Derivation method, derivation device, derivation system, program

Abstract

To calculate the number of movable bodies that constitute a movable body traveling in a structure with a lower load.SOLUTION: An acquisition step for acquiring time sequence data which includes the physical quantity generated at a prescribed observation point in a structure in response to the travel of a formation movable body formed by one or more movable bodies in the structure; an environment information acquisition step for acquiring information on the structure length which is the length of the structure, the movable body length which is the length of the movable body and the installation position of the contact area of the movable body with the structure as environment information; a basic frequency derivation step for deriving the basic frequency of the time sequence data on the basis of the time sequence data; a transit time derivation step for deriving a transit time required for the formation movable body to pass through the structure on the basis of the time sequence data; and a number derivation step for deriving the number of movable bodies included in the formation movable body on the basis of the environment information, the basic frequency and the transit time: are included.SELECTED DRAWING: Figure 20

Description

Technical Field

[0001] The present invention relates to a derivation method, a derivation device, a derivation system, and a program.

Background Art

[0002] In recent years, many social infrastructures have deteriorated over time, and there is a demand for a method for diagnosing the condition of structures that make up social infrastructures such as railway bridges. Patent Document 1 discloses a method for investigating the structural performance of a railway bridge that enables the structural performance of a bridge to be suitably investigated and evaluated using observation data of the acceleration response of the bridge during train travel. The method for investigating the structural performance of the railway bridge in Patent Document 1 formulates a theoretical analysis model of the dynamic response of the railway bridge during train travel, assuming the train as a moving load train and the bridge as a simple beam, measures the acceleration of the bridge during train travel, and estimates unknown parameters of the theoretical analysis model from the acceleration data by an inverse analysis method. Further, Patent Document 2 discloses a method for obtaining the impact coefficient (dynamic response component) of a bridge using the vertical acceleration response of a running train particularly when passing over the bridge.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0004] There are cases where a formation moving body formed by one or more moving bodies, such as a railway train, moves on a structure such as a bridge. In such a case, for the purpose of generating a motion model of the structure for diagnosis or the like, there is a desire to grasp how many moving bodies are formed in the formation moving body that moves the structure. In Patent Document 1, the amount of calculation in the inverse analysis method for obtaining unknown parameters becomes enormous. Also, in Patent Document 2, it was not possible to determine how many moving bodies are formed in the moving body that moves the structure. Thus, in Patent Documents 1 and 2, it was not possible to determine how many moving bodies are formed in the moving body that moves the structure with a lower load.

Means for Solving the Problem

[0005] The derivation method for solving the above problem includes an acquisition step of acquiring time-series data including a physical quantity generated at a predetermined observation point in the structure as a response caused by a formation moving body formed by one or more moving bodies moving the structure, an environmental information acquisition step of acquiring information on the structure length which is the length of the structure, the moving body length which is the length of the moving body, and the installation position of the contact portion between the moving body and the structure as environmental information, a fundamental frequency derivation step of deriving the fundamental frequency of the time-series data based on the time-series data, a passing period derivation step of deriving the passing period during which the formation moving body passes through the structure based on the time-series data, and a number derivation step of deriving the number of the moving bodies included in the formation moving body based on the environmental information, the fundamental frequency, and the passing period. The derivation device for solving the above problems includes an acquisition unit that acquires time-series data including a physical quantity generated at a predetermined observation point in the structure as a response to the movement of a structured moving body formed by one or more moving bodies moving the structure, an environmental information acquisition unit that acquires information on the structure length that is the length of the structure, the moving body length that is the length of the moving body, and the installation position of the contact portion between the moving body and the structure as environmental information, a fundamental frequency derivation unit that derives the fundamental frequency of the time-series data based on the time-series data, a passing period derivation unit that derives the passing period during which the structured moving body passes through the structure based on the time-series data, and a number derivation unit that derives the number of moving bodies included in the structured moving body based on the environmental information, the fundamental frequency, and the passing period. The derivation system for solving the above problems is a derivation system including a derivation device and a sensor. The derivation device includes an acquisition unit that acquires time-series data including a physical quantity generated at a predetermined observation point in the structure as a response to the movement of a structured moving body formed by one or more moving bodies moving the structure, the physical quantity being measured via the sensor, an environmental information acquisition unit that acquires information on the structure length that is the length of the structure, the moving body length that is the length of the moving body, and the installation position of the contact portion between the moving body and the structure as environmental information, a fundamental frequency derivation unit that derives the fundamental frequency of the time-series data based on the time-series data, a passing period derivation unit that derives the passing period during which the structured moving body passes through the structure based on the time-series data, and a number derivation unit that derives the number of moving bodies included in the structured moving body based on the environmental information, the fundamental frequency, and the passing period. A program for solving the above problems causes a computer to execute an acquisition step of acquiring time-series data including a physical quantity generated at a predetermined observation point in the structure as a response to the movement of a structured moving body in which one or more moving bodies are organized; an environment information acquisition step of acquiring information on the length of the structure, the length of the moving body, and the installation position of the contact portion between the moving body and the structure as environment information; a fundamental frequency derivation step of deriving the fundamental frequency of the time-series data based on the time-series data; a passing period derivation step of deriving the passing period during which the organized moving body passes through the structure based on the time-series data; and a number derivation step of deriving the number of the moving bodies included in the organized moving body based on the environment information, the fundamental frequency, and the passing period.

Brief Description of the Drawings

[0006]

Figure 1

Figure 2

Figure 3

Figure 4

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Figure 8

Figure 9

Figure 10

Figure 11

Figure 12

Figure 13

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Embodiments for Carrying Out the Invention

[0007] Here, embodiments of the present invention will be described in the following order. (1) Configuration of the derivation system: (1-1) Outline of the derivation system: (1-2) Flexure model: (1-3) Verification experiment: (1-4) Details of elements: (2) Derivation process: (3) Other embodiments:

[0008] (1) Configuration of the derivation system: (1-1) Outline of the derivation system: FIG. 1 is a block diagram showing an example of the configuration of a derivation system 10 according to the present embodiment. The derivation system 10 is a system that derives the number of railway vehicles included in a railway train 6 based on time-series data including physical quantities at a predetermined observation point on a bridge 5 on which a railway train 6 formed of one or more railway vehicles moves. The railway train 6 is an example of a formed moving body. Each of the railway vehicles included in the railway train 6 is an example of a moving body. The bridge 5 is an example of a structure on which a moving body moves. Each railway vehicle of the railway train 6 moves on the bridge 5 via wheels provided on the axles. The wheels are an example of a contact part between the railway vehicle and the bridge. In the present embodiment, each of the railway vehicles formed in the railway train 6 is a railway vehicle having the same structure. As shown in FIG. 1, the derivation system 10 includes a measurement device 1, at least one sensor device 2 provided in the superstructure 7 of the bridge 5, and a server device 3.

[0009] The measurement device 1 calculates the deflection, that is, the displacement of the superstructure 7 due to the running of the railway train 6, based on the acceleration data output from each sensor device 2. The measurement device 1 is installed, for example, on the abutment 8b. The measurement device 1 and the server device 3 can communicate with each other via a communication network 4 such as a wireless network of a mobile phone and the Internet. The measurement device 1 transmits information on the displacement of the superstructure 7 due to the running of the railway train 6 to the server device 3. The server device 3 derives the number of railway vehicles formed in the railway train 6 based on the transmitted displacement data.

[0010] In this embodiment, the bridge 5 is a railway bridge, such as a steel bridge, a truss bridge, an RC bridge, etc. RC is an abbreviation for Reinforced-Concrete. Further, in this embodiment, the bridge 5 is a structure to which BWIM (Bridge Weigh In Motion) can be applied. BWIM is a technology that measures the weight, number of axles, etc. of a moving body passing over a bridge by regarding the bridge as a "scale" and measuring the deformation of the bridge. A bridge capable of analyzing the weight of a moving body passing through from responses such as the deformation and strain of the bridge is considered a structure to which BWIM can be applied. Therefore, it is possible to measure the weight of a moving body moving over the bridge by a BWIM system that applies the physical process between the action and response of the bridge. The measurement of the weight of the moving body is performed by previously measuring the correlation coefficient between displacement and load, and deriving the load of the passing moving body from the measurement result of the displacement of the bridge when the moving body passes, using the correlation coefficient.

