Method, apparatus, and program for estimating the deformation of railway structures.

Abstract

To more accurately estimate the deformation of railway structures such as bridges. [Solution] A method for estimating the deformation of a railway structure, the method comprising: Step S1, acquiring the difference between two track displacements actually measured continuously by a vehicle on the track on the railway structure to be estimated, the railway structure to be estimated being composed of n girders; Step S2, acquiring multiple differences between two track displacements measured by simulation by a vehicle on the track on the reference railway structure, with the vehicle's position changed, for a reference railway structure composed of a single girder and sections of rigid ground adjacent to its entry and exit sides, and using these as reference waveforms; and Step S3, estimating the amplitude of each reference waveform for each girder so that the result obtained in Step S1 approximates a curve formed by arranging and superimposing the n reference waveforms with a shift equal to the length of the girder, where each reference waveform for each girder has its own unique amplitude.

Description

[Technical Field]

[0001] This invention relates to a method, apparatus, and program for estimating the deformation of railway structures such as railway bridges. [Background technology]

[0002] The girder deflection of a railway bridge is a fundamental performance indicator of the bridge, directly impacting its running safety and ride comfort. Knowing this fundamental performance indicator, girder deflection, allows for proper maintenance of railway bridges. Similarly, knowing the deformation of other railway structures can lead to more efficient maintenance of those structures as well.

[0003] However, actually checking the deformation of railway structures such as railway bridges requires workers to go to the site and use specialized equipment, which incurs significant costs. Therefore, it is being considered to estimate the deformation of railway structures using measurement results from sensors installed on vehicles passing over the railway structures. For example, it is being considered to estimate the deflection of a railway bridge by utilizing dynamic track displacement, which is the track displacement measured when a train load is applied. Dynamic track displacement includes two components: static track displacement, which is the shape component of the track such as rail distortion and unevenness, and structural deformation components such as girder deflection. Therefore, a method is being considered to extract only the structural deformation component by canceling out the static track displacement as a common component of both using the difference in dynamic track displacement measured at two locations on the vehicle. In other words, a method is being considered to estimate the deformation of a structure based on the difference in dynamic track displacement measured at two locations on the vehicle.

[0004] Another method for measuring dynamic track displacement is the difference finite method. In inspection vehicles with a two-bogie system, which are widely used mainly on conventional lines, dynamic track displacement is measured based on the difference finite method.

[0005] Patent Document 1 discloses a method for measuring the deflection of a railway bridge based on dynamic track displacements at two locations measured using the difference method by a two-bogie inspection vehicle. [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2024-051192 [Overview of the Initiative] [Problems that the invention aims to solve]

[0007] In the difference method, as shown in Figure 1, the reference line L is defined as the line connecting the vertical position (vertical position) of rail R1 at reference positions A2 and A3 before and after the measurement position A1. The distance d from the reference line L to rail R1 at measurement position A1 is measured as the dynamic track displacement at measurement position A1. However, in the difference method, if, for example, a structural displacement occurs at reference position A2, rail R1 will also be displaced at reference position A2, causing the reference line L to move as shown by the dotted line in Figure 1. Therefore, even if there is no change in the vertical position of rail R1 at measurement position A1, the above distance d changes to d', and the dynamic track displacement changes. Specifically, in the case of a bridge as a railway structure with multiple bridge girders, if the bridge girder to which measurement position A1 and reference position A2 belong is different, the dynamic track displacement will change due to the influence of reference position A2.

[0008] Therefore, simply using the difference between two dynamic track displacements measured using the finite difference method to estimate the deformation of a railway structure is insufficient in terms of estimation accuracy, because deformation of structures before and after the railway structure being estimated will affect the estimation results.

[0009] This invention has been made in view of the above circumstances, and aims to more accurately estimate the deformation of railway structures such as bridges. [Means for solving the problem]

[0010] To achieve the above objective, the present invention provides a method for estimating the deformation of a railway structure, wherein the railway structure to be estimated is composed of n (where n is an integer of 2 or more) connected unit sections, and includes an acquisition step of acquiring the difference between two track displacements continuously measured by a vehicle that actually travels on the track on the railway structure to be estimated; a reference waveform acquisition step of acquiring multiple differences between two track displacements measured by simulation by the vehicle on the track on the reference railway structure, with the vehicle's position changed, for a reference railway structure composed of a single connected unit section and sections of rigid ground adjacent to its entry and exit sides where no deformation occurs, and using these as reference waveforms; and an estimation step of estimating the amplitude of the reference waveforms for each of the unit sections such that the curve obtained by arranging and superimposing the n reference waveforms, shifted by the length of the travel direction of the unit section, and in which each of the reference waveforms for each unit section has a unique amplitude, approximates the acquisition results from the acquisition step.

[0011] In this invention, the amplitude of a reference waveform belonging to a unit interval is estimated to correspond to the deformation of that unit interval. Furthermore, the estimated amplitude for each unit interval is a superimposed representation of the reference waveforms belonging to adjacent unit intervals, that is, it reflects the influence of the adjacent unit intervals. Therefore, according to this invention, deformation of a unit interval can be estimated more accurately.

[0012] The estimation step may calculate matrix a such that matrix y, which is represented by the product of a characteristic matrix X including a matrix showing the reference waveform and a matrix a showing the amplitude of each unit section of the track structure to be estimated, approximates matrix Y showing the acquisition results in the acquisition step.

[0013] The estimation step may involve calculating the matrix a using the least squares method.

[0014] In the above estimation method, the characteristic matrix X is the matrix of the reference waveform, with each column representing the number of samples d in the unit section constituting the reference line structure. bThis is a matrix in which the rows are shifted downwards by minutes, and the number of samples d b This may be the number of differences in the unit interval included in the reference waveform.

[0015] In the estimation method described above, the simulation may include a simulation based on finite element analysis.

[0016] In the estimation method described above, the vehicle is a two-car inspection vehicle that measures track displacement at four axle positions from the first to the fourth axle of one vehicle, and the difference in track displacement at the two locations may be the difference between the straight-line track displacement calculated from the eccentric-line track displacement at the second axle relative to the first and fourth axles, and the straight-line track displacement calculated from the eccentric-line track displacement at the third axle relative to the first and fourth axles.

[0017] In the estimation method described above, the railway structure may be a bridge, and the deformation may be the deflection of the girders constituting the bridge.

[0018] Another aspect of the present invention is a device for estimating the deformation of a railway structure, wherein the railway structure to be estimated is composed of n (where n is an integer of 2 or more) connected unit sections, and the device includes: an acquisition unit that acquires the difference between two track displacements continuously measured by a vehicle that actually runs on the track on the railway structure to be estimated; a reference waveform acquisition unit that, for a reference railway structure composed of a single connected unit section and sections of rigid ground adjacent to its entry and exit sides where no deformation occurs, acquires multiple differences between two track displacements measured by simulation by the vehicle on the track on the reference railway structure, changing the position of the vehicle, and uses these as reference waveforms; and an estimation unit that estimates the amplitude of the reference waveforms for each of the unit sections such that the curve obtained by the acquisition unit approximates the curve obtained by arranging and superimposing the n reference waveforms with a shift equal to the length of the running direction of the unit section, where each of the reference waveforms for each unit section has its own amplitude.

[0019] The estimation unit may calculate the matrix a such that the matrix y, which is represented by the product of a characteristic matrix X including a matrix showing the reference waveform and a matrix a showing the amplitude of each unit section of the track structure to be estimated, approximates the matrix Y showing the acquisition results from the acquisition unit.

[0020] The estimation unit may calculate the matrix A using the least squares method.

