An extreme coherent gust probability modeling method based on average wind speed condition distribution

Abstract

The application relates to an extreme coherent gust probability modeling method based on average wind speed condition distribution, which comprises the following steps: firstly, fitting the edge distribution of wind speed, rising time, wind direction angle change and gust amplitude; then, mapping to a standard normal space through Nataf forward transformation to calculate exceeding probability and reliability index; then, realizing variable decorrelation through Rosenblatt inverse transformation with the average wind speed as a condition; then, inversely transforming back to the physical space to obtain target recurrence period parameters; finally, constructing environmental equivalent curves under different wind speeds, satisfying the physical constraint that the gust amplitude increases and the wind direction angle change decreases under high wind speed, and verifying the compliance with the IEC 50-year recurrence period requirement; solving the problems that the existing extreme coherent gust probability modeling method generally ignores the influence of the average wind speed, does not impose physical boundary constraints on the wind direction angle change and the rising time, does not depict the dependent relationship among variables, and the reliability analysis is conservative or the result violates the physical law.

Description

Technical Field

[0001] This invention belongs to the field of wind power technology and relates to a method for probabilistic modeling of extreme coherent gusts based on the conditional distribution of average wind speed. The core of this method is that, under the Gaussian Copula characteristics of the Nataf distribution, the conditional distribution theory of binary variables combines the Nataf transform with the Rosenblatt transform. Background Technology

[0002] Among the various extreme wind condition models defined in the IEC 61400-1 standard, extreme coherent gusts (ECDs) have become a key factor restricting turbine design and affecting the safety and reliability of the entire life cycle due to their ability to impose extremely large dynamic loads on wind turbines in a short period of time. Traditional deterministic design methods, such as the IEC 61400-1 standard, have greatly simplified the extreme coherent gust model, directly defining the gust amplitude as 15 m / s and the rise time as 10 s. Although this standard can ensure basic safety, it cannot accurately characterize the true statistical characteristics of extreme coherent gust wind conditions at a specific site, making it difficult to support the refined design of wind turbines and site suitability assessment.

[0003] To meet the design requirements of specific sites, probabilistic modeling methods based on the Nataf distribution model, namely Inverse First-Order Reliability (IFORM) and Inverse Second-Order Reliability (ISORM), have been increasingly applied. However, the IFORM probabilistic modeling method based on the Nataf distribution model underestimates the true failure probability when the failure surface at the design point is concave, leading to a risky design. While the existing ISORM probabilistic modeling method based on the Nataf distribution model avoids this problem, it does not limit the range of values ​​for wind direction angle change and rise time when fitting the distribution. This often results in non-physical results where the wind direction angle change exceeds 180° and the rise time exceeds 600s, which seriously violates the physical constraints of IEC standards.

[0004] Furthermore, existing methods generally neglect the crucial impact of average wind speed on ECD characteristic parameters. Actual observations show that wind direction is unlikely to change significantly under high wind speed conditions, and gust amplitude increases with increasing average wind speed. However, existing models do not include average wind speed in their variable system, nor do they consider the dependency and order of gust amplitude, change in wind direction angle, and rise time. This often leads to the paradoxical phenomenon in modeling results where "as rise time increases, gust amplitude and change in wind direction angle decrease," contradicting objective physical laws.

[0005] In summary, existing ECD probabilistic modeling methods suffer from insufficient conservatism, parameter out-of-bounds errors, and neglect of key variable coupling relationships, leading to distorted load assessment results. Therefore, there is an urgent need for a probabilistic modeling method for extreme coherent gusts that can introduce mean wind speed variables, clearly define parameter boundary constraints, accurately characterize variable dependencies, and combine conservatism with physical consistency. Summary of the Invention

[0006] In view of this, in order to solve the problems that existing methods for probabilistic modeling of extreme coherent gusts generally ignore the influence of average wind speed, do not impose physical boundary constraints on the change in wind direction angle and rise time, do not characterize the dependencies between variables, and have insufficient conservatism in reliability analysis or results that violate physical laws, this invention provides a method for probabilistic modeling of extreme coherent gusts based on the distribution of average wind speed conditions. This method fully considers the coupled complex environmental state under the combined effect of factors such as gust amplitude, change in wind direction angle, rise time and average wind speed of extreme coherent gusts at a specific site.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A method for probabilistic modeling of extreme coherent gusts based on the distribution of average wind speed conditions includes the following steps:

[0009] S1. Variable distribution fitting; Obtain wind speed time series data for the target site, identify extreme coherent gust events, and extract the average wind speed for each event. Ascent time Change in wind direction angle Gust amplitude Four environmental variables were used to fit the corresponding marginal cumulative distribution function, where the mean wind speed was... As a condition variable and following a Weibull distribution, the rise time is... Change in wind direction angle Gust amplitude As conditional response variables, they respectively follow the inverse Weibull distribution, the three-parameter Weibull distribution, and the extreme value type I distribution;

[0010] in, The range of values ​​is , The range of values ​​is .

