Bridge deflection estimation method, deflection estimation device, and deflection estimation program

Abstract

This invention provides a bridge deflection estimation method, deflection estimation device, and deflection estimation program that can easily estimate the amount of bridge deflection by utilizing track displacement measured from vehicles traveling on the bridge. [Solution] Deflection estimation method #100 is a method for estimating the deflection of a bridge, and includes a natural frequency / mode damping ratio estimation step (#140) which estimates the natural frequency and mode damping ratio of the bridge in a resonant state when a vehicle is passing over the bridge, based on the measurement results of a track displacement measuring device for a vehicle passing over the bridge, and a deflection amount estimation step (#150) which estimates the amount of deflection of the bridge in a resonant state when a vehicle is passing over, based on the natural frequency and mode damping ratio. In the natural frequency / mode damping ratio estimation step (#140), the natural frequency and the mode damping ratio are estimated based on the peak amplitude and peak position of the waveform of the measured value of the track displacement difference.

Description

[Technical Field]

[0001] This invention relates to a bridge deflection estimation method, a deflection estimation device, and a deflection estimation measurement program for estimating the deflection of a bridge. [Background technology]

[0002] Bridge deflection during train passage is a fundamental performance indicator evaluated in design and other processes. Bridge deflection is measured not only when a new line opens or when a train enters service, but also in recent years during routine maintenance for efficient, performance-based maintenance. Various methods exist, such as measuring the deflection of a bridge by measuring the displacement between the girder and the ground using a contact-type displacement meter, integrating the output signal of an accelerometer attached to the girder, using a ring-type displacement meter equipped with a circular leaf spring on the ground, a piano wire attached to one end of the leaf spring and the other end of the leaf spring, and a strain gauge attached to the leaf spring, measuring the deflection of a bridge by image measurement by continuously taking images of a train passing and comparing a reference image before the train passes with a series of images taken during the train's passage, and measuring the deflection of a bridge by receiving the reflected laser light from the ground side onto an image measurement marker attached to the bridge girder and using a laser displacement meter to measure the deflection of the girder. However, all of these typical bridge deflection measurement methods involve measuring the deflection from the ground while a train passes over the bridge, resulting in enormous time and expense required each year for bridge deflection measurement. For this reason, a method for evaluating bridge performance from a vehicle has been proposed.

[0003] As a more efficient method for inspecting bridges, a technique that indirectly grasps the condition of a bridge by using sensors installed on a moving vehicle and analyzing the response when passing over the bridge (on-vehicle measurement bridge inspection method) has been widely studied around the world. In the vehicle scanning method for the dynamic characteristics of bridges, a test vehicle equipped with vibration sensors moves over the bridge, and the output bridge frequency is extracted from the output signal of the vibration sensors to investigate the condition of the bridge (see, for example, Non-Patent Document 1). However, most on-vehicle measurement bridge inspection methods to date have been methods that indirectly detect the performance of the bridge, such as the bridge's natural frequency, vibration mode shape, or damage, using a single sensor installed on the vehicle.

[0004] In indirect bridge frequency estimation using two vehicles, the bridge's natural frequency, which is a vibration component common to the responses of multiple vehicles, is extracted by signal processing including cross-spectral density function estimation (see, for example, Non-Patent Document 2). In this indirect bridge frequency estimation, the use of multiple sensors has been considered, but the performance indicator of the bridge detected is the natural frequency, and it was not possible to directly evaluate the performance (deflection).

[0005] Conventional bridge resonance detection methods detect bridge resonance based on track displacement measured at the lead car of a train and track displacement measured at the rear car of the same train (see, for example, Patent Document 1). Conventional bridge resonance detection methods detect bridge resonance based on vertical acceleration measured at the lead car of a train and vertical acceleration measured at the rear car of the same train (see, for example, Patent Documents 2 and 3). These conventional bridge resonance detection methods propose techniques to detect bridges where vibrations are greatly amplified when a train passes over them (resonant bridges) by measuring track displacement measurement devices or vehicle body sway acceleration installed on the lead and rear cars of a commercial train, but they have not been able to measure the magnitude of bridge deflection.

[0006] Conventional methods for measuring bridge deflection detect bridge resonance based on track displacement measured at the lead car of a train and track displacement measured at the rear car of the same train (see, for example, Patent Documents 4 and 5). These conventional methods estimate the magnitude of bridge deflection from the difference between the track displacement measured at the lead car of a train and the track displacement measured at the rear car of the same train. However, these conventional methods for measuring bridge deflection cannot take into account the dynamic response component that increases when a train passes over a resonant bridge, and therefore could not be applied to bridges in a resonant state where the girder deflection value is most desired. For these reasons, even with the development of these prior arts, measuring deflection from the ground, especially on conventional lines, still incurs enormous costs and resources every year. [Prior art documents] [Patent Documents]

[0007] [Non-Patent Document 1] YBYang, JPYang, Y. Wu, B. Zhang, “Vehicle Scanning Method for Bridges”, USA, John Wiley & Sons Ltd, 28 October 2019.

[0008] [Non-Patent Document 2] T. Nagayama, APReksowardojo, D. Su, T. Mizutani, “Bridge natural frequency estimation by extracting the common vibration component from the responses of two vehicles”, Engineering Structures, 150 (2017) 821-829.

[0009] [Patent Document 1] Japanese Patent Publication No. 2021-152250

[0010] [Patent Document 2] Japanese Patent Publication No. 2022-108892

[0011] [Patent Document 3] Japanese Patent Publication No. 2022-114187

[0012] [Patent Document 4] Japanese Patent Publication No. 2023-009905

[0013] [Patent Document 5] Japanese Patent Publication No. 20214-051192 [Overview of the project] [Problems that the invention aims to solve]

[0014] Conventional methods using track displacement measured on board a vehicle only determine whether resonance is occurring, and do not determine the girder deflection value in the case of resonance. Therefore, it was necessary to measure from the ground after detecting the resonance state. Furthermore, the girder deflection estimation method already proposed using track displacement measured on board a vehicle was limited to low speeds where the dynamic response component of the bridge can be ignored. Moreover, in order to estimate the girder deflection value of a bridge in a resonant state where the dynamic response is dominant, a theory and method for on-board measurement that takes into account the dynamic response of the bridge, which has been ignored until now, is necessary, but this has not been theoretically developed. In summary, there were two major challenges: (1) theoretical elucidation of the influence of the dynamic response of a bridge in a resonant state on track displacement measured on board a vehicle, and (2) a method for evaluating the dynamic response of a bridge from track displacement.

[0015] The object of this invention is to provide a bridge deflection estimation method, a deflection estimation device, and a deflection estimation program that can easily estimate the amount of deflection of a bridge by utilizing track displacement measured from a vehicle traveling on the bridge. [Means for solving the problem]

[0016] This invention solves the aforementioned problem by the following means of solution. The embodiments of this invention will be described using corresponding reference numerals, but the invention is not limited to these embodiments. The invention of claim 1 is a bridge deflection estimation method for estimating the deflection of a bridge (B), as shown in Figures 2 and 9, wherein a vehicle (V) passing over the bridge... F ,V L Based on the measurement results of the track displacement measuring devices (2A, 2B) of the vehicle, the natural frequency (n) of the bridge in a resonant state when this vehicle is passing over it is determined. ∧ b,1 ) and mode damping ratio (ξ ∧ b,1 A natural frequency / mode damping ratio estimation step (#140) to estimate the natural frequency / mode damping ratio, and based on the natural frequency and the mode damping ratio, the amount of deflection of the bridge in the resonant state when the vehicle is passing over (z b,1 This is a bridge deflection estimation method (#100) that includes a deflection amount estimation step (#150) which estimates the deflection amount.

[0017] The invention of claim 2 relates to the bridge deflection estimation method described in claim 1, wherein, as shown in Figures 7 and 8(C), the natural frequency / mode damping ratio estimation step involves measuring the actual value of the track displacement difference, which is the difference between the track displacement measured at the last vehicle and the track displacement measured at the first vehicle when passing over the bridge in the resonant state (dI ~ The method for estimating bridge deflection is characterized by including the step of estimating the natural frequency and the mode damping ratio based on the peak amplitude and peak position of the waveform.

[0018] The invention of claim 3 is a bridge deflection estimation method according to claim 1, characterized in that the natural frequency / mode damping ratio estimation step includes a step of estimating the natural frequency and the mode damping ratio based on measured and theoretical values ​​of the track displacement difference, which is the difference between the track displacement measured by the last vehicle and the track displacement measured by the first vehicle when passing over the bridge in a resonant state.

[0019] The invention according to claim 4 is the bridge deflection estimation method according to claim 3, wherein as shown in FIG. 8(C), the natural frequency / mode damping ratio estimating step is characterized in that a theoretical value (dI) of the track displacement difference matches a measured value (dI ~ ) of the track displacement difference, and the method comprises the step of estimating the natural frequency and the mode damping ratio.

[0020] The invention according to claim 5 is the bridge deflection estimation method according to claim 3, wherein as shown in FIG. 8(C), the natural frequency / mode damping ratio estimating step comprises the step of comparing three peak amplitudes appearing in a waveform of a measured value (dI ~ ) of the track displacement difference with three peak amplitudes in a waveform of a theoretical value (dI) of the track displacement difference, to estimate the natural frequency and the mode damping ratio.

[0021] The invention according to claim 6 is a bridge deflection estimating apparatus for estimating deflection of a bridge (B) as shown in FIGS. 2 and 3, wherein the apparatus estimates a natural frequency (n F , V L ) of a bridge in a resonant state when a vehicle (V) passing the bridge is passing through, based on measurement results of track displacement measuring devices (2A, 2B) ∧ b,1 ) and a mode damping ratio (ξ ∧ b,1 ), the apparatus comprising: a natural frequency / mode damping ratio estimating unit (11) configured to estimate the above values; and a deflection amount estimating unit (12) configured to estimate a deflection amount (z b,1 ) of the bridge in the resonant state when the vehicle is passing through, based on the natural frequency and the mode damping ratio, which is the bridge deflection estimating apparatus (6).

