three significant limitations: 1. Limitations of Static Models: Traditional Copula models generally employ fixed-parameter marginal distributions and static Copula-dependent structures. These models completely ignore "wind speed (U)" as the core physical driving force for wave generation and evolution, which has a strong dynamic control effect on the joint distribution of wave height and wave period. In real ocean environments, static models cannot capture this dynamism, leading to serious biases in the probability prediction of extreme joint events. 2. Existing dynamic models are incomplete: In recent years, although some studies have attempted to introduce dynamic Copula, they often only assign dynamism to a single link - either only making the edge distribution parameters change with environmental factors, or only making the Copula dependent parameters change. This "local dynamic" approach fails to construct a "full-link" dynamic evolution model framework that is synchronously and systematically driven by wind speed covariates to drive the edge distribution and dependent structure. It cannot completely and coherently depict the complete physical process of the wave energy joint probability distribution changing with wind speed in real time. 3. Lack of refined interval modeling and validation: Existing methods generally do not perform differentiated refined modeling and validation for the significant heterogeneity of the joint distribution of wave height and wave period in different wind speed intervals (such as low, medium and high wind speeds). The concentrated distribution at low wind speeds and the dispersed and multi-peak distribution at high wind speeds are described by the same set of fixed parameter models, which inevitably leads to fitting distortion. The predictive reliability of the model in the extreme high wind speed range, which is the main source of wave energy, is seriously insufficient. Therefore, there is an urgent need to propose a new method for predicting extreme wave energy that can deeply couple the effects of wind speed, achieve full dynamic characterization of edge and dependent structures, and perform refined modeling and verification for different wind speed ranges, so as to solve the fundamental problems of insufficient prediction accuracy and poor adaptability to extreme conditions of existing technologies. Summary of the Invention

[0003] The purpose of this invention is to address the shortcomings of existing static Copula models and incomplete dynamic Copula models in extreme wave energy prediction, and to provide a dynamic Copula extreme wave energy prediction method based on wind speed covariate full-link driving. The core inventive idea of ​​this invention lies in constructing a "full-link" model framework that uses wind speed as the sole physical covariate to synchronously drive the edge distribution of wave elements and the dynamic evolution dependent on structures. To achieve this, this invention proposes a set of coordinated parameterized mapping mechanisms: (1) For the nonlinearity of the position parameter (μ): a cubic B-spline function is used for fitting, which accurately captures the complex nonlinear characteristics of the position parameter as a function of wind speed with its superior local control capability and flexibility. (2) Regarding the positive definiteness and monotonicity of the scale parameter (σ): a log-linear function is used for fitting, which effectively characterizes the trend of its variation with wind speed while ensuring that the parameter is always positive. (3) Regarding the boundedness of the Copula dependency parameter (ρ): the Logistic function is used for mapping to ensure that the dependency parameter is always within its effective domain and can sensitively reflect the control of wind speed on the dependency intensity. This entire design tightly couples the edge distribution and dependent structure under the same physical driving force (wind speed), forming a more complete and physically interpretable dynamic joint probability distribution model that is different from existing technologies. This invention is achieved using the following technical solution: A dynamic Copula extreme wave energy prediction method based on wind speed covariates, characterized by the following steps: S1: Collect marine meteorological and wave observation data containing wave height (H), wave period (T) and corresponding wind speed (U), and preprocess the data to obtain a valid sample dataset; S2: Construct a dynamic marginal distribution model driven by wind speed covariates and with coordinated parameter responses: Establish log-normal distributions for wave height (H) and wave period (T), and establish the coordinated response function relationship between their location parameter (μ) and scale parameter (σ) and wind speed (U), where: a) To accurately capture the nonlinear dynamics of the position parameter, a cubic B-spline function is used to fit the position parameter (μ) as a nonlinear function of the wind speed (U); b) To ensure the positive definiteness of the scale parameter and reflect its changing trend, a log-linear function is used to fit the scale parameter (σ) as a function of wind speed (U); S3: Based on the goodness-of-fit criterion, select the optimal basic Copula function from the preset Copula function family to describe the dependence of wave height on wave period; S4: Construct a dynamic Copula dependency structure that is synchronous with the edge distribution and driven by wind speed: Map the dependency parameter (θ) of the basic Copula function selected in step S3 to a function of wind speed (U) through the Logistic function, thereby unifying the dynamic evolution of the dependency structure with the dynamic evolution of the edge distribution under the same wind speed covariate, and ensuring that the value of the dependency parameter is always within its effective domain. S5: Integration and Prediction: Integrate the dynamic edge distribution model obtained in step S2 with the dynamic Copula dependency structure obtained in step S4, construct a full-link dynamic Copula joint probability distribution model based on Sklar's theorem, and calculate the probability that the wave energy power density exceeds a preset threshold in different wind speed ranges based on this model, so as to realize the probability prediction of extreme wave energy events.

