A Separate Monitoring Method for the Flexural Force of CWR Tracks on Ultra-Large Span Bridges

By setting measuring points on the bridge and using sensors to monitor the bridge deflection and daily temperature, a linear regression model and trend term method were established to separate the flexural forces on the ultra-long span bridge. Real-time and intelligent monitoring of each flexural force was achieved, solving the problem of unclear flexural force separation.

CN115950564BActive Publication Date: 2025-10-03BEIJING JIAOTONG UNIV
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Patent Information

Application Number
CN202310076719.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-01-16
Publication Date
2025-10-03
Estimated Expiration
2043-01-16

AI Technical Summary

Technical Problem

The existing technology lacks an effective method to separate and monitor the flexural forces of seamless rails on super-long span bridges, especially the temperature flexural forces, train flexural forces and road flexural forces.

Method used

By setting up multiple measuring points at key locations of seamless lines on long-span bridges, using sensors to monitor bridge deflection, daily temperature and rail longitudinal stress, a linear regression model and trend term extraction method are established, and the various flexural forces are separated by combining frequency differences.

Benefits of technology

It realizes the real-time monitoring of each flexural force, solves the problem of unclear flexural force separation, and forms an intelligent monitoring system for the longitudinal force of seamless lines on kilometer-level road-rail dual-use bridges, supporting the operation management and health monitoring of the line-bridge structure.

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Abstract

The present invention provides a method for separately monitoring the flexural force of a seamless track on an ultra-long span bridge. The method comprises: setting a plurality of measuring points at key positions of the seamless track on the long-span bridge, and using sensors to monitor the bridge deflection, daily temperature, and rail longitudinal stress at each measuring point; calculating the rail flexural additional force based on the linear correlation between the bridge deflection and the rail flexural additional force; calculating the separated temperature flexural force based on the linear correlation between the daily temperature and the temperature flexural force or using the frequency difference between the temperature effect and the live load effect; and obtaining the train flexural force by subtracting the live load flexural force from the average of the highway flexural force before and after the train passes the bridge based on the difference in frequency between the highway flexural force and the train flexural force in a short period of time. The method of the present invention can intuitively obtain the numerical value and variation law of the flexural force generated by different factors, solving the problem of unclear force on the flexural additional force of the seamless track on a kilometer-level highway-railway dual-use bridge.
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Description

Technical Field

[0001] The present invention relates to the technical field of seamless lines on bridges, and in particular to a method for separately monitoring the flexural force of seamless lines on ultra-long span bridges. Background Art

[0002] With the development of seamless railways (CRTs), they are subject not only to basic thermal forces but also to additional longitudinal forces caused by various factors. For CRTs on ultra-long-span dual-use highway and railway bridges, not only are these forces combined with the basic thermal forces and additional expansion and contraction forces, but also train loads and other factors, all of which can cause vertical displacement of the bridge, leading to beam-rail interaction. The additional forces generated by the relative displacement of the beam and rail due to bridge flexure are collectively referred to as flexural forces.

[0003] For super-large span dual-use highway and railway bridges that have been put into operation, such as the Wufengshan Yangtze River Bridge and the Shanghai-Nantong Yangtze River Bridge, the bridges will experience large-scale flexural deformations due to temperature changes in bridge cables and vehicle loads, resulting in temperature flexural forces and vehicle flexural forces. Figure 1 These are the daily monitoring results of the mid-span deflection of a kilometer-long dual-use highway-rail bridge. The results show that both the daily variation curves of the mid-span deflection and the daily temperature variation curve exhibit sinusoidal characteristics. Furthermore, the daily deflection curve exhibits spikes caused by train and road loads.

[0004] Currently, there are proposals in the prior art for separate monitoring methods of basic temperature force and additional telescopic force, but further research is needed on separate monitoring methods of flexural force. Summary of the Invention

[0005] An embodiment of the present invention provides a method for separately monitoring the flexural force of a seamless railway track on a super-long span bridge, so as to realize real-time monitoring of various forces of the seamless railway track on the super-long span bridge.

