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: Time sequence data which includes the physical quantity generated at an observation point in response to the travel of a formation movable body formed by one or more movable bodies in the structure is acquired; a temporary value which is a temporary value of the number of movable bodies that are organized into the formation movable body is acquired; the estimated amount of deflection of the structure generated at the observation point due to the passage of the formation movable body is derived on the basis of the temporary value, using a deflection model in the structure; and the number of movable bodies that are organized into the formation movable body is derived on the basis of comparison results of the time sequence data and the estimated amount.SELECTED DRAWING: Figure 33

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 with 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. In addition, 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 a 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 formed moving body composed of one or more moving bodies, such as a railway train, moves on a structure such as a bridge. In such cases, for the purpose of generating a motion model of the structure for diagnosis or the like, there is a desire to know how many moving bodies are composed in the formed moving body that moves on 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 composed in the moving body that moves on the structure. Thus, in Patent Documents 1 and 2, it was not possible to determine how many moving bodies are composed in the moving body that moves on the structure with a lower load.

Means for Solving the Problem

[0005] The derivation method for solving the above problems 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 formed moving body composed of one or more moving bodies moving on 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 time derivation step of deriving the entry time and the exit time of the formed moving body with respect to the structure based on the time-series data, a provisional value acquisition step of acquiring a provisional value which is a provisional value of the number of the moving bodies composed in the formed moving body, a deflection derivation step of deriving an estimated value of the deflection amount of the structure generated at the observation point due to the passage of the formed moving body by using a deflection amount model of the structure based on the environmental information, the entry time, the exit time, and the provisional value, and a number derivation step of deriving the number of the moving bodies composed in the formed moving body based on the comparison result between the time-series data and the estimated value of the deflection amount. 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, a structure length that is the length of the structure, a moving body length that is the length of the moving body, and information on the installation position of the contact portion between the moving body and the structure as environmental information, an environmental information acquisition unit, a time derivation unit that derives the entry time and the exit time of the structured moving body with respect to the structure based on the time-series data, a temporary value acquisition unit that acquires a temporary value that is a temporary value of the number of the moving bodies formed in the structured moving body, and a deflection derivation unit that derives an estimated value of the amount of deflection of the structure generated at the observation point due to the passage of the structured moving body using a model of the amount of deflection in the structure based on the environmental information, the entry time, the exit time, and the temporary value, and a number derivation unit that derives the number of the moving bodies formed in the structured moving body based on a comparison result between the time-series data and the estimated value of the amount of deflection. 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, a structure length that is the length of the structure, a moving body length that is the length of the moving body, and information on the installation position of the contact portion between the moving body and the structure as environmental information, an environmental information acquisition unit, a time derivation unit that derives the entry time and the exit time of the structured moving body with respect to the structure based on the time-series data, a temporary value acquisition unit that acquires a temporary value that is a temporary value of the number of the moving bodies formed in the structured moving body, and a deflection derivation unit that derives an estimated value of the amount of deflection of the structure generated at the observation point due to the passage of the structured moving body using a model of the amount of deflection in the structure based on the environmental information, the entry time, the exit time, and the temporary value, and a number derivation unit that derives the number of the moving bodies formed in the structured moving body based on a comparison result between the time-series data and the estimated value of the amount of deflection. A program for solving the above problems causes a computer to perform 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 time derivation step of deriving the entry time and the exit time of the organized moving body with respect to the structure based on the time-series data; a provisional value acquisition step of acquiring a provisional value that is a provisional value of the number of the moving bodies organized in the organized moving body; a deflection derivation step of deriving an estimated value of the amount of deflection of the structure generated at the observation point due to the passage of the organized moving body using a model of the amount of deflection in the structure based on the environment information, the entry time, the exit time, and the provisional value; and a number derivation step of deriving the number of the moving bodies organized in the organized moving body based on a comparison result between the time-series data and the estimated value of the amount of deflection.

Brief Description of Drawings

[0006]

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Figure 33

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) Deflection 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 in which one or more railway vehicles are connected in series is moving. The railway train 6 is an example of an articulated 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 a railway vehicle and a bridge. In the present embodiment, each of the railway vehicles configured 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] Based on the acceleration data output from each sensor device 2, the measurement device 1 calculates the displacement of the deflection of the superstructure 7 due to the running of the railway train 6. The measurement device 1 is installed, for example, on the bridge abutment 8b. The measurement device 1 and the server device 3 can communicate 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 composed in the railway train 6 based on the transmitted displacement data.

[0010] In this embodiment, the bridge 5 is a railway bridge, for example, a steel bridge, a truss bridge, an RC bridge, etc. RC is an abbreviation of Reinforced-Concrete. Also, 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 that can analyze the weight of a moving body passing through from the 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 on the bridge by a BWIM system that applies the physical process between the action and response on the bridge. The measurement of the weight of the moving body is performed by previously measuring the correlation coefficient between the displacement and the load, and deriving the load of the moving body passing through using the correlation coefficient from the measurement result of the displacement of the bridge when the moving body passes.

[0011] The bridge 5 includes a superstructure 7 which is the part where the moving body moves, and a substructure 8 which 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 deck F, main girders G, cross girders (not shown), etc., bearings 7b, rails 7c, sleepers 7d, and ballast 7e. Also, as shown in FIG. 1, the substructure 8 includes bridge piers 8a and abutments 8b. The superstructure 7 is a structure spanning 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 parts. In the present embodiment, a set of support parts and the part of the bridge girder of the superstructure 7 spanning between this set of support parts are collectively regarded as one bridge girder. That is, a simple beam-like structure supported at both ends by two support parts 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 used for deriving the displacement (deflection) at the observation point set on the superstructure 7. In the present embodiment, this predetermined physical quantity is acceleration. Also, in the present 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 the moving body at the observation point.

[0013] In this embodiment, the sensor device 2 is installed at the longitudinal center of the superstructure 7, specifically, at the longitudinal center 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 center of the superstructure 7. When 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 deflected vertically by the load of the railway train 6 running on the superstructure 7. Each sensor device 2 measures the acceleration of the deflection 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) Deflection model: Here, the model of the deflection of the bridge when a railway train moves on one bridge will be described. Here, the model is information such as an equation showing the correspondence between the given information and the estimation 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 when the railway train enters the bridge will be denoted as t i Here, the entry of the railway train onto the bridge means that the wheels of the first axle of the railway vehicle C1 (the first railway vehicle from the front of the railway train) have entered the bridge. Also, hereinafter, the exit time when the railway train exits the bridge will be denoted as t o Here, the exit of the railway train from the bridge means that the wheels of the last axle of the railway vehicle C N (the last 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 the entry time t i to the exit time t o ) will be denoted as t s Hereinafter, N, t i , t o , t s will be collectively referred to as the observation information.

[0017] Also, hereinafter, the bridge length, which is the length of the bridge, is denoted as L B The bridge length is an example of the structure length. Also, the distance from the end of the longitudinal direction of the bridge on the side where the railway train enters to the observation point is denoted as L x as shown in FIG. 3. L B and L x are shown. Hereinafter, the end of the longitudinal direction of the bridge on the side where the railway train enters is defined as the entry end. Also, hereinafter, the end of the longitudinal direction of the bridge on the side where the railway train exits is defined as the exit end. Also, the vehicle length of the m-th railway vehicle from the front of the railway train is denoted as L C (m). The vehicle length is an example of the moving body length. Hereinafter, L c (1) to L c (N) are collectively denoted as L c . Also, the m-th railway vehicle from the front of the railway train is denoted as C m . Also, the number of axles of the railway vehicle C m is denoted as a r (m). Hereinafter, a r (1) to a r (N) are collectively denoted as a r . Hereinafter, the a m (m) axles of the railway vehicle C r are numbered 1st axle, 2nd axle, 3rd axle, ···, a m (m)th axle in order from the front of the railway vehicle C r . Also, the distance from the front vehicle 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 railway train. Also, the distance between the (n - 1)th axle (n: an integer of 2 or more) and the nth axle of the railway vehicle C m is denoted as L a (a w (m, n)). That is, L a (a w (α, β)) is the railway train C αIndicates the distance between the β-axis and the (β - 1)-axis. Also, L a (a w (α, 1)) indicates the distance between the 1-axis in the railway train C α and the front end in the traveling direction of the railway train C α . The distance between the β-axis in the railway train C α and the front end in the traveling direction of the railway train C α is shown. Hereinafter, L a (a w (1, 1)) to L 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 1-axis exists at a distance of L a (a w (m, 1)) behind from the front end. Also, L a (a w (m, 2)) indicates that in the railway vehicle C m , the 2-axis exists at a distance of L a (a w (m, 2)) behind from the 1-axis. Here, the railway train is composed of railway vehicles with the same 4-axle configuration. That is, a r (m) (m = 1, 2, ···, N) is 4. Figure 4 shows L m in the railway vehicle C 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)). 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]

Number

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

[0021]

Number

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

[0023]

Number

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

[0025]

Number

[0026] Equation (5) below holds from Equations (3) and (4).

[0027]

Number

[0028] Next, the deflection that occurs in the bridge when a load is applied to the bridge will be described. Fig. 5 shows a schematic diagram of the bridge. Fig. 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 Equation (6).

[0029]

Number

[0030] Fig. 6 shows the bending moment at each position of the bridge due to the load P. As shown in Fig. 6, the bending moment generated in the bridge by the load P is 0 at the entrance end, and increases proportionally as it approaches the position where the load P is applied from the entrance 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 an arbitrary position X on the bridge is represented by the following Equation (7).

[0031]

Number

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

[0033]

Mathematics

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

[0035]

Mathematics

[0036] θ in formula (9) is the angle formed by the horizontal line and the deflected bridge at position X. The following formula (10) is established from formulas (7) and (9).

[0037]

Mathematics

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

[0039]

Mathematics

[0040] g1 and g2 in formula (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 formula (11), when x = 0 and x = L B both sides become 0. Therefore, g1 and g2 are as shown in the following formulas (12) and (13).

[0041]

Mathematics

[0042]

Mathematics

[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 in 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 in the longitudinal direction of the bridge. This maximum deflection is denoted as w 0.5l and an equation representing w 0.5l is obtained. When the load P is applied at the center in the longitudinal direction of the bridge, a = b = 0.5L B Also, since the position X for which the deflection is sought is at the center in the longitudinal direction of the bridge, x = 0.5L B Also, in this case, since x <= a, from equation (8), H a = 0. With x = 0.5L B , a = b = 0.5L B , H a = 0 are substituted into equation (14), and the following equation (15) representing the deflection w 0.5l is obtained.