[0022] The invention according to claim 7 is a bridge deflection estimation program for estimating deflection of a bridge (B) as shown in FIGS. 2, 3 and 10, wherein the program is for estimating deflection of a bridge (B), and relates to a vehicle (V F , V LBased on the measurement results of the track displacement measuring devices (2A, 2B) of the vehicle, the natural frequency (n) of the bridge in a resonant state when this vehicle is passing over it is determined. ∧ b,1 ) and mode damping ratio (ξ ∧ b,1 A procedure for estimating the natural frequency / mode damping ratio (S140) and, based on the natural frequency and the mode damping ratio, the amount of deflection of the bridge in the resonant state when the vehicle is passing over (z b,1 This bridge deflection estimation program is characterized by having a computer execute a deflection estimation procedure (S150) that estimates the deflection amount. [Effects of the Invention]

[0023] According to this invention, the amount of deflection of a bridge can be easily estimated by utilizing the track displacement measured from a vehicle traveling on the bridge. [Brief explanation of the drawing]

[0024] [Figure 1] This is a schematic diagram of a moving body that moves over a bridge whose girder deflection is estimated by a bridge deflection estimation device according to an embodiment of this invention. [Figure 2] This is a schematic overall diagram showing a bridge deflection estimation system according to an embodiment of this invention. [Figure 3] This is a schematic diagram illustrating a bridge deflection estimation system according to an embodiment of this invention. [Figure 4] This is a schematic diagram of the bridge analysis model in the bridge deflection estimation method according to an embodiment of this invention. [Figure 5] This graph shows, as an example, a theoretical solution of the bridge dynamic response around resonance observed from a vehicle in a bridge deflection estimation method according to an embodiment of this invention. [Figure 6] This is a schematic diagram showing the data structure of the data storage unit of a bridge deflection estimation device according to an embodiment of the present invention. [Figure 7]The graphs show the characteristics and effects of trajectory displacement of a 20m chord symmetrical axis as an example; (A) is the graph for a mode damping ratio of 1%, and (B) is the graph for a mode damping ratio of 3%. [Figure 8] This is a conceptual diagram illustrating the estimation process of natural frequency and mode damping ratio, and the estimation process of deflection amount, by the natural frequency / mode damping ratio estimation unit of the bridge deflection estimation device according to an embodiment of the present invention. (A) is a conceptual diagram showing a moving load series model used for calculating the theoretical value of the track displacement difference as an example. (B) is a graph showing the convergence process by the MCMC method as an example. (C) is a graph showing an example of the estimation of the track displacement difference as an example. (D) is a graph showing an example of the estimation of girder deflection as an example. [Figure 9] This is a process diagram of a bridge deflection estimation method according to an embodiment of the present invention. [Figure 10] This is a flowchart illustrating the operation of a bridge deflection estimation device according to an embodiment of this invention. [Figure 11] The graphs show the estimated posterior distribution of parameters in an actual bridge. (A) shows the changes in natural frequency and mode damping ratio, and (B) compares the measured and theoretical values ​​of the trajectory displacement difference during the convergence process. [Figure 12] This graph compares the estimated girder deflection results for each sampling cycle of an actual bridge with the measured results. [Modes for carrying out the invention]

[0025] Hereinafter, embodiments of this invention will be described in detail with reference to the drawings. The track R shown in Figures 1 and 2 is the path (railway) on which train T travels. The track R is equipped with a pair of rails on the left and right to guide the wheels of train T. For example, the track R is a double track consisting of two main lines, an up line on which train T travels from the terminal to the starting point, and a down line on which train T travels from the starting point to the terminal point.

[0026] The train T shown in Figures 1 and 2 is a moving object that travels along the track R. The train T is a railway vehicle such as an electric train, diesel train, or passenger car that travels on a bridge B. The train T shown in Figures 1 and 2 is, for example, a Shinkansen (registered trademark) railway vehicle traveling at high speed. The train T is a commercial train formed for the purpose of transporting passengers or freight. The train T is, for example, composed of one or more vehicles. The train T shown in Figure 1 has a vehicle length (body length) L C The train consists of 12 passenger cars, each approximately 25 meters long. When train T travels over bridge B, the wheels periodically apply load to bridge B due to the regular axle arrangement, causing bridge B to vibrate.

[0027] Train T is a vehicle V as shown in Figures 1 and 2. F ,V M ,V L It is composed of and moves across bridge B at a nearly constant speed (train speed) v. Vehicle V F This is the leading car located at the front of the train formation, and is car V M This is an intermediate car located in the middle of the train formation, and is car V L This is the last car in the train formation. F ,V M ,V L As shown in Figures 1 and 2, the vehicle is equipped with bogies T1 and T2, and one vehicle body is supported by the two bogies T1 and T2. Bogies T1 and T2 are located on each vehicle V F ,V M ,V L This is a device that supports the vehicle body and allows it to run on the track R. The bogies T1 and T2 shown in Figures 1 and 2 are two-axle bogies (bogie trucks) composed of two pairs of wheelsets, and each vehicle V F ,V M ,V L It supports one end and the other end of the car body. Bogie T1 supports each vehicle V F ,V M ,V L The first bogie is positioned on the front side in the direction of travel and supports one end of the car body, and bogie T2 is located on each vehicle V F ,V M ,V LThis is the second bogie, positioned at the rear in the direction of travel, supporting the other end of the vehicle body.

[0028] Bridge B, shown in Figure 1, is a fixed structure constructed to form a space below the track R. Bridge B is constructed to cross a body of water such as a river, valley, or lake, or a transportation route such as a road or railway. Bridge B is a concrete railway bridge, for example, a reinforced concrete structure (RC structure) or a type of prestressed concrete structure, where concrete is the main material, and it is a structure (PRC structure) that allows cracking under normal use conditions and controls the crack width by the arrangement of deformed reinforcing bars and the introduction of prestressing. As shown in Figure 1, Bridge B comprises girders B1 and columns B2. Girder B1 is a structure arranged horizontally and supporting the track R. Girder B1 is a beam such as a PRC girder that straddles one support point and the other support point with column B2 as the support point. Column B2 is a structure that supports girder B1. Column B2 is constructed at predetermined intervals along the length of Bridge B and is a reinforced concrete column arranged vertically. Bridge B shown in Figure 1 has a span length L b is 25m or more (vehicle length L c (That's all.)

[0029] The deflection estimation system 1 shown in Figures 2 and 3 is a system for estimating the deflection of bridge B. As shown in Figure 3, the deflection estimation system 1 comprises track displacement measuring devices 2A and 2B, a running speed measuring device 3, a running distance measuring device 4, a communication device 5, and a deflection estimation device 6. The deflection estimation system 1 transmits the measurement results of the track displacement measuring devices 2A and 2B, the running speed measuring device 3, and the running distance measuring device 4 to the deflection estimation device 6 via the communication device 5, and estimates the deflection of bridge B based on these measurement results.

[0030] The track displacement measuring devices 2A and 2B shown in Figures 2 and 3 are devices for measuring track displacement on bridge B. As shown in Figure 2, track displacement measuring device 2A measures track displacement in front of train T, and track displacement measuring device 2B measures track displacement behind train T. Track displacement measuring device 2A measures track displacement in front of the leading vehicle V of train T. FIt is located on the underside of the vehicle body, a predetermined distance from the front bogie T1 in the direction of travel towards the rear. The track displacement measuring device 2B is located at the rear of the last vehicle V of train T. L It is located on the underside of the vehicle body, a predetermined distance in the forward direction from the rear bogie T2 in the direction of travel. Both track displacement measuring devices 2A and 2B have the same structure and are track inspection devices that measure track displacement while moving along the track R with the train T. Here, track displacement is a phenomenon in which the track R, which is the running surface of the train T, gradually changes due to repeated passage of the train T, causing the shape of the rail in the longitudinal direction to change, and is also called track irregularity or track misalignment.

[0031] The track displacement measuring devices 2A and 2B measure track displacement by utilizing the relative difference in rail displacement at multiple points, thereby measuring the vertical displacement of the rail. For example, the track displacement measuring devices 2A and 2B measure the chord-arrow track displacement on bridge B from a train T traveling on bridge B. Here, the chord-arrow is a track measurement method that takes a reference line connecting two points on the rail and measures the amount of vertical displacement (deviation) of the rail relative to the reference line at the midpoint of the reference line. The track displacement measuring devices 2A and 2B are installed, for example, on some high-speed rail trains or test vehicles, and are vehicle-mounted track irregularity measuring instruments that measure track displacement using the inertial arrow method. They are vehicle-mounted inertial arrow measuring devices that are installed on the body of train T. Here, the inertial arrow method is an inertial measurement method that obtains an output with the same shape as the measurement waveform by the arrow method by combining a low-pass filter type integrating circuit with a speed-variable cutoff frequency and amplification ratio, and subsequent digital processing that simultaneously performs phase compensation and cutoff of specific frequencies. Track displacement measuring devices 2A and 2B are used, for example, for vehicle V F ,V M ,V L Vehicle length L c Since the length is 25m and the dynamic vibration component in the bridge section mainly consists of a 25m wavelength component, the 20m chord rifling trajectory displacement is measured by measuring the distance between the center of a chord stretched between two points 20m apart and the rail. The trajectory displacement measuring devices 2A and 2B output the height displacement measured by the chord rifling trajectory displacement of trajectory R as trajectory displacement data D1 and D2 to the deflection estimation device 6.