[0011] The bridge 5 includes a superstructure 7 where the moving body moves and a substructure 8 that supports the superstructure 7. FIG. 2 is a cross-sectional view of the superstructure 7 cut along the line A-A in FIG. 1. As shown in FIGS. 1 and 2, the superstructure 7 includes a bridge floor 7a including a floor slab F, main girders G, transverse girders (not shown), etc., bearings 7b, rails 7c, sleepers 7d, and ballast 7e. Further, as shown in FIG. 1, the substructure 8 includes bridge piers 8a and abutments 8b. The superstructure 7 is a structure spanned between adjacent abutments 8b and bridge piers 8a, between two adjacent abutments 8b, or between two adjacent bridge piers 8a. Hereinafter, the abutments 8b and the bridge piers 8a are collectively referred to as support portions. In this embodiment, one set of support portions and the bridge girder portion of the superstructure 7 spanned between this one set of support portions are collectively regarded as one bridge girder. That is, a simple beam-like structure supported at both ends by two support portions is regarded as one bridge girder. Therefore, the bridge 5 shown in FIG. 1 includes two bridge girders. Hereinafter, each bridge girder included in the bridge 5 is referred to as a unit bridge girder. The measuring device 1 and the sensor device 2 are connected, for example, by wire or wirelessly, and communicate via a communication network such as CAN (Controller Area Network).

[0012] The sensor device 2 is used for measuring a predetermined physical quantity that is used to derive the displacement (flexure) at an observation point set on the superstructure 7. In this embodiment, this predetermined physical quantity is acceleration. Also, in this embodiment, the sensor device 2 is installed at this observation point. Further, the sensor device 2 includes an acceleration sensor such as a crystal acceleration sensor or a MEMS (Micro Electro Mechanical Systems) acceleration sensor. The sensor device 2 outputs acceleration data for deriving the displacement of the superstructure 7 due to the movement of the railway train 6, which is a moving body, at the observation point.

[0013] In this embodiment, the sensor device 2 is installed at the central portion in the longitudinal direction of the superstructure 7, specifically, at the central portion in the longitudinal direction of the main girder G. However, the sensor device 2 only needs to be able to detect the acceleration for calculating the displacement of the superstructure 7, and its installation position is not limited to the central portion of the superstructure 7. Note that if the sensor device 2 is provided on the floor slab F of the superstructure 7, it may be damaged by the running of the railway train 6, and the measurement accuracy may be affected by the local deformation of the bridge floor 7a. Therefore, in the examples of FIGS. 1 and 2, the sensor device 2 is provided on the main girder G of the superstructure 7.

[0014] The floor slab F, main girder G, etc. of the superstructure 7 are bent in the vertical direction by the load of the railway train 6 running on the superstructure 7. Each sensor device 2 measures the acceleration of the flexure of the floor slab F and the main girder G due to the load of the railway train 6 running on the superstructure 7.

[0015] (1-2) Flexure model: Here, the flexure model of a bridge when a railway train moves on it will be described. Here, the model is information such as an equation showing the correspondence between predetermined information and a derivation result.

[0016] Also, hereinafter, the number (number of units) of railway vehicles formed in the railway train moving on the bridge will be denoted as N. The entry time, which is the time when the railway train enters the bridge, is t iLet it be so. Here, the entry of the railway train onto the bridge means that the wheels of one axle of the railway vehicle C1 (the first railway vehicle from the head of the railway train) have entered the bridge. Also, hereinafter, the exit time, which is the time when the railway train exits the bridge, is denoted as t o Let it be so. Here, the exit of the railway train from the bridge means that the wheels of the rearmost axle of the railway vehicle C N (the rearmost railway vehicle of the railway train) have exited the bridge. Also, hereinafter, the period during which the railway train passes through the bridge (the period from time t i to time t o ) is denoted as t s Let it be so. Hereinafter, N, t i , t o , t s are collectively referred to as observation information.

[0017] Also, hereinafter, the length of the bridge in the traveling direction of the railway train, which is the bridge length, is denoted as L B Let it be so. The bridge length is an example of the structure length. Also, the distance from the end on the side where the railway train enters among the longitudinal ends of the bridge to the observation point is denoted as L x Let it be so. Fig. 3 shows L B and L x . Hereinafter, the end on the side where the railway train enters among the longitudinal ends of the bridge is referred to as the entry end. Also, hereinafter, the end on the side where the railway train exits among the longitudinal ends of the bridge is referred to as the exit end. Also, the vehicle length, which is the length in the traveling direction of the m-th railway vehicle from the head of the railway train, is denoted as L c (m). The vehicle length is an example of the moving body length, which is the length in the traveling direction of the moving body. Hereinafter, L c (1) to L c (N) are collectively referred to as L c . Also, the m-th railway vehicle from the head of the railway train is referred to as C m . Also, the number of axles in the railway vehicle C m is denoted as a r (m). Hereinafter, a r (1) to a r (N) are collectively referred to as a r . Hereinafter, in the railway vehicle C m , a r(m) axles are assigned to the railway vehicle C m in order from the front of the vehicle as the 1st axle, 2nd axle, 3rd axle, ···, a r (m) axles. Also, the distance from the front end in the traveling direction of the railway vehicle C m to the 1st axle is denoted as L a (a w (m, 1)). Here, a w (α, β) indicates the β-th axle from the leading axle of the α-th railway vehicle in the train. Also, the distance between the (n - 1)-th axle (n: an integer of 2 or more) and the n-th axle in the railway vehicle C m is denoted as L a (a w (m, n)). That is, for β of 2 or more, L a (a w (α, β)) indicates the distance between the β-th axle and the (β - 1)-th axle in the railway train C α . Also, L a (a w (α, 1)) indicates the distance between the 1st axle and the front end in the traveling direction of the railway train C α . Hereinafter, L α (a a (1, 1)) to L w (a a (a w (N, a r (N))) are collectively referred to as L a . Each of L a indicates the position of the corresponding axle in the corresponding railway vehicle. For example, L a (a w (m, 1)) indicates that in the railway vehicle C m , the 1st axle exists at a distance of L a (a w (m, 1)) behind the tip. Also, L a (a w (m, 2)) indicates that in the railway vehicle C m , the 2nd axle exists at a distance of L a (a w (m, 2)) behind the 1st axle. Here, in the railway train, railway vehicles with the same 4-axle configuration are composed. That is, a r(m) (where m = 1, 2, ···, N) is 4. Railway vehicle C is shown in Figure 4. m L in c (m), L a (a w (m, 1)), L a (a w (m, 2)), L a (a w (m, 3)), L a (a w (m, 4)) are shown. Hereinafter, L B , L x , L c , a r , L a are collectively regarded as environmental information.

[0018] t s is obtained as the difference between t o and t i as shown in the following formula (1).

[0019]

Equation

[0020] Also, the total number of wheels T of the railway train ar is obtained by the following formula (2).

[0021]

Equation

[0022] The distance from the first axle of the leading railway vehicle C1 of the railway vehicle to the nth axle of the mth railway vehicle C m of the railway vehicle is expressed as D wa (a w (m, n)). D wa (a w (m, n)) is obtained from the following formula (3).

[0023]

Equation

[0024] From the first axle of the leading railway vehicle C1 of the railway vehicle to the last axle a N of the last railway vehicle C r (N) of the distance is D wa (a w (N, a r (N))). D wa (a w (N, a r (N))) is used to calculate the average speed v of the railway train passing through the bridge a is expressed as the following formula (4).

[0025]

Number

[0026] The following formula (5) holds from formula (3) and formula (4).

[0027]

Number

[0028] Subsequently, the deflection generated in the bridge when a load is applied to the bridge will be described. Figure 5 shows a schematic diagram of the bridge. Figure 5 shows a situation where a load P is applied to the bridge. Here, the distance between the position where the load P is applied on the bridge and the entrance end is represented by a. Also, the distance between the position where the load P is applied on the bridge and the exit end is represented by b. In this case, the bending moment at the position where the load P is applied on the bridge is represented by the following formula (6).

[0029]

Number

[0030] Figure 6 shows the bending moment at each position of the bridge due to the load P. As shown in Figure 6, the bending moment generated in the bridge by the load P is 0 at the entry end, and increases proportionally as it approaches the position where the load P is applied from the entry end, and at the position where the load P is applied, it becomes the value shown in Equation (6). Also, the bending moment generated in the bridge by the load P decreases proportionally as it approaches the exit end from the position where the load P is applied, and becomes 0 at the exit end. Therefore, the bending moment at any position X in the bridge is represented by the following Equation (7).

[0031]

Number

[0032] In Equation (7), x represents the distance from the entry end in the traveling direction of the railway train to the position X. Also, Ha in Equation (7) is the value shown by the following Equation (8).

[0033]

Number

[0034] There is a relationship shown by the following Equation (9) between the deflection w of the bridge at any position X and the bending moment.

[0035]

Number

[0036] In Equation (9), θ is the angle formed by the horizontal line and the deflected bridge at the position X. From Equation (7) and Equation (9), the following Equation (10) holds.

[0037]

Number

[0038] By integrating both sides of Equation (10) twice with respect to x, the following Equation (11) representing the deflection w at the position X is obtained.

[0039]

Number

[0040] g1 and g2 in Equation (11) are constant terms. Here, since the bridge is supported at the entrance end and the exit end, there is no deflection at the positions of the entrance end and the exit end. That is, in Equation (11), when x = 0 and x = L B both sides become 0. Therefore, g1 and g2 are as shown in the following Equations (12) and (13).