[0021] In the estimation device described above, the characteristic matrix X is the matrix of the reference waveform, with each column representing the number of samples d in the unit section constituting the reference line structure. b This is a matrix in which the rows are shifted downwards by minutes, and the number of samples d b This may be the number of differences in the unit interval included in the reference waveform.

[0022] In the estimation device described above, the simulation may include a simulation based on finite element analysis.

[0023] In the estimation device described above, the vehicle is a two-car inspection vehicle that measures track displacement at four axle positions from the first to the fourth axle of one vehicle, and the difference in track displacement at the two locations may be the difference between the straight-line track displacement calculated from the eccentric-line track displacement at the second axle relative to the first and fourth axles, and the straight-line track displacement calculated from the eccentric-line track displacement at the third axle relative to the first and fourth axles.

[0024] In the estimation device described above, the railway structure may be a bridge, and the deformation may be the deflection of the girders constituting the bridge.

[0025] Another aspect of the present invention is a program that causes a computer to function as: an acquisition unit that acquires the difference between two track displacements, continuously measured by a vehicle that actually travels on the track of a target railway structure composed of n (where n is an integer of 2 or more) consecutive unit sections; a reference waveform acquisition unit that, for a reference railway structure composed of single and consecutive unit sections and sections of rigid ground adjacent to the entry and exit sides thereof where no deformation occurs, acquires multiple differences between two track displacements, measured by simulation by the vehicle on the track of the reference railway structure, by changing the position of the vehicle, and uses these as reference waveforms; and an estimation unit that estimates the amplitude of the reference waveforms for each of the unit sections such that the curve obtained by the acquisition unit approximates the curve obtained by arranging and superimposing the n reference waveforms with a shift equal to the length of the travel direction of the unit sections, where each of the reference waveforms for each unit section has its own unique amplitude. [Effects of the Invention]

[0026] According to the present invention, the deformation of railway structures such as bridges can be estimated more accurately. [Brief explanation of the drawing]

[0027] [Figure 1] This figure illustrates the effect of deformation of adjacent structures on dynamic trajectory displacement using the finite difference method. [Figure 2] This is a schematic diagram showing a train running on a railway structure whose deformation is estimated by the method described herein. [Figure 3] This is a schematic diagram showing an example of a railway structure whose deformation can be estimated by the method described herein. [Figure 4] This figure illustrates the track displacement measured by the vehicles that make up the train shown in Figure 2. [Figure 5] This figure shows an overview of an example of an FEM model used for simulating the dynamic track displacement difference for a single-span bridge. [Figure 6] Figure 5 is a graph showing the waveform of the dynamic track displacement difference for a single-span bridge, based on analysis using the FEM model. [Figure 7] This diagram shows seven reference waveforms arranged in a sequence, each shifted by the length of a digit to correspond to a 7-digit sequence. [Figure 8] This is a schematic diagram illustrating an example of the configuration of an estimation device. [Figure 9] This figure shows the elements of the matrix that make up equation (8). [Figure 10] This flowchart shows the main steps of an example of a method for estimating the deformation of a railway structure, as performed by the estimation device shown in Figure 8. [Figure 11] This figure shows an example of a characteristic matrix that takes into account the influence of adjacent girders when the deformation estimation target is a five-span bridge section. [Figure 12] This figure shows an example of a reference waveform. [Figure 13] This figure compares the estimation results obtained using the method described herein with the ground measurement results when the target of the estimation of deformation of five spans is a five-span bridge section. [Modes for carrying out the invention]

[0028] The method and apparatus for estimating the deformation of railway structures relating to this disclosure will be described below with reference to the drawings. Elements having substantially the same functional configuration in this specification and the drawings are denoted by the same reference numerals, thus omitting redundant explanations.

[0029] <Trains, bridges> Figure 2 is a schematic diagram showing a train running on a track structure whose deformation is estimated by the method described herein. Figure 3 is a schematic diagram showing an example of a track structure whose deformation is estimated by the method described herein. Figure 4 is a diagram illustrating the track displacement measured by the vehicles constituting the train in Figure 2.

[0030] The train T in Figures 2 and 3 travels along a track R provided on a bridge B, which is a railway structure. The track R has a pair of rails R1 on the left and right that guide the wheels of the train T. The train T is composed of two vehicles, for example, test vehicles V1 and V2. When in operation, one of the vehicles V1 or V2 is the leading vehicle and the other is the trailing vehicle (last vehicle). In the following description, it will be assumed that vehicle V1 is the leading vehicle.

[0031] Vehicle V1 is a track inspection vehicle equipped with a track displacement measuring device 10, which continuously measures track displacement while traveling on track R. Vehicle V2 is an electrical inspection vehicle equipped with a signal / communication inspection device (not shown) that inspects and measures electrical ground equipment such as signals and communications, which continuously measures these ground equipment while traveling on track R. Vehicle V1 does not have a propulsion system, and vehicle V2, which has a propulsion system, is coupled to the rear of vehicle V1 in the direction of travel. Here, vehicle V2 may have a different weight from vehicle V1.

[0032] Vehicle V1 is specifically a two-bogie inspection vehicle (a two-bogie inspection vehicle) that measures track displacement at four axle positions, from the first axle A1 to the fourth axle A4, within a single vehicle, as shown in Figure 4. Vehicle V1 is equipped with bogies T1 and T2, and one car body is supported by two bogies T1 and T2 in the same bogie arrangement as a commercial vehicle. Unlike a three-bogie inspection vehicle (a three-bogie inspection vehicle) that measures track displacement every 5m using three bogies, Vehicle V1 measures the relative height displacement of three of the four axles of the two bogies T1 and T2 as track displacement. Vehicle V2 is equipped with bogies T3 and T4, and the same bogie configuration as the commercial vehicles, with one car body supported by two bogies T3 and T4.

[0033] Bogies T1, T2, T3, and T4 are two-axle bogies (bogie trucks) composed of two pairs of wheelsets. Bogies T1 and T3 support the front end of the vehicle body in the direction of travel of vehicles V1 and V2, while bogies T2 and T4 support the rear end of the vehicle body in the direction of travel of vehicles V1 and V2. In this disclosure, the four axles of vehicles V1 and V2 are designated as the first axle A1, the second axle A2, the third axle A3, and the fourth axle A4, in order from the front of the vehicle body in the direction of travel.

[0034] Bridge B in Figure 3 is an example of a railway structure whose deformation can be estimated by the method described herein. Bridge B is a multi-span bridge with two or more spans, each consisting of two or more girders B1, and the lengths of each girder B1 are equal. That is, Bridge B is composed of n (n is an integer of 2 or more) unit sections, with each girder B1 serving as a unit section. In addition to the girders B1, Bridge B also has abutments B2, piers B3, bearings B4, etc.

[0035] Girder B1 is a structure positioned horizontally to support track R. Girder B1 is a simple girder supported by two supports, and is the main girder spanning between the two supports. Abutment B2 is a structure constructed at both ends of bridge B. Abutment B2 supports the superstructure load and the earth pressure load from the backfill, as well as supporting girder B1. Pier B3 is a structure that supports girder B1. Pier B3 is provided at predetermined intervals along the length of bridge B, between the abutment B2 at both ends. Bearing B4 is the part that transmits the forces applied to the superstructure of bridge B to the substructure. Bearing B4 supports both ends of girder B1.

[0036] The track displacement measuring device 10 of vehicle V1 is a device for measuring track displacement on bridge B, etc. The track displacement measuring device 10 measures at least vertical displacement, i.e., height displacement, as track displacement by utilizing the relative difference in rail displacement at multiple points.

