Large-span bridge high-speed railway beam end area management unit division method

Abstract

The invention relates to the technical field of rail transit transportation, in particular to a large-span bridge high-speed railway beam end area management unit division method, which comprises the following steps: step 1, data preprocessing; performing first-order difference and moving average in sequence to pre-process the data so as to extract unsmooth fluctuation characteristics of the beam; 2, determining the position of a beam end unit based on a sliding window principal component analysis method; and step 3, determining the length of the beam end unit based on an optimization algorithm. According to the method, beam end area management unit division can be well carried out.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of rail transit technology, in particular to a large-span bridge high-speed railway beam end area management unit division method. BACKGROUND

[0002] The track inspection car measures the track dynamic irregularity data by the inertia reference method, wherein the track dynamic irregularity includes left high-low, right high-low, left track alignment, right track alignment, track gauge, level and triangular pit, etc., which together constitute the dynamic inspection data.

[0003] Railway bridges are developing rapidly, and kilometer-span bridges are gradually appearing in people's field of vision, but the maintenance strategy related thereto has not been updated and improved. Therefore, the development of high-speed railway large-span bridges is both an opportunity and a challenge.

[0004] Due to the large span of the main bridge of the kilometer-span bridge, the longitudinal expansion and contraction deformation thereof is greater than that of the approach bridge side, which will seriously damage the track quality. To solve this problem, a rail expansion adjuster (referred to as "adjuster") is configured in the beam end area between the main bridge and the approach bridge. Although the adjuster plays a role in adjusting the expansion and contraction deformation of the bridge, due to its special structure, the track irregularity in this area is also more prominent.

[0005] Currently, some scholars have proposed a high-speed railway ballastless track line management unit unequal length division method considering factors such as line parameters, structural characteristics, line state, maintenance capacity and operation means, which realizes automatic division through a two-stage method and establishes a dynamic unequal length division model. Other scholars have improved the bottom-up algorithm based on his research, which can more effectively identify poor sections and avoid dividing the worst section in two consecutive unit sections, while integrating the concept of multi-specialty comprehensive maintenance into the unit section division method, better adapting to the needs of multi-specialty collaborative maintenance of high-speed railways and improving the comprehensiveness and universality of the division method.

[0006] However, the existing unit division technology only divides stations, switches, bridges, tunnels, curves, slopes, etc. into unequal and fixed unit sections, without further dividing the internal unit of the kilometer-span bridge. If the entire kilometer-span bridge is taken as a unit section, the local irregularity characteristics cannot be clearly expressed, thereby hiding and diluting the track irregularity caused by the bridge structure, and thus it is impossible to make a reasonable maintenance decision. SUMMARY

[0007] The present invention provides a method for dividing the management unit area of ​​the beam end region of a (kilometer-level) long-span bridge for high-speed railways, which can solve the problems of the gap in the research on the division of beam end unit sections of long-span bridges for high-speed railways and the dilution of the smoothness difference in the beam end region.

[0008] According to a method for dividing the management unit area of ​​a (kilometer-level) long-span bridge high-speed railway beam end area, the present invention includes the following steps: Step 1: Data preprocessing; The data were preprocessed by first-order difference and moving average to extract the undulation characteristics of the beam ends. Step 2: Determine the position of beam end elements based on sliding window principal component analysis; Step 3: Determine the length of the beam end element based on the optimization algorithm.

[0009] As a preferred embodiment, in step 1, the first-order difference and moving average are performed sequentially on each channel of the motion detection data, as shown in the following formula:

[0010]

[0011] In the formula: Let be the first difference value of the i-th track dynamic irregularity data; This represents the (i+1)th orbital dynamic irregularity data; For the i-th orbital dynamic irregularity data; The value is the size of the sliding window, which is the number of consecutive data points used to calculate the average; t is the current time point. For time point t Simple moving average over a period of time.

[0012] Seven irregularity data points were obtained after preprocessing. The irregularities were compared with each other and combined with the beam end characteristics to determine the track gauge as an important channel.

