Measurement method, measurement device, measurement system, and storage medium

Abstract

A measurement method, a measurement device, a measurement system, and a storage medium capable of calculating a decay rate of a dynamic response of a moving body when moving on a structure with high precision, the measurement method including: generating second measurement data by filtering processing first measurement data, calculating a first deflection amount based on an approximate formula of a deflection of the structure, calculating a second deflection amount by filtering processing the first deflection amount, calculating a third deflection amount based on a first order coefficient and a zero order coefficient calculated based on the second measurement data and the second deflection amount, calculating an offset amount based on the zero order coefficient, the second deflection amount, and the third deflection amount, calculating a static response by adding a product of the first order coefficient and the first deflection amount to the offset amount, calculating a first dynamic response by subtracting the static response from the first measurement data, calculating a second dynamic response by removing an unnecessary signal from the first dynamic response, and calculating a decay rate of the second dynamic response based on an envelope line amplitude of the second dynamic response.

Description

Technical Field

[0001] This invention relates to measurement methods, measuring devices, measuring systems, and measurement procedures. Background Technology

[0002] Patent Document 1 describes a method for evaluating the dynamic response of a railway bridge. Accelerometers measuring vertical acceleration are installed on the first and last vehicles of a train. The vertical acceleration of the first and last vehicles is measured during travel. Accelerometer data is extracted when the bridge crosses the bridge. The characteristic value of the vertical acceleration measured by the accelerometer on the last vehicle is divided by the characteristic value of the vertical acceleration measured by the first vehicle to calculate the acceleration amplification factor. This amplification factor is then applied to a pre-determined relationship between the bridge's impact factor and the acceleration amplification factor to calculate the bridge's impact factor (dynamic response component). This dynamic response evaluation method focuses on the fact that almost no dynamic response occurs on the bridge when the first vehicle passes, while both static and dynamic responses occur when the last vehicle passes. Based on the vertical acceleration measured by the accelerometers on the first and last vehicles, the bridge's impact factor (dynamic response component) can be calculated simply and comprehensively.

[0003] Patent Document 1: Japanese Patent Application Publication No. 2017-20172

[0004] However, the dynamic response evaluation method described in Patent Document 1 suffers from insufficient accuracy in calculating the dynamic response due to several main reasons. These include: the acceleration amplification factor obtained by dividing the characteristic quantity of vertical acceleration measured by the accelerometer of the last vehicle by the characteristic quantity of vertical acceleration measured by the first vehicle; the inadequacy of the formula relating the bridge's impact coefficient to the acceleration amplification factor; and errors arising from the measurement location of vertical acceleration or vehicle vibration. Therefore, the dynamic response evaluation method described in Patent Document 1 struggles to accurately calculate the attenuation rate of the dynamic response. Summary of the Invention

[0005] One aspect of the measurement method involved in this invention includes:

[0006] The first measurement data generation process generates first measurement data based on the observation data output from the observation device at the observation point of the observed structure, which is a physical quantity that is the response of multiple parts of a moving body moving on the structure to the action of the observation point.

[0007] The second measurement data generation process generates second measurement data by filtering the first measurement data to reduce the vibration component.

[0008] The observation information generation process generates observation information including the entry time and departure time of the moving body relative to the structure;

[0009] The average velocity calculation process calculates the average velocity of the moving body based on the observation information and environmental information including the dimensions of the pre-fabricated moving body and the dimensions of the structure.

[0010] The first deflection calculation step calculates the first deflection of the structure caused by the moving body based on the approximate formula of the structure's deflection, the observation information, the environmental information, and the average velocity.

[0011] The second deflection calculation step calculates the second deflection that reduces the vibration component by filtering the first deflection.

[0012] The coefficient calculation process involves using a linear function of the second deflection amount to approximate the second measured data, and calculating the first-order coefficient and the zero-order coefficient of the linear function.

[0013] The third deflection calculation step calculates the third deflection based on the first-order coefficient, the zero-order coefficient, and the second deflection.

[0014] The offset calculation process calculates the offset based on the zero-order coefficient, the second deflection, and the third deflection.

[0015] The static response calculation step involves adding the product of the first-order coefficient and the first deflection to the offset to calculate the static response.

[0016] The first dynamic response calculation step involves subtracting the static response from the first measured data to calculate the first dynamic response;

[0017] The second dynamic response calculation process involves filtering the signal that is not needed due to the attenuation of the first dynamic response, and then calculating the second dynamic response.

[0018] The envelope amplitude calculation process calculates the envelope amplitude of the second dynamic response; and

[0019] The attenuation rate calculation step calculates the attenuation rate of the vibration components included in the second dynamic response based on the envelope amplitude.

[0020] One aspect of the measuring device involved in this invention includes:

[0021] The first measurement data generation unit generates first measurement data based on the observation data output from the observation device at the observation point of the observed structure, which is a physical quantity that is a response to the action of multiple parts of a moving body moving on the structure on the observation point.

[0022] The second measurement data generation unit generates second measurement data by filtering the first measurement data to reduce the vibration component.

[0023] The observation information generation unit generates observation information including the entry time and departure time of the moving body relative to the structure;

[0024] The average speed calculation unit calculates the average speed of the moving body based on the observation information and environmental information including the dimensions of the pre-fabricated moving body and the dimensions of the structure;

[0025] The first deflection calculation unit calculates the first deflection of the structure caused by the moving body based on the approximate formula of the structure's deflection, the observation information, the environmental information, and the average velocity.

[0026] The second deflection calculation unit calculates a second deflection that reduces the vibration component by filtering the first deflection.

[0027] The coefficient calculation unit uses a linear function of the second deflection amount to approximate the second measurement data, and calculates the first-order coefficient and the zero-order coefficient of the linear function;

[0028] The third deflection calculation unit calculates the third deflection based on the first-order coefficient, the zero-order coefficient, and the second deflection.

[0029] The offset calculation unit calculates the offset based on the zero-order coefficient, the second deflection, and the third deflection;

[0030] The static response calculation unit adds the product of the first-order coefficient and the first deflection to the offset to calculate the static response;

[0031] The first dynamic response calculation unit subtracts the static response from the first measurement data to calculate the first dynamic response;

[0032] The second dynamic response calculation unit performs filtering processing on signals that are not needed due to the attenuation of the first dynamic response, and calculates the second dynamic response;

[0033] The envelope amplitude calculation unit calculates the envelope amplitude of the second dynamic response; and

[0034] The attenuation rate calculation unit calculates the attenuation rate of the vibration component included in the second dynamic response based on the envelope amplitude.

[0035] One aspect of the measurement system according to the present invention comprises:

[0036] One aspect of the measuring device; and

[0037] The observation device.

[0038] In one aspect of the storage medium involved in this invention, the storage medium stores a measurement program that causes a computer to execute:

[0039] The first measurement data generation process generates first measurement data based on the observation data output from the observation device at the observation point of the observed structure, which is a physical quantity that is the response of multiple parts of a moving body moving on the structure to the action of the observation point.

[0040] The second measurement data generation process generates second measurement data by filtering the first measurement data to reduce the vibration component.

[0041] The observation information generation process generates observation information including the entry time and departure time of the moving body relative to the structure;

[0042] The average velocity calculation process calculates the average velocity of the moving body based on the observation information and environmental information including the dimensions of the pre-fabricated moving body and the dimensions of the structure.

[0043] The first deflection calculation step calculates the first deflection of the structure caused by the moving body based on the approximate formula of the structure's deflection, the observation information, the environmental information, and the average velocity.

[0044] The second deflection calculation step calculates the second deflection that reduces the vibration component by filtering the first deflection.

[0045] The coefficient calculation process involves using a linear function of the second deflection amount to approximate the second measured data, and calculating the first-order coefficient and the zero-order coefficient of the linear function.

[0046] The third deflection calculation step calculates the third deflection based on the first-order coefficient, the zero-order coefficient, and the second deflection.

[0047] The offset calculation process calculates the offset based on the zero-order coefficient, the second deflection, and the third deflection.

[0048] The static response calculation step involves adding the product of the first-order coefficient and the first deflection to the offset to calculate the static response.

[0049] The first dynamic response calculation step involves subtracting the static response from the first measured data to calculate the first dynamic response;

[0050] The second dynamic response calculation process involves filtering the signal that is not needed due to the attenuation of the first dynamic response, and then calculating the second dynamic response.

[0051] The envelope amplitude calculation process calculates the envelope amplitude of the second dynamic response; and

[0052] The attenuation rate calculation step calculates the attenuation rate of the vibration components included in the second dynamic response based on the envelope amplitude. Attached Figure Description

[0053] Figure 1 This is a diagram showing an example of the configuration of a measurement system.

[0054] Figure 2 It is cut along line AA Figure 1 A cross-sectional view of the superstructure.

[0055] Figure 3 This is an explanatory diagram of acceleration detected by an accelerometer.

[0056] Figure 4 This is a graph showing an example of the measured data u(t).

[0057] Figure 5 This is a graph showing the power spectral density of the measured data u(t).

[0058] Figure 6 This shows the measured data u lp A diagram of an example of (t).

[0059] Figure 7 This shows the measured data u lp (t) and entry time t i and departure time t o A diagram illustrating an example of a relationship.

[0060] Figure 8 This shows the length L of the vehicle. c (C m ) and the distance between the axles La(a w (C m A diagram of an example of ,n).

[0061] Figure 9 This is an explanatory diagram of the structural model of the bridge's superstructure.

[0062] Figure 10 This shows the deflection amount w std (a w (C m A diagram of an example of ,n),t).

[0063] Figure 11 This shows the deflection C. std (C m A diagram of an example of ,t).

[0064] Figure 12 This shows the deflection T. std A diagram of an example of (t).

[0065] Figure 13 This shows the deflection T. std_lp A diagram of an example of (t).

[0066] Figure 14 The measurement data is shown in an overlapping manner. lp (t) and deflection T std_lp The graph of (t).

[0067] Figure 15 This shows the deflection T. Estd_lp A diagram of an example of (t).

[0068] Figure 16 This shows the deflection T. Estd A diagram of an example of (t).

[0069] Figure 17 This shows the deflection T. Estd_lp (t) and deflection T std_lp (t) and the specified interval T for calculating their average value avg A diagram illustrating an example of a relationship.

[0070] Figure 18 This shows the offset T. offset_std A diagram of an example of (t).

[0071] Figure 19 This shows the deflection T. EOstd A diagram of an example of (t).

[0072] Figure 20 This shows the measured data u(t) and the deflection T. EOstd A graph showing the relationship between (t).

[0073] Figure 21 This shows the inherent vibration u nv A diagram of an example of (t).

[0074] Figure 22 This shows the inherent vibration u nv A plot of the power spectral density of (t).

[0075] Figure 23 This is a graph showing the frequency characteristics of a high-pass filter.

[0076] Figure 24 This shows the inherent vibration u nv_hp A diagram of an example of (t).

[0077] Figure 25 This is a graph showing the transfer characteristics of a moving average filter.

[0078] Figure 26 This shows the inherent vibration u nv_3lp A diagram of an example of (t).

[0079] Figure 27 This shows the envelope amplitude u. nv_mag A diagram of an example of (t).

[0080] Figure 28 This shows the envelope amplitude u. nv_mag A graph of the logarithm y(t) of (t) and an example of the first interval T1.

[0081] Figure 29 The overlapping shows the damped vibration u env (t) and natural vibration u nv_3lp The graph of (t).

[0082] Figure 30 This is a flowchart illustrating an example of the steps of the measurement method of this embodiment.

[0083] Figure 31 This is a flowchart illustrating an example of the steps in the first measurement data generation process.

[0084] Figure 32 This is a flowchart illustrating an example of the steps in the second measurement data generation process.

[0085] Figure 33 This is a flowchart illustrating an example of the steps involved in generating observation information.

[0086] Figure 34 This is a flowchart illustrating an example of the steps involved in calculating the average speed.

[0087] Figure 35 This is a flowchart illustrating an example of the steps in the first deflection calculation process.

[0088] Figure 36 This is a flowchart illustrating an example of the steps in the second deflection calculation process.

[0089] Figure 37 This is a flowchart illustrating an example of the steps involved in the offset calculation process.

[0090] Figure 38 This is a flowchart illustrating an example of the steps in the second dynamic response calculation process.

[0091] Figure 39 This is a flowchart illustrating an example of the steps involved in calculating the attenuation rate.

[0092] Figure 40 This is a diagram illustrating an example of the configuration of a sensor, measuring device, and monitoring device.

[0093] Figure 41 This is a diagram illustrating other configuration examples of a measurement system.

[0094] Figure 42 This is a diagram illustrating other configuration examples of a measurement system.

[0095] Figure 43 This is a diagram illustrating other configuration examples of a measurement system.

[0096] Figure 44 It is cut along line AA Figure 43 A cross-sectional view of the superstructure.

[0097] Explanation of reference numerals in the attached figures

[0098] 1…Measuring device; 2…Sensor; 3…Monitoring device; 4…Communication network; 5…Bridge; 6…Railway vehicle; 6a…Vehicle; 7…Superstructure; 7a…Bridge deck; 7b…Support; 7c…Track; 7d…Sleeper; 7e…Battery; F…Ground; G…Main beam; 8…Substructure; 8a…Pier; 8b…Abutment; 10…Measuring system; 11…First communication unit; 12…Second communication unit; 13…Storage unit; 14…Processor; 21…Communication unit; 22…Acceleration sensor; 23…Processor; 24…Storage unit; 31…Communication unit; 32…Processor; 33…Display unit; 34…Operation unit; 35…Storage unit; 40…Ring displacement gauge; 41…Piano wire; 50…Camera; 51…Target; 131…Measurement program; 132…Environmental information; 133…Observation data; 34…Observation information; 135…Measurement data; 141…Observation data acquisition unit; 142…First measurement data generation unit; 143…Second measurement data generation unit; 144…Observation information generation unit; 145…Average velocity calculation unit; 146…First deflection calculation unit; 147…Second deflection calculation unit; 148…Coefficient calculation unit; 149…Third deflection calculation unit; 150…Offset calculation unit; 151…Static response calculation unit; 152…First dynamic response calculation unit; 153…Second dynamic response calculation unit; 154…Envelope amplitude calculation unit; 155…Attenuation rate calculation unit; 156…Measurement data output unit; 241…Observation program; 242…Observation data; 321…Measurement data acquisition unit; 322…Monitoring unit; 351…Monitoring program; 352…Measurement data column. Detailed Implementation

[0099] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that the embodiments described below are not intended to unduly limit the scope of the invention as defined in the claims. Furthermore, not all of the components described below are essential elements of the present invention.

[0100] 1. Composition of the measurement system

[0101] The moving body passing through the superstructure of the bridge, which is the structure involved in this embodiment, is a heavy vehicle or railway vehicle that can be measured using BWIM. BWIM is an abbreviation for Bridge Weigh in Motion, a technique that uses the bridge as a "scale" to determine the weight, number of axles, etc., of moving bodies passing over the bridge by measuring the deformation of the bridge. The superstructure of the bridge, which can analyze the weight of passing moving bodies based on responses such as deformation or strain, is the structure in which BWIM functions. The BWIM system, which applies the physical process between the action and response of the bridge superstructure, makes it possible to measure the weight of passing moving bodies. Hereinafter, an example of a railway vehicle as the moving body will be given to describe the measurement system used to implement the measurement method of this embodiment.

[0102] Figure 1 This diagram illustrates an example of the measurement system according to this embodiment. Figure 1 As shown, the measurement system 10 according to this embodiment includes a measurement device 1 and at least one sensor 2 installed on the superstructure 7 of the bridge 5. Additionally, the measurement system 10 may also include a monitoring device 3.

[0103] Bridge 5 consists of a superstructure 7 and a substructure 8. Figure 2 It is along Figure 1 The cross-sectional view of the upper structure 7 cut off by line AA. (See diagram below.) Figure 1 and Figure 2 As shown, the superstructure 7 includes a bridge deck 7a (composed of the ground F, main beams G, and crossbeams not shown), supports 7b, tracks 7c, sleepers 7d, and ballast 7e. Additionally, as... Figure 1 As shown, the substructure 8 includes piers 8a and abutments 8b. The superstructure 7 is a structure erected on any one of adjacent abutments 8b and piers 8a, two adjacent abutments 8b, or two adjacent piers 8a. The two ends of the superstructure 7 are located at the positions of adjacent abutments 8b and piers 8a, two adjacent abutments 8b, or two adjacent piers 8a.

[0104] If railway vehicle 6 enters the superstructure 7, the superstructure 7 will deflect due to the load of railway vehicle 6. However, since railway vehicle 6 connects multiple vehicles, the deflection of the superstructure 7 will periodically repeat as each vehicle passes. This phenomenon is called static response. In contrast, since the superstructure 7 has its own natural vibration frequency, the natural vibration of the superstructure 7 will be excited as railway vehicle 6 passes through it. This excitation of the natural vibration of the superstructure 7 will then cause the deflection of the superstructure 7 to periodically repeat. This phenomenon is called dynamic response.

