A method for calculating extreme wave spectrum based on co-occurrence recurrence period of wave elements

Abstract

The application discloses an extreme wave spectrum calculation method based on wave element co-occurrence return period, and belongs to the technical field of coast and ocean engineering. The method comprises the following steps: obtaining long time series data of effective wave height and spectral peak period of a site, constructing a pair of annual extreme value samples, and mapping the pair of annual extreme value samples to a unified probability space; quantitatively representing the dependence structure between wave elements based on Copula theory, and optimizing candidate Copula models according to AIC information criterion; determining a joint exceedance target probability according to the definition of co-occurrence return period, and determining a joint design point based on the maximum probability density criterion; based on the joint design point, inversely calculating spectral scale parameters through zero-order spectral moment energy matching and completing consistency checking of effective wave height, and then calculating an extreme wave spectrum density function curve meeting the co-occurrence return period constraint. The method determines the co-occurrence return period design sea state and realizes self-consistency of wave spectrum calculation, and improves the rationality and engineering applicability of the extreme wave spectrum calculation result.

Description

Technical Field

[0001] This invention belongs to the field of coastal and marine engineering technology. Specifically, it relates to a method for estimating extreme wave spectra based on the co-occurrence and return periods of wave elements. Background Technology

[0002] In coastal and marine engineering design, numerical simulation, and structural safety assessment, the proper determination of extreme sea states is a crucial foundation for engineering analysis. Engineering projects often require wave elements representing extreme sea states, from which the corresponding wave frequency spectral density function is calculated for wave load calculation, time-domain response analysis, and reliability assessment.

[0003] In existing technologies, the determination of extreme sea states is usually based on the return period of a single variable. Design values ​​such as significant wave height and spectral peak period are calculated separately and then combined, and a parametric wave frequency spectrum model is selected for wave spectrum calculation. However, in actual sea states, significant wave height and spectral peak period are generally interdependent. Simply combining multiple single-variable design values ​​can easily lead to sea states that do not meet the target return period constraint in a joint probabilistic sense, resulting in unreasonable design sea states.

[0004] Furthermore, when calculating the wave frequency spectral density function curve from design wave elements, if the energy consistency of the spectral scale parameters is not checked and matched, inconsistencies may arise between the effective wave height calculated from the spectral integral and the target value. This leads to inconsistent wave spectrum calculations, which in turn affects the numerical simulation results and engineering applicability. Therefore, there is an urgent need for a method that, while considering the interdependence of wave elements, determines the joint design sea state based on co-occurrence return period constraints, and further calculates extreme wave spectra that satisfy the constraints and are energy-consistent. Summary of the Invention

[0005] In view of this, the present invention discloses an extreme wave spectrum estimation method based on the co-occurrence return period of wave elements. This method mainly solves the problem that the traditional design sea state determination process takes the effective wave height and spectral peak period as single variable return periods and directly combines them, ignoring the dependence between the two, which leads to unreasonable design sea states. On this basis, it achieves the self-consistency of extreme wave spectrum estimation, thereby improving the rationality and engineering applicability of the extreme wave spectrum estimation results.

[0006] The objective of this invention is achieved through the following technical solutions:

[0007] An extreme wave spectrum estimation method based on the co-occurrence and return periods of wave elements includes the following steps:

[0008] S1. Obtain long-term time-series data of wave elements at a certain station, construct annual extreme value sample pairs, and analyze the extreme value attributes of the annual extreme value sample pairs. Among them, wave elements include significant wave height. With spectral peak period Marginal distribution fitting was performed on the annual extreme value sample pairs of effective wave height and spectral peak period respectively, and the annual extreme value sample pairs were mapped to a unified probability space.

[0009] S2. Based on Copula theory, the interdependent structure between wave elements is quantitatively characterized, a joint distribution model of effective wave height and spectral peak period is established, and the candidate Copula models are selected according to the AIC information criterion to obtain the optimal joint distribution model.

