Bridge displacement measurement method

A measurement method include a step to obtain observation point information, including physical quantities in association of a plurality of times, via observation devices at observation points of a structure on which a moving object moves, a step to calculate a correction coefficient that corrects the physical quantities based on a plurality of time periods and a reference time periods, a step to calculate a plurality of deflection waveforms of the structure generated by a plurality of parts of the moving object, a step to calculate a second deflection waveform of the structure generated by the moving object by adding the plurality of deflection waveforms, and a step to calculate a displacement of the structure based on the second deflection waveform. The structure is a superstructure of a road bridge or a railway bridge.

The present application is based on, and claims priority from JP Application Serial Number 2020-047309, filed Mar. 18, 2020, the disclosure of which is hereby incorporated by reference herein in its entirety.

BACKGROUND

1. Technical Field

The present disclosure relates to a measurement method, a measurement device, a measurement system, and a measurement program.

2. Related Art

In maintaining and managing a bridge, an axle load of a large vehicle passing through the bridge is important information for predicting damage to the bridge. For axle load measurement, JP-A-2009-237805 proposes weight in motion, which is a method of continuously measuring a strain value when the vehicle passes from a strain gauge installed on a main girder of the bridge and calculating the axle load. JP-A-2009-237805 discloses a bridge-passing vehicle monitoring system that measures a vehicle weight of a vehicle passing through a bridge based on a strain waveform measured by a strain gauge arranged on a main girder of the bridge.

Specifically, in the bridge-passing vehicle monitoring system, the strain gauge is arranged, a passage timing of the axle is detected based on the strain waveform measured by the strain gauge, an inter-axle ratio of the vehicle is calculated, the calculated inter-axle ratio is compared with an inter-axle ratio calculated based on an inter-axle distance registered in an inter-axle distance database, and the inter-axle distance, a vehicle speed, and a vehicle type of the vehicle are identified. The bridge-passing vehicle monitoring system generates a strain waveform in which a reference axle load strain waveform is arranged on a time axis according to the passage timing of the axle, and calculates the axle load of each axle by comparing the reference axle load strain waveform with a strain waveform measured by the strain gauge. Then, the bridge-passing vehicle monitoring system calculates the vehicle weight by summing the axle loads of each axle.

Since the load of each axle when the vehicle is traveling is influenced by a distance moment from a center of gravity, the load of each axle when the vehicle is traveling may be greatly different from the load of each axle when the vehicle is stationary. In the system described in JP-A-2009-237805, the vehicle weight of the vehicle can be measured without measuring a displacement of the bridge by using the strain waveform and the inter-axle distance database. However, in consideration of the difference in loads between a case where the moving object such as the vehicle is stationary and a case where the moving body is moving, it is not possible to calculate the deflection waveform of the structure generated by the moving object that moves on the structure such as the bridge.

SUMMARY

According to a first aspect of the present disclosure, a measurement method includes: a first observation point information acquisition step of acquiring, based on observation information obtained by an observation device that observes, among a first observation point and a second observation point which are arranged along a first direction in which a moving object moves on a structure, the first observation point, first observation point information including a time point when each of a plurality of parts of the moving object passes the first observation point and a first physical quantity which is a response to an action of each of the plurality of parts on the first observation point; a second observation point information acquisition step of acquiring, based on observation information obtained by an observation device that observes the second observation point, second observation point information including a time point when the plurality of parts passes the second observation point and a second physical quantity which is a response to an action of each of the plurality of parts on the second observation point; a first time calculation step of calculating, using the first observation point information, a time from a first leading time point, which is a time point when a leading part among the plurality of parts passes the first observation point, to a time point when each of the plurality of parts passes the first observation point, and a time from the first leading time point to a first reference time point, which is a time point when a total sum of first physical quantities is distributed at a predetermined distribution ratio; a correction coefficient calculation step of calculating, based on the time from the first leading time point to the time point when each of the plurality of parts passes the first observation point, and the time from the first leading time point to the first reference time point, a correction coefficient that corrects the first physical quantity; a deflection waveform calculation step of calculating, based on the first observation point information, the second observation point information, a predetermined coefficient, the correction coefficient, and an approximate expression of deflection of the structure, a deflection waveform of the structure generated by each of the plurality of parts; and a moving object deflection waveform calculation step of calculating a deflection waveform of the structure generated by the moving object by adding the deflection waveform of the structure generated by each of the plurality of parts and calculated in the deflection waveform calculation step.

The measurement method according to the first aspect may further include: a second time calculation step of calculating, using the second observation point information, a time from a second leading time, which is a time point when the leading part among the plurality of parts passes the second observation point, to a time point when each of the plurality of parts passes the second observation point, and a time from the second leading time point to a second reference time point, which is a time point when a total sum of second physical quantities is distributed at a predetermined distribution ratio, in which in the correction coefficient calculation step, based on the time from the first leading time point to the time point when each of the plurality of parts passes the first observation point, the time from the first leading time point to the first reference time point, the time from the second leading time point to the time point when each of the plurality of parts passes the second observation point, and the time from the second leading time point to the second reference time point, a correction coefficient that corrects the first physical quantity and the second physical quantity may be calculated.

In the first aspect of the measurement method, when the distribution ratio is R:1−R, R may be 0.4 or more and 0.6 or less.

In the first aspect of the measurement method, the first observation point may be set at a first end portion of the structure, and the second observation point may be set at a second end portion of the structure different from the first end portion.

In the first aspect of the measurement method, the structure may be a superstructure of a bridge, the superstructure may be a structure across any one of a bridge abutment and a bridge pier adjacent to each other, two adjacent bridge abutments, or two adjacent bridge piers, both end portions of the superstructure may be located at positions of the bridge abutment and the bridge pier adjacent to each other, at positions of the two adjacent bridge abutments, or at positions of the two adjacent bridge piers, and the bridge may be a road bridge or a railway bridge.

In the first aspect of the measurement method, the moving object may be a railroad vehicle, an automobile, a tram, a construction vehicle, or a military vehicle, and the plurality of parts may be axles or wheels.

In the first aspect of the measurement method, the approximate expression of deflection of the structure may be an expression based on a structural model of the structure.

In the first aspect of the measurement method, the structural model may be a simple beam that supports both ends.

In the first aspect of the measurement method, the approximate expression of deflection of the structure may be an expression normalized by a maximum amplitude of deflection at a central position between the first observation point and the second observation point.

In the first aspect of the measurement method, the observation device that observes the first observation point, and the observation device that observes the second observation point may be acceleration sensors.

In the first aspect of the measurement method, the observation device that observes the first observation point and the observation device that observes the second observation point may be impact sensors, microphones, strain gauges, or load cells.

In the first aspect of the measurement method, the structure may be a structure in which bridge weigh in motion (BWIM) functions.

According to a second aspect of the present disclosure, a measurement device includes: a first observation point information acquisition unit that acquires, based on observation information obtained by an observation device that observes, among a first observation point and a second observation point which are arranged along a first direction in which a moving object moves on a structure, the first observation point, first observation point information including a time point when each of a plurality of parts of the moving object passes the first observation point and a first physical quantity which is a response to an action of each of the plurality of parts on the first observation point; a second observation point information acquisition unit that acquires, based on observation information obtained by an observation device that observes the second observation point, second observation point information including a time point when each of the plurality of parts passes the second observation point and a second physical quantity which is a response to an action of each of the plurality of parts on the second observation point; a first time calculation unit that calculates, using the first observation point information, a time from a first leading time point, which is a time point when a leading part among the plurality of parts passes the first observation point, to a time point when each of the plurality of parts passes the first observation point, and a time from the first leading time point to a first reference time point, which is a time point when a total sum of first physical quantities is distributed at a predetermined distribution ratio; a correction coefficient calculation unit that calculates, based on the time from the first leading time point to the time point when each of the plurality of parts passes the first observation point, and the time from the first leading time point to the first reference time point, a correction coefficient that corrects the first physical quantity; a deflection waveform calculation unit that calculates, based on the first observation point information, the second observation point information, a predetermined coefficient, the correction coefficient, and an approximate expression of deflection of the structure, a deflection waveform of the structure generated by each of the plurality of parts; and a moving object deflection waveform calculation unit that calculates a deflection waveform of the structure generated by the moving object by adding the deflection waveform of the structure generated by each of the plurality of parts and calculated in the deflection waveform calculation unit.

According to a third aspect of the present disclosure, a measurement system includes: the measurement device according to the first aspect; the observation device that observes the first observation point; and the observation device that observes the second observation point.

According to a fourth aspect of the present disclosure, a non-transitory computer-readable storage medium stores a measurement program, the measurement program causing a computer to execute: a first observation point information acquisition step of acquiring, based on observation information obtained by an observation device that observes, among a first observation point and a second observation point which are arranged along a first direction in which a moving object moves on a structure, the first observation point, first observation point information including a time point when each of a plurality of parts of the moving object passes the first observation point and a first physical quantity which is a response to an action of each of the plurality of parts on the first observation point; a second observation point information acquisition step of acquiring, based on observation information obtained by an observation device that observes the second observation point, second observation point information including a time point when the plurality of parts passes the second observation point and a second physical quantity which is a response to an action of each of the plurality of parts on the second observation point; a first time calculation step of calculating, using the first observation point information, a time from a first leading time point, which is a time point when a leading part among the plurality of parts passes the first observation point, to a time point when each of the plurality of parts passes the first observation point, and a time from the first leading time point to a first reference time point, which is a time point when a total sum of first physical quantities is distributed at a predetermined distribution ratio; a correction coefficient calculation step of calculating, based on the time from the first leading time point to the time point when each of the plurality of parts passes the first observation point, and the time from the first leading time point to the first reference time point, a correction coefficient that corrects the first physical quantity; a deflection waveform calculation step of calculating, based on the first observation point information, the second observation point information, a predetermined coefficient, the correction coefficient, and an approximate expression of deflection of the structure, a deflection waveform of the structure generated by each of the plurality of parts; and a moving object deflection waveform calculation step of calculating a deflection waveform of the structure generated by the moving object by adding the deflection waveform of the structure generated by each of the plurality of parts and calculated in the deflection waveform calculation step.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. The embodiments described below do not in any way limit contents of the present disclosure described in the appended claims. Not all configurations described below are necessarily essential components of the present disclosure.

1. First Embodiment

1-1 Measurement System

Hereinafter, a measurement system for implementing a measurement method according to the present embodiment will be described by taking a case where a structure is a superstructure of a bridge and a moving object is a vehicle as an example. The vehicle passing through the bridge according to the present embodiment is a vehicle having a large weight such as a railroad vehicle, an automobile, a tram, a construction vehicle, or a military vehicle, and can be measured by bridge weigh in motion (BWIM). The BWIM is a technology that uses a bridge as a “scale” and that measures the weight and the number of axles of the vehicle passing through the bridge by measuring deformation of the bridge. The superstructure of the bridge, which enables analysis of the weight of the vehicle passing by based on a response such as deformation and strain, is a structure in which the BWIM functions. A BWIM system, which applies a physical process between an action on the superstructure of the bridge and the response, enables the measurement of the weight of the vehicle passing by.

FIG.1is a diagram showing an example of a measurement system according to the present embodiment. As shown inFIG.1, a measurement system10according to the present embodiment includes a measurement device1, and at least one sensor21and at least one sensor22which are provided on a superstructure7of a bridge5. The measurement system10may include a server2.

The bridge5is formed of the superstructure7and a substructure8. The superstructure7includes abridge floor7aformed of a floor plate F, a main girder G, a cross girder which is not shown, and bearings7b. The substructure8includes bridge piers8aand bridge abutments8b. The superstructure7is a structure across any one of the bridge abutment8band the bridge pier8aadjacent to each other, two adjacent bridge abutments8b, or two adjacent bridge piers8a. Both end portions of the superstructure7are located at positions of the bridge abutment8band the bridge pier8aadjacent to each other, at positions of the two adjacent bridge abutments8b, or at positions of the two adjacent bridge piers8a.

The measurement device1and the sensors21and22are coupled by, for example, a cable which is not shown and communicate with one another via a communication network such as a controller area network (CAN). Alternatively, the measurement device1and the sensors21and22may communicate with one another via a wireless network.

For example, each sensor21outputs data representing an impact caused by entry of the vehicle6which is a moving object to the superstructure7. Each sensor22outputs data representing an impact caused by exit of the vehicle6from the superstructure7. In the present embodiment, each of the sensors21and22is an acceleration sensor, and may be, for example, a crystal acceleration sensor or a micro electro mechanical systems (MEMS) acceleration sensor.

In the present embodiment, each sensor21is installed at a first end portion of the superstructure7in a longitudinal direction. Each sensor22is installed at a second end portion of the superstructure7which is different from the first end portion in the longitudinal direction.

Each sensor21detects an acceleration of the superstructure7generated when the vehicle6enters the superstructure7. Each sensor22detects the acceleration of the superstructure7generated when the vehicle6exits the superstructure7. That is, in the present embodiment, each sensor21is an acceleration sensor that detects the entry of the vehicle6to the superstructure7. Each sensor22is an acceleration sensor that detects the exit of the vehicle6from the superstructure7.

The measurement device1calculates a displacement of bending of the superstructure7due to the traveling of the vehicle6based on acceleration data output from the sensors21and22.

