DERIVATION METHOD, DERIVATION DEVICE, DERIVATION SYSTEM, AND PROGRAM

Abstract

To make it possible to acquire the amount of deflection at a position other than an observation point.SOLUTION: On the basis of the number of movable bodies organized into a formation movable body, the entry time, the exit time and environment information, a first index value which is the index value of the amount of deflection of a structure generated at an observation point and a second index value which is the index value of the amount of deflection at a specified position in the structure are acquired; and the estimated amount of deflection of the structure at the specified position is derived on the basis of time sequence data measured at the observation point, the first index value and the second index value.SELECTED DRAWING: Figure 19

Description

[Technical field]

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

[0002] In recent years, many social infrastructures have deteriorated with age, and there is a demand for methods to diagnose the condition of structures that make up social infrastructure, such as railway bridges. Patent Document 1 discloses a method for investigating the structural performance of railway bridges that makes it possible to appropriately investigate and evaluate the structural performance of bridges by using observed data on the acceleration response of the bridge when a train is running. The method for investigating the structural performance of railway bridges in Patent Document 1 is characterized in that it formulates a theoretical analysis model of the dynamic response of a railway bridge when a train is running, with the train as a moving load train and the bridge as a simple beam, measures the acceleration of the bridge when a train is running, and estimates unknown parameters of the theoretical analysis model from the acceleration data by inverse analysis. Furthermore, Patent Document 2 discloses a method for determining the impact coefficient (dynamic response component) of a bridge by using the vehicle vertical acceleration response of a running train when passing over the bridge. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Patent No. 6543863 [Patent Document 2] Patent No. 6467304 Summary of the Invention [Problem to be solved by the invention]

[0004] There are cases where a train or other such configured mobile body, which is made up of one or more mobile bodies, travels across a structure such as a bridge. In such cases, there is a demand for determining the amount of deflection at a specified position on the structure for the purpose of diagnosing the structure or the like. When measuring the amount of deflection using a sensor or the like at an observation point on the structure, it is not possible to determine the amount of deflection at positions other than the observation point. Furthermore, Patent Documents 1 and 2 also fail to determine the amount of deflection at positions other than the observation position. [Means for solving the problem]

[0005] The derivation method for solving the above problem includes an acquisition step of acquiring time series data including a physical quantity occurring at a predetermined observation point on a structure as a response to a movement of a composed mobile body, which is a composition of one or more mobile bodies, through the structure; an environmental information acquisition step of acquiring information on a structure length, which is the length of the structure, a mobile body length, which is the length of the mobile body, and an installation position of a contact portion of the mobile body with the structure, as environmental information; and a time information acquisition step of deriving an entry time and an exit time of the composed mobile body with respect to the structure based on the time series data. The method includes a derivation step, a number acquisition step of acquiring the number of the moving bodies organized into the organized moving body, an index value acquisition step of acquiring a first index value which is an index value of the amount of deflection of the structure occurring at the observation point and a second index value which is an index value of the amount of deflection at a specified position of the structure based on the number, the entry time, the exit time, and the environmental information, and a deflection derivation step of deriving an estimated value of the amount of deflection of the structure at the position based on the time series data, the first index value, and the second index value. The derivation device for solving the above problem includes an acquisition unit that acquires time series data including physical quantities occurring at a predetermined observation point on a structure as a response to a structure movement of a train of one or more moving bodies, an environmental information acquisition unit that acquires information on a structure length, which is the length of the structure, a moving body length, which is the length of the moving body, and an installation position of a contact portion of the moving body with the structure as environmental information, and derives an entry time and an exit time of the train of moving bodies with respect to the structure based on the time series data. The system comprises a time derivation unit, a number acquisition unit that acquires the number of the moving bodies organized into the organized moving body, an index value acquisition unit that acquires a first index value that is an index value of the amount of deflection of the structure occurring at the observation point and a second index value that is an index value of the amount of deflection at a specified position of the structure based on the number, the entry time, the exit time, and the environmental information, and a deflection derivation unit that derives an estimated value of the amount of deflection of the structure at the position based on the time series data, the first index value, and the second index value. A derivation system for solving the above problem is a derivation system including a derivation device and a sensor, the derivation device including an acquisition unit that acquires time series data including a physical quantity generated at a predetermined observation point in a structure as a response to a structure movement of a structure formed by an organized moving body of one or more moving bodies, the physical quantity being measured via the sensor, an environmental information acquisition unit that acquires information on a structure length, which is the length of the structure, a moving body length, which is the length of the moving body, and an installation position of a contact portion of the moving body with the structure, as environmental information, and a derivation device that performs a pre-determining process based on the time series data. The system comprises a time derivation unit that derives the entry time and exit time of the organized moving body with respect to the structure; a number acquisition unit that acquires the number of the moving bodies organized in the organized moving body; an index value acquisition unit that acquires a first index value that is an index value of the amount of deflection of the structure occurring at the observation point and a second index value that is an index value of the amount of deflection at a specified position of the structure based on the number, the entry time, the exit time, and the environmental information; and a deflection derivation unit that derives an estimated value of the amount of deflection of the structure at the position based on the time series data, the first index value, and the second index value. The program for solving the above problem includes, on a computer, an acquisition step of acquiring time series data including a physical quantity occurring at a predetermined observation point on a structure as a response to a movement of a composed mobile body, which is a combination of one or more mobile bodies, through the structure; an environmental information acquisition step of acquiring information on a structure length, which is the length of the structure, a mobile body length, which is the length of the mobile body, and an installation position of a contact portion of the mobile body with the structure, as environmental information; and deriving an entry time and an exit time of the composed mobile body with respect to the structure based on the time series data. The system executes a time derivation step of acquiring the number of moving bodies organized into the organized moving body, a number acquisition step of acquiring the number of moving bodies organized into the organized moving body, an index value acquisition step of acquiring a first index value which is an index value of the amount of deflection of the structure occurring at the observation point and a second index value which is an index value of the amount of deflection at a specified position of the structure based on the number, the entry time, the exit time, and the environmental information, and a deflection derivation step of deriving an estimated value of the amount of deflection of the structure at the position based on the time series data, the first index value, and the second index value. [Brief description of the drawings]

[0006] [Figure 1] FIG. 1 is a block diagram showing a configuration of a derivation system. [Diagram 2] FIG. [Diagram 3] FIG. 1 is a diagram showing the dimensions of a unit bridge girder. [Figure 4] FIG. 1 is a diagram showing the dimensions of a railway vehicle. [Diagram 5] FIG. 2 is a diagram showing an overview of a unit bridge girder. [Figure 6] FIG. 13 is a diagram illustrating the bending moment in a unit bridge girder. [Figure 7] FIG. 13 is a diagram showing an overview of the deflection of a unit girder due to wheels. [Figure 8] FIG. 1 is a diagram showing an overview of deflection of a unit bridge girder due to a railway vehicle. [Figure 9] FIG. 1 is a diagram showing an overview of deflection of a unit bridge girder due to a railway train. [Figure 10]FIG. 13 is a diagram showing the deflection of a unit bridge girder due to a railway vehicle. [Figure 11] FIG. 13 is a diagram showing the FFT results of the deflection of a unit bridge girder. [Figure 12] FIG. 13 illustrates the deflection of a unit girder due to a railway train after high-pass filtering. [Figure 13] FIG. 13 is a diagram showing the deflection of a unit bridge girder due to each railway vehicle. [Figure 14] FIG. 13 shows the deflection of a unit bridge girder due to each rail car and a rail train. [Figure 15] FIG. 2 is a diagram showing details of each element of the derivation system. [Figure 16] FIG. 13 is a diagram showing time-series data that has been subjected to low-pass filtering. [Figure 17] 11A and 11B are diagrams for explaining a process of deriving an entry time and an exit time. [Figure 18] 11A and 11B are diagrams for explaining a process of deriving an entry time and an exit time. [Figure 19] 13 is a flowchart showing a derivation process. [Figure 20] FIG. 13 is a diagram showing an estimated value of the amount of deflection. [Figure 21] FIG. 1 shows the amplitude at a specified position. [Figure 22] FIG. [Figure 23] FIG. [Figure 24] FIG. 13 is a diagram showing an estimated value of the amount of deflection. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0007] Here, the embodiments of the present invention will be described in the following order. (1) First embodiment (1-1) Configuration of the derivation system: (1-1-1) Overview of the derivation system: (1-1-2) Deflection model: (1-1-3) Verification experiment: (1-1-4) Element details: (1-2) Derivation process: (2) Second embodiment (2-1) Configuration of the derivation system: (2-1-1) Overview of the derivation system: (2-1-2) Verification experiment: (2-1-3) Element details: (2-2) Derivation process: (3) Other embodiments:

[0008] (1) First embodiment (1-1) Configuration of the derivation system: (1-1-1) Overview 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 a deflection amount at a designated position 9, which is a designated position on a bridge 5, based on time-series data of physical quantities at a predetermined observation point on a bridge 5 on which a railway train 6 composed of one or more railway cars moves. The railway train 6 is an example of a train-formed moving body. Each of the railway cars 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 car of the railway train 6 moves on the bridge 5 via wheels provided on the axles. The wheels are an example of a contact portion between the railway car and the bridge. In the present embodiment, each of the railway cars composed of the railway train 6 is a railway car 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 on a superstructure 7 of the bridge 5, and a server device 3.

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

[0010] In this embodiment, the bridge 5 is a railway bridge, such as a steel bridge, a girder bridge, or an RC bridge. RC is an abbreviation for Reinforced Concrete. 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 and number of axles of a moving object passing over a bridge by treating the bridge as a "scale" and measuring the deformation of the bridge. A bridge that can analyze the weight of a moving object passing over the bridge from the response of the deformation and strain of the bridge is considered to be a structure to which BWIM can be applied. Therefore, the weight of a moving object moving over the bridge can be measured by a BWIM system that applies a physical process between the action on the bridge and the response. The weight of the moving object is measured by measuring the correlation coefficient between the displacement and the load in advance, and deriving the load of the moving object passing over the bridge using the correlation coefficient from the measurement result of the displacement of the bridge when the moving object passes over the bridge.

[0011] The bridge 5 includes a superstructure 7, which is a portion on which the moving body moves, and a substructure 8 that supports the superstructure 7. FIG. 2 is a cross-sectional view of the superstructure 7 cut along the line AA in FIG. 1. As shown in FIGS. 1 and 2, the superstructure 7 includes a bridge deck 7a including a deck F, a main girder G, a cross girder (not shown), a support 7b, a rail 7c, a sleeper 7d, and a ballast 7e. As shown in FIG. 1, the substructure 8 includes a pier 8a and an abutment 8b. The superstructure 7 is a structure that is bridged between adjacent abutments 8b and pier 8a, between two adjacent abutments 8b, or between two adjacent piers 8a. Hereinafter, the abutments 8b and pier 8a are collectively referred to as a support portion. In this embodiment, a pair of support portions and a portion of the bridge girder of the superstructure 7 that is bridged between the pair of support portions are collectively referred to as a bridge girder. In other words, a simple beam-like structure with both ends supported by two supports is considered to be one bridge girder. Therefore, the bridge 5 shown in Figure 1 includes two bridge girders. Below, 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 with each other via a communication network such as a Controller Area Network (CAN).