[0006] In order to achieve the above-mentioned purpose, the present invention adopts the following technical solutions.

[0007] A method for separately monitoring the flexural force of a seamless track on a super-long span bridge, comprising:

[0008] Multiple measuring points are set up at key locations of the CRT on long-span bridges, and sensors are used to monitor the bridge deflection, daily temperature, and rail longitudinal stress at each measuring point.

[0009] According to the linear correlation between bridge deflection and rail deflection additional force, the rail deflection additional force is obtained by calculating the bridge deflection;

[0010] The separated temperature deflection force is calculated based on the linear correlation between daily temperature and temperature deflection force;

[0011] According to the frequency difference between the road deflection force and the train deflection force, the train deflection force is obtained by subtracting the live load deflection force during the period when the train passes the bridge from the average road deflection force before and after the train passes the bridge.

[0012] Preferably, multiple measuring points are set at key positions of the seamless track on the long-span bridge, and sensors are used to monitor the bridge deflection, daily temperature and rail longitudinal stress at each measuring point, including:

[0013] Set up multiple measuring points at key locations of the CRT on a large-span bridge in an actual online-bridge project;

[0014] Based on the selected measuring points, the bridge deflection D(t), day temperature T and rail longitudinal stress at the measuring point are measured using sensors. σ Real-time monitoring is performed, and the sensors include: thermometer, GNSS, fiber grating stress sensor and acceleration sensor.

[0015] Preferably, the method of calculating the rail deflection additional force based on the bridge deflection according to the linear correlation between the bridge deflection and the rail deflection additional force comprises:

[0016] Establish the bridge deflection D(t) and the rail deflection additional force σ D (t), and the rail deflection additional force σ is calculated by using the linear regression model through the bridge deflection D(t) D (t), the functional expression of the linear regression model is:

[0017] σ D (t)=b1+a1D(t)+μ(t) (2)

[0018] Among them, a1 and b1 are the regression parameters in the linear regression model, D(t) is the deflection response at the measuring point at time t, σ D (t) is the additional rail bending force σ at the corresponding moment D (t), μ(t) is the random error.

[0019] Preferably, the calculation of the separation temperature deflection force based on the linear correlation between the daily temperature and the temperature deflection force includes:

[0020] Establish the relationship between daily temperature T and temperature deflection force σ TD (t), and the temperature deflection force σ is calculated by the linear regression model through the daily temperature T. TD (t), the functional expression of the linear regression model is:

[0021] σ TD (t)b2+a2T(tt d )+ μ (t) (3)

[0022] Where T is the daily temperature at time t, σ TD (t) is the temperature bending force caused by the temperature at time t, t d is the lag time of temperature deflection force relative to temperature, and the meanings of other parameters are the same as those in formula (2).

[0023] Preferably, the method also includes: utilizing the frequency difference between the temperature effect and the live load effect to calculate and separate the temperature flexural force, based on the long-period low-frequency trend term and high-frequency fluctuation term of the flexural force data corresponding to the temperature flexural force caused by the temperature load and the flexural force caused by the train and highway live-loaded vehicles, and using wavelet decomposition, empirical mode decomposition EMD and its variant algorithm trend term extraction method to separate the temperature flexural force.

[0024] Preferably, the train deflection force is obtained by subtracting the live load deflection force during the period when the train passes the bridge from the average of the road deflection force before and after the train passes the bridge based on the frequency difference between the road deflection force and the train deflection force, including:

[0025] When there is no train passing on the bridge, there is only the road deflection force σ generated by the road load GD , and the amplitude of the road flexural force will not change suddenly in a short period of time. During the period when the train passes the bridge, the live load flexural force σ HD (t) is generated by both road and train loads and has a sudden change. The live load deflection force during the period when the train passes the bridge is subtracted from the average road deflection force before and after the train passes the bridge to obtain the monitoring value of the train deflection force during this period. The train deflection force is expressed as:

[0026]

[0027] Where, σ LD (t) is the train bending force at time t during the train crossing the bridge, σ HD (t) is the live load deflection force at the corresponding moment, σ GD (t) The road bending force when there is no train passing the bridge. t1 and t2 correspond to the times before and after the train passes the bridge, respectively.