[0011] S2. Nataf Forward Transformation: Based on the Nataf forward transformation, the marginal cumulative distribution functions corresponding to the four environmental variables in step S1 are mapped to the standard normal space to obtain the corresponding standard normal space variables, and the exceedance probability is calculated according to the target return period. and reliability index ;

[0012] The formula for the Nataf forward transform is: In the formula: It is the inverse function of the standard normal distribution function; For random variables The marginal cumulative distribution function, where They represent average wind speeds. Ascent time Change in wind direction angle and gust amplitude ; For the corresponding random variable Standard normal space variables.

[0013] Exceedance probability under the target year return period The calculation formula is: The exceedance probability is calculated based on the ISORM method. Reliability index under The calculation formula is: In the formula: For sampling reference time; The target year return period is the same as the reference period. The number of extreme coherent gusts identified; Total duration of wind data; For degrees of freedom The chi-square distribution and inverse cumulative distribution function.

[0014] S3. Condition independence processing; using the average wind speed in step S2. The corresponding standard normal variable is the conditional variable, and the remaining rise time... Change in wind direction angle Gust amplitude The corresponding standard normal variables are subjected to Rosenblatt transformation to remove the correlation between variables, resulting in mutually independent standard normal space variables;

[0015] Specifically, S31, regarding the average wind speed Ascent time Change in wind direction angle Gust amplitude The quaternary correlation standard normal joint distribution blocks obtained after Nataf transformation are: In the formula: Corresponding average wind speed variable; separate rise time Change in wind direction angle Gust amplitude Variables; calculation of given values hour conditional mean vector Conditional covariance matrix : , ;

[0016] S32. Given that the standard normal spatial variable has a mean of 0 and a variance of 1, the conditional mean vector simplifies to: Conditional covariance matrix Simplified to: ;

[0017] In the formula: To achieve average wind speed rise time under conditions The conditional mean; To achieve average wind speed Change in wind direction angle under certain conditions The conditional mean; To achieve average wind speed Gust amplitude under conditions The conditional mean; For the original standard normal space variables and The Pearson correlation coefficient between them, i.e., the number of corresponding correlation coefficient elements in the conditional covariance matrix R;

[0018] S33, to Perform Cholesky decomposition This yields the lower triangular matrix L; combined with the independent standard normal variables generated by spherical sampling. , , The mutually independent conditionally normal variables can be calculated using the following formula: ;

[0019] S4. Nataf inverse transform: Map the independent standard normal space variables from step S3 back to physical space using the Nataf inverse transform to obtain the given average wind speed. Under the given conditions, the rise time of the corresponding target return period Change in wind direction angle and gust amplitude ;

[0020] The formula for the inverse Nataf transform is: In the formula: It is the inverse function of the marginal cumulative distribution function fitted in step S2. The standard normal distribution function is used; the output is... , , This refers to the rise time of the corresponding target's recurrence period in physical space. Change in wind direction angle and gust amplitude ;

[0021] S5. Environmental isometry construction; based on the parameters mapped back to physical space in step S4, construct different average wind speeds. Environmental isopleth curves under given conditions.

[0022] Traversing the average wind speed Setting values Range, for each given average wind speed value Repeat steps S2 to S4 to generate the rise time for the corresponding target return period. Change in wind direction angle Gust amplitude A sample set; based on this sample set, plot the average wind speeds. Environmental isometry curves under constraints; the extreme coherent gust parameter combination specified in the IEC 61400-1 standard is selected and substituted into the constructed extreme coherent gust probability model to calculate its return period in reverse. The calculation results are verified to be in the 50-55 year range, which meets the 50-year return period requirement specified in the standard and is conservative.

[0023] The beneficial effects of this invention are as follows:

[0024] 1. The extreme coherent gust probability modeling method based on the distribution of average wind speed disclosed in this invention introduces average wind speed as a condition variable into the extreme coherent gust probability modeling system, and clarifies that "average wind speed" is a condition variable. →Rise time →Change in wind direction angle → Gust amplitude The variable dependency order is defined by the measured data. The model output strictly follows the order of "average wind speed". Increase, gust amplitude Increased extreme values ​​and changes in wind direction angle The objective law of "extreme value reduction" is consistent with the definition requirements of extreme coherent gusts in the IEC 61400-1 standard. It fits the objective characteristic that wind direction is difficult to change significantly under high wind speed conditions. It solves the anti-physical phenomenon of "increased rise time and decreased gust parameters" in the traditional ISORM method, making the model more consistent with the fluid dynamic characteristics that wind direction is difficult to change significantly under high wind speed conditions.

[0025] 2. The extreme coherent gust probability modeling method based on the average wind speed condition distribution disclosed in this invention uses the inverse second-order reliability method (ISORM) for reliability analysis, avoiding the risk of underestimating the failure probability at the concave failure surface by the ISORM method; at the same time, by applying a certain condition to the edge distribution... and The rigid boundary constraints completely eliminate non-physical consequences such as excessive wind direction angle and excessively long rise time. Verified by back-calculation of IEC standard parameters, the return period of this extreme coherent gust probability model under IEC standard operating conditions is 55 years, slightly higher than the 50 years specified in the standard. This ensures design safety while avoiding cost waste caused by over-design.