[0105] The measuring device 1 and each sensor 2 are connected, for example, via cables not shown, and communicate via a communication network such as CAN. CAN is an abbreviation for Controller Area Network. Alternatively, the measuring device 1 and each sensor 2 can also communicate via a wireless network.

[0106] Each sensor 2 outputs data used to calculate the attenuation rate of the dynamic response of the railway vehicle 6, as a moving body, as it moves on the superstructure 7, which is a structure. In this embodiment, each sensor 2 is an accelerometer, such as a crystal accelerometer or a MEMS accelerometer. MEMS is an abbreviation for Micro Electro Mechanical Systems.

[0107] In this embodiment, each sensor 2 is located at the center of the superstructure 7 along its length, specifically at the center of the main beam G along its length. Each sensor 2 only needs to detect the acceleration used to calculate the decay rate of the dynamic response; its location is not limited to the center of the superstructure 7. It should be noted that if the sensors 2 are placed on the ground F of the superstructure 7, they may be damaged by the movement of railway vehicles 6, and the measurement accuracy may be affected by local deformation of the bridge deck 7a. Therefore, in… Figure 1 and Figure 2 In the example, each sensor 2 is installed on the main beam G of the superstructure 7.

[0108] The ground F and main beam G of the superstructure 7 deflect vertically due to the load of the railway vehicle 6 passing through the superstructure 7. Each sensor 2 detects the acceleration of the deflection of the ground F and main beam G caused by the load of the railway vehicle 6 passing through the superstructure 7.

[0109] The measuring device 1 calculates the attenuation rate of the dynamic response of the railway vehicle 6 as it passes over the superstructure 7 based on the acceleration data output from each sensor 2. The measuring device 1 is, for example, installed on the abutment 8b.

[0110] The measuring device 1 and the monitoring device 3 can communicate, for example, via a mobile phone wireless network or a communication network 4 such as the Internet. The measuring device 1 sends measurement data, including the attenuation rate of the dynamic response of the railway vehicle 6 as it passes over the superstructure 7, to the monitoring device 3. The monitoring device 3 can also store this information in a storage device (not shown), for example, for monitoring the railway vehicle 6 or determining anomalies in the superstructure 7.

[0111] It should be noted that in this embodiment, bridge 5 is a railway bridge, such as a steel bridge, beam bridge, or RC bridge. RC is an abbreviation for Reinforced-Concrete.

[0112] like Figure 2 As shown, in this embodiment, an observation point R is set corresponding to sensor 2. Figure 2 In this example, the observation point R is set at a position on the surface of the upper structure 7, which is located vertically upwards from the sensor 2 mounted on the main beam G. That is, the sensor 2 is an observation device that observes the observation point R, detecting physical quantities as responses to the action of multiple parts of the railway vehicle 6 moving on the upper structure 7 (which is a structure) to the observation point R, and outputting data including the detected physical quantities. For example, the multiple parts of the railway vehicle 6 may be axles or wheels, but will be hereinafter referred to as axles. Furthermore, in this embodiment, each sensor 2 is an acceleration sensor that detects acceleration as a physical quantity. The sensor 2 only needs to be positioned at a location capable of detecting the acceleration generated at the observation point R due to the movement of the railway vehicle 6, but it is preferable to position it close to the vertical direction of the observation point R.

[0113] It should be noted that the number and placement of sensor 2 are not limited to... Figure 1 and Figure 2 The example shown can be implemented in various variations.

[0114] The measuring device 1 acquires the acceleration in the direction intersecting the surface of the superstructure 7 that is moving with the railway vehicle 6, based on the acceleration data output from the sensor 2. The surface of the superstructure 7 that is moving with the railway vehicle 6 is defined by the X direction, which is the length direction of the superstructure 7, and the Y direction, which is orthogonal to the direction of the railway vehicle 6, and is the width direction of the superstructure 7. Due to the movement of the railway vehicle 6, the observation point R deflects in the direction orthogonal to the X and Y directions. Therefore, in order to accurately calculate the magnitude of the deflection acceleration, the measuring device 1 preferably acquires the acceleration in the Z direction, which is orthogonal to the X and Y directions and is the normal direction to the ground F.

[0115] Figure 3 This diagram illustrates the acceleration detected by sensor 2. Sensor 2 is an acceleration sensor that detects acceleration generated along each of the three mutually orthogonal axes.

[0116] To detect the deflection acceleration of observation point R caused by the movement of railway vehicle 6, sensor 2 is configured such that one of the three detection axes (x-axis, y-axis, z-axis) intersects the X and Y directions. Figure 1 and Figure 2In this configuration, sensor 2 is configured such that one axis intersects the X and Y directions. Since the observation point R flexes in a direction orthogonal to the X and Y directions, ideally, in order to accurately detect the acceleration of the flexure, sensor 2 should be configured such that one axis is aligned with the Z direction, which is orthogonal to the X and Y directions and is the normal direction of the ground F.

[0117] In cases where sensor 2 is mounted on the upper structure 7, the mounting location may be tilted. Even if one of the three detection axes of sensor 2 is not aligned with the normal direction of the ground F, the measurement device 1 can minimize the error by generally aligning it with the normal direction. Furthermore, even if one of the three detection axes of sensor 2 is not aligned with the normal direction of the ground F, the measurement device 1 can use the triaxial composite acceleration (combining the accelerations of the x, y, and z axes) to correct for detection errors caused by the tilt of sensor 2. Additionally, sensor 2 can be a single-axis accelerometer that detects acceleration generated in a direction approximately parallel to the vertical or acceleration in the normal direction of the ground F.

[0118] The following describes in detail the measurement method of this embodiment performed by the measuring device 1.

[0119] 2. Details of the measurement method

[0120] First, as shown in equation (1), the measuring device 1 integrates the acceleration data a(k) output from the sensor 2, which is an acceleration sensor, to generate velocity data v(k). Then, as shown in equation (2), the velocity data v(k) is integrated to generate measurement data u(k). The acceleration data a(k) is the acceleration change data after removing the acceleration deviation that is not needed to calculate the displacement change of the railway vehicle 6 when it passes the bridge 5. For example, the acceleration of the railway vehicle 6 before it passes the bridge 5 can be set to 0, and the acceleration change thereafter can be set as acceleration data a(k). In equations (1) and (2), k is the sample number, and ΔT is the time interval between samples. The measurement data u(k) is the displacement data of the observation point R caused by the movement of the railway vehicle 6.

[0121]

Mathematical Formula 1

[0122] v(k)=a(k)ΔT+v(k-1)…(1)

[0123]

Mathematical Formula 2

[0124] u(k)=v(k)ΔT+u(k-1)…(2)

[0125] Let time t = kΔT, and transform the measurement data u(k) with sample number k as the variable into measurement data u(t) with time t as the variable. Figure 4 An example of the measured data u(t) is shown. Since the measured data u(t) is generated based on the acceleration data a(t) output from the sensor 2 at the observation point R, it is based on the acceleration data as a response to the action of the multiple axles of the railway vehicle 6 moving on the superstructure 7 on the observation point R.

[0126] Next, the measuring device 1 generates measurement data u(t) that has been filtered by the measuring data u(t). lp (t), to reduce the fundamental frequency F included in the measured data u(t). f The vibrational components and their higher harmonics. Filtering processing can be, for example, low-pass filtering or band-pass filtering.

[0127] Specifically, firstly, the measuring device 1 performs high-speed Fourier transform processing on the measured data u(t) to calculate the power spectral density, and calculates the peak value of the power spectral density as the fundamental frequency F. f . Figure 5 Showing the Figure 4 The power spectral density is obtained by performing high-speed Fourier transform processing on the measured data u(t). Figure 5 In the example, the fundamental frequency F f It is calculated to be approximately 3Hz. Then, measuring device 1, according to equation (3), calculates the fundamental frequency F. f Calculate the fundamental period T f As shown in equation (4), the fundamental period T is calculated. f The moving average interval k is adjusted to the time resolution of the data by dividing by ΔT. mf The basic period T f It is related to the fundamental frequency F f The corresponding period, T f >2ΔT.

[0128]

Mathematical Expression 3

[0129]

[0130]

Mathematical Expression 4

[0131]

[0132] Then, as a filtering process, the measuring device 1, according to equation (5), uses a fundamental period T. f The measured data u(t) is processed by moving average to generate measured data u(t) with reduced vibrational components. lp (t). This moving average process requires little computation, and the fundamental frequency F fThe signal components and their higher harmonic components attenuate significantly, thus enabling the acquisition of measurement data with effectively reduced vibration components. lp (t). Figure 6 The measured data u are shown lp An example of (t). Figure 6 As shown, it is possible to obtain measurement data u(t) in which the vibrational components are almost completely removed. lp (t).

[0133]

Mathematical Expression 5

[0134]

[0135] It should be noted that, as a filtering process, the measuring device 1 can also adjust the measured data u(t) to make the fundamental frequency F f The above frequency signal components are attenuated by FIR filtering to generate measurement data u. lp (t). FIR is an abbreviation for Finite Impulse Response. Although FIR filtering requires more computation than moving average filtering, it can reduce the fundamental frequency F. f All signal components at the above frequencies are attenuated.

[0136] Next, measuring device 1 calculates the measurement data u. lp The amplitude of (t) and the predetermined coefficient C L And based on the measured data u lp The amplitude u calculated by (t) a Threshold C of the product L u a Consistent, or exceeding the threshold C L u a The two moments, t, are the entry moments of the railway vehicle 6 relative to the superstructure 7. i and departure time t o Where, let 0 <C L <1, let the amplitude be u a For example, measurement data u lp The average value of the amplitude shift of (t) from time t1 to time t2 is calculated according to equation (6).

[0137]

Mathematical Expression 6

[0138]

[0139] Entering time t i It is the moment when the first axle of the multiple axles of railway vehicle 6 passes the entry end of the superstructure 7. Additionally, the departure time t... oIt is the moment when the last axle of the multiple axles of the railway vehicle 6 passes the departure end of the superstructure 7. Figure 7 The measured data u are shown lp (t) and entry time t i and departure time t o An example of a relationship.

[0140] Next, the measuring device 1 calculates the passage time t of the railway vehicle 6 through the superstructure 7 of the bridge 5 according to equation (7). s , as the departure time t o and entry time t i difference.

[0141]

Mathematical Expression 7

[0142] t s =t o -t i …(7)

[0143] In addition, the measuring device 1 calculates the time t from the passage according to equation (8). s and fundamental frequency F f The largest integer less than or equal to the product minus 1 is taken as the number of railway vehicles C for 6. T .

[0144]

Mathematical Expression 8

[0145]

[0146] Measuring device 1 will include the entry time t i Departure time t o Through time t s and the number of vehicles C T The observation information is stored in a storage unit not shown in the diagram. It should be noted that... Figure 7 In the example, entering time t i = 7.155 seconds, departure time t o = 12.845 seconds, passing through time t s = 5.69 seconds, number of vehicles C T =16.

[0147] Then, the measuring device 1 performs further processing based on the observation information and environmental information, including the dimensions of the prefabricated railway vehicle 6 and the superstructure 7.

[0148] As for the dimensions of the superstructure 7, environmental information includes, for example, the length L of the superstructure 7. B and the location L of observation point R x The length L of the upper structure 7 BThis is the distance between the entry and exit points of the superstructure 7. Additionally, the position L of observation point R... x This is the distance from the entrance of the superstructure 7 to the observation point R. Additionally, environmental information, such as the length L of each car in the railway vehicle 6, is included as part of the dimensions of the railway vehicle 6. c (C m ), Number of axles a for each vehicle T (C m ) and the distance La (a) between the axles of each vehicle w (C m ,n)). C m These are vehicle numbers, and the length L of each vehicle. c (C m ) is from the beginning, number C m The distance between the two ends of each vehicle. The number of axles (a) of each vehicle. T (C m ) is from the beginning, number C m The number of axles in each vehicle. n is the axle number of each vehicle, 1 ≤ n ≤ a. T (C m The distance La (a) between the axles of each vehicle. w (C m When n=1, the Cth element starts from the beginning. m The distance between the front end of a vehicle and the first axle starting from the beginning is the distance between the (n-1)th axle and the nth axle starting from the beginning when n≥2. Figure 8 The Cth section of railway vehicle 6 is shown. m The length L of each vehicle c (C m ) and the distance between the axles La(a w (C m An example of this is the railway vehicle 6 and the superstructure 7. The dimensions of the railway vehicle 6 and the superstructure 7 can be determined using known methods. Alternatively, a database of the dimensions of the railway vehicles 6 that cross the bridge 5 can be prepared in advance, and the dimensions of the corresponding vehicles can be referenced based on the crossing time.

[0149] It should be noted that, assuming that a railway vehicle 6, consisting of any number of identical vehicles, travels on the superstructure 7 of the bridge 5, the environmental information only needs to include the length L of each vehicle. c (C m ), the number of axles of the vehicle a T (C m ) and the distance between the axles La(a w (C m That's all.

[0150] Total number of axles Ta for railway vehicles 6 TUse the number of vehicles C included in the observation information T The number of axles for each vehicle included in the environmental information. T (C m ), calculated according to formula (9).

[0151]

Mathematical Expression 9

[0152]

[0153] From the first axle of railway vehicle 6 to the Cth... m The distance D of the nth axle of a vehicle wa (a w (C m The length L of each vehicle included in the environmental information is used. c (C m ), Number of axles a for each vehicle T (C m ) and the distance La (a) between the axles of each vehicle w (C m ,n)), calculated according to equation (10). It should be noted that in equation (10), let L c (C m ) = L c (1).

[0154]

Mathematical Formula 10

[0155]

[0156] Measuring device 1 is set as C according to equation (10). m =C T n = a T (C T Equation (11) is used to calculate the distance D from the first axle of the first train car 6 to the last axle of the last train car 6. wa (a w (C T ,a T (C T ))).

[0157]

Mathematical Expression 11

[0158]

[0159] The average speed v of railway vehicle 6 a The length L of the superstructure 7 included in the environmental information is [not specified]. B The observation information includes the transit time t. s and the calculated distance D wa (a w (C T,a T (C T According to equation (12), the average speed v of the railway vehicle 6 is calculated. a .

[0160]

Mathematical Expression 12

[0161]

[0162] Measuring device 1 calculates the average speed v of railway vehicle 6 based on equation (13), which substitutes equation (11) into equation (12). a .

[0163]

Mathematical Expression 13

[0164]

[0165] Next, the measuring device 1 calculates the deflection of the superstructure 7 caused by the movement of the railway vehicle 6 as follows.

[0166] In this embodiment, in the superstructure 7 of the bridge 5, considering the continuous arrangement of one or more bridge decks 7a composed of ground F and main beams G, the measuring device 1 calculates the displacement of one bridge deck 7a as the displacement of the central part in the length direction. The load applied to the superstructure 7 moves from one end of the superstructure 7 to the other. At this time, using the position and amount of the load on the superstructure 7, the deflection amount as the displacement of the central part of the superstructure 7 can be represented. In this embodiment, in order to represent the deflection deformation of the axle of the railway vehicle 6 when it moves on the superstructure 7 as the trajectory of the deflection amount caused by the movement of a single-point load on the beam, the following is considered: Figure 9 The structural model shown is used to calculate the deflection of the middle section. Figure 9 In this context, P represents the load. a is the load position at the entry end of the superstructure 7 from the side where the railway vehicle 6 enters. b is the load position at the exit end of the superstructure 7 from the side where the railway vehicle 6 leaves. L B It is the length of the upper structure 7, that is, the distance between the two ends of the upper structure 7. Figure 9 The structural model shown is a simply supported beam supported at both ends.

[0167] exist Figure 9 In the structural model shown, when the position of the entry end of the superstructure 7 is set to zero and the observation position of the deflection is set to x, the bending moment M of the simply supported beam is represented by equation (14).

[0168]

Mathematical Expression 14

[0169]

[0170] In equation (14), the function Ha As defined in equation (15).

[0171]

Mathematical Expression 15

[0172]

[0173] Transforming equation (14) yields equation (16).

[0174]

Mathematical Expression 16

[0175]

[0176] On the other hand, the bending moment M is represented by equation (17). In equation (17), θ is the angle, I is the second moment, and E is Young's modulus.

[0177]

Mathematical Expression 17

[0178]

[0179] Substituting equation (17) into equation (16), we obtain equation (18).

[0180]

Mathematical Expression 18

[0181]

[0182] Equation (19) is calculated by integrating equation (18) with respect to the observation position x, resulting in equation (20). In equation (20), C1 is the integration constant.