[0010] S3. Determine the joint exceedance probability based on the definition of co-occurrence return period, solve the co-occurrence contour lines under the optimal joint distribution model, and determine the joint design point based on the maximum probability density criterion.

[0011] S4. Based on the joint design point, a parametric wave frequency spectrum model is selected. The spectral scale parameters are inversely calculated through zero-order spectral moment energy matching, and the effective wave height consistency check is completed. Then, the extreme wave spectral density function that satisfies the co-occurrence and return period constraint is calculated. curve.

[0012] Preferably, the annual extreme value sample pairs mentioned in S1 are selected annually. Each independent wave process corresponds to Sample composition, in which And record the annual event occurrence rate as Once per year.

[0013] Preferably, the mapping of annual extreme value sample pairs to a unified probability space as described in S1 includes the following steps:

[0014] Record No. The annual extreme value sample pairs are ,in The corresponding probability value is calculated using the following formula:

[0015] ,

[0016] The resulting probability space sample sequence .

[0017] Preferably, S2 includes the following steps:

[0018] S21. Construct a candidate model library: Select various Copula functions suitable for describing the interdependence of wave elements as candidate models;

[0019] S22. Parameter estimation: Using the probability space sample sequence obtained in step S1 The maximum likelihood estimation (MLE) method was used to evaluate the model parameters of each candidate Copula function. Make an estimate;

[0020] S23. Model Selection: The goodness of fit of each candidate model is evaluated based on the Akaike Information Criterion (AIC).

[0021] Preferably, S22 is the parameter estimate that maximizes the probability of the sample appearing. The calculation formula is:

[0022] ,

[0023] in, For the total number of sample pairs, is the Copula density function.

[0024] Preferably, the formula for calculating the S23 Akaike information content criterion is as follows:

[0025] ,

[0026] in, The number of model parameters, The value of AIC corresponds to the maximum log-likelihood function. The smaller the AIC value, the better the model achieves a balance between fitting accuracy and complexity.

[0027] Preferably, S3 includes the following steps:

[0028] S31. Set the return period of the target co-occurrence as... In 2018, the annual event rate was [missing information]. Once per year, determine the probability of simultaneous and joint exceeding the target;

[0029] S32, Order and The marginal distribution functions of the effective wave height and spectral peak period obtained in step S1 are respectively, for any wave element variable pair. Perform probability transformation;

[0030] S33. Solve to obtain the co-occurring contour lines.

[0031] Preferred,

[0032] The probability of co-occurrence and joint transcendence of the target as stated in S31 is:

[0033] ;

[0034] The probability transformation formula described in S32 is:

[0035] ,

[0036] in, Design variables for effective wave height. Design variables for spectral peak periods; These are the cumulative probability values ​​calculated using the marginal distribution function in step S1;

[0037] According to Copula theory, let the optimal Copula function obtained in step S2 be... Then the joint transcendence probability is... satisfy:

[0038] ,

[0039] S33. Solve the following equation to obtain the co-occurring contour lines:

[0040] ,

[0041] Calculate the joint probability density on the co-occurrence contour lines:

[0042] ,

[0043] in and These are the marginal probability density functions, Let be the density function of the optimal Copula model in S2, i.e. Based on the maximum probability density criterion, select the co-occurrence contour lines that make The point with the maximum value is taken as the joint design point, denoted as . .

[0044] Preferably, S4 includes the following steps:

[0045] S41. Determine the peak frequency of the parametric wave frequency spectrum model based on the joint design point:

[0046] ,

[0047] S42. Constructing a parameterized wave frequency spectral density function When the parameterized wave frequency spectrum model is the JONSWAP spectrum, The expression is:

[0048] ,

[0049] in It is the acceleration due to gravity. For spectral scale parameters, As the peak enhancement factor, For spectral width parameters, and in a segmented form: when hour ,when hour ;

[0050] S43. Calculate the zeroth order spectral moment:

[0051] ,

[0052] in accordance with For spectral scale parameters Perform energy matching back calculation to ensure that the effective wave height obtained from the spectral integral back calculation matches the joint design point. Consistency is achieved, thereby determining the wave frequency spectrum model parameters and generating extreme wave spectral density functions that satisfy the co-occurrence period constraint. curve.

