Wind speed and temperature return period calculation method based on joint distribution

Abstract

The invention relates to the technical field of environmental parameter analysis methods, and discloses a wind speed and temperature return period calculation method based on joint distribution, and the method comprises the following steps: obtaining wind speed and temperature data based on an on-site actual measurement system, and carrying out the fixed-period temperature extreme value and corresponding wind speed screening; determining a wind speed and temperature one-dimensional distribution model based on the goodness-of-fit index of regression analysis; and acquiring a wind speed and temperature joint distribution model by using an Archimedes Copula theory based on the rank correlation coefficient. According to the wind speed and temperature return period calculation method based on joint distribution, a method for accurately reflecting extreme temperature and corresponding wind speed distribution characteristics is provided to accurately estimate local environmental parameters; and the joint distribution characteristics of the most key factors in the environmental parameters are clarified by using the joint distribution of the two factors, and a plurality of return period calculation results capable of being used for different targets are provided, so that the widely developed engineering structure production and life activities are guided through accurate identification of the environmental parameters and description of the distribution characteristics.

Description

Technical Field

[0001] The present invention relates to the technical field of environmental parameter analysis methods, and in particular to a method for calculating the return period of wind speed and temperature based on joint distribution. Background Art

[0002] With the continuous construction of infrastructure in my country, dangerous and even extreme natural environments such as strong winds and rainstorms, sun exposure, and sudden drop in temperature often occur during the construction and operation cycle of structures; therefore, it is very important to fully consider the influence of wind speed and temperature in environmental parameters. Among all environmental parameters, temperature and wind are two important environmental parameters, and there is an obvious correlation between the two. The structural temperature difference caused by temperature changes and the sudden drop in temperature caused by wind on the surface of the structure will directly affect the temperature field distribution of the structure.

[0003] The present invention discloses a method for calculating the joint recurrence period of wind speed and temperature based on joint distribution. The method comprises the following steps: screening the fixed-period extreme values ​​of temperature based on existing wind speed and temperature data and extracting the corresponding wind speed; then performing regression analysis on the screened samples through the goodness of fit index of the unidimensional distribution to determine the distribution function; then obtaining the joint distribution model of the extreme value samples through the rank correlation coefficient using the Archimedean Copula theory. Finally, the present invention establishes a method for calculating the univariate recurrence period of extreme temperature and the multivariate recurrence period of wind speed and temperature. Summary of the invention

[0004] 1. Technical issues to be resolved

[0005] In view of the deficiencies of the prior art, the present invention provides a method for calculating the return period of wind speed and temperature based on joint distribution.

[0006] (II) Technical solution

[0007] To achieve the above object, the present invention provides the following technical solution: a method for calculating the return period of wind speed and temperature based on joint distribution, comprising the following steps:

[0008] Based on the on-site measurement system, wind speed and temperature data are obtained and periodic temperature extreme values ​​and corresponding wind speeds are screened;

[0009] The one-dimensional distribution model of wind speed and temperature was determined based on the goodness of fit index of regression analysis;

[0010] Based on the rank correlation coefficient, Archimedean Copula theory is used to obtain the wind speed and temperature joint distribution model;

[0011] Combined with the joint distribution model, the return period temperature is calculated and the joint return period of various wind speeds and temperatures is calculated.

[0012] Preferably, the environmental parameters are screened for periodic extreme values, that is, the single-dimensional temperature data array is screened for periodic extreme values, such as the highest temperature of a day or a month is recorded as Thot, the lowest temperature is recorded as Tcold, and the wind speeds corresponding to the highest temperature and the lowest temperature are extracted and recorded as Whot and Wcold respectively.

[0013] Preferably, a regression algorithm is used to determine the unidimensional distribution function of the screening data, as follows:

[0014] (1) GEV distribution

[0015] Its probability density function is

[0016]

[0017] Where μ represents the location parameter, σ represents the scale parameter, and k represents the shape parameter.

[0018] (2) LogNormal distribution

[0019] Its probability density function is

[0020]

[0021] Where μ represents the location parameter and σ represents the scale parameter.

[0022] (3) Gamma distribution

[0023] Its probability density function is

[0024]

[0025] Where α is the shape parameter, β is the scale parameter, and Γ(α) is the gamma function, usually written as

[0026] (4) Logistic distribution

[0027] Its probability density function is

[0028]

[0029] Where μ represents the location parameter and σ represents the scale parameter.

