Long-life railway steel box girder bridge vertical temperature gradient fatigue load spectrum and construction method

Abstract

A long-life railway steel box girder bridge vertical temperature gradient fatigue load spectrum and construction method, the load spectrum contains four vertical temperature sub-gradient and its occurrence probability. According to the temperature field distribution characteristics of railway steel box girder bridge, temperature sensors are arranged for long-term monitoring of temperature field, and K-means clustering method is used to analyze temperature data, to clarify the seasonal vertical temperature gradient difference of railway steel box girder, to determine the four types of temperature fatigue load spectrum of railway steel box girder bridge, and to obtain the occurrence probability of different temperature sub-gradient by statistical means, to construct the vertical temperature gradient fatigue load spectrum of railway steel box girder bridge suitable for design service life of 100 years, 150 years and 200 years. The constructed railway steel box girder temperature fatigue load spectrum reflects the temperature gradient characteristics of railway steel box girder bridge in different seasons, which can be used for temperature fatigue damage calculation of railway steel box girder bridge.

Description

Technical Field

[0001] The present 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 for a long-life railway steel box girder bridge. Background Art

[0002] Railway steel box girders, characterized by their large height and short flanges, exhibit complex vertical temperature gradients. These nonlinear vertical temperature gradients can generate longitudinal thermal fatigue stresses in their cross-sections, leading to thermal fatigue damage. Because railway steel box girders are subject to temperature cycles that include both daily and seasonal temperature gradients, a temperature gradient fatigue load spectrum can be used to characterize the thermal fatigue of railway steel box girder bridges. Therefore, it is necessary to utilize long-term temperature field monitoring data for railway steel box girders to construct a thermal fatigue load spectrum that reflects the characteristics of these periodic temperature cycles. 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 long-life railway steel box girder bridge.

[0004] The technical solution adopted to solve the above technical problems is: a vertical temperature gradient fatigue load spectrum for long-life railway steel box girder bridges. The model consists of four vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0005]

[0006] Where, T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, H is the height of the railway steel box girder bridge section, in meters, 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, at a height of 0.91H from the bottom plate, at a height of 1 / 2H from the bottom plate, and at 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, 0.91H height, 1 / 2H height from the bottom plate, and the bottom plate in the first vertical temperature sub-gradient, respectively. G1,1 The value range is [2.4,3.0], the unit is ℃, T G1,3 The value range is [2.5,3.0], 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, TG1,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 These are the representative temperature values ​​at the top plate of the four vertical temperature sub-gradients.

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

[0008] Step 1: Temperature data collection

[0009] Temperature measuring points are arranged on the top plate, bottom plate and web of the railway steel box girder bridge and the temperature values ​​of each measuring point are collected at regular intervals. There are m measuring points in total. The measured temperature gradient time history curve is obtained. 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 typical locations, calculate the daily temperature maximum value of each measuring point, and construct the daily temperature extreme value matrix S,

[0010]

[0011] Where y m is the position coordinate of the mth measuring point, is the maximum temperature value on the first day at the first measuring point, The Nth position at the first measuring point d ×365 days of maximum temperature, T Nd (y m ,1) is the maximum temperature value of the first day at the mth measuring point, The Nth measurement point at the mth measurement point d × Maximum temperature for 365 days;

[0012] Step 2: Use the K-means clustering method to define cluster families and classify each row vector of the daily temperature extreme value matrix S into the corresponding cluster family.

[0013] Step 2.1, define the number of clusters c l , randomly select c from the daily temperature extreme value matrix S l The row vectors are used as cluster centers, and a cluster family is constructed with each cluster center, and a total of c l cluster families;

[0014] Step 2.2: Calculate the Euclidean distance between each row vector of the daily temperature extreme value matrix S and each cluster center, and classify each row vector into the cluster group corresponding to the cluster center with the smallest Euclidean distance.

