Vertical temperature gradient fatigue load spectrum of steel box girder bridge with wing plate and construction method

Abstract

The invention discloses a vertical temperature gradient fatigue load spectrum of a steel box girder bridge with a wing plate and a construction method. The vertical temperature gradient fatigue load spectrum comprises five vertical temperature sub-gradients and occurrence probabilities thereof. According to the structural characteristics of the steel box girder with the wing plate and the spatial and temporal distribution characteristics of a temperature field, temperature field measuring point arrangement and temperature data monitoring are carried out, clustering analysis is carried out on a temperature representative value by adopting an EM algorithm, and a vertical temperature gradient fatigue load spectrum of the steel box girder bridge with the wing plate, which is adaptive to the designed service life of 100 years, 150 years and 200 years, is constructed. The constructed vertical temperature gradient fatigue load spectrum of the steel box girder bridge with the wing plate can provide a technical basis for temperature fatigue damage analysis and temperature-vehicle coupling fatigue damage analysis.

Description

Technical Field

[0001] The invention belongs to the technical field of bridge engineering, and in particular relates to a vertical temperature gradient fatigue load spectrum and a construction method of a steel box girder bridge with a wing plate. Background Art

[0002] During operation, steel box girder bridges with wing plates will inevitably be subject to the combined effects of vehicle loads and temperature loads. Under the coupled cyclic effects of temperature loads and vehicle loads, the fatigue detail damage of steel box girders with wing plates will increase significantly, and the fatigue damage under the effects of temperature and vehicle alone cannot be simply superimposed. Through the analysis of the temperature field data of steel box girders with wing plates, it can be seen that the temperature loads they bear include the cyclic effects of various types of temperature differences, such as daily temperature differences and seasonal temperature differences. Therefore, it is necessary to use the temperature field monitoring data of steel box girders with wing plates to establish a temperature gradient fatigue load spectrum, calculate the temperature fatigue stress history, and couple it with vehicle fatigue stress to conduct fatigue damage analysis. Summary of the invention

[0003] The technical problem to be solved by the present invention is to provide a vertical temperature gradient fatigue load spectrum and a construction method for a steel box girder bridge with wing plates.

[0004] The technical solution adopted to solve the above technical problems is: a vertical temperature gradient fatigue load spectrum of a steel box girder bridge with flanges, which consists of 5 vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0005]

[0006] In formula (1), T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, h is the cross-sectional height of the steel box girder bridge with flange, Gi is the ith vertical temperature sub-gradient, T Gi,1 , T Gi,2 , T Gi,3 are the representative values ​​of the temperature at the top plate, at a height of 0.86h from the bottom plate, and at the bottom plate in the i-th vertical temperature sub-gradient, respectively, T G1,1 , T G1,2 , T G1,3 are the representative values ​​of the temperature at the top plate, at a height of 0.86h from the bottom plate, and at the bottom plate in the first vertical temperature sub-gradient, T G1,1 The value range is [5.3,6.2], the unit is ℃, T G1,2 The value range is [4.8,5.4], the unit is ℃, T Gi,j is the temperature at the jth typical height in the ith vertical temperature sub-gradient, N d is the design service life, T G1,j is the temperature representative value at the jth typical height in the first vertical temperature sub-gradient, P(TG1 (y))、P(T G2 (y))、P(T G3 (y))、P(T G4 (y))、P(T G5 (y)) are the occurrence probabilities of the five vertical temperature sub-gradients within the design service life, T G1,1 , T G2,1 , T G3,1 , T G4,1 , T G5,1 They are the representative values ​​of temperature at the top plate of the five vertical temperature sub-gradients.