[0053] Beneficial effects

[0054] This invention provides a method for extrapolating extreme wave spectra based on the co-occurrence return periods of wave elements. This method combines edge extremum modeling of wave elements with Copula joint distribution modeling. Considering the dependence between significant wave height and spectral peak period, it solves for co-occurrence contour lines through co-occurrence return period constraints and determines the joint design point using the maximum probability density criterion, avoiding the problem of unreasonable design sea state combinations caused by traditional single-variable design value combinations. Simultaneously, it combines the joint design point with the construction of parameterized wave frequency spectra and the inverse calculation of zero-order spectral moment energy matching, achieving self-consistent determination of spectral scale parameters and consistency verification of significant wave height, thereby obtaining the extreme wave spectral density function that satisfies the co-occurrence return period constraints. This method, which utilizes wave curves, boasts advantages such as high result rationality, strong stability, and good engineering applicability. Based on this method, extreme sea state spectra consistent with the target co-occurrence return period can be provided for engineering numerical simulations, thereby improving the reliability of wave load calculations and structural response assessments, and providing important references for the design, construction, and safety assessment of coastal and marine engineering projects. Furthermore, applying this method to long-term wave data from different sites or sea areas can form a regional co-occurrence return period extreme wave spectrum estimation system, providing technical support for coastal disaster prevention and mitigation, marine resource development, and maritime activity safety assurance. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0056] Figure 1 This is a schematic diagram of the extreme wave spectrum estimation method based on the co-occurrence and return periods of wave elements according to the present invention.

[0057] Figure 2 The figure shows the fitting and verification diagrams of the effective wave height and the periodic edge distribution of the spectral peak in the embodiment; where (a) is the effective wave height. The empirical cumulative distribution and the fitting curve of the generalized extreme value distribution (GEV), (b) is the significant wave height. The PP plot test, also called the probability-probability plot test, (c) is the spectral peak period. The empirical cumulative distribution and the fitting curve of the generalized extreme value distribution (GEV) are shown, and (d) is the spectral peak period. The PP plot test, also known as the probability-probability plot test;

[0058] Figure 3 The following is a diagnostic diagram of the joint distribution model of effective wave height and optimal Copula peak period in the embodiment; where (a) is the CDF curve of the joint distribution model of effective wave height and optimal Copula peak period, and (b) is the PP diagram test of the joint distribution model of effective wave height and optimal Copula peak period.

[0059] Figure 4 This is a schematic diagram illustrating the determination of the co-occurrence contour lines and AND-50 year joint design points in the embodiment;

[0060] Figure 5 The extreme wave spectral density function curves that satisfy the co-occurrence return period constraint are shown in the example.

[0061] Figure 6 This is a schematic diagram showing the location of the combination points of the traditional single-variable 50-year design value in the equipotential contour field in the comparative example.

[0062] Figure 7 The extreme wave spectral density function curves are calculated using the traditional single-variable 50-year design value combination method in the comparative example. Detailed Implementation

[0063] 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.

[0064] Example 1

[0065] This invention discloses a method for estimating extreme wave spectra based on the co-occurrence and return periods of wave elements. Figure 1 This is a flowchart illustrating this embodiment. For ease of explanation, this embodiment uses the Yellow Sea and Bohai Sea deep-sea point (longitude approximately...) latitude approximately Taking long-term wave data as an example, this embodiment uses annual extreme value samples from 42 valid years (1979-2020) to perform extrapolation and explanation (this does not limit the scope of protection of this invention). This embodiment includes the following steps:

[0066] S1. Obtain long-term time-series data on significant wave height and spectral peak period at deep-sea points in the Yellow and Bohai Seas, construct annual extreme value sample pairs, and analyze their extreme value attributes. Among these, wave elements include significant wave height. With spectral peak period Marginal distribution fitting is performed on the annual extreme value sample pairs for both significant wave height and spectral peak period, mapping the annual extreme value sample pairs to a unified probability space. In this embodiment, the method of retaining the first three maxima each year is used to construct the annual extreme value sample pairs, and the three extreme values ​​come from different wave processes; therefore, the number of sample pairs per year is... Based on 42 valid years, the total number of sample pairs is The corresponding annual event incidence rate is:

[0067] .