The measurement device1and the server2can communicate with each other via, for example, a wireless network of a mobile phone and a communication network4such as the Internet. The measurement device1transmits, to the server2, information such as a time point when the vehicle6travels on the superstructure7and the displacement of the superstructure7due to the traveling of the vehicle6. The server2may store the information in a storage device which is not shown, and may perform, based on the information, processing such as monitoring of an overloaded vehicle or determination of an abnormality in the superstructure7.

In the present embodiment, the bridge5is a road bridge, for example, a steel bridge, a girder bridge, or a reinforced-concrete (RC) bridge.

FIGS.2and3are diagrams showing installation examples of the sensors21and22on the superstructure7.FIG.2is a diagram of the superstructure7as viewed from above.FIG.3is a cross-sectional view ofFIG.2cut along a line A-A or a line B-B.

As shown inFIGS.2and3, the superstructure7has N lanes L1to LNand K main girders G1to GKas first to N-th paths through which the vehicle6, which is the moving object, can move. Here, N and K are integers of 1 or more. In examples shown inFIGS.2and3, each position of the main girders G1to GKcoincides with a position of each boundary between the lanes L1to LN, and N=K−1. Alternatively, each position of the main girders G1to GKdoes not have to coincide with the position of each boundary between the lanes L1to LN, and N≠K−1.

In the examples shown inFIGS.2and3, the sensor21is provided on each of the main girders G1to GK−1at a first end portion EA1of the superstructure7in the longitudinal direction. The sensor22is provided on each of the main girders G1to GK−1at a second end portion EA2of the superstructure7in the longitudinal direction. In the examples shown inFIGS.2and3, N=K−1, and the sensors21and22are not provided on the main girder GK. However, the sensors21and22may be provided on the main girder GK, and the sensors21and22may not be provided on any one of the main girders G1to GK−1. Alternatively, N=K, and the sensors21and22may be provided on the main girders G1to GK.

When the sensors21and22are provided on the floor plate F of the superstructure7, the sensors may be destroyed by a traveling vehicle, and measurement accuracy may be influenced by local deformation of the bridge floor7a. Therefore, in the examples shown inFIGS.2and3, the sensors21and22are provided on the main girders G1to GK−1of the superstructure7.

In the present embodiment, N observation points P1to PNare set in association with the N sensors21. The observation points P1to PNare N observation points for the superstructure7arranged along a second direction intersecting a first direction in which the vehicle6moves along the superstructure7. In the examples shown inFIGS.2and3, for each integer j of 1 or more and N or less, an observation point Pjis set at a position on a surface of the floor plate F in a vertically upward direction of the sensor21provided on a main girder Gjat the first end portion EA1. That is, the sensor21provided on the main girder Gjis an observation device that observes the observation point Pj. The sensor21that observes the observation point Pjmay be provided at a position where the acceleration generated at the observation point Pjdue to the traveling of the vehicle6can be detected, and it is desirable that the sensor21is provided at a position close to the observation point Pj. In this way, the observation points P1to PNhave a one-to-one relationship with the N sensors21.

In the present embodiment, N observation points Q1to QNare set in association with the N sensors22. The observation points Q1to QNare N observation points for the superstructure7arranged along a third direction intersecting the first direction in which the vehicle6moves along the superstructure7. In the examples shown inFIGS.2and3, for each integer j or 1 more and N or less, an observation point Q1is set at a position on the surface of the floor plate F in a vertically upward direction of the sensor22provided on the main girder Gjat the second end portion EA2. That is, the sensor22provided on the main girder Gjis an observation device that observes the observation point Qj. The sensor22that observes the observation point Qjmay be provided at a position where the acceleration generated at the observation point Qjdue to the traveling of the vehicle6can be detected, and it is desirable that the sensor22is provided at a position close to the observation point Qj. In this way, the observation points Q1to QNhave a one-to-one relationship with the N sensors22.

In the present embodiment, the N observation points P1to PNare associated with the lanes L1to LN, respectively. Similarly, the N observation points Q1to QNare associated with the lanes L1to LN, respectively. The observation point Pjand the observation point Qj, which are set in association with the lane Lj, are arranged along the first direction in which the vehicle6moves along the superstructure7. In the examples shown inFIGS.2and3, the first direction is an X direction along the lanes L1to LNof the superstructure7, that is, the longitudinal direction of the superstructure7. The second direction and the third direction are a Y direction orthogonal to the X direction in a surface of the superstructure7on which the vehicle6travels, that is, a width direction of the superstructure7. However, when the lanes L1to LNare curved, the second direction and the third direction do not have to coincide with each other. The second direction and the third direction do not have to be orthogonal to the first direction. For example, a distance from an end of the superstructure7on a side where the vehicle6enters to the observation points P1to PNand a distance from an end of the superstructure7on a side where the vehicle6exits to the observation points Q1to QNmay be different. For each integer j of 1 or more and N or less, the observation point Pjis an example of a “first observation point”, and the observation point Qjis an example of a “second observation point”.

The number and installation positions of the N sensors21and22are not limited to the examples shown inFIGS.2and3, and various modifications can be made.

The measurement device1acquires, based on the acceleration data output from each of the sensors21and22, an acceleration in a fourth direction which intersects the X direction, which is the first direction, and the Y direction, which is the second direction and the third direction. The observation points P1to PNand Q1to QNare displaced by an impact in a direction orthogonal to the X and Y directions. Therefore, in order to accurately calculate a magnitude of the impact, it is desirable for the measurement device1to acquire the acceleration in the fourth direction orthogonal to the X and Y directions, that is, in a normal direction of the floor plate F.

FIG.4is a diagram illustrating the acceleration detected by the sensors21and22. The sensors21and22are acceleration sensors that detect the accelerations generated in three axes orthogonal to one another.

In order to detect the impact applied to the observation points P1to PNdue to the entry of the vehicle6to the superstructure7, each sensor21is installed such that one of three detection axes, which are an x axis, a y axis, and a z axis, intersects the first direction and the second direction. Similarly, in order to detect the impact applied to the observation points Q1to QNdue to the exit of the vehicle6from the superstructure7, each sensor22is installed such that one of the three detection axes, which are the x axis, the y axis, and the z axis, intersects the first direction and the third direction. In the examples shown inFIGS.2and3, since the first direction is the X direction, the second direction and the third direction are the Y direction, the sensors21and22are installed such that one axis intersects the X direction and the Y direction. The observation points P1to PNand Q1to QNare displaced by the impact in the direction orthogonal to the X direction and the Y direction. Therefore, in order to accurately detect the magnitude of the impact, ideally, the sensors21and22are installed such that one axis is in the direction orthogonal to the X direction and the Y direction, that is, the normal direction of the floor plate F.

When the sensors21and22are installed on the superstructure7, an installation location may be inclined. In the measurement device1, even if one of the three detection axes of each of the sensors21and22is not installed in the normal direction of the floor plate F, since the direction is substantially oriented in the normal direction, an error is small and thus can be ignored. The measurement device1can correct a detection error due to the inclination of the sensors21and22by a three-axis combined acceleration that combines the accelerations in the x axis, the y axis, and the z axis even if one of the three detection axes of each of the sensors21and22is not installed in the normal direction of the floor plate F. Each of the sensors21and22may be a one-axis acceleration sensor that detects the acceleration generated in a direction at least substantially parallel to the vertical direction or the acceleration in the normal direction of the floor plate F.

Hereinafter, details of the measurement method according to the present embodiment executed by the measurement device1will be described.

1-2. Generation of Axle Information

In the present embodiment, the measurement device acquires, based on the acceleration data, which is observation information obtained by the N sensors21as the observation device, first observation point information including a time point when each of a plurality of parts of the vehicle6which is the moving object passes the observation point P and a first physical quantity which is a response to an action of each of the plurality of parts on the observation point Pj. Similarly, in the present embodiment, the measurement device1acquires, based on the acceleration data, which is observation information obtained by the N sensors22as the observation device, second observation point information including a time point when each of the plurality of parts of the vehicle6passes the observation point Qjand a second physical quantity which is a response to an action of each of the plurality of parts on the observation point Qj. Here, j is an integer of 1 or more and N or less.

In the present embodiment, it is considered that a load generated by a plurality of axles or wheels of the vehicle6is applied to the superstructure7. Accordingly, each of the plurality of parts for which the first observation point information and the second observation point information are to be acquired is an axle or a wheel. Hereinafter, in the present embodiment, it is assumed that each of the plurality of parts is an axle.

In the present embodiment, each sensor21, which is the acceleration sensor, detects the acceleration due to the action of each of the plurality of axles on the observation point Pj. Similarly, each sensor22, which is the acceleration sensor, detects the acceleration due to the action of each of the plurality of axles on the observation point Qj.

In the present embodiment, as shown inFIG.2, the observation points P1to PNare set at the first end portion EA1, and the observation points Q1to QNare set at the second end portion EA2. Therefore, a time point when each of the plurality of axles of the vehicle6passes the observation point Pjcan be regarded as an entry time point of each axle to the superstructure7and, more specifically, an entry time point to the lane Lj. A time point when each of the plurality of axles of the vehicle6passes the observation point Qjcan be regarded as an exit time point of each axle from the superstructure7, and more specifically, an exit time point from the lane Lj.

Therefore, in the present embodiment, the first observation point information includes an entry time point of each axle of the vehicle6to the lane Ljand acceleration intensity as the first physical quantity that is the response to the action when each axle enters the lane Lj. The second observation point information includes an exit time point of each axle of the vehicle6from the lane Ljand acceleration intensity as the second physical quantity that is the response to the action when each axle exits the lane Lj.

Further, since the entry and the exit of each axle of the vehicle6correspond to each other, the first observation point information and the second observation point information can be stratified. The first observation point information, the second observation point information, and stratified information thereof are collectively referred to as axle information.

That is, in addition to the first observation point information and the second observation point information, the axle information includes correspondence information on the entry time point to the lane Ljand the acceleration intensity at the time of entry, the exit time point from the lane Ljand the acceleration intensity at the time of exit for each axle, and correspondence information between the vehicle6and the above corresponding information for each axle. Therefore, with the axle information, for each vehicle6passing through the superstructure7, the time points when each axle passes the lane Ljand the observation points Pjand Qj, and the acceleration intensities at the time of passing are identified.

FIG.5shows an example of the axle information. In the example inFIG.5, information in first to fourth rows is information related to the vehicle6whose vehicle number is 1. Information in the first row is information related to a leading axle whose axle number is 1. Information in the second row is information related to a second axle whose axle number is 2. Information in the third row is information related to a third axle whose axle number is 3. Information in the fourth row is information related to a fourth axle whose axle number is 4. For example, the correspondence information in the first row shows that, for the leading axle, whose axle number is 1, of the vehicle6whose vehicle number is 1, the entry time point to the lane L2is ti11, the acceleration intensity at the time of the entry is pai11, the exit time point from the lane L2is to11, and the acceleration intensity at the time of the exit is pao11.

Information in fifth and sixth rows is information related to the vehicle6whose vehicle number is 2. The information in the fifth row is the correspondence information related to the leading axle whose axle number is 1. The information in the sixth row is the correspondence information related to the second axle whose axle number is 2. For example, the correspondence information in the fifth row shows that, for the leading axle, whose axle number is 1, of the vehicle6whose vehicle number is 2, the entry time point to the lane L1is ti21, the acceleration intensity at the time of the entry is pai21, the exit time point from the lane L1is to21, and the acceleration intensity at the time of the exit is pao21.

Information in seventh and eighth rows is information related to the vehicle6whose vehicle number is 3. The information in the seventh row is the correspondence information related to the leading axle whose axle number is 1. The information in the eighth row is the correspondence information related to the second axle whose axle number is 2. For example, the correspondence information in the seventh row shows that, for the leading axle, whose axle number is 1, of the vehicle6whose vehicle number is 3, the entry time point to the lane L1is ti31, the acceleration intensity at the time of the entry is pai31, the exit time point from the lane L1is to31, and the acceleration intensity at the time of the exit is pao31.

As an example,FIGS.6and7show arrangement examples of the sensors21and22and the observation points P1, P2, Q1, and Q2when N=2. In the case of the arrangement examples shown inFIGS.6and7, a procedure for the measurement device1to generate the axle information will be described.

FIG.6is a diagram of the superstructure7as viewed from above.FIG.7is a cross-sectional view ofFIG.6cut along a line A-A or a line B-B. In the examples shown inFIGS.6and7, one sensor21is provided on each of the main girders G1and G3at the first end portion EA1of the superstructure7. One sensor22is provided on each of the main girders G1and G3at the second end portion EA2of the superstructure7. Observation points P1and Q1corresponding to the lane L1are respectively set at the positions on the surface of the floor plate F in the vertically upward direction of the sensors21and22provided on the main girder G1. Observation points P2and Q2corresponding to the lane L2are respectively set at the positions on the surface of the floor plate F in the vertically upward direction of the sensors21and22provided on the main girder G3. The sensor21provided on the main girder G1observes the observation point P1. The sensor21provided on the main girder G3observes the observation point P2. The sensor22provided on the main girder G1observes the observation point Q1. The sensor22provided on the main girder G3observes the observation point Q2. In order to generate the axle information, the measurement device1converts the acceleration at each time point detected by each of the sensors21and22into an amplitude, and acquires the acceleration intensity.

