Concrete box girder bridge temperature gradient fatigue load spectrum and construction method

Abstract

A concrete box girder bridge temperature gradient fatigue load spectrum and construction method, the temperature gradient fatigue load spectrum contains vertical and lateral temperature gradient fatigue load spectrum, both composed of four temperature sub-gradient and its probability. Using long-term monitoring data of concrete box girder bridge temperature field, the space-time distribution characteristics of concrete box girder temperature field are analyzed, and the construction method of concrete box girder bridge temperature gradient fatigue load spectrum is proposed based on K-medians clustering method. The temperature gradient fatigue load spectrum of concrete box girder bridge suitable for design service life of 100 years, 150 years and 200 years is constructed, which can calculate the stress history of concrete box girder bridge and be used for long-life fatigue design of concrete box girder bridge.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge engineering, and in particular relates to a temperature gradient fatigue load spectrum of a concrete box girder bridge and a construction method thereof. Background Art

[0002] During operation, concrete box-girder bridges must withstand not only vehicle loads but also fluctuating temperature loads. Analysis of temperature field monitoring data for concrete box-girder bridges reveals that the temperature stresses they experience include cyclic effects of daily and seasonal temperature fluctuations. Previous studies have shown that the fatigue damage caused by the coupled effects of temperature and vehicle loads is 7% to 15% higher than that caused by vehicle loads alone. Furthermore, the fatigue damage caused by temperature and vehicle loads alone cannot be simply combined. Therefore, it is necessary to utilize temperature field monitoring data for fatigue damage analysis of concrete box-girder bridges.

[0003] Concrete box girder bridges are typical closed-section bridges with thicker walls, resulting in thermal conductivity significantly different from that of steel bridges. Under solar radiation, temperature gradients not only occur vertically or transversely along the cross-section height or width, but also along the thickness of the box girder wall. Because concrete box girder bridges are subject to temperature fluctuations, including cyclical effects such as daily and seasonal temperature differences, it is necessary to construct a temperature gradient fatigue load spectrum for concrete box girder bridges to calculate their thermal fatigue stress history and meet the requirements of fatigue damage analysis. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a temperature gradient fatigue load spectrum of a concrete box girder bridge and a construction method thereof.

[0005] The technical solution adopted to solve the above technical problems is: a temperature gradient fatigue load spectrum for concrete box girder bridges, which includes a vertical temperature gradient fatigue load spectrum and a transverse temperature gradient fatigue load spectrum; the vertical temperature gradient fatigue load spectrum is composed of four vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0006]

[0007] Where, T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, H is the cross-sectional height of the concrete box girder bridge, Gi is the ith vertical temperature sub-gradient, T Gi,1 、T Gi,2 、T Gi,3 、T Gi,4 are the representative values ​​of the temperature at the top plate, 0.9H from the bottom plate, 1 / 6H from the bottom plate, and the bottom plate in the i-th vertical temperature sub-gradient, respectively. G1,1 、TG1,2 、T G1,3 、T G1,4 are the representative temperature values ​​at the top plate, 0.9H height, 1 / 6H height, and bottom plate in the first vertical temperature sub-gradient, respectively. G1,1 The value range is [18.0, 23.0], the unit is ℃, T G1,2 The value range is [14.0,18.0], the unit is ℃, T Gi,j is the temperature representative value at the jth typical height in the i-th 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)) are the occurrence probabilities of the four vertical temperature sub-gradients within the design service life, T G1,1 、T G2,1 、T G3,1 、T G4,1 are the representative temperature values ​​at the top plate of the four vertical temperature sub-gradients;

[0008] The transverse temperature gradient fatigue load spectrum is composed of four transverse temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0009]