[0030] After regression analysis, the coefficient of determination (R 2 ), root mean square error (RMSE) and Bayesian information criterion (BIC) to judge the goodness of fit of the target parameters.

[0031] The determination coefficient expression is:

[0032] The root mean square error expression is:

[0033] The Bayesian information criterion expression is:

[0034] In the formula, y is the true value of the measured data, is the average value of the measured data, is the predicted value of the measured data, and n is the total sample size.

[0035] Preferably, the rank correlation coefficient and Archimedean Copula function cluster are used to establish a binary joint distribution of wind temperature in the cold and hot seasons:

[0036] The Spearman rank correlation coefficient ρ can be expressed as

[0037] ρ=12∫∫ D C(u,v)dudv-3

[0038] Kendall rank correlation coefficient τ can be expressed as

[0039] τ=4∫∫ D C(u,v)dC(u,v)-1

[0040] The expression of Archimedean Copula function is:

[0041]

[0042] The function It is the generator of the Archimedean Copula function, which is a continuous strictly monotonically decreasing convex function with a domain of [0, 1] and a range of [0, ∞]. For function The inverse function of For function The pseudo-inverse function of is defined as follows:

[0043]

[0044] The expressions of the three types of Archimedean Copula functions are as follows:

[0045] (1) Clayton Copula Function

[0046] The generator function of the Clayton Copula function is Where θ∈(0,∞), its two-dimensional distribution function C(u,v) is as follows:

[0047] C(u,v)=(u -θ +v -θ -1) -1 / θ

[0048] When θ approaches 0, the variables tend to be independent, and when θ approaches infinity, the variables are completely correlated. The Kendall rank correlation coefficient of the Clayton Copula function is:

[0049]

[0050] (2) Frank Copula Function

[0051] Generator Functions of Frank Copula Functions Where θ∈R, its two-dimensional distribution function C(u, v) is as follows:

[0052]

[0053] When θ tends to 0, the variables tend to be independent, when θ>0, the variables are positively correlated, and when θ<0, the variables are negatively correlated. The Kendall rank correlation coefficient of the Frank Copula function is:

[0054]

[0055] (3) Gumbel Copula Function

[0056] The generator function of the Gumbel Copula function is Where θ∈[1,∞), its two-dimensional distribution function C(u,v) is as follows:

[0057] C(u,v)=exp{-[(-lnu) θ +(-lnv) θ ] 1 / θ}

[0058] When θ = 0, the variables are completely independent, and when θ tends to infinity, the variables are completely correlated. The Kendall rank correlation coefficient of the GumbelCopula function is:

[0059] Preferably, the calculation method of the single-dimensional return period and the multi-dimensional joint return period based on the joint distribution model is:

[0060] Univariate return period: In the formula, λ T is the time interval between events, F x (x) is the distribution of the random variable.

[0061] Multivariate return period:

[0062] (1) Joint return period: It represents the return period when either variable exceeds a certain value.

[0063] (2) Co-occurrence recurrence period: It indicates the recurrence period when two variables exceed a certain value at the same time.

[0064] (3) Kendall return period: Where K C (t) is the measurement scale, is the generator of the Archimedean Copula function, for The Kendall return period divides events into three categories: safe area C1, warning surface C2 and dangerous area C3.

[0065] Under the binary joint distribution C(u,v), the recurrence period corresponding to when any one of the two variables exceeds a certain value is called the joint recurrence period; under the binary joint distribution C(u,v), the recurrence period corresponding to when both variables exceed a certain value at the same time is called the co-occurrence recurrence period.