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

[0013] In this embodiment, the sensor device 2 is installed in the longitudinal center of the superstructure 7, specifically, in the longitudinal center of the main girder G. However, the sensor device 2 only needs to be able to detect acceleration for calculating the displacement of the superstructure 7, and its installation position is not limited to the central part of the superstructure 7. If the sensor device 2 is installed on the deck F of the superstructure 7, it may be destroyed by the running of the railway train 6, and the measurement accuracy may be affected by local deformation of the bridge deck 7a. Therefore, in the example of Figs. 1 and 2, the sensor device 2 is installed on the main girder G of the superstructure 7.

[0014] The deck F, main girders G, etc. of the superstructure 7 are deflected in the vertical direction due to the load of the railway train 6 running on the superstructure 7. Each sensor device 2 measures the acceleration of the deflection of the deck F and main girders G due to the load of the railway train 6 running on the superstructure 7. The designated position 9 is a position on the bridge 5 that is designated as a position for which the amount of deflection is to be estimated.

[0015] (1-1-2) Deflection model: Here, a model of the deflection of a bridge when a railway train moves across the bridge will be described. Here, the model is information such as an equation that indicates the correspondence between predetermined information and an estimated result.

[0016] In the following, the number of railroad cars in a train traveling on a bridge is defined as N. The entry time when the train enters the bridge is defined as t i Here, the entry of a train onto a bridge means that the wheels of one axle of the train C1 (the first train from the front of the train) enter the bridge. In the following, the exit time, which is the time when the train exits the bridge, is defined as t o Here, the departure of a train from a bridge is defined as the departure of train C. N The wheel of the rear axle of the last railcar of the train has left the bridge. In the following, the period during which the train passes the bridge (time t i From time t o The period until s In the following, N, t i , t o , t s These are compiled together and used as observation information.

[0017] In the following, the bridge length is defined as L B The bridge length is an example of the length of a structure. The distance from the end of the bridge in the longitudinal direction toward the direction in which the train approaches to the observation point is defined as L x In Figure 3, B and L x In the following, the end of the bridge in the longitudinal direction from which the train approaches is referred to as the approach end. In the following, the end of the bridge in the longitudinal direction from which the train approaches is referred to as the exit end. In addition, the length of the mth train from the front of the train is defined as L C (m). The vehicle length is an example of the length of the moving object. In the following, L c (1)~L c (N) to L c The mth train car from the front of the train is called C m Also, railroad car C m The number of axles in r (m). In the following, r (1)~a r (N) to a rIn the following, collectively referred to as railway vehicle C m in a r (m) axles of railcar C m Starting from the top, the first axis, the second axis, the third axis, ..., a r (m) axis and distance. In addition, railcar C m The distance from the front end of the vehicle to one axis in the direction of travel is L a (a w (m, 1)), where a w (α, β) indicates the β axis of the αth railcar in the railcar train. m The distance from the n-1 axis (n: an integer of 2 or more) to the n axis in a (a w (m, n)). That is, L a (a w (α, β)) is a railway train C α The distance between the β axis and the (β-1) axis in the α β axis and railway train C α In the following, L a (a w (1, 1))~L a (a w (N, a r (N))) to L a Collectively referred to as L a Each indicates the position of the corresponding axle on the corresponding railcar. For example, L a (a w (m, 1)) is a railcar C m At L from the tip a (a w (m, 1)) behind the axis. Also, L a (a w (m, 2)) is the railcar C m In the case of 1 axis to L a (a w This indicates that there are two axes behind the distance (m, 2). Here, the train is made up of rail cars with the same four-axle configuration: r (m) (m = 1, 2, . . . , N) is 4.m L in c (m), L a (a w (m, 1)), L a (a w (m, 2)), L a (a w (m, 3)), L a (a w (m, 4)). In the following, L B , L x , L c , a r , L a These are summarized as environmental information.

[0018] t s As shown in the following equation (1), t o and i It is calculated as the difference between

[0019]

number

[0020] In addition, the total number of wheels of a railway train, T ar is calculated using the following equation (2).

[0021]

number

[0022] From the first axle of the leading railcar C1, the m-th railcar C m The distance to the n-axis is D wa (a w (m, n)). D wa (a w (m, n)) is calculated from the following equation (3).

[0023]

number

[0024] From one axle of the front railcar C1 to the rear railcar C N The last axis a r The distance to (N) is D wa (a w (N, a r (N))). D wa (a w (N, a r (N)) to find the average speed of a train passing through a bridge, v a is expressed as the following equation (4).

[0025]

number

[0026] From equations (3) and (4), the following equation (5) holds.

[0027]

number

[0028] Next, a description will be given of the deflection that occurs in a bridge when a load is applied to the bridge. A schematic diagram of a bridge is shown in Figure 5. Figure 5 shows the situation where load P is applied to the bridge. Here, the distance between the position on the bridge where load P is applied and the approach end is represented as a. Also, the distance between the position on the bridge where load P is applied and the exit end is represented as b. In this case, the bending moment at the position on the bridge where load P is applied is expressed by the following equation (6).

[0029]

number

[0030] Figure 6 shows the bending moment at each position on the bridge due to load P. As shown in Figure 6, the bending moment generated in the bridge due to load P is 0 at the approaching end, and increases proportionally as it approaches the position where load P is applied from the approaching end, reaching the value shown by equation (6) at the position where load P is applied. In addition, the bending moment generated in the bridge due to load P decreases proportionally as it approaches the exit end from the position where load P is applied, reaching 0 at the exit end. Therefore, the bending moment at any position X on the bridge is expressed by the following equation (7).

[0031]

number

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

[0033]

number

[0034] The relationship between the deflection w of the bridge at any position X and the bending moment is expressed by the following equation (9).

[0035]

number

[0036] In equation (9), θ is the angle between the horizontal line and the deflected bridge at position X. The following equation (10) holds true from equations (7) and (9).

[0037]

number

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

[0039]

number

[0040] In equation (11), g1 and g2 are constant terms. Here, the bridge is supported at the entrance and exit ends, so there is no deflection at the entrance and exit ends. That is, in equation (11), x=0 and x=L B In this case, both sides are 0. Therefore, g1 and g2 are expressed as the following equations (12) and (13).

[0041]

number

[0042]

number

[0043] From equations (11), (12), and (13), the following equation (14) expressing the deflection w at position X can be obtained.

[0044]

number

[0045] When load P is applied to the center of the bridge in the longitudinal direction, the maximum deflection of the bridge due to the application of load P occurs at the center of the bridge in the longitudinal direction. This maximum deflection is called w 0.5l As, w 0.5l If the load P is applied to the center of the bridge in the longitudinal direction, a = b = 0.5L. B In addition, the position X for which the deflection is to be calculated is the center of the bridge in the longitudinal direction, so x = 0.5L B In this case, x<=a, so from equation (8), H a = 0. x = 0.5L B , a=b=0.5L B , Ha By substituting =0 into equation (14), the deflection w 0.5l The following equation (15) is obtained.

[0046]

number

[0047] w 0.5l The deflection at any position on the bridge expressed by equation (14) is normalized using When the position of the load P is closer to the entry end than the position X, that is, when x>a, from the formula (8), H a =1, and equation (14) can be expressed as the following equation (16).

[0048]

number

[0049] a=L B Let r be the real number between 0 and 1. b=L B -a, so b=L B (1-r). In equation (16), a = L B r, b=L B Substituting (1-r), w 0.5l When normalized by dividing by x>a, the normalized deflection w at position X is std The following equation (17) is obtained.

[0050]

number

[0051] Similarly, when the load P is located on the exit side of the position X, that is, when x<=a, H a =0, and equation (14) can be expressed as the following equation (18).

[0052]

number

[0053] a=L B Let r be the real number between 0 and 1. b=L B -a, so b=L B (1-r). In equation (18), a = L B r, b=L B Substituting (1-r), w 0.5l When normalized by dividing by x<=a, the normalized deflection w at position X is std The following equation (19) is obtained.

[0054]

number

[0055] In equations (17) and (19), x is L x By substituting, the normalized deflection amount w at the deflection observation point is std is expressed as a function of r as shown in the following equation (20).

[0056]

number

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

[0058]

number

[0059] Here, using equations (20) and (21), any one axle a w A function is obtained that shows the time change in deflection caused at the observation point due to the load applied to the bridge through the wheel (m, n). First, the time it takes for a wheel on one axle of a railroad train to travel from the approach end to the observation point is t xn Far away. xn, L x and v a From this, it can be calculated using the following equation (22).

[0060]

number

[0061] The time it takes for one wheel of a railway train to cross a bridge, i.e., from the approach end to the exit end, is defined as t ln Far away. ln , L B and v a From this, it can be calculated using the following equation (23).

[0062]

number

[0063] Also, the n-axis a of the m-th railcar of the railcar train w The time when the wheel (m, n) reaches the entry end is t o Let (m, n). t o (m, n) is t i and v a and D wa (a w (m, n)), it can be calculated using the following equation (24).

[0064]

number

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

[0066]

number

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

[0068]

number

[0069] Axle A w The position (m, n) is the load position. Therefore, axle a w The position of (m, n) is a=L from the entrance end to the exit end. B The position is the distance r. Also, if the variable indicating time is t, then a at time t is w The distance from the entrance of (m, n) is o is equal to the distance traveled by the railcar from (m, n) to time t. Therefore, the following equation (27) holds true.

[0070]

number

[0071] From equation (27), r is expressed as follows:

[0072]

number

[0073] Using equations (25), (26), and (28), L in equations (20) and (21) x , L B , r is replaced by axle a w The function w of the following equation (29) is used as a model showing the time change of the deflection caused at the observation point by the load applied to the bridge through the wheels (m, n). std (a w (m, n), t) are obtained. The function R(t) in equation (29) is the function shown in equation (30) below.

[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 If (N)))) is known, then we can use this information to find w std (a w (m, n), t) is obtained. For example, t i , t o Using equation (1), t s t s ,N,a r , L a , L c From this, using equation (5), v a is obtained. v a and L B and L x From this, using equations (22) and (23), t xn , t ln is obtained. L a , L c , ti, using equations (3) and (24), t o (m, n) is found. Then, the calculated t xn , t ln , t o By substituting (m, n) into equations (29) and (30), we obtain the function w of t. std (a w (m, n), t) are found.

[0077] w std (a w An example of the change in the amount of deflection at the observation points indicated by (m, n), t) is shown in FIG. 7. The horizontal axis of the graph in FIG. 7 indicates time, and the vertical axis indicates the amount of deflection. m According to the movement of ar A pair of wheels on each of the (m) axles will move across the bridge. m A function C as a model showing the time change in the deflection caused at the observation point by the movement of std (m, t) is the w std (a w This is calculated as the sum of (m, n), t) using the following equation (31).