[0041]

Number

[0042]

Number

[0043] From Equations (11), (12), and (13), the following Equation (14) representing the deflection w at position X is obtained.

[0044]

Number

[0045] When the load P is applied at the center of the longitudinal direction of the bridge, the maximum deflection among the deflections generated in the bridge due to the application of the load P occurs at the center of the longitudinal direction of the bridge. Let this maximum deflection be w 0.5l and find the equation representing w 0.5l When the load P is applied at the center of the longitudinal direction of the bridge, a = b = 0.5L B Also, since the position X for which the deflection is to be obtained is the center of the longitudinal direction of the bridge, x = 0.5L B Also, in this case, since x <= a, from Equation (8), H a = 0. x = 0.5L B a = b = 0.5L B Ha By substituting =0 into Equation (14), the deflection w 0.5l The following Equation (15) representing it is obtained.

[0046]

Equation

[0047] w 0.5l is used to normalize the deflection at any position in the bridge represented by Equation (14). When the position of the load P exists on the entrance end side of the position X, that is, when x > a, from Equation (8), H a =1, and Equation (14) is expressed as the following Equation (16).

[0048]

Equation

[0049] a = L B Let r. Here, r is a real number between 0 and 1. b = L B -a, so b = L B (1 - r). Substitute a = L B r, b = L B (1 - r) into Equation (16) and divide by w 0.5l to normalize. Then, the normalized deflection w std at position X when x > a is obtained as the following Equation (17).

[0050]

Equation

[0051] Similarly, when the position of the load P exists on the exit end side of the position X, that is, when x <= a, from Equation (8), H a =0, and Equation (14) is expressed as the following Equation (18).

[0052]

Equation

[0053] a = L B Let r be such that r is a real number between 0 and 1. b = L B Since it is -a, b = L B is expressed as (1 - r). In Equation (18), a = L B r, b = L B Substitute r and b = L 0.5l (1 - r) and divide by w std to normalize. The following Equation (19) for the normalized deflection w at position X when x <= a is obtained.

[0054]

Equation

[0055] Substitute L for x in Equation (17) and Equation (19). x The normalized deflection w at the observation point of the deflection std is expressed as a function of r as in the following Equation (20).

[0056]

Equation

[0057] The function R(r) in Equation (20) is the function shown in the following Equation (21).

[0058]

Equation

[0059] Here, using Equation (20) and Equation (21), find the function showing the time change of the deflection generated at the observation point due to the load applied to the bridge through the wheels of any one axle a w (m, n). First, let t be the period it takes for the wheel of one axle of the railway train to reach the observation point from the entry end. xn Let t xn be Lx and v a From this, it is obtained by the following formula (22).

[0060]

Number

[0061] Also, let t be the period during which one wheel of a railway train crosses a bridge, that is, the period from the entry end to the exit end. ln Let it be t ln t is L B and v a From this, it is obtained by the following formula (23).

[0062]

Number

[0063] Also, let t(m, n) be the time when the wheel of the n -th axle a of the m -th railway vehicle of a railway train reaches the entry end. w (m, n) Let it be t o (m, n) t o (m, n) is t i and v a and D wa (a w (m, n)) From this, it is obtained by the following formula (24).

[0064]

Number

[0065] From formula (22), L x is expressed as the following formula (25).

[0066]

Number

[0067] Also, from formula (23), L B is expressed as the following formula (26).

[0068]

Number

[0069] Axle a w (m, n) is the load position. Therefore, axle a w (m, n) is at a position of a distance r in the direction from the entry end to the exit end. Also, if the variable indicating time is t, then at time t, a B (m, n)'s distance from the entry end is equal to the distance the railway vehicle has traveled from (m, n) to time t. Therefore, the following equation (27) holds. w (m, n)'s distance from the entry end is at time t o (m, n)'s distance from the entry end is equal to the distance the railway vehicle has traveled from (m, n) to time t. Therefore, the following equation (27) holds.

[0070]

Number

[0071] From equation (27), r is expressed as in the following equation (28).

[0072]

Number

[0073] Using equations (25), (26), and (28) to replace L in equations (20) and (21), L x , L B , r, a model function w of the time variation of the deflection generated at the observation point by the load applied to the bridge through the wheels of axle a w (m, n) at (a std (a w (m, n), t) is obtained. The function R(t) in equation (29) is a function represented by the following equation (30).

[0074]

Number

[0075]

Number

[0076] Observation information and environmental information (t i , t o , N, L B , L x , L c (1)~L c (N), a r (1)~a r (N), L a (a w (1, 1))~L a (a w (N, a r (N)))) are known, and using these information, w std (a w (m, n), t) can be obtained. For example, t i , t o From formula (1), t s is obtained. t s , N, a r , L a , L c From, using formula (5), v a is obtained. v a and L B and L x and From, using formula (22) and formula (23), t xn , t ln is obtained. L a , L c , ti From, using formula (3) and formula (24), t o (m, n) is obtained. And the obtained t xn , t ln , t o (m, n) is substituted into formula (29) and formula (30), and the function w of t std (a w (m, n), t) is obtained.

[0077] w std (a w (m, n), t) shows an example of the change in the deflection amount at the observation point, which is shown in Figure 7. The horizontal axis of the graph in Figure 7 is time, and the vertical axis shows the deflection amount. Also, with the movement of one railway vehicle C m , a rA set of wheels for each of (m) axles will move across the bridge. Therefore, for one railway vehicle C m A function C as a model showing the time change of the deflection amount generated at the observation point due to the movement of std (m, t) is obtained as the sum of w for each axle std (a w (m, n), t) as shown in the following equation (31).

[0078] [Number]

[0079] a r When a(m) is 4, that is, when the railway vehicle C m has a 4-axle configuration, the state of change of the deflection amount at the observation point indicated by the function C std (m, t) is shown in Fig. 8. The horizontal axis of the graph in Fig. 8 is time, and the vertical axis indicates the deflection amount. Also, the solid line graph in Fig. 8 shows C std (m, t), and each dotted line graph shows w for each axle std (a w (m, n), t).

[0080] Also, as the railway train moves, N railway vehicles move across the bridge. Therefore, a function T as a model showing the time change of the deflection amount generated at the observation point due to the movement of one railway train std (t) is obtained as the sum of C for each railway vehicle std (m, t) as shown in the following equation (32).

[0081] [Number]

[0082] When N is 16, that is, when 16 railway vehicles are composed in the railway train, the state of change of the deflection amount at the observation point indicated by the function T std (t) is shown in Fig. 9. The horizontal axis of the graph in Fig. 9 is time, and the vertical axis indicates the deflection amount. Also, the solid line graph in Fig. 9 shows Tstd Shows (t), and each dotted line graph represents C for each railway vehicle std Shows (m, t). As shown in the graph of Fig. 9, it can be seen that the waveform of the deflection added for each passing railway vehicle results in vibrations at the period when consecutive vehicles pass over the bridge The above is the description of the deflection model in the bridge

[0083] (1 - 3) Verification experiment: Under the condition that the observation information and the environmental information are the values shown below, the deflection amount C generated when a railway train composed of similar railway vehicles passes over the bridge std (1, t) ~ C std (N, t), T std Consider about (t). That is, N = 4, t i = 7.21 [seconds], t o = 8.777 [seconds], t s = 1.567 [seconds], L B = 25 [m], L x = 12.5 [m], L c Each = 25 [m], a r Each = 4, m = 1 to N for each L a (a w (m, 1)) = 2.5 [m], m = 1 to N for each L a (a w (m, 2)) = 2.5 [m], m = 1 to N for each L a (a w (m, 3)) = 15 [m], m = 1 to N for each L a (a w (m, 4)) = 2.5 [m].

[0084] The deflection amount C caused by each of the 4 railway vehicles included in the railway train at this time std (1, t) ~ C std (4, t) is shown in Fig. 10. Let T be the period of the vibration generated in the bridge when railway vehicles continuously pass over the bridge f Set. The vibration generated in the bridge when railway vehicles continuously pass over the bridge is the vibration caused by the consecutive passing of railway vehicles over the bridge. Therefore, the period T fThis is the time difference between the times when consecutive railway vehicles enter the bridge as they pass over the bridge. Since deflection occurs in the bridge due to the railway vehicle when the railway vehicle enters the bridge, C std The start time of the deflection indicated by C std (m, t) and the start time of the deflection indicated by C f (m + 1, t) have a time difference of the period T f as shown in FIG. 10 shows the deflection generated in the bridge by the passage of each railway vehicle of the railway train when the railway train passes over the bridge. The horizontal axis of the graph in FIG. 10 represents time, and the vertical axis represents the amount of deflection. As shown in FIG. 10, the deflections caused by consecutive railway vehicles occur with a time difference of T

[0085] The period T f is the time difference between the times when consecutive railway vehicles enter the bridge as they pass over the bridge. Therefore, as shown in the following formula (33), the vehicle length L c (m) can be regarded as the period during which it passes at a speed v a

[0086]

Equation

[0087] Let the period during which the railway vehicle C m of the railway train passes over the bridge be t c (m). t c (m) is an example of the moving body passing period, which is the period during which the moving body, the railway vehicle C m , passes over the structure, the bridge. t c (m) is the period from the time when the first axis of the railway vehicle C m reaches the entry end to the time when the a m (m) axis of the railway vehicle C r reaches the exit end. That is, t c (m) is the period during which the railway vehicle C m moves the total distance of the bridge length L B and the distance from the first axle, which is the foremost axle of the railway vehicle C m , to the a r (m) axle, which is the last axle. Therefore, t c ​(m) is represented by the following formula (34).