[0046]

Number

[0047] Using w 0.5l , the deflection at an arbitrary position in the bridge represented by equation (14) is normalized. When the position of the load P exists on the entry end side relative to 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]

Number

[0049] Let a = L B Let r be such that r is a real number between 0 and 1. Let b = L B Since b = -a, then b = L B (1 - r). Substitute a = L B r and b = L B (1 - r) into Equation (16). Divide by w 0.5l to normalize. Then, for x > a, the normalized deflection w at position X is given by the following Equation (17). std is obtained.

[0050]

Equation

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

[0052]

Equation

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

[0054]

Equation

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

[0056]

Number

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

[0058]

Number

[0059] Here, using formula (20) and formula (21), 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) is obtained. 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 t xn is L x and v a and is obtained by the following formula (22).

[0060]

Number

[0061] Also, let t be the period it takes for one wheel of the railway train to cross the bridge, that is, the period it takes to reach the exit end from the entry end. ln t ln is L B and v a and is obtained by the following formula (23).

[0062]

Number

[0063] Also, the nth axle a of the mth railway vehicle of the railway train wThe time when the wheels at (m, n) reach the entry end is t o Let it be (m, n). t o (m, n) is related to t i and v a and D wa (a w (m, n)) and 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] The position of the axle a w (m, n) becomes the load position. Therefore, the position of the axle a w (m, n) is at a distance of a = L B r in the direction from the entry end to the exit end. Also, if the variable indicating time is set as t, the distance of a w (m, n) from the entry end at time t is equal to the distance that the railway vehicle has traveled from the exit time t o (m, n) to time t. Therefore, the following formula (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), x , L B , r, a function w of the following Equation (29) is obtained as a model showing the time change of the deflection generated at the observation point by the load applied to the bridge through the wheels of the axle a w (m, n). Equation (29) The function R(t) in is a function represented by the following Equation (30). 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, using these information, w std (a w (m, n), t) is obtained. For example, t i , t o Using Equation (1) from t s is obtained. t s , N, ar 、L a 、L c From, using equation (5), v a is obtained. v a and L B and L x and from, using equations (22) and (23), t xn 、t ln is obtained. L a 、L c 、ti from, using equations (3) and (24), t o (m, n) is obtained. And the obtained t xn 、t ln 、t o (m, n) is substituted into equations (29) and (30) to obtain the function w of t std (a w (m, n), t).

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

[0078]

Number

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

[0080] In addition, N railroad cars move on the bridge in response to the movement of the railroad train. Therefore, we use a function T std (t) is the C for each railcar std As a sum of (m, t), it is obtained as shown in the following equation (32).

[0081]

number

[0082] If N is 16, i.e., if a train has 16 railcars, then the function T std FIG. 9 shows the change in the amount of deflection at the observation point indicated by (t). The horizontal axis of the graph in FIG. 9 indicates time, and the vertical axis indicates the amount of deflection. The solid line in FIG. 9 indicates the time std (t), and each dotted line graph represents the C std As shown in the graph in Fig. 9, the waveform is the sum of the deflections of each passing train, and it can be seen that vibrations occur with a period when successive trains pass over the bridge. The above is an explanation of the model of the deflection in the bridge. As described above, the model of the deflection in this embodiment is an equation based on the structure of a simple beam-like bridge.

[0083] (1-3) Verification experiment: The inventors have determined that the deflection amount T std (t) was calculated. That is, N=4, t i =7.21[seconds], t o =8.777[seconds], ts = 1.567 [per second], L B = 25 [m], L x = 12.5 [m], L C Each = 25 [m], a r Each = 4, for m = 1 to N for each L a (a w (m, 1)) = 2.5 [m], for m = 1 to N for each L a (a w (m, 2)) = 2.5 [m], for m = 1 to N for each L a (a w (m, 3)) = 15 [m], for m = 1 to N for each L a (a w (m, 4)) = 2.5 [m].

[0084] The deflection amount T std (t) at this time is shown in Fig. 10. The horizontal axis of the graph in Fig. 10 represents time, and the vertical axis represents the deflection amount. Also, the inventors obtained T std (t) and performed fast Fourier transform (FFT) on it to obtain the intensity of each frequency component contained in T std (t). The result of the FFT for T std (t) is shown in Fig. 11. The horizontal axis of the graph in Fig. 11 represents frequency, and the vertical axis represents the intensity of the corresponding frequency component. And the inventors determined, as the frequency of the vibration generated in the bridge according to the movement of successive railway vehicles, the fundamental frequency F std of T std (t) from the result of the FFT of T f (t). Here, the fundamental frequency is the frequency of the lowest frequency component contained in the signal. Specifically, the inventors obtained T stdFrom the results of the FFT of (t), excluding the side lobes caused by the influence of the window function used in the FFT, the peak corresponding to the lowest frequency was identified, and the identified peak was used as the fundamental frequency. In the example of FIG. 11, as shown in the portion surrounded by the dashed-dotted line, two peaks of the side lobes caused by the influence of the window function used in the FFT are seen in the range of less than 2 Hz. The inventors identified the peak in the portion surrounded by the dotted line as the peak with the lowest frequency among the peaks excluding these peaks, and the frequency corresponding to the identified peak was designated as the fundamental frequency F f and obtained it. The inventors obtained the fundamental frequency of 3.1 Hz from the graph of FIG. 11.

[0085] The inventors obtained the wave number ν of the fundamental frequency F f included in the passing period ts using the following formula (33).

[0086]

Equation

[0087] In this case, ν = 1.567 × 3.1 = 4.8577. Here, the number N of railway vehicles of the moving railway train is 4. The inventors found that the wave number ν of the fundamental frequency F f included in the passing period ts is about 1 higher than N. Hereinafter, this feature is referred to as the first feature. Therefore, the inventors found that the number N of railway vehicles included in the railway train can be obtained as a value obtained by rounding to an integer the value obtained by subtracting 1 from the wave number ν of the fundamental frequency F f included in the passing period ts, and can be obtained using the following formula (34). The round function is a function that returns the rounded value of the argument. Also, the method of rounding to an integer is not limited to rounding, and other methods such as truncation and ceiling may be used according to the characteristics of the bridge to be observed.

[0088]

Equation

[0089] Also, the inventors used the following formula (35) to obtain the fundamental frequency F f to obtain the fundamental period T f .

[0090]

Equation

[0091] Then, the inventors performed a low-pass filter process to attenuate components with frequencies higher than the fundamental frequency by moving-averaging the deflection amount T f (t) over the fundamental period T std . The low-pass filter process may also be a process of applying another FIR filter that attenuates components with frequencies higher than the fundamental frequency. The T std (t) subjected to the low-pass filter process is set as T std (t)=T std_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 std_lp . As shown in the following formula (36), from the fundamental period T f and ΔT, the moving-average interval k mf adjusted to the time resolution of the data is obtained

[0092]

Equation

[0093] k mf is used, and T std_lp (t) is obtained by the following formula (37)

[0094]

Equation

[0095] The inventors obtained T std (t) from the deflection amount Tstd_lp By subtracting T(t), a high-pass filter process that attenuates components of frequencies below the fundamental frequency was performed on T(t). The high-pass filter process may be a process of applying another FIR filter that attenuates components of frequencies below the fundamental frequency. The T(t) subjected to the high-pass filter process was set as T(t). Specifically, as shown in the following equation (38), the inventors obtained T(t) by subtracting T(t) from T(t). std By subtracting T(t) from T(t), T(t) was obtained. The inventors found that the number of positive peaks of T(t) in the passing period t (the period from the entry time t to the exit time t) is 6. Here, a positive peak is a peak of T(t) that is convex upward with respect to the bridge. Also, the number of negative peaks of T(t) in the passing period t is 5. Here, a negative peak is a peak of T(t) that is convex downward with respect to the bridge. From this, the inventors found the characteristic that the number of positive peaks (6) of T(t) in the passing period t is 2 more than the number N (4) of railway vehicles included in the railway train, and the number of negative peaks (5) is 1 more than N (4). Hereinafter, this characteristic is referred to as the second characteristic. std The T(t) subjected to the high-pass filter process was set as T(t). std_hp Specifically, as shown in the following equation (38), the inventors obtained T(t) by subtracting T(t) from T(t). std By subtracting T(t) from T(t), T(t) was obtained. std_lp By subtracting T(t) from T(t), T(t) was obtained. std_hp The obtained T(t) was set as T(t).

[0096]

Equation

[0097] The obtained T(t) was set as T(t). std_hp The obtained T(t) was superimposed on T(t) and shown in FIG. 12. The graph in FIG. 12 shows the time (t = kΔT) on the horizontal axis and the deflection amount on the vertical axis. The solid line graph in FIG. 12 shows T(k), and the dotted line graph shows T(t). std The obtained T(t) was superimposed on T(t) and shown in FIG. 12. The graph in FIG. 12 shows the time (t = kΔT) on the horizontal axis and the deflection amount on the vertical axis. The solid line graph in FIG. 12 shows T(k), and the dotted line graph shows T(t). std_hp The solid line graph in FIG. 12 shows T(k), and the dotted line graph shows T(t). std The solid line graph in FIG. 12 shows T(k), and the dotted line graph shows T(t). From the graph in FIG. 12, the number of positive peaks of T(t) in the passing period t (the period from the entry time t to the exit time t) is 6. Here, a positive peak is a peak of T(t) that is convex upward with respect to the bridge. Also, the number of negative peaks of T(t) in the passing period t is 5. Here, a negative peak is a peak of T(t) that is convex downward with respect to the bridge. From this, the inventors found the characteristic that the number of positive peaks (6) of T(t) in the passing period t is 2 more than the number N (4) of railway vehicles included in the railway train, and the number of negative peaks (5) is 1 more than N (4). Hereinafter, this characteristic is referred to as the second characteristic. s (the period from the entry time t i to the exit time t o ), the number of positive peaks of T(t) is 6. Here, a positive peak is a peak of T(t) that is convex upward with respect to the bridge. Also, in the passing period t std_hp (the period from the entry time t to the exit time t), the number of negative peaks of T(t) is 5. Here, a negative peak is a peak of T(t) that is convex downward with respect to the bridge. From this, the inventors found the characteristic that the number of positive peaks (6) of T(t) in the passing period t is 2 more than the number N (4) of railway vehicles included in the railway train, and the number of negative peaks (5) is 1 more than N (4). Hereinafter, this characteristic is referred to as the second characteristic. std_hp (the period from the entry time t to the exit time t), the number of positive peaks of T(t) is 6. Here, a positive peak is a peak of T(t) that is convex upward with respect to the bridge. Also, in the passing period t s (the period from the entry time t to the exit time t), the number of negative peaks of T(t) is 5. Here, a negative peak is a peak of T(t) that is convex downward with respect to the bridge. From this, the inventors found the characteristic that the number of positive peaks (6) of T(t) in the passing period t is 2 more than the number N (4) of railway vehicles included in the railway train, and the number of negative peaks (5) is 1 more than N (4). Hereinafter, this characteristic is referred to as the second characteristic. std_hp (the period from the entry time t to the exit time t), the number of negative peaks of T(t) is 5. Here, a negative peak is a peak of T(t) that is convex downward with respect to the bridge. From this, the inventors found the characteristic that the number of positive peaks (6) of T(t) in the passing period t is 2 more than the number N (4) of railway vehicles included in the railway train, and the number of negative peaks (5) is 1 more than N (4). Hereinafter, this characteristic is referred to as the second characteristic. std_hp (the period from the entry time t to the exit time t), the number of negative peaks of T(t) is 5. Here, a negative peak is a peak of T(t) that is convex downward with respect to the bridge. From this, the inventors found the characteristic that the number of positive peaks (6) of T(t) in the passing period t is 2 more than the number N (4) of railway vehicles included in the railway train, and the number of negative peaks (5) is 1 more than N (4). Hereinafter, this characteristic is referred to as the second characteristic. s From this, the inventors found the characteristic that the number of positive peaks (6) of T(t) in the passing period t is 2 more than the number N (4) of railway vehicles included in the railway train, and the number of negative peaks (5) is 1 more than N (4). Hereinafter, this characteristic is referred to as the second characteristic. std_hp (the period from the entry time t to the exit time t), the number of positive peaks (6) of T(t) is 2 more than the number N (4) of railway vehicles included in the railway train, and the number of negative peaks (5) is 1 more than N (4). Hereinafter, this characteristic is referred to as the second characteristic.