[0007] The present invention also provides a method for constructing a temperature gradient fatigue load spectrum of a steel box girder bridge with a flange, comprising the following steps:

[0008] Step 1: Arrange a measuring point on the bottom plate of the steel box girder bridge with flanges, and take the measuring point as the coordinate origin, arrange measuring points on the middle web and top plate along the vertical height direction, and arrange K measuring points in total. Collect the temperature value of each measuring point at a certain interval to obtain the measured temperature gradient time history curve at each height position; expand the measured temperature gradient time history curve to the design service life N through the long short-term memory recursive neural network d The temperature history at typical positions is calculated, and the daily temperature difference between each measuring point on the middle web and top plate and the measuring point on the bottom plate is calculated, and the maximum and minimum values ​​of the daily temperature difference are selected to obtain the daily temperature difference extreme value matrix Q = [S1, S2,,…, S K-1 ],S m is the daily temperature difference extreme value matrix of the mth measuring point, m∈[1,K-1],

[0009]

[0010] Where, t is the tth day within the design service life, y m is the position coordinate of the mth measuring point, for y m The temperature maximum on day t is for y m The temperature minimum on day t;

[0011] Step 2: Use the expectation maximization algorithm EM to obtain the daily temperature difference extreme value matrix S of the mth measuring point m The clustering results

[0012] 1) Initialize the mean parameter μ, variance parameter σ, and prior parameter π of the expectation maximization algorithm EM

[0013] Set the number of clusters c l The initial value is 2, and the mean parameter μ is 2×c lThe matrix, the value range of the elements in the mean parameter μ is [0,1], and the variance parameter σ is c l ×2×2 spatial unit diagonal matrix, with a priori parameter π and length c l The initial value of the element in the prior parameter π is 1 / c l ;

[0014] 2) According to the daily temperature difference extreme value matrix S m Get the posterior probability matrix Γ of the daily temperature difference extreme value ztk

[0015] Define the vector of the temperature difference extreme value at the mth measuring point on the tth day as the kth cluster z tk , k∈[1,c l ], the coordinates of the cluster center C of the kth cluster group are μ k,: , using the set mean parameter μ, variance parameter σ, and prior parameter π, a mixed multivariate normal joint distribution probability density function is constructed to obtain the posterior probability of the initial daily temperature difference extreme value at the mth measuring point

[0016]

[0017] In the formula, is the posterior probability The kth column data, is the kth data in the mean parameter π before updating, is the k-th row of data of the mean parameter μ before updating, To update the kth group c in the forward error parameter σ l ×c l Plane matrix data, N(*) is to satisfy the following is the mean and is the two-dimensional normal distribution of the covariance matrix, S m t，: For S m The t-th row vector of the matrix;

[0018] 3) According to the posterior probability of the initial daily temperature difference extreme value of the mth measuring point Update the parameters of the expectation maximization algorithm EM according to the following formula;

[0019]

[0020] In the formula, (*) T is the transpose of the matrix, is the updated parameter of the expectation maximization algorithm EM, N k is the sum of the posterior probabilities;

[0021] 4) Repeat steps 2) and 3) until the difference between the updated parameters of the expectation maximization algorithm EM and the corresponding parameters before the update is less than 0.01, and obtain the final posterior probability of the extreme value of the daily temperature difference at the mth measuring point;

[0022] 5) According to the final posterior probability of the daily temperature difference extreme value of the mth measuring point, the daily temperature difference extreme value matrix S of the mth measuring point m Classify the daily temperature difference extreme data;

[0023] The daily temperature difference extreme value data has a posterior probability for each clustering group. The daily temperature difference extreme value data of the mth measuring point is divided into the clustering group with the highest corresponding posterior probability, and the mth measuring point c is obtained. l cluster data, where the coordinates of the cluster center of the kth cluster are (π 1,k ,π 2,k );

[0024] 6) At the mth measuring point c obtained in step 5) l Based on the clustering clusters, add one clustering cluster, repeat steps 2), 3), 4), and 5), and obtain the optimal number of clustering clusters c for the mth measurement point according to the Akaike information criterion. l =5;