[0013] As a preferred option, step 2 specifically involves: With a window length of 10m and an overlap rate of 0.5, a sliding window method is used to calculate the standard deviation and maximum amplitude of the track gauge within each window. Principal component analysis is then used to reduce the dimensionality of the two indicators within each window to a linear combination of the two, i.e., the first principal component. The standard deviation and maximum amplitude within each window are then normalized to form a two-dimensional feature vector. X Then standardize it to obtain To ensure they are compared on the same scale, the eigenvalues ​​are then solved using the covariance matrix C of the data from different dimensions. , and eigenvectors , The transformation matrix P is constructed using eigenvectors, and the data is finally projected onto the principal component space to obtain the first principal component PC1. The specific formula is as follows: The two most prominent maxima of the first principal component are taken as the center of the beam end element.

[0014]

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021] In the formula: Let be the normalized standard deviation within the i-th window; represents the normalized maximum amplitude within the i-th window; n is the total number of windows. The average value for each column vector; The standard deviation of each column vector; Let be the standardized standard deviation within the i-th window; The maximum normalized amplitude within the i-th window; This is the transpose of a standardized two-dimensional vector; v Represents the eigenvector. λ Represents eigenvalues; The value of the first principal component within the i-th window; The value of the second principal component within the i-th window; and These represent the standard deviations in the first principal component PC1, respectively. and maximum amplitude The weight (first principal direction).

[0022] Eigenvalues ​​are obtained by solving the covariance matrix C of data from different dimensions. , and eigenvectors , The transformation matrix P is constructed using eigenvectors, and finally the data is projected onto the principal component space to obtain the first principal component PC1 and the second principal component PC2.

[0023] Preferably, step 3 specifically involves: binning the gauge data within a certain unit length range according to the Freedman-Diaconis criterion, the formula of which is as follows:

[0024]

[0025] In the formula: This refers to the width of the container. It is the interquartile range, which is the difference between the 75th percentile and the 25th percentile; This represents the total number of data points. This represents the maximum gauge within the unit length. This represents the minimum track gauge within the unit length. This refers to the number of boxes; The track gauge data after Freedman-Diaconis binning is substituted into the information entropy calculation formula, which is as follows:

[0026] In the formula: unit length Values Track gauge information entropy at time; For falling in the first i Number of data points in each bin Total number of data points within the cell length range The ratio is the number of data points that fall on the th... i The probability of each box; the target length range of the beam end element is [30, 110] m; The optimal cell length is found using the Particle Swarm Optimization (PSO) algorithm with the objective of maximizing the orbital mass index. The PSO formula is as follows:

[0027]

[0028] In the formula: ω is the inertia weight, which controls the influence of historical velocity; c 1 and c 2 represents the individual cognitive factor and the group cognitive factor, which modulate the weights of individual cognition and social cooperation, respectively. r 1 and r 2 represents a random number within the range [0,1], increasing the randomness of the search; pbest i For particles i The historical best position; gbest This represents the current globally optimal position for the group. Finally, the length of the element with the highest track quality index is taken as the length of the beam end element.

[0029] To obtain the reasonable management length of dynamic irregularity sections in high-speed railway bridges with spans of over 1,000 meters, this invention proposes a method for rapidly determining the location and length of bridge end units based on dynamic inspection data. This method is based on the idea of ​​dividing the bridge into unequal-length unit segments and considering the irregularity characteristics within each unit segment of a kilometer-span bridge. This provides a guarantee for the bridge health monitoring and long-term operational safety of kilometer-span high-speed railway bridge beam end areas. The effects achieved by this invention are as follows: 1) Obtain the standard deviation and maximum amplitude within the gauge window through a sliding window, and use principal component analysis to reduce the two-dimensional vector to a linear combination of the two, and determine the maximum point of the first principal component at the beam end as the center mileage of the two beam end units. 2) The IEG-PSO algorithm is proposed. By calculating the orbital gauge information entropy of units with different lengths, the exploration boundary of the optimization algorithm particles is determined to be [30, 110] m. The optimal beam end unit length is determined by maximizing TQI as the fitness function. 3) Compared to summer, the optimal beam end unit length is longer in winter, but the optimal unit length of beam ends of different mileages is not much different. The target bridge beam end unit length was determined to be 50m through two aspects: track maintenance management and operation and data and model stability. Attached Figure Description

