Wind speed distribution prediction method for bridge wind vibration fatigue analysis

Abstract

This invention specifically relates to a wind speed distribution prediction method for bridge wind-induced vibration fatigue analysis, comprising: establishing a cumulative distribution function and a probability density distribution function for the main wind speed component based on kernel density estimation; establishing a cumulative distribution function and a probability density distribution function for the extreme wind speed component based on a GPD model; fusing these to obtain a mixed cumulative distribution function and a mixed probability density distribution function; establishing a wind direction probability density function based on a conditional probability model, and then fusing it with the mixed cumulative distribution function and the mixed probability density distribution function to obtain a wind speed distribution model considering the influence of wind direction; inputting the measured data into the wind speed distribution model, outputting the corresponding predicted wind speed and wind direction distribution, and then completing the bridge structure wind-induced vibration fatigue analysis based on the predicted wind speed and wind direction distribution. This invention can apply kernel density estimation and the GPD model to describe wind speed distribution, can adapt to complex application scenarios with bimodal or multimodal distributions, and can consider the influence of wind direction on wind speed.

Description

Technical Field

[0001] This invention relates to the field of bridge wind field simulation technology, and more specifically to a method for predicting wind speed distribution for bridge wind-induced vibration fatigue analysis. Background Technology

[0002] As bridges in mountainous areas develop towards longer spans and greater flexibility, the wind sensitivity of bridge structures has increased, making wind load one of the main control loads in the design of long-span bridges in mountainous areas. Therefore, clarifying the wind field parameters at the bridge site is a crucial factor in ensuring the safe operation of the bridge. However, due to the influence of topography, the wind field in mountainous areas is difficult to accurately describe according to current standards. Therefore, conducting research on near-ground wind characteristics in mountainous areas is a very fundamental and important step in the wind-resistant design of bridges.

[0003] To address the problem of wind characteristic research, Chinese Patent Publication No. CN104036121A discloses a "Wind Speed ​​Correction Method Based on Probability Distribution Transfer" for wind measurement data. This method first uses the Weibull distribution function to statistically describe wind speed. Then, it calculates the probability distribution estimates of wind speed for the i-th sequence of long-term meteorological stations, wind field observation stations, representative long-term meteorological stations, and representative wind field observation stations. Finally, for hourly wind speed data and probability distribution estimates, the corrected wind speed for the representative wind field observation station corresponding to the i-th sequence is calculated using the measured wind speed from the i-th sequence of the wind field observation station, either through the probability distribution difference transfer method or the probability distribution proportional transfer method. This existing wind speed correction method uses the Weibull distribution function to statistically describe wind speed.

[0004] The applicant found that while the Weibull distribution function in the existing scheme can fit the wind speed probability distribution model, it cannot match bimodal or multimodal distribution functions. However, wind speed distributions in real-world applications are typically not simple unimodal distributions; due to the significantly increased influence of random factors such as climate change, bimodal or even multimodal distributions are extremely common. Furthermore, the existing scheme neglects the influence of wind direction when constructing the wind speed distribution model. Generally, wind speeds at the same location are not uniform across different wind directions, and long-span structures exhibit significant differences in scale across different wind directions, particularly for bridge structures, where differences in scale, stiffness, and vibration performance are evident along and perpendicular to the bridge span.

[0005] The applicant further discovered that kernel density (KDE) estimation and the GPD (Generalized Pareto Distribution) model can describe wind speed distribution well. However, how to design a wind speed distribution prediction method that can apply kernel density estimation and GPD model to describe wind speed distribution, adapt to complex application scenarios with bimodal or multimodal distributions, and consider the influence of wind direction on wind speed is an urgent technical problem to be solved. Summary of the Invention

[0006] To address the shortcomings of the existing technologies, the technical problem to be solved by this invention is: how to provide a wind speed distribution prediction method for bridge wind vibration fatigue analysis, which can apply kernel density estimation and GPD model to describe wind speed distribution, adapt to complex application scenarios with bimodal or multimodal distributions, and consider the influence of wind direction on wind speed, thereby improving the accuracy and effectiveness of wind field distribution prediction, and enabling structural wind vibration fatigue analysis based on the wind field distribution prediction results.

[0007] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0008] A method for predicting wind speed distribution for bridge wind-induced vibration and fatigue analysis includes the following steps:

[0009] S1: Obtain the measured wind speed and wind direction data at the location of the bridge to be tested as the test data;

[0010] S2: Establish the cumulative distribution function and probability density distribution function of the main wind speed component based on kernel density estimation;

[0011] S3: Establish the cumulative distribution function and probability density distribution function of the extreme wind speed part based on the GPD model;

[0012] S4: Combine the cumulative distribution function and probability density distribution function of the main part of wind speed and the extreme part of wind speed respectively to obtain the mixed cumulative distribution function and the mixed probability density distribution function;

[0013] S5: Establish the wind direction probability density function based on the conditional probability model, and then fuse the wind direction probability density function with the mixed cumulative distribution function and the mixed probability density distribution function to obtain the wind speed distribution model that takes into account the influence of wind direction.