[0183]

Mathematical Expression 19

[0184]

[0185]

Mathematical Expression 20

[0186]

[0187] Then, by integrating equation (20) with respect to the observation position x, equation (21) is calculated, resulting in equation (22). In equation (22), C2 is the integration constant.

[0188]

Mathematical Expression 21

[0189]

[0190]

Mathematical Expression 22

[0191]

[0192] In equation (22), θx represents the deflection. Replacing θx with the deflection w yields equation (23).

[0193]

Mathematical Expression 23

[0194]

[0195] according to Figure 9 Since b = L B -a, so equation (23) is transformed into equation (24).

[0196]

Mathematical Expression 24

[0197]

[0198] Let x = 0, and the deflection w = 0. According to x ≤ a, H a =0, therefore, if x = w = H a Substituting 0 into equation (24) and rearranging, we get equation (25).

[0199]

Mathematical Expression 25

[0200] C2=0…(25)

[0201] Additionally, let x = L B The deflection w = 0, according to x > a, H a =1, therefore, if x = L B w = 0, H a Substituting 1 into equation (24) and rearranging, we get equation (26).

[0202]

Mathematical Expression 26

[0203]

[0204] Let b = L B Substituting -a into equation (26), we get equation (27).

[0205]

Mathematical Expression 27

[0206]

[0207] Substituting the integration constant C1 of equation (25) and the integration constant C2 of equation (26) into equation (23), we obtain equation (28).

[0208]

Mathematical Expression 28

[0209]

[0210] By transforming equation (28), the deflection w at the observed position x when the load P is applied to position a is expressed by equation (29).

[0211]

Mathematical Expression 29

[0212]

[0213] Let x = 0.5L B a = b = 0.5L B H a =0, the deflection w at the central observation position x when the load P is located at the center of the superstructure 7. 0.5LB It is expressed by equation (30). The deflection amount w 0.5LB The maximum amplitude of the deflection w.

[0214]

Mathematical Expression 30

[0215]

[0216] The deflection w at any observation position x is determined by the deflection w 0.5LB Standardization. When the load P is located closer to the entry end than the observation position x, based on x>a, H... a Substituting 1 into equation (30), we get equation (31).

[0217]

Mathematical Expression 31

[0218]

[0219] If the position a of load P is set to a = L B r, let a = L B r, b = L B Substituting (1-r) into equation (31) and rearranging, we obtain the deflection w standardized by equation (32). std r represents the position of load P relative to the length L of the superstructure 7. B than.

[0220]

Mathematical Expression 32

[0221]

[0222] Similarly, when the load P is located at a position a further away from the end than the observation position x, according to x≤a, H a Substituting 0 into equation (30), we get equation (33).

[0223]

Mathematical Expression 33

[0224]

[0225] If the position a of load P is set to a = L B r, let a = L B r, b = L B Substituting (1-r) into equation (33) and rearranging, we obtain the deflection w standardized by equation (34). std.

[0226]

Mathematical Expression 34

[0227]

[0228] Summarizing equations (32) and (34), for any observation position x = L x deflection w std (r) is represented by equation (35). In equation (35), the function R(r) is represented by equation (36). Equation (35) is an approximation of the deflection of the superstructure 7 as a structure, and is a mathematical expression based on the structural model of the superstructure 7. Specifically, equation (35) is an approximation normalized to the maximum amplitude of the deflection at the central position of the entry and exit ends of the superstructure 7.

[0229]

Mathematical Expression 35

[0230]

[0231]

Mathematical Expression 36

[0232]

[0233] In this embodiment, the load P is the load of any axle of the railway vehicle 6. Any axle of the railway vehicle 6 reaches the observation point R from the entry end of the superstructure 7 at position L. x The required time t xn The average velocity v calculated according to equation (12) is used. a , calculated according to formula (37).

[0234]

Mathematical Expression 37

[0235]

[0236] In addition, any axle of railway vehicle 6 passes through length L B The time t required for the superstructure 7 ln Calculate according to formula (38).

[0237]

Mathematical Expression 38

[0238]

[0239] Railway vehicle 6, C m The time t when the nth axle of a vehicle reaches the entry end of the superstructure 7. o (C m (n), using the entry time t included in the observation information. i The distance D calculated according to equation (10) wa (a w (Cm ,n)) and the average velocity v calculated according to equation (12) a , calculated according to formula (39).

[0240]

Mathematical Expression 39

[0241]

[0242] Measuring device 1 uses equations (37), (38), and (39), and according to equation (40), calculates the result from the Cth... m The deflection w caused by the nth axle of a vehicle, as expressed by equation (35) std (r) is replaced with the deflection w after time. std (a w (C m In equation (40), the function R(t) is represented by equation (41). Figure 10 The deflection amount w is shown std (a w (C m An example of ,n),t).

[0243]

Mathematical Expression 40

[0244]

[0245]

Mathematical Expression 41

[0246]

[0247] In addition, the measuring device 1 calculates the result from the Cth equation according to formula (42). m The deflection C caused by the vehicle std (C m ,t). Figure 11 The Cth axle of vehicle with n=4 axles is shown. m The deflection C caused by the vehicle std (C m An example of ,t).

[0248]

Mathematical Expression 42

[0249]

[0250] Then, the measuring device 1 calculates the deflection T caused by the railway vehicle 6 according to equation (43). std (t). Figure 12 The number of vehicles C is shown. T =16 The deflection T caused by the railway vehicle 6 = std An example of (t). It should be noted that in Figure 12 In the middle, the dashed lines indicate sixteen deflection values ​​C. std (1,t)~Cstd (16,t).

[0251]

Mathematical Expression 43

[0252]

[0253] Next, measuring device 1 generates a value for the deflection T. std (t) Filtered deflection T std_lp (t) to reduce the deflection T std The fundamental frequency F included in (t) M The vibrational components and their higher harmonics. Filtering processing can be, for example, low-pass filtering or band-pass filtering.

[0254] Specifically, firstly, the measuring device 1 measures the deflection T. std (t) Perform high-speed Fourier transform processing to calculate the power spectral density, and calculate the peak value of the power spectral density as the fundamental frequency F. M Then, the measuring device 1, according to equation (44), calculates the fundamental frequency F. M Calculate the fundamental period T M As shown in equation (45), the fundamental period T is calculated. M The moving average interval k is adjusted to the time resolution of the data by dividing by ΔT. mM The basic period T M It is related to the fundamental frequency F M The corresponding period, T M >2ΔT.

[0255]

Mathematical Expression 44

[0256]

[0257]

Mathematical Expression 45

[0258]

[0259] Then, as a filtering process, the measuring device 1, according to equation (46), uses a fundamental period T. M For the deflection T std (t) is processed using a moving average to calculate the reduction in deflection T. std The deflection T of the vibrational component included in (t) std_lp (t). This moving average process requires little computation, and the fundamental frequency F M The signal components and their higher harmonic components have very large attenuation, thus effectively reducing the deflection T of the vibration components. std_lp (t). Figure 13 Showing the deflection T std_lp An example of (t). Figure 13 As shown, the deflection T can be obtained. std The deflection T in (t) is almost entirely devoid of vibrational components. std_lp (t).

[0260]

Mathematical Expression 46

[0261]

[0262] It should be noted that, as a filtering process, measuring device 1 can also measure the deflection T. std (t) is used to make the fundamental frequency F M The deflection T is calculated by attenuating the signal components at the above frequencies using FIR filtering. std_lp (t). Although this FIR filtering process involves more computation than the moving average process, it can reduce the fundamental frequency F. f All signal components at the above frequencies are attenuated.

[0263] Figure 14 Overlapping display Figure 6 The measurement data u shown lp (t) and Figure 13 The deflection T shown std_lp (t). Considering the deflection T std_lp (t) is the deflection proportional to the load of the railway vehicle 6 passing through the superstructure 7, assuming the deflection T std_lp A linear function of (t) and measured data u lp (t) are approximately equal. That is, as shown in equation (47), the measuring device 1 utilizes the deflection T std_lp To approximate the measurement of data u using a linear function of (t). lp (t). It should be noted that the approximate time interval is set as the entry time t. i With departure time t o Between, or the amount of deflection T std_lp The time interval during which the amplitude of (t) is not zero.

[0264]

Mathematical Expression 47

[0265]

[0266] Then, measuring device 1 calculates the first-order coefficient c1 and the zero-order coefficient c0 of the linear function represented by equation (47). For example, measuring device 1 calculates the error e(t) represented by equation (48), i.e., the measured data u, using the least squares method. lp The difference between (t) and the linear function of equation (47) is minimized by the first-order coefficient c1 and the zero-order coefficient c0.

[0267]

Mathematical Expression 48

[0268]

[0269] The first-order coefficient c1 and the zero-order coefficient c0 are calculated according to equations (49) and (50), respectively. The data interval corresponding to the approximate time interval is set as k. a ≤k≤k b .

[0270]

Mathematical Expression 49

[0271]

[0272]

Mathematical Expression 50

[0273]

[0274] Then, as shown in equation (51), the measuring device 1 uses the first-order coefficient c1 and the second-order coefficient c0 to calculate and adjust the deflection T. std_lp The deflection T of (t) Estd_lp (t). As shown in equation (51), the deflection T Estd_lp (t) is essentially equivalent to the right side of equation (47), but at the entry time t i Previous interval and departure time t o In the subsequent interval, the coefficient c0 of the 0th power is set to 0. Figure 15 Showing the deflection T Estd_lp An example of (t).

[0275]

Mathematical Expression 51

[0276]

[0277] Furthermore, as shown in equation (52), it is assumed that the deflection T is calculated using the first-order coefficient c1 calculated according to equation (49) and the zero-order coefficient c0 calculated according to equation (50). std The linear function of u(t) is approximately equal to the measured data u(t).

[0278]

Mathematical Expression 52

[0279]

[0280] The deflection T was adjusted using a first-order coefficient c1 and a second-order coefficient c0. std The deflection T of (t) Estd (t) is calculated according to equation (53). The right side of equation (53) is T, which is the right side of equation (51). std_lp (t) is replaced with T std (t) is obtained. Figure 16 Showing the deflection T Estd An example of (t).

[0281]

Mathematical Expression 53

[0282]

[0283] Next, let t = kΔT, and the measuring device 1 calculates the deflection T in the specified interval according to equation (54). Estd_lp (t) and deflection T std_lp The amplitude ratio of (t) to R T In equation (54), the numerator is the deflection T. Estd_lp Waveform and deflection T of (t) std_lp The portion of the waveform offset interval of (t) specifies the deflection T included in the interval. Estd_lp The average of n+1 samples of (t), with the denominator being the deflection T included in the specified interval. std_lp The average of n+1 samples of (t). Figure 17 Showing the deflection T Estd_lp (t) and deflection T std_lp (t) and the specified interval T for calculating their average value avg An example of a relationship.

[0284]

Mathematical Expression 54

[0285]

[0286] Next, the measuring device 1 will measure the amplitude ratio R T and deflection T std_lp The product R of (t) T T std_lp (t) is compared with the zero-order coefficient c0 to calculate the offset T. offset_std (t). Specifically, as shown in equation (55), the measuring device 1 will measure the amplitude ratio R T and deflection T std_lp The product R of (t) T T std_lp The absolute value of (t) is greater than the product R of the absolute values ​​of the zero-order coefficient c0. T T std_lp Replace the interval of (t) with the zero-order coefficient c0, and calculate the offset T. offset_std (t). Figure 18 Showing the offset T offset_std An example of (t). Figure 18 In the example, due to the deflection T std_lp The amplitude of (t) is 0 or negative, therefore the measuring device 1 will integrate R. T T std_lp Replace the interval of (t) with a coefficient c0 of order less than 0 with a coefficient c0 of order 0, and calculate the offset T. offset_std (t).

[0287]

Mathematical Expression 55

[0288]

[0289] Next, as shown in equation (56), the measuring device 1 measures the first-order coefficient c1 and the deflection T. std The product of (t) c1T std (t) and offset T offset_std Add (t) together to calculate the deflection T. EOstd (t). The deflection T EOstd (t) is equivalent to the static response of the railway vehicle 6 when it passes over the superstructure 7. Figure 19 Showing the deflection T EOstd One example of (t). Additionally... Figure 20 The measured data u(t) and the deflection T are shown. EOstd The relationship between (t).

[0290]

Mathematical Expression 56

[0291] TE Ostd (t)=c1T std (t)+T offset_std (t)…(56)

[0292] Then, as shown in equation (57), the measuring device 1 subtracts the deflection T from the measured data u(t). EOstd (t), calculate the natural vibration u nv (t). This inherent vibration u nv (t) is equivalent to the dynamic response of the railway vehicle 6 when it passes over the superstructure 7. Figure 21 The inherent vibration u is shown nv An example of (t).

[0293]

Mathematical Expression 57

[0294] u nv (t)=u(t)-T EOstd (t)…(57)

[0295] The natural vibration u, calculated according to equation (57), is the first dynamic response. nv (t) includes unwanted signals in addition to the fundamental frequency. Therefore, in order to extract the natural vibration u nv The fundamental wave of (t) is measured by the measuring device 1 from the inherent vibration u, which is the first dynamic response. nv (t) Filtering to attenuate unwanted signals and calculating the natural vibration u as the second dynamic response. nv_3lp (t). Unwanted signals, such as the frequency F of the fundamental wave. N Low-frequency signal components or high-order harmonic components.

[0296] From inherent vibration u nv(t) Filtering to attenuate unwanted signals includes reducing the inherent vibration u nv The fundamental frequency F included in (t) N The higher harmonic components of the vibrational components are attenuated, and the fundamental frequency F is corrected. N Low-pass filtering of the gain in the process. Furthermore, it is used to extract the natural vibration u. nv (t) Filtering to attenuate unwanted signals may also include methods to reduce the frequency F from the fundamental frequency. N High-pass filtering attenuates low-frequency signal components.

[0297] For example, measuring device 1 can also be used to measure the inherent vibration u nv (t) After high-pass filtering, low-pass filtering is further performed. Specifically, firstly, the measuring device 1 performs low-pass filtering on the natural vibration u. nv (t) performs a vibration that is greater than the natural vibration u nv The fundamental frequency F of (t) N High-pass filtering for attenuation of low-frequency signal components is used to calculate the natural vibration u. nv_hp (t).

[0298] Specifically, firstly, the measuring device 1 measures the natural vibration u. nv (t) Perform high-speed Fourier transform processing to calculate the power spectral density, and calculate the peak value of the power spectral density as the fundamental frequency F. N . Figure 22 Showing the Figure 21 The inherent vibration u nv (t) is the power spectral density obtained by performing a high-speed Fourier transform. Figure 22 In the example, the fundamental frequency F N It is calculated to be approximately 3 Hz. Then, measuring device 1, according to equation (58), calculates based on the fundamental frequency F. N Calculate the fundamental period T N As shown in equation (59), the fundamental period T is calculated. N The moving average interval k is adjusted to the time resolution of the data by dividing by ΔT. mN The basic period T N It is related to the fundamental frequency F N The corresponding period is TN>2ΔT.

[0299]

Mathematical Expression 58

[0300]

[0301]

Mathematical Expression 59

[0302]

[0303] Then, the measuring device 1 performs a measurement from the inherent vibration u according to equation (60). nv Subtract the fundamental period T from (t) N For natural vibration u nv (t) High-pass filtering is applied to reduce the low-frequency signal components of the vibration by performing moving average processing, and the natural vibration u is calculated. nv_hp (t). This moving average process requires little computation, and the fundamental frequency F N The attenuation of the signal components and their higher harmonic components is very large, thus it is possible to obtain low-frequency signal components with effectively reduced vibration components. Therefore, according to equation (60), the natural vibration u with effectively reduced low-frequency signal components is obtained. nv_hp (t). Figure 23 The frequency characteristics of the high-pass filter according to equation (60) are shown. Additionally, Figure 24 The inherent vibration u is shown nv_hp An example of (t).

[0304]

Mathematical Expression 60

[0305]

[0306] It should be noted that, as a high-pass filter, measuring device 1 can also process the natural vibration u. nv (t) is performed to make the fundamental frequency F N FIR filtering for attenuation of low-frequency signal components, and calculation of natural vibration u. nv_hp (t).

[0307] Furthermore, the measuring device 1 performs a process that causes the natural vibration u nv_hp The fundamental frequency F included in (t) N The higher harmonic components of the vibrational components are attenuated, and the fundamental frequency F is corrected. N The gain is low-pass filtered to calculate the natural vibration u, which is the second dynamic response. nv_31p (t). For example, in Figure 22 The natural vibration u shown nv In the power spectral density of (t), the third harmonic component is large. Therefore, in order to attenuate the third harmonic component, the measuring device 1 calculates the fundamental period T as shown in equation (61). N The moving average interval k is adjusted to the time resolution of the data by dividing the period by 3 times ΔT. mL Among them, 3T N >2ΔT.