[0004] Preferably, in step S2, the process of fitting the position parameters using cubic B-spline includes: determining internal nodes based on the quantiles of the wind speed sample, constructing a node vector, and fitting the position parameters of wave height (H) and wave period (T) using cubic B-spline (B-spline). The process of capturing the nonlinear dynamic characteristics of location parameters and wind speed (U) to achieve dynamic adjustment of parameters with wind speed includes: Three internal nodes are determined based on the wind speed quantiles, and the nodes are repeated at both ends by deg+1 times (deg=3 for cubic splines) to form a node vector. ; The core advantage of using cubic B-spline fitting for the position parameter μ lies in its local support and flexibility. Compared to traditional linear fitting or simple polynomial fitting, it can more accurately capture the nonlinear dynamic characteristics of wave height and wave period position parameters under different wind speed ranges. The fitting expression for the position parameter is: In the formula: U is the wind speed covariate, , These are the positional parameters for wave height and wave period, respectively. The number of basis functions. , For B-spline coefficients, The basis functions are cubic B-spline functions. Preferably, in step S2, a log-linear fitting of the scale parameter σ is used. An exponential transformation ensures the scale parameter remains positive, while the linear structure simplifies the complexity of parameter estimation and effectively captures the monotonic relationship between the scale parameter and wind speed. The fitting expression for the location parameter is: In the formula: , These are the scale parameters for wave height and wave period, respectively. , , , These are parameters to be estimated.

[0005] Preferably, in step S4, the Logistic function is used to map Copula parameters to wind speed. Compared with other boundary constraint functions, the Logistic function is very suitable for mapping wind speed to Copula parameter ranges such as (-1,1) or (0,∞) because it can smoothly and monotonically map real number field inputs to a finite interval. Moreover, parameter estimation is simpler, dynamic adjustment sensitivity is higher, and the control effect of wind speed on variable dependence is more accurate. The correlation coefficient of Gaussian-Copula ( For example, the mapping expression is: In the formula: For the Logistic function, , These are parameters to be estimated.

[0006] Furthermore, the integration portion in step S5 includes: S501: The parameters of the dynamic model of marginal distribution covariates are solved by using maximum likelihood estimation combined with numerical optimization algorithm; S502: Establish a dynamic mapping relationship between Copula-dependent parameters and wind speed covariates in a joint distribution using nonlinear optimization methods; S503: Based on Sklar's theorem, integrate the dynamic Copula functions of marginal distribution and joint distribution to construct the joint probability density function: In the formula: , Let the marginal probability density function be the wave height and wave period. , This is a probability integral transform of the edge distributions of wave height and wave period. For Copula density function, The Copula-dependent parameter varies with wind speed; S504: Wind speed is divided into three typical ranges: low, medium, and high, based on wind speed percentile values. S505: The model's fitting accuracy is quantitatively evaluated using three indicators: KL divergence, RMSE, and correlation coefficient. The calculation formulas are as follows: In the formula: To observe the joint frequency value, To predict the joint probability for the model, The average of the observed frequencies. The model predicts the mean probability. Preferably, in the prediction part of step S5, the preset threshold Defined as the 90th or 95th percentile of the wave energy power density values ​​in the training set, and satisfying the requirements in the test set. The event is defined as an extreme wave energy exceedance event; the formula for calculating the wave energy power density J is: In the formula: Seawater density, It is the acceleration due to gravity. Wave height (m). The wave period (s); Then, a multi-dimensional evaluation system was constructed using RMSE, mean absolute error (MAE), and Kolmogorov-Smirnov (KS) tests to verify the model's predictive performance on the probability of extreme wave energy events and output the predicted probability of extreme wave energy events in different wind speed ranges, providing support for marine engineering design and wave energy grid-connected scheduling.