[0088] [Number]

[0089] When a railway train passes over a bridge, for the railway vehicles that make up the railway train, the number of railway vehicles that have subsequent railway vehicles among them is denoted as C. Tn Let it be so. Among the railway vehicles that make up the railway train, for the railway vehicles other than the last railway vehicle, there are subsequent railway vehicles. Therefore, C Tn is a number that is 1 less than N. That is, the following formula (35) holds.

[0090] [Number]

[0091] In FIG. 11, C std (1, t) to C std (N, t), and T std (t) are shown. The horizontal axis of the graph in FIG. 11 represents time, and the vertical axis represents the amount of deflection. The solid-line graph in FIG. 11 shows T std (t), and the dotted-line graph shows C std (1, t) to C std (4, t) respectively. As shown in FIG. 11, the passing period t s is the sum of the periods of C Tn units of T f and the period t m during which one railway vehicle C c (m) passes over the bridge. That is, the following formula (36) holds.

[0092] [Number]

[0093] From formula (35) and formula (c36), the number N of railway vehicles that make up the railway train is represented by the following formula (37).

[0094]

Number

[0095] T f is also the period it takes for a railway train to move a vehicle length for one railway vehicle. Therefore, the distance traveled by the railway train during the passing period t s is the sum of the lengths of (N - 1) railway vehicles and the distance traveled at speed v a in t c (m) during the period. Therefore, the following equation (38) holds.

[0096]

Number

[0097] The following equation (39) holds from equation (38). It can be confirmed that equation (37) also holds from equation (39).

[0098]

Number

[0099] The amount of deflection T std (t) generated in the bridge when the railway train passes through the bridge is considered to include, as components of the fundamental frequency, the components of the vibration generated in the bridge in response to the movement of successive railway vehicles. Here, the fundamental frequency is the frequency of the lowest-frequency component contained in the signal. Let this fundamental frequency be F f be denoted as. F f is also the frequency of the vibration generated in the bridge in response to the movement of successive railway vehicles. Therefore, as shown in the following equation (40), it can be expressed as the reciprocal of t f .

[0100]

Number

[0101] From equations (33) and (40), the speed v ais represented by the product of F f and L c and L(m).

[0102]

Number

[0103] Therefore, t(m) represented by Equation (34) is the total distance from the first axle, which is the front axle of the railway vehicle C, to the last axle, which is the a(m)th axle, divided by the product of F c and L B and the railway vehicle C m and the railway vehicle C r from the first axle to the a(m)th axle, the last axle, and is the value obtained by dividing the total distance by the product of F f and L c and L(m). From Equations (37) and (40), the number N of railway vehicles formed in a railway train is represented as the value obtained by adding 1 to the product of the value obtained by subtracting the passing period t(m) of the bridge by one railway vehicle C s from the passing period t of the bridge by the railway train and the fundamental frequency Ff, and is represented as follows in Equation (42). m from the passing period t of the bridge by one railway vehicle C c (m), and is represented as the value obtained by adding 1 to the product of the fundamental frequency Ff and the passing period t of the bridge by one railway vehicle C

[0104]

Number

[0105] As shown in Equation (41), the inventors found that the average speed v a of the railway train is represented by the product of the fundamental frequency Ff and the length of one railway vehicle C m included in the railway train. Also, as shown in Equation (34), the passing period t m (m) during which one railway vehicle C c passes through the bridge is the distance from the length L m of the bridge and the railway vehicle C B from the first axle to the a m (m)th axle of the railway vehicle C r is the total distance divided by the speed v aIt has been found that it is expressed as the period of movement. Further, as shown in Equation (42), the inventors have found that the number N of railway vehicles formed into a railway train is expressed as a value obtained by adding 1 to the product of the value obtained by subtracting the value from t s to t c (m) and the fundamental frequency Ff. Then, the inventors have come up with a method for deriving the number of railway vehicles formed into a railway train by using the time series data of the displacement at the observation point set on the bridge where the railway train moves.

[0106] The method conceived by the inventors is as follows. Obtain the time series data of the displacement at the observation point set on the bridge where the railway train moves. Hereinafter, the time series data of the displacement at the observation point set on the bridge is denoted as u(t). u(t) is data of discrete values of the displacement measured at a predetermined period, and each discrete value is associated with the measurement time. Also, L B and L c and L a are obtained as environmental information. Then, based on the time series data u(t), the fundamental frequency F f of u(t) is obtained as the frequency of the vibration generated in the bridge by the passage of consecutive railway vehicles formed into a railway train. Also, based on u(t), the period t s during which the railway train passes through the bridge is derived. Then, L B and L c and L a and F f and t s are used to derive the number of railway vehicles included in the railway train by using the relationships shown in Equation (34), Equation (41), and Equation (42).

[0107] The inventors conducted an experiment to confirm the effectiveness of the conceived method. This experiment will be described below. The inventors measured the displacement time series data at the observation points on the bridge periodically at a predetermined period ΔT when a railway train composed of 16 railway vehicles passed through a predetermined bridge, thereby obtaining the displacement time series data at the observation points. This predetermined bridge is referred to as the first bridge. In the first bridge, resonance with the vibration generated in the first bridge by the passage of a railway train composed of consecutive railway vehicles did not occur as the railway train passed. Here, resonance means that the vibration generated in the bridge by the passage of the railway train approximates the natural vibration frequency of the bridge, and thus the vibration generated in the bridge by the passage of the railway train excites the natural vibration frequency or the vibration of the harmonic of the natural vibration frequency of the bridge. Hereinafter, the vibration generated by resonance is referred to as dynamic response.

[0108] The environmental information at this time is known and is as follows. L B = 25 [m], L x = 12.5 [m], L c Each = 25 [m], a r Each = 4, m = 1 to N for each L a (a w (m, 1)) = 2.5 [m], m = 1 to N for each L a (a w (m, 2)) = 2.5 [m], m = 1 to N for each L a (a w (m, 3)) = 15 [m], m = 1 to N for each L a (a w (m, 4)) = 2.5 [m]. Also, regarding the observation information, it is not known except for N. That is, t i , t o , t s are not known in advance. The number of railway vehicles N in the railway train is 16.

[0109] Fig. 12 shows the displacement time series data u(t) at the observation points on the first bridge obtained by the inventors. The horizontal axis of the graph in Fig. 12 is time, and the vertical axis is the deflection amount. The inventors performed a fast Fourier transform (FFT) on u(t). The result of the FFT for u(t) is shown in FIG. 13. The horizontal axis of the graph in FIG. 13 represents the frequency, and the vertical axis represents the intensity of the component corresponding to the frequency. Then, the inventors determined the fundamental frequency F of u(t) from the result of the FFT of u(t) as the frequency of the vibration generated in the first bridge in response to the movement of successive railway vehicles. f Specifically, the inventors identified the peak corresponding to the lowest frequency from the result of the FFT of u(t), excluding the side lobes caused by the influence of the window function used in the FFT, and determined the identified peak as the fundamental frequency. In the example of FIG. 13, the inventors determined 3.01 Hz as the fundamental frequency F f from the graph of FIG. 13.

[0110] Also, the inventors determined the period T of the vibration generated in the first bridge due to the passage of the railway train by obtaining the reciprocal of the determined fundamental frequency F f . The inventors performed a low-pass filter process on u(t) to attenuate the components of frequencies higher than the fundamental frequency by performing a moving average of u(t) with a period of T f . Let the u(t) subjected to the low-pass filter process be u f (t) = u lp (kΔT). Here, k is a variable indicating which observation it is in the case where the deflection amount is periodically observed at the observation point. That is, assuming that the data period (time resolution) of the observation of the deflection amount is ΔT, then t = kΔT. The details of the low-pass filter process will be described below. lp As shown in the following formula (43), from the period T and ΔT, the moving average interval k f adjusted to the time resolution of the data is obtained. mf

[0111]

Equation

[0112] Using k mf , u lp (t) is obtained by the following formula (44).