[0014] S6: Input the data to be measured into the wind speed distribution model, output the corresponding predicted wind speed and direction distribution, and then complete the wind vibration fatigue analysis of the bridge structure based on the predicted wind speed and direction distribution.

[0015] Preferably, in step S2, the cumulative distribution function of the main wind speed component is obtained by one-dimensional kernel density estimation.

[0016] Preferably, in step S2, the probability density distribution function of the main part of the wind speed is expressed by the following formula:

[0017]

[0018] in,

[0019]

[0020] Where: g KED (u) represents the probability density distribution function of the main wind speed component; u represents the wind speed; M represents the number of wind speed samples used for kernel density estimation; u i Let f(u) represent the i-th wind speed sample in M; f(u) represent the true probability density function; K(·) represent the kernel function; h′ represents the bandwidth parameter. It represents the standard deviation of the sample.

[0021] Preferably, in step S3, the cumulative distribution function and probability density distribution function of the extreme wind speed portion are expressed by the following formulas:

[0022]

[0023] In the formula: F GPD (u) represents the cumulative distribution function of the extreme wind speed portion; f GPD (u) represents the probability density distribution function of the extreme wind speed portion; P represents the probability; U represents the wind speed sample (u1, u2, ..., u...). M ,...,u n The random variables in ) represent the shape and scale parameters of the GPD model, respectively; x T This indicates the threshold value set.

[0024] Preferably, the threshold x is first obtained through extreme value analysis of the wind turbine response. T1 Then, the threshold x is determined using the CME criterion. T2 Finally, select the threshold x. T1 and threshold x T2 The maximum value in x is used as the threshold. T .

[0025] Preferably, the threshold x is determined through the following steps. T :

[0026] S301: The threshold x is determined by the following formula. T1 ;

[0027]

[0028] In the formula: This represents the mean of the wind speed sample;

[0029] S302: Determine the threshold x using the CME criterion T2 If the threshold x is exceeded T2 If the wind speed samples follow a GPD distribution, then for any wind speed sample u exceeding the threshold... i (u i >x T2 Given a variable Y, where i = 1, 2, ..., nM, i = 1, 2, ..., nM.i =Uu i |U>u i |Also satisfies the GPD distribution, when Y i mean and u i -x T2 The following linear relationship exists and x T2 When the initial point is used, the initial point of the linear relationship is used as the threshold x. T2 ;

[0030]

[0031] In the formula: E represents the expectation; U represents the wind speed sample (u1, u2, ..., u M ,…,u n Random variables in )

[0032] S303: The threshold x is determined by the following formula. T ;

[0033] x T =max(x T1 ,x T2 ).

[0034] Preferably, in step S4, the mixed cumulative distribution function and the mixed probability density distribution function are represented by the following formulas:

[0035]

[0036]

[0037] In the formula: P U (u) represents the mixed cumulative distribution function; f U (u) represents the mixture probability density distribution function; G KDE (u) means u≤x T The cumulative distribution function estimated by kernel density, i.e., the cumulative distribution function of the main part of wind speed; G KDE (x T ) represents G KDE (u) at u=x T The cumulative probability value at time g; KED (u) represents the probability density distribution function of the main part of the wind speed; F GPD (u) represents the cumulative distribution function of the extreme wind speed portion; f GPD (u) represents the probability density distribution function of the extreme wind speed portion;

[0038] in,

[0039] In the formula: N represents wind speed u less than or equal to threshold x TThe number of wind speed samples; n represents the total number of wind speed samples.

[0040] Preferably, in step S5, in the conditional probability model, it is assumed that wind speed and wind direction are independent of each other and that the wind speed distribution is a conditional distribution under a fixed wind direction. The wind direction probability density function satisfies the following assumptions:

[0041] 1) Assume that the wind speed in any given wind direction conforms to the same distribution model;

[0042] 2) Assume that the probability of any wind direction is the proportion of the number of wind speeds in that wind direction to the total number of wind speeds.

[0043] Preferably, the wind direction probability density function is expressed by the following formula:

[0044]

[0045] In the formula: f Θ (θ) represents the wind direction probability density function; n θ n represents the total number of wind speed samples with wind direction θ; tol This represents the total number of wind speed samples across all wind directions; Θ represents the wind direction angle.