[0007] Beneficial effects: Compared with the prior art, the technical solution provided by the present invention has the following outstanding advantages and beneficial effects: 1) Achieved dynamic modeling driven by the entire link and physical mechanism: This invention breaks through the limitations of simultaneously and systematically introducing wind speed covariates into the dynamic process of marginal distribution parameters (location parameter μ, scale parameter σ) and joint distribution Copula dependency parameter (ρ); through the coordinated parameterized mapping framework of "B-spline fitting of location parameters + log-linear fitting of scale parameters + Logistic mapping of dependency parameters", the entire joint probability distribution model can respond to wind speed changes in real time and adaptively, realizing a deeper mathematical description of the physical process of wave generation and solving the problem of incomplete characterization by traditional static models or "local dynamic" models; 2) Significantly improves the accuracy of extreme wave energy prediction, especially in the high wind speed range: Since the model can accurately capture the heterogeneous changes in the wave height-wave period dependence relationship under high wind speed, its probability prediction ability for extreme joint events is greatly enhanced. The data from the implementation examples show that the RMSE and MAE indices of the model in the prediction of extreme wave energy exceedance probability are reduced by more than 90% compared with the traditional static model, and the KS test P value is closer to 1, which proves the high consistency between the predicted distribution and the measured distribution. This provides a more reliable and accurate design basis for marine engineering to resist extreme loads. 3) Innovatively proposed a refined verification paradigm for wind speed intervals: This invention not only models according to wind speed intervals, but also emphasizes the independent verification of the model's goodness of fit within each interval. This verification method directly proves the model's universal applicability and superiority in the entire wind speed spectrum, especially in the high wind speed extreme interval where conventional models fail, thus enhancing the robustness and persuasiveness of the model's conclusions. 4) It has good scalability and engineering practical value: The modeling framework provided by this invention is clear and the parameter estimation method is mature. It can be easily transferred to different geographical sea areas. Only the B-spline coefficients, log-linear parameters and Logistic function parameters need to be recalibrated according to local data. The method directly outputs the probability of extreme events, and the results are intuitive and easy to be adopted and applied by engineering design specifications and safety scheduling systems. Attached Figure Description

[0008] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram comparing the cumulative distribution function (CDF) of the traditional static model, the dynamic model of this invention, and the empirical distribution in the low, medium, and high wind speed ranges of the embodiment. Figure 3 This is a schematic diagram comparing the joint probability density distribution of wave height and wave period fitted by the traditional static model and the dynamic model of the present invention under low, medium and high wind speed ranges in the embodiment. Detailed Implementation