[0037] The track displacement measuring device 10 measures the vertical displacement of each of the first to fourth axles A1 to A4 of the vehicle V1. Based on the measurement results, the track displacement measuring device 10 measures the eccentric arrow track displacement z on the bridge B from the vehicle V1 traveling on the bridge B. t,A ,z t,B Measure the eccentric arrow trajectory displacement z t,A This is the eccentric arrow trajectory displacement of the second axis A2 relative to the first axis A1 and the fourth axis A4, and the eccentric arrow trajectory displacement z t,Bis the eccentric vector orbit displacement of the third axis A3 with respect to the first axis A1 and the fourth axis A4. The orbit displacement measuring device 10 includes a laser reference line generating unit 11, a vertical displacement measuring unit (not shown), an eccentric vector orbit displacement calculating unit 12, a travel distance calculating unit 13, a measurement data storage unit 14, a measurement data transmitting unit 15, and a control unit 16.

[0038] The laser reference line generating unit 11 generates a laser reference line L1 that serves as a reference for measurement in order to prevent detection errors caused by the deflection of the vehicle body of the vehicle V1. The laser reference line generating unit 11 includes, for example, an irradiation unit 11a such as a gas laser irradiator that irradiates laser light on the first axis A1 of the carriage T1, and a light receiving unit 11b such as a light position detector (Position Sensitive Detect (PSD)) that receives laser light on the fourth axis A4 of the carriage T2. The laser reference line generating unit 11 outputs the generated laser reference line L1 to the control unit 16 as a laser reference line signal (laser reference line data).

[0039] The vertical displacement measuring unit is a means for measuring the vertical displacement of each of the first axis A1 to the fourth axis A4 of the vehicle V1. The vertical displacement measuring unit measures the vertical displacement of the wheels of the carriages T1 and T2 by utilizing the fact that the wheels of the carriages T1 and T2 are always in contact with the top surface of the rail R1, and measures the vertical displacement of the rail R1. Specifically, the vertical displacement measuring unit measures the vertical displacement of the rail R1 below these first axis A1 to the fourth axis A4 by measuring the vertical displacement of the first axis A1 to the fourth axis A4 of the vehicle V1. The vertical displacement measuring unit has a mechanical-electrical conversion unit that converts the vertical displacement (mechanical displacement) of the axle boxes that rotatably accommodate both ends of the axles of the wheels of the carriages T1 and T2 into an electrical signal, and a link mechanism unit including an arm and a ball joint that transmits the vertical displacement of the axle boxes to the mechanical-electrical conversion unit. The vertical displacement measuring unit outputs the measured vertical displacement of the axle boxes to the control unit 16 as a rail vertical displacement signal (rail vertical displacement data) indicating the vertical displacement of the rail R1.

[0040] The eccentric vector orbit displacement calculating unit 12 calculates the eccentric vector orbit displacement z t,A , z t,BThe eccentric arrow method is a track measurement technique that takes a reference line L0 connecting two points on the rail R1 and measures the vertical displacement (amount of deviation) of the rail R1 relative to the reference line L0 at a point other than the midpoint of the reference line L0. The eccentric arrow track displacement calculation unit 12 calculates the eccentric arrow track displacement z based on the laser reference line L1 generated by the laser reference line generation unit 11 and the vertical displacement of the rail R1 measured by the vertical displacement measurement unit. t,A ,z t,B Perform the calculation.

[0041] Eccentric arrow trajectory displacement z t,A Specifically, this refers to the vertical relative displacement of rail R1 on the second axis A2 with respect to a reference line L0 connecting the vertical position on the first axis A1 and the vertical position on the fourth axis A4 of rail R1, and is sometimes referred to as the 1-2-4 axis eccentric arrow trajectory displacement. Also, eccentric arrow trajectory displacement z t,B Specifically, this refers to the vertical relative displacement of rail R1 on the third axis A3 with respect to a reference line L0 connecting the position on the first axis A1 and the position on the fourth axis A4 of rail R1, and is sometimes referred to as the 1-3-4 axis eccentric arrow trajectory displacement.

[0042] The eccentric arrow trajectory displacement calculation unit 12 calculates the eccentric arrow trajectory displacement z t,A ,z t,B This is output to the control unit 16 as eccentric arrow trajectory displacement data.

[0043] The method for estimating the deformation of a track structure according to this disclosure uses the difference between two track displacements, but the eccentric arrow track displacement z t,A ,z t,B There is a phase difference between them. Therefore, in this estimation method, the eccentric arrow trajectory displacement z t,A ,z t,BThe estimation is performed based on the difference in chord-arch track displacement using the phase-less arch method, which is converted from the original data. The arch method is a track measurement technique that takes a reference line L0 (a chord stretched between two points on rail R1) connecting two points on rail R1, and measures the vertical displacement (amount of deviation) of rail R1 relative to the reference line L0 at the midpoint of the reference line L0. The arch track displacement is, for example, the 10m chord-arch track displacement, which is common in track maintenance and management as a waveform of track displacement with flat phase characteristics. The 10m chord-arch track displacement is the track displacement measured using an arch with a chord length of 10m, and is the distance from the midpoint of the 10m reference line L0 to rail R1. Eccentric arch track displacement z t,A ,z t,B The conversion from cylindrical displacement to finite impulse response (Finite) is a type of digital filter. This is done using a transformation filter such as an Impulse Response (FIR) filter.

[0044] In the following explanation, the eccentric arrow trajectory displacement z t,A ,z t,B The conversion from to symmetrical track displacement is performed by an estimation device for estimating the deformation of the track structure, as described later. However, this conversion may also be performed by the track displacement measuring device 10. That is, the track displacement measuring device may measure the symmetrical track displacement mentioned above. Furthermore, below, the eccentric arrow trajectory displacement z of the 1-2-4 axis t,A The 10m chord arsenal orbital displacement converted from is the 10m chord arsenal orbital displacement z t,A,10 , or 1-2-4 axis 10m chord recti trajectory displacement z t,A,10 That's what they say. 1-3-4 axis eccentric arrow trajectory displacement z t,B For the 10m chord arsenal orbital displacement converted from, the 10m chord arsenal orbital displacement z t,B,10 , or 1-3-4 axis 10m chord recti trajectory displacement z t,B,10 That's what they say.

[0045] The distance calculation unit 13 calculates the distance traveled by the vehicle V1. For example, the distance calculation unit 13 receives absolute position information output by an ATS on-board unit of an automatic train stop (ATS) system installed at a specific point on the track R to detect the absolute position of the vehicle V1, and calculates the distance traveled by the vehicle V1 by accumulating distance pulse signals output by a speed generator that detects the speed of the vehicle V1 until the vehicle V1 reaches the next ATS ground unit. The distance calculation unit 13 outputs the distance traveled (travel distance) of the vehicle V1 from the starting point to the ending point as distance data D2 to the control unit 16.

[0046] The measurement data storage unit 14 stores various types of data. The measurement data storage unit 14 stores the eccentric arrow trajectory displacement data D1 calculated by the eccentric arrow trajectory displacement calculation unit 12 and the travel distance data D2 calculated by the travel distance calculation unit 13 as measurement data (inspection data) D. Here, the measurement data storage unit 14 stores the eccentric arrow trajectory displacement data D1 in correspondence with the travel distance data D2 in distance sequence order. That is, the measurement data storage unit 14 converts the eccentric arrow trajectory displacement data D1 into distance sequence data with predetermined distance increments and stores it.

[0047] The measurement data transmission unit 15 transmits measurement data D from the track displacement measuring device 10. Specifically, the measurement data transmission unit 15 transmits measurement data D from the track displacement measuring device 10 to an estimation device that estimates the deformation of the track structure, as described later. For example, the measurement data transmission unit 15 transmits the measurement data D to the estimation device in real time.

[0048] The control unit 16 controls various operations related to the orbital displacement measuring device 10 and includes a processor such as a CPU.