[0113] [Number]

[0114] The inventors used Equation (43) to obtain k from the period T f and ΔT, and then used the obtained k mf and u(t) to obtain u mf (t) using Equation (44). The above is the details of the low-pass filter processing. This low-pass filter processing may also be a process of applying a FIR filter that attenuates components above the fundamental frequency lp f. F And then, the inventors identified two consecutive data that sandwich a predetermined threshold C regarding the amount of deflection from u lp (t). Here, two consecutive data of u L (t) sandwiching C lp means that C L is included in the range sandwiched by the values of two continuously measured displacement data included in u lp (t), that is, the range from the smaller value to the larger value among these displacement data. This threshold C L is the value of the deflection generated in the bridge in response to the entry of a railway train onto the bridge. For example, it is the value of the deflection of the observation point of the bridge when the railway vehicle is arranged such that the wheels of one axle at the front of the railway vehicle are placed near the entry end. Also, this threshold C L may be other values as long as it can detect the entry of a railway train onto the bridge. For example, it may be the amount of deflection of the observation point of the bridge when a predetermined weight is applied near the entry end. Also, the threshold C L may be a value such as a predetermined ratio (e.g., 10%, 1%, etc.) of the maximum value of the amount of deflection of the observation point of the bridge when the railway train passes over the bridge. Also, the threshold C L may be set to the value of any data included in u L (t). lp (t).

[0115] In FIG. 14, ulp (t) and the threshold value C L are shown. The horizontal axis of the graph in FIG. 14 indicates time (t = kΔT), and the vertical axis indicates the amount of deflection. The solid line graph in FIG. 14 represents u lp (t), and the dotted line graph represents u(t). In the portion surrounded by the dotted circle in FIG. 14, u lp (k) and the threshold value C L intersect. Also, FIG. 15 shows an enlarged view of the intersection point of u lp (t) and C L (the portion of the left dotted circle in the graph of FIG. 14). The horizontal axis of the graph in FIG. 15 indicates time, and the vertical axis indicates the amount of deflection. Each black dot in FIG. 15 represents the discrete value data included in u lp (t). In the example of FIG. 15, it is shown that the data k - 1 and the data k included in u lp (t) sandwich the threshold value C L .

[0116] The inventors specified the later one among the two times corresponding to two consecutive data sandwiching the specified C L . In the example of FIG. 15, the time kΔT corresponding to the data k is specified. In the example of FIG. 14, the inventors also specified, as two consecutive data sandwiching C L , the two data in the portion of the right dotted circle in FIG. 14, and specified the later one among the two times corresponding to the specified two data.

[0117] Then, the inventors derive the earlier one among the specified times as the entry time t i of the railway train onto the bridge. Also, the inventors derive the later one among the specified times as the exit time t o of the railway train from the bridge. In the example of FIG. 14, the inventors derived the entry time t i = 7.2 [s] and the exit time t o = 12.795 [s]. And the inventors derived t s as t o - t i = 12.795 - 7.2 = 5.595 [seconds].[[]END]]

[0118] The inventors obtained F c = 3.01 [Hz] based on L(m) = 25 [m], and using Equation (41), they derived the average speed v of the railway train f as 25 [m] × 3.01 [Hz] = 75.25 [m / s]. Also, the inventors derived v a based on L B and L a and using Equation (34), they derived the period t a (m) for a single railway vehicle C to pass through the first bridge as (25 + 2.5 + 2.5 + 15 + 2.5 - 2.5) / 75.25 = 0.5980 [seconds]. Also, the inventors derived N, the number of railway vehicles comprising the railway train, as (5.595 - 0.5980) × 3.01 + 1 = 16.04097 using Equation (42) based on the derived F m and t c (m) and t f and t s and t c (m). This estimated value approximates 16, which is the number N of railway vehicles. Therefore, the inventors confirmed that they could accurately derive the number of railway vehicles included in the railway train using the conceived method.

[0119] In addition, the inventors conducted an experiment to derive the number of railway vehicles comprising the railway train using the conceived method when a similar railway train passed through a second bridge different from the first bridge. In the second bridge, resonance occurred between the vibration generated in the bridge by the passage of the railway train composed of consecutive railway vehicles as the railway train passed. The environmental information at this time was known and was as follows. L B = 25 [m], L x = 12.5 [m], L c each = 25 [m], a r each = 4, for m = 1 to N, L a (a w (m, 1)) = 2.5 [m], for m = 1 to N, L a (a w (m, 2)) = 2.5 [m], for m = 1 to N, L a (a w(m, 3)) = 15[m], for each m = 1 to N, L a (a w (m, 4)) = 2.5[m]. Also, regarding the observation information, it is not known except for N. That is, t i , t o , t s are assumed to be unknown in advance. The number of railway vehicles N configured in the railway vehicle is 16.

[0120] The inventors obtained time-series data of displacements at the observation points of the bridge by periodically measuring the displacements of the bridge at the observation points set on the second bridge at a predetermined period ΔT when the railway train passes through the second bridge. Let the time-series data of the displacements at the observation points on the second bridge obtained by the inventors be u(t). This u(t) is shown in FIG. 16. The horizontal axis of the graph in FIG. 16 is time, and the vertical axis is the deflection amount. In the graph of FIG. 16, compared with the graph of FIG. 12, the dynamic response generated in the bridge is shown. The inventors performed FFT on u(t). The result of the FFT on u(t) is shown in FIG. 17. The horizontal axis of the graph in FIG. 17 is frequency, and the vertical axis shows the intensity of the components corresponding to the frequencies. Note that the dynamic response is generated by resonance with the vibration generated in the second bridge due to the passage of the railway train. Therefore, the components of the dynamic response are components of frequencies approximately the same as the frequency of the vibration generated in the second bridge due to the passage of the railway train, and components of frequencies that are integer multiples of this frequency. Therefore, the inventors found that even when the influence of the dynamic response is included in u(t), the fundamental frequency of u(t) indicates the frequency of the vibration generated in the second bridge due to the passage of the railway train.

[0121] Therefore, the inventors derived the fundamental frequency F f of u(t) from the result of the FFT of u(t) as the frequency of the vibration generated in the second bridge in response to the movement of consecutive railway vehicles. f In the example of FIG. 17, the inventors obtained 2.8 Hz as the fundamental frequency F

[0122] Also, the inventors obtained the derived fundamental frequency F fBy obtaining the reciprocal, the period T of the vibration generated in the second bridge due to the passage of the railway train f was obtained. The inventors performed a moving average on u(t) to perform a low-pass filter process that attenuates components with frequencies equal to or higher than the fundamental frequency on u(t), and obtained u lp (t). Specifically, the inventors used Equation (43) to obtain k f from the period T mf and ΔT, and obtained u mf (t) from the obtained k lp and u(t) using Equation (44). Thereby, the influence of the dynamic response in u(t) is reduced. In FIG. 18, u lp (t) is superimposed on u(t) and shown. The horizontal axis of the graph in FIG. 18 is time, and the vertical axis is the amount of deflection. The solid line graph in FIG. 18 shows u lp (t), and the dotted line graph shows u(t). FIG. 18 shows a state in which the influence of the dynamic response is reduced.

[0123] Then, the inventors specified two sets of two consecutive data sandwiching a predetermined threshold value C lp relating to the amount of deflection from u L (t). For each of the two specified sets, the inventors specified the later of the two times corresponding to the two consecutive data sandwiching the specified C L . The inventors derived the earlier of the specified times as the entry time t i , and the later as the exit time t o . The inventors derived t i as 5.984 [seconds] and t o as 12.284 [seconds]. The inventors derived t s as t o -t i = 12.284 - 5.984 = 6.3 [seconds]. By using u lp (t) subjected to the low-pass filter process, the influence of the dynamic response is reduced, so that the entry time t i and the exit time t o can be derived with higher accuracy.

[0124] The inventors determined L cBased on the obtained \(F = 25[m]\) and \(f = 2.8[Hz]\), using Equation (41), the average speed \(v\) of the railway train was derived as \(25[m]\times2.8[Hz]=70[m / s]\). Also, the inventors derived \(L\) and \(L\), and based on the derived \(v\), using Equation (34), the period \(t\) during which a single railway vehicle \(C\) passes over the bridge was derived as \((25 + 2.5+2.5 + 15+2.5 - 2.5) / 70 = 0.954\) [seconds]. Further, the inventors derived \(F\), \(t\), and \(t\), and based on these, using Equation (42), the number \(N\) of railway vehicles forming the railway train was derived as \((6.3 - 0.954)\times2.8+1 = 15.9692\). This estimated value approximates 16, which is the number \(N\) of railway vehicles. Therefore, the inventors confirmed that they could accurately derive the number of railway vehicles included in the railway train using the conceived method. f Based on \(f = 2.8[Hz]\), using Equation (41), the average speed \(v\) of the railway train was derived as follows. a \(25[m]\times2.8[Hz]=70[m / s]\). Also, the inventors derived \(L\) and \(L\), and based on the derived \(v\), using Equation (34), the period \(t\) during which a single railway vehicle \(C\) passes over the bridge was derived as follows. B and \(L\) a and the derived \(v\) a Based on these, using Equation (34), the period \(t\) during which a single railway vehicle \(C\) passes over the bridge was derived as follows. m \((25 + 2.5+2.5 + 15+2.5 - 2.5) / 70 = 0.954\) [seconds]. Also, the inventors derived \(F\), \(t\), and \(t\), and based on these, using Equation (42), the number \(N\) of railway vehicles forming the railway train was derived as follows. c \((25 + 2.5+2.5 + 15+2.5 - 2.5) / 70 = 0.954\) [seconds]. Also, the inventors derived \(F\), \(t\), and \(t\), and based on these, using Equation (42), the number \(N\) of railway vehicles forming the railway train was derived as follows. f and \(t\) s and \(t\) c Based on these, using Equation (42), the number \(N\) of railway vehicles forming the railway train was derived as \((6.3 - 0.954)\times2.8+1 = 15.9692\). This estimated value approximates 16, which is the number \(N\) of railway vehicles. Therefore, the inventors confirmed that they could accurately derive the number of railway vehicles included in the railway train using the conceived method.

