Physical constraint-considered random sea condition Copula probability model efficient sampling method

Abstract

The invention discloses a random sea condition Copula probability model efficient sampling method considering physical constraints, belongs to the technical field of ocean engineering wave load probability modeling and evaluation, and can be applied to random wave probability modeling analysis of ocean structures such as an ocean oil and gas platform, an ocean photovoltaic platform and an offshore wind turbine. Specifically, on the basis of a Copula method for joint probability modeling of the significant wave height and the wave spectrum peak period, a physical background of wave breakage is introduced, and physical constraints are considered in the random sampling process of the significant wave height and the wave spectrum peak period, so that a more reasonable sampling result is obtained. According to the method provided by the invention, not only can the correlation between the effective wave height and the spectrum peak period be considered during sampling, but also the physical constraint between the two parameters caused by wave breakage can be considered, a more reasonable random sea condition sampling result can be obtained, and meanwhile, the method is more efficient.

Description

Technical Field

[0001] The 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 state Copula probability model taking physical constraints into consideration. Background Art

[0002] Wave load is one of the main environmental loads on marine structures such as offshore oil and gas platforms, offshore photovoltaic platforms, and offshore wind turbines, and has an important impact on the long-term service and safety performance of the structure. In order to accurately evaluate the wave load on marine structures, it is necessary to analyze and predict the various sea conditions that the structure may experience during its service. In practice, two parameters, effective wave height and spectral peak period, are usually used to describe a stable sea state. Due to the complexity and variability of the marine environment, the long-term sea conditions of the site have significant randomness, so the effective wave height and spectral peak period are two random variables. In addition, due to the physical mechanism of wave generation, these two parameters also have complex correlations. Therefore, in order to reasonably describe the long-term sea conditions of the site, it is necessary to obtain the joint probability distribution of the effective wave height and spectral peak period based on long-term wave observation data. In addition, due to the physical mechanism of wave development and propagation, there is a certain constraint relationship between wave height and wave period, which is manifested in that under given wave height conditions, the wave period usually has a lower limit value, 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 are many studies on the joint probability modeling of significant wave height and spectral peak period, for example, conditional probability modeling and Copula model can be used to obtain the joint probability distribution of these two parameters, the physical constraints between these two parameters are rarely considered. In the existing probability modeling studies that consider the physical constraints of these two parameters, the discriminant screening method is directly used to obtain random sea state samples that meet the conditions, and the sampling efficiency is not high. Therefore, how to reasonably and efficiently extract random sea conditions that meet the physical constraints based on the Copula model of the joint probability distribution of significant wave height and spectral peak period is a technical problem to be solved by the present invention. Summary of the invention

[0004] In view of the above problems, the present invention proposes an efficient sampling method for random sea conditions that takes physical constraints into consideration, so as to solve the deficiencies in the existing random sea condition probability sampling. Based on the Copula method of joint probability modeling of effective wave height and spectral peak period, this method incorporates the physical constraint inequality relationship between these two parameters into the sampling process, and by correcting the conditional probability distribution of the spectral peak period, and then combining the probability transformation, it can efficiently obtain random samples of effective wave height and spectral peak period that meet the physical constraints. This method can improve the accuracy and efficiency of random sea condition probability sampling, avoid extracting sea conditions that do not exist in reality, and is conducive to the 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 solution:

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

[0007] (I) Estimation of marginal probability distribution of significant wave height and spectral peak period and Copula correlation structure

[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 the peak period T p The marginal probability distribution model of ;

[0009] (1.2) Based on 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] (II) 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 the marginal probability distribution functions of the significant wave height and spectral peak period obtained in step (i), and use the inverse transformation and forward transformation of the probability function in turn to obtain the inequality relationship satisfied between the probability distribution function values ​​of the significant wave height and spectral peak period;

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

[0013] (3.1) Randomly select z1 from the interval [0,1] according to uniform distribution, and record u1 = z1, where u1 is the effective wave height H s The probability distribution function value of ; then based on the H obtained in step (a) s and T p The marginal probability distribution of , and according to the H obtained in step (ii) sand T p The inequality relationship between the probability distribution function values ​​is used to calculate the minimum value of the probability distribution function of the peak period corresponding to u1. Then, according to the Copula function result obtained in step (a), calculate the u1 condition The conditional probability distribution function value of

[0014] (3.2) Randomly select z2 from the interval [0,1] according to uniform distribution, where z2 is the conditional probability distribution function value of the spectrum peak period after considering physical constraints; then calculate the corrected value of the conditional probability distribution function of the spectrum peak period when physical constraints are not considered corresponding to z2 And remember Then, according to the Copula function result obtained in step (a), solve u2 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 u1, u2 are transformed by the inverse probability distribution function to calculate the sample values ​​of the effective wave height and spectrum peak period after considering the physical constraints, that is,

[0016] (3.4) z1 and z2 are randomly generated in the interval [0,1] multiple times, and multiple sample values ​​of effective wave height and spectrum peak period can be obtained according to the above steps, that is, multiple random sea condition samples that meet the physical constraints are obtained.