[0049] <Background to the method for estimating the deformation of railway structures as described in this disclosure> Next, we will explain the process that led to the method for estimating the deformation of the railway structure described in this disclosure.

[0050] The deformation estimation target of the method described herein is a track structure composed of n (where n is an integer of 2 or more) units, specifically a bridge composed of multiple girders, and more specifically, each girder of the above bridge. In the case of a single bridge, the dynamic track displacement difference (specifically, the 1-2-4 axis 10m chord straight-arrow track displacement z) is used. t,A,10 and 1-3-4 axis 10m chord rectitrajectory displacement z t,B,10 It has been theoretically derived that the maximum value of the difference between the two values ​​is proportional to the maximum girder deflection at the center of the girder span as measured from the ground.

[0051] Therefore, we first obtained the dynamic track displacement difference for single-span bridges through simulation, and then attempted to reconstruct the dynamic track displacement difference for multi-span bridge sections from the obtained results.

[0052] Figure 5 shows an overview of an example of a Finite Element Method (FEM) model used for the simulation, i.e., analysis, of the dynamic track displacement difference for a single-span bridge. Figure 5(A) is the girder-track model, and Figure 5(B) is the train model. The specifications of girder B1 and rail R1 in the above model are the same as those in known literature, so only an overview is given below. In the analysis of the single-span bridge, it was assumed that bridge B was a steel bridge. In the model used for the analysis, the single girder B1 and rail R1 were modeled using beam elements, and the track pad R2 and bearing B4 were modeled using spring elements. Furthermore, it was assumed that the ground outside the bridge section K1 was rigid; that is, the section adjacent to the approach side of bridge section K1 (pre-running section) K2 and the section adjacent to the exit side (post-running section) K3 were assumed to be rigid ground where no deformation occurs, and one side of the spring element of track pad R2 was fixed. In addition, only one side of the rail R1 and girder B1 were modeled.

[0053] Furthermore, some of the specifications for bridge B and rail R1 are as follows. Length of beam B1: 13.1 (m) Span length: 12.3 (m) Bending stiffness of rail R1: 6.47 × 10 6(N·m 2 ) Vertical spring constant of track pad R2: 4.00 × 10⁻⁶ 7 (N / m) Bending stiffness of girder B1: 1.41 × 10 9 (N·m 2 ) Vertical spring coefficient of bearing B4: 1.00 × 10 11 (N / m)

[0054] For the train model, two vehicles, V1 and V2, were coupled together and modeled as a load train. The specifications were matched to those of an actual track inspection vehicle. The load of train T was calculated by converting the wheel load, which is determined from the design weight, into a wheel load per rail and then applying it. Specifically, the wheel load per axle P1-P4 of vehicle V1, which is a track inspection vehicle, was set to 48.5 (kN), and the wheel load P5-P8 of vehicle V2, which is a railcar, was set to 60.5 (kN). The load spacing Δ1 (the distance between the axles within the bogies T1, T2, T3, and T4 of vehicles V1 and V2) was set to 2.1m, and the load spacing Δ2 (the distance from the second axle A2 to the third axle A3) was set to 12.3m. The load spacing Δ3 is the distance from the fourth axle A4 of vehicle V1 to the third axle A1 of vehicle V2, which is the distance between the couplers of vehicles V1 and V2.

[0055] The analysis was performed quasi-statically, by moving the load sequence by 0.1m increments. As an analysis result, the vertical position of rail R1 on each of the four axles (1st axle A1 to 4th axle A4) of vehicle V1 was obtained and recorded, and based on the obtained results, the eccentric arrows of the 1-2-4 axis track displacement z were calculated. t,A , and the eccentric arrow trajectory displacement z of the 1-3-4 axis t,B The following was calculated. Subsequently, the axial eccentric arrow trajectory displacement z t,A , z t,B In contrast, by performing the processing using the aforementioned conversion filter, the phase characteristics of the 1-2-4 axis 10m chord arquebus trajectory displacement z are flat. t,A,10 , 1-3-4 axis 10m chord rectus orbital displacement z t,B,10 The result was calculated. And then, the trajectory displacement z of the 10m chord yaw t,A,10 , z t,B,10 The difference was calculated, that is, the dynamic trajectory displacement difference was calculated, which includes only the deformation of the structure after the static trajectory displacement has been removed. Furthermore, each process, from obtaining the vertical position of rail R1 to calculating the dynamic track displacement difference, was performed with the load sequence moving by 0.1m increments.

[0056] Figure 6 is a graph showing the waveform of the dynamic track displacement difference for a single-span bridge, based on the analysis using the FEM model in Figure 5. In Figure 6, the vertical axis represents the dynamic track displacement difference [mm], and the horizontal axis represents the position of the center of the vehicle V1 in the direction of travel [mm]. Furthermore, as shown in Figure 6, the dynamic track displacement difference is the 10m chord truss track displacement z that is not affected by the second vehicle V2. t,A,10 Therefore, the 10m chord truss trajectory displacement z is strongly influenced by the second vehicle V2. t,B,10 Because of the subtraction, the maximum positive value occurred in the center of digit B1, and the maximum negative value occurred at the support on the front side in the direction of travel. In the following, the waveform of the difference in dynamic trajectory displacement for a single-span bridge, obtained by analysis using the FEM model as shown in Figure 6 (the difference in dynamic trajectory displacement at each measurement position), will be referred to as the reference waveform.

[0057] Furthermore, for the section consisting of seven consecutive girders with the same girder length and span length as analyzed above, we modeled all seven girders, that is, we used an FEM model of the section with seven consecutive girders to perform an analysis on the difference in dynamic track displacement. The FEM model for a single-span bridge and the FEM model for a section with seven consecutive girders have commonalities other than the number of girders. In sections where seven girders are consecutive, the girders are referred to as girders B1 to B7, starting from the approach side. Even in the analysis using the FEM model for a section with seven consecutive girders, the load sequence was moved 0.1m at a time, and the analysis was performed quasi-statically. As a result of the analysis, the vertical position of the rail R1 above each of the four axles (1st axle A1 to 4th axle A4) of the vehicle V1 was obtained and recorded, and based on the obtained results, the eccentric arrows of the 1-2-4 axis track displacement z t,A , and the eccentric arrow trajectory displacement z of the 1-3-4 axis t,B The following was calculated. Subsequently, the eccentric arrow trajectory displacement z t,A , z t,BIn contrast, by performing the processing using the aforementioned conversion filter, the phase characteristics of the 1-2-4 axis 10m chord arquebus trajectory displacement z are flat. t,A,10 , 1-3-4 axis 10m chord rectus orbital displacement z t,B,10 The result was calculated. And then, the trajectory displacement z of the 10m chord yaw t,A,10 , z t,B,10 The difference was calculated, that is, the dynamic trajectory displacement difference was calculated, which includes only the deformation of the structure after the static trajectory displacement has been removed. Furthermore, each process, from obtaining the vertical position of rail R1 to calculating the dynamic track displacement difference, was performed with the load sequence moving by 0.1m increments.

[0058] Based on these analysis results, as shown in Figure 7, the aforementioned reference waveforms were arranged in seven positions, shifted by 13.1m each, corresponding to digits B1 to B7. For example, the reference waveform for digit B4 is obtained by shifting the reference waveform to the right from the starting point of digit B4 by 39.3m (= three digits of a 13.1m length), which is the starting point of digit B4. Then, by arranging seven reference waveforms as described above and superimposing them, we compared the waveform of the dynamic orbital displacement difference for seven consecutive girders with the waveform of the dynamic orbital displacement difference obtained by analysis using an FEM model for the section with seven consecutive girders. The two waveforms showed good agreement.