[0028] It can be seen from the technical solutions provided by the above-mentioned embodiments of the present invention that the present invention provides a method for separate monitoring of the flexural force of seamless lines on kilometer-level dual-purpose road-rail bridges. Based on the linear relationship between temperature flexural force and temperature, and utilizing the frequency difference between temperature effect and live load effect, the various flexural forces are effectively separated by establishing a linear regression model and trend item extraction, thereby realizing real-time monitoring of various forces.

[0029] Additional aspects and advantages of the present invention will be set forth in part in the following description, will become apparent from the following description, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0031] Figure 1 This is a schematic diagram of daily monitoring results of the mid-span deflection of the main span of a kilometer-long span highway-railway dual-purpose bridge in the prior art;

[0032] Figure 2 A processing flow chart for force separation monitoring of seamless track deflection on an ultra-long span road-rail dual-purpose bridge provided by an embodiment of the present invention;

[0033] Figure 3 A schematic diagram of the overall layout of health monitoring points for the Shanghai-Suzhou-Jiangyin Yangtze River Bridge provided in an embodiment of the present invention;

[0034] Figure 4 A schematic diagram of daily monitoring results of the mid-span deflection of a main span provided by an embodiment of the present invention;

[0035] Figure 5 A schematic diagram of the correlation between mid-span deflection and temperature provided by an embodiment of the present invention;

[0036] Figure 6 A schematic diagram of the correlation between temperature deflection force and temperature deflection provided by an embodiment of the present invention;

[0037] Figure 7 A schematic diagram of the correlation between train flexural force and bridge deflection provided by an embodiment of the present invention;

[0038] Figure 8 A schematic diagram of the correlation between highway flexural force and bridge deflection provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limiting the present invention.

[0040] It will be understood by those skilled in the art that, unless expressly stated otherwise, the singular forms "a", "an", "said" and "the" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the description of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. In addition, "connected" or "coupled" as used herein may include wireless connections or couplings. The term "and / or" used herein includes any unit and all combinations of one or more associated listed items.

[0041] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those skilled in the art in the art to which the present invention pertains. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art and, unless defined as such herein, will not be interpreted in an idealized or overly formal sense.

[0042] To facilitate understanding of the embodiments of the present invention, several specific embodiments will be further explained below with reference to the accompanying drawings, and each embodiment does not constitute a limitation on the embodiments of the present invention.

[0043] The embodiment of the present invention provides a processing flow chart of force separation monitoring of seamless track deflection on a super-long span road-rail dual-purpose bridge. Figure 2 As shown, the processing steps include the following:

[0044] Step S1: Set up measuring points at key locations on the CRT on a large-span bridge in an actual online-bridge project for safety monitoring during construction and health monitoring during operation. Then, select multiple measuring points as key points for monitoring.

[0045] The health monitoring points already deployed in actual projects can be used as the monitoring points of the present invention.

[0046] Figure 3 The figure shows the overall layout of the health monitoring measurement points of the Shanghai-Suzhou-Jiangyin Yangtze River Highway-Rail Bridge, which has been opened to traffic. The 1 / 4 of the main span (measurement point 1, measurement point 3) and the mid-span (measurement point 2) are selected as the measurement points for the specific implementation case of the present invention.

[0047] Step S2: Based on the selected measuring points, use sensors to perform all-weather monitoring of the bridge deflection D(t), daily temperature T, and rail longitudinal stress σ at the measuring points.

