An efficient sampling method for random sea state Copula probability model considering physical constraints

Abstract

The present invention discloses an efficient sampling method for a random sea state Copula probability model considering physical constraints, which belongs to the technical field of probability modeling and evaluation of wave loads in marine engineering, and can be applied to random wave probability modeling and analysis of marine structures such as marine oil and gas platforms, marine photovoltaic platforms, and offshore wind turbines. Specifically, on the basis of the Copula method of joint probability modeling of significant wave height and wave spectrum peak period, the physical background of wave breaking is introduced, and the physical constraint is considered in the random sampling process of significant wave height and spectrum peak period, so as to obtain more reasonable sampling results. The method proposed in the present invention can not only consider the correlation between significant wave height and spectrum peak period when sampling, but also consider the physical constraint between the two parameters caused by wave breaking, so as to obtain more reasonable random sea state sampling results, and the method is more efficient.

Description

Technical Field

[0001] The present invention belongs to the technical field of probabilistic modeling and evaluation of ocean engineering wave loads, and in particular relates to an efficient sampling method for a random sea condition Copula probability model considering physical constraints. Background Art

[0002] Wave loads are one of the primary environmental loads on marine structures, such as offshore oil and gas platforms, photovoltaic platforms, and offshore wind turbines, significantly impacting their long-term service life and safety. Accurately assessing wave loads on marine structures requires analyzing and predicting the various sea conditions they may experience during their service life. In practice, stable sea conditions are typically described using two parameters: significant wave height and spectral peak period. Due to the complexity and variability of the marine environment, the long-term sea conditions at a site exhibit significant randomness, making significant wave height and spectral peak period two random variables. Furthermore, due to the physical mechanisms of wave generation, these two parameters exhibit complex correlations. Therefore, to adequately describe the long-term sea conditions at a site, it is necessary to derive a joint probability distribution of significant wave height and spectral peak period based on long-term wave observation data. Furthermore, due to the physical mechanisms of wave development and propagation, there is a certain constraint between wave height and wave period. For a given wave height, the wave period typically has a lower limit; otherwise, the wave will break. If this physical background is ignored and sampling is performed directly based on the joint probability model of wave height and wave period, sea conditions that do not exist in reality may be obtained, which is not conducive to the accurate assessment of wave loads on marine structures.

[0003] Although there has been considerable research on the joint probability modeling of significant wave height and spectral peak period, for example, conditional probability modeling and Copula models can be used to obtain the joint probability distribution of these two parameters, the physical constraints between these two parameters are rarely considered. In existing probabilistic modeling studies that consider the physical constraints of these two parameters, discriminant screening methods are directly used to obtain random sea state samples that meet the conditions, resulting in low sampling efficiency. Therefore, how to reasonably and efficiently extract random sea state samples that meet the physical constraints based on the Copula model of the joint probability distribution of significant wave height and spectral peak period is the technical problem to be solved by the present invention. Summary of the Invention

[0004] In response to the above problems, the present invention proposes an efficient sampling method for random sea conditions that takes physical constraints into account, which addresses the shortcomings of existing random sea condition probability sampling. Based on the Copula method for joint probability modeling of significant wave height and spectral peak period, this method incorporates the physical constraint inequality relationship between these two parameters into the sampling process. By correcting the conditional probability distribution of the spectral peak period and then combining it with probability transformation, it can efficiently obtain random samples of significant wave height and spectral peak period that meet physical constraints. This method can improve the accuracy and efficiency of random sea condition probability sampling, avoid sampling sea conditions that do not exist in reality, facilitate accurate and efficient assessment of wave loads on marine structures, and has important engineering application value.

[0005] To achieve the above object, the present invention adopts the following technical solutions:

[0006] An efficient sampling method for a random sea state Copula probability model considering physical constraints includes the following steps:

[0007] (1) Estimation of marginal probability distributions and copula correlation structures for significant wave height and spectral peak period

[0008] (1.1) Based on long-term wave observation data, the common probability distribution model is used to estimate the significant wave height H s and spectrum peak period T p The marginal probability distribution model of ;

[0009] (1.2) Based on the long-term wave observation data, the common binary Copula function model is used to estimate H s and T p The probabilistic correlation structure between

[0010] (2) Obtaining the inequality relationship between the significant wave height and the probability distribution function value of the spectrum peak period

[0011] Select the constraint relationship that describes the significant wave height and spectral peak period caused by wave breaking, combine it with the marginal probability distribution function of significant wave height and spectral peak period obtained in step (1), and use the inverse transformation and forward transformation of the probability function to obtain the inequality relationship between the probability distribution function values ​​of significant wave height and spectral peak period;