[0009] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments; it should be understood that these embodiments are only for illustrating the invention and are not intended to limit the scope of the invention; A preferred embodiment of the present invention is illustrated using measured data from a site of the National Data Buoy Center (NDBC) in the United States in 2015. The sampling interval was 1 hour, and 8,624 valid samples were obtained after preprocessing. Figure 1 This paper presents a flowchart of a dynamic Copula extreme wave energy prediction method based on wind speed covariates, as described in this application. (Refer to...) Figure 1The method specifically includes the following steps: Step S1: Data collection and preprocessing. Outlier detection (using the 3σ criterion) and missing value imputation were performed on the raw data to ensure data integrity, ultimately yielding 8624 valid samples. S2: Construct a wind-driven dynamic edge distribution model: Express the edge distribution parameters (position parameter μ, scale parameter σ) of wave height and wave period as a function of wind speed covariates, so as to realize the dynamic adjustment of parameters with wind speed; In S2: The wind speed-driven Lognormal marginal distribution model is constructed by fitting the positional parameters μ of wave height and wave period using cubic B-splines and fitting the scale parameter σ using log-linear fitting. The steps are as follows: Step 1: Determine the internal nodes as [5.30, 7.70, 10.30] (m / s) based on the wind speed quantiles, repeating them 4 times at both ends (deg=3) to form a complete node vector; Step 2: Use cubic B-spline fitting to accurately capture the nonlinear dynamic characteristics of wave height and wave period position parameters under different wind speed ranges, avoiding distribution deviations caused by overly simplistic fitting methods. The fitting expression for the position parameters is: In the formula: For wind speed covariance, , These are the positional parameters for wave height and wave period, respectively. The number of basis functions. , For B-spline coefficients, The basis functions are cubic B-spline functions. Then, the maximum likelihood estimation method is used to obtain the solution. , The parameters enable nonlinear dynamic adjustment of position parameters with wind speed; Step 3: Log-linear fitting of the scale parameter σ is used. An exponential transformation ensures the scale parameter remains positive, and the linear structure simplifies the complexity of parameter estimation, effectively capturing the monotonic relationship between the scale parameter and wind speed. The fitting expression for the location parameter is: In the formula: , These are the scale parameters for wave height and wave period, respectively. , , , The parameter to be estimated; The solution was obtained through numerical optimization algorithm. , , , This ensures that the scale parameters are always positive and monotonically correlated with wind speed. Step 4: Comparison of Marginal Distribution Fitting Goodness: By comparing different distribution models using AIC, BIC, and RMSE indices, the results show that the Lognormal distribution performs best in fitting both wave height and wave period (wave height: AIC=29271, BIC=29258, RMSE=0.013083; wave period: AIC=29271, BIC=29258, RMSE=0.013083). The fitting results show that the AIC and BIC values ​​of the Lognormal distribution are significantly lower than other distributions, and its RMSE is also the smallest. Therefore, the Lognormal distribution is determined to be the optimal marginal distribution. Step 5: Verification of the edge distribution fitting effect: like Figure 2 As shown in the figure, the comparison between the empirical CDF, the traditional fixed parameter model CDF, and the covariate model CDF of this invention is shown in the three wind speed ranges of low, medium, and high. It can be clearly seen from the figure that, regardless of the wind speed range, the traditional model CDF deviates significantly from the empirical CDF, while the covariate model CDF always highly overlaps with the empirical CDF. This proves that the dynamic edge distribution achieved by cubic B-splines and log-linear fitting can accurately capture the heterogeneity of wave parameter distribution under different wind speed scenarios. S3: Selecting the optimal basic Copula function; Five Copula functions—Gaussian, Frank, Gumbel, Clayton, and Joe-Clayton—were used to fit the probability integral transformation data of wave height and wave period. The log-likelihood values ​​(logL), AIC, and BIC of each function were compared. In this embodiment, the Gaussian Copula, with AIC = -16232 and BIC = -16225, was the optimal choice. S4: Constructing dynamic Copula dependency parameter expressions In S4: for the selected Gaussian-Copula, the dependency parameter is the linear correlation coefficient. The value range is (-1, 1), and the mapping relationship between the value and wind speed is constructed using the Logistic function: In the formula: For the Logistic function, , The parameter to be estimated; Then, the maximum likelihood estimation method is used to obtain the solution. , This expression ensures This enables the correlation coefficient to be dynamically adjusted according to wind speed; S5: Integration, Validation, and Prediction Step 1: Divide the wind speed range according to the quantile method, and divide the wind speed into low wind speed range (0-6.2m / s), medium wind speed range (6.2-9.3m / s), and high wind speed range (>9.3m / s); Step 2: Solve the parameters using the Newton-Raphson numerical optimization algorithm, and combine it with maximum likelihood estimation to find the optimal values ​​of the marginal distribution and Copula-dependent parameters. Substitute these values ​​into the dynamic parameter models obtained in steps S2 and S4 to form the dynamic Copula joint probability density function specific to this interval. Step 3: Integrate the dynamic edge distribution and the dynamic Copula function to construct a joint distribution function, forming a dynamic Copula joint distribution model for each wind speed interval; Step 4: Verification of the joint distribution fitting effect: like Figure 3 As shown in the figure, the joint distribution of wave height and wave period under different wind speed ranges is compared. In the low wind speed range, the covariate model accurately reproduces the "single peak, small-area concentration" feature, while in the high wind speed range, the "double peak, large-area extension" feature is fully reproduced. The density concentration area highly overlaps with the observation data, further verifying the fitting superiority of the joint distribution model. Step 5: Probability Prediction and Assessment of Extreme Wave Energy Events Based on the constructed dynamic Copula joint distribution model, the model fitting accuracy is verified in different wind speed ranges, and the probability of extreme wave energy events is predicted. (1) Definition of extreme wave energy events: The 90th or 95th percentile of the wave energy power density in the training set is used as the threshold for exceeding the limit. The formula for calculating wave energy power density is: In the formula: Seawater density, It is the acceleration due to gravity. Wave height (m). The wave period (s); (2) Probability Prediction: For the test set, the dynamic joint distribution model constructed in step S5 is used to predict the event in the low, medium, and high wind speed ranges respectively. The probability of occurrence; (3) Evaluation of predictive effectiveness: A multi-dimensional evaluation system was constructed using RMSE, MAE, and KS indicators, with the following calculation formulas: In the formula: n is the number of effective wind speed intervals, Predict the out-of-limit probability for the model in the i-th interval. Let be the measured frequency of exceeding the limit in the test set for the i-th interval. The RMSE, MAE, and KS test p-values ​​of the traditional static model are 0.0901, 0.0843, and 0.3197, respectively. However, the RMSE, MAE, and KS test p-values ​​of the dynamic covariate model of this invention are 0.0074, 0.0073, and 0.9762, respectively. The data shows that the RMSE and MAE of the model of this invention have decreased by more than 90%, and the KS test p-value is closer to 1, indicating that its prediction results are highly consistent with the actual situation and significantly improve the ability to quantify the risks of extreme wave energy events.