[0048] Step S3: Figure 4 A schematic diagram of daily monitoring results of the mid-span deflection of a main span provided by an embodiment of the present invention; Figure 5 A schematic diagram of the correlation between mid-span deflection and temperature provided by an embodiment of the present invention; Figure 6 A schematic diagram of the correlation between temperature deflection force and temperature deflection provided by an embodiment of the present invention; Figure 7 A schematic diagram of the correlation between train flexural force and bridge deflection provided by an embodiment of the present invention; Figure 8 A schematic diagram of the correlation between highway flexural force and bridge deflection provided in an embodiment of the present invention.

[0049] like Figures 4 to 8 As shown in Figure 2, the temperature deflection force, train deflection force, and road deflection force are all positively correlated with the bridge deflection. First, based on the bridge deflection D(t) and the rail deflection additional force σ D (t) has a high linear correlation, and the rail deflection additional force σ caused by the bridge deflection D(t) is separated by establishing a linear regression model D (t), the functional expression of the regression model is:

[0050] σ D (t)=b1+a1D(t)+μ(t) (2)

[0051] Among them, a1 and b1 are the regression parameters in the linear regression model, D(t) is the deflection response at the measuring point at time t, σ D (t) is the additional rail bending force σ at the corresponding moment D (t), μ(t) is the random error. When obtaining the two parameters a1 and b1, it is necessary to obtain them based on the rail longitudinal stress σ. Therefore, it is necessary to monitor the rail longitudinal stress σ parameter.

[0052] Step S4: Based on the linear regression idea or trend term extraction method, the temperature deflection force σ TD (t) separation, which is divided into the following sub-steps:

[0053] S41: Arrange a temperature measuring device at the selected measuring point to obtain the daily temperature T.

[0054] S42 establishes a linear regression equation based on the linear correlation between temperature and temperature deflection force, taking into account the hysteresis effect. The functional expression of the regression model is:

[0055] σ TD (t)b2+a2T(tt d )+μ(t) (3)

[0056] Where T is the daily temperature at time t, σ TD (t) is the temperature bending force caused by the temperature at time t, t dis the lag time of temperature deflection force relative to temperature, and the meanings of other parameters are the same as those in formula (2).

[0057] In addition to the linear regression method described above, the temperature effect in the rail deflection force time history can also be determined through trend term extraction. Deflection force data can be divided into long-period, low-frequency trend terms and high-frequency fluctuation terms, corresponding to changes in rail deflection force caused by temperature loads and live loads from trains and roads, respectively. Based on this characteristic, wavelet decomposition, empirical mode decomposition (EMD), and its variants are used to extract trend terms to separate temperature deflection force from live load deflection force.

[0058] Step S5: When there is no train passing on the bridge, there is only the road deflection force σ generated by the road load. GD , and the amplitude of the road flexural force will not fluctuate too much in a short period of time. In the tens of seconds when the train passes the bridge, the live load flexural force σ HD (t) is generated by both road and train loads and has a sudden and drastic change. Therefore, the live load deflection force during the train crossing the bridge can be subtracted from the average road deflection force before and after the train crossing the bridge to obtain the monitoring value of the train deflection force during this period. The train deflection force is expressed as:

[0059]

[0060] Where, σ LD (t) is the train bending force at time t during the train crossing the bridge, σ HD (t) is the live load deflection force at the corresponding moment, σ GD (t) The road bending force when there is no train passing the bridge. t1 and t2 correspond to the times before and after the train passes the bridge, respectively.

[0061] The present invention also provides an embodiment for exemplarily showing the process of monitoring flexural force separation using the method provided by the present invention.

[0062] According to the flexure force separation monitoring method implemented by this patent, the present invention will be described in detail through specific embodiments below:

[0063] Step 1: Test point selection.

[0064] This embodiment uses the Shanghai-Suzhou-Jiangyin Yangtze River Highway-Railway Bridge, which has been put into operation, as the object to separate the various flexural forces. There are three measuring points distributed throughout the bridge. The measuring point layout diagram is shown in the accompanying figure. Figure 3 As shown in the figure, GNSS, deflectometers, thermometers and hygrometers are deployed on the bridge at the measuring point, and fiber Bragg grating stress sensors, deflectometers, accelerometers, etc. are deployed on the rails.