[0025] Step 3, according to step 2, traverse the daily temperature difference extreme value matrix of each measuring point in the daily temperature difference extreme value matrix Q of the measuring points on the middle web and the top plate, and obtain 5 clustering groups for each measuring point. Sort the 5 clustering groups of each measuring point from small to large according to the value of the cluster center point. The clustering groups of K measuring points constitute a measuring point clustering group matrix with 5 columns and K rows. The clustering groups in the same column of the measuring point clustering group matrix are merged, and the new clustering group obtained is the sub-gradient of the temperature gradient fatigue load spectrum. The value of the cluster center point of the temperature measuring point clustering group at each height is the representative temperature value at each height of the sub-gradient. The ratio of the number of daily temperature difference extreme value vectors in the original top plate measuring point clustering group in the sub-gradient to the total number of daily temperature difference extreme value vectors in the sub-gradient is the occurrence probability of the sub-gradient in the design service life.

[0026] Preferably, the arrangement method of the K measuring points in step 1 is: arrange one measuring point on the bottom plate of the steel box girder bridge with wing plates, and take the measuring point as the coordinate origin, arrange measuring points on the middle web and the top plate along the vertical height direction, and arrange K=8 measuring points in total. The positions of the measuring points are expressed as the vertical distance from the lower surface of the bottom plate of the steel box girder bridge with wing plates as 0.0m, h-1.20m, h-0.60m, h-0.30m, h-0.20m, h-0.10m, h-0.05m, h.

[0027] Preferably, the temperature value interval of each measuring point in step 1 is 60 to 1200 seconds.

[0028] The beneficial effects of the present invention are as follows:

[0029] 1. The present invention establishes a vertical temperature gradient fatigue load spectrum for a steel box girder bridge with wing plates based on the structural characteristics and the spatiotemporal distribution characteristics of the temperature field of the steel box girder bridge with wing plates. This spectrum can more accurately reflect the temperature loads to which the bridge is subjected during actual operation, and is suitable for long-life anti-fatigue design and fatigue life assessment of 100, 150 and 200 years, providing a scientific design basis for the long-term performance of the bridge.

[0030] 2. The present invention adopts the EM algorithm to propose a corresponding method for constructing a temperature gradient fatigue load spectrum, which can reasonably sort and cluster each measuring point according to probability, improve the accuracy and efficiency of load spectrum construction, and provide a technical basis for temperature fatigue damage analysis and temperature-vehicle coupled fatigue damage analysis.

[0031] 3. The present invention reduces unnecessary design conservatism through scientific methods, thereby optimizing bridge design and reducing costs while ensuring bridge safety. At the same time, the present invention takes into account the cyclic effects of various types of temperature differences such as daily temperature differences and seasonal temperature differences, so that the load spectrum can adapt to different environmental conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a schematic diagram of the three-dimensional structure of a steel box girder bridge with wing plates.

[0033] Figure 2 This is the vertical temperature sub-gradient model of the temperature gradient fatigue load spectrum of the steel box girder bridge with flange.

[0034] Figure 3 is the probability of occurrence of the gradient of the temperature gradient fatigue load spectrum of the steel box girder bridge with flange.

[0035] Figure 4 Schematic diagram of the process of constructing the temperature gradient fatigue load spectrum of the steel box girder bridge with flange in Example 1.

[0036] Figure 5 This is the layout diagram of temperature measurement points for steel box girder bridge with wing plates.

[0037] Figure 6 This is the temperature time history curve at a typical height of a steel box girder bridge with flanges.

[0038] Figure 7 Results of Akaike information criterion analysis of temperature data of steel box girder bridge with flanges.

[0039] Figure 8 EM cluster analysis results of steel box girder bridge with flange. DETAILED DESCRIPTION

[0040] The present invention is further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to these embodiments.