[0308]

Mathematical Expression 61

[0309]

[0310] If the moving average interval kmL The natural vibration u nv_hp (t) is processed using a moving average, then due to the fundamental frequency F N 3F, which is 3 times its frequency N The frequency intervals are small, therefore, as Figure 25 As shown, the fundamental frequency F N Gain g N Less than 1. Since the transfer characteristic of the moving average filter is represented by equation (62), the measuring device 1 can calculate ω = 2πF according to equation (62). N Gain g at time N .

[0311]

Mathematical Expression 62

[0312]

[0313] Therefore, let the fundamental frequency F be... N The gain correction factor is g, which is set to 1. N -1 The measuring device 1 causes the natural vibration u according to equation (63). nv The third harmonic component included in (t) is attenuated, and the fundamental frequency F is reduced. N The gain is corrected to 1 by low-pass filtering, and the natural vibration u, which is the second dynamic response, is calculated. nv_31p (t). The natural vibration u calculated in this way nv_31p (t) can basically be regarded as a natural vibration u nv The fundamental frequency F included in (t) N The vibrational components. Figure 26 The inherent vibration u is shown nv_31p An example of (t).

[0314]

Mathematical Expression 63

[0315]

[0316] It should be noted that in the natural vibration u nv When the second harmonic component included in (t) is large, the measuring device 1 performs a moving average process to attenuate the second harmonic component. Additionally, in the case of the inherent vibration u... nv When both the second and third harmonic components included in (t) are large, the measuring device 1 only needs to perform both moving average processing to attenuate the second harmonic component and moving average processing to attenuate the third harmonic component. Generalized, then in the natural vibration u... nv If the nth harmonic component included in (t) is large, the measuring device 1 only needs to perform a moving average process to attenuate the nth harmonic component.

[0317] In addition, as a low-pass filter, the measuring device 1 can also process the natural vibration u. nv_hp (t) is performed to make the fundamental frequency F N FIR filtering for attenuation of high-frequency signal components, and calculation of natural vibration u. nv_31p (t).

[0318] It should be noted that, for measuring device 1, the natural vibration u nv (t) The case of performing high-pass filtering followed by low-pass filtering has been explained, but the measuring device 1 can also perform low-pass filtering on the natural vibration u. nv (t) After low-pass filtering, high-pass filtering is performed. Additionally, in the natural vibration u... nv The frequency F included in (t) is the fundamental frequency. N When the low-frequency signal components are small, the measuring device 1 may not need to perform high-pass filtering.

[0319] Next, measuring device 1 calculates the natural vibration u. nv_31p The envelope amplitude u of (t) nv_mag (t). Specifically, due to the inherent vibration u nv_3lp (t) can be roughly considered as the fundamental frequency F N The vibration components, therefore the measuring device 1 sets the wave height ratio to π / 2, and according to equation (64), for the natural vibration u nv_3lp The absolute value of (t) is low-pass filtered to calculate the envelope amplitude u. nv_mag (t). Figure 27 Show the envelope amplitude u nv_mag An example of (t).

[0320]

Mathematical Expression 64

[0321]

[0322] Natural vibration u nv_31p The absolute value of (t) includes the fundamental frequency F. N The signal components have a frequency twice that of 2F, therefore the passband of the low-pass filter is preferably located at a frequency greater than 2F. N The low range. For example, in the case of low-pass filtering as shown in equation (64) which is a moving average process, if the moving average interval length t is... MA Let's say we divide the integer k by the fundamental frequency F. N The value after that, let k = 4, F N =2.7917Hz, ΔT =0.012 seconds, then as shown in equation (65), t MA =118ΔT is sufficient.

[0323]

Mathematical Expression 65

[0324]

[0325] Next, the measuring device 1 measures the natural vibration u nv_31p In the first interval T1, which includes at least a portion of the interval where the vibrational components decay, the envelope amplitude u is approximated using an exponential function. nv_mag (t). The first interval T1 starts from time t. e0 At time t e1 The interval, the start time t of the first interval T1 e0 It is the departure time t o Later, for example, the measuring device 1 can also calculate the time t at which the last axle of the railway vehicle 6 exits the superstructure 7 according to equation (66). out The range of time t that satisfies equation (67) is taken as the first interval T1. Based on the relationships between equations (7), (12), and (66) above, the exit time t... out With departure time t o They are equal, therefore the starting time t of the first interval T1 that satisfies equation (67) is equal. e0 It is the departure time t o after.

[0326]

Mathematical Expression 66

[0327]

[0328]

Mathematical Expression 67

[0329] t out <t e0 ≤t≤t e1 …(67)

[0330] The start time t of the first interval T1 e0 and the end time t e1 For example, in the envelope amplitude u shown in equation (68) nv_mag The logarithm y(t) of (t) is chosen within a range that is approximately linear. Figure 28 Show the envelope amplitude u nv_mag The logarithm y(t) of (t) and an example of the first interval T1.

[0331]

Mathematical Expression 68

[0332] y(t)=ln{u nv_mag (t)}…(68) as Figure 28 As shown, after the railway vehicle 6 passes, the logarithm y(t) in the first interval T1 of vibration attenuation in the superstructure 7 is approximately linear. The logarithm y(t) in the first interval T1 is approximated by the linear function Q(t) shown in equation (69).

[0333]

Mathematical Expression 69

[0334] Q(t)q1t+q0…(69)

[0335] The measuring device 1 calculates the first-order coefficient q1 and the zero-order coefficient q0 that minimize the difference between the error e(t) expressed by equation (70), i.e. the logarithm y(t) and the linear function Q(t) of equation (69), using the least squares method.

[0336]

Mathematical Expression 70

[0337] e(t)=y(t)-(q1t+q0)…(70)

[0338] The first-order coefficient q1 and the zero-order coefficient q0 are calculated according to equations (71) and (72), respectively. Here, the data interval corresponding to the approximate time interval is set as t. e0 ≤t≤t e1 .

[0339]

Mathematical Expression 71

[0340]

[0341]

Mathematical Expression 72

[0342]

[0343] If we approximate the envelope amplitude u in the first interval T1 nv_mag The exponential function of (t) is set as the damped vibration curve u. env_b (t), then the damped vibration curve u env_b (t) is calculated using the first-order coefficient q1 and the zero-order coefficient q0 according to equation (73).

[0344]

Mathematical Expression 73

[0345]

[0346] On the other hand, according to the equation of motion, the damped vibration u b (t) is represented by equation (74). In equation (74)...

[0347] In this context, ζ is the decay rate, and ω is the natural vibration number.

[0348]

Mathematical Expression 74

[0349]

[0350] If the damped vibration u is made b The envelope portion of (t) and the damped vibration curve u env_b (t) corresponds to the equation (75).

[0351]

Mathematical Expression 75

[0352]

[0353] The attenuation rate ζ is calculated according to equation (75) and equation (76).

[0354]

Mathematical Expression 76

[0355]

[0356] If the damped vibration u is made b The initial value of the envelope portion of (t) and the initial time t of the first interval T1. e0 The damped vibration curve u env_b The amplitude of (t) corresponds to the equations (77) and (78).

[0357]

Mathematical Expression 77

[0358]

[0359]

Mathematical Expression 78

[0360]

[0361] damped vibration u env (t) is represented by equation (79). Figure 29 Overlapping shows damped vibration u env (t) and the inherent vibration u as the second dynamic response nv_31p (t). For example... Figure 29 As shown, damped vibration u env (t) and natural vibration u nv_31p (t) Approximates with high precision.

[0362]

Mathematical Expression 79

[0363]

[0364] 3. Measurement Method Steps

[0365] Figure 30 This is a flowchart illustrating an example of the steps of the measurement method according to this embodiment. In this embodiment, the measuring device 1 performs... Figure 30 The steps are shown.

[0366] like Figure 30 As shown, firstly, in the observation data acquisition process S10, the measuring device 1 acquires acceleration data a(k) as observation data output from the sensor 2, which is the observation device.

[0367] Next, in the first measurement data generation step S20, the measuring device 1 generates measurement data u(t) as the first measurement data based on the acceleration data a(k) acquired as observation data in step S10, which is a physical quantity representing the response of the multiple axles of the railway vehicle 6 moving on the superstructure 7 to the observation point R. An example of the steps in the first measurement data generation step S20 will be described later.

[0368] Next, in the second measurement data generation step S30, the measuring device 1 generates measurement data u, which is a second measurement data with reduced vibration components, obtained by filtering the measurement data u(t) generated in step S20. lp (t). For example, as a filtering process, the measuring device 1 performs a filtering operation to make the fundamental frequency F of the measured data u(t) equal to the fundamental frequency F. f The vibrational components at the above frequencies are attenuated by low-pass filtering. An example of the steps in the second measurement data generation process S30 will be described later.

[0369] Next, in the observation information generation process S40, the measuring device 1 generates the entry time t of the railway vehicle 6 relative to the superstructure 7. i and departure time t o Observational information. Entering time t i It is the time when the first axle of the multiple axles of railway vehicle 6 passes the entry end of the superstructure 7, and the departure time t. o It is the moment when the last axle of the multiple axles of the railway vehicle 6 passes the departure end of the superstructure 7. In this embodiment, the measuring device 1 is based on the measurement data u generated in process S30. lp (t), calculate the entry time t i and departure time t o Furthermore, measuring device 1 generates the number of vehicles C. T An example of the steps in the observation information generation process S40 will be described later.

[0370] Next, in the average speed calculation step S50, the measuring device 1 calculates the average speed v of the railway vehicle 6 based on the observation information generated in step S40 and environmental information including the dimensions of the pre-fabricated railway vehicle 6 and the dimensions of the superstructure 7. a Environmental information includes the length L of the superstructure 7. B The location of observation point R L x The length L of each of the 6 railway vehicles C (C m ), Number of axles a for each vehicle T (C m) and the distance La(a) between each axle at each position of multiple axles of railway vehicle 6. w (C m An example of the steps in the average speed calculation process S50 will be described later.

[0371] Next, in the first deflection calculation step S60, the measuring device 1 calculates the deflection of the upper structure 7 as an approximation of the above formula (35), the observation information generated in step S40, the environmental information, and the average speed v of the railway vehicle 6 calculated in step S50. a Calculate the deflection T, which is the first deflection of the superstructure 7 caused by the railway vehicle 6. std (t). Specifically, the measuring device 1 is based on an approximation of the deflection of the upper structure 7, observation information, environmental information, and average velocity v. a Calculate the deflection w of the superstructure 7 caused by multiple axles. std (a w (C m ,n),t), the deflection w of the superstructure 7 caused by multiple axles respectively std (a w (C m The deflection T is calculated by adding n and t. std (t). An example of the steps in the first deflection calculation process S60 will be described later.

[0372] Next, in the second deflection calculation step S70, the measuring device 1 calculates the deflection T calculated in step S60 as a comparison. std (t) The deflection T of the second deflection component, which is reduced by filtering, is the amount of deflection that reduces the vibration component. std_lp (t). For example, as a filtering process, the measuring device 1 performs a deflection T. std The fundamental frequency F of (t) M The vibration components at the above frequencies are attenuated by low-pass filtering. An example of the steps in the second deflection calculation process S70 will be described later.

[0373] Next, in the coefficient calculation step S80, the measuring device 1 uses the deflection T calculated in step S70. std_lp The measurement data u generated in process S30 is approximated by a linear function of (t). lp (t), calculate the first-order coefficient c1 and the zero-order coefficient c0 of the linear function. Specifically, the measuring device 1 is as shown in equation (47) above, using the deflection T std_lp To approximate the measurement of data u using a linear function of (t). lp(t), and using the least squares method according to the above equations (49) and (50), calculate the first-order coefficient c1 and the zero-order coefficient c0.

[0374] Next, in the third deflection calculation step S90, the measuring device 1 calculates the first-order coefficient c1 and the zero-order coefficient c0 based on the calculation in step S80, and the deflection T calculated in step S70. std_lp (t), calculate the deflection T as the third deflection. Estd_lp (t). Specifically, the measuring device 1 calculates the deflection T as shown in equation (51) above. Estd_lp (t), the deflection T Estd_lp (t) at entry time t i Previous interval and departure time t o The subsequent interval contains the first-order coefficient c1 and the deflection T. std_lp The product of (t) c1T std_lp (t), at the entry time t i With departure time t o The interval between them is the product c1T std_lp (t) and the sum of the zero-order coefficient c0.

[0375] Next, in the offset calculation step S100, the measuring device 1 calculates the zero-order coefficient c0 calculated in step S80 and the deflection T calculated in step S70. std_lp (t) and the deflection T calculated in process S90 Estd_lp (t), calculate the offset T offset_std (t). An example of the steps in the offset calculation process S100 will be described later.

[0376] Next, in the static response calculation step S110, the measuring device 1, as shown in the above formula (56), calculates the first-order coefficient c1 calculated in step S80 and the deflection T calculated in step S60. std The product of (t) c1T std (t), and the offset T calculated in process S100 offset_std Add (t) together to calculate the deflection T as the static response. EOstd (t).

[0377] Next, in the first dynamic response calculation step S120, the measuring device 1, as shown in the above formula (57), subtracts the deflection amount T, which is the static response calculated in step S110, from the measurement data u(t) generated in step S20. EOstd (t), calculate the natural vibration u as the first dynamic response. nv (t).

[0378] Next, in the second dynamic response calculation step S130, the measuring device 1 calculates the natural vibration u, which is the first dynamic response, from the calculation in step S120. nv (t) Filtering to attenuate unwanted signals and calculating the natural vibration u as the second dynamic response. nv_3lp (t). This filtering process may also include reducing the inherent vibration u. nv The fundamental frequency F included in (t) N The higher harmonic components of the vibrational components are attenuated, and the fundamental frequency F is corrected. N The gain is low-pass filtered. Furthermore, this filtering process may also include reducing the gain compared to the fundamental frequency F. N High-pass filtering attenuates low-frequency signal components. An example of the steps in the second dynamic response calculation process S130 will be described later.

[0379] Next, in the envelope amplitude calculation step S140, the measuring device 1 calculates the natural vibration u, which is the second dynamic response, calculated in step S130. nv_31p The envelope amplitude u of (t) nv_mag (t). Specifically, the measuring device 1, as shown in equation (64) above, measures the natural vibration u. nv_31p The absolute value of (t) is low-pass filtered and multiplied by π / 2 to calculate the envelope amplitude u. nv_mag (t).

[0380] Next, in the attenuation rate calculation step S150, the measuring device 1 calculates the envelope amplitude u based on the calculation in step S140. nv_mag (t), calculate the natural vibration u as the second dynamic response. nv_3lp The attenuation rate ζ of the vibration component included in (t). An example of the steps in the attenuation rate calculation process S150 will be described later.

[0381] Next, in the measurement data output step S160, the measuring device 1 outputs the measurement data, including the attenuation rate ζ calculated in step S150, to the monitoring device 3. Specifically, the measuring device 1 transmits the measurement data to the monitoring device 3 via the communication network 4. In addition to the attenuation rate ζ, the measurement data may also include the measured data u(t), u... lp (t), deflection T std (t), T std_lp (t), T Estd_lp (t), deflection T EOstd (t), natural vibration u nv (t), u nv_3lp (t) and envelope amplitude u nv_mag (t) etc.

[0382] Then, the measuring device 1 repeatedly performs the processes S10 to S160 until the measurement ends in process S170.

[0383] Figure 31 It is shown Figure 30 A flowchart of an example of the steps in the first measurement data generation process S20.

[0384] like Figure 31 As shown, in process S201, the measuring device 1 integrates the acceleration data a(t) output from the sensor 2 to generate velocity data v(t), as shown in the above formula (1).

[0385] Then, in process S202, the measuring device 1 integrates the velocity data v(t) generated in process S201 to generate measurement data u(t), as shown in equation (2) above.

[0386] In this embodiment, the measured data u(t) is data on the displacement of the superstructure 7 caused by the railway vehicle 6, which is a moving body moving on the superstructure 7, which is a structure. It is data obtained by integrating twice the acceleration in the direction intersecting the surface of the superstructure 7 moving with the railway vehicle 6. Therefore, the measured data u(t) includes waveforms that bulge in the positive or negative direction; specifically, it includes data on rectangular waveforms, trapezoidal waveforms, or sinusoidal half-wave waveforms. It should be noted that rectangular waveforms include not only true rectangular waveforms but also waveforms that approximate rectangular waveforms. Similarly, trapezoidal waveforms include not only true trapezoidal waveforms but also waveforms that approximate trapezoidal waveforms. Likewise, sinusoidal half-wave waveforms include not only true sinusoidal half-wave waveforms but also waveforms that approximate sinusoidal half-wave waveforms.