[0098] The inventors verified whether the first feature and the second feature hold while changing the observation information and the environmental information to various values. As a result, the inventors found that when L c / 2 < L B < 3L c / 2 is satisfied, the first feature and the second feature hold. The inventors found that based on the first feature and the second feature, the number of railway vehicles formed into railway train 6 can be derived from the time-series data of the displacement (deflection) of the bridge at the observation point of the bridge. Hereinafter, the time-series data of the displacement at the observation point of the bridge is denoted as u(t).

[0099] The inventors considered the deflection amounts C std (1, t) to C std (N, t), T std (t) under the condition that the observation information and the environmental information take the values shown below. 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].

[0100] At this time, the deflection amounts C caused by each of the four railway vehicles included in the railway train std (1, t) to C std(4, t) is shown in FIG. 13. Let T be the period of the vibration generated in the bridge when railway vehicles continuously pass over the bridge. f The vibration generated in the bridge when railway vehicles continuously pass over the bridge is the vibration caused by the continuous passage of railway vehicles over the bridge. Therefore, the period T f is the time difference between the entry times of consecutive railway vehicles passing over the bridge. Since deflection occurs in the bridge from the moment a railway vehicle enters the bridge, the time difference between the start time of the deflection indicated by C std (m, t) and the start time of the deflection indicated by C std (m + 1, t) is the period T f . FIG. 13 shows the deflection generated in the bridge by the passage of each railway vehicle of a railway train when the railway train passes over the bridge. The horizontal axis of the graph in FIG. 13 represents time, and the vertical axis represents the amount of deflection. As shown in FIG. 13, the deflections caused by consecutive railway vehicles occur with a time difference of T f .

[0101] The period T f is the time difference between the entry times of consecutive railway vehicles passing over the bridge. Therefore, as shown in the following formula (39), the vehicle length L C (m) can be regarded as the period during which it passes at a speed v a .

[0102]

Equation

[0103] Let the period during which railway vehicle C m of a 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, railway vehicle C m , passes over the structure, the bridge. t c (m) is the period from the time when the first axis of railway vehicle C m reaches the entry end to the time when the a m (m) axis of railway vehicle C r reaches the exit end. That is, t c (m) is the period of railway vehicle Cm is the bridge length L B and the railway vehicle C m from the first axle, which is the front axle of the railway vehicle C, to the last axle, which is the a r (m) axle, and it is the period during which the total distance is traveled. Therefore, t c (m) is expressed by the following formula (40).

[0104]

Number

[0105] When a railway train passes over a bridge, among the railway vehicles that make up the railway train, the number of railway vehicles with subsequent railway vehicles is denoted as C Tn and is set. Among the railway vehicles that make up the railway train, except for 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 (41) holds.

[0106]

Number

[0107] In FIG. 14, C std (1, t) to C std (N, t), T std (t) are shown. The horizontal axis of the graph in FIG. 14 represents time, and the vertical axis represents the deflection amount. The solid line graph in FIG. 14 represents T std (t), and the dotted line graph represents C std (1, t) to C std (4, t) respectively. As shown in FIG. 14, the passing period t s is the sum of C Tn number 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 (42) holds.

[0108]

Number

[0109] From Formula (41) and Formula (42), the number N of railway vehicles formed into a railway train is expressed by the following Formula (43).

[0110]

Number

[0111] T f is also the period required for the railway train to move the vehicle length of 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 the speed v a in t c (m) during the period. Therefore, the following Formula (44) holds.

[0112]

Number

[0113] The following Formula (45) holds from Formula (44). It can be confirmed that Formula (43) also holds from Formula (45).

[0114]

Number

[0115] The deflection T std (t) generated in the bridge when the railway train passes through the bridge is considered to include the component of the vibration generated in the bridge in response to the movement of consecutive railway vehicles as a component of the fundamental frequency F f . Since F f is also the frequency of the vibration generated in the bridge in response to the movement of consecutive railway vehicles, it can be expressed as the reciprocal of T f as shown in the following Formula (46).

[0116]

Number

[0117] From equations (39) and (46), the speed v a is represented by the product of F f and L C (m).

[0118]

Number

[0119] Therefore, t c (m) represented by equation (40) is the total distance from the length L of the bridge B to the last axle a m (m) of the railway vehicle C, which is the foremost axle of the railway vehicle C, divided by the product of F r and L f and L C (m). From equations (43) and (46), the number N of railway vehicles formed in a railway train is the product of the value obtained by subtracting the passing period t s of the bridge by one railway vehicle C m from the passing period t c (m) of the bridge by the railway train, and the fundamental frequency Ff, plus 1, and is represented as follows by equation (48).

[0120]

Number

[0121] As shown in equation (47), 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 (40), the period t m during which one railway vehicle C c (m) passes through the bridge is the total distance from the length L of the bridge m to the last axle a B of the railway vehicle C m from the first axle to a r (m) axles, divided by the speed va It has been found that it is expressed as the period of movement in. Further, as shown in Equation (48), the inventors have found that the number N of railway vehicles formed in a railway train is t s from t c It has been found that it is expressed as a value obtained by adding 1 to the product of the value obtained by subtracting (m) from and the fundamental frequency Ff. Then, the inventors have conceived of the following method for deriving the number of railway vehicles formed in a railway train using the time series data of displacement at the observation point set on the bridge on which the railway train moves.

[0122] Obtain the time series data u(t) of displacement at the observation point set on the bridge on which the railway train moves. Also, L B and L C and L a and are obtained as environmental information. Then, based on the time series data u(t), the fundamental frequency F of u(t) f is obtained as the frequency of vibration generated in the bridge by the passage of consecutive railway vehicles formed in the railway train. Also, based on u(t), the period t during which the railway train passes over the bridge s is derived. Then, L B and L C and L a and F f and t s and based on, the method of deriving the number of railway vehicles included in the railway train using the relationships shown in Equation (40), Equation (47), and Equation (48).

[0123] As described above, the inventors have found that the number of railway vehicles formed in a railway train can be derived based on the time series data u(t). However, due to causes such as noise occurring in the measurement result of displacement at the observation point, there is a possibility that the number of railway vehicles formed in the railway train may be erroneously derived. Therefore, in this embodiment, the derivation system 10 uses the derivation result of the number of railway vehicles configured in a railway train as a provisional value, and based on the provisional value, uses a deflection model of a bridge to derive the amount of deflection at an observation point when a railway train configured with the number of railway vehicles of the provisional value passes through the bridge. Then, the derivation system 10 obtains the final estimated value of the number of railway vehicles configured in the railway train based on the comparison result between the derived amount of deflection and the time series data u(t) actually measured.

[0124] A method for deriving the amount of deflection at an observation point when a railway train configured with the number of railway vehicles of a provisional value passes through a bridge will be described using a deflection model of the bridge based on the provisional value. Here, the environmental information and the observation information are N = 16, t i = 7.155 [seconds], t o = 12.845 [seconds], t s = 5.69 [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]. Also, assume the provisional value = 16.

[0125] Entry time t i Exit time t o From, using equation (1), t s is derived. Assuming the provisional value is N, t s , N, a r , L a , L c From, using equation (5), v a is derived. v a and L Band L x From this, using Equation (22) and Equation (23), t xn , t ln is derived. L a , L c , t i From this, using Equation (3) and Equation (24), t o (m, n) is derived. The derived t xn , t ln , t o (m, n) is substituted into Equation (29) and Equation (30), and for each axle of each railway vehicle of the railway train 6, the function w std (a w (m, n), t) is derived. For N (provisional value) railway vehicles, using Equation (31), by adding up w std (a w (m, n), t) for each axle, C std (m, t) indicating the deflection of the unit bridge girder due to the passage of the railway vehicle is derived. By adding up C std (m, t) for N (provisional value) railway vehicles, T std (t) is derived as the deflection of the unit bridge girder due to the passage of the railway train. The method is as described above. Thus, the normalized deflection amount T std (t) at the observation point when a railway train composed of a provisional number of railway vehicles passes through the bridge is derived.

[0126] Also, based on the normalized deflection amount T std (t) at the observation point when a railway train composed of a provisional number of railway vehicles passes through the bridge, a method for deriving the original non-normalized deflection amount T Estd (t) will be explained. A low-pass filter that attenuates components above the fundamental frequency is applied to T std (t). Specifically, FFT is performed on T std (t), peaks are detected from the FFT results, and among the detected peaks, the peak corresponding to the minimum frequency excluding the peaks of the sidelobes caused by the influence of the window function used in the FFT is identified. The frequency corresponding to the identified peak is the fundamental frequency F std of T TIt is derived as follows.