[0026] 3. The extreme coherent gust probability modeling method based on average wind speed condition distribution disclosed in this invention constructs environmental isopleth curves considering average wind speed conditions through a combination of Nataf and Rosenblatt transformations. This method can output the joint probability distribution of gust amplitude, wind direction angle change, and rise time under different average wind speeds (e.g., 5 m / s, 10 m / s, 15 m / s, 20 m / s). This provides accurate input conditions for load simulation of wind turbines in different wind speed ranges, helping to more accurately evaluate the load adaptability of the turbine at specific sites and improve the overall economy and reliability of wind turbine design.

[0027] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0028] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0029] Figure 1 This is a flowchart of the extreme coherent gust probability modeling method based on the average wind speed condition distribution of the present invention.

[0030] Figure 2 (a), (b), and (c) represent the rise time in Comparative Example 1, respectively. Change in wind direction angle Gust amplitude The cumulative distribution fitting curves for the three key variables;

[0031] Figure 3 (a), (b), and (c) are environmental isovalue curves of the three major ECD variables under the return periods of 10, 50, and 100 years, respectively, in Comparative Example 1.

[0032] Figure 4 For comparison, Figure 1 shows the changes in gust amplitude and wind direction angle under different rise times with a 50-year return period.

[0033] Figure 5 (a) and (b) are comparison diagrams of isopleths under the 50-year return period of Comparative Example 1 and Comparative Example 2, respectively;

[0034] Figure 6 This is a diagram showing the changes in gust amplitude and wind direction angle under different rise times with a 50-year return period.

[0035] Figure 7 (a), (b), (c), and (d) represent the average wind speeds in the embodiments, respectively. Ascent time Change in wind direction angle Gust amplitude The cumulative distribution fitting curves for the four key variables;

[0036] Figure 8 (a), (b), (c), and (d) are environmental isometry curves of the three major ECD variables under average wind speeds of 5 m / s, 10 m / s, 15 m / s, and 20 m / s, respectively, in the examples.

[0037] Figure 9 This is a graph showing the changes in gust amplitude and wind direction angle under different rise times with a 50-year return period in Example 1. Detailed Implementation

[0038] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0039] like Figure 1 The proposed method for probabilistic modeling of extreme coherent gusts based on the distribution of average wind speed conditions first transforms environmental variables in physical space into variables in standard normal space using the Nataf transform. Second, it obtains independent standard normal space variables through the Rosenblatt transform. Finally, it obtains the values ​​of environmental variables in physical space through the inverse Nataf transform, thereby constructing environmental isopleth curves. The average wind speed variable is introduced to construct the environmental isopleth curves because a four-dimensional model cannot be intuitively represented in three-dimensional space. Therefore, the average wind speed is used as a conditional variable to construct environmental isopleth curves for gust amplitude, wind direction angle change, and rise time under the average wind speed condition, thus conforming to the Rosenblatt transform form. Specifically, the method includes the following steps:

[0040] S1. Variable distribution fitting; Obtain wind speed time series data for the target site, identify extreme coherent gust events, and extract the average wind speed for each event. Ascent time Change in wind direction angle Gust amplitude Four environmental variables were used to fit the corresponding marginal cumulative distribution function, where the mean wind speed was... As a condition variable and following a Weibull distribution, the rise time is... Change in wind direction angle Gust amplitude As conditional response variables, they respectively follow the inverse Weibull distribution, the three-parameter Weibull distribution, and the extreme value type I distribution;

[0041] Specifically, before modeling the probability of extreme coherent gusts based on the distribution of average wind speed conditions, it is necessary to calculate the distribution function of each environmental variable. Average wind speed Ascent time Change in wind direction angle Gust amplitude The marginal cumulative distribution functions are shown in equations (1), (2), (3), and (4), respectively:

[0042] (1)

[0043] (2)

[0044] (3)

[0045] (4)

[0046] In the formula: is the location parameter for the change in wind direction angle; k is the shape parameter for each distribution function; Location parameters for gust amplitude; For scale parameters, The range of values ​​is , The range of values ​​is The probability distributions of wind speed, duration, and wind direction angle change are based on the classic Weibull distribution and its variant models. For relevant distribution forms, please refer to "Weibull Models" by Murthy, Xie, and Jiang (John Wiley & Sons, 2004). The gust amplitude is described by the Gumbel extreme value distribution, and the specific distribution functions are shown in equations (1) to (4).

[0047] in, Let be the rise time of an extreme coherent gust with practical physical significance, ranging from (0s, 600s). When fitting the rise time probability distribution using an inverse Weibull distribution, a sign transformation is performed on the physical rise time, defining the rise time transformation quantity. Therefore, X t The corresponding value range is [-600s, 0s). See the attached instruction manual. Figure 2 (a) Figure 5 (a) and Figure 7 The coordinate range (-600s, 0s) appearing in (b) corresponds to the rise time transformation X. t rather than physical rise time In short, it refers to the rise time.

[0048] S2. Nataf forward transformation: Based on the Nataf transformation, the marginal cumulative distribution functions corresponding to the four environmental variables in step S1 are mapped to the standard normal space to obtain the corresponding standard normal space variables, and the exceedance probability is calculated according to the target return period. and reliability index .

