Patent ID: 12233923

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Hereinafter, preferred 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 claims. Not all configurations to be described below are necessarily essential components of the present disclosure.

1. Configuration of Measurement System

A moving object passing through a superstructure of a bridge that is a structure according to a first embodiment is a vehicle, a railway vehicle, or the like that has a large weight and can be measured by BWIM. The BWIM is an abbreviation of bridge weigh in motion, and is a technology in which a bridge is regarded as a “scale”, deformation of the bridge is measured, and thereby a weight and the number of axles of the moving object passing through the bridge are measured. The superstructure of the bridge, which enables analysis of the weight of the moving object passing through the bridge, based on a response such as deformation or strain, is a structure in which the BWIM functions. The 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 moving object that travels on the bridge. Hereinafter, a measurement system for implementing a measurement method according to the present embodiment will be described by taking a case where the moving object is a railway vehicle as an example.

FIG.1is a diagram showing an example of the 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 sensor2provided on a superstructure7of a bridge5. The measurement system10may include a monitoring device3.

The bridge5includes the superstructure7and a substructure8.FIG.2is a cross-sectional view of the superstructure7taken along line A-A ofFIG.1. As shown inFIGS.1and2, the superstructure7includes a bridge floor7a, a support7b, rails7c, ties7d, and a ballast7e, and the bridge floor7aincludes a floor plate F, a main girder G, a cross girder (not shown), and the like. As shown inFIG.1, 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, and 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.

When a railway vehicle6enters the superstructure7, the superstructure7is bent due to a load of the railway vehicle6. Since the railway vehicle6includes a plurality of vehicles coupled to each other, a phenomenon occurs in which the bending of the superstructure7is periodically repeated as the vehicles pass through the superstructure7. This phenomenon is called a static response. On the other hand, as a structure, the superstructure7has a natural vibration frequency, and therefore, natural vibration of the superstructure7may be excited when the railway vehicle6passes through the superstructure7. When the natural vibration of the superstructure7is excited, a phenomenon occurs in which the bending of the superstructure7is periodically repeated. This phenomenon is called a dynamic response.

The measurement device1and the sensors2are coupled by, for example, a cable (not shown) and communicate with each other via a communication network such as a CAN. CAN is an abbreviation for controller area network. Alternatively, the measurement device1and the sensors2may communicate with each other via a wireless network.

Each sensor2outputs data used to calculate an attenuation rate of a dynamic response when the railway vehicle6, which is a moving object, moves on the superstructure7which is a structure. In the present embodiment, each sensor2is an acceleration sensor, and may be, for example, a crystal acceleration sensor or a MEMS acceleration sensor. MEMS is an abbreviation for micro electro mechanical systems.

In the present embodiment, each sensor2is installed at a central portion of the superstructure7in a longitudinal direction, specifically, at a central portion of the main girder G in the longitudinal direction. However, each sensor2is not limited to being installed at the central portion of the superstructure7as long as each sensor2can detect an acceleration for calculating the attenuation rate of the dynamic response. When each sensor2is provided on the floor plate F of the superstructure7, the sensor2may be damaged due to traveling of the railway vehicle6, and the measurement accuracy may be affected by local deformation of the bridge floor7a, so that in the example ofFIGS.1and2, each sensor2is provided at the main girder G of the superstructure7.

The floor plate F, the main girder G, and the like of the superstructure7are bent in a vertical direction due to a load of the railway vehicle6passing through the superstructure7. Each sensor2detects an acceleration of the bending of the floor plate F or the main girder G caused by the load of the railway vehicle6passing through the superstructure7.

The measurement device1calculates the attenuation rate of the dynamic response when the railway vehicle6passes through the superstructure7based on acceleration data output from each sensor2. The measurement device1is installed on, for example, the bridge abutment8b.

The measurement device1and the monitoring device can communicate with each other via, for example, a wireless network of a mobile phone and a communication network4such as the Internet. The measurement device1transmits measurement data including the attenuation rate of the dynamic response when the railway vehicle6passes through the superstructure7to the monitoring device3. The monitoring device3may store the information in a storage device (not shown), and may perform, for example, processing such as monitoring of the railway vehicle6and abnormality determination of the superstructure7based on the information.

In the present embodiment, the bridge5is a railway bridge, and is, for example, a steel bridge, a girder bridge, or an RC bridge. RC is an abbreviation for reinforced-concrete.

As shown inFIG.2, in the present embodiment, an observation point R is set in association with the sensor2. In the example ofFIG.2, the observation point R is set at a position on a surface of the superstructure7located vertically above the sensor2provided at the main girder G. That is, the sensor2is an observation device that observes the observation point R. The sensor2detects a physical quantity which is a response to actions of a plurality of parts of the railway vehicle6moving on the superstructure7, which is a structure, on the observation point R, and outputs data including the detected physical quantity. For example, each of the plurality of parts of the railway vehicle6is an axle or a wheel, and is hereinafter assumed to be an axle. In the present embodiment, each sensor2is an acceleration sensor and detects an acceleration as the physical quantity. The sensor2may be provided at a position where the acceleration generated at the observation point R due to the traveling of the railway vehicle6can be detected, but the sensor2is preferably provided at a position close to the observation point R in the vertical direction.

The number and installation positions of the sensors2are not limited to the example shown inFIGS.1and2, and various modifications can be made.

The measurement device1acquires, based on the acceleration data output from the sensor2, an acceleration in a direction intersecting a surface of the superstructure7on which the railway vehicle6moves. The surface of the superstructure7on which the railway vehicle6moves is defined by a direction in which the railway vehicle6moves, that is, an X direction which is the longitudinal direction of the superstructure7, and a direction orthogonal to the direction in which the railway vehicle6moves, that is, a Y direction which is a width direction of the superstructure7. Since the observation point R is bent in a direction orthogonal to the X direction and the Y direction due to the traveling of the railway vehicle6, the measurement device1preferably acquires an acceleration in the direction orthogonal to the X direction and the Y direction, that is, a Z direction which is a normal direction of the floor plate F, in order to accurately calculate a magnitude of the acceleration of the bending.

FIG.3is a diagram showing the acceleration detected by the sensor2. The sensor2is an acceleration sensor that detects accelerations generated in three axes orthogonal to one another.

In order to detect the acceleration of the bending at the observation point R caused by the traveling of the railway vehicle6, the sensor2is installed such that one of three detection axes thereof, which are the x axis, the y axis, and the z axis, is in a direction intersecting the X direction and the Y direction. InFIGS.1and2, the sensor2is installed such that one axis thereof is in a direction intersecting the X direction and the Y direction. The observation point R is bent in the direction orthogonal to the X direction and the Y direction. Therefore, in order to accurately detect the acceleration of the bending, ideally, the sensor2is installed such that one axis thereof is aligned with the direction orthogonal to the X direction and the Y direction, that is, the normal direction of the floor plate F.

However, when the sensor2is installed on the superstructure7, an installation location may be inclined. In the measurement device1, even if one of the three detection axes of the sensor2is not installed in alignment with the normal direction of the floor plate F, since the one axis 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 inclination of the sensor2based on a three-axis combined acceleration obtained by combining the accelerations in the x axis, the y axis, and the z axis even if one of the three detection axes of the sensor2is not installed in alignment with the normal direction of the floor plate F. Further, the sensor2may be a one-axis acceleration sensor that detects an acceleration generated at least in a direction substantially parallel to the vertical direction or an 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.

2. Details of Measurement Method

First, the measurement device1integrates acceleration data a(k) output from the sensor2, which is an acceleration sensor, to generate velocity data v(k) as in Equation (1), and further integrates the velocity data v(k) to generate measurement data u(k) as in Equation (2). The acceleration data a(k) is data of an acceleration change excluding an acceleration bias unnecessary for calculating a displacement change when the railway vehicle6passes through the bridge5. For example, the acceleration directly before the railway vehicle6passes through the bridge5may be set to 0, and the subsequent acceleration change may be set as the acceleration data a(k). In Equation (1) and Equation (2), k is a sample number, and ΔT is a time interval of samples. The measurement data u(k) is data of the displacement of the observation point R due to the traveling of the railway vehicle6.
v(k)=a(k)ΔT+v(k−1)  (1)
u(k)=v(k)ΔT+u(k−1)  (2)

The measurement data u(k) having the sample number k as a variable is converted into measurement data u(t) having the time point t as a variable at the time point t=kΔT.FIG.4shows an example of the measurement data u(t). Since the measurement data u(t) is generated based on the acceleration data a(t) output from the sensor2that observes the observation point R, the measurement data u(t) is data based on the acceleration that is a response to the actions of a plurality of parts of the railway vehicle6moving on the superstructure7on the observation point R.

Next, the measurement device1generates measurement data ulp(t) obtained by performing filter processing on the measurement data u(t) in order to reduce a vibration component having a fundamental frequency Ffincluded in the measurement data u(t) and a harmonic of the vibration component. The filter processing may be, for example, low-pass filter processing or band-pass filter processing.

Specifically, first, the measurement device1calculates a power spectrum density by performing fast Fourier transform processing on the measurement data u(t), and calculates a peak of the power spectrum density as the fundamental frequency Ff.FIG.5shows the power spectrum density obtained by performing fast Fourier transform processing on the measurement data u(t) ofFIG.4. In the example ofFIG.5, the fundamental frequency Ffis calculated as about 3 Hz. Then, the measurement device1calculates a basic cycle Tfbased on the fundamental frequency Ffaccording to Equation (3), and calculates a moving average interval kmfadjusted to a time resolution of the data by dividing the basic cycle Tfby ΔT as in Equation (4). The basic cycle Tfis a cycle corresponding to the fundamental frequency Ff, and Tf>2ΔT.

Tf=1Ff(3)kmf=2⁢⌊Tf2⁢Δ⁢T⌋+1(4)

Then, the measurement device1performs, as the filter processing, moving average processing on the measurement data u(t) in the basic cycle Tf according to Equation (5) to generate the measurement data ulp(t) in which the vibration component included in the measurement data u(t) is reduced. In the moving average processing, not only the necessary calculation amount is small, but also an attenuation amount of a signal component of the fundamental frequency Ffand a harmonic component of the signal component is very large, so that the measurement data ulp(t) in which the vibration component is effectively reduced is obtained.FIG.6shows an example of the measurement data ulp(t). As shown inFIG.6, the measurement data ulp(t) from which the vibration component included in the measurement data u(t) is almost removed is obtained.

ulp(k)=1kmf⁢∑n=k-kmf-12k+kmf-12u⁡(n)(5)

The measurement device1may generate the measurement data ulp(t) by performing, as the filter processing, FIR filter processing for attenuating a signal component having a frequency equal to or higher than the fundamental frequency Ffon the measurement data u(t). FIR is an abbreviation of finite impulse response. In the FIR filter processing, although a calculation amount is larger than that of the moving average processing, all signal components having a frequency equal to or higher than the fundamental frequency Ffcan be attenuated.

Next, the measurement device1calculates two time points at which an amplitude of the measurement data ulp(t) matches a threshold CLuawhich is a product of a predetermined coefficient CLand an amplitude uacalculated based on the measurement data ulp(t), or two times at which the amplitude of the measurement data ulp(t) exceeds the threshold CLua, as an entry time point tiand an exit time point toof the railway vehicle6with respect to the superstructure7. However, 0<CL<1, and the amplitude uais calculated as, for example, an average value in an interval from a time point t1to a time point t2in which the amplitude of the measurement data ulp(t) is shifted, according to Equation (6).

ua=1t2-t1⁢∑t=t1t2ulp(t)(6)

The entry time point tiis a time point at which a leading axle of the plurality of axles of the railway vehicle6passes through an entry end of the superstructure7. The exit time point tois a time point at which a rearmost axle of the plurality of axles of the railway vehicle6passes through an exit end of the superstructure7.FIG.7shows an example of a relation between the measurement data ulp(t), the entry time point ti, and the exit time point to.

Next, the measurement device1calculates a difference between the exit time point toand the entry time point ti, as a passing time tsduring which the railway vehicle6passes through the superstructure7of the bridge5according to Equation (7).
ts=to−ti(7)

The measurement device1calculates, as the number of vehicles CTof the railway vehicle6, a maximum integer less than or equal to a number obtained by subtracting 1 from a product of the passing time tsand the fundamental frequency Ff, according to Equation (8).
CT=└tsFf−1┘=floor(tsFf−1)={tsFf−1}  (8)

The measurement device1stores observation information including the entry time point ti, the exit time point to, the passing time ts, and the number of vehicles CT in a storage unit (not shown). In the example ofFIG.7, the entry time point tiis at 7.155 second, the exit time point tois at 12.845 second, the passing time tsis 5.69 seconds, and the number of vehicles CT is 16.

Then, the measurement device1performs the following processing based on the observation information and environment information which is created in advance and includes dimensions of the railway vehicle6and dimensions of the superstructure7.

The environment information includes, for example, a length LBof the superstructure7and a position Lxof the observation point R as the dimensions of the superstructure7. The length LBof the superstructure7is a distance between the entry end and the exit end of the superstructure7. The position Lxof the observation point R is a distance from the entry end of the superstructure7to the observation point R. The environment information includes, for example, a length LC(Cm) of each vehicle of the railway vehicle6, the number of axles aT(Cm) of each vehicle, and a distance La(aw(Cm,n)) between axles of each vehicle, as the dimensions of the railway vehicle6. Cmis a vehicle number, and the length LC(Cm) of each vehicle is a distance between two ends of a Cm-th vehicle. The number of axles aT(Cm) of each vehicle is the number of axles of the Cm-th vehicle, n is an axle number of each vehicle, and 1≤n≤aT(Cm). The distance La(aw(Cm,n)) between axles of each vehicle is a distance between a front end of the Cm-th vehicle and a first axle when n=1, and is a distance between the (n−1)-th axle and the n-th axle when n≥2.FIG.8shows an example of the length LC(Cm) of the Cm-th vehicle of the railway vehicle6and the distance La(aw(Cm,n)) between the axles. The dimensions of the railway vehicle6and the dimensions of the superstructure7can be measured by a known method. A database of the dimensions of the railway vehicle6passing through the bridge5may be created in advance, and the dimensions of a corresponding vehicle may be referred to according to the passing time point.