[0387] Figure 32 It is shown Figure 30 A flowchart of an example of the second measurement data generation process S30.

[0388] like Figure 32 As shown, in process S301, measuring device 1 pairs... Figure 31 The measured data u(t) calculated in process S202 is processed by high-speed Fourier transform to calculate the power spectral density, and the peak value of the power spectral density is calculated as the fundamental frequency F. f .

[0389] Then, in process S302, the measuring device 1 sets the fundamental frequency F of the measured data u(t) to... f The measurement data is generated by low-pass filtering of the vibrational components at the above frequencies. lp (t). As a low-pass filter, the measuring device 1 can also be as shown in equation (5) above, to be connected to the fundamental frequency F. f The corresponding basic period Tf The measured data u(t) is processed by moving average to generate the measured data u. lp (t). Alternatively, as a low-pass filter, the measuring device 1 can also perform a low-pass filtering process on the measured data u(t) to make the fundamental frequency F. f The above frequency signal components are attenuated by FIR filtering to generate measurement data. lp (t).

[0390] Figure 33 It is shown Figure 30 A flowchart of an example of the steps in the observation information generation process S40.

[0391] like Figure 33 As shown, firstly, in process S401, the measuring device 1 calculates the value of the sample according to the above formula (6). Figure 32 The measurement data u generated in process S302 lp The average value of the amplitude shift of (t) over the interval from time t1 to time t2 is used as the amplitude u. a .

[0392] Next, in process S402, the measuring device 1 calculates the measurement data u. lp The amplitude of (t) and the predetermined coefficient C L And the amplitude u calculated in process S401 a Threshold C of the product L u a Consistent, or exceeding the threshold C L u a The first moment, as the entry moment t i .

[0393] In addition, in process S403, measuring device 1 calculates the measurement data u. lp The amplitude of (t) and the threshold C L u a Consistent, or exceeding the threshold C L u a The second moment after the first moment, as the departure moment t o .

[0394] In addition, in process S404, the measuring device 1 calculates the departure time t as shown in equation (7) above. o and entry time t i The difference, as a result of time t s .

[0395] Next, in step S405, the measuring device 1 calculates the transit time t calculated in step S404, as shown in equation (8) above. s and in Figure 32The fundamental frequency F calculated in process S301 f product t s F f The largest integer less than or equal to the number after subtracting 1 from the given number is taken as the number of railway vehicles C in the 6-car fleet. T .

[0396] Then, in step S406, measuring device 1 generates the entry time t calculated in step S402. i The departure time t calculated in process S403 o The throughput time t calculated in process S404 s and the number of vehicles C calculated in process S405 T Observational information.

[0397] Figure 34 It is shown Figure 30 A flowchart of an example of the steps in the average speed calculation process S50.

[0398] In process S501, the measuring device 1 calculates the distance D from the first axle to the last axle of the railway vehicle 6 based on environmental information and according to the above formula (11). wa (a w (C T ,a T (C T ))).

[0399] Furthermore, in process S502, the measuring device 1 calculates the distance from the entry end to the exit end of the upper structure 7 based on environmental information. In this embodiment, the distance from the entry end to the exit end of the upper structure 7 is the length L of the upper structure 7 included in the environmental information. B .

[0400] Then, in process S503, the measuring device 1 is based on... Figure 33 The entry time t is included in the observation information generated in process S406. i and departure time t o The distance D calculated in process S501 from the first axle to the last axle of railway vehicle 6. wa (a w (C T ,a T (C T The length L of the upper structure 7, calculated in process S502, is the distance from the entry end to the exit end of the upper structure 7. B According to the above formula (12), the average speed v of the railway vehicle 6 is calculated. a .

[0401] Figure 35It is shown Figure 30 A flowchart of an example of the steps in the first deflection calculation process S60.

[0402] First, in process S601, the measuring device 1, based on environmental information and according to the above formula (10), calculates the distance from the first axle of the railway vehicle 6 to the Cth axle. m The distance D of the nth axle of a vehicle wa (a w (C m ,n)).

[0403] Next, in process S602, the measuring device 1 uses the location L of the observation point R included in the environmental information. x and in Figure 34 The average speed v calculated in process S503 a According to the above formula (37), the position L of any axle of the railway vehicle 6 from the entry end of the superstructure 7 to the observation point R is calculated. x The required time t xn .

[0404] Additionally, in process S603, the measuring device 1 is used in... Figure 34 The length L of the upper structure 7, calculated in process S502, is the distance from the entry end to the exit end of the upper structure 7. B and average velocity v a According to the above formula (38), the time t required for any axle of the railway vehicle 6 to pass through the superstructure 7 is calculated. ln .

[0405] Furthermore, in process S604, the measuring device 1 is used in... Figure 33 The entry time t is included in the observation information generated in process S406. i The distance D calculated in process S601 wa (a w (C m ,n)) and average velocity v a According to the above formula (39), the Cth digit of the railway vehicle 6 is calculated respectively. m The time t0(C) when the nth axle of a vehicle reaches the entry end of the superstructure 7. m ,n).

[0406] Next, in step S605, the measuring device 1 uses the approximate formula for the deflection of the upper structure 7 as described in equation (35), and the time t calculated in step S602. xn The time t calculated in process S603 ln and the time t0(C) calculated in process S604 mAccording to the above formula (40), calculate the value of C from the first n). m The deflection w of the superstructure 7 caused by the nth axle of a vehicle std (a w (C m ,n),t).

[0407] Next, in process S606, the measuring device 1 measures the amount of deflection w of the superstructure 7 caused by each axle, which will be calculated in process S605 for each vehicle, according to the above formula (42). std (a w (C m Add the values ​​of n and t to calculate the deflection C of the superstructure 7 caused by each vehicle. std (C m ,t).

[0408] Then, in process S607, the measuring device 1 measures the amount of deflection C of the upper structure 7 caused by each vehicle, calculated in process S606, according to the above formula (43). std (C m Add the values ​​of t and t to calculate the deflection T of the superstructure 7 caused by the railway vehicle 6. std (t).

[0409] Figure 36 It is shown Figure 30 A flowchart of an example of the steps in the second deflection calculation process S70.

[0410] like Figure 36 As shown, in process S701, measuring device 1 pairs... Figure 35 The deflection T calculated in process S607 std (t) Perform high-speed Fourier transform processing to calculate the power spectral density, and calculate the peak value of the power spectral density as the fundamental frequency F. M .

[0411] Then, in process S702, the measuring device 1 measures the deflection amount T. std The fundamental frequency F of (t) M The deflection T is calculated by low-pass filtering the vibration components at the above frequencies after attenuation. std_lp (t). As a low-pass filtering process, the measuring device 1 can also be as shown in equation (46) above, to be connected to the fundamental frequency F. M The corresponding basic period T M For the deflection T std (t) is processed using a moving average to calculate the deflection T. std_lp (t). Alternatively, as a low-pass filter, the measuring device 1 can also measure the deflection T. std (t) is used to make the fundamental frequency F MThe deflection T is calculated by attenuating the signal components at the above frequencies using FIR filtering. std_lp (t).

[0412] Figure 37 It is shown Figure 30 A flowchart of an example of the steps in the offset calculation process S100.

[0413] like Figure 37 As shown, in process S1001, measuring device 1 calculates the value of a given interval according to the above formula (54). Figure 30 The deflection T calculated in process S90 Estd_lp (t) and in Figure 36 The deflection T calculated in process S702 std_lp The amplitude ratio of (t) to R T .

[0414] Then, in step S1002, the measuring device 1, as shown in the above formula (55), measures the amplitude ratio R calculated in step S1001. T and deflection T std_lp The product R of (t) T T std_lp The absolute value of (t) is greater than in Figure 30 The product R of the absolute values ​​of the zero-order coefficient c0 calculated in process S80 T T std_lp Replace the interval of (t) with the zero-order coefficient c0, and calculate the offset T. offset_std (t).

[0415] Figure 38 It is shown Figure 30 A flowchart of an example of the steps in the second dynamic response calculation process S130.

[0416] like Figure 38 As shown, in process S1301, the measuring device 1 performs measurement from the above formula (60) according to the formula. Figure 30 The natural vibration u calculated in process S120 nv Subtract the fundamental period T from (t) N For natural vibration u nv (t) High-pass filtering is applied to reduce the low-frequency signal components of the vibration by performing moving average processing, and the natural vibration u is calculated. nv_hp (t).

[0417] Furthermore, in process S1302, the measuring device 1 performs a measurement based on the above formula (63) to measure the natural vibration u calculated in process S1301. nv_hp The fundamental frequency F included in (t) N The higher harmonic components of the vibrational components are attenuated, and the fundamental frequency F is corrected.N The gain is low-pass filtered to calculate the natural vibration u, which is the second dynamic response. nv_31p (t).

[0418] Figure 39 It is shown Figure 30 A flowchart of an example of the steps in the attenuation rate calculation process S150.

[0419] like Figure 39 As shown, in process S1501, the measuring device 1 is used as a... Figure 38 The natural vibration u of the second dynamic response calculated in process S1302 nv_3lp In the first interval T1, which includes at least a portion of the interval where the vibrational components decay in (t), an exponential function is used to approximate the decay. Figure 30 The envelope amplitude u calculated in process S140 nv_mag (t), calculate the coefficient q1 of the exponential function. The starting time t of the first interval T1. e0 It is the departure time t o Later, for example, the measuring device 1, as shown in equation (69) above, uses a linear function Q(t) to approximate the envelope amplitude u in the first interval T1. nv_mag The logarithm y(t) of (t) is used to calculate the coefficient q1 of the power according to the above formula (71).

[0420] In step S1502, the measuring device 1, as shown in equation (76) above, divides the coefficient q1 of the power calculated in step S1501 by the natural vibration u, which is the second dynamic response. nv_3lp The natural vibration number of (t) is ω = 2πF N Calculate the attenuation rate ζ.

[0421] 4. Composition of observation, measuring, and monitoring devices

[0422] Figure 40 This is a diagram showing an example of the configuration of the sensor 2, the measuring device 1, and the monitoring device 3 as an observation device.

[0423] like Figure 40 As shown, sensor 2 includes a communication unit 21, an acceleration sensor 22, a processor 23, and a storage unit 24.

[0424] The storage unit 24 is a memory that stores various programs and data for the processor 23 to perform calculations and control processing. In addition, the storage unit 24 stores programs and data for the processor 23 to implement specified application functions.

[0425] Accelerometer 22 detects the acceleration generated in each of the three axes.

[0426] The processor 23 controls the accelerometer 22 by executing the observation program 241 stored in the storage unit 24, generates observation data 242 based on the acceleration detected by the accelerometer 22, and stores the generated observation data 242 in the storage unit 24. In this embodiment, the observation data 242 is acceleration data a(k).

[0427] The communication unit 21, under the control of the processor 23, sends the observation data 242 stored in the storage unit 24 to the measuring device 1.

[0428] like Figure 40 As shown, the measuring device 1 includes a first communication unit 11, a second communication unit 12, a storage unit 13, and a processor 14.

[0429] The first communication unit 11 receives observation data 242 from the sensor 2 and outputs the received observation data 242 to the processor 14. As described above, the observation data 242 is acceleration data a(k).

[0430] Storage unit 13 is a memory that stores programs and data used by processor 14 for computational and control processing. In addition, storage unit 13 stores various programs and data used by processor 14 to implement specified application functions. Furthermore, processor 14 can also receive various programs and data via communication network 4 and store them in storage unit 13.

[0431] The processor 14 generates measurement data 135 based on the observation data 242 received by the first communication unit 11 and the environmental information 132 pre-stored in the storage unit 13, and stores the generated measurement data 135 in the storage unit 13.

[0432] In this embodiment, the processor 14 executes the measurement program 131 stored in the storage unit 13, and functions as an observation data acquisition unit 141, a first measurement data generation unit 142, a second measurement data generation unit 143, an observation information generation unit 144, an average velocity calculation unit 145, a first deflection calculation unit 146, a second deflection calculation unit 147, a coefficient calculation unit 148, a third deflection calculation unit 149, an offset calculation unit 150, a static response calculation unit 151, a first dynamic response calculation unit 152, a second dynamic response calculation unit 153, an envelope amplitude calculation unit 154, an attenuation rate calculation unit 155, and a measurement data output unit 156. That is, the processor 14 includes an observation data acquisition unit 141, a first measurement data generation unit 142, a second measurement data generation unit 143, an observation information generation unit 144, an average velocity calculation unit 145, a first deflection calculation unit 146, a second deflection calculation unit 147, a coefficient calculation unit 148, a third deflection calculation unit 149, an offset calculation unit 150, a static response calculation unit 151, a first dynamic response calculation unit 152, a second dynamic response calculation unit 153, an envelope amplitude calculation unit 154, an attenuation rate calculation unit 155, and a measurement data output unit 156.

[0433] The observation data acquisition unit 141 acquires the observation data 242 received by the first communication unit 11 and stores it as observation data 133 in the storage unit 13. That is, the observation data acquisition unit 141 performs... Figure 30 The processing of observation data acquisition step S10 in the process.

[0434] The first measurement data generation unit 142 reads the observation data 133 stored in the storage unit 13, and generates measurement data u(t) based on the acceleration data a(t) of the observation data 133, which is the first measurement data based on the acceleration as a physical quantity, wherein the physical quantity is the response of the multiple axles of the railway vehicle 6 moving on the upper structure 7 to the observation point R. Specifically, as shown in equation (1) above, the first measurement data generation unit 142 integrates the acceleration data a(t) of the observation data 133 to generate velocity data v(t), and then, as shown in equation (2) above, integrates the velocity data v(t) to generate measurement data u(t). That is, the first measurement data generation unit 142 performs... Figure 30 The first measurement data generation step S20 in the process specifically involves... Figure 31 The processing of processes S201 and S202.

[0435] The second measurement data generation unit 143 generates measurement data u(t) as second measurement data with reduced vibration components by filtering the measurement data u(t) generated by the first measurement data generation unit 142. lp(t). For example, as a filtering process, the second measurement data generation unit 143 sets the fundamental frequency F of the measurement data u(t) to... f The vibrational components at the above frequencies are attenuated by low-pass filtering. Specifically, the second measurement data generation unit 143 performs high-speed Fourier transform processing on the measurement data u(t) to calculate the power spectral density, and calculates the peak value of the power spectral density as the fundamental frequency F. f The fundamental frequency F of the measured data u(t) is determined. f The measurement data is generated by low-pass filtering of the vibrational components at the above frequencies. lp (t). As a low-pass filtering process, the second measurement data generation unit 143 can also be as shown in equation (5) above, to be connected to the fundamental frequency F. f The corresponding basic period T f The measured data u(t) is processed by moving average to generate the measured data u. lp (t). Alternatively, as a low-pass filtering process, the second measurement data generation unit 143 can also perform a fundamental frequency F on the measurement data u(t). f The above frequency signal components are attenuated by FIR filtering to generate measurement data. lp (t). That is, the second measurement data generation unit 143 performs... Figure 30 The second measurement data generation step S30 in the process specifically involves performing... Figure 32 The processing of processes S301 and S302.

[0436] The observation information generation unit 144 generates measurement data u based on the measurement data generated by the second measurement data generation unit 143. lp (t), generating the entry time t of the railway vehicle 6 relative to the superstructure 7. i and departure time t o The observation information 134 is stored in the storage unit 13. Specifically, firstly, the observation information generation unit 144 calculates the measurement data u according to the above formula (6). lp The average value of the amplitude shift of (t) over the interval from time t1 to time t2 is used as the amplitude u. a Next, the observation information generation unit 144 calculates the measured data u. lp The amplitude of (t) and the predetermined coefficient C L and amplitude u a Threshold C of the product L u a Consistent, or exceeding the threshold C L u a The first moment, as the entry moment t i In addition, the observation information generation unit 144 calculates the measurement data u. lp The amplitude of (t) and the threshold CL u a Consistent, or exceeding the threshold C L u a The second moment after the first moment, as the departure moment t o Furthermore, the observation information generation unit 144, as shown in equation (7) above, calculates the departure time t. o and entry time t i The difference, as a result of time t s Next, the observation information generation unit 144, as shown in equation (8) above, calculates the time from the passage time t. s and fundamental frequency F f product t s F f The largest integer less than or equal to the number after subtracting 1 from the given number is taken as the number of railway vehicles C in the 6-car fleet. T Then, the observation information generation unit 144 generates information including the entry time t. i Departure time t o Through time t s and the number of vehicles C T The observation information 134. That is, the observation information generation unit 144 performs... Figure 30 The processing of observation information generation step S40 in the process, specifically, involves... Figure 33 Processing steps S401 to S406.