[0030] Figure 1 This is a flowchart of a method for dividing the management unit area of ​​a (kilometer-level) long-span bridge high-speed railway beam end area in Example 1; Figure 2 This is a comparison chart of the original data and the preprocessed data in Example 2; Figure 3 The first principal component PC1 diagram of the track gauge in Example 2; Figure 4 This is a schematic diagram of the Freedman-Diaconis criterion binning in Example 2; Figure 5 This is an entropy distribution diagram of the track gauge information at the beam end in Example 2; Figure 6 This is a graph showing the change of cell length and corresponding TQI with the number of iterations in Example 2; Figure 7(a) is a schematic diagram of the beam end at a small mileage in summer in Example 2; Figure 7(b) is a schematic diagram of the beam end at high mileage in summer in Example 2; Figure 7(c) is a schematic diagram of the beam end at low mileage in winter in Example 2; Figure 7(d) is a schematic diagram of the beam end at high mileage in winter in Example 2. Detailed Implementation

[0031] To further understand the content of this invention, a detailed description of the invention will be provided in conjunction with the accompanying drawings and embodiments. It should be understood that the embodiments are merely illustrative and not limiting of the invention.

[0032] Example 1 like Figure 1 As shown in the figure, this embodiment provides a method for dividing the management unit area of ​​the beam end of a (kilometer-level) long-span bridge on a high-speed railway, which includes the following steps: Step 1: Data preprocessing.

[0033] The data was preprocessed by performing first-order difference and moving average successively to extract the fluctuation characteristics of beam end irregularities; for each channel of the dynamic test data, first-order difference and moving average were performed successively, as shown in the following formula:

[0034]

[0035] In the formula: Let be the first difference value of the i-th track dynamic irregularity data; This represents the (i+1)th orbital dynamic irregularity data; For the i-th orbital dynamic irregularity data; The value is the size of the sliding window, which is the number of consecutive data points used to calculate the average; t is the current time point. For time point t Simple moving average over a period of time.

[0036] Seven irregularity data points were obtained after preprocessing. The irregularities were compared with each other and combined with the beam end characteristics to determine the track gauge as an important channel.

[0037] Step 2: Determine the position of beam end elements based on sliding window principal component analysis.

[0038] Specifically: With a window length of 10m and an overlap rate of 0.5, a sliding window method is used to calculate the standard deviation and maximum amplitude of the track gauge within each window. Then, principal component analysis is used to reduce the dimensionality of the two indicators within each window to a linear combination of the two, i.e., the first principal component. After normalizing the standard deviation and maximum amplitude within each window, a two-dimensional feature vector is constructed. X Then standardize it to obtain To ensure they are compared on the same scale, the eigenvalues ​​are then solved using the covariance matrix C of the data from different dimensions. , and eigenvectors , The transformation matrix P is constructed using eigenvectors, and the data is finally projected onto the principal component space to obtain the first principal component PC1, as shown in the following formula; the two most prominent maxima of the first principal component are taken as the center of the beam end element.

[0039]

[0040]

[0041]

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[0043]

[0044]

[0045]

[0046]

[0047] In the formula: Let be the normalized standard deviation within the i-th window; represents the normalized maximum amplitude within the i-th window; n is the total number of windows. The average value for each column vector; The standard deviation of each column vector; Let be the standardized standard deviation within the i-th window; The maximum normalized amplitude within the i-th window; This is the transpose of a standardized two-dimensional vector; v Represents the eigenvector. λ Represents eigenvalues; The value of the first principal component within the i-th window; The value of the second principal component within the i-th window; and These represent the standard deviations in the first principal component PC1, respectively. and maximum amplitude The weight (first principal direction).

[0048] Eigenvalues ​​are obtained by solving the covariance matrix C of data from different dimensions. , and eigenvectors , The transformation matrix P is constructed using eigenvectors, and finally the data is projected onto the principal component space to obtain the first principal component PC1 and the second principal component PC2.

[0049] Step 3: Determine the length of the beam end element based on the optimization algorithm.