[0066] (III) Beneficial effects

[0067] Compared with the prior art, the present invention provides a method for calculating the return period of wind speed and temperature based on joint distribution, which has the following beneficial effects:

[0068] 1. This wind speed and temperature return period calculation method based on joint distribution provides a method to accurately reflect the extreme temperature and the corresponding wind speed distribution characteristics to accurately estimate the local environmental parameters. It uses the joint distribution of the two to clarify the joint distribution characteristics of the most critical factors in the environmental parameters and provide a variety of return period calculation results that can be used for different purposes. Its purpose is to guide the widely carried out engineering structure production and life activities through accurate identification of environmental parameters and description of distribution characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a scatter plot of monitoring data of the present invention;

[0070] Figure 2 This is a schematic diagram of the single-dimensional distribution of monitoring data of the present invention;

[0071] Figure 3 It is a schematic diagram of the joint distribution of the present invention;

[0072] Figure 4 It is a schematic diagram of the return period of a single variable of the present invention;

[0073] Figure 5 Schematic diagram of the multivariate return period of the present invention. DETAILED DESCRIPTION

[0074] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0075] See also Figure 1-5 The present invention provides a technical solution: a method for calculating the return period of wind speed and temperature based on joint distribution, comprising the following steps:

[0076] Based on the on-site measurement system, wind speed and temperature data are obtained and periodic temperature extreme values ​​and corresponding wind speeds are screened;

[0077] The one-dimensional distribution model of wind speed and temperature was determined based on the goodness of fit index of regression analysis;

[0078] Based on the rank correlation coefficient, Archimedean Copula theory is used to obtain the wind speed and temperature joint distribution model;

[0079] Combined with the joint distribution model, the return period temperature is calculated and the joint return period of various wind speeds and temperatures is calculated.

[0080] In the present invention, in order to screen the periodic extreme values ​​of environmental parameters, the periodic extreme values ​​of environmental parameters are screened, that is, the one-dimensional temperature data array is screened for periodic extreme values, such as the highest temperature of a day or a month is recorded as Thot, the lowest temperature is recorded as Tcold, and the wind speeds corresponding to the highest temperature and the lowest temperature are extracted and recorded as Whot and Wcold respectively.

[0081] In the present invention, in order to determine the unidimensional distribution function of the screening data using a regression algorithm, the following method is made:

[0082] (1) GEV distribution

[0083] Its probability density function is

[0084]

[0085] Where μ represents the location parameter, σ represents the scale parameter, and k represents the shape parameter.

[0086] (2) LogNormal distribution

[0087] Its probability density function is

[0088]

[0089] Where μ represents the location parameter and σ represents the scale parameter.

[0090] (3) Gamma distribution

[0091] Its probability density function is

[0092]

[0093] Where α is the shape parameter, β is the scale parameter, and Γ(α) is the gamma function, usually written as

[0094] (4) Logistic distribution

[0095] Its probability density function is

[0096]

[0097] Where μ represents the location parameter and σ represents the scale parameter.

[0098] After regression analysis, the coefficient of determination (R 2 ), root mean square error (RMSE) and Bayesian information criterion (BIC) to judge the goodness of fit of the target parameters.

[0099] The determination coefficient expression is:

[0100] The root mean square error expression is:

[0101] The Bayesian information criterion expression is:

[0102] In the formula, y is the true value of the measured data, is the average value of the measured data, is the predicted value of the measured data, and n is the total sample size.

[0103] In the present invention, in order to establish a binary joint distribution of wind temperature in cold and hot seasons by using the rank correlation coefficient and the Archimedean Copula function cluster, the following solution is made:

[0104] The Spearman rank correlation coefficient ρ can be expressed as

[0105] ρ=12∫∫ D C(u,v)dudv-3

[0106] Kendall rank correlation coefficient τ can be expressed as

[0107] τ=4∫∫ D C(u,v)dC(u,v)-1

[0108] The expression of Archimedean Copula function is:

[0109]

[0110] The function It is the generator of the Archimedean Copula function, which is a continuous strictly monotonically decreasing convex function with a domain of [0, 1] and a range of [0, ∞]. For function The inverse function of For function The pseudo-inverse function of is defined as follows:

[0111]

[0112] The expressions of the three types of Archimedean Copula functions are as follows:

[0113] (1) Clayton Copula Function

[0114] The generator function of the Clayton Copula function is Where θ∈(0,∞), its two-dimensional distribution function C(u,v) is as follows:

[0115] C(u,v)=(u -θ +v -θ -1) -1 / θ

[0116] When θ approaches 0, the variables tend to be independent, and when θ approaches infinity, the variables are completely correlated. The Kendall rank correlation coefficient of the Clayton Copula function is:

[0117]

[0118] (2) Frank Copula Function

[0119] Generator Functions of Frank Copula Functions Where θ∈R, its two-dimensional distribution function C(u, v) is as follows:

[0120]

[0121] When θ tends to 0, the variables tend to be independent, when θ>0, the variables are positively correlated, and when θ<0, the variables are negatively correlated. The Kendall rank correlation coefficient of the Frank Copula function is:

[0122]

[0123] (3) Gumbel Copula Function

[0124] The generator function of the Gumbel Copula function is Where θ∈[1,∞), its two-dimensional distribution function C(u,v) is as follows:

[0125] C(u,v)=exp{-[(-lnu) θ +(-lnv) θ ] 1 / θ}

[0126] When θ = 0, the variables are completely independent, and when θ tends to infinity, the variables are completely correlated. The Kendall rank correlation coefficient of the GumbelCopula function is:

[0127] In the present invention, in order to calculate the single-dimensional return period and the multi-dimensional joint return period based on the joint distribution model, the following calculation method is made:

[0128] Univariate return period: In the formula, λ T is the time interval between events, F x (x) is the distribution of the random variable.

[0129] Multivariate return period:

[0130] (1) Joint return period: It represents the return period when either variable exceeds a certain value.

[0131] (2) Co-occurrence recurrence period: It indicates the recurrence period when two variables exceed a certain value at the same time.

[0132] (3) Kendall return period: Where K C (t) is the measurement scale, is the generator of the Archimedean Copula function, for The Kendall return period divides events into three categories: safe area C1, warning surface C2 and dangerous area C3.

[0133] Under the binary joint distribution C(u,v), the recurrence period corresponding to when any one of the two variables exceeds a certain value is called the joint recurrence period; under the binary joint distribution C(u,v), the recurrence period corresponding to when both variables exceed a certain value at the same time is called the co-occurrence recurrence period.

[0134] By providing a method that accurately reflects the extreme temperature and the corresponding wind speed distribution characteristics to accurately estimate the local environmental parameters, the joint distribution of the two is used to clarify the joint distribution characteristics of the most critical factors in the environmental parameters and provide a variety of recurrence period calculation results that can be used for different purposes. Its purpose is to guide the widespread production and life activities of engineering structures through the accurate identification of environmental parameters and the description of distribution characteristics.

[0135] When in use, the wind speed and temperature data are obtained from the field measurement system, and the temperature extreme values ​​and corresponding wind speeds are screened at regular intervals. The environmental parameters are screened at regular intervals, that is, the single-dimensional temperature data array is screened at regular intervals. For example, the highest temperature of a day or a month is recorded as Thot, the lowest temperature is recorded as Tcold, and the wind speeds corresponding to the highest and lowest temperatures are extracted and recorded as Whot and Wcold, respectively. In this process, the regression algorithm is used to determine the single-dimensional distribution function of the screened data. After regression analysis, the coefficient of determination (R 2 ), root mean square error (RMSE) and Bayesian information criterion (BIC) are used to judge the goodness of fit of the target parameters. Then, the unidimensional distribution model of wind speed and temperature is determined according to the goodness of fit index of regression analysis. Subsequently, the rank correlation coefficient and Archimedean Copula function cluster are used to establish the binary joint distribution of wind temperature in cold and hot seasons. Therefore, the wind speed and temperature joint distribution model can be obtained based on the rank correlation coefficient using Archimedean Copula theory. Finally, the return period temperature is calculated in combination with the joint distribution model, and the joint return period of multiple wind speeds and temperatures is calculated. Under the binary joint distribution, the return period corresponding to any one of the two variables exceeding a certain value is called the joint return period; under the binary joint distribution, the return period corresponding to the simultaneous excess of the two variables at the same time is called the co-occurrence return period.

[0136] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the return period of wind speed and temperature based on joint distribution, comprising the following steps: Based on the on-site measurement system, wind speed and temperature data are obtained and periodic temperature extreme values ​​and corresponding wind speeds are screened; The one-dimensional distribution model of wind speed and temperature was determined based on the goodness of fit index of regression analysis; Based on the rank correlation coefficient, Archimedean Copula theory is used to obtain the wind speed and temperature joint distribution model; Combined with the joint distribution model, the return period temperature is calculated and the joint return period of various wind speeds and temperatures is calculated.