[0437] The average speed calculation unit 145 calculates the average speed v of the railway vehicle 6 based on the observation information 134 stored in the storage unit 13 and the environmental information 132, including the dimensions of the railway vehicle 6 and the superstructure 7 prefabricated and stored in the storage unit 13. a Specifically, the average speed calculation unit 145 calculates the distance D from the first axle to the last axle of the railway vehicle 6 based on the environmental information 132 and according to the above formula (11). wa (a w (C T ,a T (C T Additionally, the average speed calculation unit 145 calculates the length L of the upper structure 7, which is the distance from the entry end to the exit end of the upper structure 7, based on the environmental information 132. B Then, the average velocity calculation unit 145 calculates the entry time t based on the observation information 134. i and departure time t o Distance D wa (a w (C T ,a T (C T ))) and the length L of the superstructure 7 BAccording to the above formula (12), the average speed v of the railway vehicle 6 is calculated. a That is, the average speed calculation unit 145 performs... Figure 30 The average speed calculation process S50 in the process, specifically, involves performing... Figure 34 The processing of processes S501, S502, and S503.

[0438] The first deflection calculation unit 146 calculates the average speed v of the railway vehicle 6 based on the approximate formula of the deflection of the upper structure 7 as the above formula (35), the observation information 134 stored in the storage unit 13, the environmental information 132 stored in the storage unit 13, and the average speed calculation unit 145. a Calculate the deflection T, which is the first deflection of the superstructure 7 caused by the railway vehicle 6. std (t). Specifically, firstly, the first deflection calculation unit 146, based on environmental information 132, calculates the deflection from the beginning of the axle of the railway vehicle 6 to the Cth axle according to the above formula (10). m The distance D of the nth axle of a vehicle wa (a w (C m Next, the first deflection calculation unit 146 uses the position L of the observation point R included in the environmental information 132. x and average velocity v a According to the above formula (37), the position L of any axle of the railway vehicle 6 from the entry end of the superstructure 7 to the observation point R is calculated. x The required time t xn Additionally, the first deflection calculation unit 146 uses the length L of the upper structure 7 as the distance from the entry end to the exit end of the upper structure 7. B and average velocity v a According to the above formula (38), the time t required for any axle of the railway vehicle 6 to pass through the superstructure 7 is calculated. ln Furthermore, the first deflection calculation unit 146 uses the entry time t included in the observation information 134. i Distance D wa (a w (C m ,n)) and average velocity v a According to the above formula (39), the Cth digit of the railway vehicle 6 is calculated. m The time t0(C) when the nth axle of a vehicle reaches the entry end of the superstructure 7. m Next, the first deflection calculation unit 146 uses an approximation of the deflection of the upper structure 7 as in the above formula (35), and time t. xn Time t ln and time t0(C mAccording to the above formula (40), the value of C is calculated. m The deflection w of the superstructure 7 caused by the nth axle of a vehicle std (a w (C m Next, the first deflection calculation unit 146 uses the deflection amount w std (a w (C m According to the above formula (42), calculate the result from the Cth... m The deflection C of the superstructure 7 caused by the vehicle std (C m Then, the first deflection calculation unit 146 uses the deflection C. std (C m According to the above formula (43), the deflection T of the superstructure 7 caused by the railway vehicle 6 is calculated. std (t). That is, the first deflection calculation unit 146 performs... Figure 30 The first deflection calculation step S60 in the process specifically involves performing... Figure 35 Processing steps S601 to S607.

[0439] The second deflection calculation unit 147 calculates the deflection T as calculated by the first deflection calculation unit 146. std (t) The deflection T of the second deflection component, which is reduced by filtering, is the amount of deflection that reduces the vibration component. std_lp (t). For example, as a filtering process, the second deflection calculation unit 147 performs a deflection amount T calculation. std The fundamental frequency F of (t) M The vibration components at the above frequencies undergo low-pass filtering attenuation. Specifically, the second deflection calculation unit 147 calculates the deflection T... std (t) Perform high-speed Fourier transform processing to calculate the fundamental frequency F. M And perform deflection T std The fundamental frequency F of (t) M The deflection T is calculated by low-pass filtering the vibration components at the above frequencies after attenuation. std_lp (t). As a low-pass filtering process, the second deflection calculation unit 147 can also be as shown in equation (46) above, to be related to the fundamental frequency F. M The corresponding basic period T M For the deflection T std (t) is processed using a moving average to calculate the deflection T. std_lp (t). Alternatively, as a low-pass filtering process, the second deflection calculation unit 147 can also calculate the deflection T. std (t) is used to make the fundamental frequency F MThe deflection T is calculated by attenuating the signal components at the above frequencies using FIR filtering. std_lp (t). That is, the second deflection calculation unit 147 performs... Figure 30 The second deflection calculation step S70 in the process specifically involves performing... Figure 36 The processing of processes S701 and S702.

[0440] The coefficient calculation unit 148 uses the deflection T calculated by the second deflection calculation unit 147. std_lp The measurement data u generated by the second measurement data generation unit 143 is approximated by a linear function of (t). lp (t), and calculate the first-order coefficient c1 and the zero-order coefficient c0 of the linear function. Specifically, the coefficient calculation unit 148 is as shown in equation (47) above, using the deflection T std_lp To approximate the measurement of data u using a linear function of (t). lp (t), and using the least squares method according to the above equations (49) and (50), calculate the first-order coefficient c1 and the zero-order coefficient c0. That is, the coefficient calculation unit 148 performs... Figure 30 The coefficient calculation process S80 in the process.

[0441] The third deflection calculation unit 149 calculates the first-order coefficient c1 and the zero-order coefficient c0 based on the coefficient calculation unit 148, and the deflection T calculated by the second deflection calculation unit 147. std_lp (t), calculate the deflection T as the third deflection. Estd_lp (t). Specifically, the third deflection calculation unit 149 calculates the deflection T as shown in the above formula (51). Estd_lp (t), the deflection T Estd_lp (t) at entry time t i Previous interval and departure time t o The subsequent interval contains the first-order coefficient c1 and the deflection T. std_lp The product of (t) c1T std_lp (t), at the entry time t i With departure time t o The interval between them is the product c1T std_lp The sum of (t) and the zero-order coefficient c0. That is, the third deflection calculation unit 149 performs... Figure 30 The third deflection calculation step S90 in the process.

[0442] The offset calculation unit 150 calculates the zero-order coefficient c0 based on the coefficient calculation unit 148 and the deflection T calculated by the second deflection calculation unit 147. std_lp (t) and the deflection T calculated by the third deflection calculation unit 149 Estd_lp (t), calculate the offset T offset_std(t). Specifically, the offset calculation unit 150 calculates the deflection T in the specified interval according to the above formula (54). Estd_lp (t) and deflection T std_lp The amplitude ratio of (t) to R T Then, the offset calculation unit 150 calculates the amplitude ratio R as shown in equation (55) above. T and deflection T std_lp The product R of (t) T T std_lp Replace the interval of (t) with a coefficient c0 of order less than 0 with a coefficient c0 of order 0, and calculate the offset T. offset_std (t). That is, the offset calculation unit 150 performs... Figure 30 The offset calculation process S100 in the middle, specifically, performs... Figure 37 The processing of processes S1001 and S1002.

[0443] As shown in equation (56) above, the static response calculation unit 151 calculates the first-order coefficient c1 calculated by the coefficient calculation unit 148 and the deflection T calculated by the first deflection calculation unit 146. std The product of (t) c1T std (t) and the offset T calculated by the offset calculation unit 150 offset_std Add (t) together to calculate the deflection T as the static response. EOstd (t). That is, the static response calculation unit 151 performs... Figure 30 The static response calculation process S110 in the process.

[0444] As shown in equation (56) above, the first dynamic response calculation unit 152 subtracts the deflection amount T calculated by the static response calculation unit 151 from the measurement data u(t) generated by the first measurement data generation unit 142. EOstd (t), calculate the natural vibration u as the first dynamic response. nv (t). That is, the first dynamic response calculation unit 152 performs... Figure 30 The first dynamic response calculation step S120 in the process.

[0445] The second dynamic response calculation unit 153 performs the natural vibration u, which is the first dynamic response, calculated from the first dynamic response calculation unit 152. nv (t) Filtering to attenuate unwanted signals and calculating the natural vibration u as the second dynamic response. nv_3lp (t). This filtering process may also include reducing the inherent vibration u. nv The fundamental frequency F included in (t) N The higher harmonic components of the vibrational components are attenuated, and the fundamental frequency F is corrected. NThe gain is low-pass filtered. Furthermore, this filtering process may also include reducing the gain compared to the fundamental frequency F. N High-pass filtering attenuates low-frequency signal components. For example, the second dynamic response calculation unit 153 performs high-pass filtering based on the above equation (60) from the natural vibration u. nv Subtract the fundamental period T from (t) N For natural vibration u nv (t) High-pass filtering is applied to reduce the low-frequency signal components of the vibration by performing moving average processing, and the natural vibration u is calculated. nv_hp (t). Furthermore, the second dynamic response calculation unit 153 performs calculations based on the above equation (63) to make the natural vibration u nv_hp The fundamental frequency F included in (t) N The higher harmonic components of the vibrational components are attenuated, and the fundamental frequency F is corrected. N The gain is low-pass filtered to calculate the natural vibration u, which is the second dynamic response. nv_31p (t). That is, the second dynamic response calculation unit 153 performs... Figure 30 The second dynamic response calculation step S130 in the process specifically involves performing... Figure 38 The processing of processes S1301 and S1302 in the process.

[0446] Envelope amplitude calculation unit 154 calculates the natural vibration u, which is the second dynamic response calculated by second dynamic response calculation unit 153. nv_31p The envelope amplitude u of (t) nv_mag (t). Specifically, the envelope amplitude calculation unit 154, as shown in equation (64) above, calculates the natural vibration u. nv_31p The absolute value of (t) is low-pass filtered and multiplied by π / 2 to calculate the envelope amplitude u. nv_mag (t). That is, the envelope amplitude calculation unit 154 performs... Figure 30 The process of calculating the envelope amplitude in step S140.

[0447] The attenuation rate calculation unit 155 calculates the envelope amplitude u based on the envelope amplitude calculation unit 154. nv_mag (t), the natural vibration u calculated by the second dynamic response calculation unit 153 as the second dynamic response. nv_3lp The attenuation rate ζ of the vibration component included in (t). Specifically, the attenuation rate calculation unit 155 calculates the attenuation rate of the inherent vibration u, which is the second dynamic response. nv_31p In the first interval T1, which includes at least a portion of the interval where the vibrational components decay, the envelope amplitude u is approximated using an exponential function. nv_mag (t), calculate the coefficient q1 of the exponential function. The starting time t of the first interval T1. e0 It is the departure time to Subsequently, for example, the attenuation rate calculation unit 155, as shown in equation (69) above, approximates the envelope amplitude u using a linear function Q(t) in the first interval T1. nv_mag The logarithm y(t) is used to calculate the coefficient q1 of the power according to the above equation (71). Then, the attenuation rate calculation unit 155 divides the coefficient q1 of the power by the natural vibration u as shown in the above equation (76). nv_3lp The natural vibration number of (t) is ω = 2πF N The attenuation rate ζ is calculated. That is, the attenuation rate calculation unit 155 performs... Figure 30 The attenuation rate calculation process S150 specifically involves... Figure 39 The processing of processes S1501 and S1502.

[0448] The attenuation rate ζ is stored in the storage unit 13 as at least a portion of the measurement data 135. In addition to the attenuation rate ζ, the measurement data 135 may also include the measured data u(t), u lp (t), deflection T std (t), T std_lp (t), T Estd_lp (t), T EOstd (t), natural vibration u nv (t), u nv_31p (t) and envelope amplitude u nv_mag (t) etc.

[0449] The measurement data output unit 156 reads the measurement data 135 stored in the storage unit 13 and outputs the measurement data 135 to the monitoring device 3. Specifically, under the control of the measurement data output unit 156, the second communication unit 12 transmits the measurement data 135 stored in the storage unit 13 to the monitoring device 3 via the communication network 4. That is, the measurement data output unit 156 performs... Figure 30 The measurement data output process S160 in the middle.

[0450] In this way, measurement program 131 is executed by the measuring device 1, which is a computer. Figure 30 The flowchart shown illustrates the procedure for each step.

[0451] like Figure 40 As shown, the monitoring device 3 includes a communication unit 31, a processor 32, a display unit 33, an operation unit 34, and a storage unit 35.

[0452] The communication unit 31 receives measurement data 135 from the measuring device 1 and outputs the received measurement data 135 to the processor 32.

[0453] Display unit 33 displays various information under the control of processor 32. Display unit 33 may be, for example, a liquid crystal display or an organic EL display. EL is an abbreviation for Electro Luminescence.

[0454] The operation unit 34 outputs operation data corresponding to the user's operation to the processor 32. The operation unit 34 may also be an input device such as a mouse, keyboard, or microphone.

[0455] The storage unit 35 is a memory that stores various programs and data for the processor 32 to perform calculations and control processing. In addition, the storage unit 35 stores programs and data for the processor 32 to implement specified application functions.

[0456] The processor 32 acquires the measurement data 135 received by the communication unit 31, and generates evaluation information based on the acquired measurement data 135 to evaluate the time-dependent change in the displacement of the upper structure 7, and displays the generated evaluation information on the display unit 33.

[0457] In this embodiment, the processor 32 functions as a measurement data acquisition unit 321 and a monitoring unit 322 by executing a monitoring program 351 stored in the storage unit 35. That is, the processor 32 includes a measurement data acquisition unit 321 and a monitoring unit 322.

[0458] The measurement data acquisition unit 321 acquires the measurement data 135 received by the communication unit 31 and appends the acquired measurement data 135 to the measurement data column 352 stored in the storage unit 35.

[0459] The monitoring unit 322 statistically evaluates the time-dependent change in the deflection of the superstructure 7 based on the measurement data column 352 stored in the storage unit 35. Then, the monitoring unit 322 generates evaluation information representing the evaluation results and displays the generated evaluation information on the display unit 33. Based on the evaluation information displayed on the display unit 33, the user can monitor the state of the superstructure 7.

[0460] The monitoring unit 322 can also perform monitoring of the railway vehicle 6 or anomaly determination of the superstructure 7 based on the measurement data column 352 stored in the storage unit 35.

[0461] Furthermore, based on the operation data output from the operation unit 34, the processor 32 sends information for adjusting the operating status of the measuring device 1 and the sensor 2 to the measuring device 1 via the communication unit 31. The measuring device 1 adjusts its operating status according to the information received via the second communication unit 12. Additionally, the measuring device 1 sends information received via the second communication unit 12 for adjusting the operating status of the sensor 2 to the sensor 2 via the first communication unit 11. The sensor 2 adjusts its operating status according to the information received via the communication unit 21.

[0462] It should be noted that processors 14, 23, and 32 can either have their respective functions implemented by separate hardware or by an integrated hardware unit. For example, processors 14, 23, and 32 may include hardware that can include at least one of circuitry for processing digital signals and circuitry for processing analog signals. Processors 14, 23, and 32 can also be CPUs, GPUs, or DSPs, etc. CPU is an abbreviation for Central Processing Unit, GPU is an abbreviation for Graphics Processing Unit, and DSP is an abbreviation for Digital Signal Processor. Furthermore, processors 14, 23, and 32 can be configured as custom ICs such as ASICs to implement their respective functions, or they can be implemented using both a CPU and an ASIC. ASIC is an abbreviation for Application Specific Integrated Circuit, and IC is an abbreviation for Integrated Circuit.

[0463] Furthermore, storage units 13, 24, and 35 may be composed of various IC memories such as ROM, flash ROM, and RAM, as well as recording media such as hard disks and memory cards. ROM is an abbreviation for Read Only Memory, RAM is an abbreviation for Random Access Memory, and IC is an abbreviation for Integrated Circuit. Storage units 13, 24, and 35 include computer-readable devices and non-volatile information storage devices as media, in which various programs and data can also be stored. The information storage device may also be an optical disc such as a DVD or CD, a hard disk drive, a card-type memory, or various other memories such as ROM.

[0464] It should be noted that, in Figure 40Only one sensor 2 is illustrated, but multiple sensors 2 can also generate observation data 242 and send it to the measuring device 1. In this case, the measuring device 1 receives multiple observation data 242 sent from multiple sensors 2, generates multiple measurement data 135, and sends it to the monitoring device 3. In addition, the monitoring device 3 receives the multiple measurement data 135 sent from the measuring device 1 and monitors the status of multiple superstructures 7 based on the received multiple measurement data 135.