[0059] From the above, it can be seen that the waveforms of the dynamic track displacement difference obtained using two inspection vehicles in a section with multiple consecutive girders are independent for each girder B1, and superposition holds true. In the case of a single-span bridge, the dynamic track displacement difference is proportional to the girder deflection, as mentioned above, that is, it has a linear relationship with the girder deflection. Therefore, the influence of adjacent girders B1 can also be expressed by superposition, and as a result, even in the case of multiple spans, the waveform of the dynamic track displacement difference has linearity with respect to the girder deflection (however, the girder deflection of adjacent girders is independent of the girder in question and is therefore a linear function).

[0060] To rephrase the previous paragraph, it has become clear that, at least for consecutive girders of the same span length, the waveform of the dynamic track displacement difference due to the girder deflection of each girder is independent between girders B1, and the waveform of the dynamic track displacement difference for a multi-span bridge section can be reproduced by superimposing the waveforms of the dynamic track displacement difference (reference waveforms) calculated for a single-span bridge. By utilizing this feature, it is thought that girder deflection can be estimated by determining only the amplitude of the reference waveform for each girder to match the measured dynamic track displacement difference waveform, without having to inversely analyze the FEM model of the entire multi-span bridge.

[0061] The estimation apparatus and estimation method described herein are based on this finding.

[0062] <Estimation device> Figure 8 is a schematic diagram illustrating an example of the configuration of the estimation device. Figure 8 also includes a block diagram of the functional configuration of the estimation device. Figure 9 shows the elements of the matrix that constitute equation (8), which will be described later.

[0063] Estimation device 1 in Figure 8 estimates the deflection of girders B1 that make up bridge B as deformation of the railway structure. Bridge B, as the railway structure to be estimated by estimation device 1, is composed of n (where n is an integer of 2 or more) unit sections, that is, it is composed of n girders B1 with a common girder length. Specifically, estimation device 1 estimates the deformation of each girder B1 that makes up bridge B.

[0064] The estimation device 1 is a computer including a processor such as a CPU and memory, and may also be a mobile terminal such as a smartphone or tablet. The estimation device 1 also has a communication unit 31, a storage unit 32, and a control unit 33.

[0065] The communication unit 31 is a communication interface that mediates communication with the network 40 and performs data communication with the track displacement measuring device 10 of the vehicle V1.

[0066] The memory unit 32 stores various types of information and includes memory such as RAM and storage devices such as HDDs. The memory unit 32 stores various data and programs that are processed by the estimation device 1. The programs stored in the memory unit 32 include programs that contain instructions for executing a method for estimating the deformation of the railway structure. Furthermore, the above programs may have been recorded on a computer-readable storage medium H and installed from said storage medium H to the estimation device 1. Also, the storage medium H may be for temporary storage or permanent storage.

[0067] The control unit 33 includes a processor such as a CPU. The control unit 33 also has an acquisition unit 33a, a reference waveform acquisition unit 33b, and an estimation unit 33c, which are realized when the processor reads and executes a program stored in the storage unit 32.

[0068] The acquisition unit 33a acquires the difference between two track displacements that were continuously measured by the train vehicle V1 of the train T that actually traveled on the track R on the bridge B that is the target of deformation estimation. In other words, the acquisition unit 33a acquires the difference between two track displacements at each measurement point based on the continuous measurement results from the train vehicle V1 of the train T that actually traveled on the track R on the bridge B that is the target of deformation estimation. The difference in orbital displacement at the two locations mentioned above is, specifically, the orbital displacement z of the 1-2-4 axis eccentric arrow mentioned earlier. t,A The straight trajectory displacement and the 1-3-4 axis eccentric trajectory displacement z calculated from this t,B The difference between the rib orbital displacement calculated from and , more specifically, the rib orbital displacement z of the 1-2-4 axis 10m chord. t,A,10 and 1-3-4 axis 10m chord rectitrajectory displacement z t,B,10 This is the difference.

[0069] Specifically, the acquisition unit 33a extracts eccentric arrow trajectory displacement data D1 corresponding to the position of the bridge B to be deformed from the measurement data D received from the trajectory displacement measuring device 10 and pre-stored in the storage unit 32. Subsequently, the acquisition unit 33a extracts the 1-2-4 axis eccentric arrow trajectory displacement z from the eccentric arrow trajectory displacement data D1. t,A , 1-3-4 axis eccentric arrow trajectory displacement z t,B Each of these is processed using the aforementioned filter, and the 1-2-4 axis 10m chord truss trajectory displacement z t,A,10 , 1-3-4 axis 10m chord rectus orbital displacement z t,B,10 Furthermore, the acquisition unit 33a acquires the eccentric arrow trajectory displacement z t,A , z t,B For each position where measurement was taken, the trajectory displacement z of the 10m chord yaw was measured. t,A,10 , 10m chord truss orbital displacement z t,B,10 The difference between this value and the current value, i.e., the difference in dynamic trajectory displacement, is calculated. The acquisition unit 33a then acquires a matrix Y as the acquisition result, which shows the waveform of the dynamic orbital displacement difference in n consecutive girders B1.

[0070] The reference waveform acquisition unit 33b acquires multiple reference waveforms for a reference track structure, using the difference between two track displacements measured by the train vehicle V1 of train T on the track R provided on the reference track structure, by changing the position of train T. In other words, the reference waveform acquisition unit 33b acquires the difference between two track displacements at each measurement point based on the results of multiple measurements taken in a simulation of a reference track structure using a train T vehicle V1 on the track R provided on the reference track structure, with the vehicle's position being changed, and uses this as the reference waveform. The track structure according to the above standards consists of a single-unit bridge section K1 and rigid ground sections adjacent to its entry and exit sides (pre-running section K2 and post-running section K3).

[0071] The simulation performed by the reference waveform acquisition unit 33b is based on finite element analysis, and the FEM model described in Figure 5 is used. The specifications of the FEM model are extracted, for example, from bridge data D3 pre-stored in the memory unit 32. The bridge data D3 consists of various information about bridge B, such as the position of bridge B (the distance traveled from the starting point of the railway line to the entrance and exit of bridge B) and the span length L of the girder B1 of bridge B. b This data relates to the above. In addition, information necessary for extracting the specifications of the FEM model (for example, identification information of the bridge to be deformed) is input via an input unit such as a keyboard or touch panel. At least a part of the above specifications themselves may be input via the input unit of the estimation device 1.

[0072] Furthermore, the reference waveform acquisition unit 33b performs a simulation using the FEM model quasi-statically by moving the load sequence at predetermined sampling intervals, and at each position, based on the analysis results, calculates the eccentric arrow trajectory displacement z t,A , 1-3-4 axis eccentric arrow trajectory displacement z t,B Calculate the trajectory displacement z of the 10m chord symmetrical arrow, and based on the calculation result, t,A,10 , z t,B,10 Further calculations are performed to determine the difference between these, i.e., the difference in dynamic trajectory displacement. The reference waveform acquisition unit 33b acquires the waveform of the dynamic trajectory displacement difference, which is the result of this calculation, as the reference waveform. The above-mentioned predetermined sampling interval is equal to the actual measurement interval of train T's vehicle V1.

[0073] The reference waveform acquisition unit 33b then generates a matrix (reference waveform matrix) x that indicates the reference waveform. ref A characteristic matrix X containing the reference waveform matrix x is obtained. The characteristic matrix X is as shown in Figure 9. ref Sample size d for each column b This is a matrix with the elements shifted downwards by d. b This represents the number of samples in the single-bridge section K1 in the simulation.

[0074] Also, the reference waveform matrix xref is a waveform obtained by normalizing a reference waveform with a design value or the like, and can be expressed by the following formula (1).