[0015] Step 3: Update cluster centers and classification results

[0016] The vector obtained by averaging all vector points in each cluster family is used as the virtual new cluster center of each cluster family, and the Euclidean distance d between the virtual new cluster center of each cluster family and the old cluster center is calculated. e , Euclidean distance d e ≤ set threshold d th The cluster center of the cluster family remains unchanged; the Euclidean distance d e >Set threshold d th The virtual new cluster center is used as the new cluster center, and step 2.2 is repeated to update until the Euclidean distance d between the virtual new cluster center and the old cluster center of all cluster families is e ≤ set threshold d th , get the final cluster family;

[0017] Step 4: Determine the reasonable number of clusters c l :

[0018] 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 clusters of the clusters are formed, and the cluster centers of each final cluster constitute the cluster center matrix. The residual sum of squares of the maximum residual temperature SSE is obtained according to the following formula for each cluster center matrix. l -SSE two-dimensional line chart, according to the elbow rule, determine the reasonable number of clusters c l value;

[0019]

[0020] Where S t,: is the t-th row vector in the daily temperature extreme value matrix S, is the k-th row vector in the cluster center matrix;

[0021] Step 5: Determine the temperature fatigue load spectrum applicable to railway steel box girder bridges

[0022] Use the number of clusters c determined in step 4 l And the corresponding cluster center matrix C endEach cluster family is a vertical temperature sub-gradient. 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 temperature fatigue load spectrum of the long-life railway steel box girder bridge.

[0023] Preferably, the threshold d th The value range is [0.00005,0.01].

[0024] Preferably, the arrangement method of the m measuring points in step 1 is: arrange a measuring point on the bottom plate of the railway steel box girder bridge, and use 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 m=8 measuring points in total. The positions of the measuring points are expressed as 0.0m, L-4.2m, L-2.4m, L-1.4m, L-0.5m, L-0.2m, L-0.1m, and L in vertical distance from the lower surface of the bottom plate of the flangeless steel box girder.

[0025] Preferably, the temperature values ​​of each measuring point collected in step 1 are collected at intervals of 60 to 1200 seconds.

[0026] The beneficial effects of the present invention are as follows:

[0027] 1. The present invention establishes a vertical temperature gradient fatigue load spectrum suitable for the long-life fatigue design and evaluation of railway steel box girder bridges. The constructed railway steel box girder vertical temperature gradient fatigue load spectrum consists of four temperature sub-gradients, reflecting the temperature gradient characteristics of railway steel box girder bridges in different seasons. It can calculate the temperature fatigue stress history within the design service life, which is of great significance to improving the anti-fatigue design system of railway steel box girder bridges in my country.

[0028] 2. The present invention uses the K-means clustering method and the damage equivalence principle to propose a method for constructing the vertical temperature gradient fatigue load spectrum of the railway steel box girder bridge. The vertical temperature gradient fatigue load spectrum can be constructed using the long-term monitoring data of the temperature field of the railway steel box girder bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 This is a schematic diagram of the three-dimensional structure of a railway steel box girder bridge.

[0030] Figure 2 It is the vertical temperature sub-gradient model of railway steel box girder bridge.

[0031] Figure 3 is the frequency of each temperature sub-gradient of the railway steel box girder bridge.

[0032] Figure 4 This is a flow chart of an embodiment of the present invention.

[0033] Figure 5This is a diagram showing the arrangement of temperature measurement points for a railway steel box girder bridge according to an embodiment of the present invention.

[0034] Figure 6 This is a temperature history diagram of a railway steel box girder bridge according to an embodiment of the present invention.

[0035] Figure 7 Cluster analysis of railway steel box girder bridges l -SSE line chart.

[0036] Figure 8 Cluster analysis results of railway steel box girder bridges. DETAILED DESCRIPTION

[0037] 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 these examples.

[0038] like Figure 1 This example uses a railway steel box girder bridge with a beam height of 4.80m in Northwest China as an example. The vertical temperature gradient fatigue load spectrum of this long-life railway steel box girder bridge consists of four vertical temperature sub-gradients and the probability of occurrence of the sub-gradients within the design service life, specifically:

[0039]

[0040] Where, T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, H is the height of the railway steel box girder bridge section, in meters, 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, at a height of 0.91H from the bottom plate, at a height of 1 / 2H from the bottom plate, and at 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, 0.91H height, 1 / 2H height from the bottom plate, and the bottom plate in the first vertical temperature sub-gradient, respectively. G1,1 The value range is [2.4,3.0], the unit is ℃, T G1,3 The value range is [2.5,3.0], 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 These are the representative temperature values ​​at the top plate of the four vertical temperature sub-gradients.