When it is assumed that the railway vehicle6in which any number of vehicles having the same dimensions are coupled to each other travels on the superstructure7of the bridge5, the environment information may include the length LC(Cm) of the vehicle, the number of axles aT(Cm) of the vehicle, and the distance La(aw(Cm,n)) between the axles, which are related to one vehicle.

A total number of axles TaTof the railway vehicle6is calculated according to Equation (9) using the number of vehicles CTincluded in the observation information and the number of axles aT(Cm) of each vehicle included in the environment information.

TaT=∑Cm=1CTaT(Cm)(9)

A distance Dwa(aw(Cm,n)) from the leading axle to the n-th axle of the Cm-th vehicle of the railway vehicle6is calculated according to Equation (10) using the length LC(Cm) of each vehicle, the number of axles aT(Cm) of each vehicle, and the distance La(aw(Cm,n)) between axles of each vehicle included in the environment information. In Equation (10), it is assumed that LC(Cm)=LC(1).

Dwa(aw(Cm,n))=∑y=1CmLC(y)+∑x=1nLa⁡(aw(Cm,x))-{LC(1)+La⁡(aw(1,1))}(10)

The measurement device1calculates a distance Dwas(aw(CT,aT(CT))) from the leading axle to the rearmost axle of the rearmost vehicle of the railway vehicle6according to Equation (11) obtained by substituting Cm=CTand n=aT(CT) into Equation (10).

Dwa(aw(CT,aT(CT)))=∑y=1CTLC(y)+∑x=1aT(CT)La⁡(aw(CT,x))-{LC(1)+La⁡(aw(1,1))}(11)

An average velocity vaof the railway vehicle6is calculated according to Equation (12) using the length LBof the superstructure7included in the environment information, the passing time tsincluded in the observation information, and the calculated distance Dwa(aw(CT,aT(CT))).

va=LBts+Dwa(aw(CT,aT(CT)))ts(12)

The measurement device1calculates the average velocity vaof the railway vehicle6according to Equation (13) obtained by substituting Equation (11) into Equation (12).

va=LBts+1ts[∑y=1CTLC(y)+∑x=1aT(CT)La⁡(aw(CT,x))-{LC(1)+La⁡(aw(1,1))}](13)

Next, the measurement device1calculates a deflection amount of the superstructure7caused by the traveling of the railway vehicle6in the following manner.

In the present embodiment, considering that the superstructure7of the bridge5has a configuration in which one or a plurality of bridge floors7aincluding the floor plate F, the main girder G, and the like are continuously arranged, the measurement device1calculates a displacement of one bridge floor7aas a displacement at the central portion in the longitudinal direction. The load applied to the superstructure7moves from one end to the other end of the superstructure7. In this case, the deflection amount, which is the displacement of the central portion of the superstructure7, can be expressed by a position of the load on the superstructure7and an amount of the load. In the present embodiment, in order to express the deflection deformation when the axles of the railway vehicle6moves on the superstructure7as a trajectory of the deflection amount caused by the movement on the bridge under one-point load, the structural model shown inFIG.9is considered, and the deflection amount at the central portion is calculated in the structural model. InFIG.9, P is a load, a is a load position from the entry end of the superstructure7on a side where the railway vehicle6enters, and b is a load position from the exit end of the superstructure7on a side where the railway vehicle6exits. LBis the length of the superstructure7, that is, the distance between two ends of the superstructure7. The structural model shown inFIG.9is a simple beam in which two ends are supported with the two ends as fulcrums.

In the structural model shown inFIG.9, when the position of the entry end of the superstructure7is zero and an observation position of the deflection amount is x, a bending moment M of the simple beam is expressed by Equation (14).

M=bLB⁢Px-PHa(x-a)(14)

In Equation (14), a function Hais defined as Equation (15).

Ha={0(if⁢x≤a)1(if⁢x>a)(15)

Equation (16) is obtained by transforming Equation (14).

-MLBP=-bx+Ha⁢LB(x-a)(16)

Meanwhile, the bending moment M is expressed by Equation (17). In Equation (17), θ is an angle, I is a secondary moment, and E is a Young's modulus.

-M=EI⁢d⁢θdx(17)

Equation (18) is obtained by substituting Equation (17) into Equation (16).

EILBP⁢d⁢θdx=-bx+Ha⁢LB(x-a)(18)

Equation (20) is obtained by calculating Equation (19) which is obtained by integrating Equation (18) with respect to the observation position x. In Equation (20), C1is an integral constant.

∫EILBP⁢d⁢θdx⁢dx=∫(-bx+Ha⁢LB(x-a))⁢dx(19)EILBP⁢θ=-bx22+Ha⁢LB(x-a)22+C1(20)

Equation (22) is obtained by calculating Equation (21) which is obtained by integrating Equation (20) with respect to the observation position x. In Equation (22), C2is an integral constant.

∫EILBP⁢θ⁢dx=∫{-bx22+Ha⁢LB(x-a)22+C1}⁢dx(21)EILBP⁢θ⁢x=-bx36+Ha⁢LB(x-a)36+C1⁢x+C2(22)

In Equation (22), θx represents the deflection amount, and Equation (23) is obtained by replacing θx with a deflection amount w.

EILBP⁢w=-bx36+Ha⁢LB(x-a)36+C1⁢x+C2(23)

As shown inFIG.9, since b=LB−a, Equation (23) is transformed as in Equation (24).

EILBP⁢w=-(LB-a)⁢x36+Ha⁢LB(x-a)36+C1⁢x+C2(24)

When x=0 and the deflection amount w=0, Ha=0 as x≤a, and therefore, when x=w=Ha=0 is substituted into Equation (24), Equation (25) is obtained.
C2=0  (25)

When x=LBand the deflection amount w=0, Ha=1 as x>a, and therefore, when x=LB, w=0, and Ha=1 are substituted into Equation (24), Equation (26) is obtained.

C1=a⁡(LB-a)⁢(a+2⁢(LB-a))6(26)

Equation (27) is obtained by substituting b=LB−a into Equation (26).

C1=a⁢b⁡(a+2⁢b)6(27)

Equation (28) is obtained by substituting an integral constant C1of Equation (25) and an integral constant C2of Equation (26) into Equation (23).

EILBP⁢w=-bx36+Ha⁢LB(x-a)36+ab⁡(a+2⁢b)6⁢x(28)

Equation (28) 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 (29).

w=P6⁢EILB⁢{-bx3+Ha⁢LB(x-a)3+ab⁡(a+2⁢b)⁢x}(29)

A deflection amount w0.5LBat the observation position x at the center when the load P is at the center of the superstructure7is expressed by Equation (30), wherein x=0.5 LB, a=b=0.5 LB, and Ha=0. The deflection amount w0.5LBis a maximum amplitude of the deflection amount w.

w0.5LB=P48⁢EI⁢LB3(30)

The deflection amount w at any observation position x is normalized by the deflection amount w0.5LB. When the position a of the load P is on an entry end side of the observation position x, as x>a, Equation (31) is obtained by substituting Ha=1 is into Equation (30).

w=P6⁢EILB⁢{-bx3+LB(x-a)3+ab⁡(a+2⁢b)⁢x}(31)

When the position a of the load P is represented by a=LBr, and a=LBr, b=LB(1−r) is substituted into Equation (31), Equation (32) is obtained, and a deflection amount wstdin which the deflection amount w is normalized is obtained according to Equation (32). r represents a ratio of the position a of the load P to the length LBof the superstructure7.

wstd=8LB⁢{xr3+(x3LB2+2⁢x)⁢r}-8LB⁢(LB⁢r3+3⁢x2LB⁢r)(32)

Similarly, when the position a of the load P is on an exit end side of the observation position x, as x≤a, Equation (33) is obtained by substituting Ha=0 into Equation (30).

w=P6⁢EILB⁢{-bx3+ab⁡(LB+b)⁢x}(33)

When the position a of the load P is represented by a=LBr, and a=LBr and b=LB(1−r) are substituted into Equation (33), Equation (34) is obtained, and the deflection amount wstdin which the deflection amount w is normalized is obtained according to Equation (34).

wstd=8LB⁢{xr3+(x3LB2+2⁢x)⁢r}-8LB⁢(3⁢xr2+x3LB2)(34)

Equation (32) and Equation (34) are combined, and a deflection amount wstd(r) at any observation position x=Lxis expressed by Equation (35). In Equation (35), a function R(r) is expressed by Equation (36). Equation (35) is an approximate equation of the deflection of the superstructure7which is a structure, and is an equation based on the structural model of the superstructure7. Specifically, Equation (35) is an approximate equation normalized by the maximum amplitude of the deflection at the center position between the entry end and the exit end of the superstructure7.

wstd(r)=8LB⁢{Lx⁢r3+(Lx3LB2+2⁢Lx)⁢r-R⁡(r)}(35)R⁡(r)={LB⁢r3+3⁢Lx2LB⁢r(if⁢Lx>LB⁢r)3⁢Lx⁢r2+Lx3LB2(if⁢Lx≤LB⁢r)(36)

In the present embodiment, the load P is a load of any axle of the railway vehicle6. A time txnrequired for a certain axle of the railway vehicle6to reach the position Lxof the observation point R from the entry end of the superstructure7is calculated according to Equation (37) using the average velocity vacalculated according to Equation (12).

txn=Lxva(37)

A time tlnrequired for a certain axle of the railway vehicle6to pass through the superstructure7having the length LBis calculated according to Equation (38).

tl⁢n=LBva(38)

A time point t0(Cm,n) at which the n-th axle of the Cm-th vehicle of the railway vehicle6reaches the entry end of the superstructure7is calculated according to Equation (39) using the entry time point tiincluded in the observation information, the distance Dwa(aw(Cm,n)) calculated according to Equation (10), and the average velocity vacalculated according to Equation (12).

t0(Cm,n)=ti+1va⁢Dwa(aw(Cm,n))(39)

Using Equation (37), Equation (38), and Equation (39), the measurement device1calculates, according to Equation (40), a deflection amount wstd(aw(Cm,n),t) obtained by replacing, with time, the deflection amount wstd(r) caused by the n-th axle of the Cm-th vehicle and represented by Equation (35). In Equation (40), a function R(t) is expressed by Equation (41).FIG.10shows an example of the deflection amount wstd(aw(Cm,n),t).

wstd(aw(Cm,n),t)={0if⁢(t<t0(Cm,n))8tl⁢n⁢{txn(t-t0(Cm,n)tl⁢n)3+(txn3tl⁢n2+2⁢txn)⁢(t-t0(Cm,n)tl⁢n)-R⁢(t)}if⁢(t0⁢(Cm,n)≤t≤t0⁢(Cm,n)+tl⁢n)0if⁢(t0(Cm,n)+tl⁢n<t)(40)R⁡(t)={0if⁢(t<t0(Cm,n))tl⁢n⁢(t-t0(Cm,n)tl⁢n)3+3⁢txn2tl⁢n⁢(t-t0(Cm,n)tl⁢n)if⁢(t0(Cm,n)≤t≤t0(Cm,n)+tl⁢n⋂txn>t-t0(Cm,n))3⁢txn(t-t0(Cm,n)tl⁢n)2+txn3tl⁢n2if⁢(t0(Cm,n)≤t≤t0(Cm,n)+tl⁢n⋂txn≤t-t0(Cm,n))0if⁢(t0(Cm,n)+tl⁢n<t)(41)

The measurement device1calculates a deflection amount Cstd(Cm,t) caused by the Cm-th vehicle according to Equation (42).FIG.11shows an example of the deflection amount Cstd(Cm,t) caused by the Cm-th vehicle with the number of axles n=4.

Cstd(Cm,t)=∑n=1aT(Cm)wstd(aw(Cm,n),t)(42)

The measurement device1further calculates a deflection amount Tstd(t) caused by the railway vehicle6according to Equation (43).FIG.12shows an example of the deflection amount Tstd(t) caused by the railway vehicle6with the number of vehicles CT=16. InFIG.12, the broken line indicates16deflection amounts Cstd(1,t) to Cstd(16,t).

Tstd(t)=∑Cm=1CTCstd(Cm,t)(43)

Next, the measurement device1generates a deflection amount Tstd_lp(t), obtained by performing filter processing on the deflection amount Tstd(t), in order to reduce the vibration component having a fundamental frequency FMincluded in the deflection amount Tstd(t) and a harmonic of the vibration component. The filter processing may be, for example, low-pass filter processing or band-pass filter processing.

Specifically, first, the measurement device1calculates a power spectrum density by performing fast Fourier transform processing on the deflection amount Tstd(t) and calculates a peak of the power spectrum density as the fundamental frequency FM. Then, the measurement device1calculates a basic cycle TMbased on the fundamental frequency FMaccording to Equation (44), and calculates a moving average interval kmM, adjusted to a time resolution of the data, by dividing the basic cycle TMby ΔT as in Equation (45). The basic cycle TMis a cycle corresponding to the fundamental frequency FM, and TM>2ΔT.

TM=1fM(44)kmM=2⁢⌊TM2⁢Δ⁢T⌋+1(45)

Then, the measurement device1performs, as the filter processing, moving average processing on the deflection amount Tstd(t) in the basic cycle TMaccording to Equation (46) to calculate the deflection amount Tstd_lp(t) in which the vibration component included in the deflection amount Tstd(t) is reduced. In the moving average processing, not only a necessary calculation amount is small, but also an attenuation amount of the signal component of the fundamental frequency FMand the harmonic component of the signal component is very large, so that the deflection amount Tstd_lp(t) in which the vibration component is effectively reduced is obtained.FIG.13shows an example of the deflection amount Tstd_lp(t). As shown inFIG.13, the deflection amount Tstd_lp(t) from which the vibration component included in the deflection amount Tstd(t) is almost removed is obtained.