[0049] Specifically, after obtaining the marginal cumulative distribution function of the corresponding environmental variable in S21, the marginal cumulative distribution function is mapped to the standard normal space through Nataf transformation, as shown in Equation (5).

[0050] (5)

[0051] In the formula: It is the inverse function of the standard normal distribution function; For random variables The marginal cumulative distribution function, where They represent average wind speeds. Ascent time Change in wind direction angle and gust amplitude ; For the corresponding random variable Standard normal space variables.

[0052] S22. Calculate the exceedance probability under the target year return period. The exceedance probability is determined using the following equations (6), (7) and (8).

[0053] (6)

[0054] (7)

[0055] (8)

[0056] In the formula: For sampling reference time; The target year return period is the same as the reference period. This represents the probability value at each reference time. The number of extreme coherent gusts identified; Total duration of wind data; For sampling reference time The following exceedance frequency; This represents the exceedance probability under the corresponding target year recurrence period.

[0057] S23. Calculate the exceedance probability based on the ISORM method. Reliability index under As shown in equation (9).

[0058] (9)

[0059] In the formula: Describing the degrees of freedom as The inverse cumulative distribution function of the chi-square distribution. Since extreme coherent gusts are represented by three environmental variables, the degrees of freedom are... It equals 3. In the standard normal space, It can also be expressed as the radius of a sphere, as shown in equation (10).

[0060] (10)

[0061] In the formula: , and For standard normal space vectors Therefore, each component can be written in spherical coordinates, as shown in equations (11), (12), and (13).

[0062] (11)

[0063] (12)

[0064] (13)

[0065] In the formula: The range is ; The range is .

[0066] S3. Condition independence processing; using the average wind speed in step S2. The corresponding standard normal variable is the conditional variable, and the remaining rise time... Change in wind direction angle Gust amplitude The corresponding standard normal variable undergoes a Rosenblatt transformation, and here the average wind speed is... As a conditional variable, a condition was constructed based on the average wind speed. rise time under certain conditions Change in wind direction angle Gust amplitude The environmental isovalue curves thus conform to the Rosenblatt transformation form. By removing the correlation between variables, we obtain mutually independent standard normal space variables.

[0067] Specifically, conditional distribution theory requires establishing a conditional standard normal space to derive environmental isopleth curves for the three major variables under average wind speed conditions. S31, Regarding average wind speed... Ascent time Change in wind direction angle Gust amplitude The quaternary correlation standard normal joint distribution blocks obtained after Nataf transformation are shown in equations (14) and (15).

[0068] (14)

[0069] (15)

[0070] In the formula: Corresponding average wind speed variable; separate rise time Change in wind direction angle Gust amplitude variable.

[0071] S32, correspondingly perform conditional mean vector calculation. Conditional covariance matrix The parameters are divided into blocks, as shown in equations (16) and (17).

[0072] (16)

[0073] (17)

[0074] In the formula: for Standard deviation; for and The covariance matrix is ​​shown in equation (18); for and The covariance matrix is ​​shown in equation (19); for and The covariance matrix is ​​shown in equation (20).

[0075] (18)

[0076] (19)

[0077] (20)

[0078] The correlation coefficient elements in the above covariance matrix are calculated using the Pearson correlation coefficient, as shown in equation (21).

[0079] (twenty one)

[0080] In the formula: These are the variable values ​​in the standard normal space; These are the values ​​of different variables in the standard normal space; where , This represents the number of samples.

[0081] Secondly, calculate the given average wind speed. conditions under conditions Mean vector As shown in equation (22).

[0082] (twenty two)

[0083] In the formula: ; ,in Then the condition The mean can be further rewritten as equation (23), as shown in the following equation.

[0084] (twenty three)

[0085] In the formula: To achieve average wind speed rise time under conditions The conditional mean; To achieve average wind speed Change in wind direction angle under certain conditions The conditional mean; To achieve average wind speed Gust amplitude under conditions The conditional mean.

[0086] Obtain the above conditional mean vector Then, establish a given average wind speed Conditional covariance matrix under given conditions As shown in equation (24).

[0087] (twenty four)

[0088] In the formula: ; . and It can also be expressed as shown in equations (25) and (26).

[0089] (25)

[0090] (26)

[0091] The conditional covariance matrix can be further expressed as equation (27), as shown below.

[0092] (27)

[0093] S33. For a conditional standard normal space constructed using conditional distribution theory for a bivariate variable, it is equivalent to... Perform a simplified Rosenblatt transformation. Implementing the Rosenblatt transformation requires knowledge of the complete joint cumulative distribution function of the variables, which is often unavailable in advance in engineering practice. However, for the first variable... Performing the Rosenblatt transform does not require knowledge of the complete joint cumulative distribution function, and is equivalent to knowing the complete joint cumulative distribution function. The Nataf transformation can be performed by simply knowing the marginal cumulative distribution function of the variable. The Rosenblatt transformation directly transforms the correlated nonnormal variable into an independent standard normal variable, as shown in equation (28).