[0046] Preferably, the wind speed distribution model considering the influence of wind direction is expressed by the following formula:

[0047] P U,Θ (u,θ)=∫∫f U,Θ (u,θ)dudθ;

[0048]

[0049] In the formula: P U,Θ (u,θ) represents the cumulative wind speed distribution function considering wind direction; f U,Θ (u,θ) represents the wind speed probability density function considering wind direction; f Θ (θ) represents the wind direction probability density function; Let be the probability density function under wind direction θ (0≤θ≤2π); This is the parameter vector under wind direction θ;

[0050] in,

[0051] In the formula: x T (θ) represents the threshold at wind direction θ; c(θ) represents the shape parameter of the GPD model at wind direction θ; d(θ) represents the scale parameter of the GPD model at wind direction θ; h′(θ) represents the bandwidth parameter at wind direction θ.

[0052] The wind speed distribution prediction method for bridge wind-induced vibration fatigue analysis in this invention has the following beneficial effects:

[0053] This invention establishes the cumulative distribution function and probability density distribution function of the main wind speed component and the extreme wind speed component using KDE estimation and GPD model, respectively. On the one hand, it can effectively describe the main wind speed component by utilizing the good fitting effect and applicability of KDE. On the other hand, it can effectively describe the extreme wind speed component by utilizing the good extreme value problem handling performance of GPD model. That is, it can effectively apply kernel density estimation and GPD model to describe wind speed distribution, so that the final fused wind speed distribution model can effectively take into account both the main wind speed component and the extreme wind speed component, and can adapt to complex application scenarios with bimodal or multimodal distributions. This can improve the accuracy and effectiveness of wind field distribution prediction, and thus enable the wind vibration fatigue analysis of bridge structures based on the wind field distribution prediction results.

[0054] This invention establishes a wind direction probability density function based on a conditional probability model, and then fuses it with a mixed cumulative distribution function and a mixed probability density distribution function to obtain a wind speed distribution model that considers the influence of wind direction. On the one hand, describing the wind direction distribution based on a relatively simple conditional probability model can reduce the difficulty of fusing and solving the wind speed distribution model. On the other hand, the wind speed distribution model that considers the influence of wind direction obtained by describing the wind direction distribution can calculate a more accurate wind speed and wind direction distribution compared to a model that only considers the wind speed distribution. This allows for a more accurate calculation of the bridge's flutter response and wind-induced fatigue damage, thus completing the wind vibration fatigue analysis of the bridge structure.

[0055] The wind speed distribution model obtained by fusing the wind direction probability density function with the mixed cumulative distribution function and the mixed probability density distribution function is a semi-parametric hybrid model. Compared with the parametric hybrid model, it can reduce the number of required parameters while ensuring the accuracy of wind speed and direction prediction, thereby further improving the practicality and efficiency of wind field simulation for bridges in mountainous areas. Attached Figure Description

[0056] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0057] Figure 1 This is a logic block diagram of a wind speed distribution prediction method used for wind-induced vibration fatigue analysis of bridges.

[0058] Figure 2 This is a schematic diagram showing the layout and location of a long-span suspension bridge.

[0059] Figure 3 This is a schematic diagram of the anemometer setup;

[0060] Figure 4 This diagram illustrates the comparison between the fitting results of the Weibull and KDE-GPD models and the actual distribution when direction is not considered.

[0061] Figure 5 A schematic diagram showing the wind direction divided into 16 sectors when considering direction;

[0062] Figure 6 A schematic diagram of the parameter vectors corresponding to the KDE-GPD model in different directions;

[0063] Figure 7 A schematic diagram comparing the fitting effects of Weibull and KDE-GPD models with the actual distribution when considering directionality. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but only to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0065] It should be noted that similar reference numerals and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the figures, or the orientation or positional relationship commonly used when the product is in use. They are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance. In addition, the terms "horizontal," "vertical," etc., do not indicate that the component is required to be absolutely horizontal or suspended, but can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted. In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0066] The following detailed explanation illustrates the specific implementation methods:

[0067] Example:

[0068] This embodiment discloses a method for predicting wind speed distribution for wind-induced vibration fatigue analysis of bridges.

[0069] like Figure 1 As shown, the wind speed distribution prediction method for bridge wind-induced vibration fatigue analysis includes the following steps:

[0070] S1: Obtain the measured wind speed and wind direction data at the location of the bridge to be tested as the test data;

[0071] In this embodiment, measured wind speed and wind direction data are collected by installing an anemometer.