[0065] Step 2: Test data collection.

[0066] The present invention needs to separate the live load flexural force, so the monitoring data needs to be collected during the train operation period. Since the train number is relatively fixed, 18 hours of uninterrupted data collection is selected from 6:00 to 24:00 on a certain day.

[0067] Step 3: Build a line-bridge intelligent analysis and monitoring system.

[0068] The present invention adopts a line-bridge intelligent analysis and monitoring system, which consists of three parts: line-bridge data acquisition part, network transmission part, data processing center, and data management center. The functions of each part are described as follows:

[0069] Data collection: The data to be collected are divided into track data and bridge data. The fiber Bragg grating structure stress sensor (2) obtains the longitudinal stress σ(t) of the rail, the thermometer and hygrometer (1) obtains the ambient temperature T(t), and the GNSS positioning monitoring system (3) collects the cumulative vertical displacement of the bridge. Its main function is to collect the position and displacement of the bridge measurement points in real time, and then obtain the real-time deflection data D(t) of the bridge. The collected data is sent to the data collection server (4) and the GNSS equipment server (5) and saved in the database.

[0070] Network transmission part: The main equipment of the network transmission part is the wireless network, which is responsible for connecting the fiber optic Bragg grating sensor equipment and the GNSS acquisition equipment, and transmitting the collected data of the track and bridge through the 4G wireless base station (6) or the Beidou wireless network (7).

[0071] Data processing center: This part includes the WIFI communication unit (8), the file storage unit (9), and the data processing unit (10). The WIFI unit (8) receives the test data from the on-site data acquisition server (4) (5), and the data processing unit (10) is responsible for processing and calculating the test data to obtain the separation values ​​of each flexural force. After the data processing unit completes the calculation, the storage unit (9) stores and records the final results.

[0072] Line-bridge intelligent analysis and management center: This management center is located in the railway engineering department and includes a PC (11) connected to the public network. The client can realize the separation monitoring and display of flexural force with high efficiency and high precision. At the same time, the engineering department staff can perform secondary calculations and operations on the data and upload it to the cloud.

[0073] In summary, the method of the present invention can intuitively obtain the numerical value and variation law of the flexural force generated by different factors, solving the problem of unclear flexural additional force of seamless lines on kilometer-level road-rail dual-use bridges. This method can be used to form an intelligent monitoring system for the longitudinal force of seamless lines on kilometer-level road-rail dual-use bridges, which is convenient for the operation management and health monitoring of the line-bridge structure.

[0074] The method for separate monitoring of the flexural force of seamless lines on kilometer-level dual-purpose road-rail bridges of the present invention can intuitively obtain the numerical value and variation law of the flexural force generated by different factors, solving the problem of unclear force on the flexural additional force of seamless lines on kilometer-level dual-purpose road-rail bridges. This method can be used to form an intelligent monitoring system for the longitudinal force of seamless lines on kilometer-level dual-purpose road-rail bridges, which is convenient for the operation management and health monitoring of the line-bridge structure.

[0075] Those skilled in the art will appreciate that the accompanying drawings are merely schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0076] From the above description of the embodiments, it can be seen that those skilled in the art can clearly understand that the present invention can be implemented by means of software plus the necessary general-purpose hardware platform. Based on this understanding, the technical solution of the present invention, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in various embodiments of the present invention or certain parts of the embodiments.

[0077] Each embodiment in this specification is described in a progressive manner. The same or similar parts between the embodiments can be referred to each other. Each embodiment focuses on the differences from other embodiments. In particular, for the device or system embodiments, since they are basically similar to the method embodiments, the description is relatively simple. For the relevant parts, refer to the partial description of the method embodiments. The device and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the scheme of this embodiment. A person of ordinary skill in the art can understand and implement it without making any creative efforts.