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

[0018] Preferably, in step (1.1), for convenience, the effective wave height H is recorded as s and the peak period T p The marginal probability distribution function of is and where h s represents the value of the effective wave height random variable, t 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 effective wave height H obtained in step (1.2) is recorded s and the peak period Tp The optimal Copula function for the probability correlation structure between

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

[0022] T p ≥g(H s ) (9)

[0023] According to the H obtained in step (a) s and T p The marginal probability distribution function of , combined with the inverse transformation of the probability distribution function, formula (17) can be further written as

[0024]

[0025] In the formula, and They are and The inverse function of H s and T p The probability distribution function value of

[0026] On both sides of inequality (18) Transformation, yes

[0027]

[0028] Formula (19) is the sea state (H s ,T p ) Effective wave height H s and the peak period T p The corresponding probability distribution function values ​​u1 and u2 should satisfy the inequality relationship.

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

[0030]

[0031] In the formula, h s 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 there is

[0033]

[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 effective wave height is:

[0035]

[0036] In the formula, h(·,·) represents the partial derivative function of the Copula function, which has an analytical expression. Therefore, formula (21) can be further written as

[0037]

[0038] In the formula, for The corresponding probability distribution function value is also the minimum value of the probability distribution function of the spectrum peak period corresponding to u1, so as to ensure that no wave breaking occurs; According to formula (19), we have

[0039]

[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 considering physical constraints. First, the marginal probability distribution of the significant wave height and the spectral peak period and the Copula correlation structure between the two are estimated based on wave observation data. Then, the constraint conditions between the significant wave height and the spectral peak period caused by the physical background of wave breaking are introduced, and the inequality relationship between the significant wave height and the spectral peak period probability distribution function is obtained in combination with the marginal probability distribution model obtained in step (one). Finally, based on the inequality relationship between the significant wave height and the spectral peak period probability distribution function obtained in step (two), the conditional probability distribution function value of the spectral peak period is corrected, and then the marginal probability distribution function of the significant wave height and the spectral peak period in step (one) is combined to obtain a random sea state sample that meets the physical constraints. The method proposed by the present invention can ensure that the sampled significant wave height and spectral peak period samples all meet the physical constraints, and the obtained random sea state samples all exist in reality, and the sampling efficiency is high, which is conducive to the accurate and efficient evaluation of the wave load on the marine structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It 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 modeling result of the marginal probability distribution of the significant wave height and the spectrum peak period;

[0045] Figure 4 It is the Copula modeling result of the probabilistic correlation structure between the significant wave height and the 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 sampled by 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 explain the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the specific implementation mode, structure, characteristics and effects of the present invention are described in detail below in combination with the accompanying drawings and preferred embodiments.

[0051] like Figure 1 As shown, an efficient sampling method of a random sea state Copula probability model considering physical constraints of the present invention 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 of the site, common probability distribution models such as lognormal distribution, Weibull distribution, Gamma distribution, etc. are used to estimate the significant wave height H s and the 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 is 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) Obtaining 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 judging wave breaking, such as the Iribarren criterion and the Goda criterion. The influence of the physical background of wave breaking on the effective wave height and the spectral peak period is reflected in the fact that for a given effective wave height, the spectral peak period has a lower limit, otherwise the wave will break and disappear. Therefore, the constraint relationship between the effective wave height and the spectral peak period caused by wave breaking can be expressed as the following inequality:

[0057] T p ≥g(H s ) (17)

[0058] 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 (17) can be further written as

[0059]

[0060] In the formula, and They are and The inverse function of H s and T p The probability distribution function value of

[0061] On both sides of inequality (18) Transformation, yes

[0062]

[0063] Formula (19) is the sea state (H s ,T p ) Effective wave height H s and the peak period T p The corresponding probability distribution function values ​​u1 and u2 should satisfy the inequality relationship.

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

[0065] Copula-based sampling of binary random variables requires 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]

[0067] In the formula, h s 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 there is

[0069]

[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 effective wave height is:

[0071]

[0072] In the formula, h(·,·) represents the partial derivative function of the Copula function, which has an analytical expression. Therefore, formula (21) can be further written as

[0073]

[0074] In the formula, for The corresponding probability distribution function value is also the minimum value of the probability distribution function of the spectrum peak period corresponding to u1, so as to ensure that no wave breaking occurs. According to formula (19), we have

[0075]

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

[0077] (a) Randomly select z1 from the interval [0,1] according to uniform distribution, and record u1=z1, where u1 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 (24) Then, according to the Copula function obtained in step 1, calculate