[0041] Example 1

[0042] This embodiment takes the Shenyang Houdingxiang Ring Expressway steel box girder bridge as an example, the beam height h is 3.00m, and the three-dimensional structure is as follows Figure 1 The temperature gradient fatigue load spectrum model of the highway steel box girder bridge with flange in this embodiment is composed of 5 vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0043]

[0044] In formula (1), T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, h is the cross-sectional height of the steel box girder bridge with flange, Gi is the ith vertical temperature sub-gradient, T Gi,1 , T Gi,2 , T Gi,3 are the representative values ​​of the temperature at the top plate, at a height of 0.86h from the bottom plate, and at the bottom plate in the i-th vertical temperature sub-gradient, respectively, T G1,1 , T G1,2 , T G1,3 are the representative values ​​of the temperature at the top plate, at a height of 0.86h from the bottom plate, and at the bottom plate in the first vertical temperature sub-gradient, T G1,1 The value range is [5.3,6.2], the unit is ℃, T G1,2 The value range is [4.8,5.4], the unit is ℃, T Gi,j is the temperature at the jth typical height in the ith vertical temperature sub-gradient, N d is the design service life, T G1,j is the temperature representative value at the jth typical height in the first vertical temperature sub-gradient, P(T G1 (y))、P(T G2 (y))、P(T G3 (y))、P(T G4 (y))、P(T G5 (y)) are the occurrence probabilities of the five vertical temperature sub-gradients within the design service life, T G1,1 , T G2,1 , T G3,1 , T G4,1 , T G5,1 They are the representative values ​​of temperature at the top plate of the five vertical temperature sub-gradients.

[0045] Among them, the temperature value at the top plate in the first vertical temperature sub-gradient is T G1,1 =5.9℃, the temperature value T at a height of 0.86h from the bottom plate G1,2 =5.2℃, bottom plate temperature value T G1,3=3.7℃. The representative values ​​of the temperature at typical locations in each sub-gradient of the temperature gradient fatigue load spectrum constructed for the design service life of 100 years, 150 years, and 200 years are shown in Table 1. The linear gradient mode of the temperature at typical vertical measuring points of the sub-gradient is as follows: Figure 2 As shown in Figure 1, 150 and 200 years are long-life design service life, and the sub-gradient T G1 ~T G5 The probability of occurrence is 11.9%, 30.5%, 21.6%, 23.2%, 12.8%, such as Figure 3 shown.

[0046] Table 1 Representative values ​​of temperature gradient fatigue load spectrum of steel box girder bridge with flange

[0047]

[0048] exist Figure 4 In this embodiment, a method for constructing a temperature gradient fatigue load spectrum model of a steel box girder bridge with flanges includes the following steps:

[0049] Step 1. Arrange a measuring point on the bottom plate of the steel box girder bridge with wing plates, and take the measuring point as the coordinate origin. Arrange measuring points on the middle web and top plate along the vertical height direction. Arrange 9 measuring points in total, denoted as K1~K9. The vertical distance from the lower surface of the bottom plate of the steel box girder with wing plates is represented by y. The positions of different measuring points can be respectively denoted as 0.00m, 0.90m, 1.80m, 2.40m, 2.70m, 2.80m, 2.90m, 2.95m, and 3.00m. The y=0.00m measuring point is arranged on the bottom plate of the steel box girder, i.e., the coordinate origin. The y=3.00m measuring point is arranged on the top plate of the steel box girder. The y=0.90m, 1.80m, 2.40m, 2.70m, 2.80m, 2.90m, and 2.95m are arranged on the middle web of the steel box girder, respectively. The specific measuring point arrangement diagram is as follows Figure 5 As shown, long-term temperature acquisition is performed on these measuring points with an acquisition interval of 1 second to obtain the effective temperature data for the most recent year, and the measured temperature gradient time history curve is calculated. The measured temperature gradient time history curve is shown in Figure 6 The measured temperature gradient time history curve is extended to the design service life N through the long short-term memory recurrent neural network. d The temperature history at typical positions is calculated, and the daily temperature difference between each measuring point on the middle web and top plate and the measuring point on the bottom plate is calculated, and the maximum and minimum values ​​of the daily temperature difference are selected to obtain the daily temperature difference extreme value matrix Q = [S1, S2,,…, S K-1 ],S m is the daily temperature difference extreme value matrix of the mth measuring point, m∈[1,K-1], and the collection interval in this embodiment can also be 1800 seconds;