[0068] To each and The extreme value samples were fitted with a marginal distribution. In this embodiment, both were fitted with the GEV distribution. The marginal distribution fitting and test results are as follows: Figure 2 As shown, (a) displays the significant wave height. H s A comparison of the empirical cumulative distribution and the fitted generalized extreme value distribution. The GEV distribution captures this well. (a) Tail features suitable for extreme wave height analysis. (b) Used to test the GEV distribution's effect on... The better the fit of the GEV distribution is indicated by points closer to the diagonal in the graph. Overall, most points are distributed along the diagonal, suggesting that the GEV distribution is more closely aligned with the diagonal. The fitting effect is good. (c) shows the spectral peak period. The empirical cumulative distribution and the fitting results of the GEV distribution are shown. The GEV distribution is also used to describe... The extreme behavior is consistent with the empirical distribution trend. (d) Used to evaluate the GEV distribution's influence on... The fitting results are generally acceptable, with the points roughly distributed along the diagonal.

[0069] The samples are mapped to a unified probability space. The specific operation in this embodiment is as follows: Let the first... The annual extreme value sample pairs are (in The probability value is calculated using the following formula:

[0070] ,

[0071] The resulting probability space sample sequence This serves as the data foundation for subsequently constructing a joint distribution model.

[0072] S2. Based on Copula theory, the interdependent structure among wave elements is quantitatively characterized, a joint distribution model of effective wave height and spectral peak period is established, and the candidate Copula models are selected according to the AIC information criterion to obtain the optimal joint distribution model.

[0073] In this embodiment, the step specifically includes the following:

[0074] (1) Constructing a candidate model library: Selecting various Copula functions suitable for describing the interdependence of wave elements as candidate models. In this embodiment, the Elliptic Copula family (including Gaussian Copula and t-Copula) and the Archimedes Copula family (including Frank, Gumbel, and Clayton Copula) were selected.

[0075] (2) Parameter estimation: using the probability space sample sequence obtained in step S1 The maximum likelihood estimation (MLE) method was used to evaluate the model parameters of each candidate Copula function. Estimate the parameters. That is, by solving the following formula, obtain the parameter estimate that maximizes the probability of the sample occurring. :

[0076] ,

[0077] in, For the total number of sample pairs, is the Copula density function.

[0078] (3) Model Selection: The goodness of fit of each candidate model was evaluated based on the Akaike Information Content Criterion (AIC). The AIC calculation formula is as follows:

[0079] ,

[0080] in, The number of model parameters, This represents the corresponding maximum log-likelihood function value. A smaller AIC value indicates that the model achieves a better balance between fitting accuracy and complexity.

[0081] In this embodiment, the AIC calculation results for each candidate model are as follows: Gaussian = -27.51, t = -25.51, Frank = -28.99, Gumbel = -22.97, Clayton = -14.30. Based on the minimum AIC criterion, FrankCopula is determined to be the optimal joint distribution model. Joint distribution diagnostic results such as Figure 3As shown. This PP plot is used to test the overall goodness of fit of the joint distribution model constructed in (a). The principle is: if the model is completely correct, then each observation data is compared with... After substituting the theoretical joint cumulative distribution function, the resulting probability values ​​should follow a uniform distribution. In the graph, the horizontal axis represents the empirical cumulative probability of these transformed values, and the vertical axis represents the cumulative probability of the theoretical uniform distribution. All scatter points are closely distributed around the diagonal, indicating that the model fits well and accurately captures the desired outcome. and The joint probability characteristics between them.