[0078]

number

[0079] a r When (m) is 4, i.e., railcar C m If it has a four-axis configuration, the function C std The 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 stdFIG. 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 at the 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] (1-1-3) 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], t s = 1.567 [seconds], L B = 25 [m], L x = 12.5 [m], L C = 25[m], a r For each m=4, m=1~N, L a (a w (m, 1)) = 2.5 [m], m = 1 to N, L a (a w (m, 2)) = 2.5 [m], m = 1 to N, L a (a w (m, 3)) = 15 [m], m = 1 to N, L a (a w (m, 4)) = 2.5 [m].

[0084] The amount of deflection at this time T std (t) is shown in FIG. 10. The horizontal axis of the graph in FIG. 10 indicates time, and the vertical axis indicates the amount of deflection. std By performing a fast Fourier transform (FFT) on (t), T std The intensity of each frequency component in (t) was calculated. T stdThe results of FFT for (t) are shown in FIG. 11. The horizontal axis of the graph in FIG. 11 indicates frequency, and the vertical axis indicates the intensity of the corresponding frequency component. The inventors then calculated T std From the FFT result of (t), std The fundamental frequency F of (t) f Here, the fundamental frequency is the frequency of the lowest frequency component contained in the signal. std From the FFT result of (t), excluding the side lobes caused by the window function used in the FFT, the peak corresponding to the lowest frequency was identified, and the identified peak was determined as the fundamental frequency. In the example of FIG. 11, as shown in the area surrounded by the dashed line, two side lobe peaks caused by the window function used in the FFT are observed in the range of less than 2 Hz. Among the peaks excluding these peaks, the inventors identified the peak in the area surrounded by the dotted line as the lowest frequency peak, and determined the frequency corresponding to the identified peak as the fundamental frequency F. f The inventors determined the fundamental frequency to be 3.1 Hz from the graph in FIG.

[0085] The inventors have determined that the fundamental frequency F f The wave number ν of was calculated using the following equation (33).

[0086]

number

[0087] In this case, ν=1.567×3.1=4.8577. Here, the number of rail cars N of the moving rail train is 4. The inventors calculate the fundamental frequency F f The inventors have found that the wave number ν of the fundamental frequency F fIt was found that it can be calculated using the following equation (34), where ν is the wave number ν minus 1 rounded to an integer. The round function returns the rounded value of its argument.

[0088]

number

[0089] In addition, the inventors calculated the fundamental frequency F f From the fundamental period T f asked for.

[0090]

number

[0091] The inventors then determined that the fundamental period T f The deflection amount T std By taking the moving average of (t), low-pass filtering is performed to attenuate the frequency components above the fundamental frequency. std The low-pass filter process may be another FIR filter process that attenuates the frequency components above the fundamental frequency. std (t) to T std_lp (t)=T std_lp Let t be (kΔT), where k is a variable that indicates the number of observations when the amount of deflection is periodically observed at the observation point. In other words, if the data period (time resolution) of the amount of deflection observation is ΔT, then t = kΔT. As shown in the following equation (36), the fundamental period T f From and ΔT, the moving average interval k adjusted to the time resolution of the data is calculated. mf is required.

[0092]

number

[0093] k mfUsing T std_lp (t) is calculated by the following equation (37).

[0094]

number

[0095] The inventors have determined that the deflection amount T std (t) to T std_lp By subtracting (t), high-pass filtering is performed to attenuate the frequency components below the fundamental frequency. std The high-pass filtering process may be any other FIR filtering process that attenuates components with frequencies less than the fundamental frequency. std (t) to T std_hp Specifically, the inventors set T std (t) to T std_lp By subtracting (t), T std_hp (t) was sought.

[0096]

number

[0097] The desired T std_hp (t) to T std 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. std_hp (k), and the dotted graph shows T std (t) is shown. From the graph in Figure 12, the transit period t s (Time t i From time t o T std_hp The number of positive peaks in (t) is 6. Here, the positive peaks are std_hp Among the peaks of (t), it is a peak that is convex upwards of the bridge. Also, during the passage period t s T in std_hpThe number of negative peaks in (t) is 5. Here, the negative peaks are T std_hp Among the peaks of (t), this is a peak that is convex downward of the bridge. From this, the inventors have s T in std_hp We found that the number of positive peaks (6) of (t) is two more than the number of railcars in the railcar train, N (4), and the number of negative peaks (5) is one more than N (4). In what follows, we refer to this feature as the second feature.

[0098] The inventors verified whether the first and second features hold while changing the observation information and the environmental information to various values. As a result, the inventors found that L c / 2 < L B < 3L c / 2 is satisfied, the inventors have found that the first and second features are established. Based on the first and second features, the inventors have found that the number of railroad cars in a railroad train 6 can be derived from time series data of bridge displacement (deflection) at an observation point on the bridge. In the following, the time series data of displacement at an observation point on the bridge is represented as u(t). u(t) is data of discrete values ​​of displacement measured at a predetermined period, and each discrete value is associated with a measurement time.

[0099] The inventors have determined that the deflection amount C occurs when a train made up of similar railcars passes over a bridge under the conditions where the observation information and the environmental information are the following values: std (1,t)~C std (N,t),T std (t) was considered. 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 = 25[m], a r For each m=4, m=1~N, L a (a w (m, 1)) = 2.5 [m], m = 1 to N, La (a w (m, 2)) = 2.5 [m], m = 1 to N, L a (a w (m, 3)) = 15 [m], m = 1 to N, L a (a w (m, 4)) = 2.5 [m].

[0100] The deflection amount C of each of the four rail cars included in the rail train at this time std (1,t)~C std (4, t) is shown in Fig. 13. The period of vibration that occurs on a bridge when trains pass over it continuously is called T f The vibrations that occur on a bridge when trains pass over it in succession are caused by trains passing over the bridge in succession. Therefore, the period T f is the time difference between the entrance times of successive trains passing over the bridge. Since the bridge is deflected by the train from the time the train enters the bridge, C std (m, t) indicates the start time of the deflection, and C std The time difference between the start time of the deflection indicated by (m+1, t) and f FIG. 13 shows the deflection of the bridge caused by the passage of each railcar of a railcar when the train passes over the bridge. The horizontal axis of the graph in FIG. 13 shows time, and the vertical axis shows the amount of deflection. As shown in FIG. 13, the deflection caused by the railcars passing before and after the bridge is expressed as T f This occurs with a time lag of .

[0101] Period T f is the time difference between the entrance times of successive railway vehicles passing through the bridge, and is expressed as the vehicle length L C (m) to velocity v a This can be considered as a period passing through

[0102]

number

[0103] Railroad train rail car C mThe period during which the bridge is crossed is called t c (m) far away. c (m) is a moving object, a railway vehicle C m is an example of a moving object passing period during which the moving object passes over a bridge, which is a structure. c (m) is railroad car C m From the time when one axle of railcar C reaches the approach end, m A r (m) The period until the axis reaches the exit end. That is, t c (m) is railroad car C m is the bridge length L B and railcar C m From the front axle 1 to the rear axle a r (m) is the total distance traveled by the axis. Therefore, t c (m) is expressed by the following equation (40).

[0104]

number

[0105] When a train passes over a bridge, the number of cars in the train that have a following car is defined as C Tn Among the railcars in a train, there are railcars following each other except for the last railcar. Therefore, C Tn is a number that is 1 smaller than N. In other words, the following equation (41) holds.

[0106]

number

[0107] Figure 14 shows the C std (1,t)~C std (N,t),T std The horizontal axis of the graph in FIG. 14 indicates time, and the vertical axis indicates the amount of deflection. The solid line in FIG. 14 indicates T std (t), and the dotted graph shows C std (1,t)~Cstd (4, t) respectively. As shown in FIG. 14, s is C Tn T's f and one rail car C m During the period t c (m) and (m). In other words, the following equation (42) holds.

[0108]

number

[0109] From equations (41) and (42), the number N of railcars in a railcar train is given by the following equation (43).

[0110]

number

[0111] T f is also the time it takes for a railroad train to travel one railcar length. Therefore, the transit time t s The distance traveled is the length of (N-1) railcars and the speed v a At c The distance traveled during the period (m) is the sum of the distance traveled during the period (m) and the distance traveled during the period (m). Therefore, the following equation (44) holds true.

[0112]

number

[0113] From equation (44), the following equation (45) holds. It can also be confirmed from equation (45) that equation (43) holds.

[0114]

number

[0115] The amount of deflection T that occurs in the bridge when a train passes over it std(t) contains the fundamental frequency F f It is considered that the component of F includes the vibration component generated on the bridge due to the continuous movement of railway vehicles. f is also the frequency of vibration that occurs on the bridge due to the continuous movement of railway vehicles, so T f It can be expressed as the reciprocal of

[0116]

number

[0117] From equation (39) and equation (46), the velocity v a is expressed as follows: F f and L C It is expressed as the product of (m).

[0118]

number

[0119] Therefore, t expressed by equation (40) c (m) is the bridge length L B and railcar C m From the front axle 1 to the rear axle a r (m) The total distance to the axis is F f and L C This is the value divided by the product of (m). From equations (43) and (46), the number of rail cars in a train, N, is determined by the period during which the train passes over the bridge, t s From, one rail car C m The period of passage of the bridge by c It is expressed as the product of the value obtained by subtracting (m) and the fundamental frequency Ff plus 1, and is expressed as shown in the following equation (48).

[0120]

number

[0121] We have determined that the average speed of a railway train, v a is the fundamental frequency Ff and the number of railcars C in a railroad train. m The inventors also found that the length of one railcar C m During the period t c (m) is railroad car C m is the bridge length L B and railcar C m From axis 1 to a r (m) The total distance to the axis is the speed v a In addition, the inventors found that the number of rail cars in a rail train, N, can be expressed as the period of travel in t s From c We found that it can be expressed as the product of the value obtained by subtracting (m) and the fundamental frequency Ff plus 1. The inventors then came up with a method of deriving the number of railcars in a railcar train by using time-series data of displacement at observation points set on bridges over which the railcar train travels.

[0122] The method conceived by the inventors involves acquiring time series data u(t) of displacement at an observation point set on a bridge over which a train travels, and calculating L B and L C and L a and are obtained as environmental information, and the fundamental frequency F of u(t) is calculated based on the time series data u(t). f is obtained as the frequency of vibration generated on the bridge by the passage of successive railcars in a railroad train, and based on u(t), the period t during which the railroad train passes the bridge is calculated as s Derive L B and L C and L a and F f and s Based on the above, the number of rail cars included in a rail train is calculated using the relationships shown in equations (40), (47), and (48).