[0125] The derivation system 10 of the present embodiment derives the number of railway vehicles forming the railway train 6 based on the time-series data of the displacement at the observation point in the unit bridge girder of the bridge 5, based on the method conceived by the inventors.

[0126] Details of elements (1 - 4): Here, with reference to FIG. 19, the details of the measuring device 1, the sensor device 2, and the server device 3 of the derivation system 10 will be described. In the present embodiment, the derivation system 10 derives the observation information (the number \(N\) of railway vehicles forming the railway train 6, the time \(t\) when the railway train 6 enters the unit bridge girder, the time \(t\) when the railway train 6 exits the unit bridge girder, the period \(t\) during which the railway train 6 passes over the unit bridge girder) based on the data measured by the measuring device 1. i the time \(t\) when the railway train 6 exits the unit bridge girder o the period \(t\) during which the railway train 6 passes over the unit bridge girder s ) based on the data measured by the measuring device 1.

[0127] The measuring device 1 measures the deflection at the observation point via the sensor device 2. In this embodiment, the measuring device 1 is installed on the abutment 8b, but it may be installed at other positions. The measuring device 1 includes a control unit 100, a storage unit 110, and a communication unit 120. The control unit 100 includes a processor such as a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), etc. The control unit 100 realizes each function of the measuring device 1 by expanding various programs recorded in the ROM or the like into the RAM and executing them via the CPU. The storage unit 110 stores various programs, measured deflection data, etc. The communication unit 120 includes a circuit used for wired or wireless communication with an external device.

[0128] The sensor device 2 detects acceleration as a predetermined physical quantity at the observation point. The sensor device 2 includes a control unit 200, an acceleration sensor 210, a storage unit 220, and a communication unit 230. The control unit 200 includes a processor such as a CPU, a ROM, a RAM, etc. The control unit 200 realizes each function of the sensor device 2 by expanding various programs recorded in the ROM or the like into the RAM and executing them via the CPU.

[0129] The acceleration sensor 210 is an acceleration sensor such as a crystal acceleration sensor or a MEMS acceleration sensor that can detect accelerations generated in the three mutually perpendicular axial directions. In this embodiment, in order to detect the acceleration in the vertical direction more accurately, one axis of the acceleration sensor 210 is arranged parallel to the vertical direction. However, there may be a case where the installation location of the sensor device 2 in the superstructure 7 is inclined. Even when one of the three detection axes of the acceleration sensor 210 is not installed in alignment with the vertical direction, the measuring device 1 synthesizes the accelerations of the three axes to detect the acceleration in the vertical direction.

[0130] The control unit 200 of the sensor device 2 periodically detects the vertical acceleration at the observation point on the bridge 5 via the acceleration sensor 210, and transmits the detected acceleration data to the measurement device 1. The control unit 100 of the measurement device 1 measures the vertical deflection of the bridge 5 at the observation point at the acceleration detection time based on the acceleration data transmitted from the sensor device 2. In the present embodiment, the control unit 100 obtains the vertical deflection of the bridge 5 at the observation point by integrating the acceleration indicated by the data transmitted from the sensor device 2 twice with respect to time. Then, the control unit 100 transmits the measured deflection data to the server device 3. In the present embodiment, the sensor device 2 detects acceleration at a predetermined period ΔT. Therefore, the measurement device 1 measures the time-series data of the deflection at the ΔT period. That is, the measured time-series data is data of discrete values of variations measured at the ΔT period, and each discrete value is data associated with the measurement time.

[0131] The server device 3 derives the number of railway vehicles included in the railway train 6 based on the deflection of the observation point measured by the measurement device 1. The server device 3 is an example of a derivation device. The server device 3 includes a control unit 300, a storage unit 310, and a communication unit 320. The control unit 300 includes a processor such as a CPU, a ROM, a RAM, etc. The control unit 300 realizes the functions of the acquisition unit 301, the environment information acquisition unit 302, the fundamental frequency derivation unit 303, the passing period derivation unit 304, and the number derivation unit 305 by expanding various programs recorded in the ROM etc. into the RAM and executing them via the CPU. The storage unit 310 stores various programs, the detected deflection data, etc. The communication unit 320 includes a circuit used for wired or wireless communication with an external device.

[0132] The acquisition unit 301 is a function of acquiring the time-series data of the deflection generated at the observation point as a response to the movement of the railway train 6 over each of the bridges on the bridge 5. The control unit 300 acquires the time-series data u(t) of the deflection generated at the observation point from the measurement device 1 by the function of the acquisition unit 301.

[0133] The environmental information acquisition unit 302 is a function that acquires environmental information including information on the bridge length of a unit bridge girder, the vehicle length of a railway vehicle of the railway train 6, and the position of an axle which is the installation position of wheels on the railway vehicle. The control unit 300, by the function of the environmental information acquisition unit 302, obtains the bridge length L of the unit bridge girder B , the vehicle length L of each railway vehicle of the railway train 6 c , and information on the distance La indicating the position for each railway vehicle of the railway train 6 as environmental information. In the present embodiment, environmental information is stored in the storage unit 310 in advance, and the control unit 300 acquires the environmental information from the storage unit 310. However, the control unit 300 may acquire environmental information by using other methods such as receiving environmental information from an external device.

[0134] The fundamental frequency derivation unit 303 is a function that derives the fundamental frequency F of u(t), which indicates the frequency of vibration generated in the unit bridge girder in response to the passage of the railway train 6, based on the time-series data u(t). f The control unit 300 executes FFT on u(t) by the function of the fundamental frequency derivation unit 303. The control unit 300 detects a peak from the FFT result. The control unit 300 identifies the peak corresponding to the lowest frequency excluding the peaks of the side lobes generated by the influence of the window function used in the FFT among the detected peaks. The control unit 300 derives the frequency corresponding to the identified peak as the fundamental frequency F of u(t). f

[0135] The passage period derivation unit 304 is a function that derives the passage period t during which the railway train 6 passes over the unit bridge girder based on the time-series data u(t). s The control unit 300, by the function of the passage period derivation unit 304, derives the period Tf of the vibration generated in the unit bridge girder in response to the passage of the railway train 6 by deriving the reciprocal of the fundamental frequency F obtained by the function of the fundamental frequency derivation unit 303. The control unit 300 derives the section k using Equation (43) based on the derived Tf and ΔT which is a predetermined period. The control unit 300, for each value of u(t), for the derived section k f mf mfBy taking the moving average in, a low-pass filter is applied to u(t), and u lp (t) which is u(t) subjected to low-pass filtering is obtained. Specifically, the control unit 300 uses Equation (44) based on the derived section k mf to derive u lp (t).

[0136] Then, the control unit 300 identifies two consecutive data sandwiching a predetermined threshold C lp relating to the amount of deflection from u L (t). The control unit 300 identifies the later of the two times corresponding to the two consecutive data sandwiching the identified C L . Then, the control unit 300 derives the earlier of the identified times as the entry time t i of the railway train 6 onto the unit bridge girder. Also, the control unit 300 derives the later of the identified times as the exit time t o of the railway train 6 from the unit bridge girder.

[0137] Thus, in this embodiment, the control unit 300 derives the later of the two times corresponding to the two consecutive data sandwiching C lp included in u L (t) as the entry time t i and the exit time t o . However, the control unit 300 may derive other times as the entry time t i and the exit time t o . For example, the control unit 300 identifies two consecutive data sandwiching a predetermined threshold C lp relating to the amount of deflection from u L (t), and derives the time within the period after one of the times corresponding to the identified two data and before the other time as the entry time t i and the exit time t o . In the example of FIG. 15, the control unit 300 is after the time (k - 1)ΔT corresponding to the data k - 1 and before the time kΔT corresponding to the data k (for example, the time (k - 1)ΔT, u lp (t) and C LThe time corresponding to the intersection point (such as the entry time t i may be derived. Also, the control unit 300 may obtain a curve obtained by interpolating between each data included in u lp (t), and the time corresponding to the intersection point between the obtained curve and C L may be obtained as t i , t o .