FIG.8shows diagrams showing examples of the acceleration detected for the observation points P1, P2, Q1and Q2when the vehicle6having four axles travels on the lane L2.FIG.9shows diagrams in which the acceleration amplitude at each time point inFIG.8is converted into the acceleration intensity. In the examples inFIGS.8and9, since the vehicle6is traveling on the lane L2, a large acceleration intensity is acquired at the time point when each of the four axles of the vehicle6passes the observation points P2and Q2. The acceleration intensity acquired at the time point when each of the four axles passes the observation point P2is included in the first observation point information. The acceleration intensity acquired at the time point when each of the four axles passes the observation point Q2is included in the second observation point information.

The measurement device1acquires a time point when the acquired acceleration intensity exceeds a predetermined threshold value as time points when the leading axle and subsequent axles successively pass the observation points P2and Q2, that is, the entry time point of each axle to the lane L2and the exit time point of each axle from the lane L2.

FIG.10is a diagram obtained by binarizing the acceleration intensities inFIG.9with the predetermined threshold value. In the example inFIG.10, the entry time point of each of the four axles to the lane L2and the exit time point of each of the four axles from the lane L2are acquired. The entry time point of each of the four axles to the lane L2is included in the first observation point information. Further, the exit time of each of the four axles from the lane L2is included in the second observation point information.

Further, the measurement device1compares a pattern1of the entry time point of each of the four axles to the lane L2and a pattern2of the exit time point of each of the four axles from the lane L2, and determines whether the two patterns are generated by the passage of the same vehicle6. Since intervals among the four axles do not change, if the vehicle6travels on the superstructure7at a constant speed, the patterns1and2coincide with each other. For example, the measurement device1slides one of the time points of the patterns1and2so as to coincide the entry time point and the exit time point of the leading axle. When a difference between the entry time point and the exit time point of each of the second to fourth axles is less than or equal to a predetermined threshold value, the measurement device1determines that the patterns1and2are generated by the passage of the same vehicle6. When the difference is greater than the predetermined threshold value, the measurement device1determines that the patterns1and2are generated by the passage of two vehicles6. When two vehicles6continuously travel on one lane at the same speed, an erroneous determination that the plurality of axles of a preceding vehicle6and the plurality of axles of a rear vehicle6all belong to the axles of one vehicle6may occur. In order to avoid the erroneous determination, when an interval between the entry time point and the exit time point of two adjacent axles is a time difference more than or equal to a predetermined time, the measurement device1may distinguish that the entry time point and the exit time point of the two axles belong to two vehicles6.

FIG.11is a diagram in which the pattern2showing the exit time point from the lane L2of each of the four axles is slid so as to coincide the entry time point and the exit time point of the leading axle with respect toFIG.10.FIG.11is enlarged in a horizontal axis direction with respect toFIG.10. In the example inFIG.11, the pattern1showing the entry time point of each of the four axles to the lane L2and the pattern2showing the exit time point of each of the four axles from the lane L2are substantially the same. It is determined that the patterns1and2are generated by the passage of the same vehicle6.

Then, by associating the four entry time points to the lane L2shown inFIG.10and peak values of the four acceleration intensities at the observation point P2shown inFIG.9, the four exit time points from the lane L2shown inFIG.10, and peak values of the four acceleration intensities at the observation point Q2shown inFIG.9with one another in order from the first, the measurement device1acquires the correspondence information of the leading axle, the correspondence information of the second axle, the correspondence information of the third axle, and the correspondence information of the fourth axle. Further, the measurement device1acquires the correspondence information in which the vehicle6traveling on the lane L2and the correspondence information of the four axles are associated with each other. These pieces of information are included in the axle information together with the first observation point information and the second observation point information.

Based on the axle information, the measurement device1can identify, for any vehicle6passing through the lane Ljof the superstructure7, the entry time point of each axle of the vehicle6to the observation point Pj, the acceleration intensity at the observation point Pjby each axle, the exit time point of each axle from the observation point Qj, and the acceleration intensity at the observation point Qjby each axle.

1-3. Generation of Deflection Waveform

In the present embodiment, considering that in the superstructure7of the bridge5, one or more bridge floors7aconstituted by the floor plate F and the main girders G1to GKare continuously arranged, the measurement device1calculates a displacement of one bridge floor7aas a displacement at a central portion in the longitudinal direction. The load applied to the superstructure7moves from one end to the other end of the superstructure7. At this time, a position of the load on the superstructure7and a load amount can be used to express a deflection amount, which is the displacement at the central portion of the superstructure7. In the present embodiment, in order to express, as a trajectory of a deflection amount due to the movement on a beam with a one-point load, the deflection deformation when the axles of the vehicle6move on the superstructure7, a structural model shown inFIG.12is considered. In the structural model, the deflection amount at the central position is calculated. InFIG.12, P is the load. a is a load position from an end of the superstructure7on a side where the vehicle6enters. b is a load position from an end of the superstructure7on a side where the vehicle6exits. I is a distance between both ends of the superstructure7. The structural model shown inFIG.12is a simple beam that supports both ends with both ends as fulcrums.

In the structural model shown inFIG.12, when the position of the end of the superstructure7on the side where the vehicle6enters is zero and the observation position for the deflection amount is x, a bending moment M of the simple beam is expressed by Equation (1).

In Equation (1), a function Hais defined as in Equation (2).

Equation (3) is obtained by transforming Equation (1).

Meanwhile, the bending moment M is expressed by Equation (4). In Equation (4), θ is an angle, I is a secondary moment, and E is a Young's modulus.

Equation (4) is substituted into Equation (3), and Equation (5) is obtained.

Equation (6) is obtained by integrating Equation (5) with respect to the observation position x, and Equation (7) is obtained by calculating Equation (6). In Equation (7), C1is an integral constant.

Further, Equation (8) is obtained by integrating Equation (7) with respect to the observation position x, and Equation (9) is obtained by calculating Equation (8). In Equation (9), C2is an integral constant.

In Equation (9), θx represents a deflection amount. Equation (10) is obtained by replacing θx with a deflection amount w.

Based onFIG.12, since b=l−a, Equation (10) is transformed as Equation (11).

Since the deflection amount w=0 when x=0, and Ha=0 based on x≤a, Equation (12) is obtained by substituting x=w=Ha=0 into Equation (11).
C2=0  (12)

Since the deflection amount w=0 when x=1, and Ha=1 based on x>a, Equation (13) is obtained by substituting x=1, w=0, and Ha=1 into Equation (11).

Equation (14) is obtained by substituting b=l−a into Equation (13).

Equation (15) is obtained by substituting the integral constant C1in Equation (12) and the integral constant C2in Equation (13) into Equation (10).

Equation (15) is transformed and the deflection amount w at the observation position x when the load P is applied to the position a is expressed by Equation (16).

FIG.13shows a state in which the load P moves from one end to the other end of the simple beam under a condition that the observation position x of the deflection amount is fixed at the central position of the simple beam, that is, when x=l/2.

When the load position a is on the left side of the observation position x=l/2, since Ha=1 based on x>a, Equation (17) is obtained by substituting x=l/2 and Ha=1 into Equation (16).

Equation (18) is obtained by substituting l=a+b into Equation (17).

Substituting a+b=l into Equation (18), a deflection amount wLat the observation position x when the position of the load P is on the left side of the central observation position x=l/2 is as shown in Equation (19).

On the other hand, when the load position a is on the right side of the observation position x=l/2, since Ha=0 based on x≤a, Equation (20) is obtained by substituting x=l/2 and Ha=0 into Equation (16).

Substituting l=a+b into Equation (20), a deflection amount wRat the observation position x when the position of the load P is on the right side of the central observation position x=l/2 is as shown in Equation (21).

When the load position a is the same as the observation position x=l/2, since Ha=0 based on x≤a, Equation (22) is obtained by substituting Ha=0 and a=b=l/2 into Equation (16).

Further, substituting a=l/2 into Equation (22), the deflection amount w at the observation position x when the position of the load P is the same as the central observation position is as shown in Equation (23).

In the simple beam with the fulcrums at both ends, a maximum deflection displacement is obtained when the load P is at the center. Therefore, according to Equation (23), a maximum deflection amount wmaxis expressed by Equation (24).

When the deflection amount wLat the observation position x when the position of the load P is on the left side of the central observation position x=l/2 is divided by the maximum deflection amount wmaxand normalized by the maximum deflection amount wmax, Equation (25) is obtained based on Equation (19) and Equation (24).

Equation (26) is obtained by setting a/l=r in Equation (25).

On the other hand, when the deflection amount wRat the observation position x when the position of the load P is on the right side of the central observation position x=l/2 is divided by the maximum deflection amount wmaxand normalized by the maximum deflection amount wmax, Equation (27) is obtained based on Equation (21) and Equation (24).

Here, since b=l×(1−r) based on a/l=r and a+b=l, Equation (28) is obtained by substituting b=l×(1−r) into Equation (27).

By summarizing Equation (25) and Equation (27), a normalized deflection amount wstdnormalized by the maximum deflection amount observed at the central portion when the load P moves on the simple beam is expressed by Equation (29).

In Equation (29), r=a/l and 1−r=b/l indicate a ratio of the position of the load P to the distance l between the fulcrums of the simple beam, and a variable R is defined as shown in Equation (30).

Equation (29) is replaced by Equation (31) using Equation (30).
wstd=3R−4R3(31)

Equation (30) and Equation (31) indicate that, when the observation position is at the center of the simple beam, the deflection amount is symmetrical on the right side and the left side of the center of the position of the load P.

FIG.14shows an example of a waveform of the normalized deflection amount wstdin the case of the observation position x=l/2. InFIG.14, the horizontal axis represents the position of the load P, and the vertical axis represents the normalized deflection amount wstd. In the example inFIG.14, the distance l between the fulcrums of the simple beam is 1.

The above-described axle information includes the entry time point of each axle of the vehicle6to the lane Ljand the exit time point of each axle of the vehicle6from the lane Lj, that is, the time points when the vehicle6passes the positions at both ends of the superstructure7. Therefore, the positions at both ends of the superstructure7correspond to the entry time point and the exit time point of the axle, and the load positions a and b are replaced with time. It is assumed that the speed of the vehicle6is substantially constant and the position and the time point are substantially proportional.

When the load position at the left end of the superstructure7corresponds to an entry time point ti, and the load position at the right end of the superstructure7corresponds to an exit time point to, the load position a from the left end is replaced with an elapsed time point tpfrom the entry time point ti. The elapsed time point tpis expressed by Equation (32).
tp=t−ti(32)

The distance l between the fulcrums is replaced by a time tsfrom the entry time point tito the exit time point to. The time tsis expressed by Equation (33).
ts=to−ti(33)

Since the speed of the vehicle6is constant, a time point tcwhen the load position a is at the center of the superstructure7is expressed by Equation (34).

By replacing the position with the time as described above, the position of the load P is expressed by Equation (35) and Equation (36).

Substituting Equation (35) and Equation (36) into Equation (29), the normalized deflection amount wstdreplaced by time is expressed by Equation (37).

Alternatively, according to Equation (30) and Equation (31), the normalized deflection amount wstdnormalized by the maximum amplitude is expressed by Equation (38) by substituting the variable R with time.

Considering that a relationship between the elapse of time and the normalized deflection amount is treated as observation data, the normalized deflection amount wstdis replaced with a normalized deflection amount model wstd(t) at the observation position at the center of the beam due to the movement of a single concentrated load on the simple beam with the fulcrums at both ends, and Equation (38) becomes Equation (39). Equation (39) is an approximate expression of deflection of the superstructure7, which is a structure, and is an equation based on the structure model of the superstructure7. Specifically, Equation (39) is an equation normalized by the maximum amplitude of deflection at the central position between the observation point Pjand the observation point Qjin the lane Ljwhere the vehicle6moves. The maximum value of the equation is 1.

Time information required for the normalized deflection amount model wstd(t) is obtained from the axle information described above. Since the normalized deflection amount model wstd(t) has a maximum deflection amount wmaxat the central position of the superstructure7, Equation (40) is obtained.

Since the deflection amount w shown in the above Equation (23) is the deflection amount at the observation position x=l/2 when the position of the load P is the same as the central observation position, and the deflection amount w coincides with the maximum deflection amount wmax, Equation (41) is obtained.

FIG.15shows an example of the normalized deflection amount model wstd(t). In the example inFIG.15, at the time point tc=(ti+to)/2=5 in which the entry time point ti=4 and the exit time point to=6, the normalized deflection amount model wstd(t) has the maximum deflection amount wmax=1 at the central position of the superstructure7.

It is assumed that the superstructure7which is the structure functions as bridge weigh in motion (BWIM), and is considered to be deformed in a manner of resembling a simple beam with both ends as fulcrums. Since the vehicle6, which is a moving object, passes through the superstructure7substantially at a constant speed from one end portion and moves to the other end portion of the superstructure7, an intermediate portion of the superstructure7and the end portion of the superstructure7receive the same load. Therefore, it can be considered that the observed displacement of the superstructure7is approximately proportional to an acceleration intensity apof the axle obtained from the axle information.