[0094] (28)

[0095] When the joint cumulative distribution function of the variables is known, the Rosenblatt transformation is an exact transformation. Each variable after the transformation is independent and follows a standard normal distribution. The correlation between environmental variables in physical space is reflected by the correlation coefficient.

[0096] When deriving the environmental isopleth curves for extreme coherent gusts under given average wind speed conditions, the average wind speed is first determined. As a baseline condition, the Rosenblatt transformation at this point starts from the second step, i.e., the conditional distribution follows a normal distribution, as shown in equation (29).

[0097] (29)

[0098] Furthermore, the normal space variables are shown in equation (30).

[0099] (30)

[0100] The conditional distribution of the next variable follows This can be interpreted as the normal spatial variable derived given the first two variables, and subsequent variables can be derived similarly. As shown in equations (31) and (32).

[0101] (31)

[0102] (32)

[0103] The environmental isopleth curve is achieved through the inverse process of the Rosenblatt transformation, as shown in equation (33).

[0104] (33)

[0105] In the formula: ; The remaining variables and It can be derived from equations (34) and (35).

[0106] (34)

[0107] (35)

[0108] In the formula: ; For the first 1-order matrix; Before standard variables A dimensional vector. Correspondingly, , , and The following equations (36), (37), (38), and (39) are used respectively.

[0109] (36)

[0110] (37)

[0111] (38)

[0112] (39)

[0113] Finally, the value of each variable in the physical space is obtained by the Rosenblatt inverse transformation, as shown in equation (40).

[0114] (40)

[0115] Furthermore, equation (27) is decomposed using Cholesky method during mathematical processing. This is used to solve for the value of each variable after the Rosenblatt transformation, simplifying mathematical calculations and engineering applications, as shown in equation (41).

[0116] (41)

[0117] Due to equation (27) The matrix is ​​a positive definite matrix, so it can be decomposed by Cholesky, as shown in equation (42).

[0118] (42)

[0119] In the formula: It can be represented as shown in equation (43).

[0120] (43)

[0121] Equation (34) above can be further expressed as shown in equation (44).

[0122] (44)

[0123] Each element of the lower triangular matrix is ​​calculated using the above formula, as shown in the following formulas (45), (46), (47), (48), (49), and (50).

[0124] (45)

[0125] (46)

[0126] (47)

[0127] (48)

[0128] (49)

[0129] (50)

[0130] Furthermore, the conditional standard variable in equation (33) can be rewritten in the form of equation (51). Comparing equations (51) and (33), it can be seen that the results are equivalent.

[0131] (51)

[0132] S4. Nataf inverse transform: Map the independent standard normal space variables from step S3 back to physical space using the Nataf inverse transform to obtain the given average wind speed. Under the given conditions, the rise time of the corresponding target return period Change in wind direction angle and gust amplitude ;

[0133] Specifically, the conditional standard variables are mapped to the physical space through the inverse Nataf transformation, as shown in equation (52).

[0134] (52)

[0135] Regarding the rise time, after inverse transformation back to physical space, according to Restore the actual physical rise time.

[0136] S5. Environmental isometry construction; based on the parameters mapped back to physical space in step S4, construct different average wind speeds. Environmental isopleth curves under given conditions.

[0137] Specifically, iterate through the average wind speed Setting values Range, for each given average wind speed value Repeat steps S2 to S4 to generate the rise time for the corresponding target return period. Change in wind direction angle Gust amplitude A sample set; based on this sample set, plot the average wind speeds. Environmental isometry curves under constraints; the extreme coherent gust parameter combination specified in the IEC61400-1 standard is selected and substituted into the constructed probability model to calculate its return period in reverse. The calculation results are verified to be in the 50-55 year range, which meets the 50-year return period requirement specified in the standard and is conservative.

[0138] Method validity verification

[0139] Using the same gust data, the effectiveness of the probabilistic modeling method proposed in this invention is verified, and its results are compared with those of traditional probabilistic modeling methods. The specific comparison process is as follows: Comparative Example 1 presents the IFORM probabilistic modeling results based on the Nataf distribution model; Comparative Example 2 presents the ISORM probabilistic modeling results based on the Nataf distribution model; and the examples provide the results of the probabilistic modeling method proposed in this invention.

[0140] Comparative Example 1: IFORM Probability Modeling Results Based on the Nataf Distribution Model

[0141] Based on the same gust data, the cumulative distribution function for each variable is derived. As shown in Equations 53, 54, and 55, the distribution fitting curves are as follows: Figure 2 As shown, Figure 2 (a), (b), and (c) represent the rise time, respectively. Change in wind direction angle Gust amplitude The cumulative distribution fitting curve for the variable.

[0142] (53)

[0143] (54)

[0144] (55)

[0145] Figure 3 (a), (b), and (c) show the environmental isovalue curves for the three major ECD variables with return periods of 10, 50, and 100 years, respectively. Figure 3 (a) It can be seen that: the maximum wind direction change is 153.1°, corresponding to an ascent time of 141.5 s; the maximum gust amplitude is 20.8 m / s, corresponding to an ascent time of 106.7 s. From Figure 3 (b) It can be seen that the maximum wind direction change is 164.5°, corresponding to a rise time of 150.5 s; the maximum gust amplitude is 22.3 m / s, corresponding to a rise time of 111.6 s. From Figure 3 (c) It can be seen that the maximum wind direction change is 178.7°, corresponding to an ascent time of 161.8 s; the maximum gust amplitude is 24.1 m / s, corresponding to an ascent time of 117.8 s. From the maximum gust amplitude and the maximum wind direction change, it can be seen that they increase with the increase of the return period, which is consistent with the physical meaning of reality.