[0075]

Number

[0076] Here, x f , x b , x r represents the waveforms of the pre-travel section K2, the single-span bridge section K1, and the post-travel section K3 among x ref . Also, T of G T is the transpose of the matrix G, d f , d b , d r are the number of samples of the pre-travel section K2, the single-span bridge section K1, and the post-travel section K3 respectively, and x represents one sample of the dynamic track displacement difference measured at the sampling interval ΔL. The number of samples of x ref is d f + d b + d r . Here, if the lengths of the pre-travel section K2, the single-span bridge section K1, and the post-travel section K3 are L f , L b , L f respectively, then d f = L f / ΔL, d b = L b / ΔL, d r = L r / ΔL (2) The following relationship holds.

[0077] Here, since the amplitude of the dynamic track displacement difference due to the single-span deflection is proportional to the deflection, consider expressing the waveform y ref of the dynamic track displacement difference with an arbitrary amplitude by multiplying the waveform of the normalized dynamic track displacement difference due to the single-span deflection, that is, the reference waveform matrix x ref by the amplitude parameter. y ref is expressed as follows.

[0078]

number

[0079] y ref The number of samples is x ref Similarly, d f +d b +d r The waveform y of the dynamic orbital displacement difference of any amplitude due to the deflection of a single girder is given. ref This involves an arbitrary amplitude parameter b and a reference waveform matrix x ref By crossbreeding with, y ref =bx ref (4) It can be expressed as follows.

[0080] Furthermore, based on the independence of the waveforms of the orbital displacement differences obtained for each digit, the reference waveform matrix x ref This allows us to re-formulate the track displacement difference obtained from multiple bridge spans. The waveform of the dynamic track displacement difference when n girders are continuous is y, and the waveform of the dynamic track displacement difference when only the i-th girder exists is y. Bi Let y, y Bi Both are 1×m column vectors with sample size m. Here, m is m=d f +d b +d r (5) It satisfies the relationship.

[0081] The waveform of the dynamic orbital displacement difference when only the i-th digit exists. Bi This is the amplitude parameter a for the i-th sequence. i Using this, we obtain equation (6) below.

[0082]

number

[0083] y Bi (i-1)*d from the beginning bThe first column is 0. When n consecutive digits are present, the waveform y of the dynamic orbital displacement difference is, due to the superposition property, waveform y Bi Since it can be expressed as a sum of, we get equation (7) below.

[0084]

number

[0085] a = [a1, a2, ..., a n ] T If we let be the amplitude parameter vector, then from equation (6), equation (7) can finally be rewritten as the following determinant. y = Xa …(8)

[0086] Equation (8) is a re-formulation of the waveform of the difference in dynamic track displacement in a multi-span bridge section, using the reference waveform of each girder.

[0087] The estimation unit 33c estimates the amplitude of each reference waveform in digit B1 such that the curve obtained by the acquisition unit 33a approximates the curve obtained by arranging and superimposing n reference waveforms shifted by the length of digit B1, where each reference waveform in digit B1 has its own unique amplitude.

[0088] Specifically, the estimation unit 33c calculates matrix a such that the matrix Y acquired by the acquisition unit 33a approximates matrix y, which is represented by the product of the characteristic matrix X and the matrix a representing the amplitude of each of the digits B1 as described above, as shown in equation (8). The values ​​of the parts of matrix Y corresponding to the pre-running section K2 and the post-running section K3 are, for example, zero.

[0089] For example, the least squares method can be used to calculate, or estimate, matrix a. Specifically, if we let a' be the estimated value of matrix a, then a' can be obtained from the following equation (9) using the least squares method. a'=(X T X) -1 X T Y …(9)

[0090] The magnitude (amplitude) of the reference waveform corresponding to each girder B1 is proportional to the girder deflection of that girder B1. Therefore, by multiplying the reference waveform by the girder deflection used to calculate the reference waveform, the girder deflection of each girder can be estimated. Note that, when the bridge type and span length are the same, the ratio of each element of a in the estimated a is equivalent to the ratio of the maximum girder deflection or the ratio of the girder stiffness.

[0091] <Example of deformation estimation method> Figure 10 is a flowchart showing the main steps of an example of a method for estimating the deformation of a railway structure, specifically, an example of a method for estimating the deflection of girder B1 that constitutes bridge B, as performed by the estimation device 1.

[0092] (Step S1: Obtain the actual orbital displacement difference) In the estimation method performed by the estimation device 1, as shown in Figure 10, first, the acquisition unit 33a acquires the difference between two track displacements that were continuously measured by the vehicle V1 of the train T that actually traveled on the track R on the bridge B that is the target of deformation estimation.

[0093] Specifically, the acquisition unit 33a extracts eccentric arrow trajectory displacement data D1 corresponding to the position of bridge B, which is the target of deformation estimation, from the measurement data D received from the trajectory displacement measuring device 10 and pre-stored in the storage unit 32. Subsequently, the acquisition unit 33a extracts the eccentric arrow trajectory displacement z in the eccentric arrow trajectory displacement data D1. t,A , z t,B From each of these, the trajectory displacement z of the 10m chord arquebus t,A,10 , z t,B,10 Furthermore, the acquisition unit 33a acquires the eccentric arrow trajectory displacement z t,A , z t,B For each position where measurement was taken, the trajectory displacement z of the 10m chord yaw was measured. t,A,10 , 10m chord truss orbital displacement z t,B,10 The difference between this value and the current value, i.e., the difference in dynamic trajectory displacement, is calculated. Then, the acquisition unit 33a acquires a matrix Y that shows the waveform of the dynamic trajectory displacement difference in the n-sequence girders B1.

[0094] (Step S2: Acquire reference waveform) Next, the reference waveform acquisition unit 33b acquires the reference waveform. Specifically, the reference waveform acquisition unit 33b generates a matrix (reference waveform matrix) x that represents the reference waveform. ref Obtain the characteristic matrix X that includes this matrix.

[0095] (Step S3: Amplitude Estimation) Then, the estimation unit 33c estimates the amplitude of each reference waveform in digit B1 such that the curve obtained by arranging n reference waveforms acquired by the reference waveform acquisition unit 33b, shifted by the length of digit B1, and superimposing them, and the curve in which each reference waveform in digit B1 has its own unique amplitude, approximates the result obtained in step S2. Specifically, the estimation unit 33c estimates the matrix a representing the amplitude using the results obtained in steps S2 and S3 and equation (9).

[0096] <Main effects of this embodiment> As described above, in this embodiment, the amplitude of each reference waveform corresponding to each girder B1 is estimated so that the curve in which n reference waveforms are arranged and superimposed with a shift equal to the length of the girder, and each reference waveform corresponding to each girder B1 has its own unique amplitude, approximates the waveform of the dynamic track displacement difference based on the inspection results by the track inspection vehicle. The amplitude estimated by this embodiment corresponds to the deformation (girder deflection) of the girder B1, and the magnitude of the amplitude is proportional to the magnitude of the girder deflection. Furthermore, the amplitude estimated for each girder B1 is a state in which the reference waveforms corresponding to adjacent girders B1 are superimposed, that is, the influence of adjacent girders B1 is reflected. Therefore, the deformation of bridge B (specifically, the girder deflection of girder B1) can be estimated more accurately.

[0097] Furthermore, according to this embodiment, the deformation of each of the n girders B1 constituting the bridge B can be estimated all at once. Therefore, the time required to estimate the deformation of all n girders B1 can be reduced.

[0098] <Other examples of characteristic matrix X> In the above example, the model of the railway structure used to obtain the reference waveform assumed that the end of the single bridge section K1 was continuous with rigid ground. However, in n (where n is a natural number greater than or equal to 2) bridge sections, i.e., multiple bridge sections, rigid ground may not exist before or after them. For example, the end of a multiple bridge section that is the target of deformation estimation may be continuous with the bridge girder. In other words, it is possible to target deformation for some or more bridge sections included in a multi-bridge section.