[0010] Where Hq is the qth transverse temperature sub-gradient, T Hq (x) is the temperature of the qth transverse temperature sub-gradient at the transverse position x, B is the top plate width of the concrete box girder bridge, T Hq,w is the temperature representative value at the wth typical transverse position in the qth transverse temperature sub-gradient, T Hq,1 、T Hq,2 、T Hq,3 、T Hq,4 are the representative values ​​of the temperature at the edge of the sunny side, 1 / 2B away from the edge of the sunny side, 3 / 4B away from the edge of the sunny side, and the edge of the shady side in the qth transverse temperature sub-gradient, respectively. H1,1 The value range is [8.0,10.0], the unit is ℃, T H1,2 The value range is [3.4,5.4], the unit is ℃, T H1,w is the temperature representative value at the wth typical transverse position in the first transverse temperature sub-gradient, P(T H1 (y))、P(T H2 (y))、P(T H3 (y))、P(TH4 (y)) are the occurrence probabilities of the four transverse temperature sub-gradients within the design service life, T H1,1 、T H2,1 、T H3,1 、T H4,1 are the representative values ​​of the temperature at the edge of the sunny side in the four transverse temperature sub-gradients.

[0011] Preferably, the designed service life N d 100 years or 150 years or 200 years.

[0012] The present invention also provides a method for constructing a temperature gradient fatigue load spectrum of a concrete box girder bridge, comprising the following steps:

[0013] Step 1: Collect temperature data of concrete box girder bridge

[0014] A total of m measuring points are arranged on the concrete box girder bridge. The temperature values ​​of each measuring point are collected at regular intervals to obtain the measured temperature gradient time history curve of each position. The measured temperature gradient time history curve is extended to the design service life N using the long short-term memory recursive neural network algorithm. d The temperature history at the typical location is used to obtain the maximum daily temperature at each measuring point every day within the design service life, and the design service life daily temperature extreme value matrix Q = [M1, M2, ..., M t ,…,M Nd×365 ],M t is the daily temperature maximum vector of each measuring point on day t;

[0015] Step 2: Use K-median clustering algorithm to define the initial cluster centers and cluster families

[0016] Step 2.1, define the number of clusters c l , randomly select c from the daily temperature extreme value matrix Q of the design service life l vectors as the initial cluster centers, and construct a cluster family with each initial cluster center, constructing a total of c l cluster families;

[0017] Step 2.2: Calculate the Euclidean distance between each initial cluster center and all vectors in the daily temperature extreme value matrix Q of the design service life, excluding the initial cluster center, and classify the vectors into the cluster family corresponding to the initial cluster center with the smallest Euclidean distance.

[0018] Step 3: Update cluster centers and cluster families

[0019] Step 3.1, calculate the Euclidean distance between the virtual new cluster center of the cluster family and other vectors in the cluster family and sum them up, select the virtual new cluster center with the smallest sum of Euclidean distances, if the virtual new cluster center is inconsistent with the initial cluster center, then the virtual new cluster center is determined as the new cluster center, otherwise the cluster center is not updated until c l The cluster centers are determined and c l Final cluster centers;

[0020] Step 3.2, from c l The updated final cluster centers are selected from the final cluster centers, the Euclidean distance between each vector in the daily temperature extreme value matrix Q of the design service life and each updated final cluster center is calculated, and the vector is classified into the cluster family corresponding to the updated cluster center with the smallest Euclidean distance;

[0021] Step 4: Determine the optimal number of clusters c l :

[0022] Let the number of clusters c l are integers from 2 to 10, and the number of corresponding clusters c is obtained by following steps 2 and 3. l The 9 final cluster families are formed, and the cluster centers of each final cluster family form a cluster center matrix. The residual square sum RMSE of the maximum residual temperature is obtained according to the following formula for each cluster center matrix, and the c l -RMSE two-dimensional line chart, based on the elbow rule, determine the optimal number of clusters c l The value is 4;

[0023]

[0024] Where, is the k-th row vector in the cluster center matrix;

[0025] Step 5: Determine the temperature gradient fatigue load spectrum of the concrete box girder bridge

[0026] Use the number of clusters c determined in step 4 l And the corresponding cluster center matrix C end Each cluster family is a sub-gradient of the vertical temperature gradient fatigue load spectrum. The row vector of the cluster center matrix is ​​the typical representative value of each temperature sub-gradient. The number of sample points in each cluster family divided by the total number is the occurrence probability of each sub-gradient, thereby obtaining the corresponding concrete box girder bridge temperature gradient fatigue load spectrum.