[0146] Figure 4 This graph shows the changes in gust amplitude and wind direction angle under a specific rise time. It can be seen that both the change in wind direction angle and the gust amplitude gradually increase with the increase in rise time. The blue curve in the graph represents the isopleths of wind direction angle change and gust amplitude for a rise time of 10 seconds. From this curve, we can deduce that the maximum gust amplitude and the maximum wind direction change are 19.5 m / s and 127.6°, respectively.

[0147] According to the ECD model in the IEC standard, the rise time is 10 s and the gust amplitude is 15 m / s. When the average wind speed is 10 m / s, the change in wind direction angle is 72°. Based on the ECD probability model established in this case, which uses the same values ​​for the three ECD variables as in the IEC standard, a reverse process is performed to calculate the return period under the same conditions. The result is 6.42 years, which is much shorter than the 50-year return period specified in the standard. The reason for this result is that when fitting the three gust variable parameters, the limits for the change in wind direction angle (0° to 180°) and rise time (0 s to 600 s) were not applied, resulting in a return period much shorter than the 50-year return period specified in the standard.

[0148] Comparative Example 2: ISORM Probability Modeling Results Based on the Nataf Distribution Model

[0149] Based on the same gust data, the cumulative distribution function of each variable is the same as in (1). As shown in Equations 53, 54, and 55, the distribution fitting curves are as follows: Figure 2 As shown, the reliability index of the probability model established by this method under a 50-year return period is 4.1802. To explore the differences in results between different probability modeling methods under the same conditions, the reliability index of the IFORM probability modeling method in the comparative example is set to 4.1802 to establish a probability model, and compared with it, as shown below. Figure 5 As shown, where Figure 5 (a) is an isopleth graph of the comparative example and the embodiment under a 50-year return period. Figure 5 (b) is an isopleth curve of Example 50 with a 50-year return period.

[0150] Figure 5 (a) shows the environmental isopleth curves under a 50-year return period using the ISORM probability model based on the Nataf distribution model. From... Figure 5 As can be seen in (a), the maximum wind direction change is 229.7°, with a corresponding rise time of 1.7 s. The maximum gust amplitude is 34.5 m / s, with a corresponding rise time of 7.3 s, exhibiting a distinct concave environmental contour curve shape.

[0151] from Figure 5 As shown in (b), the maximum wind direction change is 229.6°, corresponding to a rise time of 203.2 s. The maximum gust amplitude is 31.5 m / s, corresponding to a rise time of 140.0 s. Because this method does not limit the change in wind direction angle from 0° to 180°, the maximum wind direction change is 228.7°, which exceeds 180° and does not comply with the IEC standard.

[0152] A comparison with the results of the ISORM probabilistic modeling method in the comparative example reveals that for the ISORM probabilistic modeling method, the included spatial region decreases as the rise time increases. At shorter rise times, the other two variables also become extreme, resulting in a larger safety domain space, which does not conform to the physical laws of ECD in the IEC 61400 standard. In contrast, the ISORM probabilistic modeling method conforms to the physical laws of ECD in the IEC 61400 standard. Furthermore, the maximum values ​​of wind direction angle change and gust amplitude are not significantly different between the two methods. This is because the same gust data is used, therefore the probability distribution functions of the three major gust variables are the same, resulting in essentially the same extreme values ​​of wind direction angle change and gust amplitude. The rise time points at which these extreme values ​​occur differ due to the different modeling methods. This comparative analysis indirectly demonstrates the accuracy of the two traditional probabilistic modeling methods.

[0153] Figure 6 This graph shows the changes in gust amplitude and wind direction angle under specific rise time conditions. It can be seen that as the rise time increases, both the change in wind direction angle and the gust amplitude gradually decrease, which does not conform to the physical laws of ECD in the IEC 61400 standard. The blue curve in the graph is the isopleth curve of wind direction angle change and gust amplitude for a rise time of 10 s. From this curve, we can deduce that the maximum gust amplitude is 34.9 m / s and the maximum wind direction change is 119.5°.

[0154] According to the ECD model in the IEC standard, the rise time is 10 s and the gust amplitude is 15 m / s. When the average wind speed is 10 m / s, the change in wind direction angle is 72°. Based on this case study, the ECD probability model uses the same values ​​for the three main variables as the IEC standard. A reverse process is performed to calculate the return period under the same conditions, yielding a value of 0.08 years, far less than the 50-year return period specified in the standard. Comparative analysis with the comparative example reveals that, under the same conditions, the probability model established by this method has a return period two orders of magnitude lower than the comparative example's probability model. Therefore, the return period obtained using this method under the same IEC conditions is extremely unconservative, contrary to the conclusions drawn from traditional literature.