[0041] In this embodiment, T G1,1 2.7℃, T G1,3 The temperature representative values ​​of the temperature fatigue load spectrum of the long-life railway steel box girder bridge constructed with a design service life of 2.8℃ and 100, 150, and 200 years are shown in Table 1. The vertical sub-gradient pattern is as follows: Figure 2 As shown, 150 years and 200 years are the long-life design service life, and the sub-gradient T G1 ~T G4 The probability of occurrence is 15.7%, 26.9%, 32.8%, 24.6%, such as Figure 3 .

[0042] Table 1 Representative values ​​of temperature gradient fatigue load spectrum of railway steel box girder bridge

[0043]

[0044] exist Figure 4 The method for constructing the temperature fatigue load spectrum of the long-life railway steel box girder bridge comprises the following steps:

[0045] Step 1: Temperature data collection

[0046] Arrange a measuring point on the bottom plate of the railway steel box girder bridge, and use this measuring point as the coordinate origin. Arrange measuring points on the web and top plate along the vertical height direction. Arrange m = 8 measuring points in total. Collect the temperature value of each measuring point at intervals of 1 second. The vertical distance from the lower surface of the bottom plate of the railway steel box girder is y. The positions of different measuring points are recorded as 0.0m, 0.6m, 2.4m, 3.4m, 4.3m, 4.5m, 4.7m, and 4.8m respectively. The measuring point arrangement diagram is shown in the figure below. Figure 5 As shown in the figure, the measured temperature gradient time history curve is obtained, as shown in the figure Figure 6 As shown in the figure, 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 typical locations, calculate the daily temperature maximum value of each measuring point, and construct the daily temperature extreme value matrix S,

[0047]

[0048] Where y m is the position coordinate of the mth measuring point, is the maximum temperature value on the first day at the first measuring point, The Nth position at the first measuring point d ×365 days of maximum temperature, is the maximum temperature value on the first day at the mth measuring point, The Nth measurement point at the mth measurement point d × 365 days of temperature maximum; the acquisition time of the temperature value of the measuring point in this embodiment can also be an interval of 1800 seconds;

[0049] Step 2: Use the K-means clustering method to define cluster families and classify each row vector of the daily temperature extreme value matrix S into the corresponding cluster family.

[0050] Step 2.1, define the number of clusters c l , randomly select c from the daily temperature extreme value matrix S l The row vectors are used as cluster centers, and a cluster family is constructed with each cluster center, and a total of c l cluster families;

[0051] Step 2.2: Calculate the Euclidean distance between each row vector of the daily temperature extreme value matrix S and each cluster center, and classify each row vector into the cluster group corresponding to the cluster center with the smallest Euclidean distance.

[0052] Step 3: Update cluster centers and classification results

[0053] The vector obtained by averaging all vector points in each cluster family is used as the virtual new cluster center of each cluster family, and the Euclidean distance d between the virtual new cluster center of each cluster family and the old cluster center is calculated. e , Euclidean distance d e ≤ set threshold d th The cluster center of the cluster family remains unchanged; the Euclidean distance d e >Set threshold d th The virtual new cluster center is used as the new cluster center, and step 2.2 is repeated to update until the Euclidean distance d between the virtual new cluster center and the old cluster center of all cluster families is e ≤ set threshold d th , get the final cluster family;

[0054] The threshold d th The value range of is [0.00005, 0.01]. The threshold d in this embodiment th =0.0001;

[0055] Step 4: Determine the reasonable number of clusters c l :

[0056] Let the number of clusters c lare integers from 2 to 10, and the number of corresponding clusters c is obtained by following steps 2 and 3. l The 9 final clusters of the clusters are formed, and the cluster centers of each final cluster constitute the cluster center matrix. The residual sum of squares of the maximum residual temperature SSE is obtained according to the following formula for each cluster center matrix. l -SSE 2D line chart, such as Figure 7 , according to the elbow rule, determine the reasonable number of clusters c l Values, such as Figure 8 ;

[0057]

[0058] Where S t,: is the t-th row vector in the daily temperature extreme value matrix S, is the k-th row vector in the cluster center matrix;

[0059] Step 5: Determine the temperature fatigue load spectrum applicable to railway steel box girder bridges

[0060] Use the number of clusters c determined in step 4 l =4 and the corresponding cluster center matrix C end Each cluster family is a vertical temperature sub-gradient. 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 temperature fatigue load spectrum of the long-life railway steel box girder bridge.