[0027] Preferably, the m measuring points in step 1 are used to construct the vertical temperature gradient fatigue load spectrum, and the arrangement method is: arrange a measuring point on the bottom plate of the concrete box girder bridge, and use the measuring point as the coordinate origin, bury measuring points on the web and the top plate along the vertical height direction, and arrange m=8 measuring points in total. The positions of the measuring points are expressed as 0.00m, H-3.71m, H-2.40m, H-1.10m, H-0.70m, H-0.40m, H-0.20m, H in terms of the vertical distance from the lower surface of the bottom plate of the concrete box girder bridge.

[0028] Preferably, the m measuring points in step 1 are used to construct the transverse temperature gradient fatigue load spectrum, and the arrangement method is: arrange a measuring point on the top plate of the concrete box girder bridge, and use the measuring point as the coordinate origin, bury measuring points on the top plate along the transverse direction, and arrange a total of m=5 measuring points. The positions of the measuring points are expressed as 1.50m, L-8.75m, L-6.00m, L-3.25m, and L-1.50m in terms of the horizontal distance from the concrete box girder bridge to the coordinate origin.

[0029] Preferably, the temperature value collection interval of each measuring point in step 1 is 60 to 1200 seconds.

[0030] The beneficial effects of the present invention are as follows:

[0031] 1. The temperature gradient fatigue load spectrum for concrete box girder bridges proposed in this invention includes transverse and vertical temperature fatigue load spectra, both of which are composed of multiple temperature sub-gradients and the probability of occurrence of sub-gradients. They can simulate the temperature stress history of concrete box girder bridges within their design service life.

[0032] 2. The method for constructing the temperature gradient fatigue load spectrum of concrete box girder bridge proposed in this invention is based on the K-median clustering algorithm, which can efficiently perform cluster analysis on long-term temperature monitoring data of the temperature field to obtain different temperature sub-gradient models.

[0033] 3. The present invention uses long-term monitoring data of the temperature field of concrete box girder bridges to analyze the spatiotemporal distribution characteristics of the temperature field of concrete box girders, ensuring the accuracy and practicality of the load spectrum. It also uses a long-short-term memory recursive neural network algorithm to expand the measured temperature gradient time history curve, thereby improving the accuracy and reliability of temperature prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is an elevation view of a concrete box girder bridge implemented in the present invention.

[0035] Figure 2 It is the vertical temperature sub-gradient model of concrete box girder bridge.

[0036] Figure 3 is the frequency of each vertical temperature sub-gradient of the concrete box girder bridge.

[0037] Figure 4 Construct a flow chart for the transverse and vertical temperature load spectrum for a concrete box girder bridge.

[0038] Figure 5 Schematic diagram of the arrangement of transverse and vertical temperature measurement points for concrete box girder bridge.

[0039] Figure 6 This is the measured vertical temperature gradient curve of the concrete box girder bridge.

[0040] Figure 7 c l -RMSE 2D line chart.

[0041] Figure 8 Cluster analysis results of vertical temperature data of concrete box girder bridge.

[0042] Figure 9 This is the transverse temperature sub-gradient model of the concrete box girder bridge.

[0043] Figure 10 is the frequency of each transverse temperature sub-gradient of the concrete box girder bridge.

[0044] Figure 11 Cluster analysis results of transverse temperature data of concrete box girder bridges. DETAILED DESCRIPTION

[0045] The present invention will be further described in detail below with reference to the accompanying drawings and examples, but the present invention is not limited to the following examples.