[0155] Analysis revealed three reasons for the above results. First, the total duration of gust screening was relatively short, while the number of events identified as ECDs was relatively large, increasing the frequency of extreme events and resulting in an extremely unconservative return period. Second, when fitting the three major gust parameters, no restrictions were placed on the change in wind direction angle (0° to 180°) and the rise time (0 s to 600 s), respectively, leading to a return period much shorter than the 50-year return period set in the standard. Third, the gust data identified using the identification method resulted in extreme values ​​for gust amplitude, change in wind direction angle, and rise time, leading to conclusions contrary to traditional literature.

[0156] Example: ECD probabilistic modeling results based on mean wind speed condition distribution

[0157] Compared to the two traditional methods, the method proposed in this paper needs to consider the influence of the mean wind speed variable and the constraints. Therefore, the probability distribution functions of four variables, including the mean wind speed, were refitted based on the same gust data, as shown in Equations 56, 57, 58, 59, and 59. Figure 7 As shown.

[0158] (56)

[0159] (57)

[0160] (58)

[0161] (59)

[0162] Figure 7 (a), (b), (c), and (d) represent the average wind speeds, respectively. Ascent time Change in wind direction angle Gust amplitude The cumulative distribution fitting curves for the four key variables show that the fitting results for the four key variables agree well with the distribution of the measured data, indicating that the probability distribution model defined above can reasonably describe the statistical characteristics of each variable. According to the definition of ECD in the IEC 61400 standard, the total change in wind direction angle during the change process should not exceed 180°. Therefore, in the parameter fitting and distribution modeling process of this method, the range of the change in wind direction angle is explicitly limited to between 0° and 180° to comply with the physical constraints of the standard. Furthermore, since a 10-minute (600-second) wind speed time history is used as the basic duration of an independent extreme gust event when identifying gust events, the rise time variable cannot physically exceed 600 seconds.

[0163] Figure 8 (a), (b), (c), and (d) are environmental isopleth curves of the three major ECD variables in the examples, respectively, when the average wind speed is 5 m / s, 10 m / s, 15 m / s, and 20 m / s. Figure 8 (a) It can be seen that the maximum wind direction change is 162.9°, corresponding to a rise time of 35.7 s, and the maximum gust amplitude is 27.3 m / s, corresponding to a rise time of 127.8 s. From Figure 8(b) It can be seen that the maximum wind direction change is 161.4°, corresponding to an ascent time of 49.9 s; the maximum gust amplitude is 31.2 m / s, corresponding to an ascent time of 157.5 s. From Figure 8 (c) It can be seen that the maximum wind direction change is 159.6°, corresponding to an ascent time of 69.5 s; the maximum gust amplitude is 36.0 m / s, corresponding to an ascent time of 194.8 s. From Figure 8 (d) It can be seen that the maximum wind direction change is 156.9°, corresponding to an ascent time of 102.5 s; the maximum gust amplitude is 43.3 m / s, corresponding to an ascent time of 251.4 s. The above results are summarized in Table 1.

[0164] Table 1. Wind speeds at different average wind speeds and Maximum value

[0165]

[0166] As can be seen from Table 1, as the average wind speed gradually increases, the maximum value of the change in wind direction angle gradually decreases, which is consistent with the IEC standard that the higher the wind speed, the smaller the change in wind direction. As the average wind speed gradually increases, the maximum value of the gust amplitude also gradually increases, which is consistent with the existing research showing that as the average wind speed gradually increases, the standard deviation of turbulence also gradually increases. The rise time corresponding to the maximum values ​​of the change in wind direction angle and the gust amplitude gradually becomes longer, which is consistent with the laws of reality.

[0167] Figure 9 The graph shows the changes in gust amplitude and wind direction angle under specific rise time conditions. It can be seen that both the change in wind direction angle and gust amplitude gradually increase with the increase in rise time. The blue curve in the graph represents the isopleths of wind direction angle change and gust amplitude for a rise time of 10 seconds. From this curve, we can deduce that the maximum gust amplitude and wind direction angle change are 24.8 m / s and 160.0°, respectively. According to the ECD model in the IEC standard, with a rise time of 10 seconds, the gust amplitude is 15 m / s. When the average wind speed is 10 m / s, the wind direction angle change is 72°. The ECD probability model established in this case uses the same values ​​for the three ECD variables as in the IEC standard. The return period under the same conditions is calculated through a reverse process, yielding a value of 55 years, which is relatively conservative compared to the standard 50-year return period. Based on the above analysis results, the probability modeling method proposed in this paper is more accurate than traditional probability modeling methods.