[0082] S3. Determine the joint exceedance probability based on the definition of co-occurrence return period, solve the co-occurrence contour lines under the optimal joint distribution model, and determine the joint design point based on the maximum probability density criterion.

[0083] This embodiment preferably includes the following steps:

[0084] S31. Set the return period of the target co-occurrence as... In 2018, the annual event rate was [missing information]. The probability of simultaneously exceeding the target time / year is determined as follows:

[0085] ，

[0086] In this embodiment, the following is taken ,and ,therefore .

[0087] S32, Order and The marginal distribution functions of the effective wave height and spectral peak period obtained in step S1 are respectively, for any wave element variable pair. Perform probability transformation

[0088] ,

[0089] in, Design variables for effective wave height. Design variables for spectral peak periods; These are the cumulative probability values ​​calculated using the marginal distribution function in step S1.

[0090] According to Copula theory, let the optimal Copula function obtained in step S2 be... Then the joint transcendence probability is... satisfy:

[0091] .

[0092] S33. Solve the following equation to obtain the co-occurring contour lines:

[0093] ,

[0094] And calculate the joint probability density on the co-occurrence contour lines:

[0095] ,

[0096] in and These are the marginal probability density functions, Let be the density function of the optimal Copula model in S2, i.e.:

[0097] ,

[0098] Based on the maximum probability density criterion, select the isopleths along the same occurrence line. The point with the maximum value is taken as the joint design point, denoted as . In this embodiment, the calculated AND-50 year joint design point is:

[0099] ,

[0100] Its meaning is: under the condition of approximately 3 events per year, and At the same time, joint events exceeding this threshold occur on average once every 50 years. Figure 4 The diagram shows the location relationship between multiple co-occurring contour lines and the AND-50 year contour lines and the joint design points.

[0101] S4. Based on the joint design point, select a parameterized wave frequency spectrum model, calculate the spectral scale parameters by matching the zero-order spectral moment energy, and complete the effective wave height consistency check, thereby deriving the extreme wave spectral density function curve that satisfies the co-occurrence and return period constraint.

[0102] In this preferred embodiment, step S4 includes the following steps:

[0103] S41, Based on joint design points Determine the peak frequencies of the parameterized wave frequency spectrum model;

[0104] ;

[0105] S42. Construct the parameterized wave frequency spectral density function. When the parameterized wave frequency spectrum model is the JONSWAP spectrum, its expression is:

[0106] ,

[0107] in It is the acceleration due to gravity. For spectral scale parameters, The peak enhancement factor (in this embodiment, a commonly used empirical value in engineering is used) is used. ), For spectral width parameters, and in a segmented form: when hour ,when hour .

[0108] S43. Calculate the zeroth order spectral moment

[0109] ;

[0110] And based on For spectral scale parameters Perform energy matching back calculation to ensure that the effective wave height obtained from the spectral integral back calculation matches the joint design point. Consistency is achieved, thereby determining the wave frequency spectrum model parameters and generating extreme wave spectral density function curves that satisfy the co-occurrence return period constraint. .

[0111] In this embodiment, the result is obtained by spectral integral back calculation. This verified the consistency of the spectral energy; the calculated values ​​were... Curves Figure 5 As shown.

[0112] Figure 5 The extreme wave spectrum shown satisfies the following: its spectral energy (characterized by the zeroth spectral moment) and the effective wave height at the joint design point are... Consistent; its spectral peak positions are determined by the joint design point spectral peak period. The only certainty is that the spectral shape exhibits a significant peak enhancement characteristic near the spectral peak. ), and exhibits typical rapid attenuation characteristics at high frequencies. Because and The joint design point is obtained from the joint distribution under the constraint of co-occurrence and return periods. Figure 5 The results shown correspond to the 50-year return period combined extreme sea state spectrum, avoiding the problems of over-conservatism and spectrum deviation caused by simply combining the design values ​​of two single-variable return periods.