[0046] Example 1

[0047] This embodiment takes a concrete box continuous beam bridge with a beam height H of 4.40m in the northwest region as an example. Its three-dimensional structure is shown in the figure below. Figure 1 As shown in Figure 1, the temperature gradient fatigue load spectrum of a concrete box continuous beam bridge includes a vertical temperature gradient fatigue load spectrum and a transverse temperature gradient fatigue load spectrum. The vertical temperature gradient fatigue load spectrum consists of four vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0048]

[0049] Where, T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, H is the cross-sectional height of the concrete box girder bridge, Gi is the ith vertical temperature sub-gradient, T Gi,1 、T Gi,2 、T Gi,3 、T Gi,4 are the representative values ​​of the temperature at the top plate, 0.9H from the bottom plate, 1 / 6H from the bottom plate, and the bottom plate in the i-th vertical temperature sub-gradient, respectively. G1,1 、TG1,2 、T G1,3 、T G1,4 are the representative temperature values ​​at the top plate, 0.9H height, 1 / 6H height, and bottom plate in the first vertical temperature sub-gradient, respectively. G1,1 The value range is [18.0, 23.0], the unit is ℃, T G1,2 The value range is [14.0,18.0], the unit is ℃, T Gi,j is the temperature representative value at the jth typical height in the i-th 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)) are the occurrence probabilities of the four vertical temperature sub-gradients within the design service life, T G1,1 、T G2,1 、T G3,1 、T G4,1 are the representative temperature values ​​at the top plate of the four vertical temperature sub-gradients;

[0050] In this embodiment, T G1,1 =21.1℃, T G1,2 =16.5℃, the temperature representative values ​​of each vertical temperature sub-gradient of the vertical temperature gradient fatigue load spectrum with a design service life of 100 years, 150 years and 200 years are obtained from the above model, as shown in Table 1. The sub-gradient mode is as follows: Figure 2 As shown in the figure, 150 years and 200 years are long-life design service life, and the vertical temperature gradient fatigue load spectrum gradient T of the concrete box continuous beam bridge is G1 ~T G4 The probability of occurrence is 3.6%, 12.5%, 33.9%, 50%, such as Figure 3 .

[0051] Table 1 Representative values ​​of vertical temperature gradient fatigue load spectrum of concrete box girder

[0052]

[0053] exist Figure 4 In this embodiment, the method for constructing a vertical temperature gradient fatigue load spectrum for a concrete box girder bridge includes the following steps:

[0054] Step 1: Figure 5As shown, a measuring point is arranged on the bottom plate of the concrete box girder bridge, and with this measuring point as the coordinate origin, measuring points are buried on the web and top plate along the vertical height direction. A total of m = 8 measuring points are arranged, and the vertical distance from the lower surface of the concrete box girder bottom plate is expressed as y. The positions of different measuring points can be recorded as 0.00m, 0.50m, 1.81m, 3.12m, 3.52m, 3.82m, 4.02m, and 4.22m, respectively. Long-term temperature collection is performed on these measuring points to obtain valid temperature data for the past year. The collection interval is 1 second. In this embodiment, the collection interval can also be 20 seconds or 1800 seconds.

[0055] The measured temperature gradient time history curve is obtained based on the collected temperature data, such as Figure 6 The measured temperature gradient time history curve is extended to the design service life N using the long short-term memory recurrent neural network algorithm. d The temperature history at the typical location is used to obtain the maximum daily temperature at each measuring point every day within the design service life, and the design service life daily temperature extreme value matrix Q = [M1, M2, ..., M t ,…,M Nd×365 ],M t is the daily temperature maximum vector of each measuring point on day t;

[0056] Step 2: Use K-median clustering algorithm to define the initial cluster centers and cluster families

[0057] Step 2.1, define the number of clusters c l , randomly select c from the daily temperature extreme value matrix Q of the design service life l vectors as the initial cluster centers, and construct a cluster family with each initial cluster center, constructing a total of c l cluster families;

[0058] Step 2.2: Calculate the Euclidean distance between each initial cluster center and all vectors in the daily temperature extreme value matrix Q of the design service life, excluding the initial cluster center, and classify the vectors into the cluster family corresponding to the initial cluster center with the smallest Euclidean distance.