Assuming that a proportional coefficient is a product of the acceleration intensity apof the axle obtained from the axle information and a predetermined coefficient p, a deflection waveform H(t) of the superstructure7generated by each axle is obtained by Equation (42). The acceleration intensity apmay be the acceleration intensity at the time of entry and the acceleration intensity at the time of exit, which are included in the axle information, or a statistical value such as an average value of the acceleration intensity at the time of entry and the acceleration intensity at the time of exit.
H(t)=papwstd(t)  (42)

Substituting Equation (39) into Equation (42), the deflection waveform H(t) is expressed by Equation (43).

Until now, the single load P is applied to the superstructure7. However, since the load from each axle of the vehicle6is applied to the lane L on which the vehicle6travels, Equation (43) is replaced by a deflection waveform Hjk(t) as in Equation (44). In Equation (44), k is an integer indicating the axle number, and j is an integer indicating the lane number. As shown in Equation (44), the deflection waveform Hjk(t) is proportional to the product of the predetermined coefficient p and an acceleration intensity apjk.

FIG.16shows an example of the deflection waveform of the superstructure7generated by each axle included in the vehicle6traveling on the lane Lj. In the example inFIG.16, the vehicle6is a four-axle vehicle, and four deflection waveforms Hj1(t), Hj2(t), Hj3(t), and Hj4(t) are shown. In the example inFIG.16, since the loads generated by the leading and second axles are relatively small and the loads generated by the third and fourth axles are relatively large, maximum amplitudes of the deflection waveforms Hj1(t) and Hj2(t) are relatively small, and maximum amplitudes of the deflection waveforms Hj3(t) and Hj4(t) are relatively large.

1-4. Calculation of Correction Coefficient

FIG.17shows an example of positions at the center of gravity and positions of the axles of a four-axle vehicle, a three-axle vehicle, and a two-axle vehicle. In the example inFIG.17, the four-axle vehicle has the center of gravity between the second axle and the third axle. The three-axle vehicle has the center of gravity between the leading axle and the second axle. The two-axle vehicle has the center of gravity between the leading axle and the second axle.

Since the acceleration intensity apjkof each axle of the vehicle6is influenced by a distance moment from the center of gravity of the vehicle6to each axle, the acceleration intensities generated by the loads of respective stationary axles may be significantly different. In this case, approximation between the deflection waveform Hjk(t) calculated according to Equation (44) and the actually measured displacement waveform decreases. Here, in the present embodiment, the measurement device1replaces, based on the first observation point information, the deflection waveform Hjk(t) obtained according to Equation (44) with a deflection waveform in consideration of the influence of the distance moment from the center of gravity of the vehicle6to each axle.

When a leading time point, which is a time point when the leading axle whose axle number is 1 among the plurality of axles of the vehicle6passes the observation point Pj, is set as tj1, the measurement device1calculates a time Δtjkfrom the leading time point tj1to a time point tjkwhen the axle whose axle number is k passes the observation point Pjas in Equation (45). k is an integer of 1 or more and last or less. The leading time point tj1is an example of a “first leading time”.
Δtjk=tjk−tj1(45)

FIG.18shows an example of times Δtj2to Δtjlastcalculated according to Equation (45). Since the time Δtj1is zero, illustration thereof is omitted.FIG.18is a diagram obtained by binarizing the acceleration intensity at the observation point Pjby each axle when each of the four-axle vehicle, the three-axle vehicle, and the two-axle vehicle travels on the lane Lj.

Next, the measurement device1calculates a normalized time Δtjstdkobtained by normalizing the time Δtjkexpressed by Equation (45) with the time Δtjlastobtained according to Equation (46). The Δtjlastis a time from the leading time point tj1to a time point when the last axle passes the observation point Pj.

Next, according to Equation (47), the measurement device1calculates an addition normalized impact poweradd{apj_stdk} which is obtained by normalizing an integrated value of acceleration intensities apj1to apjkat the observation point Pjgenerated by each axle from the leading axle whose axle number is 1 to the axle whose axle number is k with a total sum of the acceleration intensities apj1to apjlastat the observation point Pjgenerated by each axle from the leading axle whose axle number is 1 to the last axle whose axle number is last.

FIG.19shows an example of correlation between the normalized time Δtjstdkcalculated according to Equation (46) and the addition normalized impact poweradd{apj_stdk} calculated according to Equation (47). InFIG.19, the horizontal axis represents the normalized time Δtjstdk, and the vertical axis represents the addition normalized impact poweradd{apj_stdk}. In the example inFIG.19, the vehicle6is a four-axle vehicle, and four points are plotted. A broken line is a straight line connecting two points. As shown inFIG.19, the addition normalized impact poweradd{apj_stdk} monotonically increases with respect to the normalized time Δtjstdk.

Next, a predetermined distribution ratio for distributing the load of the vehicle6to a load before the center of gravity of the vehicle6and a load after the center of gravity of the vehicle6is set as R:1−R=imagRF:(1−imagRF). The measurement device1calculates a shift addition normalized impact powershift_add{apj_stdk} obtained by subtractingimagRFfrom the addition normalized impact poweradd{apj_stdk} as in Equation (48).
shift_add{apj_stdk}=add{apj_stdk}−imagRF(48)

Since the distribution ratioimagRF:(1−imagRF) is an unknown number that cannot be measured, for example, a load distribution ratio before and after the center of gravity recommended in terms of steering stability of a general vehicle is assumed. For example, when the distribution ratio is 0.4:0.6,imagRFis 0.4. TheimagRFassumed in terms of the steering stability of the general vehicle is 0.4 or more and 0.6 or less.

FIG.20shows correlation between the normalized time Δtjstdkand the shift addition normalized impact powershift_add{apj_stdk} obtained by subtractingimagRF=0.4 from the addition normalized impact poweradd{apj_stdk} shown inFIG.19. InFIG.20, the horizontal axis represents the normalized time Δtjstdk, and the vertical axis represents the shift addition normalized impact powershift_add{apj_stdk}.

Next, the measurement device1interpolates a reference time ΔtjGOCwhen the shift addition normalized impact powershift_add{apj_stdk} is zero based on the correlation between the normalized time Δtjstdkand the shift addition normalized impact powershift_add{apj_stdk}.

Next, the measurement device1obtains an axle number s in which the shift addition normalized impact powershift_add{apj_stds} for the axles whose axle numbers are 1 to s is a negative value and the shift addition normalized impact powershift_add{apj_stds} for the axles whose axle numbers are s+1 to last is a positive value.

As in Equation (49), coordinates indicating the normalized time Δtjstdsand the shift addition normalized impact powershift_add{apj_stds}, which is a negative value, for the axle whose axle number is s are set as (xs, ys).
pointn(Δtjstdsshift_add{apj_stds})=(xsys)  (49)

Similarly, as in Equation (50), coordinates indicating the normalized time Δtjstdsand the shift addition normalized impact powershift_add{apj_stds+1}, which is a positive value, for the axle whose axle number is s+1 are set as (xs+1, ys+1).
pointp(Δtjstds+1shift_add{apj_stds+1})=(xs+1ys+1)  (50)

A straight line passing through the point of the coordinates (xs, ys) and the point of the coordinates (xs+1, ys+1) is given by Equation (51).

According to Equation (52) the measurement device1calculates, an x coordinate of an intersection between the straight line expressed by Equation (51) and y=0, and sets the calculated x coordinate as the reference time ΔtjGOC.

Here, when the time point when the total sum of the acceleration intensities apj1to apjlastfrom the leading axle whose axle number is 1 to the last axle whose axle number is last is distributed at the predetermined distribution ratioimagRF:(1−imagRF) is defined as the reference time point tjGOC, the reference time ΔtjGOCis a time from the time point when the leading axle passes the observation point Pjto the reference time point tjGOC. The reference time point tjGOCis a time point when the center of gravity of the vehicle6is estimated to pass the observation point Pj.

FIG.21shows a relationship between the reference time ΔtjGOCand the reference time point tjGOCcalculated for the correlation between the normalized time Δtjstdkand the shift addition normalized impact powershift_add{apj_stdk} shown in FIG.20. In the present embodiment, since the time point when the leading axle passes the observation point P is set to zero, the reference time ΔtjGOCand the reference time point tjGOCare equal to each other. The reference time point tjGOCis an example of a “first reference time”.

Next, the measurement device1calculates a normalized time difference Δtjstd-GOCk, which is a time difference between the normalized time Δtjstdkof each axle and the reference time ΔtjGOC, as in Equation (53).
Δtjstd-GOCk=|Δtjstdk−ΔtjGOC|  (53)

Next, according to Equation (54), the measurement device1calculates a ratio of the normalized time difference Δtjstd-GOCkof axles whose axle numbers are 1 to s, in which the shift addition normalized impact powershift_add{apj_stdk} is a negative value, to a sum of the normalized time differences Δtjstd-GOC1to Δtjstd-GOCsof axles whose axle numbers are 1 to s, and uses the ratio as a correction coefficient Rjk. k is an integer of 1 or more and s or less.

Similarly, according to Equation (55), the measurement device1calculates a ratio of the normalized time difference Δtjstd-GOCkof axles whose axle numbers are s+1 to last, in which the shift addition normalized impact powershift_add{apj_stdk} is a positive value, and a sum of the normalized time differences Δtjstd-GOCs+1to Δtjstd-GOClastof axles whose axle numbers are s+1 to last, and uses the ratio as a correction coefficient Rjk. k is an integer of s+1 or more and last or less.

According to Equations (54) and (55), correction coefficients Rj1to Rjlastof the axles whose axle numbers are 1 to last are obtained. The correction coefficient Rjkis a coefficient for correcting the acceleration intensity apjkso as to reduce the influence of the distance moment. The above Equation (44) for calculating the deflection waveform Hjk(t) is replaced with Equation (56) using the correction coefficient Rjk.

The measurement device1calculates the deflection waveform Hjk(t) of the superstructure7generated by the axle whose axle number is k according to Equation (56).

FIG.22shows an example of the deflection waveform of the superstructure7generated by each axle and calculated according to Equation (56).FIG.22shows deflection waveforms Hj1(t), Hj2(t), Hj3(t), and Hj4(t) obtained by correcting the four deflection waveforms shown inFIG.16, respectively. When the example ofFIG.22is compared with the example ofFIG.16, the maximum amplitudes of the deflection waveforms Hj1(t) and Hj2(t) increase, and the maximum amplitudes of the deflection waveforms Hj3(t) and Hj4(t) decrease. That is, the influence of the distance moment on the acceleration intensities apj1to apjlastis corrected by the correction coefficients Rj1to Rjlast.

As shown in Equation (57), a deflection waveform CPjm(t) of the superstructure7generated by the vehicle6traveling on the lane Ljis obtained by adding the deflection waveform Hjk(t) of the superstructure7generated by each axle. In Equation (57), m is an integer indicating the vehicle number, k is an integer indicating the axle number, and j is an integer indicating the lane number.

The measurement device1calculates the deflection waveform CPjm(t) of the superstructure7generated by the vehicle6, whose vehicle number is m, traveling on the lane Ljaccording to Equation (57).

InFIG.23, a deflection waveform CPjm(t) of the superstructure7generated by the vehicle6whose vehicle number is m, which is obtained by adding the four deflection waveforms Hj1(t), Hj2(t), Hj3(t), and Hj4(t) shown inFIG.22, is indicated by a solid line. InFIG.23, a deflection waveform CPjm(t) obtained by adding the four deflection waveforms Hj1(t), Hj2(t), Hj3(t), and Hj4(t) shown inFIG.16is indicated by a broken line. As shown inFIG.23, the maximum amplitude of the deflection waveform CPjm(t) and the time point when the deflection waveform CPjm(t) reaches the maximum amplitude are corrected by the correction coefficients Rj1to Rjlast.

1-5. Calculation of Displacement

The correlation between the deflection waveform CPjm(t) shown in Equation (57) and an observed displacement CU(t) is approximated by a polynomial equation. For example, as in Equation (58), the displacement CU(t) is approximated by a linear equation of the deflection waveform CPjm(t). In Equation (58), s is a first-order coefficient, and i is a zero-order coefficient.
CU(t)≅sCPjm(t)+i(58)

The first-order coefficient s and the zero-order coefficient i are calculated by, for example, a load test performed on a plurality of test vehicles. For example, a displacement meter is installed at the center of the lane Lj, and each of the plurality of test vehicles independently travels on the lane Lj. The measurement device1generates the axle information and acquires the displacement measured by the displacement meter. Then, the measurement device1plots the maximum value of the measured displacement as CUmaxand the maximum value of the deflection waveform CPjm(t) obtained according to Equation (57) and from the axle information as CPjm-maxon a graph, and obtains a first-order coefficient scuand a zero-order coefficient icuof an approximate straight line.

FIG.24is a diagram obtained by plotting the results of the load test performed on six test vehicles. InFIG.24, the horizontal axis represents the maximum value CPjm-maxof the deflection waveform of the superstructure7generated by the test vehicle, and the vertical axis represents the maximum value CUmaxof the measured displacement. InFIG.24, the six points are arranged in a straight line, and an approximate straight line with respect to the six points is indicated by a dotted line. In the example inFIG.24, in the approximate straight line, the first-order coefficient scuis 3084.435944, and the zero-order coefficient icuis 0.229180174.