[0050] Specifically, the gauge data within a certain unit length range is binned according to the Freedman-Diaconis criterion, and the formula is as follows:

[0051]

[0052] In the formula: This refers to the width of the container. It is the interquartile range, which is the difference between the 75th percentile and the 25th percentile; This represents the total number of data points. This represents the maximum gauge within the unit length. This represents the minimum track gauge within the unit length. This refers to the number of boxes.

[0053] The track gauge data after Freedman-Diaconis binning is substituted into the information entropy calculation formula, which is as follows:

[0054] In the formula: unit length Values Track gauge information entropy at time; For falling in the first i Number of data points in each bin Total number of data points within the cell length range The ratio is the number of data points that fall on the th... i The probability of being in each box.

[0055] When the unit length is 30m and 110m, the gauge information entropy curve is divided into three parts. Within the unit length range of [10, 30]m, the gauge information entropy increases sharply, indicating that the information density is low at this stage, and the information entropy is more sensitive to changes in unit length, making it difficult to accurately reflect the gauge fluctuation characteristics. Within the range of [30, 110]m, the information entropy increases almost linearly, indicating that the uncertainty and complexity of the gauge data gradually increase, and the distribution becomes more uniform and discrete. When the unit length increases to [110, 200]m, the growth of information entropy slows down and gradually stabilizes, reflecting that the data is too dispersed, the fluctuation characteristics are diluted by large-scale units, and the gauge irregularities at the beam end are weakened. If the beam end unit length is too short, it cannot completely cover the rail expansion joint, which will cause omissions of structural irregularities; while if the unit length is too long, it will dilute the irregularities in the beam end area. In summary, the target length range of the beam end element is [30, 110] m. Within this range, the linear characteristic of the gauge information entropy with the element length can better reflect the uncertainty of the gauge data fluctuation distribution with the change of the element length. The gauge is the most representative indicator of the smoothness at the beam end. The element length range determined in this way effectively reduces the complexity of determining the specific element length in the subsequent process and provides a specific and accurate particle exploration boundary for the particle swarm optimization algorithm.

[0056] The optimal cell length is found using the Particle Swarm Optimization (PSO) algorithm with the objective of maximizing the orbital mass index. The PSO formula is as follows:

[0057]

[0058] In the formula: ω is the inertia weight, which controls the influence of historical velocity; c 1 and c 2 represents the individual cognitive factor and the group cognitive factor, which modulate the weights of individual cognition and social cooperation, respectively. r 1 and r 2 represents a random number within the range [0,1], increasing the randomness of the search; pbest i For particles i The historical best position; gbest This represents the current global optimal position for the group.

[0059] Considering only the particles exploring in one-dimensional space, where dimension D is 1. Since the particle's motion direction is only along the direction of increasing distance and its opposite direction, its velocity can be approximated as a scalar. An excessively large particle swarm size will cause the particles to explore repeatedly, so the particle swarm size can be appropriately reduced to improve the particle exploration efficiency.

[0060] Finally, the length of the element with the highest track quality index is taken as the length of the beam end element.

[0061] This embodiment, based on dynamic inspection data and combined with the irregularity characteristics of the beam ends of long-span bridges on high-speed lines, determines the location and length range of beam end units. By comparing the pre-processed dynamic irregularity data, the track gauge is identified as a crucial factor affecting beam end smoothness. A sliding window principal component analysis method is proposed to determine the maximum point of the linear combination of the standard deviation and maximum amplitude of the track gauge as the center mileage of the beam end unit. Track gauge data of different unit lengths are binned according to the Freedman-Diaconis criterion, and the track gauge information entropy is calculated to narrow down the beam end unit length range, providing a boundary for particle exploration in the particle swarm optimization algorithm. The optimal unit length for different seasons is determined by maximizing the TQI (Total Quality I).