[0059] Step 3: Update cluster centers and cluster families

[0060] Step 3.1: All vectors in the same cluster family are taken as the virtual new cluster center of the cluster family in turn. The Euclidean distance between the virtual new cluster center of the cluster family and other vectors in the cluster family is calculated and summed up. The virtual new cluster center with the smallest sum of Euclidean distance is selected. If the virtual new cluster center is inconsistent with the initial cluster center, the virtual new cluster center is determined as the new cluster center. Otherwise, the cluster center is not updated until c l The cluster centers are determined and c l Final cluster centers;

[0061] Step 3.2, from c l The updated final cluster centers are selected from the final cluster centers, the Euclidean distance between each vector in the daily temperature extreme value matrix Q of the design service life and each updated final cluster center is calculated, and the vector is classified into the cluster family corresponding to the updated cluster center with the smallest Euclidean distance;

[0062] Step 4: Determine the optimal number of clusters c l :

[0063] Let the number of clusters c l are integers from 2 to 10, and the number of corresponding clusters c is obtained by following steps 2 and 3. l The 9 final cluster families are formed, and the cluster centers of each final cluster family form a cluster center matrix. The residual square sum RMSE of the maximum residual temperature is obtained according to the following formula for each cluster center matrix, and the c l -RMSE two-dimensional line chart, such as Figure 7 As shown, according to the elbow rule, the optimal number of clusters cl is determined to be 4, as shown in Figure 8 As shown;

[0064]

[0065] Where, is the k-th row vector in the cluster center matrix;

[0066] Step 5: Determine the temperature gradient fatigue load spectrum of the concrete box girder bridge

[0067] Use the number of clusters cl and the corresponding cluster center matrix C determined in step 4 end Each cluster family is a sub-gradient of the vertical temperature gradient fatigue load spectrum. The row vector of the cluster center matrix is ​​the typical representative value of each temperature sub-gradient. The number of sample points in each cluster family divided by the total number is the occurrence probability of each sub-gradient, thereby obtaining the corresponding concrete box girder bridge temperature gradient fatigue load spectrum.

[0068] The transverse temperature gradient fatigue load spectrum is composed of four transverse temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0069]

[0070] Where Hq is the qth transverse temperature sub-gradient, T Hq (x) is the temperature of the qth transverse temperature sub-gradient at the transverse position x, B is the top plate width of the concrete box girder bridge, T Hq,w is the temperature representative value at the wth typical transverse position in the qth transverse temperature sub-gradient, T Hq,1 、THq,2 、T Hq,3 、T Hq,4 are the representative temperature values ​​at the edge of the sunny side, 1 / 2B away from the edge of the sunny side, 3 / 4B away from the edge of the sunny side, and the edge of the shady side in the qth transverse temperature sub-gradient, respectively. H1,1 The value range is [8.0,10.0], the unit is ℃, T H1,2 The value range is [3.4,5.4], the unit is ℃, T H1,w is the temperature representative value at the wth typical transverse position in the first transverse temperature sub-gradient, P(T H1 (y))、P(T H2 (y))、P(T H3 (y))、P(T H4 (y)) are the occurrence probabilities of the four transverse temperature sub-gradients within the design service life, T H1,1 、T H2,1 、T H3,1 、T H4,1 are the representative values ​​of the temperature at the edge of the sunny side in the four transverse temperature sub-gradients.

[0071] In this embodiment, T H1,1 =8.9℃, T H1,2 =4.3℃, the temperature gradient fatigue load spectra constructed based on the design service life of 100 years, 150 years and 200 years are shown in Table 2. The transverse gradient mode is as follows Figure 9 As shown. Among them, 150 years and 200 years are the long-life design service life, and the sub-gradient T H1 ~T H4 The probability of occurrence is 12.3%, 40.7%, 28.4% and 18.5%. Figure 10 .