[0465] 5. Effects

[0466] According to the measurement method of this embodiment described above, the measuring device 1 measures the deflection T by utilizing the measurement method of this embodiment. std (t) The deflection T of the vibration component is reduced by filtering. std_lp The measured data u(t) is approximated by a linear function of u(t) and filtered to reduce the vibration component. lp (t), which can separate and calculate the static response from the static and dynamic responses included in the measured data u(t).

[0467] Furthermore, according to the measurement method of this embodiment, in the measuring device 1, since the measured data u... lp (t) The first-order coefficient c1 and deflection T of the first-order term of the approximation linear function. std The product of (t) c1T std (t) is equivalent to the displacement of the superstructure 7, which is proportional to the load of the railway vehicle 6, and the offset T. offset_std (t) is equivalent to the clearance or buoyancy of the superstructure 7, or other displacements that are not proportional to the load of the railway vehicle 6. Therefore, by accumulating c1T std (t) and offset T offset_std By adding (t), the static response can be calculated with high precision.

[0468] Furthermore, according to the measurement method of this embodiment, since the measuring device 1 utilizes the deflection T std_lp The fundamental frequency F included in the measured data u(t) is approximated by a linear function of u(t). f The above vibration component measurement data u lp The accuracy of calculating the first-order coefficient c1 and the zero-order coefficient c0 of the linear function (t) is improved, thus enabling the calculation of the static response with high precision.

[0469] Furthermore, according to the measurement method of this embodiment, since the measuring device 1 calculates the offset T according to the above formula (55), which reflects the displacement of the superstructure 7 that is not proportional to the load of the railway vehicle 6, such as clearance or buoyancy, that occurs in the section where the railway vehicle 6 passes through the superstructure 7, and the displacement of the superstructure 7 does not occur in other sections. offset_std(t), thus enabling high-precision calculation of the static response.

[0470] Furthermore, according to the measurement method of this embodiment, since the measuring device 1 is able to determine the entry time t of the railway vehicle 6 onto the upper structure 7 based on the above formula (8), i and departure time t o Calculate the number C of railway vehicles 6. T Therefore, it is possible to calculate the number of vehicles C with high accuracy. T Static response of unknown railway vehicle 6 moving on superstructure 7.

[0471] Furthermore, according to the measurement method of this embodiment, since the measuring device 1 is based on measurement data u with reduced vibration components... lp (t), capable of calculating with high precision the entry time t of the railway vehicle 6 onto the upper structure 7. i and departure time t o Therefore, it is possible to calculate the static response with high accuracy.

[0472] Furthermore, according to the measurement method of this embodiment, the measuring device 1 subtracts the deflection T, which is calculated with high precision as a static response, from the measured data u(t) according to the above formula (57). EOstd (t), calculate the natural vibration u as the first dynamic response. nv (t), and furthermore, by performing filtering to attenuate unwanted signals, the natural vibration u, which is the second dynamic response, can be calculated with high accuracy. nv_31p (t).

[0473] In particular, the measuring device 1 measures the inherent vibration u nv (t) is performed to make the fundamental frequency F N High-pass filtering, which attenuates low-frequency signal components, reduces the inherent vibrations of signal components caused by low-frequency noise and environmental vibrations. nv_hp (t). The measuring device 1 measures the inherent vibration u. nv_hp (t) is used to make the fundamental frequency F N The higher harmonic components of the vibrational components are attenuated, and the fundamental frequency F is corrected. N The gain is low-pass filtered to obtain the natural vibration u with reduced higher harmonic components and enhanced fundamental frequency signal components. nv_31p (t). Therefore, according to the measurement method of this embodiment, the measuring device 1 is based on the inherent vibration u, which is calculated with high precision as the second dynamic response. nv_31p The envelope amplitude u of (t) nv_mag (t) can calculate the decay rate of dynamic response with high accuracy.

[0474] Furthermore, according to the measurement method of this embodiment, the measuring device 1 generates measurement data u(t) based on the acceleration data a(t) output from the sensor 2, and calculates the deflection T of the superstructure 7 caused by the railway vehicle 6 based on the measurement data u(t) and equation (35), which is an approximation of the deflection based on the structural model reflecting the structure of the superstructure 7 of the bridge 5. std (t). Then, the measuring device 1 used the measured data u(t) and the deflection T. std The measurement device 1 uses a relatively simple process (t) to calculate the attenuation rate of the dynamic response when the railway vehicle 6 moves on the superstructure 7. Therefore, according to the measurement method of this embodiment, the measurement device 1 can calculate the attenuation rate of the dynamic response with relatively small computational complexity.

[0475] Furthermore, according to the measurement method of this embodiment, since the actual speed of the railway vehicle 6 changes slightly but almost does not change, the measuring device 1 is set so that the railway vehicle 6 travels at a certain average speed v. a Driving, via average speed v a Calculate the deflection T std (t), which can maintain the deflection T std The calculation accuracy of (t) is improved while the computational load is significantly reduced.

[0476] Furthermore, according to the measurement method of this embodiment, the measuring device 1 does not need to directly measure the average speed v of the railway vehicle 6. a The average speed v of the railway vehicle 6 can be calculated based on the acceleration data a(t) output from sensor 2, using a simple calculation based on equation (13). a .

[0477] 6. Variations

[0478] This invention is not limited to this embodiment, and various modifications can be made within the scope of the spirit of this invention.

[0479] In the above embodiments, the sensor 2, which serves as the observation device, is an acceleration sensor that outputs acceleration data a(k), but the observation device is not limited to an acceleration sensor. For example, the observation device may also be an impact sensor, a pressure sensor, a strain gauge, an image measuring device, a force sensor, or a displacement gauge.

[0480] Impact sensors detect impact acceleration as the response of each axle of the railway vehicle 6 to the action of the observation point R. Pressure sensors, strain gauges, and force sensors detect stress changes as the response of each axle of the railway vehicle 6 to the action of the observation point R. An image measurement device detects displacement as the response of each axle of the railway vehicle 6 to the action of the observation point R through image processing. Displacement gauges, such as contact displacement gauges, ring displacement gauges, laser displacement gauges, pressure sensors, or displacement measurement devices utilizing optical fibers, detect displacement as the response of each axle of the railway vehicle 6 to the action of the observation point R.

[0481] As an example, Figure 41 An example of the configuration of a measurement system 10 using a ring displacement gauge as the observation device is shown. Additionally, Figure 42 An example of the configuration of a measurement system 10 using an image measuring device as an observation device is shown. Figure 41 and Figure 42 In the middle, to and Figure 1 Identical components are labeled with the same symbols, and their descriptions are omitted. Figure 41 In the measurement system 10 shown, a piano wire 41 is fixed between the upper surface of the ring displacement gauge 40 and the lower surface of the main beam G located directly above it. The ring displacement gauge 40 measures the displacement of the piano wire 41 caused by the deflection of the upper structure 7 and sends the measured displacement data to the measuring device 1. The measuring device 1 generates measurement data 135 based on the displacement data sent from the ring displacement gauge 40. Furthermore, in Figure 42 In the measurement system 10 shown, camera 50 captures an image of a target 51 positioned on the side of the main beam G and sends it to measuring device 1. Measuring device 1 processes the image sent from camera 50, calculates the displacement of target 51 caused by the deflection of the superstructure 7, generates displacement data, and generates measurement data 135 based on the generated displacement data. Figure 42 In the example, measuring device 1 generates displacement data as an image measuring device, but displacement data can also be generated by an image measuring device (not shown) that is different from measuring device 1 through image processing.

[0482] In addition, in the above embodiments, bridge 5 is a railway bridge and the moving body moving on bridge 5 is a railway vehicle 6. However, bridge 5 can also be a road bridge and the moving body moving on bridge 5 can be a car, tram, truck, construction vehicle, or other vehicle. Figure 43 This diagram shows an example of the configuration of a measurement system 10 when bridge 5 is a road bridge and vehicle 6a moves on bridge 5. Figure 43 In the middle, to and Figure 1 The same constituent elements are assigned the same symbols. For example... Figure 43 As shown, the bridge 5, which serves as a road bridge, is similar to the railway bridge in that it consists of a superstructure 7 and a substructure 8. Figure 44 It is along Figure 43 The cross-sectional view of the upper structure 7 cut off by line AA. (See diagram below.) Figure 43 and Figure 44 As shown, the superstructure 7 includes a bridge deck 7a and supports 7b, consisting of the ground surface F, main beams G, and crossbeams (not shown). Additionally, as... Figure 43 As shown, the substructure 8 includes piers 8a and abutments 8b. The superstructure 7 is a structure erected on any one of adjacent abutments 8b and piers 8a, two adjacent abutments 8b, or two adjacent piers 8a. The two ends of the superstructure 7 are located at the positions of adjacent abutments 8b and piers 8a, two adjacent abutments 8b, or two adjacent piers 8a. The bridge 5 is, for example, a steel bridge, a beam bridge, or an RC bridge.

[0483] Each sensor 2 is positioned at the center of the superstructure 7 along its length, specifically at the center of the main beam G along its length. Each sensor 2 only needs to detect the acceleration used to calculate the displacement of the superstructure 7; its placement is not limited to the center of the superstructure 7. It should be noted that if the sensors 2 are placed on the ground F of the superstructure 7, they may be damaged by the movement of vehicles 6a, and the measurement accuracy may be affected by local deformation of the bridge deck 7a. Therefore, in... Figure 43 and Figure 44 In the example, each sensor 2 is installed on the main beam G of the superstructure 7.

[0484] like Figure 44 As shown, the superstructure 7 has two lanes L1 and L2 that a vehicle 6a can move on, and three main beams G. Figure 43 and Figure 44 In the example, at the center of the superstructure 7 along its length, sensors 2 are respectively installed on the two main beams at both ends. An observation point R1 is installed on the surface of lane L1 perpendicular to the direction of elevation of one sensor 2, and an observation point R2 is installed on the surface of lane L2 perpendicular to the direction of elevation of the other sensor 2. That is, the two sensors 2 are observation devices that observe observation points R1 and R2 respectively. The two sensors 2 that observe observation points R1 and R2 only need to be positioned to detect the acceleration generated at observation points R1 and R2 due to the movement of vehicle 6a, but are preferably positioned close to observation points R1 and R2. It should be noted that the number and placement of sensors 2, as well as the number of lanes, are not limited. Figure 43 and Figure 44 The example shown can be implemented in various variations.

[0485] The measuring device 1 calculates the displacement of lanes L1 and L2 caused by the movement of vehicle 6a based on the acceleration data output from each sensor 2, and transmits the displacement information of lanes L1 and L2 to the monitoring device 3 via the communication network 4. The monitoring device 3 may also store this information in a storage device (not shown), for example, for monitoring vehicle 6a and determining anomalies in the superstructure 7.

[0486] Furthermore, in the above embodiments, each sensor 2 is respectively installed on the main beam G of the superstructure 7, but it can also be installed on the surface or interior of the superstructure 7, the lower surface of the ground F, the pier 8a, etc. Also, in the above embodiments, the superstructure of a bridge is used as an example of a structure, but it is not limited to this; any structure can be an object that deforms through the movement of a moving body.

[0487] Furthermore, in the above embodiments, the measuring device 1 calculates the entry time t based on the observation data output from the observation device at the observation point R. i However, the entry time t can also be calculated based on observation data output from other observation devices at the entry end of the superstructure 7. i Similarly, in the embodiments described above, the measuring device 1 calculates the departure time t based on the observation data output from the observation device at the observation point R. o However, the departure time t can also be calculated based on observation data output from other observation devices at the departure end of the superstructure 7. o .

[0488] The above-described embodiments and modifications are examples only and are not limited thereto. For example, the embodiments and modifications can be appropriately combined.

[0489] This invention includes configurations that are substantially the same as those described in the embodiments, such as configurations with the same function, method, and result, or configurations with the same purpose and effect. Additionally, this invention includes configurations that replace non-essential parts of the configurations described in the embodiments. Furthermore, this invention includes configurations that have the same effect as those described in the embodiments or that can achieve the same purpose. Additionally, this invention includes configurations incorporating known techniques into the configurations described in the embodiments.

[0490] The following content is derived from the above implementation methods and variations.

[0491] One aspect of the measurement method includes:

[0492] The first measurement data generation process generates first measurement data based on the observation data output from the observation device at the observation point of the observed structure, which is a physical quantity that is the response of multiple parts of a moving body moving on the structure to the action of the observation point.

[0493] The second measurement data generation process generates second measurement data by filtering the first measurement data to reduce the vibration component.

[0494] The observation information generation process generates observation information including the entry time and departure time of the moving body relative to the structure;

[0495] The average velocity calculation process calculates the average velocity of the moving body based on the observation information and environmental information including the dimensions of the pre-fabricated moving body and the dimensions of the structure.

[0496] The first deflection calculation step calculates the first deflection of the structure caused by the moving body based on the approximate formula of the structure's deflection, the observation information, the environmental information, and the average velocity.

[0497] The second deflection calculation step calculates the second deflection that reduces the vibration component by filtering the first deflection.

[0498] The coefficient calculation process involves using a linear function of the second deflection amount to approximate the second measured data, and calculating the first-order coefficient and the zero-order coefficient of the linear function.

[0499] The third deflection calculation step calculates the third deflection based on the first-order coefficient, the zero-order coefficient, and the second deflection.

[0500] The offset calculation process calculates the offset based on the zero-order coefficient, the second deflection, and the third deflection.

[0501] The static response calculation step involves adding the product of the first-order coefficient and the first deflection to the offset to calculate the static response.

[0502] The first dynamic response calculation step involves subtracting the static response from the first measured data to calculate the first dynamic response;

[0503] The second dynamic response calculation process involves filtering the signal that is not needed due to the attenuation of the first dynamic response, and then calculating the second dynamic response.

[0504] The envelope amplitude calculation process calculates the envelope amplitude of the second dynamic response; and

[0505] The attenuation rate calculation step calculates the attenuation rate of the vibration components included in the second dynamic response based on the envelope amplitude.

[0506] According to this measurement method, by using a linear function of the second deflection that reduces the vibration component by filtering the first deflection, the second measurement data that reduces the vibration component by filtering the first measurement data can be approximated, and the static response can be separated and calculated from the static response and dynamic response included in the first measurement data.

[0507] Furthermore, according to this measurement method, since the product of the first-order coefficient of the first-order term, which is a first-order function approximating the first deflection, and the first deflection is equivalent to the displacement of the structure proportional to the load of the moving body, and the offset is equivalent to the displacement of the structure such as clearance or buoyancy that is not proportional to the load of the moving body, the static response can be calculated with high precision by adding the product of the first-order coefficient and the first deflection to the offset.

[0508] Furthermore, according to this measurement method, by subtracting the precisely calculated static response from the first measurement data and then performing filtering to attenuate unwanted signals, the second dynamic response can be calculated with high precision. Therefore, according to this measurement method, based on the envelope amplitude of the precisely calculated second dynamic response, the attenuation rate of the dynamic response can be calculated with high precision.

[0509] Furthermore, in this measurement method, the attenuation rate of the dynamic response when the moving body moves on the structure is calculated using a relatively simple process that utilizes first measured data generated from observation data and a first deflection amount generated from an approximation of the structure's deflection. Therefore, according to this measurement method, the attenuation rate of the dynamic response can be calculated with relatively little computational effort.

[0510] Furthermore, according to this measurement method, since the actual speed of the moving body changes slightly but hardly changes, it is assumed that the moving body moves at a certain average speed. By calculating the first deflection based on the average speed, the calculation accuracy of the first deflection can be maintained and the amount of calculation can be greatly reduced.

[0511] In one aspect of the measurement method,

[0512] In the attenuation rate calculation process,

[0513] Alternatively, in at least a portion of the first interval in which the vibration component decays within the second dynamic response, the envelope amplitude can be approximated using an exponential function, the coefficient of the power of the exponential function can be calculated, and the coefficient of the power can be divided by the natural vibration number of the second dynamic response to calculate the decay rate.

[0514] In one aspect of the measurement method,

[0515] The departure time is the moment when the last of the plurality of parts of the moving body passes through the departure end of the structure.

[0516] The start time of the first interval can also be after the departure time.

[0517] In one aspect of the measurement method,

[0518] The filtering process that attenuates unwanted signals from the first dynamic response may also include a low-pass filtering process that attenuates the higher harmonic components of the fundamental frequency vibrational component included in the first dynamic response and corrects the gain in the fundamental frequency.

[0519] According to this measurement method, since the envelope amplitude of the second dynamic response is obtained, in which the higher harmonic components are reduced and the signal components of the fundamental frequency are enhanced, the attenuation rate of the dynamic response can be calculated with high accuracy based on the envelope amplitude.

[0520] In one aspect of the measurement method,

[0521] The filtering process that attenuates unwanted signals from the first dynamic response may also include high-pass filtering that attenuates signal components at frequencies lower than the fundamental frequency.