Tstd⁢_⁢lp(k)=1kmM⁢∑n=k-kmM-12k+kmM-12Tstd(n)(46)

The measurement device1may generate the deflection amount Tstd_lp(t) by performing, as the filter processing, FIR filter processing for attenuating a signal component having a frequency equal to or higher than the fundamental frequency FM, on the deflection amount Tstd(t). In the FIR filter processing, although a calculation amount is larger than that of the moving average processing, all signal components having a frequency equal to or higher than the fundamental frequency Ffcan be attenuated.

FIG.14shows the measurement data ulp(t) shown inFIG.6and the deflection amount Tstd_lp(t) shown inFIG.13in an overlapping manner. The deflection amount Tstd_lp(t) is considered to be a deflection amount proportional to the load of the railway vehicle6passing through the superstructure7, and it is assumed that a linear function of the deflection amount Tstd_lp(t) is substantially equal to the measurement data ulp(t). That is, the measurement device1approximates the measurement data ulp(t) by the linear function of the deflection amount Tstd_lp(t) as in Equation (47). An approximate time interval is a time interval between the entry time point tiand the exit time point toor a time interval in which the amplitude of the deflection amount Tstd_lp(t) is 0.
ulp(t)≅c1Tstd_lp(t)+c0(47)

Then, the measurement device1calculates a first-order coefficient c1and a zero-order coefficient c0of the linear function represented by Equation (47). For example, the measurement device1calculates, using a least-squares method, the first-order coefficient c1and the zero-order coefficient c0at which an error e(t) represented by Equation (48), that is, a difference between the measurement data ulp(t) and the linear function of Equation (47) is minimized.
e(t)=ulp(t)−c1Tstd_lp(t)+c0(48)ti≤t≤to

The first-order coefficient c1and the zero-order coefficient c0are calculated according to Equation (49) and Equation (50), respectively. A data section corresponding to the approximate time interval is set as ka≤k≤kb.

c1={n⁢∑k=kakbulp⁢(k)⁢Tstdlp(k)-∑k=kakbTstdlp⁢(k)⁢∑k=kakbulp⁢(k)}/{n⁢∑k=kakbTstdip(k)2-∑k=kakbTstdlp(k)2}(49)n=∑k=kakb1c0={∑k=kakbulp(k)-c1⁢∑k=kakbTstd⁢_⁢lp(k)}/n⁢n=∑k=kakb1(50)

Then, the measurement device1calculates a deflection amount TEstd_lp(t) in which the deflection amount Tstd_lp(t) is adjusted using the first-order coefficient c1and the zero-order coefficient c0, as in Equation (51). As shown in Equation (51), the deflection amount TEstd_lp(t) basically corresponds to a right side of Equation (47), and the zero-order coefficient c0is set to 0 in an interval before the entry time point tiand an interval after the exit time point to.FIG.15shows an example of the deflection amount TEstd_lp(t).

TEstd⁢_⁢lp(t)={t<tic1⁢Tstd⁢_⁢lp(t)ti≤t≤toc1⁢Tstd⁢_⁢lp(t)+c0to<tc1⁢Tstd⁢_⁢lp(t)(51)

As in Equation (52), it is assumed that a linear function of the deflection amount Tstd(t) using the first-order coefficient c1calculated according to Equation (49) and the zero-order coefficient c0calculated according to Equation (50) is substantially equal to the measurement data u(t).
u(t)≅c1Tstd(t)+c0(52)ti≤t≤to

A deflection amount TEstd(t) obtained by adjusting the deflection amount Tstd(t) using the first-order coefficient c1and the zero-order coefficient c0is calculated according to Equation (53). A right side of Equation (53) is obtained by replacing Tstd_lp(t) on a right side of Equation (51) with Tstd(t).FIG.16shows an example of the deflection amount TEstd(t).

TEstd(t)={t<tic1⁢Tstd(t)ti≤t≤toc1⁢Tstd(t)+c0to<tc1⁢Tstd(t)(53)

Next, the measurement device1calculates an amplitude ratio RTbetween the deflection amount TEstd_lp(t) and the deflection amount Tstd_lp(t) in a predetermined interval according to Equation (54) with t=kΔT. In Equation (54), a numerator is an average value of n+1 samples of the deflection amount TEstd_lp(t) included in a predetermined interval which is a part of an interval in which the waveform of the deflection amount TEstd_lp(t) and the waveform of the deflection amount Tstd_lp(t) are shifted, and a denominator is an average value of n+1 samples of the deflection amount Tstd_lp(t) included in the predetermined interval.FIG.17shows an example of a relation between the deflection amount TEstd_lp(t) and the deflection amount Tstd_lp(t) and a predetermined interval Tavgfor calculating the average values thereof.

RT=(1n+1⁢∑k=k0k0+nTEstd⁢_⁢lp(k))/(1n+1⁢∑k=k0k0+nTstd⁢_⁢lp(k))(54)

Next, the measurement device1compares a product RTTstd_lp(t) of the amplitude ratio RT and the deflection amount Tstd_lp(t) with the zero-order coefficient c0to calculate an offset Toffset_std(t). Specifically, the measurement device1calculates the offset Toffset_std(t) by replacing, with the zero-order coefficient c0, an interval of the product RTTstd_lp(t) in which an absolute value of the product RTTstd_lp(t) of the amplitude ratio RT and the deflection amount Tstd_lp(t) is bigger than an absolute value of the zero-order coefficient c0, as in Equation (55). FIG. shows an example of the offset Toffset_std(t). In the example ofFIG.18, since the amplitude of the deflection amount Tstd_lp(t) is 0 or negative, the measurement device1calculates the offset Toffset_std(t) by replacing, with the zero-order coefficient c0, an interval in which the product RTTstd_lp(t) is smaller than the zero-order coefficient c0.

Toffset_std(t)={RT⁢Tstd_lp(t)≥c0RT⁢Tstd_lp⁢(t)RT⁢Tstd_lp(t)<c0c0(55)

Next, the measurement device1calculates a deflection amount TEOstd(t) by adding a product c1Tstd(t) of the first-order coefficient c1and the deflection amount Tstd(t) and the offset Toffset_std(t), as in Equation (56). The deflection amount TEOstd(t) corresponds to the static response when the railway vehicle6passes through the superstructure7.FIG.19shows an example of the deflection amount TEOstd(t).FIG.20shows a relation between the measurement data u(t) and the deflection amount TEOstd(t).
TEOstd(t)=c1Tstd(t)+Toffset_std(t)  (56)

Then, the measurement device1calculates natural vibration unv(t) by subtracting the deflection amount TEOstd(t) from the measurement data u(t) as in Equation (57). The natural vibration unv(t) corresponds to the dynamic response when the railway vehicle6passes through the superstructure7.FIG.21shows an example of the natural vibration unv(t).
unv(t)=u(t)−TEOstd(t)  (57)

The natural vibration unv(t) as a first dynamic response calculated according to Equation (57) includes an unnecessary signal in addition to a fundamental wave. Therefore, in order to extract the fundamental wave of the natural vibration unv(t), the measurement device1performs filter processing for attenuating the unnecessary signal from the natural vibration unv(t) which is the first dynamic response, to calculate natural vibration unv_31p(t) as a second dynamic response. The unnecessary signal is, for example, a signal component having a frequency lower than a frequency FNof the fundamental wave or a harmonic component of the fundamental wave.

The filter processing for attenuating the unnecessary signal from the natural vibration unv(t) includes low-pass filter processing for attenuating a harmonic component of a vibration component having the fundamental frequency FNincluded in the natural vibration unv(t) and correcting a gain at the fundamental frequency FN. Further, the filter processing for attenuating the unnecessary signal from the natural vibration unv(t) may include high-pass filter processing for attenuating a signal component having a frequency lower than the fundamental frequency FN.

For example, after performing high-pass filter processing on the natural vibration unv(t), the measurement device1may further perform low-pass filter processing. Specifically, first, the measurement device1calculates the natural vibration unv_hp(t) by performing, on the natural vibration unv(t), the high-pass filter processing for attenuating a signal component having a frequency lower than the fundamental frequency FNof the natural vibration unv(t).

Specifically, first, the measurement device1calculates a power spectrum density by performing fast Fourier transform processing on the natural vibration unv(t), and calculates a peak of the power spectrum density as the fundamental frequency FN.FIG.22shows a power spectrum density obtained by performing fast Fourier transform processing on the natural vibration unv(t) ofFIG.21. In the example ofFIG.22, the fundamental frequency FNis calculated as about 3 Hz. Then, the measurement device1calculates a basic cycle TNbased on the fundamental frequency FNaccording to Equation (58), and calculates a moving average interval kmNadjusted to a time resolution of the data by dividing the basic cycle TNby ΔT as in Equation (59). The basic cycle TNis a cycle corresponding to the fundamental frequency FN, and TN>2ΔT.

TN=1FN(58)kmN=2⁢⌊TN2⁢Δ⁢T⌋+1(59)

Then, the measurement device1calculates the natural vibration unv_hp(t) according to Equation (60) by performing high-pass filter processing for subtracting, from the natural vibration unv(t), a low-frequency signal component in which a vibration component is reduced by performing moving average processing on the natural vibration unv(t) in the basic cycle TN. In the moving average processing, not only the necessary calculation amount is small, but also an attenuation amount of a signal component of the fundamental frequency FNand a harmonic component of the signal component is very large, so that a low-frequency signal component in which the vibration component is effectively reduced can be obtained. Therefore, the natural vibration unv_hp(t) in which the low-frequency signal component is effectively reduced can be obtained according to Equation (60).FIG.23shows a frequency characteristic of a high-pass filter according to Equation (60).FIG.24shows an example of the natural vibration unv_hp(t).

unv_hp(k)=unv(k)-1kmN⁢∑n=k-kmN-12k+kmN-12unv(n)(60)

The measurement device1may calculate the natural vibration unv_hp(t) by performing, as the high-pass filter processing, FIR filter processing for attenuating a signal component having a frequency lower than the fundamental frequency FNon the natural vibration unv(t).

Further, the measurement device1calculates the natural vibration unv_31p(t) as the second dynamic response by performing the low-pass filter processing for attenuating the harmonic component of the vibration component having the fundamental frequency FN included in the natural vibration unv_hp(t) and correcting the gain at the fundamental frequency FN. For example, in the power spectrum density of the natural vibration unv(t) shown inFIG.22, a third harmonic component is large. Therefore, in order to attenuate the third harmonic component, the measurement device1calculates a moving average interval kmL, adjusted to a time resolution of the data, by dividing a cycle three times the basic cycle TNby ΔT, as in Equation (61). 3TN>2ΔT.

kmL=2⁢⌊3⁢TN2⁢Δ⁢T⌋+1(61)

When the natural vibration unv_hp(t) is subjected to the moving average processing in the moving average interval kmL, since a frequency interval between the fundamental frequency FNand a frequency 3FNthat is three times the fundamental frequency FNis small, a gain gNof the fundamental frequency FNis smaller than 1, as shown inFIG.25. Since a transfer characteristic of a moving average filter is expressed by Equation (62), the measurement device1can calculate the gain gNwhen ω=2πFNaccording to Equation (62).

H⁡(z)=1-z-N1-z-1⁢(N=kmf-1,z=e-i⁢ω⁢Δ⁢T)(62)

Therefore, assuming that a correction coefficient for correcting the gain of the fundamental frequency FNto 1 is gN−1, the measurement device1calculates, according to Equation (63), the natural vibration unv_31p(t) as the second dynamic response by performing low-pass filter processing for attenuating the third harmonic component included in the natural vibration unv(t) and correcting the gain at the fundamental frequency FNto 1. The natural vibration unv_31p(t) calculated as described above can be basically regarded as a vibration component having the fundamental frequency FN included in the natural vibration unv(t).FIG.26shows an example of the natural vibration unv_31p(t).

unv⁢_⁢3⁢lp(t)=gf-1⁢flp(unv_hp(t))=gf-1⁢1kmL⁢∑n=k-kmL-12k+kmL-12unv_hp(n)(63)

When a second harmonic component included in the natural vibration unv(t) is large, the measurement device1performs moving average processing for attenuating the second harmonic component. When both the second harmonic component and the third harmonic component included in the natural vibration unv(t) are large, the measurement device1may perform both moving average processing for attenuating the second harmonic component and moving average processing for attenuating the third harmonic component. In general, when an n-th harmonic component included in the natural vibration unv(t) is large, the measurement device1may perform moving average processing for attenuating the n-th harmonic component.

The measurement device1may calculate the natural vibration unv_31p(t) by performing, as the low-pass filter processing, FIR filter processing for attenuating a signal component having a frequency higher than the fundamental frequency FNon the natural vibration unv_hp(t).

Although a case where the measurement device1performs the low-pass filter processing after performing the high-pass filter processing on the natural vibration unv(t) is described, the measurement device1may perform the high-pass filter processing after performing the low-pass filter processing on the natural vibration unv(t). When a signal component having a frequency lower than the fundamental frequency FNincluded in the natural vibration unv(t) is small, the measurement device1may not perform the high-pass filter processing.