[0099] In such cases, it is necessary to appropriately consider the influence of adjacent girders B1 at the ends of the multiple bridge sections being estimated for deformation. One possible method for doing this is to modify the section of the aforementioned characteristic matrix X that corresponds to rigid ground.

[0100] Figure 11 shows an example of a characteristic matrix X that takes into account the influence of the five-span bridge section, i.e., the adjacent girder B1, when the deformation estimation target is a five-span bridge section. The characteristic matrix X in Figure 11 shows that the track structure has virtual adjacent girders B1 with amplitude parameters a0 and a6 on both the entry and exit sides of the estimated section. Since the data acquired by the acquisition unit 33a is only data for girders B1 for 5 sections, the characteristic matrix X is trimmed (a portion of the reference waveform is not considered) for parts other than those corresponding to this data. In the characteristic matrix X in Figure 11, columns 1 to 4 partially disregard the front side of the reference waveform in the direction of vehicle travel, and columns 3 to 7 partially disregard the rear side of the reference waveform in the direction of travel. Also, in the characteristic matrix X in Figure 11, as shown in Figure 12, the length of the section influencing the adjacent entry side of the reference waveform (pre-running section K2) is 3 digits (d f =3d b ), the length of the influence interval (post-travel interval K3) on the exit side adjacent part in the reference waveform is four orders of magnitude (d r =4d b )

[0101] In this example as well, in step S3, the estimation unit 33c calculates matrix a such that the matrix Y acquired by the acquisition unit 33a approximates matrix y, which is represented by the product of the characteristic matrix X in Figure 11 and the aforementioned matrix a containing amplitude parameters a0 to a6, as shown in equation (8).

[0102] The inventors of this invention selected five spans of girders B1 from a bridge B consisting of several hundred girders B1 of the same span length and specifications as the target for deformation estimation. Using the track displacement (eccentric arrow track displacement) previously measured in the section by a two-bogie inspection vehicle, they calculated matrix a based on the characteristic matrix X in Figure 11 using the method according to this embodiment. This matrix was then compared with the actual girder deflection measured by a ground-based displacement meter for each of the five spans of girders B1. The comparison results are shown in Figure 13. Hereafter, the five spans of girders B1 in question will be referred to as T5, T4, T3, T2, and T1, starting from the train entry side.

[0103] In the table in Figure 13, each parameter included in matrix a measured by the method according to this embodiment and the actually measured digit deflection are standardized by the value of digit T4 and shown as relative deflection. As shown in Figure 13, the estimated girder deflection for each girder B1 using the method according to this embodiment showed an error of less than 15% compared to the relative deflection based on ground measurement results. In particular, the error for girders T1-T3 and T5 was about 1-3%.

[0104] According to this embodiment, even when there is no rigid ground before or after the multiple bridge sections targeted for deformation estimation, the girder deflection of each girder B1 can be estimated more accurately.

[0105] Preferred embodiments of the present invention have been described above, but the present invention is not limited to these examples. It will be obvious to those skilled in the art that various modifications or alterations can be conceived within the scope of the technical idea described in the claims, and these will naturally also fall within the technical scope of the present invention.

[0106] Furthermore, the effects described herein are merely descriptive or illustrative and not limiting. In other words, the technology relating to this disclosure may produce other effects that are obvious to those skilled in the art from the description herein, in addition to or instead of the effects described herein.

[0107] Furthermore, the following configurations also fall within the technical scope of this disclosure. (1) A method for estimating the deformation of a railway structure, The track structure being estimated consists of n (where n is an integer greater than or equal to 2) unit sections. The acquisition process involves obtaining the difference between two track displacements, which are continuously measured by a vehicle that actually traveled on the track on the aforementioned track structure that is the target of estimation, A standard track structure consisting of a single unit section and sections of rigid ground adjacent to its entry and exit sides where deformation does not occur, is acquired multiple times by changing the position of the vehicle, with the difference in track displacement at two locations measured by simulation using the vehicle on the track on the standard track structure, and this is used as the standard waveform. An estimation method comprising: an estimation step of estimating the amplitude of each of the reference waveforms in each of the unit intervals such that the curve obtained by arranging and superimposing n of the reference waveforms in the unit intervals, shifted by the length of the travel direction of the unit interval, and in which each of the reference waveforms in the unit intervals has a unique amplitude, approximates the acquisition result in the acquisition step. (2) The estimation method according to (1), wherein the estimation step is to calculate the matrix a such that the matrix y, which is represented by the product of a characteristic matrix X including a matrix showing the reference waveform and a matrix a showing the amplitude of each unit section of the line structure to be estimated, approximates the matrix Y showing the acquisition results in the acquisition step. (3) The estimation method described in (2), wherein the estimation step is to calculate the matrix a by the least squares method. (4) The characteristic matrix X is the matrix of the reference waveform, with each column representing the number of samples d in the unit section that constitutes the reference line structure. b This is a matrix in which the rows are shifted downwards by one minute. The aforementioned sample size d bThe estimation method according to (2) or (3), wherein is the number of differences in the unit interval included in the reference waveform. (5) The simulation is an estimation method according to any one of (1) to (4) above, including a simulation based on finite element analysis. (6) The vehicle is a two-car inspection vehicle that measures track displacement at four axle positions from the first to the fourth axle of one vehicle, The estimation method according to any one of (1) to (5) above, wherein the difference in the trajectory displacements at the two locations is the difference between the straight trajectory displacement calculated from the eccentric trajectory displacement in the second axis relative to the first and fourth axes and the straight trajectory displacement calculated from the eccentric trajectory displacement in the third axis relative to the first and fourth axes. (7) The aforementioned railway structure is a bridge, The estimation method according to any one of (1) to (6) above, wherein the deformation is the deflection of the girders constituting the bridge. (8) A device for estimating the deformation of a railway structure, The track structure being estimated consists of n (where n is an integer greater than or equal to 2) unit sections. An acquisition unit that acquires the difference between two track displacements, which are continuously measured by a vehicle that actually traveled on the track on the aforementioned track structure that is the target of estimation, A reference waveform acquisition unit acquires multiple differences in track displacement at two locations, measured by simulation using the vehicle on the track of the reference track structure, by changing the position of the vehicle, for a reference track structure consisting of a single unit section and sections of rigid ground adjacent to the entry and exit sides where deformation does not occur, and uses these differences as a reference waveform. An estimation device comprising: an estimation unit that estimates the amplitude of each of the reference waveforms in each unit section such that the curve obtained by arranging and superimposing n of the reference waveforms in the unit section, shifted by the length of the travel direction of the unit section, and in which each of the reference waveforms in the unit section has a unique amplitude, approximates the acquisition result from the acquisition unit. (9) The estimation apparatus according to (8), wherein the estimation unit calculates the matrix a such that the matrix y, which is represented by the product of a characteristic matrix X including a matrix showing the reference waveform and a matrix a showing the amplitude of each unit section of the line structure to be estimated, approximates the matrix Y showing the acquisition results in the acquisition unit. (10) The estimation device according to (9), wherein the estimation unit calculates the matrix a by the least squares method. (11) The characteristic matrix X is the matrix of the reference waveform, with each column representing the number of samples d in the unit section that constitutes the reference line structure. b This is a matrix in which the rows are shifted downwards by one minute. The aforementioned sample size d b The estimation device according to (9) or (10), wherein is the number of differences in the unit interval included in the reference waveform. (12) The estimation apparatus according to any one of (8) to (11) above, wherein the simulation includes a simulation based on finite element analysis. (13) The vehicle is a two-car inspection vehicle that measures track displacement at four axle positions from the first to the fourth axle of one vehicle, The estimation device according to any one of (8) to (12) above, wherein the difference in the trajectory displacements at the two locations is the difference between the straight trajectory displacement calculated from the eccentric trajectory displacement in the second axis relative to the first and fourth axes and the straight trajectory displacement calculated from the eccentric trajectory displacement in the third axis relative to the first and fourth axes. (14) The aforementioned railway structure is a bridge, The deformation is the deflection of the girders constituting the bridge, as described in any one of (8) to (13) above, in the estimation device. (15) Computers, An acquisition unit that acquires the difference between two track displacements, which are continuously measured by a vehicle that actually traveled on the track on the track structure of the target railway, consisting of n (where n is an integer of 2 or more) consecutive unit intervals, A reference waveform acquisition unit acquires multiple differences in track displacement at two locations, measured by simulation using the vehicle on the track of the reference track structure, by changing the position of the vehicle, for a reference track structure consisting of a single unit section and sections of rigid ground adjacent to the entry and exit sides where deformation does not occur, and uses these differences as a reference waveform. A program that functions as an estimation unit, which estimates the amplitude of each of the reference waveforms in each unit section such that the curve obtained by arranging and superimposing n of the reference waveforms in the unit section, shifted by the length of the travel direction of the unit section, and having each of the reference waveforms in the unit section have its own unique amplitude, approximates the acquisition result from the acquisition unit. [Industrial applicability]