The measurement device1calculates a displacement CUest(t) at the center of the lane L according to Equation (59) and using the first-order coefficient scu, the zero-order coefficient icu, and the deflection waveform CPjm(t) obtained according to Equation (57) from the axle information of an unknown vehicle6.
CUest(t)=scuCPjm(t)+icu(59)

FIG.25shows an example of the measured displacement CU (t) and the displacement CUest(t) calculated based on the corrected deflection waveform CPjm(t) obtained according to Equation (57). InFIG.25, the solid line indicates the measured displacement CU (t), and the broken line indicates the displacement CUest(t) calculated based on the deflection waveform CPjm(t). InFIG.25, the displacement CUest(t) calculated based on the deflection waveform CPjm(t) obtained by adding the deflection waveforms Hjk(t) of the superstructure7generated by each axle calculated by Equation (44), that is, the uncorrected deflection waveform CPjm(t), is indicated by a one-dot chain line. As shown inFIG.25, a difference between the displacement CUest(t) calculated based on the uncorrected deflection waveform CPjm(t) and the measured displacement CU (t) is large, whereas a difference between the displacement CUest(t) calculated based on the corrected deflection waveform CPjm(t) and the measured displacement CU (t) is very small. Therefore, according to Equation (59), the measurement device1can accurately calculate the displacement at the center generated by an unknown vehicle6traveling on the lane Ljwithout measuring the displacement at the center of the lane Lj.

In Equation (59), the zero-order coefficient icuis a small value. By substituting icu=0 into Equation (59), Equation (60) is obtained based on Equation (56) and Equation (57).

According to Equation (60), since the predetermined coefficient p and the first-order coefficient scucan be exchanged, the predetermined coefficient p is a coefficient having the same function as the first-order coefficient scu. That is, the predetermined coefficient p is a coefficient of a function that approximates the correlation between a deflection of a portion of the superstructure7and a displacement of the portion of the superstructure7between the observation point P and the observation point Q

1-6. Measurement Method

FIG.26is a flowchart showing an example of a procedure of the measurement method according to the first embodiment. In the present embodiment, the measurement device1executes the procedure shown inFIG.26.

As shown inFIG.26, first, based on the observation information obtained by the N sensors21that observe the observation points P1to PN, the measurement device1acquires the first observation point information including the time point when each of the plurality of axles of the vehicle6passes each of the observation points P1to PN, and the acceleration intensity as the first physical quantity which is the response to the action of each of the plurality of axles on each of the observation points P1to PN(step S1). As described above, the N sensors21are acceleration sensors. The observation information obtained by the N sensors21is detection information on the acceleration generated at the observation points P1to PN. The measurement device1acquires the first observation point information based on the acceleration detected by each of the N sensors21. The step S1is a first observation point information acquisition step.

Next, based on the observation information obtained by the N sensors22that observe the observation points Q1to QN, the measurement device1acquires the second observation point information including the time point when each of the plurality of axles of the vehicle6passes each of the observation points Q1to QN, and the acceleration intensity as the second physical quantity which is the response to the action of each of the plurality of axles on each of the observation points Q1to QN(step S2). As described above, the N sensors22are acceleration sensors. The observation information obtained by the N sensors22is detection information on the acceleration generated at the observation points Q1to QN. The measurement device1acquires the second observation point information based on the acceleration detected by each of the N sensors22. The step S2is a second observation point information acquisition step.

Next, using the first observation point information acquired in step S1, the measurement device1calculates the normalized times Δtjstd1to Δtjstdlast, which are times from the leading time point tj1when the leading axle among the plurality of axles passes the observation point Pjto the time points tj1to tjlastwhen each of the plurality of axles passes the observation point Pj, and the reference time ΔtjGOC, which is the time from the leading time point tj1to the reference time point tjGOC, which is the time point when the total sum of acceleration intensities apj1to apjlastgenerated by the plurality of axles is distributed at the predetermined distribution ratioimagRF:(1−imagRF) (step S3). Specifically, the measurement device1calculates the normalized times Δtjstd1to Δtjstdlastand the reference time ΔtjGOCaccording to the above Equations (45) to (52). The step S3is a first time calculation step.

Next, based on the normalized times Δtjstd1to Δtjstdlastand the reference time ΔtjGOCcalculated in step S3, the measurement device1calculates the correction coefficients Rj1to Rjlastfor correcting the acceleration intensities apj1to apjlastgenerated by the plurality of axles (step S4). Specifically, the measurement device1calculates the correction coefficients Rj1to Rjlastaccording to the above Equations (53) to (55). The step S4is a correction coefficient calculation step.

Next, based on the first observation point information acquired in step S1, the second observation point information acquired in step S2, the predetermined coefficient p, the correction coefficient Rjkcalculated in step S4, and the approximate expression of deflection of the superstructure7, the measurement device1calculates the deflection waveform Hjk(t) of the superstructure7generated by each of the plurality of axles (step S5). Specifically, the measurement device1calculates the deflection waveform Hjk(t) of the superstructure7generated by each axle of the vehicle6traveling on each lane L according to the above Equation (56). The step S5is a deflection waveform calculation step.

Next, according to the above Equation (57), the measurement device1calculates the deflection waveform CPjm(t) of the superstructure7generated by the vehicle6by adding the deflection waveform Hjk(t) of the superstructure7generated by each of the plurality of axles of the vehicle6and calculated in step S5(step S6). The step S6is a moving object deflection waveform calculation step.

Next, based on the deflection waveform CPjm(t) of the superstructure7generated by the vehicle6calculated in step S6, the measurement device1calculates the displacement CUest(t) of the superstructure7according to the above Equation (59) (step S7). The step S7is a displacement calculation step.

Next, the measurement device1outputs the displacement CUest(t) of the superstructure7calculated in step S7to the server2(step S8). The step S8is an output step.

The measurement device1repeats the processing in steps S1to S8until the measurement is completed (N in step S9).

FIG.27is a flowchart showing an example of a procedure of the first time calculation step, which is step S3inFIG.26.

As shown inFIG.27, first, the measurement device1sets an integer j to 1 (step S30), and determines the presence or absence of the vehicle6traveling on the lane L using the first observation point information (step S31).

Then, when it is determined in step S31that there is a vehicle6traveling on the lane Lj(Y in step S32), the measurement device1calculates the times Δtj1to Δtjlastaccording to the above Equation (45) and using the first observation point information (step S33). That is, the measurement device1calculates the times Δtj1to Δtjlastfrom the leading time point tj1when the leading axle of the vehicle6passes the observation point P to the time points tj1to tjlastwhen each of the plurality of axles passes the observation point Pj.

Next, according to the above Equation (47), the measurement device1calculates the addition normalized impact powersadd{apj_std1} toadd{apj_stdlast} by dividing the integrated value of the acceleration intensities apj1to apjkof the first observation point information by the total sum of the acceleration intensities apj1to apjlast(step S35).

Next, according to the above Equation (48), the measurement device1calculates shift addition normalized impact powersshift_add{apj_std1} toshift_add{apj_stdlast} by subtractingimagRFfrom the addition normalized impact powersadd{apj_std1} toadd{apj_stdlast} calculated in step S35(step S36).

Next, the measurement device1sets the x coordinate of the intersection between the straight line passing through the coordinates (Δtjstds,shift_add{apj_stds} (<0)) and the coordinates (Δtjstds+1,shift_add{apj_stds+1} (>0)) and y=0 as the reference time ΔtjGOCaccording to the above Equations (49) to (52) (step S37).

When it is determined in step S31that there is no vehicle6traveling on the lane Lj(N in step S32), the measurement device1does not perform the processing in steps S33to S37.

When the integer j is not N (N in step S38), the measurement device1adds 1 to the integer j (step S39), and repeats the processing in steps S31to S37.

Then, when the integer j is N (Y in step S38), the measurement device1ends the processing in the first time calculation step.

FIG.28is a flowchart showing an example of a procedure of the correction coefficient calculation step, which is step S4inFIG.26.

As shown inFIG.28, first, the measurement device1sets the integer j to 1 (step S41). When it is determined that there is a vehicle6traveling on the lane Ljin step S31inFIG.27(Y in step S42), according to the above Equation (53), the measurement device1calculates differences between the normalized times Δtjstd1to Δtjstdlastcalculated in step S34inFIG.27and the reference time ΔtjGOCcalculated in step S37inFIG.27, and sets the differences as the normalized time differences Δtstd-GOC1to Δtjstd-GOClast(step S43).

Next, according to the above Equation (54), the measurement device1calculates the correction coefficients Rj1to Rjsby dividing the normalized time differences Δtjstd-GOC1to Δtjstd-GOCscalculated in step S43by the sum of the normalized time differences Δtjstd-GOC1to Δtjstd-GOCs(step S44).

Next, according to the above Equation (55), the measurement device1calculates the correction coefficients Rjs+1to Rjlastby dividing the normalized time differences Δtjstd-GOCs+1to Δtjstd-GOClastcalculated in step S43by the sum of the normalized time differences Δtjstd-GOCs+1to Δtjstd-GOClast(step S45).

When it is determined in step S31inFIG.27that there is no vehicle6traveling on the lane Lj(N in step S42), the measurement device1does not perform the processing in steps S43to S45.

When the integer j is not N (N in step S46), the measurement device1adds 1 to the integer j (step S47), and repeats the processing in steps S42to S45.

Then, when the integer j is N (Y in step S46), the measurement device1ends the processing in the correction coefficient calculation step.

1-7. Configuration of Measurement Device

FIG.29is a diagram showing a configuration example of the measurement device1according to the first embodiment. As shown inFIG.29, the measurement device1includes a control unit110, a first communication unit120, a storage unit130, a second communication unit140, and an operation unit150.

The control unit110calculates the time point when the vehicle6travels on the superstructure7or the displacement or the like of the superstructure7based on the acceleration data output from each of the sensors21and22installed in the superstructure7.

The first communication unit120receives the acceleration data from each of the sensors21and22. The acceleration data output from each of the sensors21and22is, for example, a digital signal. The first communication unit120outputs to the control unit110the acceleration data received from each of the sensors21and22.

The storage unit130is a memory that stores a program, data, and the like for the control unit110to perform calculation processing and control processing. In addition, the storage unit130stores a program, data, and the like for the control unit110to implement a predetermined application function. The storage unit130is implemented by, for example, various integrated circuit (IC) memories such as a read only memory (ROM), a flash ROM, and a random access memory (RAM), and a recording medium such as a hard disk and a memory card.

The storage unit130includes a non-volatile information storage device that is a device or a medium that can be read by a computer. Various programs, data, and the like may be stored in the information storage device. The information storage device may be an optical disk such as an optical disk DVD or a CD, a hard disk drive, or various types of memories such as a card-type memory or a ROM. In addition, the control unit110may receive various programs, data, and the like via the communication network4and store the programs, the data, and the like in the storage unit130.

The second communication unit140transmits information such as a calculation result of the control unit110to the server2via the communication network4.

The operation unit150acquires operation data from the user and transmits the operation data to the control unit110.

The control unit110includes a first observation point information acquisition unit111, a second observation point information acquisition unit112, a first time calculation unit113, a correction coefficient calculation unit114, a deflection waveform calculation unit115, a moving object deflection waveform calculation unit116, a displacement calculation unit117, a coefficient value calculation unit118, and an output processing unit119.

Based on the observation information obtained by the N sensors21that observe the observation points P1to PN, the first observation point information acquisition unit111performs processing of acquiring the first observation point information including the time point when each of the plurality of axles of the vehicle6passes each of the observation points P1to PN, and the acceleration intensity as the first physical quantity which is the response to the action of each of the plurality of axles on each of the observation points P1to PN. That is, the first observation point information acquisition unit111performs the processing of the first observation point information acquisition step inFIG.26. The first observation point information acquired by the first observation point information acquisition unit111is stored in the storage unit130.

Based on the observation information obtained by the N sensors22that observe the observation points Q1to QN, the second observation point information acquisition unit112performs processing of acquiring the second observation point information including the time point when each of the plurality of axles of the vehicle6passes each of the observation points Q1to QN, and the acceleration intensity as the second physical quantity which is the response to the action of each of the plurality of axles on each of the observation points Q1to QN. That is, the second observation point information acquisition unit112performs the processing of the second observation point information acquisition step inFIG.26. The second observation point information acquired by the second observation point information acquisition unit112is stored in the storage unit130.

Using the first observation point information acquired by the first observation point information acquisition unit111, the first time calculation unit113performs processing of calculating the normalized times Δtjstd1to Δtjstdlast, which are times from the leading time point tj1when the leading axle among the plurality of axles passes the observation point Pjto the time points tj1to tjlastwhen each of the plurality of axles passes the observation point Pj, and the reference time ΔtjGOC, which is the time from the leading time point tj1to the reference time point tjGOC, which is the time point when the total sum of acceleration intensities apj1to apjlastgenerated by the plurality of axles is distributed at the predetermined distribution ratioimagRF:(1−imagRF). That is, the first time calculation unit113performs the processing of the first time calculation step inFIG.26. The normalized times Δtjstd1to Δtjstdlastand the reference time ΔtjGOCcalculated by the first time calculation unit113are stored in the storage unit130.