[0072] S2: Establish the cumulative distribution function and probability density distribution function of the main wind speed component based on kernel density estimation (hereinafter referred to as KDE estimation);

[0073] S3: Establish the cumulative distribution function and probability density distribution function of the extreme wind speed part based on the GPD model;

[0074] In this embodiment, the GPD (Generalized Pareto Distribution) model refers to the generalized Pareto distribution model, which is a power-law distribution discovered from a large number of real-world phenomena. This invention simply applies the existing generalized Pareto distribution model; therefore, the specific details of the generalized Pareto distribution model will not be elaborated here.

[0075] S4: Combine the cumulative distribution function and probability density distribution function of the main part of wind speed and the extreme part of wind speed respectively to obtain the mixed cumulative distribution function and the mixed probability density distribution function;

[0076] S5: Based on the conditional probability model, establish the wind direction probability density function, and then fuse the wind direction probability density function with the mixed cumulative distribution function and the mixed probability density distribution function to obtain the wind speed distribution model that takes into account the influence of wind direction (hereinafter referred to as the KDE-GPD model).

[0077] S6: Input the data to be measured into the wind speed distribution model (hereinafter referred to as the KDE-GPD model) to output the corresponding predicted wind speed and direction distribution, and then complete the wind vibration fatigue analysis of the bridge structure based on the predicted wind speed and direction distribution.

[0078] In this embodiment, after obtaining the predicted wind speed and direction distribution, the average wind speed distribution is first obtained; then the average wind speed interval is defined and the corresponding annual occurrence frequency is determined. Taking the commonly used 10-minute average wind speed as an example, the total number of occurrences of different wind speeds in a year is statistically analyzed. Combined with the wind spectrum model specified in the standard, the 10-minute wind speed time history is simulated, and this time history is applied to the bridge structure to obtain the stress time history at key nodes. Finally, the stress amplitude and cycle number are extracted using the rainflow counting method, and then the fatigue life of the bridge is estimated by combining the linear damage theory.

[0079] In practical implementation, the wind speed distribution model considering the influence of wind direction is expressed by the following formula:

[0080] P U,Θ (u,θ)=∫∫f U,Θ (u,θ)dudθ;

[0081]

[0082] In the formula: P U,Θ (u,θ) represents the cumulative wind speed distribution function considering wind direction; f U,Θ (u,θ) represents the wind speed probability density function considering wind direction; f Θ (θ) represents the wind direction probability density function; Let be the probability density function under wind direction θ (0≤θ≤2π); This is the parameter vector under wind direction θ;

[0083] in,

[0084] In the formula: x T (θ) represents the threshold at wind direction θ; c(θ) represents the shape parameter of the GPD model at wind direction θ; d(θ) represents the scale parameter of the GPD model at wind direction θ; h′(θ) represents the bandwidth parameter at wind direction θ.

[0085] This invention establishes the cumulative distribution function and probability density distribution function of the main wind speed component and the extreme wind speed component using KDE estimation and GPD model, respectively. On the one hand, it can effectively describe the main wind speed component by utilizing the good fitting effect and applicability of KDE. On the other hand, it can effectively describe the extreme wind speed component by utilizing the good extreme value problem handling performance of GPD model. That is, it can effectively apply kernel density estimation and GPD model to describe wind speed distribution, so that the final fused wind speed distribution model can effectively take into account both the main wind speed component and the extreme wind speed component, and can adapt to complex application scenarios with bimodal or multimodal distributions. This can improve the accuracy and effectiveness of wind field distribution prediction, and thus enable the wind vibration fatigue analysis of bridge structures based on the wind field distribution prediction results.

[0086] Meanwhile, this invention establishes a wind direction probability density function based on a conditional probability model, and then merges it with a mixed cumulative distribution function and a mixed probability density distribution function to obtain a wind speed distribution model that considers the influence of wind direction. On the one hand, describing the wind direction distribution based on a relatively simple conditional probability model can reduce the difficulty of fusion and solution of the wind speed distribution model. On the other hand, the wind speed distribution model that considers the influence of wind direction obtained by describing the wind direction distribution can calculate a more accurate wind speed and wind direction distribution compared with a model that only considers the wind speed distribution. This allows for a more accurate calculation of the bridge's flutter response and wind-induced fatigue damage, thus completing the wind vibration fatigue analysis of the bridge structure.

[0087] Furthermore, the wind speed distribution model obtained by fusing the wind direction probability density function with the mixed cumulative distribution function and the mixed probability density distribution function is a semi-parametric hybrid model. Compared with the parametric hybrid model, it can reduce the number of required parameters while ensuring the accuracy of wind speed and direction prediction, thereby further improving the practicality and efficiency of wind field simulation for bridges in mountainous areas.

[0088] In the specific implementation process, the cumulative distribution function G of the main wind speed component is obtained through one-dimensional kernel density estimation. KDE (u).