[0138] Also, for two consecutive data sandwiching C lp included in u L , it is conceivable that one of them is equal to C L . For example, in the example of FIG. 15, it is conceivable that the value of data k is equal to C L . In that case, the control unit 300 may select any one of the two sets: the set of the data equal to C L and the previous data, and the set of the data equal to C L and the next data, as two consecutive data sandwiching C L . In the example of FIG. 15, when data k is equal to C L , the control unit 300 selects any one of the two sets: the set of data k-1 and data k, and the set of data k and data k+1, as two consecutive data sandwiching C L . The control unit 300 may derive the time within the period between the two times corresponding to the two data included in the selected set as t i or t o .

[0139] In this embodiment, the control unit 300 derives the time associated with any data included in u lp (t) as the entry time t i , the exit time t o . Thereby, the control unit 300 can easily obtain and utilize the data of u i corresponding to each measurement time at intervals of ΔT including the entry time t o by referring to u lp (t). On the other hand, the control unit 300 may use u lp (t). lpWhen there is no time associated with any of the data included in (t), the entry time t i , the exit time t o is derived as, t i , t o For each measurement time within the ΔT interval including, the u lp data of (t) is obtained by resampling etc. from the original u lp (t), increasing the processing effort.

[0140] The control unit 300 uses u lp (t) in which vibration components equal to or higher than the fundamental frequency are attenuated to derive the entry time and the exit time, thereby reducing the influence of vibration components equal to or higher than the fundamental frequency and enabling more accurate derivation of the entry time and the exit time. However, the control unit 300 may not derive u lp (t). In that case, the control unit 300 may use, for example, u lp (t) instead of u(t) to derive t i , t o . And the control unit 300 derives the passage period t s as t o - t i .

[0141] The number derivation unit 305 is a function of deriving the number of railway vehicles included in the railway train 6 based on the environmental information acquired by the function of the environmental information acquisition unit 302, the fundamental frequency F f derived by the function of the fundamental frequency derivation unit 303, and the passage period t s derived by the function of the passage period derivation unit 304. The control unit 300 uses the function of the number derivation unit 305 to use the vehicle length L c (m) of the railway vehicle of the railway train 6 indicated by the environmental information and the fundamental frequency F f to derive the average speed v a of the railway train using Equation (41). In this embodiment, since the railway train 6 is composed of similar railway vehicles, for each m = 1 to N, L c (m) is the same value. Further, the control unit 300 uses the derived v a and the L indicated by the environmental information B and L a and based on these, using Equation (34), the period t c (m) during which a single railway vehicle passes over the bridge is derived. Then, the control unit 300 uses the derived F f and t s and t c (m) and based on these, using Equation (42), the number N of railway vehicles forming the railway vehicle formation is derived.

[0142] As described above, with the configuration of the present embodiment, the derivation system 10 can derive the number of railway vehicles based on the time-series data of deflection at the observation point and the environmental information. Further, the derivation system 10 derives the fundamental frequency F f from the result of the FFT of u(t), and using Equation (41), based on the vehicle length L c (m), F f and, the average speed v a of the railway train is derived. Then, using the derived v a and L B and L a and based on these, using Equation (34), the period t c (m) during which a single railway vehicle passes over the bridge is derived. Then, using the derived F f and t s and t c (m) and based on these, using Equation (42), the number N of railway vehicles forming the railway vehicle formation is derived. In this way, the derivation system 10 can obtain the number of railway vehicles forming the railway train 6 with a smaller amount of calculation and a lower load compared to the case of obtaining the number by the inverse analysis method. In this way, the derivation system 10 can obtain the number of railway vehicles forming the railway train 6 with a lower load. Further, since the derivation system 10 can derive the number of railway vehicles with higher accuracy, it is possible to perform a more accurate diagnosis of the bridge using the derived number. For example, based on the number N derived by the processing of the present embodiment, using the deflection model, T std (t) shown in Equation (32) is derived. Since the number N is derived with higher accuracy, the deflection amount T std(t) can be derived with higher precision. Also, by using the amount of deflection T std (t) thus derived, it becomes possible to accurately calculate the impact coefficient of the impact on the bridge. By using such an impact coefficient, an accurate diagnosis of the bridge becomes possible. Therefore, in dynamic design including risk factors such as the resonance phenomenon of railway bridges, accurate measurement and derivation of the number of vehicles are effective.

[0143] (2) Derivation process: Using FIG. 20, the derivation process of the number of railway vehicles of the railway train 6 executed by the server device 3 will be described. The server device 3 starts the process of FIG. 20 in response to the displacement data at the observation point being transmitted from the measurement device 1, but may also start the process of FIG. 20 at an arbitrary timing such as a specified timing. In S100, the control unit 300 acquires the time-series data u(t) of the deflection occurring at the observation point from the measurement device 1 by the function of the acquisition unit 301. S100 is an example of an acquisition step.

[0144] In S105, the control unit 300 acquires, as environmental information, the bridge length L of the unit bridge girder B , the vehicle length L of each railway vehicle of the railway train 6 c , and information on the distance La indicating the position of each railway vehicle of the railway train 6 by the function of the environmental information acquisition unit 302. S105 is an example of an environmental information acquisition step. In S110, the control unit 300 executes FFT on u(t) acquired in S100 by the function of the fundamental frequency derivation unit 303. The control unit 300 detects peaks from the FFT results. The control unit 300 identifies the peak corresponding to the lowest frequency excluding the peaks of the side lobes generated by the influence of the window function used in the FFT among the detected peaks. The control unit 300 derives the frequency corresponding to the identified peak as the fundamental frequency F f of u(t). S110 is an example of a fundamental frequency derivation step.

[0145] In S115, the control unit 300, by the function of the passing period derivation unit 304, the fundamental frequency Ff By deriving the reciprocal, the period T f is derived. The control unit 300 uses the derived T f and the predetermined period ΔT to derive k using Equation (43). mf Then, the control unit 300 derives u using Equation (44) from the derived k mf and u(t). The control unit 300 determines the intersection of the derived u lp (t) with the predetermined threshold value C for the deflection amount, that is, the two points where u lp (t) = C L are identified, and the earlier of the times corresponding to the identified points is derived as the entry time t lp , and the later one is derived as the exit time t L . Then, the control unit 300 determines the passing period t i as t o -t s and derives it. S115 is an example of a passing period derivation step. o -t i and derives it. S115 is an example of a passing period derivation step.

[0146] In S120, the control unit 300 uses the function of the number derivation unit 305 to determine the vehicle length L c (m) of the railway vehicle of the railway train 6 indicated by the environmental information, the fundamental frequency F f , and uses Equation (41) to derive the average speed v a of the railway train. Further, the control unit 300 uses the derived v a , the L B indicated by the environmental information, and L a to derive the period t c (m) during which one railway vehicle passes over the bridge using Equation (34). Then, the control unit 300 uses the derived F f , t s , and t c (m) to derive the number N of railway vehicles configured in the railway vehicle using Equation (42). S120 is an example of a number derivation step. Also, the process of deriving t c (m) in S120 is an example of a moving object passing period derivation step.

[0147] (3) Other embodiments: The above embodiments are examples for implementing the present invention, and various other embodiments can also be adopted. The method of deriving the number of railway vehicles of a railway train from the displacement at the observation point as in the above embodiments can also be realized as an invention of a program or an invention of a method.

[0148] Furthermore, a configuration may be adopted in which the functions of the server device 3 are realized by a plurality of devices. Each function of the server device 3 may be distributed and implemented in a plurality of devices. Also, each function of the server device 3 may be implemented in other devices. For example, each function of the acquisition unit 301, the environment information acquisition unit 302, the fundamental frequency derivation unit 303, the passing period derivation unit 304, and the number derivation unit 305 may be implemented in the measurement device 1. The server device 3 may be configured to be distributed among a plurality of devices. Furthermore, the above embodiments are examples, and embodiments in which some configurations are omitted or other configurations are added may be adopted.

[0149] In the above embodiment, the derivation system 10 derives the number of railway vehicles included in the railway train 6 in which one or more railway vehicles as moving bodies are configured. However, the derivation system 10 may derive the number of moving bodies included in other configured moving bodies. The derivation system 10 may derive the number of moving bodies included in other configured moving bodies. For example, the derivation system 10 may derive the number of sleds included in a configured sled in which one or more sleds are connected.

[0150] Also, in the above embodiment, the derivation system 10 derives the number of moving bodies included in the configured moving body that moves on the bridge 5. However, the derivation system 10 may derive the number of moving bodies included in a configured moving body that moves on a structure different from a bridge such as a base that supports a railway track.

[0151] Also, in the above embodiment, the number of sensor devices 2 included in the derivation system 10 is assumed to be two, but it may be one, or three or more.