Based on the normalized times Δtjstd1to Δtjstdlastand the reference time ΔtjGOCcalculated by the first time calculation unit113, the correction coefficient calculation unit114performs processing of calculating the correction coefficients Rj1to Rjlastfor correcting the acceleration intensities apj1to apjlastgenerated by the plurality of axles. That is, the correction coefficient calculation unit114performs the processing of the correction coefficient calculation step inFIG.26. The correction coefficients R1to Rjlastcalculated by the correction coefficient calculation unit114are stored in the storage unit130.

Based on the first observation point information acquired by the first observation point information acquisition unit111, the second observation point information acquired by the second observation point information acquisition unit112, the predetermined coefficient p, the correction coefficient Rjkcalculated by the correction coefficient calculation unit114, and the approximate expression of deflection of the superstructure7, the deflection waveform calculation unit115performs processing of calculating the deflection waveform Hjk(t) of the superstructure7generated by each of the plurality of axles. That is, the deflection waveform calculation unit115performs the processing of the deflection waveform calculation step inFIG.26. The deflection waveform Hjk(t) calculated by the deflection waveform calculation unit115is stored in the storage unit130. The predetermined coefficient p and the approximate expression of deflection of the superstructure7are previously stored in the storage unit130.

The moving object deflection waveform calculation unit116performs processing of calculating the deflection waveform CPjm(t) of the superstructure7generated by the vehicle6by adding the deflection waveform Hjk(t) of the superstructure7generated by each of the plurality of axles of the vehicle6and calculated by the deflection waveform calculation unit115. That is, the moving object deflection waveform calculation unit116performs the processing of the moving object deflection waveform calculation step inFIG.26. The deflection waveform CPjm(t) calculated by the moving object deflection waveform calculation unit116is stored in the storage unit130.

Based on the deflection waveform CPjm(t) of the superstructure7generated by the vehicle6calculated by the moving object deflection waveform calculation unit116, the displacement calculation unit117performs processing of calculating the displacement CUest(t) of the superstructure7. That is, the displacement calculation unit117performs the processing of the displacement calculation step inFIG.26. The displacement CUest(t) calculated by the displacement calculation unit117is stored in the storage unit130.

When each of the plurality of test vehicles independently travels on the superstructure7, the coefficient value calculation unit118performs processing of obtaining an approximate straight line that approximates the correlation between the maximum value of the displacement CUmaxof the superstructure7measured by a displacement meter (not shown) and the maximum value CPjm-maxof the deflection waveform CPjm(t) calculated by the moving object deflection waveform calculation unit116, and calculating the value of the first-order coefficient scuand the value of the zero-order coefficient icuof the above Equation (59). The value of the first-order coefficient scuand the value of the zero-order coefficient icucalculated by the coefficient value calculation unit118are stored in the storage unit130.

The output processing unit119performs processing of outputting the displacement CUest(t) of the superstructure7calculated by the displacement calculation unit117to the server2via the second communication unit140. That is, the output processing unit119performs the processing of the output step inFIG.26.

For example, based on the operation data from the operation unit150, the control unit110switches between a first mode for calculating the time point when an unknown vehicle6travels on the superstructure7and the displacement of the superstructure7and the like, and a second mode for calculating the value of the first-order coefficient scuand the value of the zero-order coefficient icu. For example, after the N sensors21and the N sensors22are installed in the superstructure7, the load test is performed on the plurality of test vehicles in a state in which the control unit110is set to the second mode. After the load test ends, the control unit110is set to the first mode.

In the present embodiment, the control unit110is a processor that executes various programs stored in the storage unit130. By executing a measurement program131stored in the storage unit130, each function of the first observation point information acquisition unit111, the second observation point information acquisition unit112, the first time calculation unit113, the correction coefficient calculation unit114, the deflection waveform calculation unit115, the moving object deflection waveform calculation unit116, the displacement calculation unit117, the coefficient value calculation unit118, and the output processing unit119is implemented. In other words, the measurement program131is a program that causes the measurement device1as a computer to execute each procedure in the flowchart shown inFIG.26.

In the processor, for example, functions of each part may be implemented by individual hardware, or the functions of each part may be implemented by integrated hardware. For example, the processor may include hardware. The hardware may include at least one of a circuit for processing a digital signal and a circuit for processing an analog signal. The processor may be a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), or the like. The control unit110is implemented as a custom integrated circuit (IC) such as an application specific integrated circuit (ASIC), and may implement the functions of each part, or may implement the functions of each part by the CPU and the ASIC.

The control unit110may not include the coefficient value calculation unit118. For example, the server2or another device may perform processing of calculating the value of the first-order coefficient scuand the value of the zero-order coefficient icu, and store the values in the storage unit130of the measurement device1.

1-8. Operation Effects

In the measurement method according to the first embodiment described above, the measurement device1acquires, based on the observation information obtained by the N sensors21that observe the observation points P1to PN, the first observation point information including the time point and the acceleration intensity when each of the plurality of axles of the vehicle6passes each of the observation points P1to PN. The measurement device1acquires, based on the observation information obtained by the N sensors22that observe the observation points Q1to QN, the second observation point information including the time point and the acceleration intensity when each of the plurality of axles of the vehicle6passes each of the observation points Q1to QN. According to Equations (45) to (52), and using the first observation point information, the measurement device1calculates the normalized times Δtjstd1to Δtjstdlast, which are times from the leading time point tj1when the leading axle passes the observation point Pjto the time points tj1to tjlastwhen each of the plurality of axles passes the observation point Pj, and the reference time ΔtjGOCfrom the leading time point t1to the reference time point tjGOCwhen the total sum of acceleration intensities apj1to apjlastgenerated by the plurality of axles is distributed at the predetermined distribution ratioimagRF:(1−imagRF). According to Equations (53) to (55), and based on the normalized times Δtjstd1to Δtjstdlastand the reference time ΔtjGOC, the measurement device1calculates the correction coefficients Rj1to Rjlastfor correcting the acceleration intensities apj1to apjlastgenerated by the plurality of axles. Next, based on the first observation point information, the second observation point information, the predetermined coefficient p, the correction coefficients Rj1to Rjlast, and the approximate expression (39) of deflection of the superstructure7, the measurement device1calculates the deflection waveform Hjk(t) of the superstructure7generated by each axle according to Equation (56), and calculates the deflection waveform CPjm(t) of the superstructure7generated by the vehicle6by adding the deflection waveform Hjk(t). Therefore, according to the measurement method in the first embodiment, the measurement device1can calculate the deflection waveform of the superstructure7generated by the vehicle6which is the moving object that moves on the superstructure7without measuring the displacement of the superstructure7which is the structure.

Further, according to the measurement method in the first embodiment, the acceleration intensities apj1to apjlastgenerated by each axle are corrected by the correction coefficients Rj1to Rjlastsuch that the influence of the distance moment from the center of gravity on the load of each axle is reduced. Therefore, calculation accuracy of the deflection waveform of the superstructure7is improved in consideration of the difference in loads between a case where the vehicle6is stationary and a case where the vehicle6is moving.

In the measurement method according to the first embodiment, according to the correlation equation (59), the measurement device1can calculate the displacement CUest(t) of the lane L based on the deflection waveform CPjm(t) of the superstructure7generated by the vehicle6. Therefore, according to the measurement method in the first embodiment, the measurement device1can estimate the displacement of the superstructure7without measuring the displacement of the superstructure7.

In addition, according to the measurement method in the first embodiment, since it is not necessary to set the observation points for measuring the displacement of the superstructure7, the number of observation points observed by the observation device is reduced. Further, since the measurement system is simplified, cost required for the measurement is reduced.

Further, according to the measurement method in the first embodiment, since the observation points P1to PNand Q1to QNare set at both end portions of the superstructure7, and no observation point is set at the central portion of the superstructure7, construction and maintenance of the measurement system10are facilitated, and the cost required for measurement is reduced.

According to the measurement method in the first embodiment, since the measurement device1can calculate the deflection waveform which is the deformation of the superstructure7due to the axle load of the vehicle6passing through the superstructure7, sufficient information can be provided for maintenance and management of the bridge5to predict the damage of the superstructure7.

2. Second Embodiment

In the measurement method according to the first embodiment, the measurement device1calculates the correction coefficients Rj1to Rjlastusing the first observation point information without using the second observation point information. In a measurement method according to a second embodiment, the measurement device1calculates the correction coefficients Rj1to Rjlastusing the first observation point information and the second observation point information. Hereinafter, the same components as those in the first embodiment will be denoted by the same reference numerals for the second embodiment, and the description repeated with the first embodiment will be omitted or simplified, and different contents from the first embodiment will be mainly described.

In the present embodiment, when a first leading time point, which is a time point when the leading axle whose axle number is 1 among the plurality of axles of the vehicle6passes the observation point Pj, is set as tj1_1, the measurement device1calculates a time Δtjk_1from the first leading time point tj1_1to a time point tjk_1when the axle whose axle number is k passes the observation point Pjas in Equation (61) which is similar to Equation (45). k is an integer of 1 or more and last or less.
Δtjk_1=tjk_1−tj1_1(61)

Next, the measurement device1calculates a first normalized time Δtjstdk_1obtained by normalizing a time Δtjk_1expressed by Equation (61) with a time Δtjlast_1obtained by Equation (62), which is similar to Equation (46). The Δtjlast_1is a time from the first leading time point tj1_1to a time point when the last axle passes the observation point Pj.

Next, according to Equation (63), which is similar to Equation (47), the measurement device1calculates a first addition normalized impact poweradd{apj_stdk_1} obtained by normalizing the integrated value of the acceleration intensities apj1_1to apjk_1at the observation point P generated by each axle from the leading axle whose axle number is 1 to the axle whose axle number is k with the total sum of the acceleration intensities apj1_1to apjlast_1at the observation point P generated by each axle from the leading axle whose axle number is 1 to the last axle whose axle number is last.

Next, a predetermined distribution ratio for distributing the load of vehicle6to a load before the center of gravity of the vehicle6and a load after the center of gravity of the vehicle6is set as R:1−R=imagRF:(1−imagRF). According to Equation (64), which is similar to Equation (48), the measurement device1calculates a first shift addition normalized impact powershift_add{apj_stdk_1} obtained by subtractingimagRFfrom the addition normalized impact poweradd{apj_stdk_1}.
shift_add{apj_stdk_1}=add{apj_stdk_1}−imagRF(64)

Next, the measurement device1obtains an axle number s in which the first shift addition normalized impact powershift_add{apj_stds_1} for the axles whose axle numbers are 1 to s is a negative value and the first shift addition normalized impact powershift_add{apj_stds_1} for the axles whose axle numbers are s+1 to last is a positive value.

Similar to Equation (49), as in Equation (65), coordinates indicating the first normalized time Δtjstds_1and the first shift addition normalized impact powershift_add{apj_stds_1}, which is a negative value, for the axle whose axle number is s are set as (xs_1, ys_1).
pointn(Δtjstds_1shift_add{apj_stds_1})=(xs_1ys_1)  (65)

Similar to Equation (50), as in Equation (66), coordinates indicating the first normalized time Δtjstds+1_1and the first shift addition normalized impact powershift_add{apj_stds+1_1}, which is a positive value, for the axle whose axle number is s are set as (xs+1_1, ys+1_1).
pointp(Δtjstds+1_1shift_add{apj_stds+1_1})=(xs+1_1ys+1_1)  (66)

A straight line passing through the point of the coordinates (xs_1, ys_1) and the point of the coordinates (xs+1_1, ys+1_1) is given by Equation (67), which is similar to Equation (51).

According to Equation (68), which is similar to Equation (52), the measurement device1calculates an x coordinate of an intersection between the straight line expressed by Equation (67) and y=0, and sets the calculated x coordinate as a first reference time ΔtjGOC_1.

Here, when the time point when the total sum of the acceleration intensities apj1_1to apjlast_1at the observation point Pjgenerated by each axle from the leading axle whose axle number is 1 to the last axle whose axle number is last is distributed at the predetermined distribution ratioimagRF:(1−imagRF) is defined as the first reference time point tjGOC_1, the first reference time ΔtjGOC_1is a time from the time point when the leading axle passes the observation point Pjto the first reference time point tjGOC_1. The first reference time point tjGOC_1is a time point when the center of gravity of the vehicle6is estimated to pass the observation point Pj.

Further, when a second leading time point, which is a time point when the leading axle whose axle number is 1 among the plurality of axles of the vehicle6passes the observation point Qj, is set as tj1_2, the measurement device1calculates a time Δtjk_2from the second leading time point tj1_2to a time point tjk_2when the axle whose axle number is k passes the observation point Qjas in Equation (69), which is similar to Equation (61).
Δtjk_2=tjk_2−tj1_2(69)

Next, the measurement device1calculates a second normalized time Δtjstdk_2obtained by normalizing a time Δtjk_2expressed by Equation (69) with a time Δtjlast_2obtained by Equation (70), which is similar to Equation (62). The Δtjlast_2is a time from the second leading time point tj1_2to a time point when the last axle passes the observation point Q

Next, according to Equation (71), which is similar to Equation (63), the measurement device1calculates a second addition normalized impact poweradd{apj_stdk_2} obtained by normalizing the integrated value of the acceleration intensities apj1_2to apjk_2at the observation point Qjgenerated by each axle from the leading axle whose axle number is 1 to the axle whose axle number is k with the total sum of the acceleration intensities apj1_2to apjlast_2at the observation point Qjgenerated by each axle from the leading axle whose axle number is 1 to the last axle whose axle number is last.