[0012] (3) Sampling to obtain random sea state samples that meet the physical constraints of significant wave height and spectral peak period

[0013] (3.1) The interval is randomly drawn according to uniform distribution , and remember , That is the effective wave height H s The probability distribution function value of ; then based on the H obtained in step (1) s and Tp The marginal probability distribution of H obtained in step (2) s and T p Inequality relationships between probability distribution function values, calculation The minimum value of the corresponding spectral peak period probability distribution function ; Then, calculate according to the Copula function result obtained in step (1) under conditions The conditional probability distribution function value of ;

[0014] (3.2) The interval is randomly drawn according to uniform distribution , is the conditional probability distribution function value of the spectrum peak period after considering physical constraints; then calculate The corresponding corrected value of the conditional probability distribution function of the spectrum peak period when physical constraints are not considered , and remember ; Then, according to the Copula function result obtained in step (1), solve , That is, the probability distribution function value of the spectrum peak period that meets the physical constraints;

[0015] (3.3) According to the obtained H s and T p The marginal probability distribution function and 、 , the inverse transformation of the probability distribution function is used to calculate the sample values ​​of the significant wave height and spectrum peak period after considering the physical constraints, that is, 、 ;

[0016] (3.4) Multiple times Random interval generation and , and following the above steps, multiple sample values ​​of significant wave height and spectrum peak period can be obtained, that is, multiple random sea state samples that meet the physical constraints can be obtained.

[0017] Preferably, the probability distribution model in step (1.1) adopts log normal distribution, Weibull distribution or Gamma distribution.

[0018] Preferably, for convenience in step (1.1), the effective wave height H is recorded as s and spectrum peak period T p The marginal probability distribution function of and ;in s represents the value of the significant wave height random variable, P Represents the value of the spectrum peak period random variable.

[0019] Preferably, the binary Copula function model in step (1.2) adopts Gaussian Copula, Frank Copula, Clayton Copula or Gumbel Copula.

[0020] Preferably, the description of the significant wave height H obtained in step (1.2) is recorded as s and spectrum peak period T p The optimal Copula function for the probability correlation structure between .

[0021] Preferably, in step (2), the effective wave height H s and spectrum peak period T p The constraint relationship between

[0022] (1)

[0023] According to the H obtained in step (1) s and T p The marginal probability distribution function of , combined with the inverse transformation of the probability distribution function, formula (1) can be further written as

[0024] (2)

[0025] Where, and They are and The inverse function of and H s and T p The probability distribution function value of 、 ;

[0026] On both sides of inequality (2) Transformation, there

[0027] (3)

[0028] Equation (3) is the sea state (H s , T p ) Medium effective wave height H s and spectrum peak period T p The corresponding probability distribution function value 、 The inequality relationship that should be satisfied.

[0029] Preferably, the step (3.1) is specifically as follows: T is considered when physical constraints are not considered and when physical constraints are considered p The conditional probability density functions are and According to the basic principles of probability theory,

[0030] (4)

[0031] Where, for The minimum value of the corresponding spectrum peak period is to ensure that no wave breaking occurs, that is, ;

[0032] The conditional probability distribution functions of the peak period without and with physical constraints are: and , then

[0033] (5)

[0034] According to the basic theory of the Copula method, the expression of the conditional probability distribution function of the spectrum peak period with respect to the significant wave height is:

[0035] (6)

[0036] Where, represents the partial derivative function of the Copula function, which has an analytical expression. Therefore, Equation (5) can be further written as

[0037] (7)

[0038] Where, for The corresponding probability distribution function value is also The minimum value of the probability distribution function of the corresponding spectrum peak period is used to ensure that no wave breaking occurs. According to formula (3),

[0039] (8).

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] The present invention proposes an efficient sampling method for a random sea state Copula probability model that considers physical constraints. First, the marginal probability distributions of significant wave height and spectral peak period, as well as the Copula correlation structure between the two, are estimated based on wave observation data. Then, the constraints between the significant wave height and spectral peak period caused by the physical background of wave breaking are introduced, and the inequality relationship between the probability distribution functions of significant wave height and spectral peak period is obtained in combination with the marginal probability distribution model obtained in step (1). Finally, based on the inequality relationship between the probability distribution functions of significant wave height and spectral peak period obtained in step (2), the conditional probability distribution function value of the spectral peak period is corrected, and then the marginal probability distribution functions of significant wave height and spectral peak period in step (1) are combined to obtain random sea state samples that meet the physical constraints. The method proposed in the present invention can ensure that the sampled significant wave height and spectral peak period samples all meet the physical constraints, the random sea state samples obtained all exist in reality, and the sampling efficiency is high, which is conducive to the accurate and efficient assessment of wave loads on marine structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is the implementation process of the efficient sampling method of the random sea state Copula probability model considering physical constraints proposed by the present invention;