Next, the measurement device1calculates an envelope amplitude unv_mag(t) of the natural vibration unv_31p(t). Specifically, since the natural vibration unv_31p(t) can be substantially regarded as a vibration component having the fundamental frequency FN, the measurement device1calculates the envelope amplitude unv_mag(t) by performing low-pass filter processing on an absolute value of the natural vibration unv_31p(t) according to Equation (64) with a crest factor set to π/2.FIG.27shows an example of the envelope amplitude unv_mag(t).

unv_mag(t)=π2⁢flp(❘"\[LeftBracketingBar]"unv_⁢3⁢lp(t)❘"\[RightBracketingBar]")=π2⁢∑s=t-kFNt+kFN❘"\[LeftBracketingBar]"unv_⁢3⁢lp(t)❘"\[RightBracketingBar]"(64)

Since the absolute value of the natural vibration unv_31p(t) includes a signal component having a frequency twice the fundamental frequency FN, a pass band of the low-pass filter processing is preferably in a range lower than 2FN. For example, in a case where the low-pass filter processing is moving average processing as in Equation (64), assuming that a moving average interval length tMAis a value obtained by dividing an integer k by the fundamental frequency FN, and when k=4, FN=2.7917 Hz, and ΔT=0.012 second, tMAmay be set to tMA=118ΔT as in Equation (65).

tM⁢A=kFN=42.7⁢9⁢1⁢7≅1.4⁢1⁢6=1⁢1⁢8⁢Δ⁢T(65)

Next, the measurement device1approximates the envelope amplitude unv_mag(t) by an exponential function in a first interval T1which is at least a part of an interval in which a vibration component included in the natural vibration unv_31p(t) attenuates. The first interval T1is an interval from a time point te0to a time point te1, and the start time point te0of the first interval T1is a time point after the exit time point to. For example, the measurement device1may calculate an exit time point toutof the rearmost axle of the railway vehicle6from the superstructure7according to Equation (66), and may set a range of the time point t satisfying Equation (67) as the first interval T1. Since the exit time point toutis equal to the exit time point toaccording to a relation between Equation (7), Equation (12), and Equation (66), the start time point te0of the first interval T1satisfying Equation (67) is after the exit time point to.

tout=ti+LBvα+Dw⁢a(aw(CT,aT(CT)))va(66)to⁢u⁢t<te⁢0≤t≤te⁢1(67)

The start time point te0and the end time point te1of the first interval T1are selected, for example, within a range in which a logarithm y(t) of the envelope amplitude unv_mag(t) represented by Equation (68) is approximately a straight line.FIG.28shows an example of the logarithm y(t) of the envelope amplitude unv_mag(t) and the first interval T1.
y(t)=ln{unv_mag(t)}  (68)

As shown inFIG.28, after the railway vehicle6passes, the logarithm y(t) in the first interval T1in which the vibration of the superstructure7attenuates is substantially a straight line. The logarithm y(t) in the first interval T1is approximated by a linear function Q(t) represented by Equation (69).
Q(t)=q1t+q0(69)

The measurement device1calculates, using a least-squares method, a first-order coefficient q1and a zero-order coefficient q0at which an error e(t) represented by Equation (70), that is, a difference between the logarithm y(t) and the linear function Q(t) of Equation (69) is minimized.
e(t)=y(t)−(q1t+q0)  (70)

The first-order coefficient q1and the zero-order coefficient q0are calculated according to Equation (71) and Equation (72), respectively. Here, it is assumed that a data interval corresponding to the approximate time interval is set as te0≤t≤te1.

q1={∑t=te⁢0te⁢11⁢∑t=te⁢0te⁢1y⁡(t)⁢t-∑t=te⁢0te⁢1t⁢∑t=te⁢0te⁢1y⁡(t)}/{∑t=ye⁢0te⁢11⁢∑t=te⁢0te⁢1t2-∑t=te⁢0te⁢1t⁢∑t=te⁢0te⁢1t}(71)q0={∑t=te⁢0te⁢1y⁡(t)-q1⁢∑t=te⁢0te⁢1t}/∑t=te⁢0te⁢11(72)

Assuming that an exponential function that approximates the envelope amplitude unv_mag(t) in the first interval T1is an attenuation vibration curve uenv_b(t), the attenuation vibration curve uenv_b(t) is calculated according to Equation (73) using the first-order coefficient q1and the zero-order coefficient q0.
uenv_b(t)=eq1t+q0(73)

On the other hand, based on an equation of motion, attenuation vibration ub(t) is expressed by Equation (74). In Equation (74), ζ is an attenuation rate, and ω is a natural frequency.

ub(t)=1ω⁢1-ζ2⁢e-ζω⁢t⁢sin⁢(ω⁢1-ζ2⁢t)(74)

By making an envelope part of the attenuation vibration ub(t) correspond to the attenuation vibration curve uenv_b(t), Equation (75) is obtained.

1ω⁢1-ζ2⁢e-ζ⁢ω⁢t=eq1⁢t+q0(75)

Based on Equation (75), the attenuation rate ζ is calculated according to Equation (76).

ζ=-q1ω=-q12⁢π⁢Ff(76)

By making a value at the start of the envelope part of the attenuation vibration ub(t) correspond to an amplitude of the attenuation vibration curve uenv_b(t) at the start time point te0of the first interval T1, Equation (77) and Equation (78) are obtained.

1ω⁢1-ζ2=eq1⁢te⁢o+qo(77)ω⁢1-ζ2=ω2-q12≈ωM(78)

Attenuation vibration uenv(t) is expressed by Equation (79).FIG.29shows the attenuation vibration uenv(t) and the natural vibration unv_31p(t), which is the second dynamic response, in an overlapping manner. As shown inFIG.29, the attenuation vibration uenv(t) and the natural vibration unv_31p(t) are accurately approximated.

uenv(t)={t<te⁢00t≥te⁢0eq1⁢teo+qo⁢e-ζω⁡(t-teo)⁢sin⁢(ωM(t-te⁢0))(79)
3. Procedure of Measurement Method

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

As shown inFIG.30, first, in an observation data acquisition step S10, the measurement device1acquires acceleration data a(k) which is observation data output from the sensor2which is an observation device.

Next, in a first measurement data generation step S20, the measurement device1generates, based on the acceleration data a(k) which is the observation data acquired in step S10, the measurement data u(t) which is first measurement data based on the acceleration as the physical quantity, which is the response to the actions of the plurality of axles of the railway vehicle6moving on the superstructure7on the observation point R. An example of a procedure of the first measurement data generation step S20will be described later.

Next, in a second measurement data generation step S30, the measurement device1generates the measurement data ulp(t), which is second measurement data in which a vibration component is reduced by the measurement device1performing filter processing on the measurement data u(t) generated in step S20. For example, the measurement device1performs, as the filter processing, low-pass filter processing for attenuating the vibration component having a frequency equal to or higher than the fundamental frequency Ffof the measurement data u(t). An example of a procedure of the second measurement data generation step S30will be described later.

Next, in an observation information generation step S40, the measurement device1generates the observation information including the entry time point tiand the exit time point toof the railway vehicle6with respect to the superstructure7. The entry time point tiis the time point at which the leading axle of the plurality of axles of the railway vehicle6passes through the entry end of the superstructure7, and the exit time point tois the time point at which the rearmost axle of the plurality of axles of the railway vehicle6passes through the exit end of the superstructure7. In the present embodiment, the measurement device1calculates the entry time point tiand the exit time point tobased on the measurement data ulp(t) generated in step S30. Further, the measurement device1generates the number of vehicles CT. An example of a procedure of the observation information generation step S40will be described later.

Next, in an average velocity calculation step S50, the measurement device1calculates the average velocity vaof the railway vehicle6based on the observation information generated in step S40and the environment information which is created in advance and includes the dimension of the railway vehicle6and the dimension of the superstructure7. The environment information includes the length LBof the superstructure7, the position Lxof the observation point R, the length LC(Cm) of each vehicle of the railway vehicle6, the number of axles aT(Cm) of each vehicle, and the distance La(aw(Cm,n)) between the axles corresponding to the position of each of the plurality of axles of the railway vehicle6. An example of a procedure of the average velocity calculation step S50will be described later.

Next, in a first deflection amount calculation step S60, the measurement device1calculates the deflection amount Tstd(t), which is a first deflection amount of the superstructure7caused by the railway vehicle6, based on the approximate equation of the deflection of the superstructure7, which is Equation (35), the observation information generated in step S40, the environment information, and the average velocity vaof the railway vehicle6calculated in step S50. Specifically, the measurement device1calculates the deflection amount wstd(aw(Cm,n),t) of the superstructure7caused by each of the plurality of axles based on the approximate equation of the deflection of the superstructure7, the observation information, the environment information, and the average velocity va, and calculates the deflection amount Tstd(t) by adding the deflection amount wstd(aw(Cm,n),t) of the superstructure7caused by each of the plurality of axles. An example of a procedure of the first deflection amount calculation step S60will be described later.

Next, in a second deflection amount calculation step S70, the measurement device1calculates the deflection amount Tstd_lp(t), which is a second deflection amount in which a vibration component is reduced by the measurement device1performing filter processing on the deflection amount Tstd(t) calculated in step S60. For example, the measurement device1performs, as the filter processing, low-pass filter processing for attenuating the vibration component having a frequency equal to or higher than the fundamental frequency FMof the deflection amount Tstd(t). An example of a procedure of the second deflection amount calculation step S70will be described later.

Next, in a coefficient calculation step S80, the measurement device1approximates the measurement data ulp(t) generated in step S30with the linear function of the deflection amount Tstd_lp(t) calculated in step S70, and calculates the first-order coefficient c1and the zero-order coefficient c0of the linear function. Specifically, the measurement device1approximates the measurement data ulp(t) with the linear function of the deflection amount Tstd_lp(t) as in Equation (47), and calculates the first-order coefficient c1and the zero-order coefficient c0according to Equation (49) and Equation (50) using the least-squares method.

Next, in a third deflection amount calculation step S90, the measurement device1calculates the deflection amount TEstd_lp(t), which is a third deflection amount, based on the first-order coefficient c1and the zero-order coefficient c0calculated in step S80and the deflection amount Tstd_lp(t) calculated in step S70. Specifically, the measurement device1calculates the deflection amount TEstd_lp(t), which is a product c1Tstd_lp(t) of the first-order coefficient c1and the deflection amount Tstd_lp(t) in the interval before the entry time point tiand the interval after the exit time point to, and is a sum of the product c1Tstd_lp(t) and the zero-order coefficient c0in an interval from the entry time point tito the exit time point to, as in Equation (51).

Next, in an offset calculation step S100, the measurement device1calculates the offset Toffset_std(t) based on the zero-order coefficient c0calculated in step S80, the deflection amount Tstd_lp(t) calculated in step S70, and the deflection amount TEstd_lp(t) calculated in step S90. An example of a procedure of the offset calculation step S100will be described later.

Next, in a static response calculation step S110, the measurement device1calculates the deflection amount TEOstd(t) as the static response by adding the product c1Tstd(t) of the first-order coefficient c1calculated in step S80and the deflection amount Tstd(t) calculated in step S60and the offset Toffset_std(t) calculated in step S100, as in Equation (56).

Next, in a first dynamic response calculation step S120, the measurement device1calculates, as in Equation (57), the natural vibration unv(t) as the first dynamic response by subtracting the deflection amount TEOstd(t) as the first static response calculated in step S110from the measurement data u(t) generated in step S20.

Next, in a second dynamic response calculation step S130, the measurement device1calculates the natural vibration unv_31p(t) as the second dynamic response by performing filter processing for attenuating an unnecessary signal from the natural vibration unv(t) which is the first dynamic response calculated in step S120. The filter processing may include low-pass filter processing for attenuating a harmonic component of a vibration component having the fundamental frequency FNincluded in the natural vibration unv(t) and correcting a gain at the fundamental frequency FN. Further, the filter processing may include high-pass filter processing for attenuating a signal component having a frequency lower than the fundamental frequency FN. An example of a procedure of the second dynamic response calculation step S130will be described later.

Next, in an envelope amplitude calculation step S140, the measurement device1calculates the envelope amplitude unv_mag(t) of the natural vibration unv_31p(t) which is the second dynamic response calculated in step S130. Specifically, the measurement device1calculates, as in Equation (64), the envelope amplitude unv_mag(t) by performing low-pass filter processing on the absolute value of the natural vibration unv_31p(t) and multiplying the result by π/2.

Next, in an attenuation rate calculation step S150, the measurement device1calculates the attenuation rate ζ of the vibration component included in the natural vibration unv_31p(t), which is the second dynamic response, based on the envelope amplitude unv_mag(t) calculated in step S140. An example of a procedure of the attenuation rate calculation step S150will be described later.

Next, in a measurement data output step S160, the measurement device1outputs the measurement data including the attenuation rate ζ calculated in step S150to the monitoring device3. Specifically, the measurement device1transmits the measurement data to the monitoring device3via the communication network4. The measurement data may include the measurement data u(t) and ulp(t), the deflection amounts Tstd(t), Tstd_lp(t), TEstd_lp(t), and TEOstd(t), the natural vibrations unv(t) and unv_31p(t), the envelope amplitude unv_mag(t), and the like, in addition to the attenuation rate ζ.

Then, the measurement device1repeats the processing of steps S10to S160until the measurement is completed in step S170.

FIG.31is a flowchart showing an example of the procedure of the first measurement data generation step S20ofFIG.30.

As shown inFIG.31, in step S201, the measurement device1integrates the acceleration data a(t) output from the sensor2to generate the velocity data v(t) as in Equation (1).

Then, in step S202, the measurement device1integrates the velocity data v(t) generated in step S201to generate the measurement data u(t), as in Equation (2).

As described above, in the present embodiment, the measurement data u(t) is data of the displacement of the superstructure7caused by the railway vehicle6which is a moving object moving on the superstructure7which is a structure, and is data obtained by integrating twice the acceleration in the direction intersecting the surface of the superstructure7on which the railway vehicle6moves. Therefore, the measurement data u(t) includes data having a waveform projecting in a positive direction or a negative direction, specifically, a rectangular waveform, a trapezoidal waveform, or a sine half-wave waveform. The rectangular waveform includes not only an accurate rectangular waveform but also a waveform approximate to the rectangular waveform. Similarly, the trapezoidal waveform includes not only an accurate trapezoidal waveform but also a waveform approximate to the trapezoidal waveform. Similarly, the sine half-wave waveform includes not only an accurate sine half-wave waveform but also a waveform approximate to the sine half-wave waveform.