[0113] Comparative Example 1

[0114] To illustrate the beneficial effects of the method of the present invention, a comparative calculation process with the traditional single-variable combination method is given below.

[0115] Traditional methods, when extracting extreme value samples, no longer retain the pairing relationship between the spectral peak period and the annual extreme value wave height. Instead, they construct separate annual extreme value sequences for the effective wave height and the spectral peak period, perform GEV fitting on each, and take the quantile value of their respective 50-year return periods as the design values. In this comparative example, we obtain:

[0116] ;

[0117] Furthermore, to assess whether this traditional combination point satisfies the 50-year co-occurrence return period constraint in the sense of joint probability, the following will be performed: Substituting the joint distribution model established in step S2 of Example 1, calculate its co-occurrence transcendence probability:

[0118] ,

[0119] And based on this, the corresponding co-occurrence recurrence period is obtained:

[0120] ,

[0121] Calculations show that the co-occurrence return period corresponding to the traditional combination point is approximately 11,320 years, much longer than 50 years. This result indicates that simply combining two univariate 50-year return period design values ​​is not equivalent to a 50-year joint extreme sea state in the co-occurrence sense. Figure 6 The positional relationship between the AND-50 year joint design point and the traditional combination point in the co-occurrence contour field is shown. It can be seen that the traditional combination point falls near the 10,000-year-level contour line, thus intuitively indicating that its corresponding co-occurrence recurrence period is much greater than the 50-year target.

[0122] In terms of spectral extrapolation, the aforementioned method is adopted. and As wave element parameters, the same JONSWAP spectral model as in Example 1 was selected, and the same spectral peak enhancement factor was used. By determining the spectral scale parameters through zero-order spectral moment energy matching, the extreme wave spectral density function curve calculated by traditional methods is obtained, such as... Figure 7 As shown.

[0123] Joint design points with Example 1 Compared to traditional methods, the results obtained separately and All are significantly larger, and due to Determined spectral peak frequencies The significant reduction leads to a concentration of spectral energy in the low-frequency band and an abnormally large increase in the proportion of long-period components; at the same time, due to the larger effective wave height, according to The corresponding total spectral energy also increases, easily leading to overly conservative and physically unreasonable extreme wave spectra. In contrast, the method of this invention determines the joint design point and performs energy matching by constraining the co-occurrence return period, thus obtaining extreme wave spectrum results consistent with the target co-occurrence return period. Figure 5 This approach better aligns with the probability constraints of joint extreme events, demonstrating greater rationality and engineering applicability.

[0124] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for extrapolating extreme wave spectra based on the co-occurrence and return periods of wave elements, characterized in that, Includes the following steps: S1. Obtain long-term time-series data of wave elements at a certain station, construct annual extreme value sample pairs, and analyze the extreme value attributes of the annual extreme value sample pairs. Among them, wave elements include significant wave height. With spectral peak period Marginal distribution fitting is performed on the annual extreme value sample pairs of effective wave height and spectral peak period respectively, and the annual extreme value sample pairs are mapped to a unified probability space. S2. Based on Copula theory, the interdependent structure between wave elements is quantitatively characterized, a joint distribution model of effective wave height and spectral peak period is established, and the candidate Copula models are selected according to the AIC information criterion to obtain the optimal joint distribution model. S3. Determine the joint exceedance probability based on the definition of co-occurrence return period, solve the co-occurrence contour lines under the optimal joint distribution model, and determine the joint design point based on the maximum probability density criterion. S4. Based on the joint design point, a parametric wave frequency spectrum model is selected. The spectral scale parameters are inversely calculated through zero-order spectral moment energy matching, and the effective wave height consistency check is completed. Then, the extreme wave spectral density function that satisfies the co-occurrence and return period constraint is calculated. curve.

2. The method for extrapolating extreme wave spectra based on the co-occurrence and return periods of wave elements according to claim 1, characterized in that, The annual extreme value sample pairs mentioned in S1 are selected annually. Each independent wave process corresponds to Sample composition, in which And record the annual event occurrence rate as Once per year.