[0089] In this invention, let (u1, u2, ..., u M ,...,u n) are independent and identically distributed random variables, i.e., all wind speed samples.

[0090] Among them, (u1,u2,...,u M The probability density distribution of (u1, u2, ..., u) is described by the KDE model, that is, (u1, u2, ..., u) M ) is used as the number of wind speed samples for kernel density estimation, while (u M+1 ,u M+2 ,...,u n The probability distribution of ) is described using the GPD model.

[0091] The probability density distribution function of the main part of the wind speed estimated by KDE is expressed by the following formula:

[0092]

[0093] Where: g KED (u) represents the probability density distribution function of the main wind speed component; u represents the wind speed; M represents the wind speed sample (u1, u2, ..., u) used for kernel density estimation. M The quantity of ); u i Let f(u) represent the i-th wind speed sample in M; f(u) represent the true probability density function; K(·) represent the kernel function; h′ represents the bandwidth parameter. It represents the standard deviation of the sample.

[0094] In addition to the influence of the number of wind speed samples M, the KDE estimation results are also related to the bandwidth parameter h′ and the kernel function K(·).

[0095] This embodiment uses the Gaussian kernel function: The Gaussian kernel function has the advantages of being convenient and fast.

[0096] In other preferred embodiments, the Epanechnikov kernel function may also be selected:

[0097] In comparison, the bandwidth parameter h′ has the greatest impact on the KDE estimation results. For example, the larger the value of the bandwidth parameter h′, the lower the proportion of actual data on the fitted curve, while the smaller the value of the bandwidth parameter h′, the higher the proportion, thus making the overall curve steeper.

[0098] Criteria are determined using standard parameters: To determine the bandwidth parameters.

[0099] This invention establishes the cumulative distribution function and probability density distribution function of the main wind speed component through KDE estimation, enabling the effective description of the main wind speed component by utilizing the good fitting effect and applicability of KDE. In other words, it can effectively apply kernel density estimation to describe wind speed distribution, thereby ensuring the accuracy and effectiveness of the description of the main wind speed component.

[0100] In the specific implementation process, let (u1,u2,...,u M ,...,u n ) are independent and identically distributed random variables, i.e., all wind speed samples.

[0101] Among them, (u1,u2,...,u M The probability density distribution of (u1, u2, ..., u) is described by the KDE model, that is, (u1, u2, ..., u) M ) is used as the number of wind speed samples for kernel density estimation, while (u M+1 ,u M+2 ,...,u n The probability distribution of ) is described using the GPD model.

[0102] The cumulative distribution function and probability density distribution function of the extreme wind speed are expressed by the following formulas:

[0103]

[0104] In the formula: F GPD (u) represents the cumulative distribution function of the extreme wind speed portion; f GPD (u) represents the probability density distribution function of the extreme wind speed portion; P represents the probability; U represents the wind speed sample (u1, u2, ..., u...). M ,...,u n The random variables in ) represent the shape and scale parameters of the GPD model, respectively; x T This indicates the threshold value set.

[0105] Regarding the threshold x T First, the threshold x is obtained through extreme value analysis of the wind turbine response. T1 Then, the threshold x is determined using the CME criterion. T2 Finally, select the threshold x. T1 and threshold x T2 The maximum value in x is used as the threshold. T .

[0106] Specifically, the threshold x is determined through the following steps. T :

[0107] S301: The threshold x is determined by the following formula. T1 ;

[0108]

[0109] In the formula: This represents the mean of the wind speed sample;

[0110] S302: Determine the threshold x using the CME criterion T2 If the threshold x is exceeded T2 If the wind speed samples follow a GPD distribution, then for any wind speed sample u exceeding the threshold... i (u i >x T2 Given a variable Y, where i = 1, 2, ..., nM, i = 1, 2, ..., nM. i =Uu i |U>u i |Also satisfies the GPD distribution, when Y i mean and u i -x T2 The following linear relationship exists and x T2 When the initial point is used, the initial point of the linear relationship is used as the threshold x. T2 ;

[0111]

[0112] In the formula: E represents the expectation; U represents the wind speed sample (u1, u2, ..., u M ,…,u n Random variables in )

[0113] S303: The threshold x is determined by the following formula. T ;

[0114] x T =max(x T1 ,x T2 ).

[0115] This invention establishes the cumulative distribution function and probability density function of the extreme wind speed component using the GPD model. This allows the excellent extremum handling performance of the GPD model to describe the extreme wind speed component, ensuring the accuracy and effectiveness of the description of the extreme wind speed component. Furthermore, this invention determines a threshold based on wind turbine response extremum analysis and the CME criterion, ensuring the continuity of the cumulative distribution function and probability density function of the extreme wind speed component at the threshold point. This allows for the fusion of these functions to obtain a more accurate mixed cumulative distribution function.