2. The method for calculating the wind speed and temperature return period based on joint distribution according to claim 1, characterized in that: The fixed-period extreme value screening of environmental parameters is to perform fixed-period extreme value screening on the single-dimensional temperature data array, such as the highest temperature of a day or a month is recorded as Thot, the lowest temperature is recorded as Tcold, and the wind speed corresponding to the highest temperature and the lowest temperature is extracted and recorded as Whot and Wcold respectively.

3. The method for calculating the wind speed and temperature return period based on joint distribution according to claim 1, characterized in that: The unidimensional distribution function of the screening data is determined using a regression algorithm as follows: (1) GEV distribution Its probability density function is Where μ represents the location parameter, σ represents the scale parameter, and k represents the shape parameter. (2) LogNormal distribution Its probability density function is Where μ represents the location parameter and σ represents the scale parameter. (3) Gamma distribution Its probability density function is Where α is the shape parameter, β is the scale parameter, and Γ(α) is the gamma function, usually written as (4) Logistic distribution Its probability density function is Where μ represents the location parameter and σ represents the scale parameter. After regression analysis, the coefficient of determination (R 2 ), root mean square error (RMSE) and Bayesian information criterion (BIC) to judge the goodness of fit of the target parameters. The determination coefficient expression is: The root mean square error expression is: The Bayesian information criterion expression is: In the formula, y is the true value of the measured data, is the average value of the measured data, is the predicted value of the measured data, and n is the total sample size.

4. The method for calculating the joint return period of wind speed and temperature based on joint distribution according to claim 1, characterized in that: The rank correlation coefficient and Archimedean Copula function cluster are used to establish the binary joint distribution of wind temperature in the cold and hot seasons: The Spearman rank correlation coefficient ρ can be expressed as ρ=12∫∫ D C(u,v)dudv-3 Kendall rank correlation coefficient τ can be expressed as τ=4∫∫ D C(u,v)dC(u,v)-1 The expression of Archimedean Copula function is: The function It is the generator of the Archimedean Copula function, which is a continuous, strictly monotonically decreasing convex function with a domain of [0, 1] and a range of [0, ∞]. For function The inverse function of For function The pseudo-inverse function of is defined as follows: The expressions of the three types of Archimedean Copula functions are as follows: (1) Clayton Copula Function The generator function of the Clayton Copula function is Where θ∈(0,∞), its two-dimensional distribution function C(u,v) is as follows: C(u,v)=(u -θ +v -θ -1) -1 / θ When θ tends to 0, the variables tend to be independent, and when θ tends to infinity, the variables are completely correlated. The Kendall rank correlation coefficient of the ClaytonCopula function is: (2) Frank Copula Function Generator Functions of Frank Copula Functions Where θ∈R, its two-dimensional distribution function C(u, v) is as follows: When θ tends to 0, the variables tend to be independent, when θ>0, the variables are positively correlated, and when θ<0, the variables are negatively correlated. The Kendall rank correlation coefficient of the Frank Copula function is: (3) Gumbel Copula Function The generator function of the Gumbel Copula function is Where θ∈[1,∞), its two-dimensional distribution function C(u,v) is as follows: C(u,v)=exp{-[(-lnu) θ +(-lnv) θ ] 1 / θ } When θ = 0, the variables are completely independent, and when θ tends to infinity, the variables are completely correlated. The Kendall rank correlation coefficient of the Gumbel Copula function is:

5. The method for calculating the joint return period of wind speed and temperature based on joint distribution according to claim 1, characterized in that: Calculation method of single-dimensional return period and multi-dimensional joint return period based on joint distribution model: Univariate return period: In the formula, λ T is the time interval between events, F x (x) is the distribution of the random variable. Multivariate return period: (1) Joint return period: It represents the return period when either variable exceeds a certain value. (2) Co-occurrence recurrence period: It indicates the recurrence period when two variables exceed a certain value at the same time. (3) Kendall return period: Where K C (t) is the measurement scale, is the generator of the Archimedean Copula function, for The Kendall return period divides events into three categories: safe area C1, warning surface C2 and dangerous area C3. Under the binary joint distribution C(u,v), the recurrence period corresponding to when any one of the two variables exceeds a certain value is called the joint recurrence period; under the binary joint distribution C(u,v), the recurrence period corresponding to when both variables exceed a certain value at the same time is called the co-occurrence recurrence period.

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