3. The method for extrapolating extreme wave spectra based on the co-occurrence and return periods of wave elements according to claim 1, characterized in that, The mapping of annual extreme value sample pairs to a unified probability space as described in S1 includes the following steps: Record No. The annual extreme value sample pairs are ,in The corresponding probability value is calculated using the following formula: ， The resulting probability space sample sequence .

4. The method for extrapolating extreme wave spectra based on the co-occurrence and return periods of wave elements according to claim 1, characterized in that, S2 includes the following steps: S21. Construct a candidate model library: Select various Copula functions suitable for describing the interdependence of wave elements as candidate models; S22. Parameter estimation: Using the probability space sample sequence obtained in step S1 The maximum likelihood estimation method was used to evaluate the model parameters of each candidate Copula function. Make an estimate; S23. Model Optimization: The goodness of fit of each candidate model is evaluated based on the Akaike Information Content Criterion.

5. The extreme wave spectrum estimation method based on the co-occurrence and return periods of wave elements according to claim 4, characterized in that, S22 is the parameter estimate that maximizes the probability of the sample appearing. The calculation formula is: ， in, For the total number of sample pairs, is the Copula density function.

6. The method for extrapolating extreme wave spectra based on the co-occurrence and return periods of wave elements according to claim 4, characterized in that, The formula for calculating the S23 Akaike Information Content Criterion is as follows: ， in, The number of model parameters, The value of AIC corresponds to the maximum log-likelihood function. The smaller the AIC value, the better the model achieves a balance between fitting accuracy and complexity.

7. The method for extrapolating extreme wave spectra based on the co-occurrence and return periods of wave elements according to any one of claims 1-6, characterized in that, S3 includes the following steps: S31. Set the return period of the target co-occurrence as... In 2018, the annual event rate was [missing information]. Once per year, determine the probability of simultaneous and joint exceeding the target; S32, Order and The marginal distribution functions of the effective wave height and spectral peak period obtained in step S1 are respectively, for any wave element variable pair. Perform probability transformation; S33. Solve to obtain the co-occurring contour lines.

8. The method for extrapolating extreme wave spectra based on the co-occurrence and return periods of wave elements according to claim 7, characterized in that, The probability of co-occurrence and joint transcendence of the target as stated in S31 is: ； The probability transformation formula described in S32 is: ， in, Design variables for effective wave height. Design variables for spectral peak periods; These are the cumulative probability values ​​calculated using the marginal distribution function in step S1; According to Copula theory, let the optimal Copula function obtained in step S2 be... Then the joint transcendence probability is... satisfy: ； S33. Solve the following equation to obtain the co-occurring contour lines: ， Calculate the joint probability density on the co-occurrence contour lines: ， in and These are the marginal probability density functions, Let be the density function of the optimal Copula model in S2, i.e. Based on the maximum probability density criterion, select the co-occurrence contour lines that make The point with the maximum value is taken as the joint design point, denoted as . .

9. The method for extrapolating extreme wave spectra based on the co-occurrence and return periods of wave elements according to any one of claims 1-6, characterized in that, S4 includes the following steps: S41. Determine the peak frequency of the parametric wave frequency spectrum model based on the joint design point: ， S42. Constructing a parameterized wave frequency spectral density function When the parameterized wave frequency spectrum model is the JONSWAP spectrum, The expression is: ， in It is the acceleration due to gravity. For spectral scale parameters, As the peak enhancement factor, For spectral width parameters, and in a segmented form: when hour ,when hour ; S43. Calculate the zeroth order spectral moment: ， in accordance with For spectral scale parameters Perform energy matching back calculation to ensure that the effective wave height obtained from the spectral integral back calculation matches the joint design point. Consistency is achieved, thereby determining the wave frequency spectrum model parameters and generating extreme wave spectral density functions that satisfy the co-occurrence period constraint. curve.

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