Claims

1. A vertical temperature gradient fatigue load spectrum for a long-life railway steel box girder bridge, characterized by: 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: Where, T Gi (y) is the temperature of the ith vertical temperature sub-gradient at position y, H is the height of the railway steel box girder bridge section, in meters, 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, at a height of 0.91H from the bottom plate, at a height of 1 / 2H from the bottom plate, and at 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, 0.91H height, 1 / 2H height from the bottom plate, and the bottom plate in the first vertical temperature sub-gradient, respectively. G1,1 The value range is [2.4,3.0], the unit is ℃, T G1,3 The value range is [2.5,3.0], 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 These are the representative temperature values ​​at the top plate of the four vertical temperature sub-gradients.

2. The method for constructing a vertical temperature gradient fatigue load spectrum for a long-life railway steel box girder bridge according to claim 1, characterized in that: The following steps are involved: Step 1: Temperature data collection Temperature measuring points are arranged on the top plate, bottom plate and web of the railway steel box girder bridge and the temperature values ​​of each measuring point are collected at regular intervals. There are m measuring points in total. The measured temperature gradient time history curve is obtained. 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 typical locations, calculate the daily temperature maximum value of each measuring point, and construct the daily temperature extreme value matrix S, Where y m is the position coordinate of the mth measuring point, is the maximum temperature value on the first day at the first measuring point, The Nth position at the first measuring point d ×365 days of maximum temperature, is the maximum temperature value on the first day at the mth measuring point, The Nth measurement point at the mth measurement point d × Maximum temperature for 365 days; Step 2: Use the K-means clustering method to define cluster families and classify each row vector of the daily temperature extreme value matrix S into the corresponding cluster family. Step 2.1, define the number of clusters c l , randomly select c from the daily temperature extreme value matrix S l The row vectors are used as cluster centers, and a cluster family is constructed with each cluster center, and a total of c l cluster families; Step 2.2: Calculate the Euclidean distance between each row vector of the daily temperature extreme value matrix S and each cluster center, and classify each row vector into the cluster group corresponding to the cluster center with the smallest Euclidean distance. Step 3: Update cluster centers and classification results The vector obtained by averaging all vector points in each cluster family is used as the virtual new cluster center of each cluster family, and the Euclidean distance d between the virtual new cluster center of each cluster family and the old cluster center is calculated. e , Euclidean distance d e ≤ set threshold d th The cluster center of the cluster family remains unchanged; the Euclidean distance d e >Set threshold d th The virtual new cluster center is used as the new cluster center, and step 2.2 is repeated to update until the Euclidean distance d between the virtual new cluster center and the old cluster center of all cluster families is e ≤ set threshold d th , get the final cluster family; Step 4: Determine the reasonable 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 clusters of the clusters are formed, and the cluster centers of each final cluster constitute the cluster center matrix. The residual sum of squares of the maximum residual temperature SSE is obtained according to the following formula for each cluster center matrix. l -SSE two-dimensional line chart, according to the elbow rule, determine the reasonable number of clusters c l value; Where S t,: is the t-th row vector in the daily temperature extreme value matrix S, is the k-th row vector in the cluster center matrix; Step 5: Determine the temperature fatigue load spectrum applicable to railway steel box girder bridges Use the number of clusters c determined in step 4 l And the corresponding cluster center matrix C end Each cluster family is a vertical temperature sub-gradient. 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 temperature fatigue load spectrum of the long-life railway steel box girder bridge.

3. The method for constructing a vertical temperature gradient fatigue load spectrum for a long-life railway steel box girder bridge according to claim 2 is characterized by: The threshold d th The value range is [0.00005,0.01].

4. The method for constructing a vertical temperature gradient fatigue load spectrum for a long-life railway steel box girder bridge according to claim 2 is characterized in that: The arrangement method of the m measuring points in step 1 is as follows: a measuring point is arranged on the bottom plate of the railway steel box girder bridge, and with the measuring point as the coordinate origin, measuring points are arranged on the middle web and the top plate along the vertical height direction, with a total of m=8 measuring points arranged. The positions of the measuring points are expressed as 0.0m, L-4.2m, L-2.4m, L-1.4m, L-0.5m, L-0.2m, L-0.1m, and L in vertical distance from the lower surface of the bottom plate of the steel box girder without flange plates.

5. The method for constructing a vertical temperature gradient fatigue load spectrum for a long-life railway steel box girder bridge according to claim 2 is characterized in that: In step 1, the temperature values ​​of each measuring point are collected at intervals of 60 to 1200 seconds.

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