[0078] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for monitoring the flexural force of a seamless track on a super-long span bridge, characterized in that: include: Multiple measuring points are set up at key locations of the CRT on long-span bridges, and sensors are used to monitor the bridge deflection, daily temperature, and rail longitudinal stress at each measuring point. According to the linear correlation between bridge deflection and rail deflection additional force, the rail deflection additional force is obtained by calculating the bridge deflection; The separated temperature deflection force is calculated based on the linear correlation between daily temperature and temperature deflection force; According to the frequency difference between the road deflection force and the train deflection force, the train deflection force is obtained by subtracting the live load deflection force during the train crossing the bridge from the average road deflection force before and after the train crossing the bridge. The method of calculating the rail deflection additional force based on the linear correlation between the bridge deflection and the rail deflection additional force includes: Establish the bridge deflection D(t) and the rail deflection additional force σ D (t), and the rail deflection additional force σ is calculated by using the linear regression model through the bridge deflection D(t) D (t), the functional expression of the linear regression model is: σ D (t)=b1+a1D(t)+µ(t) (2) Among them, a1 and b1 are the regression parameters in the linear regression model, D(t) is the deflection response at the measuring point at time t, σ D (t) is the additional rail bending force σ at the corresponding moment D (t), μ(t) is the random error; The calculation of the separation temperature deflection force based on the linear correlation between the daily temperature and the temperature deflection force includes: Establish the relationship between daily temperature T and temperature deflection force σ TD (t), and the temperature deflection force σ is calculated by the linear regression model through the daily temperature T. TD (t), the functional expression of the linear regression model is: σ TD (t)=b2+a2T(t-t d )+μ(t) (3) Where T is the daily temperature at time t, σ TD (t) is the temperature bending force caused by the temperature at time t, t d is the hysteresis time of temperature deflection force relative to temperature, and the meanings of other parameters are the same as those in formula (2); The train deflection force is obtained by subtracting the live load deflection force during the period when the train passes the bridge from the average of the road deflection force before and after the train passes the bridge based on the frequency difference between the road deflection force and the train deflection force, including: When there is no train passing on the bridge, there is only the road deflection force σ generated by the road load GD , and the amplitude of the road flexural force will not change suddenly in a short period of time. During the period when the train passes the bridge, the live load flexural force σ HD (t) is generated by both road and train loads and has a sudden change. The live load deflection force during the period when the train passes the bridge is subtracted from the average road deflection force before and after the train passes the bridge to obtain the monitoring value of the train deflection force during this period. The train deflection force is expressed as: Where, σ LD (t) is the train bending force at time t during the train crossing the bridge, σ HD (t) is the live load deflection force at the corresponding moment, σ GD (t) The road bending force when there is no train passing the bridge. t1 and t2 correspond to the times before and after the train passes the bridge, respectively.

2. The method according to claim 1, characterized in that Multiple measuring points are set at key locations of the CRT on the long-span bridge, and sensors are used to monitor the bridge deflection, daytime temperature, and rail longitudinal stress at each measuring point, including: Set up multiple measuring points at key locations of the CRT on a large-span bridge in an actual online-bridge project; Based on the selected measuring points, sensors are used to monitor the bridge deflection D(t), daily temperature T and rail longitudinal stress σ at the measuring points in real time. The sensors include thermometers, GNSS, fiber Bragg grating stress sensors and accelerometers.

3. The method according to claim 1, characterized in that The method also includes: utilizing the frequency difference between the temperature effect and the live load effect to calculate and separate the temperature flexural force; based on the long-period low-frequency trend term and high-frequency fluctuation term of the flexural force data corresponding to the temperature flexural force caused by the temperature load and the flexural force caused by the train and highway live-loaded vehicles, wavelet decomposition, empirical mode decomposition (EMD) and its variant algorithm trend term extraction method are used to separate the temperature flexural force.

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