[0062] Example 2 Taking a dual-purpose (road and rail) steel truss suspension bridge as an example, the main bridge is 1428m long, with a span arrangement of (84+84+1092+84+84)m. The upper level houses an eight-lane highway, and the lower level has four high-speed railway tracks. The existing double-track railway has a design speed of 250km / h, with a reserved double-track design speed of 200km / h. To balance the expansion and contraction differences between the track and bridge caused by temperature changes, train loads, and concrete shrinkage and creep, the bridge uses SA60-1800 type rail expansion joints. These joints have a standard length of 18400mm and a design expansion range of ±900mm. Approximately 100 dynamic monitoring data points from 2022 and 2023 were selected.

[0063] The data processed by the "first-order difference-moving average" two-step method is as follows: Figure 2 As shown, the track gauge data in the beam end region exhibits significant fluctuations. Even though the elevation and alignment of the beam end region showed some abnormal fluctuations in the original data, these fluctuations were significantly reduced after preprocessing. However, the maximum peak value of the track gauge in the beam end region was not smoothed out; instead, it became more prominent than in other locations, indicating that the track gauge fluctuations in the beam end region are very drastic and are a key issue affecting the ride comfort at the beam end.

[0064] Principal component analysis (PC) was performed on the track gauge data. The variance explained ratio of the first principal component (PC1) to the second principal component (PC2) was 0.975:0.025. PC1 captured almost all variance information, and its first principal directions a1 and a2 were very close, approximately 0.707. PC2, on the other hand, contained almost no variance information. Therefore, PC1 can be used to replace the standard deviation and maximum amplitude to achieve data dimensionality reduction. (The text then abruptly shifts to a seemingly unrelated topic about track gauge PC1.) Figure 3 As shown.

[0065] The Freedman-Diaconis criterion is a method for determining histogram bin widths based on the interquartile range and the number of data points. Its core idea is to dynamically adjust the bin widths based on the data dispersion and quantity, thereby better reflecting the data's distribution characteristics. This method is independent of the data's distribution shape, making it particularly suitable for handling non-normally distributed data. Furthermore, the interquartile range itself is insensitive to extreme values, thus having low sensitivity to outliers and effectively reducing their impact. A binning diagram is shown below. Figure 4 As shown.

[0066] A higher gauge information entropy indicates a more variable and disordered gauge state. The gauge information entropy in the beam end region generally increases in three segments with increasing element length, such as... Figure 5 As shown, when the unit length is 30m and 110m, the gauge information entropy curve is divided into three parts, with the rate of change of each part being K1>K2>K3. Within the range of unit length [10,30]m, the gauge information entropy increases sharply, indicating that the information density is low at this stage, and the information entropy is more sensitive to changes in unit length, making it difficult to accurately reflect the gauge fluctuation characteristics. Within the range of [30,110]m, the information entropy increases almost linearly, indicating that the uncertainty and complexity of the gauge data gradually increase, and the distribution becomes more uniform and discrete. When the unit length increases to [110,200]m, the growth of information entropy slows down and gradually stabilizes, reflecting that the data is too dispersed, the fluctuation characteristics are diluted by large-scale units, and the irregularity characteristics of the gauge at the beam end are weakened.

[0067] The datasets were divided into summer and winter categories based on season. The summer dataset was sampled in June, July, and August of 2022 and 2023, while the winter dataset was sampled in December, January, and February of 2022 and 2023. The intra-cell TQI was negative, and the PSO algorithm was performed using TQI maximization as the fitness function. The particle number was set to 5, and the number of iterations was set to 20. The TQI and cell length of a specific motion detection data point from the summer dataset changed with the number of iterations as follows: Figure 6 As shown in Figures 7(a), 7(b), 7(c), and 7(d), the summer and winter datasets were optimized and averaged to obtain the optimal values ​​of the length of the beam end elements of different mileages in different seasons.

[0068] The present invention and its embodiments have been described above illustratively. This description is not restrictive, and the figures shown are only one embodiment of the present invention; the actual structure is not limited thereto. Therefore, if those skilled in the art are inspired by this description and design similar structures and embodiments without departing from the spirit of the present invention, such designs should fall within the protection scope of the present invention.

Claims

1. A method for dividing the management unit area of ​​long-span bridge beam ends in high-speed railways, characterized by: Includes the following steps: Step 1: Data preprocessing; The data were preprocessed by first-order difference and moving average to extract the undulation characteristics of the beam ends. Step 2: Determine the position of beam end elements based on sliding window principal component analysis; Step 3: Determine the length of the beam end element based on the optimization algorithm.