FIG.32is a flowchart showing an example of the procedure of the second measurement data generation step S30ofFIG.30.

As shown inFIG.32, in step S301, the measurement device1calculates the power spectrum density by performing fast Fourier transform processing on the measurement data u(t) calculated in step S202ofFIG.31, and calculates the peak of the power spectrum density as the fundamental frequency Ff.

Then, in step S302, the measurement device1generates the measurement data ulp(t) by performing low-pass filter processing for attenuating the vibration component having a frequency equal to or higher than the fundamental frequency Ffof the measurement data u(t). The measurement device1may generate the measurement data ulp(t) by performing, as the low-pass filter processing, moving average processing on the measurement data u(t) in the basic cycle Tfcorresponding to the fundamental frequency Ff, as in Equation (5). Alternatively, the measurement device1may generate the measurement data ulp(t) by performing, as the low-pass filter processing, FIR filter processing for attenuating the signal component having a frequency equal to or higher than the fundamental frequency Ffon the measurement data u(t).

FIG.33is a flowchart showing an example of the procedure of the observation information generation step S40ofFIG.30.

As shown inFIG.33, first, in step S401, the measurement device1calculates, as the amplitude ua, the average value in the interval from a time point t1to a time point t2in which the amplitude of the measurement data ulp(t) generated in step S302ofFIG.32is shifted, according to Equation (6).

Then, in step S402, the measurement device1calculates, as the entry time point ti, a first time point at which the amplitude of the measurement data ulp(t) matches or exceeds the threshold CLuawhich is the product of the predetermined coefficient CLand the amplitude uacalculated in step S401.

In step S403, the measurement device1calculates, as the exit time point to, a second time point after the first time point at which the amplitude of the measurement data ulp(t) matches or exceeds the threshold CLua.

In step S404, the measurement device1calculates the difference between the exit time point toand the entry time point tias the passing time tsas in Equation (7).

Then, in step S405, the measurement device1calculates, as the number of vehicles CTof the railway vehicle6, the maximum integer less than or equal to the number obtained by subtracting 1 from the product tsFfof the passing time tscalculated in step S404and the fundamental frequency Ffcalculated in step S301ofFIG.32, as in Equation (8).

Then, in step S406, the measurement device1generates the observation information including the entry time point ticalculated in step S402, the exit time point tocalculated in step S403, the passing time tscalculated in step S404, and the number of vehicles CT calculated in step S405.

FIG.34is a flowchart showing an example of the procedure of the average velocity calculation step S50ofFIG.30.

In step S501, the measurement device1calculates, based on the environment information, the distance Dwa(aw(CT,aT(CT))) from the leading axle to the rearmost axle of the railway vehicle6according to Equation (11).

In step S502, the measurement device1calculates, based on the environment information, the distance from the entry end to the exit end of the superstructure7. In the present embodiment, the distance from the entry end to the exit end of the superstructure7is the length LBof the superstructure7included in the environment information.

Then, in step S503, the measurement device1calculates the average velocity vaof the railway vehicle6according to Equation (12) based on the entry time point tiand the exit time point toincluded in the observation information generated in step S406ofFIG.33, the distance Dwa(aw(CT,aT(CT))) from the leading axle to the rearmost axle of the railway vehicle6calculated in step S501, and the length LBof the superstructure7which is the distance from the entry end to the exit end of the superstructure7calculated in step S502.

FIG.35is a flowchart showing an example of the procedure of the first deflection amount calculation step S60ofFIG.30.

First, in step S601, the measurement device1calculates, based on the environment information, each distance Dwa(aw(Cm,n)) from the leading axle to the n-th axle of the Cm-th vehicle of the railway vehicle6, according to Equation (10).

Next, in step S602, the measurement device1calculates, according to Equation (37), the time txnrequired for a certain axle of the railway vehicle6to reach the position Lxof the observation point R from the entry end of the superstructure7using the position Lxof the observation point R included in the environment information and the average velocity vacalculated in step S503ofFIG.34.

In step S603, the measurement device1calculates, according to Equation (38), the time tlnrequired for a certain axle of the railway vehicle6to pass through the superstructure7using the length LBof the superstructure7, which is the distance from the entry end to the exit end of the superstructure7calculated in step S502ofFIG.34, and the average velocity va.

In step S604, the measurement device1calculates, according to Equation (39), the time point t0(Cm,n) at which the n-th axle of the Cm-th vehicle of the railway vehicle6reaches the entry end of the superstructure7using the entry time point tiincluded in the observation information generated in step S406ofFIG.33, the distance Dwa(aw(Cm,n)) calculated in step S601, and the average velocity va.

Next, in step S605, the measurement device1calculates the deflection amount wstd(aw(Cm,n),t) of the superstructure7caused by the n-th axle of the Cm-th vehicle using the approximate equation of the deflection of the superstructure7, which is Equation (35), the time txncalculated in step S602, the time tlncalculated in step S603, and the time point t0(Cm,n) calculated in step S604, according to Equation (40).

Next, in step S606, the measurement device1calculates, according to Equation (42), the deflection amount Cstd(Cm,t) of the superstructure7caused by each vehicle by adding the deflection amount wstd(aw(Cm,n),t) of the superstructure7caused by each axle of each vehicle calculated in step S605.

Then, in step S607, the measurement device1calculates, according to Equation (43), the deflection amount Tstd(t) of the superstructure7caused by the railway vehicle6by adding the deflection amount Cstd(Cm, t) of the superstructure7caused by each vehicle, which is calculated in step S606.

FIG.36is a flowchart showing an example of the procedure of the second deflection amount calculation step S70ofFIG.30.

As shown inFIG.36, in step S701, the measurement device1calculates the power spectrum density by performing fast Fourier transform processing on the deflection amount Tstd(t) calculated in step S607ofFIG.35, and calculates the peak of the power spectrum density as the fundamental frequency FM.

Then, in step S702, the measurement device1calculates the deflection amount Tstd_lp(t) by performing low-pass filter processing for attenuating the vibration component having a frequency equal to or higher than the fundamental frequency FMof the deflection amount Tstd(t). The measurement device1may calculate the deflection amount Tstd_lp(t) by performing, as the low-pass filter processing, moving average processing on the deflection amount Tstd(t) in the basic cycle TMcorresponding to the fundamental frequency FM, according to Equation (46). Alternatively, the measurement device1may calculate the deflection amount Tstd_lp(t) by performing, as the low-pass filter processing, FIR filter processing for attenuating the signal component having a frequency equal to or higher than the fundamental frequency FMon the deflection amount Tstd(t).

FIG.37is a flowchart showing an example of the procedure of the offset calculation step S100ofFIG.30.

As shown inFIG.37, in step S1001, the measurement device1calculates, according to Equation (54), the amplitude ratio RTin a predetermined interval between the deflection amount TEstd_lp(t) calculated in step S90ofFIG.30and the deflection amount Tstd_lp(t) calculated in step S702ofFIG.36.

Then, in step S1002, the measurement device1calculates, as in Equation (55), the offset Toffset_std(t) by replacing, with the zero-order coefficient c0, the interval of the product RTTstd_lp(t) in which the absolute value of the product RTTstd_lp(t) of the amplitude ratio RTcalculated in step S1001and the deflection amount Tstd_lp(t) is bigger than the absolute value of the zero-order coefficient c0calculated in step S80ofFIG.30.

FIG.38is a flowchart showing an example of the procedure of the second dynamic response calculation step S130ofFIG.30.

As shown inFIG.38, in step S1301, the measurement device1calculates the natural vibration unv_hp(t) according to Equation (60) by performing high-pass filter processing for subtracting, from the natural vibration unv(t) calculated in step S120ofFIG.30, a low-frequency signal component in which the vibration component is reduced by performing moving average processing on the natural vibration unv(t) in the basic cycle TN.

Further, in step S1302, the measurement device1calculates, according to Equation (63), the natural vibration unv_31p(t) as the second dynamic response by performing the low-pass filter processing for attenuating the harmonic component having the vibration component of the fundamental frequency FN included in the natural vibration unv_hp(t) calculated in step S1301and correcting the gain at the fundamental frequency FN.

FIG.39is a flowchart showing an example of the procedure of the attenuation rate calculation step S150ofFIG.30.

As shown inFIG.39, in step S1501, the measurement device1approximates the envelope amplitude unv_mag(t) calculated in step S140ofFIG.30by an exponential function in the first interval T1which is at least a part of an interval in which the vibration component included in the natural vibration unv_31p(t), which is the second dynamic response calculated in step S1302ofFIG.38, attenuates to calculate a power coefficient q1of the exponential function. The start time point te0of the first interval T1is after the exit time point to. For example, the measurement device1approximates the logarithm y(t) of the envelope amplitude unv_mag(t) in the first interval T1by the linear function Q(t) as in Equation (69), and calculates the power coefficient q1according to Equation (71).

Then, in step S1502, the measurement device1calculates, as in Equation (76), the attenuation rate ζ by dividing the power coefficient q1calculated in step S1501by the natural frequency ω=2πFNof the natural vibration unv_31p(t) which is the second dynamic response.

4. Configuration of Observation Device, Measurement Device, and Monitoring Device

FIG.40is a diagram showing a configuration example of the sensor2which is the observation device, the measurement device1, and the monitoring device3.

As shown inFIG.40, the sensor2includes a communication unit21, an acceleration sensor22, a processor23, and a storage unit24.

The storage unit24is a memory that stores various programs, data, and the like for the processor23to perform calculation processing and control processing. Further, the storage unit24stores programs, data, and the like for the processor23to implement predetermined application functions.

The acceleration sensor22detects an acceleration generated in each axial direction of the three axes.

The processor23controls the acceleration sensor22by executing an observation program241stored in the storage unit24, generates observation data242based on the acceleration detected by the acceleration sensor22, and stores the generated observation data242in the storage unit24. In the present embodiment, the observation data242is the acceleration data a(k).

The communication unit21transmits the observation data242stored in the storage unit24to the measurement device1under the control of the processor23.

As shown inFIG.40, the measurement device1includes a first communication unit11, a second communication unit12, a storage unit13, and a processor14.

The first communication unit11receives the observation data242from the sensor2, and outputs the received observation data242to the processor14. As described above, the observation data242is the acceleration data a(k).

The storage unit13is a memory that stores programs, data, and the like for the processor14to perform calculation processing and control processing. The storage unit13stores programs, data, and the like for the processor14to implement predetermined application functions. The processor14may receive various programs, data, and the like via the communication network4and store the programs, data, and the like in the storage unit13.

The processor14generates measurement data135based on the observation data242received by the first communication unit11and environment information132stored in advance in the storage unit13, and stores the generated measurement data135in the storage unit13.

In the present embodiment, the processor14functions as an observation data acquisition unit141, a first measurement data generation unit142, a second measurement data generation unit143, an observation information generation unit144, an average velocity calculation unit145, a first deflection amount calculation unit146, a second deflection amount calculation unit147, a coefficient calculation unit148, a third deflection amount calculation unit149, an offset calculation unit150, a static response calculation unit151, a first dynamic response calculation unit152, a second dynamic response calculation unit153, an envelope amplitude calculation unit154, an attenuation rate calculation unit155, and a measurement data output unit156by executing a measurement program131stored in the storage unit13. That is, the processor14includes the observation data acquisition unit141, the first measurement data generation unit142, the second measurement data generation unit143, the observation information generation unit144, the average velocity calculation unit145, the first deflection amount calculation unit146, the second deflection amount calculation unit147, the coefficient calculation unit148, the third deflection amount calculation unit149, the offset calculation unit150, the static response calculation unit151, the first dynamic response calculation unit152, the second dynamic response calculation unit153, the envelope amplitude calculation unit154, the attenuation rate calculation unit155, and the measurement data output unit156.

The observation data acquisition unit141acquires the observation data242received by the first communication unit11, and stores the observation data242in the storage unit13as observation data133. That is, the observation data acquisition unit141performs the processing of the observation data acquisition step S10inFIG.30.

The first measurement data generation unit142reads the observation data133stored in the storage unit13, and generates, based on the acceleration data a(t) which is the observation data133, the measurement data u(t) which is the first measurement data based on the acceleration as the physical quantity, which is the response to the actions of the plurality of axles of the railway vehicle6moving on the superstructure7on the observation point R. Specifically, the first measurement data generation unit142integrates the acceleration data a(t), which is the observation data133, to generate the velocity data v(t) as in Equation (1), and further integrates the velocity data v(t) to generate the measurement data u(t) as in Equation (2). That is, the first measurement data generation unit142performs the processing of the first measurement data generation step S20inFIG.30, specifically, the processing of steps S201and S202inFIG.31.

The second measurement data generation unit143generates the measurement data ulp(t), which is the second measurement data in which the vibration component is reduced by performing filter processing on the measurement data u(t) generated by the first measurement data generation unit142. For example, the second measurement data generation unit143performs, as the filter processing, low-pass filter processing for attenuating the vibration component having a frequency equal to or higher than the fundamental frequency Ffof the measurement data u(t). Specifically, the second measurement data generation unit143calculates the power spectrum density by performing fast Fourier transform processing on the measurement data u(t), calculates the peak of the power spectrum density as the fundamental frequency Ff, and generates the measurement data ulp(t) by performing low-pass filter processing for attenuating the vibration component having a frequency equal to or higher than the fundamental frequency Ffof the measurement data u(t). The second measurement data generation unit143may generate the measurement data ulp(t) by performing, as the low-pass filter processing, moving average processing on the measurement data u(t) in the basic cycle Tf corresponding to the fundamental frequency Ff, as in Equation (5). Alternatively, the second measurement data generation unit143may generate the measurement data ulp(t) by performing, as the low-pass filter processing, FIR filter processing for attenuating the signal component having a frequency equal to or higher than the fundamental frequency Ffon the measurement data u(t). That is, the second measurement data generation unit143performs the processing of the second measurement data generation step S30inFIG.30, specifically, the processing of steps S301and S302inFIG.32.