[0032] The speed measuring device 3 shown in Figure 3 is a device for measuring the running speed v of train T. The speed measuring device 3 is a speedometer such as a speed generator that detects the rotation of the wheels of train T and generates a pulse signal corresponding to the rotation speed of these wheels. For example, the speed measuring device 3 detects the rotation speed of the wheels of train T based on a predetermined number of pulse signals (distance pulse signals) generated for each rotation of the wheels of train T. The speed measuring device 3 measures the running speed of train T based on the rotation speed of the wheels of train T and outputs the running speed of train T as running speed data D3 to the deflection estimation device 6.

[0033] The distance measuring device 4 is a device that measures the distance traveled by train T. For example, the distance measuring device 4 detects the absolute position of train T by receiving 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. The distance measuring device 4 measures the distance traveled by train T by accumulating distance pulse signals output by a speed generator that detects the train speed of train T until train T reaches the next ATS ground unit. The distance measuring device 4 outputs the distance traveled (kilometers) of train T from the starting point to the ending point or from the ending point to the starting point as distance data D4 to the deflection estimation device 6.

[0034] Communication device 5 is a device that transmits track displacement data D1, D2, track speed data D3, and track distance data D4 from track displacement measuring devices 2A, 2B, track speed measuring device 3, and track distance measuring device 4 to the deflection estimation device 6. Communication device 5 is a telecommunication line such as a telephone line or internet line that connects the track displacement measuring devices 2A, 2B, track speed measuring device 3, and track distance measuring device 4 to the measurement data receiving unit 7 so that they can communicate with each other.

[0035] The deflection estimation device 6 shown in Figures 2 and 3 is a device for estimating the deflection of bridge B. The deflection estimation device 6 estimates the amount of deflection of girder B1 of bridge B in a resonant state. Here, the resonant state includes not only general resonance where the excitation period of train T running on bridge B matches the natural frequency of bridge B, but also states close to resonance where the two differ somewhat and a hum occurs. The deflection estimation device 6 excludes static displacements (static response) such as rail irregularities on bridge B over which train T passes, and estimates the deflection of bridge B in a resonant state by the dynamic displacement (dynamic response) of bridge B in a resonant state over which train T passes, and the quasi-static displacement (quasi-static response) due to the load of the train when the train passes over bridge B in a resonant state. The deflection estimation device 6 uses the leading vehicle V measured by track displacement measuring devices 2A and 2B. F and the last vehicle V L The system calculates the measured and theoretical values ​​of the difference in orbital displacement. The deflection estimation device 6 estimates the natural frequency and modal damping ratio of girder B1 of bridge B so that the measured and theoretical values ​​of the difference in orbital displacement match, and estimates the amount of deflection of girder B1 based on this natural frequency and modal damping ratio. Here, the natural frequency is the frequency at which vibrations become very large in response to external vibrations. The modal damping ratio is an index that represents how easily vibrations subside.

[0036] (Bridge analysis model) The analytical model shown in Figure 4 is a simply supported beam model under the action of a series of moving loads, and it models the behavior of the beam when a series of moving loads, arranged in the same configuration as the axles of train T, travels along the simply supported beam. The vertical displacement z of the beam shown in Figure 4. b When (x,t) is given as the x-coordinate in the direction of train T's movement and the z-coordinate in the vertical direction, with the support point at the left end of the beam as 0, it can be expressed by the following equation 1 when converted to a modal coordinate system.

[0037]

number

[0038] (The effect of the dynamic response of a resonant bridge on track displacement measured on board the vehicle) As shown in Figure 4, by assuming that the resonant bridge is a beam vibrating in the first bending mode, the dynamic response characteristics (amplitude and phase) due to resonance under the periodic excitation force of a moving train can be formulated by a transfer function. The transfer function is expressed as amplitude |G(v)| by the following equation 2, and as phase |∠G(v)| by the following equation 3.

[0039]

number

[0040]

number

[0041] Dynamic displacement z of bridge B b d (x) is represented by the following number 4.

[0042]

number

[0043] Equation 4 shows the dynamic response of bridge B in a resonant state when observed from the vehicle coupling position of train T traveling on bridge B, with vehicle length L c Waves with wavelength and span length L b It is expressed as a product of waves that are half the wavelength of the first mode (mode shape of the first mode).

[0044] Figure 5 is a graph showing, as an example, a theoretical solution of the dynamic response of bridge B around the resonance, as observed from a train T traveling on bridge B. The vertical axis in Figure 5 represents the normalized displacement, with the perfect resonance state normalized to 1, and the horizontal axis represents position [m]. The graph in Figure 5 shows the span length L of bridge B. b The distance is 30m, the running speed v of train T is equal to the resonance speed and within ±5% of the resonance speed, and the position of the track inspection device is approximately 3m towards the center of the vehicle from the center of the rear bogie in the direction of travel of the last car. Here, the resonance speed is the running speed v of train T when resonance occurs in bridge B.

[0045] As shown in Figure 5, when the travel speed v is lower than the resonant velocity, the position of the waveform minimum (lower peak) shifts towards the approach side of bridge B, and when the travel speed v is higher than the resonant velocity, the position of the waveform minimum (lower peak) shifts towards the exit / approach side of bridge B. Therefore, the difference between the travel speed v and the resonant velocity (the natural frequency of bridge B) is reflected in the position of the lower peak of the waveform. Also, when the mode damping ratio is 1%, the peak amplitude of the waveform is relatively high, and when the mode damping ratio is 3%, the peak amplitude of the waveform is relatively low. Therefore, the difference in mode damping ratio is reflected in the magnitude of the peak amplitude of the waveform. As a result, by determining the amplitude of the lower peak of the waveform corresponding to the mode damping ratio, it is possible to determine the natural frequency and mode damping ratio from the position and amplitude of the lower peak.

[0046] By converting the transfer function formulated by Equations 1 and 2 to the case observed from the track inspection position of a moving train, the dynamic response caused by bridge resonance is given by the vehicle length L, as shown in Equation 4. c Wave and span length L b The trajectory displacement is observed as a product of the half-waves. Also, as shown in Figure 5, the vehicle length L is determined by the discrepancy between the resonance velocity (corresponding to the natural frequency) and the running speed. c The position of a wave with wavelength on the bridge (distance from the starting point of the bridge) changes.

[0047] (Information necessary for estimating digit deflection) As shown in Equation 1, in order to evaluate the dynamic response of bridge B in a resonant state, the natural frequency n of bridge B is b,1 and mode damping ratio ξ b,1 These two things are necessary, and if these two are known, the dynamic response can be roughly reproduced. The dynamic response of the resonant bridge B, observed as track displacement from a moving train T, is as shown in Figure 5, where the wavelength is the vehicle length L. c The peak amplitude of the wave (mode attenuation ratio ξ b,1 (corresponding to) and peak position (natural frequency n) b,1It can be expressed using two pieces of information (corresponding to). Since there are two features for the two unknown parameters, the natural frequency n can be obtained from the peak amplitude and peak position measured on the vehicle. b,1 and mode damping ratio ξ b,1 It is theoretically possible to estimate this.

[0048] The deflection estimation device 6 shown in Figures 2 and 3 takes the position and amplitude of the lower peak of the dynamic response of bridge B, measured as track displacement from a train T traveling on bridge B, as input. The deflection estimation device 6 takes two unknown parameters (natural frequency n) shown in number 1 of the dynamic analysis model of bridge B in the resonant state shown in Figure 3. ∧ b,1 and mode damping ratio ξ ∧ b,1 The deflection estimation device 6 estimates the deflection of digit B1 by equation 1 using an analytical model with the estimated parameters. The deflection estimation device 6 estimates the deflection of the last vehicle V L and the leading vehicle V F Measured value dI of the orbital displacement difference between and ~ The deflection estimation device 6 calculates the theoretical value dI of the orbital displacement difference between these values. ~ The natural frequency n such that the theoretical value dI of the orbital displacement difference matches b,1 and mode damping ratio ξ b,1 Correct the following. The deflection estimation device 6 uses the measured value dI of the orbital displacement difference. ~ The natural frequency n that minimizes the error between the theoretical value dI and the actual value. ∧ b,1 and mode damping ratio ξ ∧ b,1 This is used as an estimated value, and based on this estimated value, the deflection z of girder B1 of bridge B in a resonant state is calculated. b,1estimating deflection. As shown in FIG. 3, the deflection estimating device 6 includes a measurement data receiving unit 7, a data storage unit 8, a resonance state determination unit 9, track displacement difference calculation units 10A and 10B, a natural frequency / mode damping ratio estimation unit 11, a deflection amount estimation unit 12, an estimation data storage unit 13, a deflection estimation program storage unit 14, a display unit 15, and a control unit 16. The deflection estimating device 6 is constituted by, for example, a personal computer or the like, and causes the computer to execute predetermined processing in accordance with the deflection estimation program.

[0049] The measurement data receiving unit 7 shown in FIG. 3 is means for receiving track displacement data D1 and D2, travel speed data D3, and travel distance data D4 transmitted by the track displacement measuring devices 2A and 2B, the travel speed measuring device 3, and the travel distance measuring device 4. The measurement data receiving unit 7 receives the track displacement data D1 and D2, the travel speed data D3, and the travel distance data D4 via the communication device 5, and stores these data in the data storage unit 8.