[0168] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for probabilistic modeling of extreme coherent gusts based on the distribution of average wind speed conditions, characterized in that, Includes the following steps: S1. Variable distribution fitting; Obtain wind speed time series data for the target site, identify extreme coherent gust events, and extract the average wind speed for each event. Ascent time Change in wind direction angle Gust amplitude Four environmental variables were used to fit the corresponding marginal cumulative distribution function, where the mean wind speed was... As a condition variable and following a Weibull distribution, the rise time is... Change in wind direction angle Gust amplitude As conditional response variables, they respectively follow the inverse Weibull distribution, the three-parameter Weibull distribution, and the extreme value type I distribution; The range of values ​​is , The range of values ​​is ; S2. Nataf Forward Transformation: Based on the Nataf forward transformation, the marginal cumulative distribution functions corresponding to the four environmental variables in step S1 are mapped to the standard normal space to obtain the corresponding standard normal space variables, and the exceedance probability is calculated according to the target return period. and reliability index ; S3. Condition independence processing; using the average wind speed in step S2. The corresponding standard normal variable is the conditional variable, and the remaining rise time... Change in wind direction angle Gust amplitude Performing the Rosenblatt inverse transform on the corresponding standard normal variables removes the correlation between variables, yielding mutually independent standard normal spatial variables; for the mean wind speed Ascent time Change in wind direction angle Gust amplitude The quaternary correlation standard normal joint distribution blocks obtained after Nataf transformation are as follows: In the formula: Corresponding average wind speed variable; separate rise time Change in wind direction angle Gust amplitude Variables; calculation of given values hour conditional mean vector Conditional covariance matrix : , ; S4. Nataf inverse transformation: Map the independent standard normal space variables from step S3 back to physical space through Nataf inverse transformation to obtain the rise time, wind direction angle change, and gust amplitude for the target return period under a given average wind speed. S5. Environmental isometry construction: Based on the parameters mapped back to physical space in step S4, construct environmental isometry curves under different average wind speed conditions.

2. The extreme coherent gust probability modeling method as described in claim 1, characterized in that, The formula for the Nataf forward transform in step S2 is: In the formula: It is the inverse function of the standard normal distribution function; For random variables The marginal cumulative distribution function, where They represent average wind speeds. Ascent time Change in wind direction angle and gust amplitude ; For the corresponding random variable Standard normal space variables.

3. The extreme coherent gust probability modeling method as described in claim 2, characterized in that, Exceedance probability under the target year return period in step S2 The calculation formula is: ; The exceedance probability is calculated using the ISORM method. Reliability index under The calculation formula is: In the formula: For sampling reference time; The target year return period is the same as the reference period. The number of extreme coherent gusts identified; Total duration of wind data; For degrees of freedom The chi-square distribution and inverse cumulative distribution function.

4. The extreme coherent gust probability modeling method as described in claim 1, characterized in that, In step S3, given that the mean of the standard normal spatial variables is 0 and the variance is 1, the conditional mean vector simplifies to: Conditional covariance matrix Simplified to: In the formula: To achieve average wind speed rise time under conditions The conditional mean; To achieve average wind speed Change in wind direction angle under certain conditions The conditional mean; To achieve average wind speed Gust amplitude under conditions The conditional mean; For the original standard normal spatial variables and The Pearson correlation coefficient between them is the corresponding correlation coefficient element in the conditional covariance matrix R.

5. The extreme coherent gust probability modeling method as described in claim 4, characterized in that, In step S3, for Perform Cholesky decomposition This yields the lower triangular matrix L; combined with the independent standard normal variables generated by spherical sampling. , , The mutually independent conditionally normal variables can be calculated using the following formula: 。 6. The extreme coherent gust probability modeling method as described in claim 1, characterized in that, The formula for the inverse Nataf transform in step S4 is: In the formula: It is the inverse function of the marginal cumulative distribution function fitted in step S2. The standard normal distribution function is used; the output is... , , This refers to the rise time of the corresponding target's recurrence period in physical space. Change in wind direction angle and gust amplitude .

7. The extreme coherent gust probability modeling method as described in claim 6, characterized in that, In step S5, the average wind speed is traversed. Setting values Range, for each given average wind speed value Repeat steps S2 to S4 to generate the rise time for the corresponding target return period. Change in wind direction angle Gust amplitude A sample set; based on this sample set, plot the average wind speeds. Environmental contour curves under constraints.

8. A modeling system for implementing the extreme coherent gust probability modeling method based on the average wind speed condition distribution as described in claim 1, characterized in that, include: The variable distribution fitting module is used to acquire wind speed time-series data at the target site, identify extreme coherent gust events, and extract the average wind speed for each event. Ascent time Change in wind direction angle Gust amplitude Four environmental variables were used, and their corresponding marginal cumulative distribution functions were fitted respectively. The Nataf forward transformation module is used to map the marginal cumulative distribution functions corresponding to four environmental variables to the standard normal space based on the Nataf forward transformation, so as to obtain the corresponding standard normal space variables. Conditional independence processing module, used for average wind speed The corresponding standard normal variable is the conditional variable, and the remaining rise time... Change in wind direction angle Gust amplitude The corresponding standard normal variables are subjected to the Rosenblatt inverse transform to remove the correlation between variables and obtain mutually independent standard normal space variables; The Nataf inverse transform module is used to map independent standard normal space variables back to physical space through Nataf inverse transform, obtaining the rise time of the corresponding target return period under a given average wind speed. Change in wind direction angle Gust amplitude ; The environmental isometry construction module is used to construct environmental isometry curves under different average wind speed conditions based on parameters mapped back to physical space.

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