Based on the measurement data ulp(t) generated by the second measurement data generation unit143, the observation information generation unit144generates observation information134including the entry time point tiand the exit time point toof the railway vehicle6with respect to the superstructure7, and stores the observation information134in the storage unit13. Specifically, first, the observation information generation unit144calculates, as the amplitude ua, the average value of the interval from the time point t1to the time point t2in which the amplitude of the measurement data ulp(t) is shifted, according to Equation (6). Next, the observation information generation unit144calculates, as the entry time point ti, the first time point at which the amplitude of the measurement data ulp(t) matches or exceeds the threshold CLuawhich is the product of the predetermined coefficient CLand the amplitude ua. The observation information generation unit144calculates, as the exit time point to, the second time point after the first time point at which the amplitude of the measurement data ulp(t) matches or exceeds the threshold CLua. The observation information generation unit144calculates the difference between the exit time point toand the entry time point tias the passing time tsas in Equation (7). Next, the observation information generation unit144calculates, as the number of vehicles CTof the railway vehicle6, a maximum integer less than or equal to the number obtained by subtracting 1 from the product tsFfof the passing time tsand the fundamental frequency Ff, as in Equation (8). Then, the observation information generation unit144generates the observation information134including the entry time point ti, the exit time point to, the passing time ts, and the number of vehicles CT. That is, the observation information generation unit144performs the processing of the observation information generation step S40inFIG.30, specifically, the processing of steps S401to S406inFIG.33.

The average velocity calculation unit145calculates the average velocity vaof the railway vehicle6based on the observation information134stored in the storage unit13and the environment information132which is created in advance and stored in the storage unit13and includes the dimensions of the railway vehicle6and the dimensions of the superstructure7. Specifically, the average velocity calculation unit145calculates, based on the environment information132, the distance Dwa(aw(CT,aT(CT))) from the leading axle to the rearmost axle of the railway vehicle6according to Equation (11). The average velocity calculation unit145calculates the length LBof the superstructure7, which is the distance from the entry end to the exit end of the superstructure7, based on the environment information132. Then, the average velocity calculation unit145calculates the average velocity vaof the railway vehicle6according to Equation (12), based on the entry time point tiand the exit time point toincluded in the observation information134, the distance Dwa(aw(CT,aT(CT))), and the length LBof the superstructure7. That is, the average velocity calculation unit145performs the processing of the average velocity calculation step S50inFIG.30, specifically, the processing of steps S501, S502, and S503inFIG.34.

The first deflection amount calculation unit146calculates the deflection amount Tstd(t), which is the first deflection amount of the superstructure7caused by the railway vehicle6, based on the approximate equation of the deflection of the superstructure7, which is Equation (35), the observation information134stored in the storage unit13, the environment information132stored in the storage unit13, and the average velocity vaof the railway vehicle6calculated by the average velocity calculation unit145. Specifically, first, the first deflection amount calculation unit146calculates, based on the environment information132, the distance Dwa(aw(Cm,n)) from the leading axle to the n-th axle of the Cm-th vehicle of the railway vehicle6, according to Equation (10). Next, the first deflection amount calculation unit146calculates the time txnrequired for a certain axle of the railway vehicle6to reach the position Lxof the observation point R from the entry end of the superstructure7using the position Lxof the observation point R included in the environment information132and the average velocity va, according to Equation (37). The first deflection amount calculation unit146calculates the time tlnrequired for a certain axle of the railway vehicle6to pass through the superstructure7using the length LBof the superstructure7, which is the distance from the entry end to the exit end of the superstructure7, and the average velocity va, according to Equation (38). Further, the first deflection amount calculation unit146calculates the time point t0(Cm,n) at which the n-th axle of the Cm-th vehicle of the railway vehicle6reaches the entry end of the superstructure7using the entry time point tiincluded in the observation information134, the distance Dwa(aw(Cm,n)), and the average velocity va, according to Equation (39). Next, the first deflection amount calculation unit146calculates the deflection amount wstd(aw(Cm,n),t) of the superstructure7caused by the n-th axle of the Cm-th vehicle using the approximate equation of the deflection of the superstructure7, which is Equation (35), the time txn, the time tln, and the time point t0(Cm,n), according to Equation (40). Next, the first deflection amount calculation unit146calculates the deflection amount Cstd(Cm,t) of the superstructure7caused by the Cm-th vehicle using the deflection amount wstd(aw(Cm,n),t), according to Equation (42). Then, the first deflection amount calculation unit146calculates the deflection amount Tstd(t) of the superstructure7caused by the railway vehicle6using the deflection amount Cstd(Cm,t), according to Equation (43). That is, the first deflection amount calculation unit146performs the processing of the first deflection amount calculation step S60inFIG.30, specifically, the processing of steps S601to S607inFIG.35.

The second deflection amount calculation unit147calculates the deflection amount Tstd_lp(t), which is the second deflection amount in which the vibration component is reduced by performing filter processing on the deflection amount Tstd(t) calculated by the first deflection amount calculation unit146. For example, the second deflection amount calculation unit147performs, as the filter processing, low-pass filter processing for attenuating the vibration component having a frequency equal to or higher than the fundamental frequency FMof the deflection amount Tstd(t). Specifically, the second deflection amount calculation unit147calculates the deflection amount Tstd(t) as the fundamental frequency FMby performing fast Fourier transform processing on the deflection amount Tstd(t), and calculates the deflection amount Tstd_lp(t) by performing low-pass filter processing for attenuating the vibration component having a frequency equal to or higher than the fundamental frequency FMof the deflection amount Tstd(t). The second deflection amount calculation unit147may calculate the deflection amount Tstd_lp(t) by performing, as the low-pass filter processing, moving average processing on the deflection amount Tstd(t) in the basic cycle TMcorresponding to the fundamental frequency FM, according to Equation (46). Alternatively, the second deflection amount calculation unit147may calculate the deflection amount Tstd_lp(t) by performing, as the low-pass filter processing, FIR filter processing for attenuating the signal component having a frequency equal to or higher than the fundamental frequency FMon the deflection amount Tstd(t). That is, the second deflection amount calculation unit147performs the processing of the second deflection amount calculation step S70inFIG.30, specifically, the processing of steps S701and S702inFIG.36.

The coefficient calculation unit148approximates the measurement data ulp(t) generated by the second measurement data generation unit143with the linear function of the deflection amount Tstd_lp(t) calculated by the second deflection amount calculation unit147, and calculates the first-order coefficient c1and the zero-order coefficient c0of the linear function. Specifically, the coefficient calculation unit148approximates the measurement data ulp(t) with the linear function of the deflection amount Tstd_lp(t) as in Equation (47), and calculates the first-order coefficient c1and the zero-order coefficient c0according to Equation (49) and Equation (50) using the least-squares method. That is, the coefficient calculation unit148performs the processing of the coefficient calculation step S80inFIG.30.

The third deflection amount calculation unit149calculates the deflection amount TEstd_lp(t), which is the third deflection amount, based on the first-order coefficient c1and the zero-order coefficient c0calculated by the coefficient calculation unit148and the deflection amount Tstd_lp(t) calculated by the second deflection amount calculation unit147. Specifically, the third deflection amount calculation unit149calculates the deflection amount TEstd_lp(t), which is the product c1Tstd_lp(t) of the first-order coefficient c1and the deflection amount Tstd_lp(t) in the interval before the entry time point tiand the interval after the exit time point to, and is the sum of the product c1Tstd_lp(t) and the zero-order coefficient c0in the interval from the entry time point tito the exit time point to, as in Equation (51). That is, the third deflection amount calculation unit149performs the processing of the third deflection amount calculation step S90inFIG.30.

The offset calculation unit150calculates the offset Toffset_std(t) based on the zero-order coefficient c0calculated by the coefficient calculation unit148, the deflection amount Tstd_lp(t) calculated by the second deflection amount calculation unit147, and the deflection amount TEstd_lp(t) calculated by the third deflection amount calculation unit149. Specifically, the offset calculation unit150calculates the amplitude ratio RTbetween the deflection amount TEstd_lp(t) and the deflection amount Tstd_lp(t) in a predetermined interval, according to Equation (54). Then, the offset calculation unit150calculates the offset Toffset_std(t) by replacing, with the zero-order coefficient c0, the interval in which the product RTTstd_lp(t) the amplitude ratio RTand the deflection amount Tstd_lp(t) is smaller than the zero-order coefficient c0, as in Equation (55). That is, the offset calculation unit150performs the processing of the offset calculation step S100inFIG.30, specifically, the processing of steps S1001and S1002inFIG.37.

The static response calculation unit151calculates the deflection amount TEOstd(t) as the static response by adding the product c1Tstd(t) of the first-order coefficient c1calculated by the coefficient calculation unit148and the deflection amount Tstd(t) calculated by the first deflection amount calculation unit146, and the offset Toffset_std(t) calculated by the offset calculation unit150, as in Equation (56). That is, the static response calculation unit151performs the processing of the static response calculation step S110inFIG.30.

The first dynamic response calculation unit152calculates, as in Equation (56), the natural vibration unv(t) as the first dynamic response by subtracting the deflection amount TEOstd(t) as the static response calculated by the static response calculation unit151from the measurement data u(t) generated by the first measurement data generation unit142. That is, the first dynamic response calculation unit152performs the processing of the first dynamic response calculation step S120inFIG.30.

The second dynamic response calculation unit153calculates the natural vibration unv_31p(t) as the second dynamic response by performing filter processing for attenuating an unnecessary signal from the natural vibration unv(t) which is the first dynamic response calculated by the first dynamic response calculation unit152. The filter processing may include low-pass filter processing for attenuating a harmonic component of a vibration component having the fundamental frequency FNincluded in the natural vibration unv(t) and correcting a gain at the fundamental frequency FN. Further, the filter processing may include high-pass filter processing for attenuating a signal component having a frequency lower than the fundamental frequency FN. For example, the second dynamic response calculation unit153calculates the natural vibration unv_hp(t) according to Equation (60) by performing high-pass filter processing for subtracting, from the natural vibration unv(t), a low-frequency signal component in which the vibration component is reduced by performing moving average processing on the natural vibration unv(t) in the basic cycle TN. Further, the second dynamic response calculation unit153calculates, according to Equation (63), the natural vibration unv_31p(t) as the second dynamic response by performing the low-pass filter processing for attenuating the harmonic component of the vibration component having the fundamental frequency FNincluded in the natural vibration unv_hp(t) and correcting the gain at the fundamental frequency FN. That is, the second dynamic response calculation unit153performs the processing of the second dynamic response calculation step S130inFIG.30, specifically, the processing of steps S1301and S1302inFIG.38.

The envelope amplitude calculation unit154calculates the envelope amplitude unv_mag(t) of the natural vibration unv_31p(t) which is the second dynamic response calculated by the second dynamic response calculation unit153. Specifically, the envelope amplitude calculation unit154calculates, as in Equation (64), the envelope amplitude unv_mag(t) by performing low-pass filter processing on the absolute value of the natural vibration unv_31p(t) and multiplying the result by π/2. That is, the envelope amplitude calculation unit154performs the processing of the envelope amplitude calculation step S140inFIG.30.

The attenuation rate calculation unit155calculates the attenuation rate ζ of the vibration component included in the natural vibration unv_31p(t), which is the second dynamic response calculated by the second dynamic response calculation unit153, based on the envelope amplitude unv_mag(t) calculated by the envelope amplitude calculation unit154. Specifically, the attenuation rate calculation unit155approximates the envelope amplitude unv_mag(t) by an exponential function in the first interval T1which is at least a part of an interval in which the vibration component included in the natural vibration unv_31p(t), which is the second dynamic response, attenuates to calculate the power coefficient q1of the exponential function. The start time point te0of the first interval T1is after the exit time point to. For example, the attenuation rate calculation unit155approximates the logarithm y(t) of the envelope amplitude unv_mag(t) in the first interval T1by the linear function Q(t) as in Equation (69), and calculates the power coefficient q1according to Equation (71). Then, the attenuation rate calculation unit155calculates, as in Equation (76), the attenuation rate ζ by dividing the power coefficient q1 by the natural frequency ω=2 πFNof the natural vibration unv_31p(t). That is, the attenuation rate calculation unit155performs the processing of the attenuation rate calculation step S150inFIG.30, specifically, the processing of steps S1501and S1502inFIG.39.

The attenuation rate ζ is stored in the storage unit13as at least a part of the measurement data135. The measurement data135may include the measurement data u(t) and ulp(t), the deflection amounts Tstd(t), Tstd_lp(t), TEstd_lp(t), and TEOstd(t), the natural vibrations unv(t) and unv_31p(t), the envelope amplitude unv_mag(t), and the like, in addition to the attenuation rate ζ.

The measurement data output unit156reads the measurement data135stored in the storage unit13and outputs the measurement data135to the monitoring device3. Specifically, the second communication unit12transmits the measurement data135stored in the storage unit13to the monitoring device3via the communication network4under the control of the measurement data output unit156. That is, the measurement data output unit156performs the processing of the measurement data output step S160inFIG.30.

As described above, the measurement program131is a program that causes the measurement device1, which is a computer, to execute each procedure of the flowchart shown inFIG.30.

As shown inFIG.40, the monitoring device3includes a communication unit31, a processor32, a display unit33, an operation unit34, and a storage unit35.

The communication unit31receives the measurement data135from the measurement device1and outputs the received measurement data135to the processor32.

The display unit33displays various types of information under the control of the processor32. The display unit33may be, for example, a liquid crystal display or an organic EL display. EL is an abbreviation for electro luminescence.

The operation unit34outputs operation data corresponding to an operation of a user to the processor32. The operation unit34may be, for example, an input device such as a mouse, a keyboard, or a microphone.

The storage unit35is a memory that stores various programs, data, and the like for the processor32to perform calculation processing and control processing. The storage unit35stores programs, data, and the like for the processor32to implement predetermined application functions.