[0043] Figure 2 are the wave parameter observation data and wave breaking physical constraints used in the case;

[0044] Figure 3 is the marginal probability distribution modeling result of significant wave height and spectrum peak period;

[0045] Figure 4 It is the result of Copula modeling of the probabilistic correlation structure between significant wave height and spectral peak period;

[0046] Figure 5 It is the scatter plot of the probability distribution function values ​​of significant wave height and spectrum peak period and the constraint relationship that should be satisfied;

[0047] Figure 6 The samples of effective wave height and spectrum peak period obtained by different sampling methods and the physical constraints that should be met;

[0048] Figure 7 It is a comparison between the original observation data and the random sea state samples obtained by sampling using the method of the present invention;

[0049] Figure 8 It is a comparison of the marginal empirical probability distribution functions of the original data and the sampling results. DETAILED DESCRIPTION

[0050] In order to further illustrate the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the specific implementation methods, structures, features and effects of the present invention are described in detail below in conjunction with the accompanying drawings and preferred embodiments.

[0051] like Figure 1 As shown, the present invention provides an efficient sampling method for a random sea state Copula probability model considering physical constraints, which specifically includes the following steps:

[0052] (1) Estimation of marginal probability distribution and Copula correlation structure of significant wave height and spectral peak period

[0053] Based on the long-term wave observation data at the site, common probability distribution models such as lognormal distribution, Weibull distribution, and Gamma distribution are used to estimate the significant wave height H s and spectrum peak period T p The marginal probability distribution model of . For convenience, we denote H s and T p The marginal probability distribution function of and .

[0054] Then, based on the observed data, common binary Copula function models such as Gaussian Copula, Frank Copula, Clayton Copula, Gumbel Copula, etc. are used to estimate H s and T p The probability correlation structure between them. Let the description H s and T p The optimal Copula function for the probability correlation structure between .

[0055] (2) Obtain the inequality relationship between the significant wave height and the probability distribution function value of the spectrum peak period

[0056] There have been many studies on the criteria for determining wave breaking, such as the Iribarren criterion and the Goda criterion. The influence of the physical background of wave breaking on the significant wave height and spectral peak period is reflected in the fact that for a given significant wave height, there is a lower limit for the spectral peak period, otherwise the wave will break and disappear. Therefore, the constraint relationship between the significant wave height and spectral peak period caused by wave breaking can be expressed as the following inequality:

[0057] (1)

[0058] According to the H obtained in step 1 s and T pThe marginal probability distribution function of , combined with the inverse transformation of the probability distribution function, formula (1) can be further written as

[0059] (2)

[0060] Where, and They are and The inverse function of and H s and T p The probability distribution function value of 、 .

[0061] On both sides of inequality (2) Transformation, there

[0062] (3)

[0063] Equation (3) is the sea state (H s , T p ) Medium effective wave height H s and spectrum peak period T p The corresponding probability distribution function value 、 The inequality relationship that should be satisfied.

[0064] (3) Sampling to obtain random sea state samples that meet the physical constraints of significant wave height and spectral peak period

[0065] The sampling of binary random variables based on Copula needs to be based on the conditional probability distribution of one of the variables. p The conditional probability density functions are and According to the basic principles of probability theory,

[0066] (4)

[0067] Where, for The minimum value of the corresponding spectrum peak period is to ensure that no wave breaking occurs, that is, .

[0068] The conditional probability distribution functions of the peak period without and with physical constraints are: and , then

[0069] (5)

[0070] According to the basic theory of the Copula method, the expression of the conditional probability distribution function of the spectrum peak period with respect to the significant wave height is:

[0071] (6)

[0072] Where, represents the partial derivative function of the Copula function and has an analytical expression. Therefore, Equation (5) can be further written as

[0073] (7)

[0074] Where, for The corresponding probability distribution function value is also The minimum value of the probability distribution function of the corresponding spectrum peak period is used to ensure that no wave breaking occurs. According to formula (3),

[0075] (8)

[0076] Therefore, the sampling steps after considering physical constraints are as follows:

[0077] (a) In The interval is randomly drawn according to uniform distribution , and remember , That is the effective wave height H s The probability distribution function value of . Then based on the H obtained in step 1 s and T p The marginal probability distribution of is calculated according to formula (8) , and then calculate according to the Copula function obtained in step 1 ;

[0078] (b) In The interval is randomly drawn according to uniform distribution , and there are Then, we can get and record the value of , so we can get , That is, the spectrum peak period T after considering physical constraints p The probability distribution function value of .