[0123] In this embodiment, the derivation system 10 derives the value of the number N of railway cars formed in the railway train 6 based on time-series data u(t) of the amount of deflection of the bridge 5 measured at the observation point and knowledge obtained through experiments. Then, the derivation system 10 uses the derived N and a bridge deflection model to derive the amount of deflection at the observation point and the amount of deflection of the bridge 5 at a designated position 9, which is a designated position. The derivation system 10 obtains an estimate of the actual amount of deflection at the designated position 9 by multiplying the time-series data u(t) by the ratio of the amount of deflection at the designated position to the derived amount of deflection at the observation point.

[0124] (1-1-4) Element details: Here, the measurement device 1, the sensor device 2, and the server device 3 of the derivation system 10 will be described in detail with reference to FIG. In this embodiment, the derivation system 10 calculates the number of trains N in the train 6, the time t i , the time when the train 6 leaves the unit bridge girder t o , period t during which train 6 passes through the unit bridge girder s is derived based on the data measured by the measurement device 1.

[0125] The measuring device 1 measures the deflection at the observation point via the sensor device 2. In this embodiment, the measuring device 1 is installed on the bridge abutment 8b, but may be installed at another location. 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 central processing unit (CPU), a read only memory (ROM), a random access memory (RAM), etc. The control unit 100 realizes each function of the measuring device 1 by expanding various programs recorded in the ROM, etc., into the RAM and executing them via the CPU. The storage unit 110 stores various programs, data on measured deflections, etc. The communication unit 120 includes a circuit used for wired or wireless communication with an external device.

[0126] The sensor device 2 detects acceleration as a predetermined physical quantity at an 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.

[0127] The acceleration sensor 210 is an acceleration sensor such as a quartz acceleration sensor or a MEMS acceleration sensor capable of detecting acceleration occurring in each of three mutually perpendicular axial directions. In this embodiment, the acceleration sensor 210 is arranged so that one axis is parallel to the vertical direction in order to detect acceleration in the vertical direction with higher accuracy. However, there are cases where the installation location of the sensor device 2 on the upper structure 7 is tilted. Even if one of the three detection axes of the acceleration sensor 210 is not aligned with the vertical direction, the measurement device 1 detects acceleration in the vertical direction by combining the acceleration of the three axes.

[0128] The control unit 200 of the sensor device 2 periodically detects the vertical acceleration at the observation point on the bridge 5 via the acceleration sensor 210, and transmits the detected acceleration data to the measurement device 1. The control unit 100 of the measurement device 1 measures the vertical deflection of the bridge 5 at the observation point at the detection time of the acceleration based on the acceleration data transmitted from the sensor device 2. In this embodiment, the control unit 100 obtains the vertical deflection of the bridge 5 at the observation point by integrating the acceleration indicated by the data transmitted from the sensor device 2 twice over time. Then, the control unit 100 transmits the measured deflection data to the server device 3. In this 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 the displacement measured at the ΔT period, and each discrete value is associated with the measurement time.

[0129] The server device 3 derives the number of rail cars included in the rail train 6 based on the deflection at the observation point measured by the measurement device 1. The server device 3 is an example of a derivation device. The server device 3 includes a control unit 300, a storage unit 310, and a communication unit 320. The control unit 300 includes a processor such as a CPU, a ROM, a RAM, etc. The control unit 300 implements the functions of an acquisition unit 301, an environmental information acquisition unit 302, a time derivation unit 303, a number acquisition unit 304, an index value acquisition unit 305, and a deflection derivation unit 306 by expanding various programs recorded in the ROM or the like into the RAM and executing them via the CPU. The storage unit 310 stores various programs, data on the detected deflection, etc. The communication unit 320 includes a circuit used for wired or wireless communication with an external device.

[0130] The acquisition unit 301 has a function of acquiring time series data of deflection occurring at the observation point as a response to the railway train 6 moving across each bridge in the bridges 5. The control unit 300 acquires the time series data u(t) of the deflection occurring at the observation point from the measurement device 1 using the function of the acquisition unit 301.

[0131] The environmental information acquisition unit 302 is a function for acquiring environmental information including information on the length of the unit bridge girder, the vehicle length which is the length of the railway cars formed in the railway train 6, and the position of the axle on which the wheels are installed in the railway cars. B , the length L of each rail car of the rail train 6 c , distance L indicating the position of each rail car of the rail train 6 a The information on the above is acquired as environmental information. In this embodiment, the environmental information is stored in advance in the storage unit 310, and the control unit 300 acquires the environmental information from the storage unit 310. However, the control unit 300 may acquire the environmental information using another method, such as receiving the environmental information from an external device.

[0132] The time derivation unit 303 calculates the approach time t of the train 6 to the unit bridge girder based on the time series data u(t). i and exit time t oThe control unit 300 executes an FFT on u(t) using the function of the time derivation unit 303. The control unit 300 detects peaks from the FFT result. Of the detected peaks, the control unit 300 identifies a peak corresponding to the minimum frequency excluding side lobe peaks caused by the influence of the window function used in the FFT. The control unit 300 calculates the frequency corresponding to the identified peak as the fundamental frequency F of u(t). f It is derived as:

[0133] The control unit 300 assigns the fundamental frequency F f First, the control unit 300 applies a low-pass filter to attenuate the fundamental frequency F f Based on this, similar to equation (35), F f By deriving the inverse of f The control unit 300 derives the derived T f Based on the predetermined period ΔT, the interval k is calculated using the following equation (49). mf Derive:

[0134]

number

[0135] The control unit 300 calculates the interval k for each value of u(t). mf By taking the moving average at , we apply a low-pass filter to u(t). The low-pass filtered u(t) is lp (t)=u lp (kΔT), where k is a variable indicating the number of observations when the amount of deflection is periodically observed at the observation point. mf Based on this, u lp Derive (t). u lp Similarly to u(t), which is a set of discrete data values, u(t) is a set of discrete data values. lp 16. The horizontal axis of the graph in FIG. 16 represents time, and the vertical axis represents the amount of deflection.

[0136]

number

[0137] Then, the control unit 300 lp From (t), the predetermined threshold value C L Identify two consecutive data that sandwich u lp Two consecutive data points in (t) are below the threshold C L By sandwiching, I mean u lp The range between the values ​​of two consecutively measured displacement data included in (t), that is, the range between the smaller value of these displacement data and the larger value, L In this embodiment, this threshold C L is a preset coefficient between 0 and 1, and the u lp (t) and the product of u. Here, the period during which the deflection amount is shifting is the period during which the deflection amount of the bridge is maintained within a predetermined range due to the carriage of a train. More specifically, the period during which the deflection amount is shifting is the period during which the deflection amount is within a predetermined width range centered on a value whose absolute value is greater than a predetermined value. The control unit 300, for example, lp From (t), data on the amount of deflection for a period of a predetermined length (e.g., 1 second, 2 seconds, etc.) is extracted, and if the absolute value of the average value of the extracted data is equal to or greater than a predetermined threshold value and the absolute value of the difference between the maximum and minimum values ​​of the extracted data is equal to or less than a predetermined width, the extracted period is determined to be the period during which the amount of deflection is shifting. The control unit 300 may also accept, via an operation unit or the like of the server device 3, specification of the start time and end time of the period during which the amount of deflection is shifting. The control unit 300 then calculates, for the period during which the amount of deflection is shifting, u lp The average value of (t) is calculated, and the product of the calculated average value and a predetermined coefficient is set as the threshold C L It is derived as:

[0138] However, the threshold C L may be other values. For example, the threshold C Lmay be the value of the deflection at the observation point of the bridge when the railroad vehicle is arranged so that the wheels of the leading axle of the railroad vehicle are located near the approach end. In addition, the threshold value C L may be the deflection of the bridge at the observation point when a predetermined weight is applied near the approach end. Also, the threshold value C L may be a value that is a predetermined percentage (e.g., 10%, 1%, etc.) of the maximum deflection amount at the observation point of the bridge when a railway train passes over the bridge.

[0139] In Figure 17, lp (t) and threshold C L The horizontal axis of the graph in FIG. 17 indicates time (t=kΔT), and the vertical axis indicates the amount of deflection. The solid line graph in FIG. 17 indicates u lp The dotted line graph shows u(t), and the dotted line graph shows u(t). lp (k) and the threshold C L Also, in Figure 18, u lp (t) and C L The horizontal axis of the graph in FIG. 18 indicates time, and the vertical axis indicates the amount of deflection. Each black dot in FIG. 18 indicates the time lp (t) shows the discrete value data included in the lp The data k-1 and data k included in (t) are the threshold C L It is shown that the two are sandwiched in between. The control unit 300 determines the specified C L 18, the control unit 300 specifies the later of two times corresponding to two consecutive data pieces that sandwich a time kΔT. In the example of FIG. In the example of FIG. 17, the control unit 300 L As two consecutive pieces of data sandwiching the time, the two pieces of data in the dotted circle on the right side of FIG. 17 are also identified, and the later of the two times corresponding to the identified two pieces of data is identified.

[0140] Then, the control unit 300 sets the earlier of the identified times as the entry time t iIn addition, the control unit 300 derives the later of the identified times as the exit time t o In the example of FIG. 17, the control unit 300 derives the entry time t i =7.2[s], exit time t o = 12.795 [s]. In this manner, in this embodiment, the control unit 300 derives u lp The time associated with any of the data included in (t) is referred to as the entry time t i , exit time t o It is derived as:

[0141] In this manner, in this embodiment, the control unit 300 lp C included in (t) L The later of the two times corresponding to the two consecutive data points that sandwich t is the entry time t i , exit time t o However, the control unit 300 derives other times as the entry time t i , exit time t o For example, the control unit 300 may derive u lp From (t), the predetermined threshold value C L Two consecutive data pieces that sandwich the entry time t are identified, and a time that is included in the period after one of the times corresponding to the two identified data pieces and before the other time is defined as the entry time t i and exit time t o In the example of FIG. 18, the control unit 300 may derive the time (k-1)ΔT corresponding to data k-1 or later and before the time kΔT corresponding to data k (for example, time (k-1)ΔT, u lp (t) and C L The time corresponding to the intersection point of t i The control unit 300 may derive the equation as u lp A curve is obtained by interpolating each data point in (t), and the obtained curve and C L The time corresponding to the intersection with i , t o It may be calculated as:

[0142] Also, ulp C in (t) L For two consecutive data that sandwich the L For example, in the example of FIG. 18, the value of data k is C L In this case, the control unit 300 sets C L The two consecutive data are C L A pair of data equal to and the previous data, and C L In the example of FIG. 18, data k is C L If it is equal to, the control unit 300 L As two consecutive data pieces sandwiching a data k-1 and a data k, two pairs are identified: a pair of data k-1 and a data k, and a pair of data k and a data k+1. In such a case, the control unit 300 selects one of the identified data pairs, and determines a time within a period between two times corresponding to two data pieces included in the selected pair as t i Or t o It may be derived as:

[0143] In this embodiment, the control unit 300 lp The time associated with any of the data included in (t) is referred to as the entry time t i , exit time t o As a result, the control unit 300 derives the entry time t i , exit time t o u corresponding to each measurement time of the ΔT interval including lp The data of (t) is lp By referring to (t), the control unit 300 can easily obtain and utilize the information. lp The time that is not associated with any of the data included in (t) is called the entry time t i , exit time t o If we derive it as t i , t o u corresponding to each measurement time of the ΔT interval including lp (t) data into the original u lp This requires resampling from (t), which increases the amount of processing work.