[0116] In practical implementation, the mixed cumulative distribution function and the mixed probability density distribution function are represented by the following formulas:

[0117]

[0118]

[0119] In the formula: P U (u) represents the mixed cumulative distribution function; f U (u) represents the mixture probability density distribution function; G KDE (u) means u≤x T The cumulative distribution function estimated by kernel density, i.e., the cumulative distribution function of the main part of wind speed; G KDE (x T ) represents G KDE (u) at u=x T The cumulative probability value at time g; KED (u) represents the probability density distribution function of the main part of the wind speed; F GPD (u) represents the cumulative distribution function of the extreme wind speed portion; f GPD (u) represents the probability density distribution function of the extreme wind speed portion;

[0120] in,

[0121] In the formula: N represents wind speed u less than or equal to threshold x T The number of wind speed samples, where N is equal to M as mentioned above; n represents the total number of wind speed samples.

[0122] The hybrid cumulative distribution function and hybrid probability density distribution function obtained by the present invention can effectively take into account both the main part of wind speed and the extreme part of wind speed, that is, it can well adapt to complex application scenarios with bimodal or even multimodal distribution, thereby further improving the accuracy and effectiveness of wind field distribution prediction.

[0123] In practical implementation, the conditional probability model assumes that wind speed and wind direction are independent of each other, and that the wind speed distribution follows a conditional distribution under a fixed wind direction. The wind direction probability density function satisfies the following assumptions:

[0124] 1) Assume that the wind speed in any given wind direction conforms to the same distribution model;

[0125] 2) Assume that the probability of any wind direction is the proportion of the number of wind speeds in that wind direction to the total number of wind speeds.

[0126] The wind direction probability density function is expressed by the following formula:

[0127]

[0128] In the formula: f Θ (θ) represents the wind direction probability density function; n θ n represents the total number of wind speed samples with wind direction θ; tol This represents the total number of wind speed samples across all wind directions; Θ represents the wind direction angle.

[0129] This invention describes wind direction distribution based on a relatively simple conditional probability model, which can reduce the difficulty of fusion and solution of wind speed distribution models that take into account the influence of wind direction, thereby improving the efficiency of wind speed and wind direction distribution prediction.

[0130] To better illustrate the advantages of the technical solution of the present invention, the following experiments are disclosed in this embodiment.

[0131] like Figure 2 As shown, this experiment investigated the complex wind field around a long-span suspension bridge in a mountainous area.

[0132] like Figure 3 As shown, a cup anemometer (NRG) and a three-dimensional ultrasonic anemometer (Young 81000) were used in the actual measurement.

[0133] Starting from a height of 10m, an NRG anemometer is installed every 10m; an NRG wind vane is installed every 20m; and two Young anemometers are installed at 30m and 50m. In addition, an NRG hygrometer, barometer, and thermometer are installed at a height of 8m on the observation tower to obtain humidity, air pressure, and temperature, respectively.

[0134] This experiment analyzed ten-minute average wind speed and direction data from the NGR anemometer over approximately 33 months, from February 9, 2013, to October 16, 2015. Furthermore, data with zero wind speed recorded in actual measurements were removed during the analysis. After this screening, 139,979 sets of ten-minute average wind speed and direction data were obtained, and a joint distribution study of average wind speed and direction was conducted based on these data.

[0135] If we disregard the influence of wind direction and assume that all wind speeds are in the same direction, we obtain the statistical characteristics of the wind speed data for all wind directions as shown in Table 1.

[0136] Table 1. Data Characteristics Description (Wind directionality not considered)

[0137]

[0138] As shown in Table 1, the data has a mean of 2.05 m / s, a variance of 1.69 m / s, a skewness of 1.22, and a kurtosis of 4.65, thus exhibiting significant non-Gaussian characteristics. To illustrate the superiority of the KDE-GPD model, this invention employs a comparative study with commonly used optimal Weibull distribution models, such as... Figure 4 As shown.

[0139] Depend on Figure 4It can be seen that the wind speed distribution in all directions is a typical unimodal distribution. The histogram represents the frequency of actual wind speed distribution, with points representing defined thresholds. The dashed line represents the Weibull distribution fitting result, and the solid line represents the KDE-GPD model fitting result. In comparison, the KDE-GPD model can better describe the actual wind speed distribution, and the distribution function is smooth at the threshold points. The corresponding model parameter values ​​are h′=0.17; c=0.033; d=1.24; x T =4.42.