The processor32acquires the measurement data135received by the communication unit31, generates evaluation information by evaluating a temporal change in the displacement of the superstructure7based on the acquired measurement data135, and displays the generated evaluation information on the display unit33.

In the present embodiment, the processor32functions as a measurement data acquisition unit321and a monitoring unit322by executing a monitoring program351stored in the storage unit35. That is, the processor32includes the measurement data acquisition unit321and the monitoring unit322.

The measurement data acquisition unit321acquires the measurement data135received by the communication unit31, and adds the acquired measurement data135to a measurement data sequence352stored in the storage unit35.

The monitoring unit322statistically evaluates a temporal change in the deflection amount of the superstructure7based on the measurement data sequence352stored in the storage unit35. Then, the monitoring unit322generates evaluation information indicating the evaluation result, and displays the generated evaluation information on the display unit33. The user can monitor a state of the superstructure7based on the evaluation information displayed on the display unit33.

The monitoring unit322may perform processing such as monitoring of the railway vehicle6and abnormality determination of the superstructure7based on the measurement data sequence352stored in the storage unit35.

The processor32transmits, based on the operation data output from the operation unit34, information for adjusting operation states of the measurement device1and the sensor2to the measurement device1via the communication unit31. The operation state of the measurement device1is adjusted according to the information received via the second communication unit12. The measurement device1transmits information for adjusting the operation state of the sensor2received via the second communication unit12to the sensor2via the first communication unit11. The operation state of the sensor2is adjusted according to the information received via the communication unit21.

In the processors14,23, and32, for example, the functions of the respective units may be implemented by individual hardware, or the functions of the respective units may be implemented by integrated hardware. For example, the processors14,23, and32include hardware, and the hardware may include at least one of a circuit that processes a digital signal and a circuit that processes an analog signal. The processors14,23, and32may be a CPU, a GPU, a DSP, or the like. CPU is an abbreviation for central processing unit, GPU is an abbreviation for graphics processing unit, and DSP is an abbreviation for digital signal processor. The processors14,23, and32may be configured as custom ICs such as ASICs so as to implement the functions of the respective units, or may implement the functions of the respective units by a CPU and an ASIC. ASIC is an abbreviation for application specific integrated circuit, and IC is an abbreviation for integrated circuit.

The storage units13,24, and35are configured by, for example, various IC memories such as a ROM, a flash ROM, and a RAM, and a recording medium such as a hard disk, a memory card, and the like. ROM is an abbreviation for read only memory, RAM is an abbreviation for random access memory, and IC is an abbreviation for integrated circuit. The storage units13,24, and35include a non-volatile information storage device that is a computer-readable device or a medium, and 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 memories such as a card type memory or a ROM.

Although only one sensor2is shown inFIG.40, each of a plurality of sensors2may generate the observation data242and transmit the observation data242to the measurement device1. In this case, the measurement device1receives a plurality of pieces of the observation data242transmitted from the plurality of sensors2, generates a plurality of pieces of measurement data135, and transmits the plurality of pieces of measurement data135to the monitoring device3. The monitoring device3receives the plurality of pieces of measurement data135transmitted from the measurement device1, and monitors a plurality of states of the superstructures7based on the plurality of pieces of received measurement data135.

5. Function and Effect

According to the measurement method of the present embodiment described above, by approximating the measurement data ulp(t), in which the vibration component is reduced by performing filter processing on the measurement data u(t), with the linear function of the deflection amount Tstd_lp(t) in which the vibration component is reduced by performing filter processing on the deflection amount Tstd(t), the measurement device1can calculate the static response separately from the static response and the dynamic response included in the measurement data u(t).

According to the measurement method of the present embodiment, since the product c1Tstd(t) of the first-order coefficient c1, which is a first-order term of the linear function for approximating the measurement data ulp(t), and the deflection amount Tstd(t) corresponds to the displacement of the superstructure7that is proportional to the load of the railway vehicle6, and the offset Toffset_std(t) corresponds to the displacement of the superstructure7that is not proportional to the load of the railway vehicle6, such as play or floating, the measurement device1can accurately calculate the static response by adding the product c1Tstd(t) and the offset Toffset_std(t).

According to the measurement method of the present embodiment, the measurement device1approximates the measurement data ulp(t), in which the vibration component having a frequency equal to or higher than the fundamental frequency Ffincluded in the measurement data u(t) is attenuated, by the linear function of the deflection amount Tstd_lp(t), and thus the calculation accuracy of the first-order coefficient c1and the zero-order coefficient c0of the linear function is improved, so that the static response can be accurately calculated.

According to the measurement method of the present embodiment, the measurement device1calculates, according to Equation (55), the offset Toffset_std(t) which reflects that in an interval where the railway vehicle6passes through the superstructure7, a displacement of the superstructure7such as play and floating that are not proportional to the load of the railway vehicle6occur, and that the displacement of the superstructure7does not occur in other intervals, and thus the static response can be accurately calculated.

According to the measurement method of the present embodiment, since the measurement device1can calculate the number of vehicles CTof the railway vehicle6based on the entry time point tiof the railway vehicle6to the superstructure7and the exit time point toof the railway vehicle6from the superstructure7according to Equation (8), the static response when the railway vehicle6of which the number of vehicles CTis unknown moves on the superstructure7can be accurately calculated.

According to the measurement method of the present embodiment, since the measurement device1can accurately calculate the entry time point tiof the railway vehicle6to the superstructure7and the exit time point toof the railway vehicle6from the superstructure7based on the measurement data ulp(t) in which the vibration component is reduced, the static response can be accurately calculated.

According to the measurement method of the present embodiment, the measurement device1calculates, according to Equation (57), the natural vibration unv(t), which is the first dynamic response, by subtracting the accurately calculated deflection amount TEOstd(t), which is the static response, from the measurement data u(t), then performs filter processing for attenuating an unnecessary signal, and thus the natural vibration unv_31p(t) which is the second dynamic response can be accurately calculated.

In particular, the measurement device1performs high-pass filter processing for attenuating a signal component having a frequency lower than the fundamental frequency FNon the natural vibration unv(t), and thus the natural vibration unv_hp(t) in which a signal component caused by low-frequency noise, environmental vibration, and the like is reduced can be obtained. Further, the measurement device1performs, on the natural vibration unv_hp(t), low-pass filter processing for attenuating a harmonic component of a vibration component having the fundamental frequency FNand correcting a gain at the fundamental frequency FN, and thus the natural vibration unv_31p(t) in which the harmonic component is reduced and the signal component of the fundamental frequency is emphasized can be obtained. Therefore, according to the measurement method of the present embodiment, the measurement device1can accurately calculate the attenuation rate of the dynamic response based on the envelope amplitude unv_mag(t) of the accurately calculated natural vibration unv_31p(t) which is the second dynamic response.

According to the measurement method of the present embodiment, the measurement device1generates the measurement data u(t) based on the acceleration data a(t) output from the sensor2, and calculates the deflection amount Tstd(t) of the superstructure7caused by the railway vehicle6, based on the measurement data u(t) and Equation (35) which is an approximate equation of the deflection based on the structural model reflecting a structure of the superstructure7of the bridge5. Then, the measurement device1calculates the attenuation rate of the dynamic response when the railway vehicle6moves on the superstructure7by relatively simple processing using the measurement data u(t) and the deflection amount Tstd(t). Therefore, according to the measurement method of the present embodiment, the measurement device1can calculate the attenuation rate of the dynamic response by processing with a relatively small calculation amount.

According to the measurement method of the present embodiment, since the velocity of the railway vehicle6actually changes slightly but hardly changes, the measurement device1calculates the deflection amount Tstd(t) based on the average velocity vaassuming that the railway vehicle6travels at a constant average velocity va, and thus it is possible to significantly reduce the calculation amount while maintaining the calculation accuracy of the deflection amount Tstd(t).

According to the measurement method of the present embodiment, the measurement device1can calculate the average velocity vaof the railway vehicle6by simple calculation according to Equation (13) based on the acceleration data a(t) output from the sensor2instead of directly measuring the average velocity vaof the railway vehicle6.

6. Modification

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 embodiments described above, the sensor2, which is an observation device, is an acceleration sensor that outputs the acceleration data a(k), but the observation device is not limited to the acceleration sensor. For example, the observation device may be an impact sensor, a pressure-sensitive sensor, a strain gauge, an image measuring device, a load cell, or a displacement meter.

The impact sensor detects an impact acceleration as a response to an action of each axle of the railway vehicle6on the observation point R. The pressure-sensitive sensor, the strain gauge, and the load cell detect a stress change as a response to an action of each axle of the railway vehicle6on the observation point R. The image measuring device detects, by image processing, a displacement as a response to an action of each axle of the railway vehicle6on the observation point R. The displacement gauge is, for example, a contact-type displacement meter, a ring-type displacement meter, a laser displacement meter, a pressure-sensitive sensor, or a displacement measurement device using an optical fiber, and detects a displacement as a response to an action of each axle of the railway vehicle6on the observation point R.

As an example,FIG.41shows a configuration example of the measurement system10using a ring-type displacement meter as the observation device.FIG.42shows a configuration example of the measurement system10using an image measuring device as the observation device. InFIGS.41and42, the same components as those inFIG.1are denoted by the same reference numerals, and description thereof will be omitted. In the measurement system10shown inFIG.41, a piano wire41is fixed between an upper surface of a ring-type displacement meter40and a lower surface of the main girder G immediately above the ring-type displacement meter40, and the ring-type displacement meter40measures a displacement of the piano wire41caused by bending of the superstructure7and transmits the measured displacement data to the measurement device1. The measurement device1generates the measurement data135based on the displacement data transmitted from the ring-type displacement meter40. In the measurement system10shown inFIG.42, a camera50transmits, to the measurement device1, an image obtained by imaging a target51provided on a side surface of the main girder G. The measurement device1processes the image transmitted from the camera50, calculates a displacement of the target51caused by bending of the superstructure7to generate displacement data, and generates the measurement data135based on the generated displacement data. In the example ofFIG.42, the measurement device1generates the displacement data as an image measuring device, but the displacement data may be generated by an image measuring device (not shown) different from the measurement device1by image processing.

In the embodiments described above, the bridge5is a railway bridge, and the moving object moving on the bridge5is the railway vehicle6, but the bridge5may be a road bridge, and the moving object moving on the bridge5may be a vehicle such as an automobile, a road train, a truck, or a construction vehicle.FIG.43shows a configuration example of the measurement system10when the bridge5is a road bridge and a vehicle6amoves on the bridge5. InFIG.43, the same components as those inFIG.1are denoted by the same reference numerals. As shown inFIG.43, the bridge5, which is a road bridge, includes the superstructure7and the substructure8, similarly to the railway bridge.FIG.44is a cross-sectional view of the superstructure7taken along line A-A ofFIG.43. As shown inFIGS.43and44, the superstructure7includes the bridge floor7aand the support7b, and the bridge floor7aincludes the floor plate F, the main girder G, and a cross girder (not shown). As shown inFIG.43, 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, and 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 bridge5is, for example, a steel bridge, a girder bridge, or an RC bridge.

Each sensor2is installed at a central portion of the superstructure7in a longitudinal direction, specifically, at a central portion of the main girder G in the longitudinal direction. However, each sensor2is not limited to being installed at the central portion of the superstructure7as long as each sensor2can detect an acceleration for calculating the displacement of the superstructure7. When each sensor2is provided on the floor plate F of the superstructure7, the sensor2may be damaged due to traveling of the vehicle6a, and the measurement accuracy may be affected by local deformation of the bridge floor7a, so that in the example ofFIGS.43and44, each sensor2is provided at the main girder G of the superstructure7.

As shown inFIG.44, the superstructure7has two lanes L1and L2on which the vehicle6aas a moving object can move and three main girders G. In the example ofFIGS.43and44, in the central portion of the superstructure7in the longitudinal direction, the sensors2are respectively provided at two main girders at two ends, an observation point R1is provided at a position of a surface of the lane L1vertically above one of the sensors2, and an observation point R2is provided at a position of a surface of the lane L2vertically above the other of the sensors2. That is, the two sensors2are observation devices for observing the observation points R1and R2, respectively. The two sensors2for respectively observing the observation points R1and R2may be provided at positions where accelerations generated at the observation points R1and R2due to the traveling of the vehicle6acan be detected, and are preferably provided at positions close to the observation points R1and R2. The number and installation position of the sensor2, and the number of lanes are not limited to the example shown inFIGS.43and44, and various modifications can be made.

The measurement device1calculates displacements of bending of the lanes L1and L2caused by the traveling of the vehicle6abased on the acceleration data output from the sensors2, and transmits information on the displacements of the lanes L1and L2to the monitoring device3via the communication network4. The monitoring device3may store the information in a storage device (not shown), and may perform processing such as monitoring of the vehicle6aand abnormality determination of the superstructure7based on the information, for example.

In the embodiments described above, each sensor2is provided at the main girder G of the superstructure7, but the sensor2may be provided on the surface of or inside the superstructure7, at the lower surface of the floor plate F, at the bridge pier8a, or the like. In the embodiments described above, the superstructure of the bridge is described as an example of the structure, but the present disclosure is not limited thereto, and any structure may be used as long as the structure is deformed due to the movement of the moving object.

In the embodiments described above, the measurement device1calculates the entry time point tibased on the observation data output from the observation device that observes the observation point R, but the measurement device1may calculate the entry time point tibased on observation data output from another observation device that observes the entry end of the superstructure7. Similarly, in the embodiments described above, the measurement device1calculates the exit time point tobased on the observation data output from the observation device that observes the observation point R, but the measurement device1may calculate the exit time point tobased on observation data output from another observation device that observes the exit end of the superstructure7.

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

The present disclosure includes a configuration substantially the same as the configuration described in the embodiment, 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. The present disclosure includes a configuration having the same function and effect as the configuration described in the embodiment, or a configuration capable of achieving the same object. Further, the present disclosure includes a configuration in which a known technique is added to the configuration described in the embodiment.