[0127] Fundamental frequency F T Based on this, similar to Equation (35), by deriving the reciprocal of F T the period T T is derived. Based on the derived T T and the period ΔT of the measurement of the displacement (flexure) at the observation point, T T is used as T f and the interval k mf is derived using Equation (36). Based on the derived interval k mf using Equation (37), T std (t) which is the T std_lp after low-pass filter processing is derived. In FIG. 15, the T std_lp (t) derived here is superimposed and shown with T std (t). The horizontal axis of the graph in FIG. 15 is time and the vertical axis is the amount of flexure. The solid line graph in FIG. 15 shows T std_lp (t). The dotted line graph in FIG. 15 shows T std (t). As shown in FIG. 15, it can be seen that the vibration component of T std_lp (t) is removed compared to T std (t).

[0128] For the time series data u(t), low-pass filter processing is performed. Specifically, FFT is executed on u(t), peaks are detected from the FFT results, and among the detected peaks, the peak corresponding to the minimum frequency excluding the peaks of the side lobes generated by the influence of the window function used in the FFT is identified. The frequency corresponding to the identified peak is derived as the fundamental frequency F f of u(t).

[0129] Fundamental frequency F f Based on this, by deriving the reciprocal of F f the period T f is derived. Based on the derived T f and the period ΔT of the measurement of the displacement (flexure) at the observation point, the interval k mf is derived using the following Equation (49).

[0130] [Number]

[0131] Derived section k mf Based on this, using the following formula (50), u(t) that has been subjected to low-pass filter processing, which is u lp (t), is derived. The low-pass filter processing here may also be a process of applying another FIR filter that attenuates components with frequencies equal to or higher than the fundamental frequency.

[0132] [Number]

[0133] In FIG. 16, u lp (t) and T std_lp (t) are shown. The horizontal axis of the graph in FIG. 16 represents time, and the vertical axis represents the amount of deflection. Here, as in the following formula (51), assume that u lp (t) can be approximated as a linear function with time series data T std_lp (t) as a variable. Here, from the entry time t i to the exit time t o in the period, u lp (t) is approximated as a linear function with respect to T std_lp (t). C1 in formula (51) is the coefficient of the linear term, and c0 is the constant term. Formula (51) is a linear function with respect to the T std (t) value obtained by attenuating components with frequencies equal to or higher than the fundamental frequency F T , and is a linear function that approximates u std_lp (t) obtained by attenuating components with frequencies equal to or higher than the fundamental frequency F f . lp (t).

[0134] [Number]

[0135] c1 and c0 that minimize the error e(t) obtained by subtracting the right side from the left side of Equation (51) shown in the following Equation (52) are derived using the least squares method. Here, the derived c1 and c0 are as shown in the following Equations (53) and (54), respectively.

[0136]

Number

[0137]

Number

[0138]

Number

[0139] The restored value of u lp (t) is denoted as T Estd_lp (t). T Estd_lp (t) is expressed as shown in the following Equation (55) using c1 and c0. As shown in Equation (55), when t is before t i and after t o , assuming that the railway train is not on the bridge and there is no deflection, c0 is set to 0. Note that T std_lp (t) is 0 when t is less than t i and when t is greater than t o because there is no deflection. Therefore, for T Estd_lp (t) as well, it is 0 when t is less than t i and when t is greater than t o .

[0140]

Number

[0141] In FIG. 17, T Estd_lp (t) obtained by Equation (55) and u lp(t) is shown. The horizontal axis of the graph in Fig. 17 represents time, and the vertical axis represents the amount of deflection. As shown in Fig. 17, it has been confirmed that a value approximating u Estd_lp (t) has been obtained. lp (t) has been obtained. Here, it is considered that a relationship similar to Equation (51) holds between T std (t) and the time-series data u(t). That is, it is considered that the following Equation (56) holds.

[0142]

Equation

[0143] In this case, the original time-series data T std (t) restored from the amount of deflection T Estd (t) derived based on the trial value using the coefficients c1 and c0 is expressed as the following Equation (57) in the same manner as Equation (55).

[0144]

Equation

[0145] Based on T std (t), C1, and C0, using Equation (56), T Estd (t) is derived as an estimated value of the amount of deflection generated at the observation point due to the passage of the train 6 formed by the number of railway vehicles indicated by the trial value.

[0146] Fig. 18 shows T Estd (t) obtained by Equation (57) and u(t). The horizontal axis of the graph in Fig. 18 represents time, and the vertical axis represents the amount of deflection. As shown in Fig. 18, it has been confirmed that a value approximating u(t) has been obtained as T Estd (t). During the passage period t s (from the entry time t i (7.155 [seconds]) to the exit time t o (12.845 [seconds])), similar vibrations occur in T Estd (t) and u(t). Fig. 19 shows T EstdThe FFT results of (t) and u(t) are shown. The horizontal axis of the graph in Fig. 19 represents frequency, and the vertical axis represents the intensity of the component corresponding to the frequency. As shown in Fig. 19, T Estd The fundamental frequencies of (t) and u(t) were confirmed to show almost the same values. That is, when the provisional value and the actual N are equal, T Estd (t) and u(t) s show similar vibrations during the passing period t. Therefore, when the provisional value and the actual N are equal, T Estd (t) and u(t) s have almost equal vibration frequencies, the number of peaks of the generated waveforms, vibration periods, etc. during the passing period t.

[0147] Also, Fig. 20 shows T std (t) and u(t) obtained by Equation (32). The horizontal axis of the graph in Fig. 20 represents time, and the vertical axis represents the amount of deflection. As shown in Fig. 20, T s during the passing period t std (t) and u(t) have almost the same number of vibrations. Fig. 21 shows the FFT results of T std (t) and u(t). As shown in Fig. 21, the fundamental frequencies of T std (t) and u(t) were confirmed to show almost the same values. Therefore, when the provisional value and the actual N are equal, T std (t) and u(t) s have almost equal vibration frequencies, the number of peaks of the generated waveforms, vibration periods, etc. during the passing period t.

[0148] Also, Fig. 22 shows T Estd (t) with a high-pass filter process that attenuates components below the fundamental frequency and u Estd_hp (t) with a high-pass filter process that attenuates components below the fundamental frequency applied to u(t). Here, T hp (t) is the value obtained by subtracting T Estd_hp (t) from T Estd (t), which is the value obtained by applying a high-pass filter process to T Estd_lp (t). Also, u Estd (t) is the value obtained by subtracting u hp (t) from u(t), which is the value obtained by applying a high-pass filter process to u(t). lpBy subtracting (t), it is the value obtained by applying a high-pass filter process to u(t). As shown in FIG. 22, T Estd_hp (t) and u hp (t) and, during the passing period t s it was confirmed that approximately the same number of vibrations occurred. Therefore, when the provisional value and the actual N are equal, T Estd_hp (t) and u hp (t) and, during the passing period t s the frequency of vibration, the number of peaks of the generated waveform, the period of vibration, etc. become approximately equal.

[0149] Also, in FIG. 23, T std (t) to which a high-pass filter process for attenuating components below the fundamental frequency is applied, T std_hp (t), and u hp (t) are shown. Here, T std_hp (t) is obtained by subtracting T std (t) from T std_lp (t), and it is the value obtained by applying a high-pass filter process to T std (t). As shown in FIG. 23, T std_hp (t) and u hp (t) and, during the passing period t s it was confirmed that approximately the same number of vibrations occurred. Therefore, when the provisional value and the actual N are equal, T std_hp (t) and u hp (t) and, during the passing period t s the frequency of vibration, the number of peaks of the generated waveform, the period of vibration, etc. become approximately equal. In the example of FIG. 23, during the passing period t s the number of positive peaks of T std_hp (t) and u hp (t) are each 18.

[0150] Also, when the value of the provisional value is set to 15, which is smaller than the actual N, T Estd (t) derived in the same way is superimposed on u(t) and shown in FIG. 24. The horizontal axis of the graph in FIG. 24 represents time, and the vertical axis represents the amount of deflection. If the provisional value is smaller than the actual N, the number of railway vehicles passing through the bridge will be less than the actual number. Therefore, it is considered that the number of vibrations generated in the bridge due to the continuous passage of railway vehicles formed in the railway train through the bridge will be smaller than the actual vibrations. Referring to Fig. 24, T Estd The passing period t in (t) s It can be confirmed that the number of vibrations in is less than u(t). That is, T Estd The fundamental frequency of (t) is considered to be smaller than the fundamental frequency of u(t). In Fig. 25, T Estd The FFT results of (t) and u(t) are shown. The horizontal axis of the graph in Fig. 25 represents the frequency, and the vertical axis represents the intensity of the components of the corresponding frequencies. As shown in Fig. 25, T Estd The fundamental frequency of (t) was confirmed to be smaller than the fundamental frequency of u(t). Thus, when the provisional value is smaller than the actual N, T Estd (t) has a smaller vibration frequency, a smaller number of peaks in the generated waveform, and a larger vibration period compared to u(t) during the passing period t s .

[0151] Also, in Fig. 26, T Estd_hp (t) and u hp (t) are shown. As shown in Fig. 26, T Estd_hp (t) has been confirmed to have fewer vibrations during the passing period t s compared to u hp (t). Thus, when the provisional value is smaller than the actual N, T Estd_hp (t) has a smaller vibration frequency, a smaller number of peaks in the generated waveform, and a larger vibration period compared to u s (t) during the passing period t hp .

[0152] Also, T Estd (t) derived in the same way when the value of the provisional value is set to 17, which is larger than the actual N, is superimposed on u(t) and shown in Fig. 27. The horizontal axis of the graph in Fig. 27 represents time, and the vertical axis represents the deflection amount. If the provisional value is larger than the actual N, the number of railway vehicles passing through the bridge will be larger than the actual number. Therefore, it is considered that the number of vibrations generated in the bridge due to the continuous passage of railway vehicles organized in a railway train through the bridge will be larger than the actually generated vibrations. Referring to Fig. 27, T Estd The passing period t in (t) s The number of vibrations in can be confirmed to be more than u(t). That is, T Estd (t)'s fundamental frequency is considered to be a smaller value than that of u(t). In Fig. 28, T Estd (t) and the FFT results of u(t) are shown. The horizontal axis of the graph in Fig. 28 represents the frequency, and the vertical axis represents the intensity of the components of the corresponding frequency. As shown in Fig. 28, T Estd (t)'s fundamental frequency was confirmed to be larger than that of u(t). Thus, when the provisional value is larger than the actual N, T Estd (t) has, during the passing period t s a larger vibration frequency, a larger number of peaks in the generated waveform, and a smaller vibration period compared to u(t).

[0153] Also, in Fig. 29, T Estd_hp (t) and u hp (t) are shown. As shown in Fig. 29, T Estd_hp (t) has, during the passing period t s a larger number of vibrations compared to u hp (t). Thus, when the provisional value is larger than the actual N, T Estd_hp (t) has, during the passing period t s a larger vibration frequency, a larger number of peaks in the generated waveform, and a smaller vibration period compared to u hp (t).