[0072] Table 2 Representative values ​​of gradient temperature for fatigue load spectrum of transverse temperature gradient of concrete box girder

[0073]

[0074] The method for constructing a transverse temperature gradient fatigue load spectrum for a concrete box girder bridge in this embodiment includes the following steps:

[0075] Step 1: Arrange a measuring point at the edge of the sunny side of the roof, and use this measuring point as the coordinate origin. Arrange m = 5 measuring points along the width of the roof. The measuring point positions are expressed as 1.50m, 3.25m, 6.00m, 8.75m, and 10.50m in horizontal distance from the coordinate origin. Figure 5 .

[0076] Steps 2 to 5 are the same as the method for constructing the vertical temperature gradient fatigue load spectrum of the concrete box girder bridge. The clustering results are as follows: Figure 11 shown.

Claims

1. A temperature gradient fatigue load spectrum for a concrete box girder bridge, characterized by: The load spectrum includes a vertical temperature gradient fatigue load spectrum and a transverse temperature gradient fatigue load spectrum. The vertical temperature gradient fatigue load spectrum is composed of four vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically: Where, T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, H is the cross-sectional height of the concrete box girder bridge, Gi is the ith vertical temperature sub-gradient, T Gi,1 、T Gi,2 、T Gi,3 、T Gi,4 are the representative values ​​of the temperature at the top plate, 0.9H from the bottom plate, 1 / 6H from the bottom plate, and the bottom plate in the i-th vertical temperature sub-gradient, respectively. G1,1 、T G1,2 、T G1,3 、T G1,4 are the representative temperature values ​​at the top plate, 0.9H height, 1 / 6H height, and bottom plate in the first vertical temperature sub-gradient, respectively. G1,1 The value range is [18.0, 23.0], the unit is ℃, T G1,2 The value range is [14.0,18.0], the unit is ℃, T Gi,j is the temperature representative value at the jth typical height in the i-th 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)) are the occurrence probabilities of the four vertical temperature sub-gradients within the design service life, T G1,1 、T G2,1 、T G3,1 、T G4,1 are the representative temperature values ​​at the top plate of the four vertical temperature sub-gradients; The transverse temperature gradient fatigue load spectrum is composed of four transverse temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically: Where Hq is the qth transverse temperature sub-gradient, T Hq (x) is the temperature of the qth transverse temperature sub-gradient at the transverse position x, B is the top plate width of the concrete box girder bridge, T Hq,w is the temperature representative value at the wth typical transverse position in the qth transverse temperature sub-gradient, T Hq,1 、T Hq,2 、T Hq,3 、T Hq,4 are the representative values ​​of the temperature at the edge of the sunny side, 1 / 2B away from the edge of the sunny side, 3 / 4B away from the edge of the sunny side, and the edge of the shady side in the qth transverse temperature sub-gradient, respectively. H1,1 The value range is [8.0,10.0], the unit is ℃, T H1,2 The value range is [3.4,5.4], the unit is ℃, T H1,w is the temperature representative value at the wth typical transverse position in the first transverse temperature sub-gradient, P(T H1 (y))、P(T H2 (y))、P(T H3 (y))、P(T H4 (y)) are the probability of occurrence of the four transverse temperature sub-gradients within the design service life, T H1,1 、T H2,1 、T H3,1 、T H4,1 They are the representative temperature values ​​at the edge of the sunny side in the four transverse temperature sub-gradients.

2. The temperature gradient fatigue load spectrum of a concrete box girder bridge according to claim 1 is characterized in that: The design service life N d 100 years or 150 years or 200 years.