The following contents are derived from the embodiments and modifications described above.

A measurement method according to an aspect includes: a first measurement data generation step of generating, based on observation data output from an observation device configured to observe an observation point of a structure, first measurement data based on a physical quantity which is a response to actions of a plurality of parts of a moving object moving on the structure on the observation point; a second measurement data generation step of generating second measurement data in which a vibration component is reduced by performing filter processing on the first measurement data; an observation information generation step of generating observation information including an entry time point and an exit time point of the moving object with respect to the structure; an average velocity calculation step of calculating an average velocity of the moving object based on the observation information and environment information which is created in advance and includes a dimension of the moving object and a dimension of the structure; a first deflection amount calculation step of calculating, based on an approximate equation of deflection of the structure, the observation information, the environment information, and the average velocity, a first deflection amount of the structure caused by the moving object; a second deflection amount calculation step of calculating a second deflection amount in which a vibration component is reduced by performing filter processing on the first deflection amount; a coefficient calculation step of approximating the second measurement data with a linear function of the second deflection amount to calculate a first-order coefficient and a zero-order coefficient of the linear function; a third deflection amount calculation step of calculating a third deflection amount based on the first-order coefficient, the zero-order coefficient, and the second deflection amount; an offset calculation step of calculating an offset based on the zero-order coefficient, the second deflection amount, and the third deflection amount; a static response calculation step of calculating a static response by adding the offset and a product of the first-order coefficient and the first deflection amount; a first dynamic response calculation step of calculating a first dynamic response by subtracting the static response from the first measurement data; a second dynamic response calculation step of calculating a second dynamic response by performing filter processing for attenuating an unnecessary signal from the first dynamic response; an envelope amplitude calculation step of calculating an envelope amplitude of the second dynamic response; and an attenuation rate calculation step of calculating, based on the envelope amplitude, an attenuation rate of a vibration component included in the second dynamic response.

According to the measurement method, the second measurement data in which the vibration component is reduced by performing filter processing on the first measurement data is approximated with the linear function of the second deflection amount in which the vibration component is reduced by performing filter processing on the first deflection amount, and thus the static response can be calculated separately from the static response and the dynamic response included in the first measurement data.

According to the measurement method, since the product of the first-order coefficient, which is the first-order term of the linear function approximating the first deflection amount, and the first deflection amount corresponds to the displacement of the structure that is proportional to the load of the moving object, and the offset corresponds to the displacement of the structure that is not proportional to the load of the moving object, such as play or floating, it is possible to accurately calculate the static response by adding the offset and the product of the first-order coefficient and the first deflection amount.

According to the measurement method, the accurately calculated static response is subtracted from the first measurement data and filter processing for attenuating an unnecessary signal is performed, and thus the second dynamic response can be accurately calculated. Therefore, according to the measurement method, the attenuation rate of the dynamic response can be accurately calculated based on the envelope amplitude of the accurately calculated second dynamic response.

In the measurement method, the attenuation rate of the dynamic response when the moving object moves on the structure is calculated by relatively simple processing using the first measurement data generated based on the observation data and the first deflection amount generated based on the approximate equation of the deflection of the structure. Therefore, according to the measurement method, the attenuation rate of the dynamic response can be calculated by processing with a relatively small calculation amount.

According to the measurement method, since the velocity of the moving object actually changes slightly but hardly changes, it is possible to calculate the first deflection amount based on the average velocity assuming that the moving object moves at a constant average velocity, and thus it is possible to significantly reduce the calculation amount while maintaining the calculation accuracy of the first deflection amount.

In the measurement method according to the above aspect, in the attenuation rate calculation step, the attenuation rate may be calculated by approximating the envelope amplitude by an exponential function in a first interval which is at least a part of an interval in which the vibration component included in the second dynamic response attenuates to calculate a power coefficient of the exponential function, and dividing the power coefficient by a natural frequency of the second dynamic response.

In the measurement method according to the above aspect, the exit time point may be a time point at which a rearmost part among the plurality of parts of the moving object passes through an exit end of the structure, and a start time point of the first interval may be after the exit time point.

In the measurement method according to the above aspect, the filter processing for attenuating an unnecessary signal from the first dynamic response may include low-pass filter processing for attenuating a harmonic component of a vibration component having a fundamental frequency included in the first dynamic response and correcting a gain at the fundamental frequency.

According to the measurement method, since an envelope amplitude of the second dynamic response in which the harmonic component is reduced and the signal component of the fundamental frequency is emphasized can be obtained, the attenuation rate of the dynamic response can be calculated with high accuracy based on the envelope amplitude.

In the measurement method according to the above aspect, the filter processing for attenuating an unnecessary signal from the first dynamic response may include high-pass filter processing for attenuating a signal component having a frequency lower than the fundamental frequency.

According to the measurement method, since an envelope amplitude of the second dynamic response, in which the signal component caused by low-frequency noise, environmental vibration, and the like are reduced together with the harmonic component, and the signal component of the fundamental frequency is emphasized, can be obtained, the attenuation rate of the dynamic response can be calculated with high accuracy based on the envelope amplitude.

In the measurement method according to the above aspect, in the envelope amplitude calculation step, the envelope amplitude may be calculated by performing low-pass filter processing on an absolute value of the second dynamic response and multiplying the result by π/2.

In the measurement method according to the above aspect, the structure may be a superstructure of a bridge.

According to the measurement method, it is possible to calculate, by processing with a relatively small calculation amount, the attenuation rate of the vibration component included in the dynamic response when the moving object moves on the superstructure of the bridge.

In the measurement method according to the above aspect, the moving object may be a vehicle or a railway vehicle, and each of the plurality of parts may be an axle or a wheel.

According to the measurement method, it is possible to calculate, by processing with a relatively small calculation amount, the attenuation rate of the vibration component included in the dynamic response when the vehicle or the railway vehicle moves on the structure.

In the measurement method according to the above aspect, the approximate equation of the deflection of the structure may be an equation based on a structural model of the structure.

According to the measurement method, it is possible to calculate the first deflection amount reflecting a configuration of the structure on which the moving object moves, and it is possible to accurately calculate the attenuation rate of the vibration component included in the dynamic response.

In the measurement method according to the above aspect, the structural model may be a simple beam whose both ends are supported.

According to the measurement method, it is possible to accurately calculate the attenuation rate of the vibration component included in the dynamic response when the moving object moves on a structure having a configuration similar to the simple beam.

In the measurement method according to the above aspect, the observation device may be an acceleration sensor, an impact sensor, a pressure-sensitive sensor, a strain gauge, an image measuring device, a load cell, or a displacement meter.

According to the measurement method, it is possible to accurately measure the attenuation rate of the vibration component included in the dynamic response using data of acceleration, a stress change, or a displacement.

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

A measurement device according to an aspect includes: a first measurement data generation unit configured to generate, based on observation data output from an observation device configured to observe an observation point of a structure, first measurement data based on a physical quantity which is a response to actions of a plurality of parts of a moving object moving on the structure on the observation point; a second measurement data generation unit configured to generate second measurement data in which a vibration component is reduced by performing filter processing on the first measurement data; an observation information generation unit configured to generate observation information including an entry time point and an exit time point of the moving object with respect to the structure; an average velocity calculation unit configured to calculate an average velocity of the moving object based on the observation information and environment information which is created in advance and includes a dimension of the moving object and a dimension of the structure; a first deflection amount calculation unit configured to calculate, based on an approximate equation of deflection of the structure, the observation information, the environment information, and the average velocity, a first deflection amount of the structure caused by the moving object; a second deflection amount calculation unit configured to calculate a second deflection amount in which a vibration component is reduced by performing filter processing on the first deflection amount; a coefficient calculation unit configured to approximate the second measurement data with a linear function of the second deflection amount to calculate a first-order coefficient and a zero-order coefficient of the linear function; a third deflection amount calculation unit configured to calculate a third deflection amount based on the first-order coefficient, the zero-order coefficient, and the second deflection amount; an offset calculation unit configured to calculate an offset based on the zero-order coefficient, the second deflection amount, and the third deflection amount; a static response calculation unit configured to calculate a static response by adding the offset and a product of the first-order coefficient and the first deflection amount; a first dynamic response calculation unit configured to calculate a first dynamic response by subtracting the static response from the first measurement data; a second dynamic response calculation unit configured to calculate a second dynamic response by performing filter processing for attenuating an unnecessary signal from the first dynamic response; an envelope amplitude calculation unit configured to calculate an envelope amplitude of the second dynamic response; and an attenuation rate calculation unit configured to calculate, based on the envelope amplitude, an attenuation rate of a vibration component included in the second dynamic response.

According to the measurement device, the second measurement data in which the vibration component is reduced by performing filter processing on the first measurement data is approximated with the linear function of the second deflection amount in which the vibration component is reduced by performing filter processing on the first deflection amount, and thus the static response can be calculated separately from the static response and the dynamic response included in the first measurement data.

According to the measurement device, since the product of the first-order coefficient, which is the first-order term of the linear function approximating the first deflection amount, and the first deflection amount corresponds to the displacement of the structure that is proportional to the load of the moving object, and the offset corresponds to the displacement of the structure that is not proportional to the load of the moving object, such as play or floating, it is possible to accurately calculate the static response by adding the offset and the product of the first-order coefficient and the first deflection amount.

According to the measurement device, the accurately calculated static response is subtracted from the first measurement data and filter processing for attenuating an unnecessary signal is performed, and thus the second dynamic response can be accurately calculated. Therefore, according to the measurement device, the attenuation rate of the dynamic response can be accurately calculated based on the envelope amplitude of the accurately calculated second dynamic response.

In the measurement device, the attenuation rate of the dynamic response when the moving object moves on the structure is calculated by relatively simple processing using the first measurement data generated based on the observation data and the first deflection amount generated based on the approximate equation of the deflection of the structure. Therefore, according to the measurement device, the attenuation rate of the dynamic response can be calculated by processing with a relatively small calculation amount.

According to the measurement device, since the velocity of the moving object actually changes slightly but hardly changes, it is possible to calculate the first deflection amount based on the average velocity assuming that the moving object moves at a constant average velocity, and thus it is possible to significantly reduce the calculation amount while maintaining the calculation accuracy of the first deflection amount.

A measurement system according to an aspect includes: the measurement device according to the above aspect; and the observation device.

According to an aspect of the present disclosure, a non-transitory computer-readable storage medium stores a measurement program, and the measurement program causes a computer to execute: a first measurement data generation step of generating, based on observation data output from an observation device configured to observe an observation point of a structure, first measurement data based on a physical quantity which is a response to actions of a plurality of parts of a moving object moving on the structure on the observation point; a second measurement data generation step of generating second measurement data in which a vibration component is reduced by performing filter processing on the first measurement data; an observation information generation step of generating observation information including an entry time point and an exit time point of the moving object with respect to the structure; an average velocity calculation step of calculating an average velocity of the moving object based on the observation information and environment information which is created in advance and includes a dimension of the moving object and a dimension of the structure; a first deflection amount calculation step of calculating, based on an approximate equation of deflection of the structure, the observation information, the environment information, and the average velocity, a first deflection amount of the structure caused by the moving object; a second deflection amount calculation step of calculating a second deflection amount in which a vibration component is reduced by performing filter processing on the first deflection amount; a coefficient calculation step of approximating the second measurement data with a linear function of the second deflection amount to calculate a first-order coefficient and a zero-order coefficient of the linear function; a third deflection amount calculation step of calculating a third deflection amount based on the first-order coefficient, the zero-order coefficient, and the second deflection amount; an offset calculation step of calculating an offset based on the zero-order coefficient, the second deflection amount, and the third deflection amount; a static response calculation step of calculating a static response by adding the offset and a product of the first-order coefficient and the first deflection amount; a first dynamic response calculation step of calculating a first dynamic response by subtracting the static response from the first measurement data; a second dynamic response calculation step of calculating a second dynamic response by performing filter processing for attenuating an unnecessary signal from the first dynamic response; an envelope amplitude calculation step of calculating an envelope amplitude of the second dynamic response; and an attenuation rate calculation step of calculating, based on the envelope amplitude, an attenuation rate of a vibration component included in the second dynamic response.

According to the measurement program, the second measurement data in which the vibration component is reduced by performing filter processing on the first measurement data is approximated with the linear function of the second deflection amount in which the vibration component is reduced by performing filter processing on the first deflection amount, and thus the static response can be calculated separately from the static response and the dynamic response included in the first measurement data.

According to the measurement program, since the product of the first-order coefficient, which is the first-order term of the linear function approximating the first deflection amount, and the first deflection amount corresponds to the displacement of the structure that is proportional to the load of the moving object, and the offset corresponds to the displacement of the structure that is not proportional to the load of the moving object, such as play or floating, it is possible to accurately calculate the static response by adding the offset and the product of the first-order coefficient and the first deflection amount.

According to the measurement program, it is possible to accurately calculate the first dynamic response by subtracting the accurately calculated static response from the first measurement data.

According to the measurement program, the accurately calculated static response is subtracted from the first measurement data and filter processing for attenuating an unnecessary signal is performed, and thus the second dynamic response can be accurately calculated. Therefore, according to the measurement program, the attenuation rate of the dynamic response can be accurately calculated based on the envelope amplitude of the accurately calculated second dynamic response.

In the measurement program, the attenuation rate of the dynamic response when the moving object moves on the structure is calculated by relatively simple processing using the first measurement data generated based on the observation data and the first deflection amount generated based on the approximate equation of the deflection of the structure. Therefore, according to the measurement program, the attenuation rate of the dynamic response can be calculated by processing with a relatively small calculation amount.

According to the measurement program, since the velocity of the moving object actually changes slightly but hardly changes, it is possible to calculate the first deflection amount based on the average velocity assuming that the moving object moves at a constant average velocity, and thus it is possible to significantly reduce the calculation amount while maintaining the calculation accuracy of the first deflection amount.