[0154] Thus, when the provisional value is equal to the actual N, the deflection amount derived based on the provisional value and the time series data have almost the same vibration frequency, number of waveform peaks, and vibration period during the passing period t s . Also, when the provisional value is smaller than the actual N, T Estd_hp (t) has, during the passing period t sIn this case, compared with u hp (t), the frequency of vibration and the number of peaks of the generated waveform become smaller, and the period of vibration becomes larger. Also, when the provisional value is larger than the actual N, T Estd_hp (t) is the passing period t s In this case, compared with u hp (t), the frequency of vibration and the number of peaks of the generated waveform become larger, and the period of vibration becomes smaller.

[0155] Details of the (1-4) elements: Here, using FIG. 30, the details of each 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, based on the data measured by the measuring device 1, the observation information (the number N of railway vehicles configured in the railway train 6, the entry time t i when the railway train 6 enters the unit bridge girder, the exit time t o when the railway train 6 exits the unit bridge girder, and the passing period t s ) during which the railway train 6 passes through the unit bridge girder.

[0156] The measuring device 1 measures the deflection at the observation point via the sensor device 2. In the present embodiment, the measuring device 1 is installed on the bridge 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 to 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.

[0157] 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, etc. into the RAM and executing them via the CPU.

[0158] 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 respective axial directions of three axes orthogonal to each other. In the present embodiment, in order to detect the acceleration in the vertical direction more accurately, the acceleration sensor 210 is arranged such that one axis is parallel to the vertical direction. However, the installation location of the sensor device 2 in the superstructure 7 may be inclined. Even when one axis of the three detection axes of the acceleration sensor 210 is not installed in alignment with the vertical direction, the measurement device 1 synthesizes the accelerations of the three axes to detect the acceleration in the vertical direction.

[0159] The control unit 200 of the sensor device 2 periodically detects the acceleration in the vertical direction at the observation point on the bridge 5 via the acceleration sensor 210, and transmits the detected acceleration data to the measurement device 1. Based on the acceleration data transmitted from the sensor device 2, the control unit 100 of the measurement device 1 measures the deflection in the vertical direction of the bridge 5 at the observation point at the acceleration detection time. In the present embodiment, the control unit 100 obtains the deflection in the vertical direction 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.

[0160] The server device 3 derives the number of railway vehicles included in the railway train 6 based on the deflection of the observation points measured by the measuring device 1. The server device 3 is an example of a deriving 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 an acquisition unit 301, an environment information acquisition unit 302, a time derivation unit 303, a provisional value acquisition unit 304, a deflection derivation unit 305, and a quantity derivation unit 306 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, data of the detected deflection, etc. The communication unit 320 includes a circuit used for wired or wireless communication with an external device.

[0161] The acquisition unit 301 is a function of acquiring time-series data of the deflection that occurs at the observation point as a response to the movement of the railway train 6 over each of the bridge girders of the bridge 5. The control unit 300 acquires, from the measuring device 1, the time-series data u(t) of the deflection that occurs at the observation point by the function of the acquisition unit 301.

[0162] The environment information acquisition unit 302 is a function of acquiring environment information including the length of a unit bridge girder, the vehicle length which is the length of the railway vehicles formed in the railway train 6, and the positions of the axles where the wheels are installed on the railway vehicles. The control unit 300 acquires, as environment information, the information of the bridge girder length L of the unit bridge girder B , the vehicle length L of each railway vehicle of the railway train 6 c , and the distance L indicating the position for each railway vehicle of the railway train 6 a . In the present embodiment, the environment information is stored in the storage unit 310 in advance, and the control unit 300 acquires the environment information from the storage unit 310. However, the control unit 300 may acquire the environment information using other methods such as receiving the environment information from an external device.

[0163] The time derivation unit 303, based on the time-series data u(t), determines the entry time t i of the railway train 6 with respect to a unit bridge girder and the exit time t oIt is a function for deriving [the following]. The control unit 300 executes FFT on u(t) by the function of the time derivation unit 303. The control unit 300 detects peaks from the FFT results. The control unit 300 identifies the peak corresponding to the minimum frequency excluding the peaks of the sidelobes caused 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 Derive it as

[0164] The control unit 300 applies a low-pass filter that attenuates components of u(t) above the fundamental frequency F as follows. First, the control unit 300 derives the reciprocal of F based on the obtained fundamental frequency F to derive the period T in the same manner as in Equation (35). The control unit 300 derives the interval k using Equation (49) based on the derived T and the predetermined period ΔT. The control unit 300 applies a low-pass filter to u(t) by taking the moving average of u(t) at each value in the derived interval k. Let the u(t) subjected to the low-pass filter processing be u f (t) = u f (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. The control unit 300 derives u f (t) using Equation (50) based on the derived interval k. u f (t) becomes data of a plurality of discrete values, similar to u(t) which is data of a plurality of discrete values. f And the control unit 300 identifies two consecutive data that sandwich the predetermined threshold value C regarding the deflection amount from u mf (t). Here, two consecutive data of u mf (t) sandwiching the threshold value C means that u lp (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. The control unit 300 derives u mf (t) using Equation (50) based on the derived interval k. u lp (t) becomes data of a plurality of discrete values, similar to u(t) which is data of a plurality of discrete values. lp (t) is data of a plurality of discrete values, similar to u(t) which is data of a plurality of discrete values.

[0165] And the control unit 300 identifies two consecutive data that sandwich the predetermined threshold value C regarding the deflection amount from u lp (t). Here, two consecutive data of u L (t) sandwiching the threshold value C means that u lp (t) = u L (t) and u lpThe range sandwiched by the values of two continuously measured displacements included in (t), that is, the range that is equal to or greater than the smaller value and equal to or less than the larger value among the displacement data contains C L is shown. u lp Since the data of (t) may not include a value that matches the threshold value, in practice, the threshold value C L exceeds u lp The time of (t) is obtained. This threshold value C L is the value of the deflection generated in the bridge in response to the entry of a railway train into the bridge. For example, it is the value of the deflection of the observation point of the bridge when the railway vehicle is arranged so that the wheels of one axle at the front of the railway vehicle are placed near the entry end. Also, this threshold value C L may be other values as long as the entry of the railway train into the bridge can be detected. 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 value C L may be a value such as a predetermined ratio (for example, 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.

[0166] In FIG. 31, u lp (t) and the threshold value C L are shown. The horizontal axis of the graph in FIG. 31 indicates time (t = kΔT), and the vertical axis indicates the amount of deflection. The solid line graph in FIG. 31 shows u lp (t), and the dotted line graph shows u(t). In the portion surrounded by the dotted circle in FIG. 31, u lp (k) and the threshold value C L intersect. Also, in FIG. 32, an enlarged view of the intersection point of u lp (t) and C L (the left dotted circle portion in the graph of FIG. 31) is shown. The horizontal axis of the graph in FIG. 32 indicates time, and the vertical axis indicates the amount of deflection. Each of the black dots in FIG. 32 shows the discrete value data included in u lp (t). In the example of FIG. 32, it is shown that the data k - 1 and the data k included in u lp (t) sandwich the threshold value C L . The control unit 300 specifies the identified C LOf the two times corresponding to two consecutive data items sandwiching [a certain value], identify the later one. In the example of FIG. 32, the control unit 300 identifies the time kΔT corresponding to data k. In the example of FIG. 31, the control unit 300 identifies, as two consecutive data items sandwiching C L also the two data items in the portion of the right dotted circle in FIG. 31, and of the two times corresponding to the identified two data items, identifies the later one.

[0167] Then, the control unit 300 derives the earlier of the identified times as the entry time t i onto the unit bridge girder of the railway train 6. Also, the control unit 300 derives the later of the identified times as the exit time t o from the unit bridge girder of the railway train 6. In the example of FIG. 31, the control unit 300 derives the entry time t i = 7.2 [s] and the exit time t o = 12.795 [s]. Thus, in the present embodiment, the control unit 300 derives the time associated with any of the data included in u lp (t) as the entry time t i , the exit time t o .

[0168] Thus, in the present embodiment, the control unit 300 derives the later of the two times corresponding to two consecutive data items sandwiching C lp included in u L as the entry time t i , the entry time t o . However, the control unit 300 may derive other times as the entry time t i , the entry time t o . For example, the control unit 300 identifies two consecutive data items sandwiching a predetermined threshold value C lp relating to the deflection amount from u L (t), and derives, as the entry time t i and the entry time t o a time that is after one of the times corresponding to the identified two data items and within the period before the other time.It may also be derived. In the example of FIG. 32, 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 L and the time corresponding to the intersection point (such as) may be derived as the entry time t i . Further, the control unit 300 obtains a curve obtained by interpolating between each data included in u lp (t), and the time corresponding to the intersection point of the obtained curve and C L is obtained as t i , t o .

[0169] Also, for two consecutive data sandwiching C lp included in u L , it is conceivable that one of them becomes equal to C L . For example, in the example of FIG. 32, it is conceivable that the value of the data k becomes equal to C L . In that case, the control unit 300 sets, as two consecutive data sandwiching C L , the pair of the data equal to C L and the previous data, and the pair of the data equal to C L and the next data. In the example of FIG. 32, when the data k is equal to C L , the control unit 300 sets, as two consecutive data sandwiching C L , the pair of the data k - 1 and the data k, and the pair of the data k and the data k + 1. In such a case, the control unit 300 selects one of the identified pairs of data, and the time within the period between the two times corresponding to the two data included in the selected pair is set as t i or t o .

[0170] 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 determines the entry time t i , the exit time to u corresponding to each measurement time of the ΔT interval including lp the data of (t) can be easily obtained and utilized by referring to u lp (t). In contrast, when the control unit 300 derives the time not associated with any data included in u lp (t) as the entry time t i and the exit time t o , for each measurement time of the ΔT interval including t i and t o , the data of u lp (t) has to be obtained by resampling or the like from the original u lp (t), increasing the processing effort.

[0171] The control unit 300 reduces the influence of vibration components above the fundamental frequency and can derive the entry time and exit time with higher accuracy by deriving the entry time and exit time using u lp (t) in which vibration components above the fundamental frequency are attenuated. However, the control unit 300 may not derive u lp (t). In that case, the control unit 300 may derive, for example, the times when u(t) intersects with the threshold value C L as t i and t o .