Next, the measurement device1calculates a second shift addition normalized impact powershift_add{apj_stdk_2} by subtractingimagRFfrom the second addition normalized impact poweradd{apj_stdk_2} according to Equation (72), which is similar to Equation (64).
shift_add{apj_stdk_2}=add{apj_stdk_2}−imagRF(72)

Next, the measurement device1obtains an axle number s in which the second shift addition normalized impact powershift_add{apj_stds_2} for the axles whose axle numbers are 1 to s is a negative value and the second shift addition normalized impact powershift_add{apj_stds_2} for the axles whose axle numbers are s+1 to last is a positive value.

Similar to Equation (65), as in Equation (73), coordinates indicating the second normalized time Δtjstds_2and the second shift addition normalized impact powershift_add{apj_stds_2}, which is a negative value, for the axle whose axle number is s are set as (xs_2, ys_2).
pointn(Δtjstds_2shift_add{apj_stds_2})=(xs_2ys_2)  (73)

Similar to Equation (66), as in Equation (74), coordinates indicating the second normalized time Δtjstds+1_2and the second shift addition normalized impact powershift_add{apj_stds+1_2}, which is a positive value, for the axle whose axle number is s are set as (xs+1_2, ys+1_2).
pointp(Δtjstds+1_2shift_add{apj_stds+1_2})=(xs+1_2ys+1_2)  (74)

A straight line passing through the point of the coordinates (xs_2, ys_2) and the point of the coordinates (xs+1_2, ys+1_2) is given by Equation (75), which is similar to Equation (67).

According to Equation (76), which is similar to Equation (68), the measurement device1calculates an x coordinate of an intersection between the straight line expressed by Equation (75) and y=0, and sets the calculated x coordinate as a second reference time ΔtjGOC_2.

Here, when the time point when the total sum of the acceleration intensities apj1_2to apjlast_2at the observation point Qjgenerated by each axle from the leading axle whose axle number is 1 to the last axle whose axle number is last is distributed at the predetermined distribution ratioimagRF:(1−imagRF) is defined as the second reference time point tjGOC_2the second reference time ΔtjGOC_2is a time from the time point when the leading axle passes the observation point Qjto the second reference time point tjGOC_2. The second reference time point tjGOC_2is a time point when the center of gravity of the vehicle6is estimated to pass the observation point Qj.

Next, the measurement device1calculates an average value of the first normalized time Δtjstdk_1and the second normalized time Δtjstdk_2of each axle according to Equation (77), and sets the average value as the normalized time Δtjstdk.

In addition, the measurement device1calculates an average value of the first reference time ΔtjGOC_1and the second reference time ΔtjGOC_2according to Equation (78), and sets the average value as the reference time ΔtjGOC.

Then, the measurement device1calculates the normalized time difference Δtjstd-GOCkaccording to the above Equation (53), and calculates the correction coefficients Rj1to Rjlastof the axles whose the axle numbers are 1 to last according to the above Equations (54) and (55).

FIG.30is a flowchart showing an example of a procedure of the measurement method according to the second embodiment. In the present embodiment, the measurement device1executes the procedure shown inFIG.30.

As shown inFIG.30, first, the measurement device1performs the processing of the first observation point information acquisition step (step S101), which is similar to step S1inFIG.26.

Next, the measurement device1performs the processing of the second observation point information acquisition step (step S102), which is similar to step S2inFIG.26.

Next, using the first observation point information acquired in step S101, the measurement device1calculates the first normalized times Δtjstd1_1to Δtjstdlast_1which are times from the first leading time point tj1_1when the leading axle among the plurality of axles passes the observation point Pjto the time points tj1_1to tjlast_1when each of the plurality of axles passes the observation point Pj, and the first reference time ΔtjGOC_1, which is the time from the first leading time point tj1_1to the first reference time point tjGOC_1, which is the time point when the total sum of acceleration intensities apj1_1to apjlast_1generated by the plurality of axles is distributed at the predetermined distribution ratioimagRF:(1−imagRF(step S103). Specifically, the measurement device1calculates the first normalized times Δtjstd1_1to Δtjstdlast_1and the first the reference time ΔtjGOC_1according to the above Equations (61) to (68). The step S103is a first time calculation step.

Next, using the second observation point information acquired in step S102, the measurement device1calculates the second normalized times Δtjstd1_2to Δtjstdlast_2, which are times from the second leading time point tj1_2when the leading axle among the plurality of axles passes the observation point Qjto the time points tj1_2to tjlast_2when each of the plurality of axles passes the observation point Qj, and the second reference time ΔtjGOC_2, which is the time from the second leading time point tj1_2to the second reference time point tjGOC_2, which is the time point when the total sum of acceleration intensities apj1_2to apjlast_2generated by the plurality of axles is distributed at the predetermined distribution ratioimagRF:(1−imagRF) (step S104). Specifically, the measurement device1calculates the second normalized times Δtjstd1_2to Δtjstdlast_2and second the reference time ΔtjGOC_2according to the above Equations (69) to (76). The step S104is a second time calculation step.

Next, based on the first normalized times Δtjstd1_1to Δtjstdlast_1and the first reference time ΔtjGOC_1calculated in step S103and the second normalized times Δtjstd1_2to Δtjstdlast_2and the second reference time ΔtjGOC_2calculated in step S104, the measurement device1calculates the correction coefficients Rj1to Rjlastfor correcting the acceleration intensities apj1_1to apjlast_1at the observation point Pjand the acceleration intensities apj1_2to apjlast_2at the observation point Qjwhich are generated by the plurality of axles (step S105). Specifically, the measurement device1calculates the normalized time Δtjstdkand the reference time ΔtjGOCaccording to the above Equations (77) and (78), and calculates the correction coefficients Rj1to Rjlastaccording to Equations (53) to (55). The step S105is a correction coefficient calculation step.

Next, the measurement device1performs processing of a deflection waveform calculation step (step S106), which is similar to step S5inFIG.26.

Next, the measurement device1performs processing of a moving object deflection waveform calculation step (step S107), which is similar to step S6inFIG.26.

Next, the measurement device1performs processing of a displacement calculation step (step S108), which is similar to step S7inFIG.26.

Next, the measurement device1performs processing of an output step (step S109), which is similar to step S8inFIG.26.

The measurement device1repeats the processing in steps S101to S109until the measurement is completed (N in step S110).

FIG.31is a flowchart showing an example of a procedure of the first time calculation step, which is step S103inFIG.30.

As shown inFIG.31, first, the measurement device1sets an integer j to 1 (step S130), and determines the presence or absence of the vehicle6traveling on the lane Ljusing the first observation point information (step S131).

Then, when it is determined in step S131that there is a vehicle6traveling on the lane Lj(Y in step S132), the measurement device1calculates the times Δtj1_1to Δtjlast_1according to the above Equation (61) and using the first observation point information (step S133). That is, the measurement device1calculates the times Δtj1_1to Δtjlast_1from the first leading time point tj1_1when the leading axle of the vehicle6passes the observation point Pjto the time points tj1_1to tjlast_1when each of the plurality of axles passes the observation point Pj.

Next, the measurement device1calculates the first normalized times Δtjstd1_1to Δtjstdlast_1by dividing the times Δtj1_1to Δtjlast_1calculated in step S133by the time Δtjlast_1according to the above Equation (62) (step S134).

Next, the measurement device1calculates the first addition normalized impact powersadd{apj_std1_1} toadd{apj_stdlast_1} by dividing the integrated value of the acceleration intensities apj1_1to apjk_1of the first observation point information by the total sum of the acceleration intensities apj1_1to apjlast_1according to the above Equation (63) (step S135).

Next, the measurement device1calculates the first shift addition normalized impact powersshift_add{apj_std1_1} toshift_add{apj_stdlast_1} by subtractingimagRFfrom the first addition normalized impact powersadd{apj_std1_1} toadd{apj_stdlast_1} calculated in step S135according to the above Equation (64) (step S136).

Next, the measurement device1sets the x coordinate of the intersection between the straight line passing through the coordinates (Δtjstds_1,shift_add{apj_stds_1} (<0)) and the coordinates (Δtjstds+1_1,shift_add{apj_stds+1_1} (>0)) and y=0 as the first reference time ΔtjGOC_1according to the above Equations (65) to (68) (step S137).

When it is determined in step S131that there is no vehicle6traveling on the lane Lj(N in step S132), the measurement device1does not perform the processing in steps S133to S137.

When the integer j is not N (N in step S138), the measurement device1adds 1 to the integer j (step S139), and repeats the processing in steps S131and S137.

Then, when the integer j is N (Y in step S138), the measurement device1ends the processing in the first time calculation step.

FIG.32is a flowchart showing an example of a procedure of the second time calculation step, which is step S104inFIG.30.

As shown inFIG.32, first, the measurement device1sets the integer j to 1 (step S141). when it is determined in step S131inFIG.31that there is a vehicle6traveling on the lane Lj(Y in step S142), the measurement device1calculates the times Δtj1_2to Δtjlast_2according to the above Equation (69) and using the second observation point information (step S143). That is, the measurement device1calculates the times Δtj1_2to Δtjlast_2from the second leading time point tj1_2when the leading axle of the vehicle6passes the observation point Qjto the time points tj1_2to tjlast_2when each of the plurality of axles passes the observation point Qj.

Next, the measurement device1calculates the second normalized times Δtjstd1_2to Δtjstdlast_2by dividing the times Δtj1_2to Δtjlast_2calculated in step S143by the time Δtjlast_2according to the above Equation (70) (step S144).

Next, the measurement device1calculates the second addition normalized impact powersadd{apj_std1_2} toadd{apj_stdlast_2} by dividing the integrated value of the acceleration intensities apj1_2to apjk_2of the second observation point information by the total sum of the acceleration intensities apj1_2to apjlast_2according to the above Equation (71) (step S145).

Next, the measurement device1calculates the second shift addition normalized impact powersshift_add{apj_std1_2} toshift_add{apj_stdlast_2} by subtractingimagRFfrom the second addition normalized impact powersadd{apj_std1_2} toadd{apj_stdlast_2} calculated in step S145according to the above Equation (72) (step S146).

Next, the measurement device1sets the x coordinate of the intersection between the straight line passing through the coordinates (Δtjstds_2,shift_add{apj_stds_2} (<0)) and the coordinates (Δtjstds+1_2,shift_add{apj_stds+1_2} (>0)) and y=0 as the second reference time ΔtjGOC_2according to the above Equations (73) to (76) (step S147).

When it is determined in step S131inFIG.31that there is no vehicle6traveling on the lane L (N in step S142), the measurement device1does not perform the processing in steps S143to S147.

When the integer j is not N (N in step S148), the measurement device1adds 1 to the integer j (step S149), and repeats the processing in steps S141and S147.

Then, when the integer j is N (Y in step S148), the measurement device1ends the processing in the second time calculation step.

FIG.33is a flowchart showing an example of a procedure of the correction coefficient calculation step, which is step S105inFIG.30.

As shown inFIG.33, first, the measurement device1sets the integer j to 1 (step S151). When it is determined in step S131inFIG.31that there is a vehicle6traveling on the lane Lj(Y in step S152), the measurement device1calculates an average value of each of the first normalized times Δtjstd1_1to Δtjstdlast_1calculated in step S134inFIG.31and each of the second normalized times Δtjstd1_2to Δtjstdlast_2calculated in step S144inFIG.32according to the above Equation (77), and sets the average values as the normalized times Δtjstd1to Δtjstdlast(step S153).

Next, the measurement device1calculates an average value of the first reference time ΔtjGOC_1calculated in step S137inFIG.31and the second reference time ΔtjGOC_2calculated in step S147inFIG.32according to Equation (78), and sets the average value as the reference time ΔtjGOC(step S154).

Next, the measurement device1calculates differences between the normalized times Δtjstd1to Δtjstdlastcalculated in step S153and the reference time ΔtjGOCcalculated in step S154according to Equation (53), and sets the differences as the normalized time differences Δtjstd-GOC1to Δtjstd-GOClast(step S155).

Next, the measurement device1calculates the correction coefficients Rj1to Rjsby dividing the normalized time differences Δtjstd-GOC1to Δtjstd-GOCscalculated in step S155by the sum of the normalized time differences Δtjstd-GOC1to Δtjstd-GOCsaccording to the above Equation (54) (step S156).

Next, the measurement device1calculates the correction coefficients Rjs+1to Rjlastby dividing the normalized time differences Δtjstd-GOCs+1to Δtjstd-GOClastcalculated in step S155by the sum of the normalized time differences Δtjstd-GOCs+1to Δtjstd-GOClastaccording to the above Equation (55) (step S157).

When it is determined in step S131inFIG.31that there is no vehicle6traveling on the lane Lj(N in step S152), the measurement device1does not perform the processing in steps S153to S157.

When the integer j is not N (N in step S158), the measurement device1adds 1 to the integer j (step S159), and repeats the processing in steps S152and S157.

Then, when the integer j is N (Y in step S158), the measurement device1ends the processing in the correction coefficient calculation step.