[0050]

[0051] Where, t is the tth day within the design service life, y m is the position coordinate of the mth measuring point, for y m The temperature maximum on day t is for y m The temperature minimum on day t;

[0052] Step 2: Use the expectation maximization algorithm EM to obtain the daily temperature difference extreme value matrix S of the mth measuring point m The clustering results

[0053] 1) Initialize the mean parameter μ, variance parameter σ, and prior parameter π of the expectation maximization algorithm EM to set the number of clusters c l The initial value is 2, and the mean parameter μ is 2×c l The matrix, the value range of the elements in the mean parameter μ is [0,1], and the variance parameter σ is c l ×2×2 spatial unit diagonal matrix, with a priori parameter π and length c l The initial value of the element in the prior parameter π is 1 / c l ;

[0054] 2) According to the daily temperature difference extreme value matrix S m Get the posterior probability matrix Γ of the daily temperature difference extreme value ztk

[0055] Define the vector formed by the extreme value of daily temperature difference at the mth measuring point on the tth day as the kth cluster z tk , k∈[1,c l ], the coordinates of the cluster center C of the kth cluster group are μ k,: , using the set mean parameter μ, variance parameter σ, and prior parameter π, a mixed multivariate normal joint distribution probability density function is constructed to obtain the posterior probability of the initial daily temperature difference extreme value at the mth measuring point

[0056]

[0057] In the formula, is the posterior probability The kth column data, is the kth data in the mean parameter π before updating, is the k-th row of data of the mean parameter μ before updating, To update the kth group c in the forward error parameter σ l ×c l Plane matrix data, N(*) is to satisfy the following is the mean and is the two-dimensional normal distribution of the covariance matrix, S m t，: For S mThe t-th row vector of the matrix;

[0058] 3) According to the posterior probability of the initial daily temperature difference extreme value of the mth measuring point Update the parameters of the expectation maximization algorithm EM according to the following formula;

[0059]

[0060] In the formula, (*) T is the transpose of the matrix, is the updated parameter of the expectation maximization algorithm EM, N k is the sum of the posterior probabilities;

[0061] 4) Repeat steps 2) and 3) until the difference between the updated parameters of the expectation maximization algorithm EM and the corresponding parameters before the update is less than 0.01, and obtain the final posterior probability of the extreme value of the daily temperature difference at the mth measuring point;

[0062] 5) According to the final posterior probability of the daily temperature difference extreme value of the mth measuring point, the daily temperature difference extreme value matrix S of the mth measuring point m Classify the daily temperature difference extreme data;

[0063] The daily temperature difference extreme value data has a posterior probability for each clustering group. The daily temperature difference extreme value data of the mth measuring point is divided into the clustering group with the highest corresponding posterior probability, and the mth measuring point c is obtained. l cluster data, where the coordinates of the cluster center of the kth cluster are (π 1,k ,π 2,k );

[0064] 6) At the mth measuring point c obtained in step 5) l Based on the clustering clusters, add one clustering cluster, repeat steps 2), 3), 4), and 5), and obtain the optimal number of clustering clusters c for the mth measurement point according to the Akaike information criterion. l =5, such as Figure 7 As shown;