[0050] The data storage unit 8 shown in FIG. 3 is means for storing various data D required for estimating deflection of the bridge B. As shown in FIG. 6, the data storage unit 8 stores track displacement data D1 measured by the track displacement measuring device 2A on the leading vehicle V F and track displacement data D2 measured by the track displacement measuring device 2A on the rearmost vehicle V L , travel speed data D3 of the train T traveling on the bridge B measured by the travel speed measuring device 3, travel distance data D4 of the train T traveling on the bridge B measured by the travel distance measuring device 4, train data D5 related to the train T, bridge data D6 related to the bridge B, and natural frequency n required for calculating a theoretical value dI of track displacement difference b,1 and mode damping ratio ξ b,1 is a storage device that stores natural frequency / mode damping ratio initial setting data D7 related to initial values of . Here, the travel distance data D4 is, for example, the position of the bridge B (the distance in kilometers from the entrance to the exit of the bridge B with reference to the starting point of the track R), or the like. The train data D5 includes, for example, an axle load (magnitude of moving load) P which is the sum of loads applied to the left and right wheels of the train T shown in FIG. 4, and the number of vehicles (number of loads) N w, vehicle length L c and the like. The bridge data D6 is, for example, the span length L of bridge B b , bending stiffness EI, unit length mass m1, and the like. The data storage unit 8 stores track displacement data D1, D2, travel speed data D3, travel distance data D4, train data D5, bridge data D6 and natural frequency / mode damping ratio initial setting data D7 in association with each bridge B.

[0051] The resonance state determination unit 9 shown in FIG. 3 is means for determining whether or not the bridge B is in a resonance state. The resonance state determination unit 9 is configured such that the track displacement measuring device 2A is mounted on the leading vehicle V F extracts a vibration component specific to a resonance-state bridge from the track displacement data D1 measured by the device, and the track displacement measuring device 2B is mounted on the rearmost vehicle V L extracts a vibration component specific to a resonance-state bridge from the track displacement data D2 measured by the device. The resonance state determination unit 9 is configured such that, from the amplitude of the vibration component specific to a resonance-state bridge of the rearmost vehicle V L the amplitude of the vibration component specific to a resonance-state bridge of the leading vehicle V F is subtracted, thereby calculating a difference in amplitude of the vibration component specific to a resonance-state bridge that is prominent only in the rearmost vehicle V L . The resonance state determination unit 9 sets the difference in amplitude of the vibration component specific to a resonance-state bridge as a determination index that is an index for determining whether or not the bridge B is in a resonance state. The resonance state determination unit 9 determines that the bridge B is in a resonance state when the determination index exceeds a predetermined value (threshold value), and determines that the bridge B is not in a resonance state when the determination index is equal to or less than the predetermined value (threshold value).

[0052] The track displacement difference calculation unit 10A shown in FIG. 3 is configured such that, when a train is passing through the bridge B in a resonance state, the rearmost vehicle V L and the track displacement measured by the leading vehicle V F is the measured value dI of the track displacement difference, which is the difference between the track displacement measured by ~ The track displacement difference calculation unit 10A calculates the measured value dI of the track displacement difference based on the measurement results of the track displacement measuring devices 2A and 2B on the train T ~The calculation is performed. The track displacement difference calculation unit 10A uses, for example, the difference in 20m chord recti track displacement measured and processed at the leading and trailing cars of a train set in a high-speed railway as observation data. Here, the original track displacement I(x) when passing over a bridge, as observed from the train, is represented by the following equation 5.

[0053]

number

[0054] The track displacement difference calculation unit 10A is the last vehicle V shown in Figure 2. L and the leading vehicle V F The measured value dI of the orbital displacement difference, obtained by the measurement, is calculated using the following equation 6.

[0055]

number

[0056] As shown in equation 6, the leading vehicle V F and the last car V L The difference in 20m chord-axis track displacement measured is not affected by the static track displacement component and is expressed solely by the track displacement based on the bridge deformation component. Here, the static track displacement component is the displacement due to rail irregularities, etc. The bridge deformation component is the displacement due to vibration of bridge B (dynamic displacement) and the displacement due to the weight of train T when passing over the bridge (quasi-static displacement). The track displacement difference calculation unit 10A is the last vehicle V L and the leading vehicle V F Measured value dI of the orbital displacement difference between ~ By performing this calculation, static displacements due to rail displacement and other factors are removed, and the dynamic displacement due to vibration of bridge B in a resonant state and the quasi-static displacement of bridge B due to the weight of train T when passing over the bridge are extracted.

[0057] The track displacement difference calculation unit 10B calculates the last vehicle V when passing over bridge B in a resonant state. L Track displacement measured by and leading vehicle V FThis is a means for calculating the theoretical value dI of the track displacement difference, which is the difference between the track displacement measured by and the track displacement measured by. The track displacement difference calculation unit 10B calculates the theoretical value dI of the track displacement difference by theory, such as numerical calculation or numerical analysis. The track displacement difference calculation unit 10B calculates, for example, the leading vehicle V F and the last vehicle V L Assuming that the orbital displacement is measured, the same filtering process as in Equations 6 and 7 is used to convert it to a 20m chord recti orbital displacement, and after synchronizing the positions of the leading and trailing ends, the theoretical value dI of the orbital displacement difference is calculated. The orbital displacement difference calculation unit 10B inputs the initial values ​​(initial settings) of the natural frequency and mode damping ratio stored in the data storage unit 8 into the following Equation 8 and calculates the theoretical value dI of the orbital displacement difference.

[0058]

number

[0059] The natural frequency / mode damping ratio estimation unit 11 estimates the natural frequency / mode damping ratio of vehicles V passing over bridge B. F ,V L Based on the measurement results of track displacement measuring devices 2A and 2B, vehicle V F ,V L The natural frequency n of bridge B in a resonant state when the object is passing over it. ∧ b,1 and mode damping ratio ξ ∧ b,1 This is a means of estimating the natural frequency / mode damping ratio. The natural frequency / mode damping ratio estimation unit 11 estimates the actual value dI of the orbital displacement difference calculated by the orbital displacement difference calculation unit 10A. ~ Natural frequency n corresponding to the peak position of the waveform ∧ b,1 And the mode attenuation ratio ξ corresponding to the peak amplitude of this waveform. ∧ b,1 The natural frequency / mode damping ratio estimation unit 11 estimates the vehicle V in the measurement results of the track displacement measuring devices 2A and 2B. F ,V L Vehicle length L c Based on the peak amplitude and peak position of a wave with wavelength n, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧b,1 The natural frequency / mode damping ratio estimation unit 11 estimates the actual value dI of the orbital displacement difference calculated by the orbital displacement difference calculation units 10A and 10B. ~ And based on the theoretical value dI, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 We estimate this.

[0060] The natural frequency / mode damping ratio estimation unit 11 calculates the measured value dI of the observed orbital displacement difference. ~ The natural frequency n, an unknown parameter, is set so that the theoretical value dI of the orbital displacement difference obtained by calculation matches this. ∧ b,1 and mode damping ratio ξ ∧ b,1 The orbital displacement difference calculation unit 10B calculates the actual value dI of the observed orbital displacement difference. ~ The error between this and the theoretical value dI of the orbital displacement difference obtained by calculation is minimized, and the natural frequency n b,1 and mode damping ratio ξ b,1 The (unknown parameter) is calculated using the following equation 8.

[0061]

number

[0062] Figure 7 is a graph showing the waveform of the theoretical value dI of the track displacement difference observed on a resonant bridge with a span length of 30m, calculated using equation 7. In Figure 7, the vertical axis represents the track displacement difference [m] and the horizontal axis represents the distance [m]. The graph shows the track displacement difference for a total of 6 cases: train speed 252km / h, number of cars 12, axle load 110kN, unit length mass 25t / m, bridge natural frequencies of 2.6Hz, 2.94Hz, and 2.66Hz (corresponding to resonant velocity, resonant velocity × 1.05, and resonant velocity × 0.95, respectively), and mode damping ratios of 1% and 3%, along with three evaluation points (lower peak, upper peak 1, and upper peak 2) for each case.

[0063] The natural frequency n is determined by equation 8. ∧ b,1and mode damping ratio ξ ∧ b,1 When estimating the difference in orbital displacement, the theoretical value dI and the measured value dI of the difference in orbital displacement are used. ~ High positional synchronization (alignment) accuracy is required between them. In the resonant state of bridge B, the leading vehicle V F The dynamic response of bridge B, which is not outstanding when passing over it, is superior to that of the last vehicle V. L This becomes particularly noticeable when passing through, so the leading vehicle V F and the last car V L The same waveform cannot be obtained in these cases. Therefore, if the alignment accuracy is insufficient, the error will increase in the parts with a large slope in the waveform of the theoretical value dI of the orbital displacement difference, in principle. On the other hand, the natural frequency n b,1 or mode damping ratio ξ b,1 What characterizes this is the amplitude and position of the lower peak (gradient 0) in the waveform of the theoretical value dI of the orbital displacement difference, as shown in Figure 7. For this reason, it is conceivable to use only the lower peak in the waveform of the theoretical value dI of the orbital displacement difference, and not use the parts with large gradients in the estimation. The lower peak observed in the waveform of the theoretical value dI of the orbital displacement difference has an amplitude and position that corresponds to the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 This corresponds to the lower peak value of a zero gradient, making it possible to achieve estimation that is robust to alignment errors.

[0064] As shown in Figure 7, differences in mode damping ratios mainly manifest as differences in the magnitude of peak amplitudes, while differences in natural frequencies (degree of deviation of train speed from resonance velocity) manifest as differences in the position of each peak. As shown in Figure 7, when the train speed is 5% faster than the resonance velocity (resonance velocity × 1.05), the position of the minimum value (lower peak value) shifts from the center of the span towards the train exiting side, the upper peak in the first half moves towards the center of the span, and the upper peak in the second half moves towards the bridge exit side. On the other hand, when the train speed is 5% slower than the resonance velocity (resonance velocity × 0.95), the position of the minimum value (lower peak value) shifts from the center of the span towards the train entering side, the upper peak in the first half moves towards the bridge entry side, and the upper peak in the second half moves towards the center of the span. Furthermore, comparing the case of a mode damping ratio of 1% and the case of a mode damping ratio of 3%, the magnitude of the peak amplitude is smaller in the case of a mode damping ratio of 3% compared to the case of a mode damping ratio of 1%. Therefore, by estimating the amplitude of the two upper peaks along with the amplitude of the lower peak, the shift in the position of the lower peak can be evaluated alternatively.