[0172] The provisional value acquisition unit 304 is a function of acquiring a provisional value that is a provisional value of the number of railway vehicles configured in the railway train 6. The control unit 300 derives the number of railway vehicles included in the railway train 6 based on the first feature by the function of the provisional value acquisition unit 304. The control unit 300 derives the passing period t i and t o using Equation (1) based on t s during which the railway train 6 passes through the unit bridge girder. Then, the control unit 300 uses Equation (33) based on the derived t s and the fundamental frequency F f derived based on u(t) to obtain the fundamental frequency F s included in the passing period t fDerive the wave number ν. Based on the derived ν, the control unit 300 uses Equation (34) to derive the number N of railway vehicles included in the railway train 6, and acquires the derived N as a provisional value. The control unit 30 records the acquired N in the RAM.

[0173] However, the control unit 300 may acquire a provisional value by other methods. For example, the control unit 300 may do so as follows based on the second feature. That is, the control unit 300 performs a high-pass filter process on u(t) to attenuate the components of frequencies below the fundamental frequency by subtracting u lp (t) from u(t), and derives u hp (t), which is the u(t) subjected to the high-pass filter process. Then, the control unit 300 identifies the number of positive peaks from the data in the period from t hp to t i in u o (t). The control unit 300 may derive, as the value of N, the value obtained by subtracting 2 from the identified number of positive peaks, and acquire the derived value as a provisional value. Also, the control unit 300 identifies the number of negative peaks from the data in the period from t hp to t i in u o (t). The control unit 300 may derive, as the value of N, the value obtained by subtracting 1 from the identified number of negative peaks, and acquire the derived value as a provisional value.

[0174] Also, the control unit 300 may do so as follows using the method conceived by the inventors. That is, the control unit 300 derives the average speed v C of the railway train using Equation (47) based on the vehicle length L f (m) of the railway vehicle of the railway train 6 indicated by the environment information and the fundamental frequency F. The control unit 300 derives the period t a (m) during which one railway vehicle passes over the bridge using Equation (40) based on the derived v a , the L B indicated by the environment information, and L a . Then, the control unit 300 derives F c derived and t (m) f and t sand t c (m) and, based on this, the number N of railway vehicles configured in the railway train 6 may be derived using Expression (48), and the derived N may be obtained as a provisional value. In this way, by deriving the value of the provisional value, the control unit 300 can use, as the provisional value, a value closer to the final derivation result of the number N of railway vehicles configured in the railway train 6. As a result, the control unit 300 can reduce the processing involved in deriving the final derivation result. However, the control unit 300 does not necessarily have to derive a provisional value. For example, the control unit 300 may receive a specification of the provisional value based on an operation of the operation unit of the server device 3 by the user, and obtain the received value as the provisional value. Further, the control unit 300 may receive a specification of the provisional value from an external device and obtain the received value as the provisional value. Further, the control unit 300 may obtain a predetermined value as the provisional value.

[0175] The deflection derivation unit 305 is a function that derives an estimated value of the deflection amount of a unit bridge girder generated at the observation point due to the passage of the railway train 6, using a model of the deflection amount in the bridge, based on the environment information, the entry time t i and the exit time t o and the provisional value recorded in the RAM. The control unit 300 derives an estimated value of the deflection amount generated at the observation point due to the passage of the railway train 6 when the number of railway vehicles indicated by the provisional value is configured in the railway train 6, by the function of the deflection derivation unit 305. Specifically, the control unit 300 derives t i t o from t using Expression (1). The control unit 300 uses the provisional value recorded in the RAM as N, and derives v s from t s N, a r L a L B L c using Expression (5). That is, v a is the sum of the distance from the foremost axle (axle 1 of the foremost railway vehicle) to the rearmost axle (axle a a (N) of the rearmost railway vehicle)) in the railway train configured with the number of railway vehicles of the provisional value, the bridge length L r (N) axles)), and, the entry time t B and, and divides this sum by the time difference between the entry time ti Departure time t from o The passing period t, which is the period until s is derived as the value divided by. The control unit 300 calculates v a and L B and L x Using equations (22) and (23), t xn , t ln is derived. Also, the control unit 300 uses L a , L c , t i to derive t o (m, n) using equations (3) and (24). Then, the control unit 300 substitutes the derived t xn , t ln , t o (m, n) into equations (29) and (30) to derive the function w std (a w (m, n), t) for each axle of each railway vehicle of the railway train 6. The control unit 300 uses equation (31) to sum up w std (a w (m, n), t) for each axle for N (temporary value) railway vehicles of the railway train 6, thereby deriving C std (m, t), which represents the deflection of the unit bridge girder due to the passage of the railway vehicles. Then, the control unit 300 sums up C std (m, t) for N (temporary value) railway vehicles using equation (32), thereby deriving T std (t) as the deflection of the unit bridge girder due to the passage of the railway train.

[0176] The control unit 300 applies a low-pass filter to attenuate the components above the fundamental frequency in T std (t) as follows. First, the control unit 300 performs an FFT on T std (t). The control unit 300 detects peaks from the FFT result. The control unit 300 identifies the peak corresponding to the minimum frequency excluding the peaks of the sidelobes caused 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 std of T T (t). Based on the acquired fundamental frequency F T the control unit 300 derives the period T T by deriving the reciprocal of F T The control unit 300 derives the section k T based on the derived T T and the predetermined period ΔT, using Equation (36) with T f as T mf The control unit 300 derives T mf (t) that has been subjected to low-pass filter processing based on the derived section k std (t), which is T std_lp (t).

[0177] The control unit 300 derives c1 and c0 in the equation that approximates u lp (t) shown in Equation (50) as a linear function of T std_lp (t). Specifically, the control unit 300 derives c1 and c0 using Equations (51) and (53) based on T std_lp (t) and u lp (t). Then, the control unit 300 derives T std (t), which is the estimated value of the original deflection amount that has not been normalized, using Equation (57) based on T Estd (t) and the derived c1 and c0.

[0178] The number derivation unit 306 is a function that derives the number of railway vehicles configured in the railway train 6 based on the comparison result between the time-series data u(t) acquired by the function of the acquisition unit 301 and the estimated value T Estd (t) derived by the function of the deflection derivation unit 305. In the present embodiment, the number derivation unit 306 is a function that derives the number of railway vehicles configured in the railway train 6 based on the comparison result of the fundamental frequencies of u(t) and T Estd (t). The control unit 300, by the function of the number derivation unit 306, T EstdExcluding the side lobes caused by the influence of the window function used in the FFT from the result of the FFT for (t), identify the peak corresponding to the lowest frequency. Then, the control unit 300 sets the frequency corresponding to the identified peak as the fundamental frequency F of T Estd (t). TE is identified. F TE is an example of the second frequency. Also, the control unit 300 excludes the side lobes caused by the influence of the window function used in the FFT from the result of the FFT for u(t), identifies the peak corresponding to the lowest frequency, and sets the frequency corresponding to the identified peak as the fundamental frequency F of u(t). f However, the control unit 300 may use the fundamental frequency F of u(t) derived in other processes such as the process for the time derivation unit 303. F f is an example of the first frequency. f

[0179] The control unit 300 compares F TE with F f . The control unit 300 determines the provisional value recorded in the RAM as the final estimated result of the number N of railway vehicles formed in the railway train 6 when the absolute value of the difference between F TE and F f is less than or equal to a predetermined threshold value (for example, 0.5, 0.4, 0, etc.).

[0180] Also, when the absolute value of the difference between F TE and F f is greater than the predetermined threshold value and F TE is less than F f , the control unit 300 adjusts the value of the provisional value recorded in the RAM to increase it on the assumption that the provisional value recorded in the RAM is smaller than the actual N. In this embodiment, this predetermined value is 1, but it may be other values such as 2, 3, etc. Also, when the absolute value of the difference between F TE and F f is greater than the predetermined threshold value and F TE is greater than F f ​If it is larger than, assuming that the provisional value recorded in the RAM is larger than the actual N, the value of the provisional value recorded in the RAM is adjusted to decrease to a default value. In this embodiment, this default value is 1, but it may be other values such as 2 or 3.

[0181] When the control unit 300 adjusts the value of the provisional value, using the adjusted provisional value, the function of the deflection derivation unit 305 is used again to calculate T Estd (t) is derived, and the newly derived T Estd (t) of the fundamental frequency F TE is obtained, and again, F TE and F f are compared. The control unit 300 performs the above processing until it determines that F TE and F f are equal, and determines the provisional value recorded in the RAM as the final estimated result of N.

[0182] As described above, with the configuration of this embodiment, the derivation system 10 can derive the value of N based on the comparison result between the estimated value of deflection T Estd (t) derived based on the provisional value of the number N of railway vehicles formed in the railway train 6 and the time series data u(t). Further, the derivation system 10 repeats the derivation process of T Estd (t) based on the provisional value and the comparison process between T Estd (t) and u(t) to derive N. In this way, the derivation system 10 can obtain the number of railway vehicles formed in the railway train 6 with a smaller amount of calculation and a lower load compared to the case of obtaining it by the inverse analysis method. In this way, the derivation system 10 can obtain the number of railway vehicles formed in the railway train 6 with a lower load.

[0183] (2) Derivation process: Using FIG. 33, 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. 33 in response to the transmission of the displacement data at the observation point from the measurement device 1, but may start the process of FIG. 33 at an arbitrary timing such as a specified timing. In S100, the control unit 300 acquires, by the function of the acquisition unit 301, the time-series data u(t) of the deflection occurring at the observation point from the measuring device 1. S100 is an example of an acquisition step. In S105, the control unit 300 acquires, by the function of the environmental information acquisition unit 302, 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 the information of the distance La indicating the position for each railway vehicle of the railway train 6 as environmental information. S105 is an example of an environmental information acquisition step.

[0184] In S110, the control unit 300 executes FFT on u(t) by the function of the time derivation unit 303 and detects a peak from the FFT result. The control unit 300 specifies the peak corresponding to the minimum frequency excluding the peak of the sidelobe 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 specified peak as the fundamental frequency F f of u(t). The control unit 300 derives, based on the acquired fundamental frequency F f , the reciprocal of F f in the same manner as in Equation (35) to derive the period T f . The control unit 300 derives the interval k f using Equation (49) based on the derived T mf and the predetermined period ΔT. The control unit 300 derives u mf (t) using Equation (50) based on the derived interval k lp . The control unit 300 obtains the time when u lp (t) intersects with the predetermined threshold value C L regarding the deflection amount. The control unit 300 derives the earlier one of the obtained times as the entry time t i of the railway train 6 onto the unit bridge girder. Further, the control unit 300 derives the later one of the obtained times as the exit time t o of the railway train 6 from the unit bridge girder. S110 is an example of a time derivation step.