[0144] The control unit 300 attenuates the vibration components of the fundamental frequency or higher. lp By using (t) to derive the approach time and exit time, the influence of vibration components higher than the fundamental frequency can be reduced, and the approach time and exit time can be derived more accurately. However, the control unit 300 lp In this case, the control unit 300 may not derive u(t) and the threshold C L The time when and intersect is t i , t o It may be derived as:

[0145] The number acquisition unit 304 is a function for acquiring the number of railcars in the railcar train 6. The control unit 300 derives the number of railcars included in the railcar train 6 based on the first feature by the function of the number acquisition unit 304. i and o Based on this, the passing period t s Then, the control unit 300 derives the derived t s and the fundamental frequency F derived based on u(t) f Based on this, we use equation (33) to calculate the passing period t s The fundamental frequency F f The control unit 300 derives the wave number ν of t s and the fundamental frequency F of u(t) f The value of N is calculated by subtracting 1 from the product of and rounding to an integer.

[0146] However, the control unit 300 may obtain N by other methods. For example, the control unit 300 may obtain N as follows based on the second feature. That is, the control unit 300 obtains N from u(t) by lp By subtracting (t), u(t) is subjected to a high-pass filter process that attenuates frequency components below the fundamental frequency, and the high-pass filtered u(t) is called u(t).hp Then, the control unit 300 derives u hp t in (t) i From o The control unit 300 may obtain the value of N by subtracting 2 from the number of identified positive peaks. In addition, the control unit 300 hp t in (t) i From o The control unit 300 may obtain the value of N by subtracting 1 from the number of negative peaks thus determined.

[0147] The control unit 300 may also use the method conceived by the inventors as follows. That is, the control unit 300 may calculate the vehicle length L of the railcar of the railcar train 6 indicated by the environmental information. C (m) and the fundamental frequency F f Based on this, the average speed of the railway train v is calculated using equation (47). a The control unit 300 derives the derived v a and environmental information indicates B and L a Based on this, we use equation (40) to calculate the period t c Then, the control unit 300 derives the derived F f and s and c Based on (m), the number N of rail cars formed in the rail train 6 may be derived using equation (48) to obtain N. However, the control unit 300 does not have to derive the value of N. For example, the control unit 300 may accept a designation of N based on a user's operation of an operation unit of the server device 3, and obtain the accepted value as N. The control unit 300 may also accept a designation of N from an external device, and obtain the accepted value as N. The control unit 300 may also obtain a predetermined value as N.

[0148] The index value acquisition unit 305 acquires the number N of railcars in the railcar train 6 and the entry time t i and exit time t o and environmental information, a first index value which is an index value of the amount of deflection of the structure occurring at the observation point, and a second index value which is an index value of the amount of deflection at a specified position 9 in the structure. In this embodiment, the position of the specified position 9 in the unit bridge girder is a distance L B ×rx, where rx is the position of L B It is a value indicating the ratio of the distance from the approach end of the unit bridge girder to the designated position 9 with respect to rx. In this embodiment, rx is 0.05. The control unit 300, by using the function of the index value acquisition unit 305, derives an estimate of the normalized amount of deflection caused at the observation point by the passage of the railway train 6 when the railway train 6 is composed of the number of railway cars indicated by N, as a first index value, which is an index value of the amount of deflection at the observation point. i , t o Using equation (1), t s The control unit 300 derives t s ,N,a r , L a , L B , L c From this, using equation (5), v a That is, v a is the distance from the front axle (one axle of the front railcar) to the rear axle (one axle of the rear railcar) in a railcar train consisting of N railcars. r (N) axis) and the bridge length L B The sum of and is taken as the approach time t i Exit time t o The transit period t s The control unit 300 calculates the value by dividing v a and L B and L x From this, using equations (22) and (23), t xn , t ln In addition, the control unit 300 derives L a , L c , t iFrom this, using equations (3) and (24), t o Then, the control unit 300 derives the derived t xn , t ln , t o By substituting (m, n) into equations (29) and (30), the function w std (a w Derive (m, n), t). The control unit 300 calculates w std (a w (m, n), and t) are added together to obtain C, which shows the deflection of the unit bridge girder due to the passage of a railway vehicle. std Then, the control unit 300 uses the formula (32) to derive C std By adding (m, t), the deflection of the unit bridge girder due to the passage of a train is calculated as T std In this way, the control unit 300 derives the normalized deflection amount T std (t) is acquired as the first index value. In the following, T std (t) to T std_R (t) Far away.

[0149] In addition, the control unit 300 derives a standardized estimated value of the amount of deflection caused at the designated position 9 by the passage of the railway train 6 in the case where the railway train 6 is composed of the number of railway cars indicated by N, as a second index value which is an index value of the amount of deflection at the designated position 9. Specifically, the control unit 300 calculates v a and L B From rx, L x L B ×rx, and using equations (22) and (23), t xn , t ln In addition, the control unit 300 derives L a , L c , t i From this, using equations (3) and (24), t o Then, the control unit 300 derives the derived t xn , tln , t o By substituting (m, n) into equations (29) and (30), the function w std (a w Derive (m, n), t). The control unit 300 calculates w std (a w (m, n), and t) are added together to obtain C, which shows the deflection of the unit bridge girder due to the passage of a railway vehicle. std Then, the control unit 300 uses the formula (32) to derive C std By adding (m, t), the deflection of the unit bridge girder due to the passage of a train is calculated as T std In this way, the control unit 300 derives the normalized deflection amount T std (t) is obtained as the second index value. In the following, the T std (t) to T std_rx (t) Far away.

[0150] The deflection deriving unit 306 calculates the time series data u(t) and the first index value T std_R (t) and the second index value T std_rx (t) and derives an estimate of the deflection of the unit girder at the specified position 9 based on the above. The control unit 300, by the function of the deflection deriving unit 306, std_R (t) and T std_rx In (t), the period from time t1 when the deflection value starts to exceed 0 to time t2 when the deflection converges to 0 is specified as the period from when the deflection starts to occur until it converges. The control unit 300 also calculates the first index value T std_R (t) and the second index value T std_rx (t) is a given amount depending on the ratio R rx_R In this embodiment, the first index value T std_R The predetermined amount according to (t) is the first index value T std_R (t). The second index value Tstd_rx The predetermined amount according to (t) is the second index value T std_rx Therefore, in this embodiment, the control unit 300 calculates the first index value T std_R (t) and the second index value T std_rx Ratio to (t) rx_R (t) is derived. However, as another example, the first index value T std_R The predetermined amount according to (t) is the first index value T std_R (t) to the first index value T std_R The second index value T std_rx The predetermined amount according to (t) is the second index value T std_R (t) to the second index value T std_R The control unit 300 may also determine the ratio R rx_R (t) is the second index value T std_R (t) to the second index value T std_R The amount by which the frequency components of (t) above the fundamental frequency are attenuated is defined as the first index value T std_R (t) to the first index value T std_R A value obtained by dividing the frequency components of (t) equal to or higher than the fundamental frequency by the amount of attenuation may be derived.

[0151]

number

[0152] The control unit 300 calculates t1, t2, and R rx_R Based on (t), a first index value T std_R (t) and the second index value T std_rx The average value Ravg of the ratio with (t) is derived.

[0153]

number

[0154] However, the control unit 300 sets, as Ravg, T std_R (t) and T std_rx For example, the control unit 300 may derive an average value of the ratio of the passing period t s T in std_R (t) and T std_rx In this case, the control unit 300 may calculate the average value of the ratio of t1 and t2 in the formula (52) to t i and o and Ravg may be derived using equation (52).

[0155] Then, the control unit 300 derives a value obtained by multiplying the time series data u(t) by Ravg as an estimate of the amount of deflection at the specified position 9. However, the control unit 300 calculates the corresponding R rx_R By multiplying this by (t), an estimate of the amount of deflection at the specified position 9 may be derived.

[0156] As described above, with the configuration of this embodiment, the derivation system 10 can derive the amount of deflection of a unit bridge girder at a specified position 9 different from the observation point.

[0157] (1-2) Derivation process: The process of deriving the amount of deflection at the specified position 9 executed by the server device 3 will be described with reference to Fig. 19. The server device 3 starts the process of Fig. 19 in response to the transmission of displacement data at the observation point from the measurement device 1, but may start the process of Fig. 19 at any timing, such as a specified timing. In S100, the control unit 300 acquires time series data u(t) of the deflection occurring at the observation point from the measurement device 1 through the function of the acquisition unit 301. S100 is an example of an acquisition step. In S105, the control unit 300 acquires the bridge length L of the unit bridge girder by the function of the environmental information acquisition unit 302. B , the length L of each rail car of the rail train 6 cThen, information on the distance La indicating the position of each railcar of the railcar train 6 is acquired as environmental information. S105 is an example of an environmental information acquiring step.

[0158] In S110, the control unit 300 executes an FFT on u(t) using the function of the time derivation unit 303, and detects peaks from the FFT result. Of the detected peaks, the control unit 300 identifies a peak corresponding to the minimum frequency excluding side lobe peaks caused by the influence of the window function used in the FFT. The control unit 300 calculates the frequency corresponding to the identified peak as the fundamental frequency F of u(t). f The control unit 300 derives the acquired fundamental frequency F f Based on this, similar to equation (35), F f By deriving the inverse of f The control unit 300 derives the derived T f Based on the predetermined period ΔT, the interval k is calculated using equation (49). mf The control unit 300 derives the derived section k mf Based on this, using equation (50), u lp Derive (t). In addition, the control unit 300 lp From (t), a section of a predetermined value (for example, 1 second, 2 seconds, etc.) is extracted, and if the absolute value of the difference between the maximum and minimum values ​​of the amount of deflection in the extracted section is equal to or less than a predetermined threshold, the extracted section is determined to be a section in which the amount of deflection has shifted. lp The average value of (t) is calculated, and the product of the calculated average value and a predetermined coefficient is set as the threshold C L It is derived as:

[0159] Then, the control unit 300 lp (t) and the derived threshold C L Specifically, the control unit 300 calculates the intersection point of u lp (t)=C L Then, the control unit 300 determines the time indicated by the smaller of the two values ​​of t as the entry time t of the railway train 6 into the unit bridge girder. iThe control unit 300 determines the time indicated by the larger of the calculated values ​​of t as the exit time t of the railway train 6 from the unit bridge girder. o S110 is an example of a time deriving step.