[0065] The natural frequency / mode damping ratio estimation unit 11 shown in Figure 3 uses three peaks that appear in the waveform of the theoretical value dI of the orbital displacement difference and the measured value dI of the orbital displacement difference. ~ By comparing the three peaks that appear in the waveform, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 The natural frequency / mode damping ratio estimation unit 11 estimates the position of the lower peak (corresponding to the mode damping ratio) by estimating the amplitudes (corresponding to the natural frequencies) of the two upper peaks before and after the lower peak of the waveform of the theoretical value dI of the orbital displacement difference shown in Figure 7. The natural frequency / mode damping ratio estimation unit 11 uses the lower peak of the waveform of the theoretical value dI of the orbital displacement difference near the center of the span, plus the two upper peaks before and after this lower peak, for a total of three peaks, to estimate the measured value dI of the orbital displacement difference. ~ The measured value dI of the orbital displacement difference is compared with the theoretical value dI. As shown in Figure 8(C), the natural frequency / mode damping ratio estimation unit 11 uses three evaluation points corresponding to the three peaks in the waveform of the theoretical value dI of the orbital displacement difference, and the measured value dI of the orbital displacement difference. ~The natural frequency n is calculated using equation 7 so that the three evaluation points corresponding to the three peaks in the waveform match. b,1 and mode damping ratio ξ b,1 This is updated by Bayesian estimation using the following number 9.

[0066]

number

[0067] The natural frequency / mode damping ratio estimation unit 11 shown in Figure 3 estimates the natural frequency n b,1 and mode damping ratio ξ b,1 The measured value dI of the orbital displacement difference has been updated. ~ The natural frequency n that minimizes the error between the measured value dI of the orbital displacement difference and the measured value n. ∧ b,1 and mode damping ratio ξ ∧ b,1 The natural frequency / mode damping ratio estimation unit 11 estimates the following posterior distribution π(θ|D) using the random walk Metropolis-Hastings (MH) method, which is one of the Markov chain Monte Carlo methods (MCMC methods). ~ We estimate the following.

[0068]

number

[0069] The deflection estimation unit 12 shown in Figure 3 uses the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 Based on this, Vehicle V F ,V L This is a means for estimating the amount of deflection of bridge B in a resonant state when an object passes over it. The deflection amount estimation unit 12 estimates the natural frequency n estimated by the natural frequency / mode damping ratio estimation unit 11. ∧ b,1 and mode damping ratio ξ ∧ b,1By substituting into equation 1 and numerically integrating equation 1, we can obtain the deflection z of girder B1 of bridge B in a resonant state. b,1 Perform the calculation.

[0070] Next, the estimation process of natural frequency and mode damping ratio, and the estimation process of deflection amount, by the natural frequency / mode damping ratio estimation unit of the bridge deflection estimation device according to an embodiment of this invention will be explained. Figure 8 shows the natural frequency n calculated by the natural frequency / mode damping ratio estimation unit 11. ∧ b,1 and mode damping ratio ξ ∧ b,1 This is a conceptual diagram illustrating the estimation process and the deflection estimation process by the deflection estimation unit 12. Figure 8(A) is a conceptual diagram showing an example of a moving load series model used to calculate the theoretical value of the track displacement difference. Figure 8(B) is a graph showing an example of the convergence process of the mode damping ratio using the MCMC method. In Figure 8(B), the vertical axis is the mode damping ratio and the horizontal axis is the number of samples. Figure 8(C) is a graph showing an example of the process of matching the waveform of the theoretical value of the track displacement difference to the waveform of the measured value of the track displacement difference. In Figure 8(C), the vertical axis is the track displacement difference [mm] and the horizontal axis is the distance [m]. Figure 8(D) is a graph showing an example of girder deflection estimation. In Figure 8(D), the vertical axis is the displacement [mm] and the horizontal axis is the time [s].

[0071] The basic deflection estimation method according to the embodiment was verified using the theoretical value dI of the track displacement difference on the bridge in a resonant state, which was created by numerical analysis. The theoretical value dI of the (20m chord yarrow) track displacement difference between the leading and trailing cars was calculated, and the bridge response during train passage was calculated by numerically integrating Equation 1. The track displacement measurement position was set to approximately 3m inward from the center of both leading bogies of the vehicle, in accordance with the actual vehicle.

[0072] As shown in Figure 8(A), the moving load train model assumes a 12-car high-speed rail train, and the theoretical value dI of the track displacement difference was calculated using the axle arrangement and axle load shown in Figure 8(A). The bridge has a span length of 25m, a unit length mass of 25t / m, and a mode damping ratio of 2.5%, which are prone to resonance. The natural frequency was set to 2.9Hz, where the train speed (260km / h) is the resonance speed.

[0073] Theoretical value dI of the track displacement difference, v of the train T's speed, and L of the span length of bridge B. b And with a unit length mass m1 as input, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 Estimated value of z, theoretical value of orbital displacement difference dI, and deflection amount (maximum girder deflection) z b,1 The following was estimated. The MCMC method used 5000 sampling iterations. The first 500 iterations were excluded as burn-in, representing the convergence process to the stationary distribution, and the subsequent 4500 iterations were used as samples from the posterior distribution. The estimation program was implemented on Matlab. The computation time for 5000 sampling iterations was approximately 120 minutes on a PC with a Core i7 (2.5GHz) processor.

[0074] Figure 8(B) shows the results of the first 1000 samplings of the mode damping ratio at the resonant velocity with a span length of 25m as an example of the convergence process of the MCMC method. It was confirmed that the value moved to approximately the correct value after about 100 samplings, and then remained steady at approximately the correct value.

[0075] Figure 8(C) shows the ground truth track displacement difference and the estimated track displacement differences for the 10th and 100th trials, assuming a bridge span length of 25m and a train speed at the resonant speed. The likelihood calculation used only the evaluation points shown in Figure 8(C). While the estimated value of the track displacement difference in the 10th trial deviates from the ground truth, the estimated value of the track displacement difference in the 100th trial agrees well with the ground truth. Furthermore, it was confirmed that not only the peak value but also the peak position of the track displacement difference is updated to match the ground truth using only the three evaluation points used for parameter estimation. This confirms that the peak position can be estimated alternatively by using the maximum values ​​before and after the minimum value near the center of the span.

[0076] Figure 8(D) shows the girder deflection (correct value) when the bridge span length is 25m and the train speed is at the resonant speed, and the girder deflection (estimated value) at the 10th and 100th sampling. Similar to the track displacement difference, the girder deflection at the 10th sampling deviates significantly from the correct value, but by repeating the sampling, the estimated waveform of the girder deflection accurately matches the correct waveform by the 100th sampling. Therefore, at least under the conditions of numerical analysis, the deflection estimation method according to the embodiment can determine the natural frequency n such that the three evaluation points match from the track displacement difference of a bridge in a resonant state. ∧ b,1 and mode damping ratio ξ ∧ b,1 It was confirmed that digit deflection can be estimated by estimating this.

[0077] The estimation data storage unit 13 shown in Figure 3 is a means for storing various estimation data related to the deflection estimation device 6. For example, the estimation data storage unit 13 stores the measured value dI of the orbital displacement difference calculated by the orbital displacement difference calculation units 10A and 10B. ~ And orbital displacement difference data related to the theoretical value dI, and the natural frequency / mode damping ratio estimation unit 11 estimated natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 Natural frequency / mode damping ratio data for the estimated value, and deflection z estimated by the deflection estimation unit 12. b,1This is a memory device that stores deflection data and other information for each bridge B.

[0078] The deflection estimation program storage unit 14 is a means for storing a deflection estimation program for estimating the deflection of bridge B. The deflection estimation program storage unit 14 is, for example, a memory device that stores a deflection estimation program read from an information recording medium or a deflection estimation program acquired through a telecommunication line.

[0079] The display unit 15 is a means for displaying various data related to the deflection estimation device 6. The display unit 15 is a display device that displays, for example, the measurement results of the track displacement measuring devices 2A and 2B and the estimation results of the deflection estimation device 6 on the screen. The display unit 15 displays, for example, track displacement difference data, natural frequency / mode damping ratio data and deflection amount data on the screen in correspondence with each bridge B.