2. The method for dividing the management unit area of ​​the beam end region of a long-span bridge for high-speed railways according to claim 1, characterized in that: In step 1, the first-order difference and moving average are performed sequentially on each channel of the motion detection data, as shown in the following formula: ； ； In the formula: Let be the first difference value of the i-th track dynamic irregularity data; For the (i+1)th orbital dynamic irregularity data; For the i-th orbital dynamic irregularity data; The value is the size of the sliding window, which is the number of consecutive data points used to calculate the average; t is the current time point. For time point t simple moving average over a period of time; Seven irregularity data points were obtained after preprocessing. The irregularities were compared with each other and combined with the beam end characteristics to determine the track gauge as an important channel.

3. The method for dividing the management unit area of ​​the beam end region of a long-span bridge for high-speed railways according to claim 2, characterized in that: Step 2 specifically involves: With a window length of 10m and an overlap rate of 0.5, a sliding window method is used to calculate the standard deviation and maximum amplitude of the track gauge within each window. Then, principal component analysis is used to reduce the dimensionality of the two indicators within each window to a linear combination of the two, i.e., the first principal component. After normalizing the standard deviation and maximum amplitude within each window, a two-dimensional feature vector is constructed. X Then standardize it to obtain To ensure they are compared on the same scale, the eigenvalues ​​are then solved using the covariance matrix C of the data from different dimensions. , and eigenvectors , The transformation matrix P is constructed using eigenvectors, and the data is finally projected onto the principal component space to obtain the first principal component PC1. The specific formula is as follows: The two most prominent maxima of the first principal component are taken as the center of the beam end element. ； ； ； ； ； ； ； ； In the formula: Let be the normalized standard deviation within the i-th window; represents the normalized maximum amplitude within the i-th window; n is the total number of windows. The average value for each column vector; The standard deviation of each column vector; Let be the standardized standard deviation within the i-th window; The maximum normalized amplitude within the i-th window; This is the transpose of a standardized two-dimensional vector; v Represents the eigenvector. λ Represents eigenvalues; The value of the first principal component within the i-th window; The value of the second principal component within the i-th window; and These represent the standard deviations in the first principal component PC1, respectively. and maximum amplitude The weights; Eigenvalues ​​are obtained by solving the covariance matrix C of data from different dimensions. , and eigenvectors , The transformation matrix P is constructed using eigenvectors, and finally the data is projected onto the principal component space to obtain the first principal component PC1 and the second principal component PC2.

4. The method for dividing the management unit area of ​​the beam end region of a long-span bridge for high-speed railways according to claim 3, characterized in that: Step 3 specifically involves binning the gauge data within a certain unit length range according to the Freedman-Diaconis criterion, using the following formula: ； ； In the formula: This refers to the width of the container. It is the interquartile range, which is the difference between the 75th percentile and the 25th percentile; This represents the total number of data points. This represents the maximum gauge within the unit length. This represents the minimum track gauge within the unit length. This refers to the number of boxes; The track gauge data after Freedman-Diaconis binning is substituted into the information entropy calculation formula, which is as follows: ； In the formula: unit length Values Track gauge information entropy at time; For falling in the first i Number of data points in each bin Total number of data points within the cell length range The ratio is the number of data points that fall on the th... i The probability of each box; The target length range for the beam end element is [30, 110] m; The optimal cell length is found using the Particle Swarm Optimization (PSO) algorithm with the objective of maximizing the orbital mass index. The PSO formula is as follows: ； ； In the formula: ω is the inertia weight, which controls the influence of historical velocity; c 1 and c 2 represents the individual cognitive factor and the group cognitive factor, which modulate the weights of individual cognition and social cooperation, respectively. r 1 and r 2 represents a random number within the range [0,1], increasing the randomness of the search; pbest i For particles i The historical best position; gbest This represents the current globally optimal position for the group. Finally, the length of the element with the highest track quality index is taken as the length of the beam end element.

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