[0160] In S115, the control unit 300, by using the function of the number acquisition unit 304, acquires the t i and o Based on this, the passing period t s Then, the control unit 300 derives the derived t s and F derived in S110 f Based on this, the fundamental frequency F included in the passing period ts is calculated using equation (33). f The control unit 300 derives the wave number v of the railcars included in the railcar train 6 using equation (34) based on the derived v, thereby acquiring the number N. S115 is an example of a number acquiring step.

[0161] In S120, the control unit 300 uses the function of the index value acquisition unit 305 to obtain t s ,N,a r , L a , L c From this, using equation (5), v a The control unit 300 derives v a and L B and L x From this, using equations (22) and (23), t xn , t ln In addition, the control unit 300 derives L a , L c , t i From this, using equations (3) and (24), t o Then, the control unit 300 derives the derived t xn , t ln , t o By substituting (m, n) into equations (29) and (30), the function w std (a w Derive (m, n), t). The control unit 300 calculates w std (a w (m, n), and t) are added together to obtain C, which shows the deflection of the unit bridge girder due to the passage of a railway vehicle. std Then, the control unit 300 uses the formula (32) to derive C std Adding (m, t) together gives the normalized deflection T of a unit bridge girder due to the passage of a train. std (t) is the first index value T std_R Obtained as (t).

[0162] In addition, the control unit 300 a and L B From rx, L x L B ×rx, and using equations (22) and (23), t xn , t ln In addition, the control unit 300 derives L a , L c , t i From this, using equations (3) and (24), t o Then, the control unit 300 derives the derived t xn , t ln , t o By substituting (m, n) into equations (29) and (30), the function w std (a w Derive (m, n), t). The control unit 300 calculates w std (a w (m, n), and t) are added together to obtain C, which shows the deflection of the unit bridge girder due to the passage of a railway vehicle. std Then, the control unit 300 uses the formula (32) to derive C std By adding (m, t), the deflection of the unit bridge girder due to the passage of a train is calculated as T std In this way, the control unit 300 derives the normalized deflection amount Tstd (t) is the second index value T std_rx The step S120 is an example of an index value obtaining step.

[0163] In S125, the control unit 300 determines, by the function of the deflection deriving unit 306, T std_R (t) and T std_rx In (t), the period from time t1 when the deflection value starts to exceed 0 to time t2 when the deflection value converges to 0 is specified as the period from when the deflection starts to occur until when the deflection converges to 0. Then, the control unit 300 calculates the first index value T std_R (t) and the second index value T std_rx (t) and the ratio R rx_R The control unit 300 derives t1, t2, and R rx_R Based on (t), a first index value T std_R (t) and the second index value T std_rx The control unit 300 derives an average value Ravg of the ratio to the time series data u(t). The control unit 300 derives a value obtained by multiplying the time series data u(t) by Ravg as an estimate of the amount of deflection at the designated position 9. S125 is an example of a deflection deriving step.

[0164] (2) Second embodiment (2-1) Configuration of the derivation system: (2-1-1) Overview of the derivation system: The derivation system 10 of this embodiment has the same configuration as that of the first embodiment, except for the process of the server device 3, which differs from that of the first embodiment. (2-1-2) Verification experiment: The inventors calculated the actual deflection amount T(t) at a certain position on the bridge by the deflection amount T std The deflection amount is proportional to (t) and the deflection amount derived from the deflection model is uncorrelated with T offset That is, the inventors came up with the idea of ​​approximating T(t) by adding T stdThe idea was to approximate it as a linear function of (t). c1 in equation (53) is a linear coefficient. Here, the part proportional to the deflection amount derived by the deflection model is the displacement proportional to the load in the unit girder to which BWIM can be applied.

[0165]

number

[0166] The inventors used u lp (t) is the normalized deflection amount T of the observation point derived using the deflection model as shown in the following equation (54). std_R (t) is processed by a low-pass filter to attenuate the components above the fundamental frequency, std_R_lp The idea was that it could be approximated as a linear function with a variable of (t) and a linear coefficient of c1. c0 in equation (54) is a zero-order coefficient and indicates a displacement that is independent of the position on the bridge. Here, i Exit time t o During the period up to lp (t) to T std_lp It is approximated as a linear function of (t).

[0167]

number

[0168] If the value obtained by subtracting the right side of equation (54) from the left side is taken as the error and c1 and c0 are derived using the least squares method to minimize this error, we obtain the following equations (55) and (56).

[0169]

number

[0170]

number

[0171] t in Equation (55) and Equation (56) a u lp (t) to T std_R_lp (t) is the start time of the predetermined period to be approximated. In this embodiment, t a is the approach time t i In addition, t b u lp (t) to T std_R_lp (t) is the end time of the predetermined period of time to be approximated. In this embodiment, t b is the exit time t o Moreover, K in equations (55) and (56) is a value expressed by the following equation (57).

[0172]

number

[0173] As shown on the right side of equation (54), T std_R_lp (t), the deflection amount restored using coefficients c1 and c0 is T Estd_R_lp (t) and so on. T Estd_R_lp (t) is as shown in the following equation (58). Here, t <t i , t>t o During this period, since no trains are on the bridge, we assume that there is no deflection and set c0 = 0.

[0174]

number

[0175] T Estd_R_lp (t) and T std_R_lp (t) and the amplitude ratio R r is calculated as the following equation (59). k0 in equation (59) is the deflection amount u lp N is a value indicating the number of observations of the earliest deflection during the period in which the waveform (t) is shifting. N is also the number of observations of the deflection u lpThis is the value obtained by subtracting k0 from the value indicating the number of the latest observation of the deflection during the shift of the waveform (t). In other words, N is the number of observations of the deflection during the shift of the waveform (t) minus k0. lp The latest observation of the deflection amount during the period in which the waveform of (t) is shifting is the k0+Nth observation.

[0176]

number

[0177] The inventors have determined the offset T offset_R_std (t) is expressed as R r and T std_R_lp (t) and rounded to c0 for elements whose absolute value is greater than c0. That is, T offset_R_std (t) represents the deflection component that approaches c0 over time from when the train enters the bridge, remains constant at c0 after reaching c0, and converges to 0 over time when the train exits the bridge.

[0178]

number

[0179] The estimated deflection at the observation point is T EO_R From the relationship shown in equation (54), the inventors determine that T EO_R (t) is expressed as c1 and the estimated value T using the deflection model as shown in the following equation (61). std_R (t) and T offset_R_std (t) and is thought to be expressed as the sum of.

[0180]

number

[0181] Figure 20 shows the time series data of the deflection amount u(t) actually measured at the observation point of the bridge and the normalized deflection amount T at the observation point derived from the deflection model.std_R (t) is the estimated deflection at the observation point, T, derived from equation (61). EO_R The horizontal axis of the graph in FIG. 20 indicates time, and the vertical axis indicates the amount of deflection. The solid line in FIG. 20 indicates T EO_R (t). The dotted line graph shows u(t). Looking at Figure 20, the estimated value T EO_R It was confirmed that (t) accurately reconstructs u(t).

[0182] From this, the inventors have come up with the following method for deriving the amount of deflection at a specified position. Here, the position from which the deflection amount is derived is the distance L from the entrance end to the exit end on the bridge. B r x Suppose the position of is specified, where r x = 0.05. Here, the normalized deflection amount at the specified position derived using the deflection model is T std_rx Let (t) be the fundamental frequency and above. std_rx (t) to T std_rx_lp (t) Far away. That is, T std_rx_lp The deflection T restored by adding c0 to the product of (t) and coefficient c1 Estd_rx_lp (t), the inventors can determine T std_rx_lp (t), using coefficients c1 and c0, T Estd_rx_lp (t) and T std_rx_lp (t) and the amplitude ratio of T std_rx_lp (t) and calculate the offset in the same way as in equation (60), and calculate T in the same way as in equation (61). std_rx We came up with a method of deriving the amount of deflection at a specified position by adding the calculated offset to the product of (t) and c1.

[0183] The steps of this method carried out by the inventors are described below. The inventors std_rx (t) is obtained, and the obtained T std_rxFor (t), a low-pass filter is applied to attenuate the components above the fundamental frequency to obtain T std_rx_lp (t) was obtained. Then, the inventors calculated T std_rx_lp Amplitude of (t) h rx The amplitude h rx Shows.

[0184]

number

[0185] In equation (62), t1 and t2 are the start time and end time of any period during which vibration occurs on the bridge due to the passage of a train. In this embodiment, t1 and t2 are respectively T std_rx_lp (t) is the start time and end time of the period set within the shift period. That is, t1 and t2 are the start and end times of the period set within the shift period. std_rx_lp The absolute value of (t) is within a range of a predetermined width centered on a value greater than a predetermined value. For example, t1 and t2 are the transit periods t s (Entry time t i Exit time t o The start time and end time of a period of a predetermined width (for example, 1 second, 2 seconds, etc.) in the center of the period from the entry time t i to a given period (e.g., transit period t s The time when a certain percentage (10%, 30%, etc.) of the time has elapsed, the exit time t o to a given period (e.g., transit period t s The time may be a period of time that is a predetermined percentage (10%, 30%, etc.) of the time in the past. In this way, the inventors use equation (62) to calculate T std_rx_lp The average value of (t) is taken as the amplitude h rx was derived as:

[0186] The inventors have applied a low-pass filter process to the time series data u(t) to attenuate components above the fundamental frequency, lp (t) and the estimated normalized deflection at the observation point T derived using the deflection model. std_R (t) is processed by a low-pass filter to attenuate the components above the fundamental frequency, std_R_lp Based on (t) and (55), the coefficients c1 and c0 were derived using equations (55) and (56).

[0187] T Estd_rx_lp Let us consider the amplitude of (t). T Estd_rx_lp (t) is the linear function shown in equation (53) with the argument T std_R_lp T instead of (t) std_rx_lp The value substituted for (t), i.e., T std_rx_lp (t) and the coefficient c1 plus c0. Therefore, T Estd_rx_lp (t) and T std_rx_lp (t) is the amplitude ratio of the time function R r_rx (t) is expressed as follows in equation (63).

[0188]

number

[0189] Function R r_rx (t) is shown in FIG. 22. Here, T std_rx_lp Since (t) shifts from t1 to t2, the denominator and numerator of the right-hand side of equation (63) are almost constant during the period from t1 to t2, and R r_rx The value of (t) is also almost constant. In other words, during the period from t1 to t2, R r_rx The absolute value of the amplitude ratio at each time indicated by (t) is within a predetermined range centered on a value equal to or greater than a predetermined value. Here, R r_rx The average amplitude ratio of (t) is R r_rx The amplitude ratio R r_rx is expressed as the following equation (64).