[0080] The control unit 16 is a central processing unit (CPU) that controls various operations related to the deflection estimation device 6. The control unit 16 reads the deflection estimation program from the deflection estimation program storage unit 14 and executes the deflection estimation process according to this deflection estimation program. For example, the control unit 16 commands the data storage unit 8 to store the trajectory displacement data D1, D2, running speed data D3, and running distance data D4 received by the measurement data receiving unit 7, reads the trajectory displacement data D1, D2 from the data storage unit 8 and outputs it to the resonance state determination unit 9, commands the resonance state determination unit 9 to determine the resonance state, reads the trajectory displacement data D1, D2 from the data storage unit 8 and outputs it to the trajectory displacement difference calculation unit 10A, reads the running speed data D3 and natural frequency / mode damping ratio initial setting data D7 from the data storage unit 8 and outputs it to the trajectory displacement difference calculation unit 10B, and outputs the measured value dI of the trajectory displacement difference to the trajectory displacement difference calculation units 10A and 10B. ~ The system also commands the calculation of the theoretical value dI, commands the estimated data storage unit 13 to store the orbital displacement difference data calculated by the orbital displacement difference calculation units 10A and 10B, and commands the natural frequency / mode damping ratio estimation unit 11 to store the natural frequency n ∧ b,1 and mode damping ratio ξ∧ b,1 The system commands the estimation of the natural frequency / mode damping ratio, commands the estimation data storage unit 13 to store the natural frequency data and mode damping ratio data estimated by the natural frequency / mode damping ratio estimation unit 11, reads the running speed data D3, train data D5, and bridge data D6 from the data storage unit 8 and outputs them to the deflection amount estimation unit 12, reads the natural frequency data and mode damping ratio data from the estimation data storage unit 13 and outputs them to the deflection amount estimation unit 12, commands the deflection amount estimation unit 12 to estimate the deflection amount of bridge B, commands the estimation data storage unit 13 to store the deflection amount data estimated by the deflection amount estimation unit 12, and commands the display unit 15 to display various data. The control unit 16 is interconnected with the measurement data receiving unit 7, data storage unit 8, resonance state determination unit 9, orbital displacement difference calculation units 10A and 10B, natural frequency / mode damping ratio estimation unit 11, deflection amount estimation unit 12, estimated data storage unit 13, deflection estimation program storage unit 14, and display unit 15, enabling communication between them.

[0081] Next, a method for estimating the deflection of a bridge according to an embodiment of this invention will be described. The deflection estimation method #100 shown in Figure 9 is a method for estimating the deflection of bridge B. Deflection estimation method #100 includes a resonant bridge extraction step #110, a trajectory displacement difference calculation step #120, a trajectory displacement difference calculation step #130, a natural frequency / mode damping ratio estimation step #140, and a deflection amount estimation step #150.

[0082] Resonant bridge extraction process #110 is a process for extracting bridge B that is in a resonant state. In resonant bridge extraction process #110, bridge B that is in a resonant state is extracted from among the bridges that train T passes over. In resonant bridge extraction process #110, as shown in Figure 2, the last vehicle V L The track displacement measured by the upper track displacement measuring device 2A when it passes over bridge B, and the leading vehicle V F Based on the trajectory displacement measured by the trajectory displacement measuring device 2B as it passes over bridge B, the resonant state of bridge B is extracted.

[0083] Track displacement difference calculation step #120 is performed when the last vehicle V is passing over bridge B in a resonant state. L Track displacement measured by and leading vehicle V F The measured value of the orbital displacement difference dI is the difference between the orbital displacement measured by [the relevant software / method] and the actual orbital displacement difference. ~ This is the process of calculating the difference. In the track displacement difference calculation process #120, as shown in Figure 2, the last vehicle V L The track displacement measured when the upper track displacement measuring device 2A passes over the resonant bridge B, and the leading vehicle V F The measured value dI of the orbital displacement difference is the difference between the orbital displacement measured when the orbital displacement measuring device 2B is passing over the resonant bridge B and the measured orbital displacement. ~ The calculation is performed.

[0084] Track displacement difference calculation step #130 is performed when the last vehicle V is passing over bridge B in a resonant state. L Track displacement measured by and leading vehicle V F This is the process of calculating the theoretical value dI of the track displacement difference, which is the difference between the track displacement measured by the vehicle V. In the track displacement difference calculation process #130, as shown in Figure 2, it is assumed that the track displacement is measured when the track displacement measuring devices 2A and 2B are passing over bridge B in a resonant state, and the vehicle V L ,V F The theoretical value dI of the orbital displacement difference is calculated by synchronizing the positions. In orbital displacement difference calculation step #130, the initial values ​​(initial settings) of the natural frequency and mode damping ratio necessary for calculating the theoretical value dI of the orbital displacement difference are input, and the theoretical value dI of the orbital displacement difference is calculated.

[0085] Natural frequency / mode damping ratio estimation process #140 is performed on the vehicle V F ,V L The natural frequency n of bridge B in a resonant state when the object is passing over it. ∧ b,1 and mode damping ratio ξ ∧ b,1 This is estimated. In the natural frequency / mode damping ratio estimation step #140, the measured value dI of the trajectory displacement difference measured when passing through bridge B in a resonant state is used. ~ And based on the theoretical value dI, the natural frequency n∧ b,1 and mode damping ratio ξ ∧ b,1 This is estimated. In the natural frequency / mode damping ratio estimation step #140, as shown in Figure 8(C), the theoretical value dI of the orbital displacement difference is equal to the measured value dI of the orbital displacement difference. ~ To match, natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 This is estimated. In the natural frequency / mode damping ratio calculation step #140, the measured value dI of the orbital displacement difference calculated in the orbital displacement difference calculation step #120 is used. ~ The natural frequency n input in the orbital displacement difference calculation process #130 is set such that the three evaluation points of the waveform and the three evaluation points of the waveform of the theoretical value dI of the orbital displacement difference calculated in orbital displacement difference calculation process #130 match. b,1 and mode damping ratio ξ b,1 The initial value of is updated. In the natural frequency / mode damping ratio calculation process #140, the measured value of the orbital displacement difference dI ~ The amplitudes of the three peaks appearing in the waveform are compared with the amplitudes of the three peaks appearing in the waveform of the theoretical value dI of the orbital displacement difference, and the natural frequency n calculated in orbital displacement difference calculation step #130 is determined by comparing these amplitudes. b,1 and mode damping ratio ξ b,1 The initial value of is updated. In the natural frequency / mode damping ratio calculation process #140, the measured value of the orbital displacement difference dI ~ The natural frequency n that minimizes the error between the theoretical value dI of the orbital displacement difference and the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 We estimate this as the estimated value.

[0086] Deflection estimation step #150 is performed using the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 Based on this, Vehicle V F ,V L This is a process to estimate the amount of deflection of bridge B in a resonant state when the object passes over it. In deflection estimation step #150, the natural frequency n estimated in natural frequency / mode damping ratio estimation step #140 is used.∧ b,1 and mode damping ratio ξ ∧ b,1 Substituting this into equation 1 and numerically integrating equation 1, we obtain the deflection z of girder B1 of bridge B in a resonant state. b,1 We estimate this.

[0087] Next is a flowchart illustrating the operation of the bridge deflection estimation device according to an embodiment of this invention. The following explanation will focus on the operation of the control unit 16 shown in Figure 3. In step 100 (hereinafter referred to as S) shown in Figure 10, the control unit 16 reads the deflection estimation program from the deflection estimation program storage unit 14. Once the control unit 16 reads the deflection estimation program, it starts a series of deflection estimation processes.

[0088] In S110, the control unit 16 instructs the resonance state determination unit 9 to determine whether or not bridge B is in a resonant state. The resonance state determination unit 9 refers to the travel distance data D4 stored in the data storage unit 8 and identifies each bridge B based on the travel distance data D4. The resonance state determination unit 9 extracts the track displacement data D1 and D2 from the entrance to the exit of each bridge B and determines whether or not each bridge B is in a resonant state. Leading vehicle V F The resonance state determination unit 9 extracts vibration components specific to a bridge in a resonant state from the track displacement data D1, and the last vehicle V L The resonance state determination unit 9 extracts vibration components specific to a bridge in a resonant state from the track displacement data D2. L From the amplitude of the vibration component specific to the resonant state of the bridge, the leading vehicle V F The resonance state determination unit 9 subtracts the amplitude of vibration components specific to the bridge in a resonant state, and calculates the difference in amplitude of vibration components specific to the bridge in a resonant state using the difference as a determination index. If the resonance state determination unit 9 determines that this determination index exceeds a predetermined value, the process proceeds to S120. If the resonance state determination unit 9 determines that this determination index is less than or equal to the predetermined value, the series of deflection estimation processes is terminated.

[0089] In S120, the measured value of the orbital displacement difference dI ~ The control unit 16 commands the track displacement difference calculation unit 10A to perform the calculation. L Track displacement data D1 measured by track displacement measuring device 2A, and leading vehicle V F The track displacement data D2 measured by the track displacement measuring device 2B is read by the track displacement difference calculation unit 10A from the data storage unit 8. As a result, the trailing vehicle V L Measured values ​​of the 20m chord recti trajectory displacement and the leading vehicle V F The orbital displacement difference calculation unit 10A calculates the measured value dI of the orbital displacement difference, which is the difference between the measured value of the 20m chord truss orbital displacement and the measured value of the orbital displacement, using equations 5 and 6.

[0090] In S130, the control unit 16 commands the track displacement difference calculation unit 10B to calculate the theoretical value dI of the track displacement difference. The track displacement difference calculation unit 10B reads the running speed data D3, train data D5, and bridge data D6 from the data storage unit 8, and also reads the natural frequency / mode damping ratio initial setting data D7 from the data storage unit 8. As a result, the data is converted to a 20m chord rectitrack displacement by a process similar to the filtering process shown in Equation 6, and the track displacement difference calculation unit 10B calculates the theoretical value dI of the track displacement difference by synchronizing the leading position and the trailing position, using Equation 7.

[0091] In S140, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 The control unit 16 commands the natural frequency / mode damping ratio estimation unit 11 to estimate the following. As shown in Figure 8(C), the measured value dI of the orbital displacement difference ~ The error between the theoretical value dI of the orbital displacement difference is minimized, and the measured value dI of the orbital displacement difference ~ The natural frequency n such that the theoretical value dI of the orbital displacement difference matches ∧ b,1 and mode damping ratio ξ ∧ b,1 The natural frequency / mode damping ratio estimation unit 11 calculates this. At this time, the measured value dI of the orbital displacement difference ~The natural frequency n, set as the initial value, is set so that the three evaluation points of the waveform and the three evaluation points of the waveform of the theoretical value dI of the orbital displacement difference match. b,1 and mode damping ratio ξ b,1 The natural frequency / mode damping ratio estimation unit 11 updates this using equations 9 and 10. As shown in Figure 8(C), the measured value dI of the orbital displacement difference ~ The amplitudes of the three peaks in the waveform match the amplitudes of the three peaks in the waveform of the theoretical value dI of the orbital displacement difference, so that the natural frequency n b,1 and mode damping ratio ξ b,1 The natural frequency / mode damping ratio estimation unit 11 updates the initial value of the orbital displacement difference dI. ~ The natural frequency n that minimizes the error between the theoretical value dI of the orbital displacement difference and the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 The natural frequency / mode damping ratio estimation unit 11 estimates this as an estimated value.