[0152] Also, in the above-described embodiment, the control unit 300 acquires, as the time-series data u(t), data of the displacement (deflection) measured from the acceleration detected via the acceleration sensor 210. However, the control unit 300 may acquire, as u(t), data of the displacement of the bridge derived from the physical quantity detected via sensors such as an impact sensor, a pressure sensor, a strain gauge, an image measurement device, a load cell, and a displacement meter. For example, the control unit 300 may detect the displacement of the observation point by periodically photographing a predetermined object arranged at the observation point of the bridge 5 via the image measurement device, and acquire the detected displacement data. Further, the control unit 300 may acquire, as u(t), data of a physical quantity different from the displacement of the bridge. For example, the control unit 300 may acquire, as u(t), the number of pixels indicating the displacement amount of a predetermined object arranged at the observation point of the bridge 5 in the image photographed via the image measurement device.

[0153] Also, in the above-described embodiment, the control unit 300 identifies, from the result of the FFT for the time-series data u(t) acquired by the function of the acquisition unit 301, the peak corresponding to the lowest frequency excluding the side lobes caused by the influence of the window function used in the FFT, and determines the identified peak as the fundamental frequency F f However, the control unit 300 may determine the fundamental frequency F f in consideration of the influence of the noise generated in the result of the FFT for u(t). For example, the control unit 300 may identify, from the result of the FFT for u(t), the peak equal to or higher than a predetermined threshold corresponding to the lowest frequency excluding the side lobes caused by the influence of the window function used in the FFT, and determine the identified peak as the fundamental frequency F f The time-series data may be data acquired at a data rate that is two times or more the frequency of the vibration assumed to be generated in the structure due to the movement of the moving object in formation.

[0154]

[0155] Furthermore, the present invention is also applicable as a program executed by a computer or as a method. Also, the above programs and methods may be realized as a single device or may be realized by using components provided in a plurality of devices, and include various aspects. Also, it can be appropriately changed, such as being partly software and partly hardware. Furthermore, the invention is also established as a recording medium for the program. Of course, the recording medium for the program may be a magnetic recording medium, a semiconductor memory, or any other recording medium developed in the future, and the same consideration can be applied.

Explanation of Signs

[0156] 1... Measuring device, 2... Sensor device, 3... Server device, 4... Communication network, 5... Bridge, 6... Railway train, 7... Superstructure, 7a... Bridge deck, 7b... Support, 7c... Rail, 7d... Sleeper, 7e... Ballast, F... Floor slab, G... Main girder, 8... Substructure, 8a... Pier, 8b... Abutment, 10... Derivation system, 100... Control unit, 110... Storage unit, 120... Communication unit, 200... Control unit, 210... Acceleration sensor, 220... Storage unit, 230... Communication unit, 300... Control unit, 301... Acquisition unit, 302... Environmental information acquisition unit, 303... Fundamental frequency derivation unit, 304... Passage period derivation unit, 305... Number derivation unit, 310... Storage unit, 320... Communication unit

Claims

1. An acquisition step of acquiring time-series data including a physical quantity generated at a predetermined observation point in the structure as a response to the movement of a structured moving body formed by one or more moving bodies; An environmental information acquisition step of acquiring information on the structure length which is the length of the structure, the moving body length which is the length of the moving body, and the installation position of the contact portion between the moving body and the structure as environmental information; A fundamental frequency derivation step of deriving the fundamental frequency of the time-series data based on the time-series data; A passing period derivation step of deriving the passing period during which the structured moving body passes through the structure based on the time-series data; A number derivation step of deriving the number of the moving bodies included in the structured moving body based on the environmental information, the fundamental frequency, and the passing period; comprising: the physical quantity is the displacement of the structure; further comprising a moving body passing period derivation step of deriving a moving body passing period which is the period during which the moving body passes through the structure; in the number derivation step, a value obtained by adding 1 to the product of the value obtained by subtracting the moving body passing period from the passing period and the fundamental frequency is derived as the number of the moving bodies included in the structured moving body; derivation method.

2. In the passing period derivation step, for each of the entry time and the exit time of the structured moving body with respect to the structure, a process of obtaining a time within a period after one of the two times corresponding to two consecutive data sandwiching a predetermined threshold value and before the other time, which is included in the time-series data subjected to low-pass filter processing for attenuating vibration components having a frequency equal to or higher than the fundamental frequency of the time-series data, is performed to derive the entry time and the exit time, and the period from the derived entry time to the exit time is derived as the passing period. The derivation method according to Claim 1.

3. The contact portion is a wheel installed on the axle of the moving body; In the moving body passing period derivation step, a value obtained by dividing the sum of the structure length and the distance between the foremost axle and the rearmost axle in the moving body by the product of the fundamental frequency and the moving body length is derived as the moving body passing period. The derivation method according to Claim 1.

4. In the basic frequency derivation step, the frequency corresponding to the peak with the lowest corresponding frequency among the peaks shown by the result of the Fourier transform on the time series data is derived as the basic frequency. The derivation method according to claim 1 or 2.

5. The model of the deflection of the structure is an equation based on the structure of the structure. The derivation method according to any one of claims 1 to 4.

6. The structure is in the form of a simple beam supported at both ends. The derivation method according to any one of claims 1 to 5.

7. The structure is a bridge. The derivation method according to any one of claims 1 to 6.

8. The structure is applicable to BWI M (Bridge Weigh in Motion). The derivation method according to any one of claims 1 to 7.

9. The moving body is a railway vehicle that moves on the structure via wheels. The derivation method according to any one of claims 1 to 8.

10. The time series data is data based on data detected via at least one of an acceleration sensor, a shock sensor, a pressure sensor, a strain gauge, an image measuring device, a load cell, and a displacement meter. The derivation method according to any one of claims 1 to 9.

11. An acquisition unit that acquires time series data including a physical quantity generated at a predetermined observation point in the structure as a response to the movement of a formation moving body formed by one or more moving bodies moving on the structure; An environmental information acquisition unit that acquires information on the structure length that is the length of the structure, the moving body length that is the length of the moving body, and the installation position of the contact portion between the moving body and the structure as environmental information; A basic frequency derivation unit that derives the basic frequency of the time series data based on the time series data; A passing period derivation unit that derives the passing period during which the formation moving body passes through the structure based on the time series data; A number derivation unit that derives the number of moving bodies included in the formation moving body based on the environmental information, the basic frequency, and the passing period; Comprising: The physical quantity is the displacement of the structure, Further comprising a moving body passing period derivation unit that derives the moving body passing period that is the period during which the moving body passes through the structure, The number derivation unit derives, as the number of moving bodies included in the formation moving body, a value obtained by adding 1 to the product of the value obtained by subtracting the moving body passing period from the passing period and the basic frequency. Derivation device.

12. A derivation system comprising a derivation device and a sensor, wherein: The derivation device: An acquisition unit that acquires time-series data including a physical quantity that occurs at a predetermined observation point in the structure as a response to the movement of a structured moving body formed by one or more moving bodies moving the structure, and the physical quantity measured via the sensor; An environmental information acquisition unit that acquires information on the structure length that is the length of the structure, the moving body length that is the length of the moving body, and the installation position of the contact portion between the moving body and the structure as environmental information; A fundamental frequency derivation unit that derives the fundamental frequency of the time-series data based on the time-series data; A passing period derivation unit that derives the passing period during which the structured moving body passes through the structure based on the time-series data; A number derivation unit that derives the number of moving bodies included in the structured moving body based on the environmental information, the fundamental frequency, and the passing period; is provided with: The physical quantity is the displacement of the structure; The derivation device further includes a moving body passing period derivation unit that derives the moving body passing period that is the period during which the moving body passes through the structure; The number derivation unit derives, as the number of moving bodies included in the structured moving body, a value obtained by adding 1 to the product of the value obtained by subtracting the moving body passing period from the passing period and the fundamental frequency; Derivation system.

13. A program for causing a computer to: An acquisition step of acquiring time-series data including a physical quantity that occurs at a predetermined observation point in the structure as a response to the movement of a structured moving body formed by one or more moving bodies moving the structure; An environmental information acquisition step of acquiring information on the structure length that is the length of the structure, the moving body length that is the length of the moving body, and the installation position of the contact portion between the moving body and the structure as environmental information; A fundamental frequency derivation step of deriving the fundamental frequency of the time-series data based on the time-series data; A passing period derivation step of deriving the passing period during which the structured moving body passes through the structure based on the time-series data; A number derivation step of deriving the number of moving bodies included in the structured moving body based on the environmental information, the fundamental frequency, and the passing period; A moving body passing period derivation step of deriving the moving body passing period that is the period during which the moving body passes through the structure; wherein: The physical quantity is the displacement of the structure; In the number derivation step, a value obtained by adding 1 to the product of a value obtained by subtracting the moving body passing period from the passing period and the fundamental frequency is derived as the number of moving bodies included in the organized moving body. Program.

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