[0065] Step 3, according to step 2, traverse the daily temperature difference extreme value vector of each measuring point in the daily temperature difference extreme value matrix Q of the measuring points on the middle web and the top plate, and obtain 5 cluster families for each measuring point. Sort the 5 cluster families of each measuring point from small to large according to the value of the cluster center point. The cluster families of 8 measuring points constitute a measuring point cluster family matrix with 5 columns and 8 rows. The cluster families in the same column of the measuring point cluster family matrix are merged, and the new cluster family obtained is the sub-gradient of the temperature gradient fatigue load spectrum model. The value of the cluster center point of the original top plate measuring point cluster family is the temperature representative value of the sub-gradient. The ratio of the number of daily temperature difference extreme value vectors in the original top plate measuring point cluster family in the sub-gradient to the total number of daily temperature difference extreme value vectors in the sub-gradient is the occurrence probability of the sub-gradient in the design service life. The clustering results are as follows: Figure 8 shown.

Claims

1. A vertical temperature gradient fatigue load spectrum for a steel box girder bridge with flanges, characterized in that: The load spectrum consists of five vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically: In formula (1), T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, h is the cross-sectional height of the steel box girder bridge with flange, Gi is the ith vertical temperature sub-gradient, T Gi,1 , T Gi,2 , T Gi,3 are the representative values ​​of the temperature at the top plate, at a height of 0.86h from the bottom plate, and at the bottom plate in the i-th vertical temperature sub-gradient, respectively, T G1,1 , T G1,2 , T G1,3 are the representative values ​​of the temperature at the top plate, at a height of 0.86h from the bottom plate, and at the bottom plate in the first vertical temperature sub-gradient, T G1,1 The value range is [5.3,6.2], the unit is ℃, T G1,2 The value range is [4.8,5.4], the unit is ℃, T Gi,j is the temperature at the jth typical height in the ith vertical temperature sub-gradient, N d is the design service life, T G1,j is the temperature representative value at the jth typical height in the first vertical temperature sub-gradient, P(T G1 (y))、P(T G2 (y))、P(T G3 (y))、P(T G4 (y))、P(T G5 (y)) are the occurrence probabilities of the five vertical temperature sub-gradients within the design service life, T G1,1 , T G2,1 , T G3,1 , T G4,1 , T G5,1 They are the representative values ​​of temperature at the top plate of the five vertical temperature sub-gradients.