[0078] (b) z2 is randomly selected from a uniform distribution in the interval [0,1], and Then, according to formula (23), we can get and record the value of Therefore, we can get u2 is the 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 effective 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 the present 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 observatory can be downloaded from its official website. In this case, 8 years of effective wave height and spectral peak period observation data of the observatory are used. The data is the mean of 30 minutes of 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] where d b is the water depth, β is the slope of the seabed, and A 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 significant wave height and spectrum peak period edge is estimated respectively. The alternative distribution models include the commonly used lognormal distribution, Weibull distribution and Gamma distribution. The optimal distribution model identified is lognormal distribution. The results are shown in Figure 3Then, the probability correlation structure between the significant wave height and the spectrum 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 map 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 these two parameters can be obtained by inverse transformation and forward transformation of the probability function. s and T p The inequality relationship satisfied by the probability distribution function values. The CDF scatter plot of the above 416 observation data and the obtained inequality constraint curve are shown in 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 8As shown. It can be seen that the probability distribution of the sampled data is in good agreement with the original data, which shows that the sea condition samples obtained by the method of the present invention can accurately reflect the random characteristics of the original sea condition data. In addition, the Spearman rank correlation coefficient between the significant wave height and the spectral peak period in the data is quantitatively analyzed, and the calculation results of the Spearman rank correlation coefficient of the sampled data and the original data are 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 the original data, which shows that the random sea condition obtained 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 condition samples obtained by the efficient sampling method of the random sea condition Copula probability model considering physical constraints proposed in the present invention can effectively reflect the randomness, correlation and physical constraints of sea condition elements, and have important engineering application value for accurately evaluating the wave loads on marine structures.

Claims

1. An efficient sampling method for the random sea state Copula probability model considering physical constraints, characterized by: The following steps are involved: (I) Estimation of marginal probability distribution of significant wave height and spectral peak period and Copula correlation structure (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 the peak period T p The marginal probability distribution model of ; (1.2) Based on 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 (II) 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 the marginal probability distribution functions of the significant wave height and spectral peak period obtained in step (i), and use the inverse transformation and forward transformation of the probability function in turn to obtain the inequality relationship satisfied between the probability distribution function values ​​of the significant wave height and spectral peak period; (III) Sampling to obtain random sea state samples that meet the physical constraints of significant wave height and spectrum peak period (3.1) Randomly select z1 from the interval [0,1] according to uniform distribution, and record u1 = z1, where u1 is the effective wave height H s The probability distribution function value of ; then based on the H obtained in step (a) s and T p The marginal probability distribution of , and according to the H obtained in step (ii) s and T p The inequality relationship between the probability distribution function values ​​is used to calculate the minimum value of the probability distribution function of the peak period corresponding to u1. Then, according to the Copula result obtained in step (a), calculate the u1 condition The conditional probability distribution function value of (3.2) Randomly select z2 from the interval [0,1] according to uniform distribution, where z2 is the conditional probability distribution function value of the spectrum peak period after considering physical constraints; then calculate the corrected value of the conditional probability distribution function of the spectrum peak period when physical constraints are not considered corresponding to z2 And remember Then, according to the Copula function result obtained in step (a), solve u2 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 u1, u2 are transformed by the inverse probability distribution function to calculate the sample values ​​of the effective wave height and spectrum peak period after considering the physical constraints, that is, (3.4) z1 and z2 are randomly generated in the interval [0,1] multiple times, and multiple sample values ​​of effective wave height and spectrum peak period can be obtained according to the above steps, that is, multiple random sea condition samples that meet the physical constraints are 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 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: In the step (1.1), for convenience, the effective wave height H is recorded as s and the peak period T p The marginal probability distribution function of is and where h s represents the value of the effective wave height random variable, t P Represents the value of the spectrum peak period random variable.

4. The efficient sampling method of the random sea state Copula probability model considering physical constraints according to claim 1 is characterized by: 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 of the random sea state Copula probability model considering physical constraints according to claim 3 is characterized by: The description of the effective wave height H obtained in step (1.2) is s and the peak period T p The optimal Copula function for the probability correlation structure between 6. The efficient sampling method of the random sea state Copula probability model considering physical constraints according to claim 5 is characterized by: In step (ii), the effective wave height H s and the peak period T p The constraint relationship is T p ≥g(H s ) (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 (17) can be further written as In the formula, and They are and The inverse function of H s and T p The probability distribution function value of On both sides of inequality (18) Transformation, yes Formula (19) is the sea state (H s ,T p ) Effective wave height H s and the peak period T p The corresponding probability distribution function values ​​u1 and u2 should satisfy the inequality relationship.

7. The efficient sampling method of the random sea state Copula probability model considering physical constraints according to claim 6 is characterized by: 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, In the formula, h s 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 there is 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 effective wave height is: In the formula, h(·,·) represents the partial derivative function of the Copula function, which has an analytical expression. Therefore, formula (21) can be further written as In the formula, for The corresponding probability distribution function value is also the minimum value of the probability distribution function of the spectrum peak period corresponding to u1, so as to ensure that no wave breaking occurs; According to formula (19), we have

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