[0140] To further illustrate the performance of the KDE-GPD model, the overall wind speed range was divided into seven distinct intervals based on an interval Δu = 2 m / s. The actual wind speed distribution and the probability distributions of the two distribution functions described above within each interval were then statistically analyzed, as shown in Table 2.

[0141] Table 2. Probability distributions of Weibull distribution and KDE-GPD distribution in different wind speed ranges.

[0142]

[0143] Table 2 shows that the main wind speed components obtained from both distribution functions are within the interval [0 m / s, 8 m / s], but the actual wind speed distribution shows a high degree of agreement with the fitting results of the KDE-GPD model. Specifically, the probability of wind speed following the Weibull distribution is higher than that following the KDE-GPD distribution in the two extreme intervals [0 m / s, 2 m / s] and [10 m / s, 14 m / s], while the probability of following the KDE-GPD model is higher in the interval [2 m / s, 10 m / s]. Therefore, using the Weibull distribution for response analysis not only overestimates the response in the extreme wind speed region but also underestimates the response in the main wind speed region.

[0144] To study the influence of wind direction, this experiment first divided wind speed into zones based on wind direction, and then fitted the wind speed within each wind direction. Theoretically, the denser the wind direction zones, the more accurate the results. However, too many zones not only increase workload but also hinder practical application. Furthermore, when wind speed data is limited, the amount of data in each zone is insufficient, leading to significant discrepancies between the fitted results and actual conditions. Typically, a reasonable number of wind direction zones is 8–16.

[0145] Figure 5(a) The wind direction is divided into 16 sectors with Δθ = 22.5. Here, zero degrees is due north and the wind direction angle increases in a clockwise direction; "E, W, S, N" represent due east, due west, due south and due north respectively; the dashed lines are the wind directions corresponding to each sector, namely "N, NNE, NE, ENE, E, ESE, SE, SSE, S, SSW, SW, WSW, W, WNW, NW, NNW". Figure 5 (b) Wind rose diagrams were obtained from measured data at the bridge site, divided into 16 sectors. The frequency of winds from the due east (E) direction was significantly higher than from other directions (which can be considered the dominant wind direction), but the wind speeds in this direction were mostly below 10 m / s. Meanwhile, strong winds were observed to mainly originate from two southwest directions (i.e., SSW and SW directions), with a maximum wind speed of 13.10 m / s (from the SW direction).

[0146] In addition, Table 3 provides a description of the data characteristics in eight typical sectors. Comparing Table 1 and Table 3, it can be seen that the wind speed characteristics in each direction are significantly different from the omnidirectional wind speed characteristics, and both exhibit significant non-Gaussian characteristics.

[0147] Table 3. Description of Data Characteristics in Some Directions

[0148]

[0149] Based on the partitioning results of the above 16 sectors, Figure 6 KDE-GPD parameter vectors for different wind directions are given. The result.

[0150] in, Figure 6 (a), (b), (c), and (d) are the sector partitioning results corresponding to the threshold, shape parameter c, scale parameter d, and bandwidth parameter h′, respectively.

[0151] For the sake of brevity, Figure 7 Fitting results based on the Weibull distribution and the KDE-GPD model are presented for some directions.

[0152] in, Figure 7 (a), (b), (c), and (d) represent the fitting results for the E, SW, WSW, and W directions, respectively.

[0153] Depend on Figure 7 It is known that when considering wind directionality, wind speed distribution can exhibit both unimodal and bimodal patterns. In comparison, the KDE-GPD model can better describe the actual wind speed distribution, especially for the actual bimodal distribution, where the advantages of the KDE-GPD model are more obvious. It not only ensures the accurate distribution of the main wind speed component but also reflects the distribution of the extreme wind speed components well.

[0154] It is worth noting that although strong winds occur less frequently, the fatigue damage they cause is significant; conversely, although fatigue damage is less severe under the prevailing wind speeds, these occur more often. Therefore, accurately describing the wind speed distribution is crucial to ensuring the reliability of wind-induced buffeting response calculations and fatigue damage estimations. In conclusion, the hybrid wind speed distribution model based on the KDE-GPD model exhibits good fitting accuracy when considering the influence of wind direction.