[0092] In S150, the amount of deflection z of bridge B b,1 The control unit 16 commands the deflection amount estimation unit 12 to estimate the natural frequency n. ∧ b,1 and mode damping ratio ξ ∧ b,1 The deflection estimation unit 12 substitutes this into equation 1, and the deflection estimation unit 12 performs numerical integration to obtain the deflection z of girder B1 of bridge B. b,1 The deflection amount estimation unit 12 calculates this.

[0093] In S160, the control unit 16 commands the display unit 15 to display the estimation result. The control unit 16 reads the deflection amount data, etc., from the estimation data storage unit 13 and outputs the deflection amount data, etc., to the display unit 15. As a result, the deflection amount z, which is the maximum deflection of bridge B, is displayed. b,1 The display unit 15 displays the following information on the screen for each bridge B.

[0094] The bridge deflection estimation method, deflection estimation device, and deflection estimation program according to the embodiment of this invention have the following effects. (1) In this embodiment, a vehicle V passing over bridge B F ,V L Based on the measurement results of track displacement measuring devices 2A and 2B, vehicle V F ,V L The natural frequency n of bridge B in a resonant state when the object is passing over it. ∧ b,1 and mode damping ratio ξ ∧ b,1 This is estimated. In this embodiment, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 Based on this, Vehicle V F ,V L The amount of deflection z of bridge B in the resonant state when the object passes over it. b,1 To estimate this, we consider the dynamic response of bridge B, which is the displacement due to the vibration of bridge B, and the amount of deflection z of bridge B. b,1 This can be estimated with high accuracy from track displacement measured on board the vehicle.

[0095] (2) In this embodiment, when passing over the bridge B in a resonant state, the last vehicle V L Track displacement measured by and leading vehicle V F The measured value of the orbital displacement difference dI is the difference between the orbital displacement measured by [the relevant software / method] and the actual orbital displacement difference. ~ Based on the peak amplitude and peak position of the waveform, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 To estimate this, we need to determine the natural frequency n of bridge B, which is necessary to evaluate the dynamic response of bridge B. ∧ b,1 and mode damping ratio ξ ∧ b,1 These two unknown parameters are used in the measurement results of the track displacement measuring devices 2A and 2B, specifically in relation to the vehicle V F ,V L Vehicle length L c It can be estimated from two feature quantities: the peak amplitude and peak position of a wave with a wavelength of .

[0096] (3) In this embodiment, when passing over a bridge in a resonant state, the last vehicle V L Track displacement measured by and leading vehicle V F The theoretical value of the orbital displacement difference dI is the difference between the orbital displacement measured by [the system] and the actual orbital displacement. ~ And based on the measured value dI, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 This is estimated. As a result, the measured value of the orbital displacement difference dI ~ Natural frequencies n cannot be directly determined from the waveform. ∧ b,1 and mode damping ratio ξ ∧ b,1 This can be estimated from the waveform of the theoretical value dI of the track displacement difference using methods such as the MCMC method. Also, for example, since the length of a Shinkansen train car is 25m, it is sufficient to include waves with a wavelength of 25m, so the 20m chord recti track displacement used in track management can be utilized. Furthermore, similar to existing resonant bridge detection methods, the last car V L From the track displacement measured, the leading vehicle V F By subtracting the track displacement measured by this method, it is possible to eliminate politically motivated components other than bridge vibration components such as rail irregularities.

[0097] (4) In this embodiment, the theoretical value dI of the orbital displacement difference is equal to the measured value dI of the orbital displacement difference. ~ To match this, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 To estimate this, the theoretical value of the orbital displacement difference is calculated using an analytical model, and the calculated theoretical value dI of the orbital displacement difference is used to estimate the measured value dI of the orbital displacement difference. ~ To match this, the natural frequency n is calculated using methods such as the MCMC method, a type of Bayesian estimation. ∧ b,1 and mode damping ratio ξ ∧ b,1 It is possible to estimate the natural frequency n. Furthermore, the parameters of the analysis model are the natural frequencies n. ∧ b,1 and mode damping ratio ξ ∧b,1 Since everything else is known, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 By estimating this, a model of bridge B in its actual resonant state is determined, and the displacement waveform (maximum value) at the center of the span calculated by this model can be estimated as the girder deflection waveform (maximum value).

[0098] (5) In this embodiment, the three peak amplitudes of the waveform of the theoretical value dI of the orbital displacement difference and the measured value dI of the orbital displacement difference ~ By comparing the three peak amplitudes of the waveform, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 This is estimated. For example, when comparing calculated track displacement with measured track displacement, the alignment error between the measured track displacement and ground equipment becomes a problem. In this embodiment, instead of comparing waveforms, the measured value dI of the track displacement difference is used. ~ Furthermore, the three peaks (one minimum and two maximums) near the center of the span observed in the theoretical value dI are used as evaluation points for comparison. Therefore, by using not only the minimum but also the surrounding maximums, the effect of the discrepancy between the resonant velocity and the train velocity is indirectly considered, and the natural frequency n is evaluated. ∧ b,1 and mode damping ratio ξ ∧ b,1 This can be estimated with high accuracy. For example, as shown in Figure 7, the difference in train speed relative to the resonant speed allows for the estimation of the measured value of the track displacement difference dI ~ Because the lower peak position of the waveform is shifted, the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 The estimation accuracy decreases. In this embodiment, the measured value dI of the orbital displacement difference ~ By using the three peak amplitudes of the waveform, the identification of the peak position can be omitted, and the natural frequency n ∧ b,1 and mode damping ratio ξ ∧ b,1 It is possible to estimate this with high accuracy. [Examples]

[0099] (Verification on actual routes) This study targeted high-speed rail lines where bridge resonance during train passage was reported. Track displacement measurements were taken at the lead and last cars of the train on these lines. After preprocessing, the deflection estimation method described in the example was applied to the difference in track displacement on the bridge. In addition, the girder deflection of the target bridge during the passage of the train was simultaneously measured from the ground, and the estimation accuracy was verified by comparing it with the maximum girder deflection estimated using the deflection estimation method described in the example.

[0100] (Train overview) Track displacement was measured using body-mounted inertial symmetrical track inspection devices installed on the leading and trailing cars of a 12-car train. The inspection devices were installed approximately 3m from the center of each leading bogie towards the center of the car body, located on the underside of the car body. The axle arrangement of the running train was the same as in Figure 9(A). The track displacement measured on the train was aligned with ground equipment based on communication records with ground beacons measured simultaneously, and converted into a distance series in 0.25m increments. Then, the 20m chord symmetrical track displacement was calculated by filtering, and the train speed was also recorded at the same time.

[0101] (Overview of the target bridge) The target bridge was one in which resonance had been confirmed through previous inspections. The bridge type is a post-tensioned simple T-shaped four-girder (double-track girder) with a span length of 29.2m, a bridge length of 30m, and a girder height of 1.9m. The target bridge has a design natural frequency of approximately 3.3Hz, and a resonance velocity of 297km / h at this frequency. However, in bridges of the same type, there have been cases where the natural frequency decreased to approximately 2.6Hz (resonance velocity of 235km / h) due to crack propagation during service, resulting in resonance. Therefore, it is presumed that a similar phenomenon has occurred in the target bridge, and that its natural frequency has decreased.

[0102] (Estimated results of the posterior distribution of parameters) Figure 11 is a graph showing the estimated posterior distribution of actual bridge parameters. Figure 11(A) is a graph showing the changes in natural frequency and mode damping ratio. In Figure 11(A), the vertical axis is the mode damping ratio and the horizontal axis is the natural frequency. Figure 11(B) is a graph comparing the measured and theoretical values ​​of the orbital displacement difference during the convergence process. In Figure 11(B), the vertical axis is the orbital displacement difference [mm] and the horizontal axis is the distance [m]. Figures 8(B) a to f show the measured, estimated, and evaluation points of the orbital displacement difference at typical iterations (1st, 10th, 50th, 100th, 200th, and 500th iterations). The estimated value of the orbital displacement difference for the first iteration, shown as a, has a smaller amplitude compared to the measured value, and two of the three evaluation points differ significantly. By repeating sampling, the estimated value of the orbital displacement difference gradually approaches the measured value. At the 100th trial, indicated as d, the lower peak of the estimated orbital displacement difference is almost the same as the measured value. Furthermore, at the 200th trial (e), where the natural frequency and mode damping ratio are considered to have converged to the posterior distribution, the estimated orbital displacement difference agrees well with the measured value, including the three evaluation points. At the 500th trial (indicated as f), the parameters have converged to the posterior distribution, and similar to e, the estimated and measured values ​​agree well, confirming that the posterior distribution (uncertainty) has been estimated. Although only three peak values ​​are used as evaluation points for the orbital displacement difference, the waveform of the estimated orbital displacement difference in the bridge section agrees well with the waveform of the measured value even at points other than the three evaluation points. Therefore, it has been confirmed that even for the orbital displacement difference of a bridge in a resonant state on an actual route, the waveform characteristics can be evaluated without omission at three points.