[0185] In S115, the control unit 300, by the function of the temporary value acquisition unit 304, based on t derived in S110 and t o , uses Equation (1) to derive the passing period t s during which the railway train 6 passes through the unit bridge girder. Then, the control unit 300, based on the derived t s and F f derived in S110, uses Equation (33) to derive the wave number ν of the fundamental frequency F f included in the passing period ts. The control unit 300 derives the number N of railway vehicles included in the railway train 6 using Equation (34) based on the derived ν, and acquires the derived N as a temporary value. The control unit 30 records the acquired N in the RAM. S115 is an example of a temporary value acquisition step. i and t o and, using Equation (1), derives the passing period t s during which the railway train 6 passes through the unit bridge girder. s And the control unit 300, based on the derived t s s and F f derived in S110 f and, using Equation (33), derives the wave number ν of the fundamental frequency F f included in the passing period ts. f The control unit 300 derives the number N of railway vehicles included in the railway train 6 using Equation (34) based on the derived ν, and acquires the derived N as a temporary value. The control unit 30 records the acquired N in the RAM. S115 is an example of a temporary value acquisition step.

[0186] In S120, the control unit 300, by the function of the deflection derivation unit 305, with the temporary value recorded in the RAM as N, from t s , N, a r , L a , L c , uses Equation (5) to derive v a . s N, a r L a L c and, using Equation (5), derives v a . a The control unit 300, from v a a and L B B and L x x uses Equations (22) and (23) to derive t xn xn t ln . Also, the control unit 300, from L a a L c c t i i uses Equations (3) and (24) to derive t o o (m, n). Then, the control unit 300 substitutes the derived t xn xn t ln ln t o o (m, n) into Equations (29) and (30) to derive the function w std std (a w w (m, n), t) for each axle of each railway vehicle of the railway train 6. The control unit 300, for N (temporary value) railway vehicles of the railway train 6, uses Equation (31) to calculate w std std (a w wBy adding (m, n), t), C indicating the deflection of the unit bridge girder due to the passage of the railway vehicle std (m, t) is derived. Then, the control unit 300 uses Equation (32) to calculate C for N (provisional value) railway vehicles std By adding (m, t), T is obtained as the deflection of the unit bridge girder due to the passage of the railway train std (t) is derived.

[0187] The control unit 300 performs FFT on T std (t) and detects peaks from the FFT results. The control unit 300 identifies the peak corresponding to the minimum frequency excluding the peaks of the side lobes caused by the influence of the window function used in the FFT among the detected peaks. The control unit 300 determines the frequency corresponding to the identified peak as the fundamental frequency F of T std (t) T and derives it. Based on the obtained fundamental frequency F, the control unit 300 derives the reciprocal of F in the same manner as Equation (35) to obtain the period T T T and derives it. The control unit 300 derives the interval k using Equation (36) with the derived T and the predetermined period ΔT as T T T T f and derives the interval k. Based on the derived interval k, the control unit 300 uses the following Equation (37) to derive T mf (t) which is the T subjected to low-pass filter processing mf std (t) std_lp and derives it.

[0188] The control unit 300 derives c1 and c0 in the equation approximating u lp (t) shown in Equation (50) as a linear function of T std_lp (t). Specifically, the control unit 300 derives c1 and c0 using Equations (51) and (53) based on T std_lp (t) and u lp (t). Then, the control unit 300 std ​​​​​(t), based on the derived c1 and c0, using Equation (57), derive T, which is the estimated value of the original unnormalized deflection amount. S120 is an example of a deflection derivation step. Estd (t).

[0189] In S125, the control unit 300, by the function of the number derivation unit 306, excluding the side lobes caused by the influence of the window function used in the FFT from the result of the FFT for T Estd (t), identifies the peak corresponding to the lowest frequency. Then, the control unit 300 designates the frequency corresponding to the identified peak as the fundamental frequency F Estd of T TE (t). Also, the control unit 300 excludes the side lobes caused by the influence of the window function used in the FFT from the result of the FFT for u(t), identifies the peak corresponding to the lowest frequency, and designates the frequency corresponding to the identified peak as the fundamental frequency F f of u(t). Then, the control unit 300 compares F TE with F f . If the difference between F TE and F f is equal to or less than a predetermined threshold value, the process proceeds to S130. If the difference between F TE and F f is greater than the predetermined threshold value and F TE is less than F f , the process proceeds to S135. If the difference between F TE and F f is greater than the predetermined threshold value and F TE is greater than F f , the process proceeds to S140.

[0190] In S130, the control unit 300, by the function of the number derivation unit 306, determines the value of the provisional value recorded in the RAM as the final estimated value of the number N of railway vehicles configured in the railway train 6. In S135, the control unit 300 adjusts by increasing the value of the temporary value recorded in the RAM by 1 through the function of the quantity derivation unit 306. Then, the control unit 300 proceeds to S120 again to derive the deflection amount based on the adjusted temporary value once more. In S140, the control unit 300 adjusts by decreasing the value of the temporary value recorded in the RAM by 1 through the function of the quantity derivation unit 306. Then, the control unit 300 proceeds to S120 again to derive the deflection amount based on the adjusted temporary value once more. S125 to S140 are an example of the quantity derivation steps.

[0191] (3) Other embodiments: The above embodiments are an example 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.

[0192] Furthermore, a configuration in which the functions of the server device 3 are realized by a plurality of devices may be adopted. 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 time derivation unit 303, the temporary value acquisition unit 304, the deflection derivation unit 305, and the quantity derivation unit 306 may be implemented in the measurement device 1. A configuration in which the server device 3 exists distributed among a plurality of devices or the like may also be possible. Furthermore, the above embodiments are examples, and embodiments in which some configurations are omitted or other configurations are added may be adopted.

[0193] In the above embodiments, the derivation system 10 derives the number of railway vehicles included in the railway train 6 formed by railway vehicles that are one or more moving bodies. However, the derivation system 10 may derive the number of moving bodies included in other formed moving bodies. The derivation system 10 may derive the number of moving bodies included in other formed moving bodies. For example, the derivation system 10 may derive the number of sleds included in a formed sled in which one or more sleds are connected.

[0194] Also, in the above-described embodiment, the number derivation unit 306 is a function of deriving the number of railway vehicles configured in the railway train 6 based on the comparison result of the fundamental frequencies of u(t) and T Estd (t). However, the number derivation unit 306 may be a function of deriving the number of railway vehicles configured in the railway train 6 based on the comparison result of the number of peaks in the passing period t Estd between u(t) and T s (t). In that case, the control unit 300 may be as follows, for example, in S125. That is, in S125, the control unit 300, by the function of the number derivation unit 306, determines the positive peak numbers of T i from the entry time t o derived by the function of the time derivation unit 303 to the exit time t Estd (t) and u(t) respectively in the passing period ts (the period from the entry time to the exit time). However, the control unit 300 may determine the number of negative peaks or the number of positive and negative peaks. The number of peaks of u(t) is an example of the first peak number. The number of peaks of T Estd (t) is an example of the second peak number.

[0195] Then, the control unit 300 compares the determined number of peaks of T Estd (t) with the number of peaks of u(t). When the determined number of peaks of T Estd (t) is equal to the number of peaks of u(t), the control unit 300 proceeds to S130. When the determined number of peaks of T Estd (t) is smaller than the number of peaks of u(t), assuming that the temporary value is smaller than the actual N, the control unit 300 proceeds to S135. When the determined number of peaks of T Estd (t) is larger than the number of peaks of u(t), assuming that the temporary value is larger than the actual N, the control unit 300 proceeds to S140.

[0196] However, the number derivation unit 306 is for the passing period t Estd between u(t) and T sBased on the comparison result of the vibration period in, it may be a function of deriving the number of railway vehicles configured in the railway train 6. In that case, the control unit 300 may, for example, in S125, be as follows. That is, in S125, the control unit 300, by the function of the number derivation unit 306, the passing period ts (the entry time t derived by the function of the time derivation unit 303 i to the exit time t o during the period) of T Estd (t), u(t) respectively identify the vibration period. For example, the control unit 300 obtains the fundamental frequencies of T Estd (t), u(t) respectively, and identifies the reciprocal of the obtained fundamental frequency as the vibration period. The period of the identified u(t) is an example of the first period. The period of the identified T Estd (t) is an example of the second period.

[0197] And the control unit 300 compares the period of T Estd (t) with the period of u(t). The control unit 300 proceeds to S130 if the absolute value of the difference between the period of the identified T Estd (t) and the period of u(t) is less than or equal to a predetermined threshold value. The control unit 300, if the absolute value of the difference between the period of T Estd (t) and the period of u(t) is greater than the predetermined threshold value, and the period of T Estd (t) is greater than the period of u(t), assuming that the temporary value is smaller than the actual N, proceeds to S135. The control unit 300, if the absolute value of the difference between the period of T Estd (t) and the period of u(t) is greater than the predetermined threshold value, and the period of T Estd (t) is smaller than the period of u(t), assuming that the temporary value is larger than the actual N, proceeds to S140.

[0198] Also, in the above-described embodiment, the control unit 300, by the function of the deflection derivation unit 305, derived T Estd (t) as an estimated value of the amount of deflection generated at the observation point by the passage of the railway train 6 configured with the number of railway vehicles indicated by the temporary value. However, T std (t), T Estd_hp(t) is the passing period t s The characteristics such as the fundamental frequency, period, number of peaks, etc. in are the same. Therefore, the control unit 300 uses T std (t), T Estd_hp (t), etc. of T Estd (t) may be derived as an estimated value of the amount of deflection generated at the observation point due to the passage of the train 6 in which the number of railway vehicles indicated by the provisional value is formed. In that case, the control unit 300 may regard the obtained estimated value as T Estd (t) and perform the processing for the number derivation unit 306.

[0199] Also, in the above-described embodiment, the derivation system 10 derives the number of moving bodies included in the formation moving body that moves the bridge 5. However, the derivation system 10 may derive the number of moving bodies included in the formation moving body that moves a structure different from the bridge such as a base that supports the track.

[0200] Also, in the above-described 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.

[0201] In the above-described embodiment, the control unit 300 acquires, as the time-series data u(t), the 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), the data of the displacement of the bridge derived from the physical quantities 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 data of the detected displacement. Further, the control unit 300 may acquire, as u(t), the data of a physical quantity different from the displacement of the bridge. For example, the control unit 300 may acquire, as u(t), the acceleration, velocity, stress, etc. at the observation point of the bridge 5. Further, the control unit 300 may acquire, as u(t), the number of pixels corresponding to 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. Further, the control unit 300 may acquire the data of a plurality of types of physical quantities (for example, displacement, stress, etc.) generated at the observation point as a response to the movement of the railway train 6 over the unit bridge girder.