[0155] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting wind speed distribution for wind-induced fatigue analysis of bridges, characterized by, The method comprises the following steps: S1: obtaining the measured wind speed data and wind direction data of the bridge position to be measured as the to-be-measured data; S2: establishing the cumulative distribution function and the probability density distribution function of the wind speed main part based on the kernel density estimation; S3: establishing the cumulative distribution function and the probability density distribution function of the wind speed extreme part based on the GPD model; In step S3, the cumulative distribution function and the probability density distribution function of the wind speed extreme part are represented by the following formula: ； where: represents the cumulative distribution function of the wind speed extreme part; represents the probability density distribution function of the wind speed extreme part; represents the probability; represents the random variable of the wind speed sample; and respectively represent the shape parameter and the scale parameter of the GPD model; represents the set threshold value; the threshold value is first obtained by fan response extreme value analysis ; then the threshold value is determined by the CME criterion ; finally, the maximum value of the threshold value and the threshold value is selected as the threshold value ; S4: respectively fusing the cumulative distribution function and the probability density distribution function of the wind speed main part and the wind speed extreme part to obtain the mixed cumulative distribution function and the mixed probability density distribution function; In step S4, the mixed cumulative distribution function and the mixed probability density distribution function are represented by the following formula: ； ； wherein: denotes the mixed cumulative distribution function; denotes the mixed probability density distribution function; denotes the cumulative distribution function estimated by the kernel density at the time t, i.e. the cumulative distribution function of the main part of the wind speed; denotes the cumulative probability value at the time t; denotes the cumulative probability value at the time t; denotes the probability density distribution function of the main part of the wind speed; denotes the cumulative distribution function of the extreme part of the wind speed; denotes the probability density distribution function of the extreme part of the wind speed; wherein ; In the formula: represents the wind speed the number of wind speed samples less than or equal to a threshold value represents the total number of wind speed samples​ S5: establishing the wind direction probability density function based on the conditional probability model, and then fusing the wind direction probability density function with the mixed cumulative distribution function and the mixed probability density distribution function to obtain the wind speed distribution model considering the influence of the wind direction; S6: inputting the to-be-measured data into the wind speed distribution model to output the corresponding predicted wind speed and wind direction distribution, and then completing the bridge structure wind vibration fatigue analysis based on the predicted wind speed and wind direction distribution.

2. The wind speed distribution prediction method for bridge wind-induced vibration fatigue analysis of claim 1, wherein: In step S2, the cumulative distribution function of the wind speed main part is obtained through one-dimensional kernel density estimation.

3. The wind speed distribution prediction method for bridge wind-induced vibration fatigue analysis of claim 1, wherein: In step S2, the probability density distribution function of the wind speed main part is represented by the following formula: ； wherein ; ； where: denotes the probability density distribution function of the wind speed main part; denotes the wind speed; denotes the number of wind speed samples for kernel density estimation; denotes the th wind speed sample in denotes the true probability density function; denotes the kernel function; denotes the bandwidth parameter; denotes the standard deviation of the samples.

4. The wind speed distribution prediction method for bridge wind-induced vibration fatigue analysis of claim 1, wherein: The threshold value is determined in particular by the following steps : S301: Determine the threshold value by the following formula ; ； wherein: denotes the mean value of the wind speed samples; S302: determining a threshold value by CME criterion : if the wind speed samples exceeding the threshold value satisfy the GPD distribution , for any wind speed sample exceeding the threshold value , there is a variable also satisfying the GPD distribution, when the mean value and there is a linear relationship and is the initial point, the initial point of the linear relationship is taken as the threshold value ; ； wherein: represents a desired; represents a random variable of the wind speed sample; S303: Determine the threshold value by the following formula ; 。 5. The wind speed distribution prediction method for bridge wind-induced vibration fatigue analysis of claim 1, wherein: In step S5, in the conditional probability model, it is assumed that the wind speed and the wind direction are independent of each other and the wind speed distribution is the conditional distribution under a fixed wind direction, and the wind direction probability density function satisfies the following assumptions: 1) It is assumed that the wind speed of any given wind direction conforms to the same distribution model; 2) It is assumed that the probability of any wind direction is the proportion of the number of wind speeds of the wind direction to the total number of wind speeds.

6. The wind speed distribution prediction method for bridge wind-induced vibration fatigue analysis of claim 5, wherein: The wind direction probability density function is represented by the following formula: ； wherein: represents the wind direction probability density function; represents the wind direction represents the total number of wind speed samples; represents the total number of wind speed samples for all wind directions; represents the wind direction angle.

7. The wind speed distribution prediction method for bridge wind-induced vibration fatigue analysis of claim 5, wherein: The wind speed distribution model considering the influence of the wind direction is represented by the following formula: ； ； wherein: represents the wind speed cumulative distribution function considering the wind direction; represents the wind speed probability density function considering the wind direction; represents the wind direction probability density function; is the probability density function of the wind direction under the wind direction is the parameter vector of the wind direction under the wind direction wherein ; In the formula: Indicates wind direction The threshold at that time; Indicates wind direction Shape parameters of the GPD model at time; Indicates wind direction The scaling parameters of the GPD model at time; Indicates wind direction The bandwidth parameters at that time.

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