[0108] This disclosure is useful when estimating the deformation of railway structures such as railway bridges. [Explanation of Symbols]

[0109] 1 Estimation device 10. Orbital displacement measuring device 11. Laser reference line generation unit 12 Eccentric Arrow Trajectory Displacement Calculation Unit 13. Distance calculation unit 14 Measurement data storage unit 15 Measurement data transmission unit 16 Control Unit 31 Communications Department 32 Storage section 33 Control Unit 33a Acquisition part 33b Reference waveform acquisition section 33c Estimation part 40 Networks B Bridge B1 digit B2 abutment B3 pier B4 bearing H storage medium R orbit T train V1 Vehicle V2 Vehicle

Claims

1. A method for estimating the deformation of railway structures, The track structure being estimated consists of n (where n is an integer greater than or equal to 2) unit sections. The acquisition process involves obtaining the difference between two track displacements, which are continuously measured by a vehicle that actually traveled on the track on the aforementioned track structure that is the target of estimation, A standard track structure consisting of a single-unit section and sections of rigid ground adjacent to its entry and exit sides where deformation does not occur, is acquired multiple times by changing the position of the vehicle, with the difference in track displacement at two locations measured by simulation using the vehicle on the track of the standard track structure, and used as a standard waveform; An estimation method comprising: an estimation step of estimating the amplitude of each of the reference waveforms in each unit section such that the curve obtained by arranging and superimposing n reference waveforms shifted by the length of the travel direction of the unit section, wherein each of the reference waveforms in the unit section has a unique amplitude, approximates the acquisition result in the acquisition step.

2. The estimation method according to claim 1, wherein the estimation step involves calculating the matrix a such that the matrix y, which is represented by the product of a characteristic matrix X including a matrix showing the reference waveform and a matrix a showing the amplitude of each unit section of the line structure to be estimated, approximates the matrix Y showing the acquisition results in the acquisition step.

3. The estimation method according to claim 2, wherein the estimation step is to calculate the matrix a by the least squares method.

4. The characteristic matrix X is the matrix of the reference waveform, with each column representing the number of samples d in the unit section constituting the reference line structure. ｂ This is a matrix in which the rows are shifted downwards by one minute. The aforementioned sample size d ｂ The estimation method according to claim 2 or 3, wherein is the number of differences in the unit interval included in the reference waveform.

5. The estimation method according to any one of claims 1 to 3, wherein the simulation includes a simulation based on finite element analysis.

6. The aforementioned vehicle is a two-car inspection vehicle that measures track displacement at four axle positions, from the first to the fourth axle of a single vehicle. The estimation method according to any one of claims 1 to 3, wherein the difference in the trajectory displacements at the two locations is the difference between the straight trajectory displacement calculated from the eccentric trajectory displacement in the second axis relative to the first and fourth axes and the straight trajectory displacement calculated from the eccentric trajectory displacement in the third axis relative to the first and fourth axes.

7. The aforementioned railway structure is a bridge, The estimation method according to any one of claims 1 to 3, wherein the deformation is the deflection of the girders constituting the bridge.

8. A device for estimating the deformation of railway structures, The track structure being estimated consists of n (where n is an integer greater than or equal to 2) unit sections. An acquisition unit that acquires the difference between two track displacements, which are continuously measured by a vehicle that actually traveled on the track on the aforementioned track structure that is the target of estimation, A reference waveform acquisition unit acquires multiple differences in track displacement at two locations, measured by simulation using the vehicle on the track of the reference track structure, by changing the position of the vehicle, for a reference track structure consisting of a single unit section and sections of rigid ground adjacent to the entry and exit sides where deformation does not occur, and uses these differences as a reference waveform. An estimation device comprising: an estimation unit that estimates the amplitude of each of the reference waveforms in each unit section such that the curve obtained by arranging and superimposing n reference waveforms shifted by the length of the travel direction of the unit section, wherein each of the reference waveforms in the unit section has a unique amplitude, approximates the acquisition result from the acquisition unit.

9. The estimation device according to claim 8, wherein the estimation unit calculates the matrix a such that the matrix y, which is represented by the product of a characteristic matrix X including a matrix showing the reference waveform and a matrix a showing the amplitude of each unit section of the line structure to be estimated, approximates the matrix Y showing the acquisition results in the acquisition unit.

10. The estimation device according to claim 9, wherein the estimation unit calculates the matrix a by the least squares method.

11. The characteristic matrix X is the matrix of the reference waveform, with each column representing the number of samples d in the unit section constituting the reference line structure. ｂ This is a matrix in which the rows are shifted downwards by one minute. The aforementioned sample size d ｂ The estimation device according to claim 9 or 10, wherein is the number of differences in the unit interval included in the reference waveform.

12. The estimation apparatus according to any one of claims 8 to 10, wherein the simulation includes a simulation based on finite element analysis.

13. The aforementioned vehicle is a two-car inspection vehicle that measures track displacement at four axle positions, from the first to the fourth axle of a single vehicle. The estimation device according to any one of claims 8 to 10, wherein the difference in the trajectory displacements at the two locations is the difference between the straight trajectory displacement calculated from the eccentric trajectory displacement in the second axis relative to the first and fourth axes and the straight trajectory displacement calculated from the eccentric trajectory displacement in the third axis relative to the first and fourth axes.

14. The aforementioned railway structure is a bridge, The estimation device according to any one of claims 8 to 10, wherein the deformation is the deflection of the girders constituting the bridge.

15. Computers, An acquisition unit that acquires the difference between two track displacements, which are continuously measured by a vehicle that actually traveled on the track on the track structure of the target railway, consisting of n (where n is an integer of 2 or more) consecutive unit sections, A reference waveform acquisition unit acquires multiple differences in track displacement at two locations, measured by simulation using the vehicle on the track of the reference track structure, by changing the position of the vehicle, for a reference track structure consisting of a single unit section and sections of rigid ground adjacent to the entry and exit sides where deformation does not occur, and uses these differences as a reference waveform. A program that functions as an estimation unit, which estimates the amplitude of each of the reference waveforms in a unit section such that the curve obtained by arranging and superimposing n of the reference waveforms in a unit section, shifted by the length of the travel direction of the unit section, and in which each of the reference waveforms in the unit section has its own amplitude, approximates the acquisition result from the acquisition unit.

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