[0103] (Estimation and verification results of the maximum digit deflection) Figure 12 is a graph comparing the estimated waveform of girder deflection at each sampling count of the actual bridge with the waveform of the measured result. In Figure 12, the vertical axis represents girder deflection [mm], and the horizontal axis represents time [s]. The sampling counts (1st, 10th, 50th, 100th, 200th, and 500th) shown as a to f in Figure 12 are the same as in Figure 11. The girder deflection waveform from the ground was measured from below the girder using a U-Doppler detector. The measurement location was the outer main girder of the train passing track (upbound track), and the vertical velocity response during train passage was measured after installing a reflective sticker in the center of the span. After measurement, the velocity response during train passage was integrated to calculate the displacement response. In addition, the girder deflection waveform measured from the ground includes a quasi-static torsional deformation component of the bridge, which is not considered in the analysis model of the deflection estimation method according to the embodiment. To compensate for this, a bridge torsional deformation component (with the same shape as the quasi-static deflection waveform and a maximum displacement of approximately 2.9 mm), calculated separately by numerical analysis, was added to the girder deflection waveform estimated by the deflection estimation method of the example.

[0104] As shown in Figure 12, the girder deflection waveform measured on the ground (thick line) shows a resonant state in which the amplitude gradually increases as the train passes, and the maximum girder deflection, which is the maximum displacement, is about 15 mm when the last car passes. The girder deflection waveform estimated from the track displacement difference measured on board the train has a different natural frequency and mode damping ratio. a: In the first sampling, the amplitude is significantly smaller than the measured value, but by repeating sampling, it gradually matches the girder deflection waveform measured on the ground. In updating the track displacement difference, at c: 50 sampling, only the minimum value matches, and the other two maximum values ​​deviate from the estimated and measured values. In contrast, in the girder deflection waveform, the maximum displacement already tends to roughly match the measured value at the time of sampling at c: 50 sampling. After that, in d, e and f from 100 sampling onwards, the estimated girder deflection waveform does not fluctuate much and all agree with the measured values ​​with good accuracy. From the above, it was confirmed that if the track displacement difference can be reproduced well even on an actual railway line, the girder deflection waveform can also be reproduced with high accuracy. Furthermore, it was confirmed that if the minimum value of the track displacement difference measured on board the vehicle can be reproduced well, it is possible to roughly evaluate at least the maximum displacement of the girder deflection waveform measured from the ground. In the case of the target bridge, the expected value of the posterior distribution of the maximum girder deflection was 15.3 mm and the measured value was 15.2 mm, with an error of about 0.5 mm (5%) between the expected value and the measured value, which is generally less than 10%, and within ±5% of the resonance velocity, the error between the expected value and the measured value is less than 3%. In addition, the maximum girder deflection can be estimated with an error of about 0.5 mm from the track displacement measured on board the vehicle using the deflection estimation method of the example. Therefore, it was confirmed that the maximum girder deflection of a bridge in a resonant state can be estimated with good accuracy.

[0105] This invention is not limited to the embodiments described above, and various modifications or changes are possible as described below, and these also fall within the scope of this invention. (1) In this embodiment, the case in which train T is a 12-car train was used as an example, but this invention can also be applied to cases in which train T is an 8-car, 10-car, or 16-car train. Furthermore, in this embodiment, the case in which train T is a Shinkansen train running on a Shinkansen line was used as an example, but this invention can also be applied to conventional trains running on conventional lines, or trains for Shinkansen and conventional through-service that can run on both lines. In addition, in this embodiment, the case in which train T is a commercial train was used as an example, but this invention can also be applied to inspection trains formed for the purpose of testing and investigating vehicles, tracks, or overhead lines. For example, this invention can also be applied to track inspection vehicles such as comprehensive electric track inspection vehicles that have the function of inspecting the condition of ground equipment.

[0106] (2) In this embodiment, each vehicle V of train T F ,V M ,V L The example given was that the car body is supported by two bogies T1 and T2, but the adjacent vehicle V F ,V M ,V L This invention can also be applied when the section is supported by an articulated trolley. Furthermore, although this embodiment describes an example where the track displacement measuring devices 2A and 2B continuously measure the track displacement from the starting point to the ending point, this invention can also be applied when the track displacement measuring devices 2A and 2B measure the track displacement only within the section on the bridge B. Moreover, although this embodiment describes an example where the track displacement measuring devices 2A and 2B and the deflection estimation device 6 are transmitted and received via the communication device 5, this invention can also be applied when the deflection estimation device 6 is integrated with the track displacement measuring devices 2A and 2B.

[0107] (3) In this embodiment, the track displacement measuring devices 2A and 2B are connected to the vehicle V F ,V L The explanation used the example of placing them on the vehicle body, but if the track displacement measuring devices 2A and 2B are placed on the vehicle V F ,V LThis invention can also be applied when the devices are placed on bogies T1 and T2. Furthermore, although this embodiment describes the case where the track displacement measuring devices 2A and 2B are string-shape measuring devices, this invention can also be applied to measuring devices other than string-shape measuring devices. Moreover, although this embodiment describes the case where the distance traveled by the train T is calculated by the distance traveled by the distance traveled by the distance traveled by the distance traveled by the distance traveled by the distance traveled by the distance traveled by the distance traveled by the distance traveled by the train T is not limited to such a method. For example, the distance traveled by the train T can also be measured by using GPS (Global Positioning System) or an autonomous navigation device (gyroscope) in combination.

[0108] (4) In this embodiment, the case in which the bridge B is in a resonant state is determined based on the track displacement measured by track displacement measuring devices 2A and 2B mounted on the front and rear of the train T has been described as an example. However, this invention can also be applied to the case in which the bridge B is in a resonant state is determined based on the vertical acceleration measured by acceleration measuring devices mounted on the front and rear of the train T. Furthermore, in this embodiment, the amount of deflection z at the center of the span of girder B1 of bridge B b,1 Although the example given was the case where the deflection amount is estimated by the deflection amount estimation unit 12, this invention can also be applied to the case where the deflection amount at any position of the girder B1 is estimated. [Explanation of Symbols]

[0109] 1. Deflection Estimation System 2A, 2B Track Displacement Measurement Device 3. Driving speed measuring device 4. Distance measuring device 6. Deflection Estimation Device 9. Resonance state determination unit 10A, 10B Orbital displacement difference calculation unit 11 Natural frequency / mode damping ratio estimation unit 12 Deflection Estimation Unit R orbit B Bridge B1 digit L b Span length T train V F Vehicle (leading vehicle) V L Vehicle (last vehicle) T1, T2 bogies n b,1 Natural frequency ξ b,1 Mode damping ratio dI ~ Measured values ​​of orbital displacement difference dI Theoretical value of orbital displacement difference n ∧ b,1 Estimated natural frequencies ξ ∧ b,1 Estimated mode decay ratio z b,1 Deflection

Claims

1. A method for estimating the deflection of a bridge, A natural frequency / mode damping ratio estimation step is performed to estimate the natural frequency and mode damping ratio of the bridge in a resonant state when the vehicle is passing over the bridge, based on the measurement results of the track displacement measuring device for the vehicle passing over the bridge. A deflection estimation step, which estimates the amount of deflection of the bridge in the resonant state when the vehicle is passing over it, based on the natural frequency and the mode damping ratio, A method for estimating the deflection of a bridge, including [the specified element].

2. In the bridge deflection estimation method described in claim 1, The aforementioned natural frequency / mode damping ratio estimation step includes the step of estimating the natural frequency and the mode damping ratio based on the peak amplitude and peak position of the waveform of the measured value of the track displacement difference, which is the difference between the track displacement measured at the last vehicle and the track displacement measured at the leading vehicle when passing over the bridge in the resonant state. A method for estimating bridge deflection characterized by the following.

3. In the bridge deflection estimation method described in claim 1, The aforementioned natural frequency / mode damping ratio estimation step includes a step of estimating the natural frequency and the mode damping ratio based on the measured and theoretical values ​​of the track displacement difference, which is the difference between the track displacement measured at the last vehicle and the track displacement measured at the leading vehicle when passing over the bridge in the resonant state. A method for estimating bridge deflection characterized by the following.

4. In the bridge deflection estimation method described in claim 3, The aforementioned natural frequency / mode damping ratio estimation step includes the step of estimating the natural frequency and the mode damping ratio such that the theoretical value of the orbital displacement difference matches the measured value of the orbital displacement difference. A method for estimating bridge deflection characterized by the following.

5. In the bridge deflection estimation method described in claim 3, The aforementioned natural frequency / mode damping ratio estimation step includes a step of estimating the natural frequency and the mode damping ratio by comparing the three peak amplitudes appearing in the waveform of the measured value of the orbital displacement difference with the three peak amplitudes appearing in the waveform of the theoretical value of the orbital displacement difference. A method for estimating bridge deflection characterized by the following.

6. A bridge deflection estimation device for estimating the deflection of a bridge, A natural frequency / mode damping ratio estimation unit estimates the natural frequency and mode damping ratio of the bridge in a resonant state when the vehicle is passing over it, based on the measurement results of a track displacement measuring device for vehicles passing over the bridge. A deflection amount estimation unit estimates the amount of deflection of the bridge in the resonant state when the vehicle is passing over it, based on the natural frequency and the mode damping ratio. A bridge deflection estimation device equipped with [a specific feature].

7. A bridge deflection estimation program for estimating the deflection of a bridge, A natural frequency / mode damping ratio estimation procedure for estimating the natural frequency and mode damping ratio of the bridge in a resonant state when the vehicle is passing over the bridge, based on the measurement results of a track displacement measuring device for a vehicle passing over the bridge, The computer is instructed to perform a deflection estimation procedure that estimates the amount of deflection of the bridge in the resonant state when the vehicle is passing over it, based on the aforementioned natural frequency and the aforementioned mode damping ratio. A bridge deflection estimation program characterized by the following.

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