FIG.34is a diagram showing a configuration example of the measurement device1according to the second embodiment. As shown inFIG.34, similar to the first embodiment, the measurement device1includes the control unit110, the first communication unit120, the storage unit130, the second communication unit140, and the operation unit150.

Since the processing performed by the first communication unit120, the storage unit130, the second communication unit140, and the operation unit150are the same as those in the first embodiment, the description thereof will be omitted.

The control unit110calculates the time point when the vehicle6travels on the superstructure7or the load or the like generated by the vehicle6based on the acceleration data output from each of the sensors21and22installed in the superstructure7.

The control unit110includes the first observation point information acquisition unit111, the second observation point information acquisition unit112, the first time calculation unit113, the correction coefficient calculation unit114, the deflection waveform calculation unit115, the moving object deflection waveform calculation unit116, the displacement calculation unit117, the coefficient value calculation unit118, the output processing unit119, and a second time calculation unit161.

Since the processing performed by the first observation point information acquisition unit111, the second observation point information acquisition unit112, the deflection waveform calculation unit115, the moving object deflection waveform calculation unit116, the displacement calculation unit117, the coefficient value calculation unit118, and the output processing unit119are the same as those in the first embodiment, the description thereof will be omitted.

Using the first observation point information acquired by the first observation point information acquisition unit111, the first time calculation unit113performs processing of calculating the first normalized times Δtjstd1_1to Δtjstdlast_1, which are times from the first leading time point tj1_1when the leading axle among the plurality of axles passes the observation point Pjto the time points tj1_1to tjlast_1when each of the plurality of axles passes the observation point Pj, and the first reference time ΔtjGOC_1, which is the time from the first leading time point tj1_1to the first reference time point tjGOC_1, which is the time point when the total sum of acceleration intensities apj1_1to apjlast_1at the observation point P generated by the plurality of axles is distributed at the predetermined distribution ratioimagRF:(1−imagRF). That is, the first time calculation unit113performs the processing of the first time calculation step inFIG.30. The first normalized times Δtjstd1_1to Δtjstdlast_1and the first reference time ΔtjGOC_1calculated by the first time calculation unit113are stored in the storage unit130.

Using the second observation point information acquired by the second observation point information acquisition unit112, the second time calculation unit161performs processing of calculating the second normalized times Δtjstd1_2to Δtjstdlast_2, which are times from the second leading time point tj1_2when the leading axle among the plurality of axles passes the observation point Qjto the time points tj1_2to tjlast_2when each of the plurality of axles passes the observation point Qj, and the second reference time ΔtjGOC_2, which is the time from the second leading time point tj1_2to the second reference time point tjGOC_2, which is the time point when the total sum of acceleration intensities apj1_2to apjlast_2at the observation point Qjgenerated by the plurality of axles is distributed at the predetermined distribution ratioimagRF:(1−imagRF). That is, the second time calculation unit161performs the processing of the second time calculation step shown inFIG.30. The second normalized times Δtjstd1_2to Δtjstdlast_2and the second reference time ΔtjGOC_2calculated by the second time calculation unit161are stored in the storage unit130.

Based on the first normalized times Δtjstd1_1to Δtjstdlast_1and the first reference time ΔtjGOC_1calculated by the first time calculation unit113and the second normalized times Δtjstd1_2to Δtjstdlast_2and the second reference time ΔtjGOC_2calculated by the second time calculation unit161, the correction coefficient calculation unit114performs processing of calculating the correction coefficients Rj1to Rjlastfor correcting the acceleration intensities apj1_1to apjlast_1at the observation point Pjand the acceleration intensities apj1_2to apjlast_2at the observation point Qjwhich are generated by the plurality of axles. That is, the correction coefficient calculation unit114performs the processing of the correction coefficient calculation step inFIG.30. The correction coefficients Rj1to Rjlastcalculated by the correction coefficient calculation unit114are stored in the storage unit130.

For example, based on the operation data from the operation unit150, the control unit110switches between a first mode for calculating the time point when an unknown vehicle6travels on the superstructure7and the load generated by the vehicle6and the like, and a second mode for calculating the value of the first-order coefficient scuand the value of the zero-order coefficient icu. For example, after the N sensors21and the N sensors22are installed in the superstructure7, the load test is performed on the plurality of test vehicles in a state in which the control unit110is set to the second mode. After the load test ends, the control unit110is set to the first mode.

As in the first embodiment, the control unit110is a processor that executes various programs stored in the storage unit130. By executing the measurement program131stored in the storage unit130, each function of the first observation point information acquisition unit111, the second observation point information acquisition unit112, the first time calculation unit113, the correction coefficient calculation unit114, the deflection waveform calculation unit115, the moving object deflection waveform calculation unit116, the displacement calculation unit117, the coefficient value calculation unit118, the output processing unit119, and the second time calculation unit161is implemented. In other words, the measurement program131is a program that causes the measurement device1as a computer to execute each procedure in the flowchart shown inFIG.30. The control unit110is implemented as a custom IC such as an ASIC, and may implement the functions of each part, or may implement the functions of each part by the CPU and the ASIC.

The control unit110may not include the coefficient value calculation unit118. For example, the server2or another device may perform the processing of calculating the value of the first-order coefficient scuand the value of the zero-order coefficient icu, and store the values in the storage unit130of the measurement device1.

In the measurement method according to the second embodiment described above, the measurement device1calculates, according to Equations (61) to (68), the first normalized times Δtjstd1_1to Δtjstdlast_1and the first reference time ΔtjGOC_1using the first observation point information. In addition, the measurement device1calculates, according to Equations (69) to (76), the second normalized times Δtjstd1_2to Δtjstdlast_2and the second reference time ΔtjGOC_2using the second observation point information. Further, the measurement device1calculates, according to Equations (77), (78), and (53) to (55), the correction coefficients Rj1to Rjlastbased on the first normalized times Δtjstd1_1to Δtjstdlast_1, the first reference time ΔtjGOC_1, the second normalized times Δtjstd1_2to Δt jstdlast_2, and the second reference time ΔtjGOC_2. Then, based on the first observation point information, the second observation point information, the predetermined coefficient p, the correction coefficients Rj1to Rjlast, and the approximate expression (39) of deflection of the superstructure7, the measurement device1calculates, according to Equation (56), the deflection waveform Hjk(t) of the superstructure7generated by each axle, and the deflection waveform CPjm(t) of the superstructure7generated by the vehicle6by adding the deflection waveform Hjk(t). Therefore, according to the measurement method in the second embodiment, the measurement device1can calculate the deflection waveform of the superstructure7generated by the vehicle6which is the moving object that moves on the superstructure7without measuring the displacement of the superstructure7which is the structure.

In addition, according to the measurement method in the second embodiment, the acceleration intensities apj1to apjlastgenerated by each axle are corrected by the correction coefficients Rj1to Rjlastsuch that the influence of the distance moment from the center of gravity on the load of each axle is reduced. Therefore, calculation accuracy of the deflection waveform of the superstructure7is improved in consideration of the difference in loads between a case where the vehicle6is stationary and a case where the vehicle6is moving.

Further, in the measurement method according to the second embodiment, the measurement device1calculates the average value of the first normalized times Δtjstd1_1to Δtjstdlast_1and the second normalized times Δtjstd1_2to Δtjstdlast_2as the normalized time Δtjstdkaccording to Equation (77), and calculates the average value of the first reference time ΔtjGOC_1and the second reference time ΔtjGOC_2as the reference time ΔtjGOCaccording to Equation (78). Then, the measurement device1calculates, according to Equations (53) to (55), the correction coefficients Rj1to Rjlastusing the normalized time Δtjstdkand the reference time ΔtjGOC. Therefore, according to the measurement method in the second embodiment, since random noise component included in the normalized time Δtjstdkand the reference time ΔtjGOCare reduced by the averaging, the accuracy of the correction coefficients Rj1to Rjlastis improved, and the calculation accuracy of the deflection waveform of the superstructure7is further improved.

Further, according to the measurement method in the second embodiment, similar to the measurement method in the first embodiment, the measurement device1can estimate the displacement of the superstructure7without measuring the displacement of the superstructure7, and the cost required for the measurement is reduced.

The present disclosure is not limited to the above embodiments, and various modifications can be made within the scope of the gist of the present disclosure.

In the first embodiment described above, the measurement device1acquires the observation point information including the time point when each axle of the vehicle6passes the observation point P and the acceleration intensity with respect to the observation point P generated by each axle as the first observation point information, and acquires the observation point information including the time point when each axle of the vehicle6passes the observation point Qjand the acceleration intensity with respect to the observation point Qjgenerated by each axle as the second observation point information. In contrast, the measurement device1may acquire the observation point information including the time point when each axle of the vehicle6passes the observation point Qjand the acceleration intensity with respect to the observation point Qjgenerated by each axle as first observation point information, and acquires the observation point information including the time point when each axle of the vehicle6passes the observation point Pjand the acceleration intensity with respect to the observation point Pjgenerated by each axle as second observation point information. Then, the measurement device1may calculate the normalized times Δtjstd1to Δtjstdlastand the reference time ΔtjGOCusing the first observation point information, and may calculate the correction coefficients Rj1to Rjlastbased on the normalized times Δtjstd1to Δtjstdlastand the reference time ΔtjGOC.

Further, in each of the above embodiments, the measurement device1calculates the displacement CUest(t) according to Equation (59). However, the displacement CUest(t) may be converted into a load using a predetermined correlation equation. For example, a relationship between a load CWk(t) and a displacement xk(t) at an observation position Rkof the superstructure7is expressed by Equation (79). Here, the load CWk(t) is a load waveform corresponding to the displacement waveform in BWIM. A first-order coefficient Sckkand a zero-order coefficient Ickin Equation (79) are obtained by a load test performed on a plurality of test vehicles.
CWk(t)=Sckk·xk(t)+Ick(79)

In Equation (80), the displacement xk(t) is replaced with the displacement CUest(t), and a correlation equation between the load CWk(t) and the displacement CUest(t) is expressed by Equation (81). The measurement device1can convert the displacement CUest(t) into the load CWk(t) according to the correlation Equation (81).
CWk(t)=Sckk·CUest(t)  (81)

In each of the above embodiments, the observation device that observes observation points P1to PNand the observation device that observes observation points Q1to QNare acceleration sensors, but the present disclosure is not limited thereto. For example, the observation device may be an impact sensor, a microphone, a strain gauge, or a load cell. It is not necessary that the observation device and the observation point have a one-to-one correspondence, and one observation device may observe apart or all of the observation points P1to PNand Q1to QN.

The impact sensor detects an impact acceleration as a response to the action of each axle of the vehicle6on the observation points P1to PNand Q1to QN. The measurement device1acquires first observation point information based on the impact acceleration for the observation points P1to PN, and acquires second observation point information based on the impact acceleration for the observation points Q1to QN. The microphone detects sound as a response to the action of each axle of the vehicle6on the observation points P1to PNand Q1to QN. The measurement device1acquires first observation point information based on the sound for the observation points P1to PN, and acquires second observation point information based on the sound for the observation points Q1to QN. The strain gauge and the load cell detect a stress change as a response to the action of each axle of the vehicle6on the observation points P1to PNand Q1to QN. The measurement device1acquires first observation point information based on the stress change for the observation points P1to PN, and acquires second observation point information based on the stress change for the observation points Q1to QN.

In each of the above embodiments, the direction in which the vehicle6travels on the lanes L1to LNis all the same. Alternatively, the traveling direction of the vehicle6may be different from at least one lane of the lanes L1to LNand other lanes. For example, the vehicle6may travel in a direction from the observation point P1to the observation point Q1on the lane L1, and may travel in a direction from the observation point Q2to the observation point P2on the lane L2. In this case, the measurement device1acquires the entry time point of the vehicle6to the lane L1based on the acceleration data output from the sensor21that observes the observation point P1, and acquires the exit time point of the vehicle6from the lane L1based on the acceleration data output from the sensor22that observes the observation point Q1. The measurement device1acquires the entry time point of the vehicle6to the lane L2based on the acceleration data output from the sensor22that observes the observation point Q2, and acquires the exit time point of the vehicle6from the lane L2based on the acceleration data output from the sensor21that observes the observation point P2.

In each of the above embodiments, the sensors21and22are provided on the main girder G of the superstructure7. Alternatively, the sensors may be provided on the surface or inside of the superstructure7, a lower surface of the floor plate F, the bridge pier8a, or the like. In each of the above embodiments, the road bridge is taken as an example of the bridge5, but the present disclosure is not limited thereto. For example, the bridge5may be a railway bridge. In each of the above embodiments, the superstructure of the bridge is taken as an example of the structure, but the present disclosure is not limited thereto. The structure may be deformed by the movement of the moving object.

The embodiments and the modifications described above are merely examples, and the present disclosure is not limited thereto. For example, the embodiments and the modifications can be combined as appropriate.

The present disclosure includes a configuration substantially the same as the configuration described in the embodiments, for example, a configuration having the same function, method, and result, or a configuration having the same object and effect. The present disclosure includes a configuration in which a non-essential portion of the configuration described in the embodiment is replaced. In addition, the present disclosure includes a configuration having the same action effect as the configuration described in the embodiment, or a configuration capable of achieving the same object. The present disclosure includes a configuration in which a known technique is added to the configuration described in the embodiment.