[0202] In the above-described embodiment, from the result of the FFT for the time-series data u(t) acquired by the function of the acquisition unit 301, the control unit 300 excludes the side lobes generated due to the influence of the window function used in the FFT, and identifies the peak corresponding to the lowest frequency, 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 exclude the side lobes generated due to the influence of the window function used in the FFT from the result of the FFT for u(t), identify the peak equal to or higher than a predetermined threshold corresponding to the lowest frequency, and determine the identified peak as the fundamental frequency F f

[0203] ​The time-series data may be data acquired at a data rate that is two times or more the frequency of vibration that is assumed to occur in the structure due to the movement of the train formation.

[0204] Furthermore, the present invention is also applicable as a program executed by a computer or as a method. Also, a program or method as described above may be realized as a single device, or may be realized by using components provided in a plurality of devices, and includes various aspects. Also, it can be appropriately changed, such as part being software and part being 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 the like, and can be considered in exactly the same way for any recording medium developed in the future.

Description of Reference Numerals

[0205] 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... Environment information acquisition unit, 303... Time derivation unit, 304... Provisional value acquisition unit, 305... Deflection derivation unit, 306... Quantity derivation unit, 310... Storage unit, 320... Communication unit

Claims

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 a plurality of moving bodies moving the structure; An environmental information acquisition step of acquiring, as environmental information, 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; A time derivation step of deriving, based on the time-series data, the entry time and the exit time of the structured moving body with respect to the structure; A provisional value acquisition step of acquiring a provisional value that is a provisional value of the number of the moving bodies formed in the structured moving body; A deflection derivation step of deriving, based on the environmental information, the entry time, the exit time, and the provisional value, estimated time-series data that is time-series data of an estimated amount of deflection of the structure generated at the observation point due to the passage of the structured moving body, using a deflection model of the structure; A number derivation step of deriving the number of the moving bodies formed in the structured moving body based on a comparison result between the observed time-series data that is the time-series data acquired in the acquisition step and the estimated time-series data; comprising; the moving body is a railway vehicle or a trolley; the structured moving body is a railway train or a structured trolley formed by a plurality of the railway vehicles or the trolleys; the structure is a bridge; the contact portion is a wheel of the moving body; Derivation method.

2. The derivation method according to claim 1, wherein in the deflection derivation step, the estimated time-series data is derived based on the average speed of the structured moving body derived based on the entry time, the exit time, and the environmental information, the entry time, the exit time, the environmental information, and the provisional value.

3. In the bending derivation step, based on the average speed of the formation mobile body derived based on the entry time, the exit time, and the environmental information, the entry time, the exit time, the environmental information, and the provisional value, the estimated time series data of the normalized bending amount of the structure generated at the observation point due to the passage of the formation mobile body is derived, and a linear function using, as a variable, the estimated time series data obtained by attenuating components having frequencies equal to or higher than the fundamental frequency of the normalized estimated time series data, and the coefficient of the linear function approximating the observed time series data obtained by attenuating components having frequencies equal to or higher than the fundamental frequency of the observed time series data is derived, and based on the coefficient and the estimated time series data of the normalized bending amount, the estimated time series data of the non-normalized bending amount is derived. The derivation method according to claim 1.

4. The mobile body moves on the structure through a plurality of parts, The average speed is derived as a value obtained by dividing the sum of the distance from the foremost part to the rearmost part in the traveling direction in the formation mobile body formed by arranging the number of the mobile bodies corresponding to the provisional value in a vertical row and the structure length by the period from the entry time to the exit time. The derivation method according to claim 2 or 3.

5. The physical quantity is the displacement of the structure. The derivation method according to any one of claims 1 to 4.

6. In the time derivation step, among the two times corresponding to two consecutive data with the earlier time sandwiching a predetermined threshold value, which are included in the observed time series data subjected to low-pass filter processing for attenuating vibration components having frequencies equal to or higher than the fundamental frequency of the time series data, the time within the period after one of the two times and before the other time is acquired as the entry time, and among the two times corresponding to two consecutive data with the later time sandwiching the threshold value, the time within the period after one of the two times and before the other time is acquired as the exit time. The derivation method according to any one of claims 1 to 5.

7. In the provisional value acquisition step, based on the entry time, the exit time, and the fundamental frequency, a value obtained by rounding down to an integer the result of subtracting 1 from the product of the period from the entry time to the exit time and the fundamental frequency is acquired as the provisional value. The derivation method according to claim 6.

8. In the number derivation step, when the absolute value of the difference between the first frequency, which is the fundamental frequency of the observed time-series data, and the second frequency, which is the fundamental frequency of the estimated time-series data, is less than or equal to a predetermined threshold value, the provisional value is derived as the number of the moving bodies organized in the organized moving body. When the absolute value of the difference between the first frequency and the second frequency is greater than the threshold value and the first frequency is greater than the second frequency, the provisional value is adjusted to be increased. When the absolute value of the difference between the first frequency and the second frequency is greater than the threshold value and the first frequency is less than the second frequency, the provisional value is adjusted to be decreased. When the provisional value is adjusted, a comparison between the second frequency obtained from the adjusted provisional value and the first frequency is performed. The adjustment of the provisional value and the comparison between the first frequency and the second frequency are repeated until the absolute value becomes less than or equal to the threshold value. The provisional value when the absolute value becomes less than or equal to the threshold value is derived as the number of the moving bodies organized in the organized moving body. The derivation method according to any one of claims 1 to 7.

9. In the number derivation step, when the first peak number, which is the number of peaks of the observed time-series data in the period from the entry time to the exit time, is equal to the second peak number, which is the number of peaks of the estimated time-series data in the period, the provisional value is derived as the number of the moving bodies organized in the organized moving body. When the first peak number is less than the second peak number, the provisional value is adjusted to be decreased. When the first peak number is greater than the second peak number, the provisional value is adjusted to be increased. When the provisional value is adjusted, a comparison between the second peak number obtained from the adjusted provisional value and the first peak number is performed. The adjustment of the provisional value and the comparison between the first peak number and the second peak number are repeated until the first peak number and the second peak number become equal. The provisional value when the first peak number and the second peak number become equal is derived as the number of the moving bodies organized in the organized moving body. The derivation method according to any one of claims 1 to 7.

10. In the number derivation step, when the absolute value of the difference between a first period, which is the period of vibration during the period from the entry time to the exit time of the observed time series data, and a second period, which is the period of vibration during the period of the estimated time series data, is equal to or less than a predetermined threshold value, the provisional value is derived as the number of the moving bodies organized in the organized moving body; when the absolute value of the difference between the first period and the second period is greater than the threshold value and the second period is greater than the first period, the provisional value is adjusted to be increased; when the absolute value of the difference between the first period and the second period is greater than the threshold value and the second period is less than the first period, the provisional value is adjusted to be decreased; when the provisional value is adjusted, a comparison is made between the second period obtained from the adjusted provisional value and the first period, and the adjustment of the provisional value and the comparison between the first period and the second period are repeated until the absolute value becomes equal to or less than the threshold value, and the provisional value when the absolute value becomes equal to or less than the threshold value is derived as the number of the moving bodies organized in the organized moving body. The derivation method according to any one of claims 1 to 7.

11. The model is an expression based on the structure of the structure. The derivation method according to any one of claims 1 to 10.

12. 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 11.

13. 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 12.

14. 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 the structure by an organized moving body formed by organizing a plurality of moving bodies; An environmental information acquisition unit that acquires information on a structure length that is the length of the structure, a moving body length that is the length of the moving body, and an installation position of a contact portion between the moving body and the structure as environmental information; A time derivation unit that derives an entry time and an exit time of the organized moving body with respect to the structure based on the time series data; A provisional value acquisition unit that acquires a provisional value that is a provisional value of the number of the moving bodies organized in the organized moving body; Based on the environmental information, the entry time, the exit time, and the provisional value, a deflection derivation unit that derives estimated time-series data, which is time-series data of an estimated amount of deflection of the structure that occurs at the observation point due to the passage of the formation moving body, using a deflection model of the structure in the structure A number derivation unit that derives the number of the moving bodies formed in the formation moving body based on a comparison result between the observed time-series data, which is the time-series data acquired by the acquisition unit, and the estimated time-series data Comprising The moving body is a railway vehicle or a trolley The formation moving body is a railway train or a formation trolley formed by arranging a plurality of the railway vehicles or the trolleys The structure is a bridge The contact part is the wheel of the moving body Derivation device

15. A derivation system comprising a derivation device and a sensor, wherein The derivation device An acquisition unit that acquires time-series data, which is a physical quantity that occurs at a predetermined observation point in the structure as a response to the movement of a formation moving body formed by a plurality of moving bodies moving the structure, and includes the physical quantity measured via the sensor An environmental information acquisition unit that acquires 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 part between the moving body and the structure, as environmental information A time derivation unit that derives the entry time and the exit time of the formation moving body with respect to the structure based on the time-series data A provisional value acquisition unit that acquires a provisional value, which is a provisional value of the number of the moving bodies formed in the formation moving body Based on the environmental information, the entry time, the exit time, and the provisional value, a deflection derivation unit that derives estimated time-series data, which is time-series data of an estimated amount of deflection of the structure that occurs at the observation point due to the passage of the formation moving body, using a deflection model of the structure in the structure A number derivation unit that derives the number of the moving bodies formed in the formation moving body based on a comparison result between the observed time-series data, which is the time-series data acquired by the acquisition unit, and the estimated time-series data Comprising The moving body is a railway vehicle or a trolley The formation moving body is a railway train or a formation trolley formed by arranging a plurality of the railway vehicles or the trolleys The structure is a bridge The contact part is the wheel of the moving body Derivation system

16. 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 a plurality of moving bodies are organized by a computer; An environmental information acquisition step of acquiring, as environmental information, 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; A time derivation step of deriving, based on the time-series data, the entry time and the exit time of the organized moving body with respect to the structure; A provisional value acquisition step of acquiring a provisional value that is a provisional value of the number of the moving bodies organized in the organized moving body; A deflection derivation step of deriving, based on the environmental information, the entry time, the exit time, and the provisional value, estimated time-series data that is time-series data of an estimated value of the amount of deflection of the structure generated at the observation point due to the passage of the organized moving body, using a deflection model of the structure; A number derivation step of deriving the number of the moving bodies organized in the organized moving body based on a comparison result between the observed time-series data that is the time-series data acquired in the acquisition step and the estimated time-series data; A program for causing the execution; The moving body is a railway vehicle or a trolley; The organized moving body is a railway train or an organized trolley in which a plurality of the railway vehicles or the trolleys are organized; The structure is a bridge; The contact portion is a wheel of the moving body; Program.

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