[0079] (c) According to the H obtained in step 1 s and T p The marginal probability distribution function of is calculated by inverse transformation to obtain the sample values ​​of the significant wave height and spectrum peak period after considering the physical constraints, that is, 、 .

[0080] Example:

[0081] Taking the observation data of the international ocean observation station FINO1 as an example, the efficient sampling method of the random sea state Copula probability model considering physical constraints proposed in this invention is used to carry out long-term random sea state probability modeling and sampling analysis of the observation station. The long-term wave data of the observation station can be downloaded from its official website. In this case, the 8-year observation data of the effective wave height and spectral peak period of the observation station are used. The data is the mean of 30-minute wave observation data, and each data represents a stable sea condition. Since the wave data has short-term correlation, which affects the accuracy of probability modeling, one data is randomly selected from the weekly data for analysis, totaling 416 data. In this case, the Goda wave breaking criterion is used to obtain the physical constraint expression between the effective wave height and the spectral peak period, that is,

[0082] ,in For water depth, is the slope of the seabed, is the correction factor. Figure 2 This is the scatter plot of the 416 data points and H s With T p The constraint relationship curve between them. It can be seen that H s With T p It has significant randomness and complex correlation, and the observed data all meet the physical constraints, which illustrates the rationality of the physical constraints adopted.

[0083] Based on the above observation data, the probability distribution of the significant wave height and the spectral peak period edge are estimated respectively. The alternative distribution models include the commonly used lognormal distribution, Weibull distribution and Gamma distribution. The optimal distribution model identified is the lognormal distribution. The results are as follows: Figure 3 Then, the probability correlation structure between the significant wave height and the spectral peak period is estimated. The candidate Copula models include the commonly used Frank Copula, Gaussian Copula, Gumbel Copula, Clayton Copula and Student's t Copula. The optimal model identified is Student's t Copula. The density function contour plot is compared with the scatter plot of the probability distribution function (CDF) value of the observed data. Figure 4 shown.

[0084] Based on the above obtained H s and T p The marginal probability distribution results and the physical constraint relationship between the two parameters can be obtained by inverse transformation and forward transformation of the probability function. s and T pThe inequality relationship satisfied between the probability distribution function values. The CDF scatter plot of the above 416 observation data and the obtained inequality constraint curve are as follows Figure 5 As shown. It can be seen that the observed data H s With T p The probability distribution function values ​​of all satisfy the inequality relationship, which shows the rationality of the results.

[0085] On the basis of the above, the sampling method proposed in this invention was used to randomly select 1000 sea condition samples. The results are as follows: Figure 6 As shown in (a). In contrast, the traditional method does not consider H in the sampling process. s With T p , 1000 random sea state samples were obtained, and the results are shown in 6(b). It can be seen that if H is not reasonably considered in the sampling process, s With T p The physical constraints between them will result in sea conditions that do not exist in reality, which will have an adverse impact on the subsequent wave load assessment of marine structures.

[0086] In order to further verify whether the probability distribution characteristics of the sampling results are consistent with the original data, the method of the present invention is used to randomly generate the same number of sea state samples as the original data and compare them with the original data. The results are as follows: Figure 7 As shown. It can be seen that the random sampling results are consistent with the probability distribution characteristics of the original data. Further, the empirical marginal probability distribution functions of the original data and the sampled data are estimated and compared. The results are shown in Figure 8 As shown. It can be seen that the probability distribution of the sampled data is in good agreement with the original data, indicating that the sea state samples obtained by the method of the present invention can accurately reflect the random characteristics of the original sea state data. In addition, the Spearman rank correlation coefficient between the significant wave height and the spectral peak period in the data was quantitatively analyzed. The calculated results of the Spearman rank correlation coefficient of the sampled data and the original data were 0.437 and 0.425, respectively. It can be seen that the correlation between the significant wave height and the spectral peak period obtained by the method of the present invention is very close to that of the original data, indicating that the random sea state sampled by the method of the present invention can accurately reflect the correlation characteristics between wave parameters.

[0087] The above results show that the random sea state samples obtained by the efficient sampling method of the random sea state Copula probability model considering physical constraints proposed in this invention can effectively reflect the randomness, correlation and physical constraints of sea state elements, and have important engineering application value for accurately evaluating the wave loads on marine structures.