[0010] The above embodiments fully illustrate the effectiveness of the present invention. Those skilled in the art can make modifications and changes within the scope of the principles and spirit of the present invention, and all such modifications and changes should be included within the protection scope of the present invention.

Claims

1. A dynamic Copula extreme wave energy prediction method based on wind speed covariate full-link driving, characterized in that, By synchronously driving the edge distribution and dependency structure of wave elements using a unified wind speed covariate (U), a complete dynamic characterization of the joint distribution of wave height and wave period is achieved, including the following steps: S1: Collect marine meteorological and wave observation data containing wave height (H), wave period (T) and corresponding wind speed (U), and preprocess the data to obtain a valid sample dataset; S2: Construct a dynamic marginal distribution model driven by wind speed covariates and with coordinated parameter responses: Establish log-normal distributions for wave height (H) and wave period (T), and establish the coordinated response function relationship between their location parameter (μ) and scale parameter (σ) and wind speed (U), where: a) To accurately capture the nonlinear dynamics of the position parameter, a cubic B-spline function is used to fit the position parameter (μ) as a nonlinear function of the wind speed (U); b) To ensure the positive definiteness of the scale parameter and reflect its changing trend, a log-linear function is used to fit the scale parameter (σ) as a function of wind speed (U); S3: Based on the goodness-of-fit criterion, select the optimal basic Copula function from the preset Copula function family to describe the dependence of wave height on wave period; S4: Construct a dynamic Copula dependency structure that is synchronous with the edge distribution and driven by wind speed: Map the dependency parameter (θ) of the basic Copula function selected in step S3 to a function of wind speed (U) through the Logistic function, thereby unifying the dynamic evolution of the dependency structure with the dynamic evolution of the edge distribution under the same wind speed covariate, and ensuring that the value of the dependency parameter is always within its effective domain. S5: Integration and Prediction: Integrate the dynamic edge distribution model obtained in step S2 with the dynamic Copula dependency structure obtained in step S4, construct a full-link dynamic Copula joint probability distribution model based on Sklar's theorem, and calculate the probability that the wave energy power density exceeds a preset threshold in different wind speed ranges based on this model, so as to realize the probability prediction of extreme wave energy events.

2. The method as described in claim 1, characterized in that, In step S2, the process of fitting the position parameter (μ) using a cubic B-spline function specifically includes: determining at least three internal nodes based on the quantiles of the wind speed sample to form a node vector. And using B-spline basis functions for linear combination, the fitting expression is: In the formula: U is the wind speed covariate, , These are the positional parameters for wave height and wave period, respectively. The number of basis functions. , For B-spline coefficients, It is a cubic B-spline basis function.

3. The method as described in claim 1, characterized in that, In step S2, the fitting expression for the scale parameter (σ) using a log-linear function is as follows: In the formula: , These are the scale parameters for wave height and wave period, respectively. , , , These are the parameters to be estimated.

4. The method as described in claim 1, characterized in that, In step S4, when the base Copula function is a Gaussian Copula, the dynamic expression of its dependent parameter ρ(U) mapped by the Logistic function is: In the formula: For the Logistic function, , For the parameter to be estimated, ensure that ρ(U)∈(-1,1).

5. The method as described in claim 1, characterized in that, The preset threshold is defined as the 90th or 95th percentile of the wave energy power density values ​​in the training set; the formula for calculating the wave energy power density J is: In the formula: Seawater density, It is the acceleration due to gravity. Wave height (m). The wave period is denoted by s.

6. The method as described in claim 1, characterized in that, The method further includes a prediction performance evaluation step: using root mean square error (RMSE), mean absolute error (MAE), and the Kolmogorov-Smirnov test to comprehensively evaluate the consistency and accuracy between the model's predicted extreme wave energy exceedance probability and the measured frequency of the test set; the calculation formulas are as follows: In the formula: n is the number of effective wind speed intervals, Predict the out-of-limit probability for the model in the i-th interval. Let be the measured out-of-limit frequency of the test set for the i-th interval.

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