[0522] According to this measurement method, since the envelope amplitude of the second dynamic response, which is obtained by obtaining higher harmonic components and signal components caused by low-frequency noise and environmental vibration, etc., are reduced while the signal components of the fundamental frequency are enhanced, the attenuation rate of the dynamic response can be calculated with high accuracy based on the envelope amplitude.

[0523] In one aspect of the measurement method,

[0524] In the envelope amplitude calculation process,

[0525] Alternatively, the absolute value of the second dynamic response can be low-pass filtered and multiplied by π / 2 to calculate the envelope amplitude.

[0526] In one aspect of the measurement method,

[0527] The structure may also be the superstructure of a bridge.

[0528] According to this measurement method, the attenuation rate of the vibration component in the dynamic response of a moving body moving on the superstructure of a bridge can be calculated with relatively small computational effort.

[0529] In one aspect of the measurement method,

[0530] The moving body can also be a vehicle or a railway vehicle.

[0531] The various parts mentioned are axles or wheels.

[0532] According to this measurement method, the attenuation rate of the vibration component included in the dynamic response of a vehicle or railway vehicle moving on a structure can be calculated with relatively small computational effort.

[0533] In one aspect of the measurement method,

[0534] The approximate formula for the deflection of the structure can also be a mathematical formula based on the structural model of the structure.

[0535] According to this measurement method, it is possible to calculate the first deflection of the structure that reflects the movement of the moving body, and to calculate the attenuation rate of the vibration components included in the dynamic response with high accuracy.

[0536] In one aspect of the measurement method,

[0537] The structural model can also be a simply supported beam with supports at both ends.

[0538] According to this measurement method, it is possible to calculate with high precision the attenuation rate of the vibration components included in the dynamic response of a moving body moving on a structure close to a simply supported beam.

[0539] In one aspect of the measurement method,

[0540] The observation device may also be an accelerometer, an impact sensor, a pressure sensor, a strain gauge, an image measuring device, a force sensor, or a displacement gauge.

[0541] According to this measurement method, the attenuation rate of the vibrational components included in the dynamic response can be measured with high precision using data on acceleration, stress change, or displacement.

[0542] In one aspect of the measurement method,

[0543] The structure can also be a structure that functions as a BWIM (Bridge Weigh in Motion) system.

[0544] One aspect of the measuring device includes:

[0545] The first measurement data generation unit generates first measurement data based on the observation data output from the observation device at the observation point of the observed structure, which is a physical quantity that is a response to the action of multiple parts of a moving body moving on the structure on the observation point.

[0546] The second measurement data generation unit generates second measurement data by filtering the first measurement data to reduce the vibration component.

[0547] The observation information generation unit generates observation information including the entry time and departure time of the moving body relative to the structure;

[0548] The average speed calculation unit calculates the average speed of the moving body based on the observation information and environmental information including the dimensions of the pre-fabricated moving body and the dimensions of the structure;

[0549] The first deflection calculation unit calculates the first deflection of the structure caused by the moving body based on the approximate formula of the structure's deflection, the observation information, the environmental information, and the average velocity.

[0550] The second deflection calculation unit calculates a second deflection that reduces the vibration component by filtering the first deflection.

[0551] The coefficient calculation unit uses a linear function of the second deflection amount to approximate the second measurement data, and calculates the first-order coefficient and the zero-order coefficient of the linear function;

[0552] The third deflection calculation unit calculates the third deflection based on the first-order coefficient, the zero-order coefficient, and the second deflection.

[0553] The offset calculation unit calculates the offset based on the zero-order coefficient, the second deflection, and the third deflection;

[0554] The static response calculation unit adds the product of the first-order coefficient and the first deflection to the offset to calculate the static response;

[0555] The first dynamic response calculation unit subtracts the static response from the first measurement data to calculate the first dynamic response;

[0556] The second dynamic response calculation unit performs filtering processing on signals that are not needed due to the attenuation of the first dynamic response, and calculates the second dynamic response;

[0557] The envelope amplitude calculation unit calculates the envelope amplitude of the second dynamic response; and

[0558] The attenuation rate calculation unit calculates the attenuation rate of the vibration component included in the second dynamic response based on the envelope amplitude.

[0559] According to the measuring device, by using a linear function of the second deflection that reduces the vibration component by filtering the first deflection, the second measurement data that reduces the vibration component by filtering the first measurement data can be approximated, and the static response can be separated and calculated from the static response and dynamic response included in the first measurement data.

[0560] Furthermore, according to this measuring device, since the product of the first-order coefficient of the first-order term, which is a first-order function approximating the first deflection, and the first deflection is equivalent to the displacement of the structure proportional to the load of the moving body, and the offset is equivalent to the displacement of the structure such as clearance or buoyancy that is not proportional to the load of the moving body, the static response can be calculated with high precision by adding the product of the first-order coefficient and the first deflection to the offset.

[0561] Furthermore, according to this measuring device, by subtracting the precisely calculated static response from the first measured data and then performing filtering to attenuate unwanted signals, the second dynamic response can be calculated with high precision. Therefore, according to this measuring device, based on the envelope amplitude of the precisely calculated second dynamic response, the attenuation rate of the dynamic response can be calculated with high precision.

[0562] Furthermore, in this measuring device, the attenuation rate of the dynamic response when the moving body moves on the structure is calculated using a relatively simple process that utilizes first measured data generated from observation data and a first deflection amount generated from an approximation of the structure's deflection. Therefore, according to this measuring device, the attenuation rate of the dynamic response can be calculated with relatively low computational complexity.

[0563] Furthermore, according to this measuring device, since the actual speed of the moving body changes slightly but hardly changes, it is assumed that the moving body moves at a certain average speed. By calculating the first deflection based on the average speed, the calculation accuracy of the first deflection can be maintained and the amount of calculation can be greatly reduced.

[0564] One aspect of the measurement system is:

[0565] One aspect of the measuring device; and

[0566] The observation device.

[0567] One aspect of the measurement procedure is to have the computer perform:

[0568] The first measurement data generation process generates first measurement data based on the observation data output from the observation device at the observation point of the observed structure, which is a physical quantity that is the response of multiple parts of a moving body moving on the structure to the action of the observation point.

[0569] The second measurement data generation process generates second measurement data by filtering the first measurement data to reduce the vibration component.

[0570] The observation information generation process generates observation information including the entry time and departure time of the moving body relative to the structure;

[0571] The average velocity calculation process calculates the average velocity of the moving body based on the observation information and environmental information including the dimensions of the pre-fabricated moving body and the dimensions of the structure.

[0572] The first deflection calculation step calculates the first deflection of the structure caused by the moving body based on the approximate formula of the structure's deflection, the observation information, the environmental information, and the average velocity.

[0573] The second deflection calculation step calculates the second deflection that reduces the vibration component by filtering the first deflection.

[0574] The coefficient calculation process involves using a linear function of the second deflection amount to approximate the second measured data, and calculating the first-order coefficient and the zero-order coefficient of the linear function.

[0575] The third deflection calculation step calculates the third deflection based on the first-order coefficient, the zero-order coefficient, and the second deflection.

[0576] The offset calculation process calculates the offset based on the zero-order coefficient, the second deflection, and the third deflection.

[0577] The static response calculation step involves adding the product of the first-order coefficient and the first deflection to the offset to calculate the static response.

[0578] The first dynamic response calculation step involves subtracting the static response from the first measured data to calculate the first dynamic response;

[0579] The second dynamic response calculation process involves filtering the signal that is not needed due to the attenuation of the first dynamic response, and then calculating the second dynamic response.

[0580] The envelope amplitude calculation process calculates the envelope amplitude of the second dynamic response; and

[0581] The attenuation rate calculation step calculates the attenuation rate of the vibration components included in the second dynamic response based on the envelope amplitude.

[0582] According to the measurement procedure, by using a linear function of the second deflection that reduces the vibration component by filtering the first deflection, the second measurement data that reduces the vibration component by filtering the first measurement data can be approximated, and the static response can be separated and calculated from the static response and dynamic response included in the first measurement data.

[0583] Furthermore, according to this measurement procedure, since the product of the first-order coefficient of the first-order term, which is a first-order function approximating the first deflection, and the first deflection is equivalent to the displacement of the structure proportional to the load of the moving body, and the offset is equivalent to the displacement of the structure such as clearance or buoyancy that is not proportional to the load of the moving body, the static response can be calculated with high precision by adding the product of the first-order coefficient and the first deflection to the offset.

[0584] Furthermore, according to this measurement procedure, the first dynamic response can be calculated with high precision by subtracting the highly calculated static response from the first measurement data.

[0585] Furthermore, according to this measurement procedure, by subtracting the precisely calculated static response from the first measurement data and then performing filtering to attenuate unwanted signals, the second dynamic response can be calculated with high precision. Therefore, according to this measurement procedure, based on the envelope amplitude of the precisely calculated second dynamic response, the attenuation rate of the dynamic response can be calculated with high precision.

[0586] Furthermore, in this measurement procedure, the attenuation rate of the dynamic response when the moving body moves on the structure is calculated using a relatively simple process that utilizes first measured data generated from observation data and a first deflection amount generated from an approximation of the structure's deflection. Therefore, according to this measurement procedure, the attenuation rate of the dynamic response can be calculated with relatively little computational effort.

[0587] Furthermore, according to this measurement procedure, since the actual speed of the moving body changes slightly but hardly changes, it is assumed that the moving body moves at a certain average speed. By calculating the first deflection based on the average speed, the calculation accuracy of the first deflection can be maintained and the amount of calculation can be greatly reduced.

Claims

1. A measurement method, characterized in that, include: The first measurement data generation process generates first measurement data based on the observation data output from the observation device at the observation point of the observed structure, which is a physical quantity that is the response of multiple parts of a moving body moving on the structure to the action of the observation point. The second measurement data generation process generates second measurement data by filtering the first measurement data to reduce the vibration component. The observation information generation process generates observation information including the entry time and departure time of the moving body relative to the structure; The average velocity calculation process calculates the average velocity of the moving body based on the observation information and environmental information including the dimensions of the pre-fabricated moving body and the dimensions of the structure. The first deflection calculation step calculates the first deflection of the structure caused by the moving body based on the approximate formula of the structure's deflection, the observation information, the environmental information, and the average velocity. The second deflection calculation step calculates the second deflection that reduces the vibration component by filtering the first deflection. The coefficient calculation process involves using a linear function of the second deflection amount to approximate the second measured data, and calculating the first-order coefficient and the zero-order coefficient of the linear function. The third deflection calculation step calculates the third deflection based on the first-order coefficient, the zero-order coefficient, and the second deflection. The offset calculation process calculates the offset based on the zero-order coefficient, the second deflection, and the third deflection. The static response calculation step involves adding the product of the first-order coefficient and the first deflection to the offset to calculate the static response. The first dynamic response calculation step involves subtracting the static response from the first measured data to calculate the first dynamic response; The second dynamic response calculation process involves filtering the signal that is not needed due to the attenuation of the first dynamic response, and then calculating the second dynamic response. The envelope amplitude calculation process calculates the envelope amplitude of the second dynamic response; as well as The attenuation rate calculation step calculates the attenuation rate of the vibration components included in the second dynamic response based on the envelope amplitude.

2. The measurement method according to claim 1, characterized in that, In the attenuation rate calculation process, In a first interval that includes at least a portion of the interval in which the vibration component decays in the second dynamic response, the envelope amplitude is approximated using an exponential function, the coefficient of the power of the exponential function is calculated, and the coefficient of the power is divided by the natural vibration number of the second dynamic response to calculate the decay rate.

3. The measurement method according to claim 2, characterized in that, The departure time is the moment when the last of the plurality of parts of the moving body passes through the departure end of the structure. The start time of the first interval is after the departure time.

4. The measurement method according to any one of claims 1 to 3, characterized in that, The filtering process for attenuating unwanted signals from the first dynamic response includes attenuating the higher harmonic components of the vibrational components of the fundamental frequency included in the first dynamic response and a low-pass filtering process for correcting the gain in the fundamental frequency.

5. The measurement method according to claim 4, characterized in that, The filtering process that attenuates unwanted signals from the first dynamic response includes a high-pass filtering process that attenuates signal components at frequencies lower than the fundamental frequency.

6. The measurement method according to any one of claims 1 to 3, characterized in that, In the envelope amplitude calculation process, The absolute value of the second dynamic response is low-pass filtered and multiplied by π / 2 to calculate the envelope amplitude.

7. The measurement method according to any one of claims 1 to 3, characterized in that, The structure in question is the superstructure of a bridge.

8. The measurement method according to any one of claims 1 to 3, characterized in that, The moving body is a vehicle or a railway vehicle. The various parts mentioned are axles or wheels.

9. The measurement method according to any one of claims 1 to 3, characterized in that, The approximate formula for the deflection of the structure is a mathematical expression based on the structural model of the structure.

10. The measurement method according to claim 9, characterized in that, The structural model is a simply supported beam with supports at both ends.

11. The measurement method according to any one of claims 1 to 3, characterized in that, The observation device is an accelerometer, an impact sensor, a pressure sensor, a strain gauge, an image measuring device, a force sensor, or a displacement gauge.

12. The measurement method according to any one of claims 1 to 3, characterized in that, The structure in question is the superstructure of a bridge that functions as a dynamic load-bearing device, including the bridge deck, supports, tracks, sleepers, and ballast.

13. A measuring device, characterized in that, include: The first measurement data generation unit generates first measurement data based on the observation data output from the observation device at the observation point of the observed structure, which is a physical quantity that is a response to the action of multiple parts of a moving body moving on the structure on the observation point. The second measurement data generation unit generates second measurement data by filtering the first measurement data to reduce the vibration component. The observation information generation unit generates observation information including the entry time and departure time of the moving body relative to the structure; The average speed calculation unit calculates the average speed of the moving body based on the observation information and environmental information including the dimensions of the pre-fabricated moving body and the dimensions of the structure; The first deflection calculation unit calculates the first deflection of the structure caused by the moving body based on the approximate formula of the structure's deflection, the observation information, the environmental information, and the average velocity. The second deflection calculation unit calculates a second deflection that reduces the vibration component by filtering the first deflection. The coefficient calculation unit uses a linear function of the second deflection amount to approximate the second measurement data, and calculates the first-order coefficient and the zero-order coefficient of the linear function; The third deflection calculation unit calculates the third deflection based on the first-order coefficient, the zero-order coefficient, and the second deflection. The offset calculation unit calculates the offset based on the zero-order coefficient, the second deflection, and the third deflection; The static response calculation unit adds the product of the first-order coefficient and the first deflection to the offset to calculate the static response; The first dynamic response calculation unit subtracts the static response from the first measurement data to calculate the first dynamic response; The second dynamic response calculation unit performs filtering processing on signals that are not needed due to the attenuation of the first dynamic response, and calculates the second dynamic response; The envelope amplitude calculation unit calculates the envelope amplitude of the second dynamic response; as well as The attenuation rate calculation unit calculates the attenuation rate of the vibration component included in the second dynamic response based on the envelope amplitude.

14. A measurement system, characterized in that, have: The measuring device according to claim 13; and The observation device.

15. A storage medium, characterized in that, The system stores a measurement program that causes a computer to execute: The first measurement data generation process generates first measurement data based on the observation data output from the observation device at the observation point of the observed structure, which is a physical quantity that is the response of multiple parts of a moving body moving on the structure to the action of the observation point. The second measurement data generation process generates second measurement data by filtering the first measurement data to reduce the vibration component. The observation information generation process generates observation information including the entry time and departure time of the moving body relative to the structure; The average velocity calculation process calculates the average velocity of the moving body based on the observation information and environmental information including the dimensions of the pre-fabricated moving body and the dimensions of the structure. The first deflection calculation step calculates the first deflection of the structure caused by the moving body based on the approximate formula of the structure's deflection, the observation information, the environmental information, and the average velocity. The second deflection calculation step calculates the second deflection that reduces the vibration component by filtering the first deflection. The coefficient calculation process involves using a linear function of the second deflection amount to approximate the second measured data, and calculating the first-order coefficient and the zero-order coefficient of the linear function. The third deflection calculation step calculates the third deflection based on the first-order coefficient, the zero-order coefficient, and the second deflection. The offset calculation process calculates the offset based on the zero-order coefficient, the second deflection, and the third deflection. The static response calculation step involves adding the product of the first-order coefficient and the first deflection to the offset to calculate the static response. The first dynamic response calculation step involves subtracting the static response from the first measured data to calculate the first dynamic response; The second dynamic response calculation process involves filtering the signal that is not needed due to the attenuation of the first dynamic response, and then calculating the second dynamic response. The envelope amplitude calculation process calculates the envelope amplitude of the second dynamic response; as well as The attenuation rate calculation step calculates the attenuation rate of the vibration components included in the second dynamic response based on the envelope amplitude.

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