Claims

1. An efficient sampling method for a random sea state Copula probability model considering physical constraints, characterized by: The following steps are involved: (1) Estimation of marginal probability distributions and copula correlation structures for significant wave height and spectral peak period (1.1) Based on long-term wave observation data, the common probability distribution model is used to estimate the significant wave height H s and spectrum peak period T p The marginal probability distribution model of ; (1.2) Based on the long-term wave observation data, the common binary Copula function model is used to estimate H s and T p The probabilistic correlation structure between (2) Obtaining the inequality relationship between the significant wave height and the probability distribution function value of the spectrum peak period Select the constraint relationship that describes the significant wave height and spectral peak period caused by wave breaking, combine it with the marginal probability distribution function of significant wave height and spectral peak period obtained in step (1), and use the inverse transformation and forward transformation of the probability function to obtain the inequality relationship between the probability distribution function values ​​of significant wave height and spectral peak period; (3) Sampling to obtain random sea state samples that meet the physical constraints of significant wave height and spectral peak period (3.1) The interval is randomly drawn according to uniform distribution , and remember , That is the effective wave height H s The probability distribution function value of ; then based on the H obtained in step (1) s and T p The marginal probability distribution of H obtained in step (2) s and T p Inequality relationships between probability distribution function values, calculation The minimum value of the corresponding spectral peak period probability distribution function ; Then, calculate according to the Copula result obtained in step (1) under conditions The conditional probability distribution function value of ; (3.2) The interval is randomly drawn according to uniform distribution , is the conditional probability distribution function value of the spectrum peak period after considering physical constraints; then calculate The corresponding corrected value of the conditional probability distribution function of the spectrum peak period when physical constraints are not considered , and remember ; Then, according to the Copula function result obtained in step (1), solve , That is, the probability distribution function value of the spectrum peak period that meets the physical constraints; (3.3) According to the obtained H s and T p The marginal probability distribution function and 、 , the inverse transformation of the probability distribution function is used to calculate the sample values ​​of the significant wave height and spectrum peak period after considering the physical constraints, that is, 、 ; (3.4) Multiple times Random interval generation and , and following the above steps, multiple sample values ​​of significant wave height and spectrum peak period can be obtained, that is, multiple random sea state samples that meet the physical constraints can be obtained.

2. The efficient sampling method of the random sea state Copula probability model considering physical constraints according to claim 1 is characterized by: The probability distribution model in the step (1.1) adopts log normal distribution, Weibull distribution or Gamma distribution.

3. The efficient sampling method of the random sea state Copula probability model considering physical constraints according to claim 1 is characterized by: For convenience in the above step (1.1), the effective wave height H is recorded as s and spectrum peak period T p The marginal probability distribution function of and ;in s represents the value of the significant wave height random variable, P Represents the value of the spectrum peak period random variable.

4. The efficient sampling method for a random sea state Copula probability model considering physical constraints according to claim 1, characterized in that: The binary Copula function model in the step (1.2) adopts Gaussian Copula, Frank Copula, Clayton Copula or Gumbel Copula.

5. The efficient sampling method for a random sea state Copula probability model considering physical constraints according to claim 3 is characterized by: The description of the significant wave height H obtained in step (1.2) is s and spectrum peak period T p The optimal Copula function for the probability correlation structure between .

6. The efficient sampling method for a random sea state Copula probability model considering physical constraints according to claim 5, characterized in that: The significant wave height H in step (2) s and spectrum peak period T p The constraint relationship is （1） According to the H obtained in step 1 s and T p The marginal probability distribution function of , combined with the inverse transformation of the probability distribution function, formula (1) can be further written as （2） Where, and They are and The inverse function of and H s and T p The probability distribution function value of 、 ; On both sides of inequality (2) Transformation, there （3） Equation (3) is the sea state (H s , T p ) Medium effective wave height H s and spectrum peak period T p The corresponding probability distribution function value 、 The inequality relationship that should be satisfied.

7. The efficient sampling method for a random sea state Copula probability model considering physical constraints according to claim 6, characterized in that: The step (3.1) is specifically as follows: T is considered when physical constraints are not considered and when physical constraints are considered p The conditional probability density functions are and According to the basic principles of probability theory, （4） Where, for The minimum value of the corresponding spectrum peak period is to ensure that no wave breaking occurs, that is, ; The conditional probability distribution functions of the peak period without and with physical constraints are: and , then （5） According to the basic theory of the Copula method, the expression of the conditional probability distribution function of the spectrum peak period with respect to the significant wave height is: （6） Where, represents the partial derivative function of the Copula function, which has an analytical expression. Therefore, Equation (5) can be further written as （7） Where, for The corresponding probability distribution function value is also The minimum value of the probability distribution function of the corresponding spectrum peak period is used to ensure that no wave breaking occurs. According to formula (3), （8）。

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