3. The method for constructing the temperature gradient fatigue load spectrum of a concrete box girder bridge according to claim 1 is characterized in that: The following steps are involved: Step 1: Collect temperature data of concrete box girder bridge A total of m measuring points are arranged on the concrete box girder bridge. The temperature values ​​of each measuring point are collected at regular intervals to obtain the measured temperature gradient time history curve of each position. The measured temperature gradient time history curve is extended to the design service life N using the long short-term memory recursive neural network algorithm. d The temperature history at the typical location is used to obtain the maximum daily temperature at each measuring point every day within the design service life, and the design service life daily temperature extreme value matrix Q = [M1, M2, ..., M t ,…,M Nd×365 ],M t is the daily temperature maximum vector of each measuring point on day t; Step 2: Use K-median clustering algorithm to define the initial cluster centers and cluster families Step 2.1, define the number of clusters c l , randomly select c from the design service life daily temperature extreme value matrix Q l vectors as the initial cluster centers, and construct a cluster family with each initial cluster center, constructing a total of c l cluster families; Step 2.2: Calculate the Euclidean distance between each initial cluster center and all vectors in the daily temperature extreme value matrix Q of the design service life, excluding the initial cluster center, and classify the vectors into the cluster family corresponding to the initial cluster center with the smallest Euclidean distance. Step 3: Update cluster centers and cluster families Step 3.1, calculate the Euclidean distance between the virtual new cluster center of the cluster family and other vectors in the cluster family and sum them up, select the virtual new cluster center with the smallest sum of Euclidean distances, if the virtual new cluster center is inconsistent with the initial cluster center, then the virtual new cluster center is determined as the new cluster center, otherwise the cluster center is not updated until c l The cluster centers are determined and c l Final cluster centers; Step 3.2, from c l The updated final cluster centers are selected from the final cluster centers, the Euclidean distance between each vector in the daily temperature extreme value matrix Q of the design service life and each updated final cluster center is calculated, and the vector is classified into the cluster family corresponding to the updated cluster center with the smallest Euclidean distance; Step 4: Determine the optimal number of clusters c l : Let the number of clusters c l are integers from 2 to 10, and the number of corresponding clusters c is obtained by following steps 2 and 3. l The 9 final cluster families are formed, and the cluster centers of each final cluster family form a cluster center matrix. The residual square sum RMSE of the maximum residual temperature is obtained according to the following formula for each cluster center matrix, and the c l -RMSE two-dimensional line chart, based on the elbow rule, determine the optimal number of clusters c l The value is 4; Where, is the k-th row vector in the cluster center matrix; Step 5: Determine the temperature gradient fatigue load spectrum of the concrete box girder bridge Use the number of clusters c determined in step 4 l And the corresponding cluster center matrix C end Each cluster family is a sub-gradient of the vertical temperature gradient fatigue load spectrum. The row vector of the cluster center matrix is ​​the typical representative value of each temperature sub-gradient. The number of sample points in each cluster family divided by the total number is the occurrence probability of each sub-gradient, thereby obtaining the corresponding concrete box girder bridge temperature gradient fatigue load spectrum.

4. The method for constructing the temperature gradient fatigue load spectrum of a concrete box girder bridge according to claim 3 is characterized in that: The m measuring points described in step 1 are used to construct the vertical temperature gradient fatigue load spectrum. The arrangement method is as follows: a measuring point is arranged on the bottom plate of the concrete box girder bridge, and the measuring point is used as the coordinate origin. Measuring points are buried on the web and top plate along the vertical height direction. A total of m = 8 measuring points are arranged. The positions of the measuring points are expressed as 0.00m, H-3.71m, H-2.40m, H-1.10m, H-0.70m, H-0.40m, H-0.20m, H from the vertical distance from the lower surface of the bottom plate of the concrete box girder bridge.

5. The method for constructing the temperature gradient fatigue load spectrum of a concrete box girder bridge according to claim 3 is characterized in that: The m measuring points described in step 1 are used to construct the transverse temperature gradient fatigue load spectrum. The arrangement method is as follows: a measuring point is arranged on the top plate of the concrete box girder bridge, and the measuring point is used as the coordinate origin. Measuring points are buried on the top plate along the transverse direction. A total of m = 5 measuring points are arranged. The positions of the measuring points are expressed as 1.50m, L-8.75m, L-6.00m, L-3.25m, and L-1.50m in terms of the horizontal distance from the concrete box girder bridge to the coordinate origin.

6. The method for constructing the temperature gradient fatigue load spectrum of a concrete box girder bridge according to claim 3 is characterized in that: The temperature value collection interval of each measuring point in step 1 is 60 to 1200 seconds.

Images