2. The method for constructing the vertical temperature gradient fatigue load spectrum of the steel box girder bridge with flange according to claim 1 is characterized in that: The following steps are involved: Step 1: Arrange a measuring point on the bottom plate of the steel box girder bridge with flanges, and take the measuring point as the coordinate origin. Arrange measuring points on the middle web and top plate along the vertical height direction. Arrange K measuring points in total. Collect the temperature value of each measuring point at a certain interval to obtain the measured temperature gradient time history curve at each height position. Extend the measured temperature gradient time history curve to the design service life N through the long short-term memory recursive neural network. d The temperature history at typical positions is calculated, and the daily temperature difference between each measuring point on the middle web and top plate and the measuring point on the bottom plate is calculated, and the maximum and minimum values ​​of the daily temperature difference are selected to obtain the daily temperature difference extreme value matrix Q = [S1, S2,,…, S K-1 ],S m is the daily temperature difference extreme value matrix of the mth measuring point, m∈[1,K-1], Where, t is the tth day within the design service life, y m is the position coordinate of the mth measuring point, for y m The temperature maximum on day t is for y m The temperature minimum on day t; Step 2: Use the expectation maximization algorithm EM to obtain the daily temperature difference extreme value matrix S of the mth measuring point m The clustering results 1) Initialize the mean parameter μ, variance parameter σ, and prior parameter π of the expectation maximization algorithm EM to set the number of clusters c l The initial value is 2, and the mean parameter μ is 2×c l The matrix, the value range of the elements in the mean parameter μ is [0,1], and the variance parameter σ is c l ×2×2 spatial unit diagonal matrix, with a priori parameter π and length c l The initial value of the element in the prior parameter π is 1 / c l ; 2) According to the daily temperature difference extreme value matrix S m Get the posterior probability matrix Γ of the daily temperature difference extreme value ztk Define the vector of the temperature difference extreme value at the mth measuring point on the tth day as the kth cluster z tk , k∈[1,c l ], the coordinates of the cluster center C of the kth cluster group are μ k,: , using the set mean parameter μ, variance parameter σ, and prior parameter π, a mixed multivariate normal joint distribution probability density function is constructed to obtain the posterior probability of the initial daily temperature difference extreme value at the mth measuring point In the formula, is the posterior probability The kth column data, is the kth data in the mean parameter π before updating, is the k-th row of data of the mean parameter μ before updating, To update the kth group c in the forward error parameter σ l ×c l Plane matrix data, N(*) is to satisfy the following is the mean and is the two-dimensional normal distribution of the covariance matrix, S mt，: For S m The t-th row vector of the matrix; 3) According to the posterior probability of the initial daily temperature difference extreme value of the mth measuring point Update the parameters of the expectation maximization algorithm EM according to the following formula; In the formula, (*) T is the transpose of the matrix, is the updated parameter of the expectation maximization algorithm EM, N k is the sum of the posterior probabilities; 4) Repeat steps 2) and 3) until the difference between the updated parameters of the expectation maximization algorithm EM and the corresponding parameters before the update is less than 0.01, and obtain the final posterior probability of the extreme value of the daily temperature difference at the mth measuring point; 5) According to the final posterior probability of the daily temperature difference extreme value of the mth measuring point, the daily temperature difference extreme value matrix S of the mth measuring point m Classify the daily temperature difference extreme data; The daily temperature difference extreme value data has a posterior probability for each clustering group. The daily temperature difference extreme value data of the mth measuring point is divided into the clustering group with the highest corresponding posterior probability, and the mth measuring point c is obtained. l cluster data, where the coordinates of the cluster center of the kth cluster are (π 1,k ,π 2,k ); 6) At the mth measuring point c obtained in step 5) l Based on the clustering clusters, add one clustering cluster, repeat steps 2), 3), 4), and 5), and obtain the optimal number of clustering clusters c for the mth measurement point according to the Akaike information criterion. l =5; Step 3, according to step 2, traverse the daily temperature difference extreme value matrix of each measuring point in the daily temperature difference extreme value matrix Q of the measuring points on the middle web and the top plate, and obtain 5 clustering groups for each measuring point. Sort the 5 clustering groups of each measuring point from small to large according to the value of the cluster center point. The clustering groups of K measuring points constitute a measuring point clustering group matrix with 5 columns and K rows. The clustering groups in the same column of the measuring point clustering group matrix are merged, and the new clustering group obtained is the sub-gradient of the temperature gradient fatigue load spectrum. The value of the cluster center point of the temperature measuring point clustering group at each height is the representative temperature value at each height of the sub-gradient. The ratio of the number of daily temperature difference extreme value vectors in the original top plate measuring point clustering group in the sub-gradient to the total number of daily temperature difference extreme value vectors in the sub-gradient is the occurrence probability of the sub-gradient in the design service life.

3. The method for constructing vertical temperature gradient fatigue load spectrum of steel box girder bridge with flange according to claim 2 is characterized in that: The arrangement method of the K measuring points in the step 1 is: arrange one measuring point on the bottom plate of the steel box girder bridge with wing plates, and take the measuring point as the coordinate origin, arrange measuring points on the middle web and the top plate along the vertical height direction, and arrange K=8 measuring points in total. The positions of the measuring points are expressed as 0.00m, h-1.20m, h-0.60m, h-0.30m, h-0.20m, h-0.10m, h-0.05m, and h from the vertical distance from the lower surface of the bottom plate of the steel box girder bridge with wing plates.

4. The method for constructing vertical temperature gradient fatigue load spectrum of steel box girder bridge with flange according to claim 2 is characterized in that: The temperature value interval of each measuring point in step 1 is 60 to 1200 seconds.

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