[0190]

number

[0191] Also, T Estd_rx_lp The amplitude of (t) is T std_rx_lp Amplitude of (t) h rx The amplitude ratio R r_rx is T Estd_rx_lp Amplitude of (t) and T std_rx_lp Amplitude of (t) h rx It can also be expressed as the ratio of

[0192]

number

[0193] The inventors have determined that t1, t2, R r_rx Based on (t), the amplitude ratio R r_rx Here, h rx , c1, c0, the amplitude ratio R r_rx It is possible to derive T std_rx_lp (t) R r_rx Deflection T multiplied by r_rx was derived.

[0194]

number

[0195] In addition, R in Eq. (65) r_rx , T Estd_rx_lp (t)(T std_rx_lp (t) and the product of coefficient c1 and c0 (t) std_rx_lp (t) and the deflection amount T r_rx can be derived.

[0196]

number

[0197] In addition, the approach time t i Before exit time t o After that, c0=0, and T r_rx may be expressed as the following equation (68).

[0198]

number

[0199] Then, the inventors used Equation (69) to calculate the derived T r_rx Based on this, the deflection offset T at the specified position offset_rx (t) was derived. That is, the inventors rounded the elements whose absolute values ​​are greater than c0 to c0. r_rx , T offset_rx (t).

[0200]

number

[0201] Figure 23 shows the derived T offset_rx The horizontal axis of the graph in FIG. 23 indicates time, and the vertical axis indicates the amount of deflection. The solid line in FIG. 23 indicates T offset_rx (t). The dotted line graph shows T r_rx (t) is shown in Fig. 23. offset_rx It is shown that the value of (t) approaches c0 over time as the train enters the bridge, remains constant at c0 for a certain period of time, and then converges to 0 over time as the train exits the bridge. Then, the inventors use the following equation (70) to calculate the coefficient c1 and T std_rx (t) and the product, T offset_rx (t) to obtain the estimated deflection T EO_rx (t) was derived. The derived value T EO_rx (t) and the estimated deflection at the observation point T derived from equation (61). EO24. In the graph of FIG. 24, the horizontal axis represents time, and the vertical axis represents the amount of deflection.

[0202]

number

[0203] The derivation system 10 of this embodiment derives the amount of deflection of a unit bridge girder at a specified position 9 based on the method devised by the inventors.

[0204] (2-1-3) Element details: The measuring device 1 and the sensor device 2 of this embodiment are similar to those of the first embodiment. The server device 3 of this embodiment is similar to those of the first embodiment, except for the function of the deflection deriving unit 306. Details of the deflection deriving unit 306 of this embodiment will be described below.

[0205] The deflection deriving unit 306, like the first embodiment, calculates the time series data u(t) and the first index value T std_R (t) and the second index value T std_rx (t) and derives an estimate of the deflection of the unit girder at the specified position 9 based on the above. The control unit 300 calculates the second index value T std_rx By applying a low-pass filter to (t), which attenuates the components above the fundamental frequency, the second index value T std_rx_lp Specifically, the control unit 300 calculates T std_rx The control unit 300 performs an FFT on (t) and identifies a peak corresponding to the minimum frequency from the FFT result excluding side lobe peaks caused by the window function used in the FFT. Then, the control unit 300 calculates the frequency corresponding to the identified peak as the fundamental frequency F f Then, using equation (36), we obtain the interval k mf The control unit 300 derives the derived k mf Based on T std (t) to T std_rx (t) and replace it with T std_lp (t) to T std_rx_lp(t) and using equation (37), T std_rx_lp However, the control unit 300 does not include another FIR filter that attenuates components of the fundamental frequency or higher. std_rx By multiplying it by (t), T std_rx_lp (t) may also be obtained.

[0206] In addition, the control unit 300 std_R By applying a low-pass filter to (t), which attenuates the components above the fundamental frequency, T std_R_lp Specifically, the control unit 300 calculates T std_R The control unit 300 performs an FFT on (t) and identifies a peak corresponding to the minimum frequency from the FFT result excluding side lobe peaks caused by the window function used in the FFT. Then, the control unit 300 calculates the frequency corresponding to the identified peak as the fundamental frequency F f Then, using equation (36), we obtain the interval k mf The control unit 300 derives the derived k mf Based on T std (t) to T std_R (t) and replace it with T std_lp (t) to T std_R_lp (t) and using equation (37), T std_R_lp However, the control unit 300 does not include another FIR filter that attenuates components of the fundamental frequency or higher. std_R By multiplying it by (t), T std_R_lp (t) may also be obtained.

[0207] The control unit 300 uses the equation (62) to calculate T std_rx_lp The amplitude h, which is the average value of (t) from t1 to t2 rx t1 and t2 are the transit periods t s (Entry time t i Exit time t o The start time and end time of a period of a predetermined width (for example, 1 second, 2 seconds, etc.) in the center of the period up to the end of the current time (the period up to the current time), but may be other periods.

[0208] The control unit 300 lp (t) and Tstd_R_lp (t) and t a (t i ) and t b (t o ) and the coefficients c1 and c0 are derived using equations (55) and (56). That is, the control unit 300 derives the coefficients c1 and c0 shown in equation (54), T std_R_lp (t) is the argument, and u lp Derive the coefficients c1 and c0 of the linear function that returns (t). T std_R_lp (t) is the first index value T std_R This is an example of a quantity corresponding to (t). lp (t) is an example of a quantity corresponding to the time series data u(t). The control unit 300 calculates c1, c0, and h rx Based on this, we use equation (63) to apply the linear function shown in equation (53) with T as an argument. std_R_lp T instead of (t) std_rx_lp (t) is substituted into the value T Estd_rx_lp (t) and T std_rx_lp (t) and the amplitude ratio function R r_rx That is, the control unit 300 derives T std_rx_lp The deflection T restored by adding c0 to the product of (t) and coefficient c1 Estd_rx_lp (t) and T std_rx_lp (t) and the amplitude ratio function R r_rx Then, the control unit 300 derives t1, t2, T std_rx_lp Based on (t), we use equation (64) to calculate R r_rx (t) Average amplitude ratio R r_rx R derived using equation (64) r_rx is the second low-pass filtered index value, T std_rx_lp (t) is substituted as an argument of a linear function with a first-order coefficient c1 and a zeroth-order coefficient c0, and T std_rx_lp (t) is the average value of this amplitude ratio during a period in which the value of the amplitude ratio falls within a predetermined range. However, the control unit 300 is rx Based on this, the amplitude ratio R r_rx We can derive R using equation (65). r_rxis the second low-pass filtered index value, T std_rx_lp This is the average amplitude over the period during which the value of (t) falls within a predefined range. The control unit 300 uses the equation (66) to calculate T std_rx_lp (t) R r_rx Deflection T multiplied by r_rx However, the control unit 300 derives T std_rx_lp Based on (t), c1, and c0, the deflection amount T is calculated using equation (67). r_rx The control unit 300 may also derive the entry time t i Before exit time t o After that, c0=0, and T r_rx may be calculated as in equation (68).

[0209] Then, the control unit 300 calculates the derived T r_rx Based on this, the offset T of the deflection amount at the specified position 9 is calculated using equation (69). offset_rx That is, the control unit 300 derives T(t) with the absolute value of the element larger than c0 rounded to c0. r_rx , offset T offset_rx The control unit 300 derives the coefficient c1 and T std_rx (t) plus offset T offset_rx (t) to obtain the estimated deflection T EO_rx Derive (t).

[0210] As described above, with the configuration of this embodiment, the derivation system 10 can derive the amount of deflection of a unit bridge girder at a specified position 9 different from the observation point.

[0211] (2-2) Derivation process: The process of the derivation system 10 of this embodiment is the same as that of the first embodiment, except for the process of S125 in the process of Fig. 19 in the first embodiment. The process of this embodiment that differs from the first embodiment will be described. In S125, the control unit 300 determines, by the function of the deflection deriving unit 306, T std_rxBy applying a low-pass filter to (t), which attenuates the components above the fundamental frequency, T std_rx_lp (t). The control unit 300 also calculates T std_R By applying a low-pass filter to (t), which attenuates the components above the fundamental frequency, T std_R_lp Find (t).

[0212] The control unit 300 uses the equation (62) to calculate T std_rx_lp Amplitude of (t) h rx The control unit 300 derives u lp (t) and T std_R_lp (t) and t a (t i ) and t b (t o ) and derives the coefficients c1 and c0 using equations (55) and (56). Estd_rx_lp (t) i.e. c1T std_rx_lp (t)+c0 and T std_rx_lp Based on (t) and (63), the amplitude ratio function R r_rx Then, the control unit 300 derives R r_rx Derive: The control unit 300 uses the equation (66) to calculate T std_rx_lp (t) R r_rx Deflection T multiplied by r_rx The control unit 300 derives the derived T r_rx Based on this, the offset T of the deflection amount at the specified position 9 is calculated using equation (69). offset_rx Then, the control unit 300 derives the coefficient c1 and T std_rx (t) and the product, T offset_rx (t) to obtain the estimated deflection T EO_rx Derive (t).

[0213] (3) Other embodiments: The above embodiment is an example for carrying out the present invention, and various other embodiments can be adopted. The method for deriving the amount of deflection at a specified position from the displacement at an observation point as in the above embodiment can also be realized as a program invention or a method invention.

[0214] Furthermore, a configuration may be adopted in which the functions of the server device 3 are realized by a plurality of devices. The functions of the server device 3 may be distributed and implemented in a plurality of devices. Also, the functions of the server device 3 may be implemented in other devices. For example, the functions of the acquisition unit 301, the environmental information acquisition unit 302, the time derivation unit 303, the number acquisition unit 304, the index value acquisition unit 305, and the deflection derivation unit 306 may be implemented in the measurement device 1. A configuration in which the server device 3 exists distributed in a plurality of devices may also be adopted. Furthermore, the above-mentioned embodiment is merely an example, and an embodiment in which some configurations are omitted or other configurations are added may be adopted.

[0215] In the above-mentioned first and second embodiments, the derivation system 10 derives the deflection amount of a bridge through which a railway train 6 formed of one or more railway cars passes. However, the derivation system 10 may derive the deflection amount of a bridge through which another formed moving body moves. For example, the derivation system 10 may derive the deflection amount of a bridge through which a formed trolley having one or more trolleys connected thereto, a trailer having multiple cars connected thereto, etc. passes. The derivation system 10 may also derive the deflection amount of a structure other than a bridge, such as a foundation that supports a railway track.

[0216] In addition, in the above-described first and second embodiments, the number of sensor devices 2 included in the derivation system 10 is two, but the number may be one, or three or more.

[0217] In the above-described first and second embodiments, the control unit 300 acquires, as the time-series data u(t), data on displacement (deflection) measured from acceleration detected via the acceleration sensor 210. However, the control unit 300 may acquire, as u(t), data on bridge displacement derived from physical quantities detected via sensors such as an impact sensor, a pressure sensor, a strain gauge, an image measuring 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 placed at the observation point of the bridge 5 via the image measuring device, and acquire data on the detected displacement. In addition, the control unit 300 may acquire, as u(t), data on a physical quantity different from the displacement of the bridge. For example, the control unit 300 may acquire, as u(t), the number of pixels indicating the amount of displacement of a predetermined object placed at the observation point of the bridge 5 in an image photographed via the image measuring device.

[0218] In the above-described first and second embodiments, the control unit 300 identifies a peak corresponding to the lowest frequency from the result of the FFT on the time series data u(t) acquired by the function of the acquisition unit 301, excluding a side lobe caused by the influence of the window function used in the FFT, and determines the identified peak as the fundamental frequency F f However, the control unit 300 takes into consideration the effect of noise that occurs in the result of the FFT for u(t) and calculates the fundamental frequency F f For example, the control unit 300 may determine, from the result of the FFT on u(t), a peak equal to or higher than a predetermined threshold value corresponding to the lowest frequency, excluding a side lobe caused by the effect of the window function used in the FFT, and calculate the fundamental frequency F f It may be calculated as:

[0219] In the above-described first embodiment, the control unit 300 determines the first index value T std_R (t) and the second index value T std_rx The controller 300 derives an estimate of the amount of deflection at the designated position 9 by multiplying the average value Ravg of the ratio to (t) by the time series data u(t). However, the controller 300 may derive an estimate of the amount of deflection at the designated position 9 by other methods. For example, the control unit 300 determines the first index value T std_R The value obtained by multiplying (t) by Ravg may be derived as an estimate of the amount of deflection at the specified position 9.

[0220] Alternatively, the control unit 300 may derive the estimated value of the amount of deflection at the specified position 9 as follows. std_R_lp Then, the control unit 300 derives T std_R_lp Based on (t), c1, and c0, using equation (58), T Estd_R_lp Derive (t). The control unit 300 lp From (t), data on the amount of deflection for a period of a predetermined length (e.g., 1 second, 2 seconds, etc.) is extracted, and if the absolute value of the average value of the extracted data is equal to or greater than a predetermined threshold value, and the absolute value of the difference between the maximum and minimum values ​​of the extracted data is equal to or less than a predetermined width, the control unit 300 determines the extracted period as the period during which the amount of deflection is shifting. The control unit 300 may also accept, via an operation unit or the like of the server device 3, a specification of the start time and end time of the period during which the amount of deflection is shifting. The control unit 300 then sets the order of observation of the earliest amount of deflection in the period during which the amount of deflection is shifting as k0. The control unit 300 also sets the value obtained by subtracting k0 from the order of observation of the latest amount of deflection in the period during which the amount of deflection is shifting as N. The control unit 300 then calculates a value between k0, N, and T. std_R_lp (t) and T Estd_R_lp Based on (t) and (59), the amplitude ratio R r Derive: The control unit 300 determines the amplitude ratio R r and T std_R_lp Based on (t) and (60), the offset T offset_R_std The control unit 300 derives c1 and T std_R (t) and T offset_R_std Based on (t), the estimated deflection at the observation point T is calculated using equation (61). EO_R Then, the control unit 300 derives T EO_RThe value obtained by multiplying (t) by Ravg may be derived as an estimate of the amount of deflection at the specified position 9.

[0221] The time series data may be data acquired at a data rate that is at least twice the frequency of vibrations that are expected to occur in the structure due to the movement of the train moving body.

[0222] Furthermore, the present invention can be applied as a program or method executed by a computer. The above-mentioned program and method may be realized as a single device or may be realized by using parts of multiple devices, and include various aspects. In addition, the invention can be modified as appropriate, such as being partly software and partly hardware. Furthermore, the invention can also be realized as a recording medium for a program. Of course, the recording medium for the program may be a magnetic recording medium or a semiconductor memory, and any recording medium developed in the future can be considered in the same way. [Explanation of symbols]

[0223] 1...measuring device, 2...sensor device, 3...server device, 4...communication network, 5...bridge, 6...railroad train, 7...superstructure, 7a...bridge deck, 7b...bearing, 7c...rail, 7d...sleeper, 7e...ballast, F...deck, G...main girder, 8...substructure, 8a...pier, 8b...abutment, 10...derivation system, 100...control unit, 110...storage unit, 120...communication unit, 200...control unit, 210...acceleration sensor, 220...storage unit, 230...communication unit, 300...control unit, 301...acquisition unit, 302...environmental information acquisition unit, 303...time derivation unit, 304...number acquisition unit, 305...index value acquisition unit, 306...deflection derivation unit, 310...storage unit, 320...communication unit

Claims

1. An acquisition step of acquiring time series data including a physical quantity occurring at a predetermined observation point in the structure as a response to a movement of a structure by a train of one or more mobile units; an environmental information acquisition step of acquiring, as environmental information, information on a structure length, which is the length of the structure, a moving body length, which is the length of the moving body, and an installation position of a contact portion of the moving body with the structure; a time derivation step of deriving an entry time and an exit time of the train of moving bodies with respect to the structure based on the time series data; a number acquisition step of acquiring the number of the moving bodies organized in the organized moving body; an index value acquisition step of acquiring a first index value which is an index value of the amount of deflection of the structure occurring at the observation point and a second index value which is an index value of the amount of deflection at a specified position on the structure, based on the number, the entry time, the exit time, and the environmental information; a deflection deriving step of deriving an estimated value of a deflection amount of the structure at the position based on the time-series data, the first index value, and the second index value; A derivation method including:

2. 2. The derivation method according to claim 1, wherein in the time derivation step, the entry time and the exit time are derived by performing a process for each of the entry time and the exit time to obtain a time within a period after one of two times corresponding to two consecutive data sets that sandwich a predetermined threshold and before the other time, the two times being included in the time series data that has been subjected to low-pass filter processing that attenuates vibration components at frequencies equal to or higher than a fundamental frequency of the time series data.

3. In the deflection deriving step, deriving the estimated value based on a first-order coefficient and a zeroth-order coefficient of a linear function that obtains an approximation of the quantity corresponding to the time-series data when a quantity corresponding to the first index value is substituted into an argument between the entry time and the exit time, and based on the second index value; the amount corresponding to the time series data is an amount obtained by attenuating frequency components of the time series data that are equal to or higher than a fundamental frequency of the time series data, 3. The method according to claim 1, wherein the amount corresponding to the first index value is an amount obtained by attenuating, from the first index value, frequency components equal to or higher than the fundamental frequency of the first index value.

4. 4. The method according to claim 3, wherein in the deflection derivation step, the estimated value is derived as a sum of an offset, which is a portion of the estimated value that is not proportional to the second index value, derived based on the second index value and a coefficient of the linear function, and a product of a first-order coefficient of the linear function and the second index value.

5. 5. The method according to claim 4, wherein the offset is a product of an average value of an amplitude ratio between a value obtained by substituting, as an argument of the linear function, the second index value that has been subjected to low-pass filtering, which attenuates frequency components equal to or higher than the fundamental frequency of the second index value, and the second index value that has been subjected to the low-pass filtering, during a period in which the value of the amplitude ratio falls within a range of a predetermined width, and the second index value, and is a value rounded to the value of the zeroth-order coefficient of the linear function for elements whose absolute values ​​are greater than the zeroth-order coefficient of the linear function.

6. 5. The method according to claim 4, wherein the offset is a product of the second index value and an amplitude ratio of a value obtained by substituting, as an argument of the linear function, an average amplitude of the second index value during a period in which the value of the second index value, after being subjected to a low-pass filter process that attenuates frequency components equal to or higher than the fundamental frequency of the second index value, falls within a predetermined range, and the amplitude, and is a value rounded to the value of the zeroth-order coefficient of the linear function for elements whose absolute values ​​are greater than the zeroth-order coefficient of the linear function.

7. 2. The method according to claim 1, wherein in the deflection derivation step, the estimated value is derived based on an average value of a ratio between a predetermined amount corresponding to the first index value and a predetermined amount corresponding to the second index value during a period from the entry time to the exit time, and on the time series data.

8. 8. The method according to claim 1, wherein in the number acquisition step, a value obtained by subtracting 1 from the product of the period from the entry time to the exit time and the fundamental frequency of the time series data and rounding the product to an integer is acquired as the number.

9. The method according to claim 1 , wherein the structure is a bridge.

10. The method according to claim 1 , wherein the moving body is a railway vehicle that moves the structure via wheels.

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

12. The method according to claim 1 , wherein Bridge Weight in Motion (BWIM) is applicable to the structure.

13. an acquisition unit that acquires time series data including a physical quantity occurring at a predetermined observation point in a structure as a response to a movement of a structure by a mobile unit formed of one or more mobile units; an environmental information acquisition unit that acquires, as environmental information, 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 of the moving body with the structure; a time derivation unit that derives an entry time and an exit time of the formed moving body with respect to the structure based on the time series data; a number acquisition unit that acquires the number of the moving bodies organized in the organized moving body; an index value acquisition unit that acquires a first index value, which is an index value of the amount of deflection of the structure occurring at the observation point, and a second index value, which is an index value of the amount of deflection at a specified position in the structure, based on the number, the entry time, the exit time, and the environmental information; a deflection deriving unit that derives an estimated value of a deflection amount of the structure at the position based on the time-series data, the first index value, and the second index value; A derivation device comprising:

14. A derivation system including a derivation device and a sensor, The delivery device is an acquisition unit that acquires time-series data including a physical quantity generated at a predetermined observation point in a structure as a response to a movement of a structure of a composed mobile unit, the physical quantity being measured via the sensor; and an environmental information acquisition unit that acquires, as environmental information, 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 of the moving body with the structure; a time derivation unit that derives an entry time and an exit time of the formed moving body with respect to the structure based on the time series data; a number acquisition unit that acquires the number of the moving bodies organized in the organized moving body; an index value acquisition unit that acquires a first index value, which is an index value of the amount of deflection of the structure occurring at the observation point, and a second index value, which is an index value of the amount of deflection at a specified position in the structure, based on the number, the entry time, the exit time, and the environmental information; a deflection deriving unit that derives an estimated value of a deflection amount of the structure at the position based on the time-series data, the first index value, and the second index value; A derivation system comprising:

15. On the computer, An acquisition step of acquiring time series data including a physical quantity occurring at a predetermined observation point in the structure as a response to a movement of a structure by a train of one or more mobile units; an environmental information acquisition step of acquiring, as environmental information, information on a structure length, which is the length of the structure, a moving body length, which is the length of the moving body, and an installation position of a contact portion of the moving body with the structure; a time derivation step of deriving an entry time and an exit time of the train of moving bodies with respect to the structure based on the time series data; a number acquisition step of acquiring the number of the moving bodies organized in the organized moving body; an index value acquisition step of acquiring a first index value which is an index value of the amount of deflection of the structure occurring at the observation point and a second index value which is an index value of the amount of deflection at a specified position in the structure, based on the number, the entry time, the exit time, and the environmental information; a deflection deriving step of deriving an estimated value of a deflection amount of the structure at the position based on the time-series data, the first index value, and the second index value; A program for executing the above.

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