DERIVATION METHOD, DERIVATION DEVICE, DERIVATION SYSTEM, AND PROGRAM

Abstract

To solve the problem in which it has been impossible to determine the dynamic response at a specified location of a structure.SOLUTION: A dynamic response at a designated position is derived based on a normalized deflection amount by a vibration component of the dynamic response, an amplitude ratio which is the ratio of a first deflection amount and a second deflection amount, the first deflection amount being a normalized deflection amount indicating a distribution of vibration amplitude at an observation point and the second deflection amount being a normalized deflection amount indicating a distribution of vibration amplitude at the designated position, a vibration component at the designated position derived based on the vibration component and the amplitude ratio, and a static response at the designated position derived based on the time-series data and the estimated value.SELECTED DRAWING: Figure 35

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 and dynamic response components 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] A train or other such configured mobile unit, which is composed of one or more mobile units, may move across a structure such as a bridge. In such a case, the movement of the successive mobile units configured in the configured mobile unit may cause vibrations in the structure. Depending on the natural frequency of the structure, the structure may resonate with the vibrations caused by the movement of the configured mobile unit. For the purpose of diagnosing the structure, etc., there is a demand to obtain a dynamic response at a specified position on the structure where no observation is made. However, Patent Documents 1 and 2 are unable to obtain a dynamic response at a specified position on the structure where no observation is made. [Means for solving the problem]

[0005] The derivation method for solving the above problems includes: an acquisition step of acquiring time-series data including a physical quantity generated at a predetermined observation point in the structure as a response caused by a structured mobile body formed by one or more mobile bodies moving the structure; an environmental information acquisition step of acquiring information on the structure length which is the length of the structure, the mobile body length which is the length of the mobile body, and the installation position of the contact portion between the mobile body and the structure as environmental information; a time derivation step of deriving the entry time and the exit time of the structured mobile body with respect to the structure based on the time-series data; a number acquisition step of acquiring the number of the mobile bodies formed in the structured mobile body; an estimated value acquisition step of acquiring an estimated value of the deflection amount of the observation point of the structure due to the static response generated as the response based on the number, the entry time, the exit time, the environmental information, and the deflection model of the structure; a deflection derivation step of deriving the dynamic response at the designated position based on the vibration component of the dynamic response which is the difference between the time-series data and the estimated value, the model, the normalized deflection amount due to the vibration component of the dynamic response, the first deflection amount which is the normalized deflection amount indicating the distribution of the vibration amplitude of the observation point, the amplitude ratio which is the ratio of the first deflection amount to the second deflection amount which is the normalized deflection amount indicating the distribution of the vibration amplitude of the designated position of the structure, the vibration component at the designated position derived based on the vibration component and the amplitude ratio, and the static response at the designated position derived based on the time-series data and the estimated value. The derivation device for solving the above problems includes: an acquisition unit that acquires time-series data including a physical quantity generated at a predetermined observation point in the structure as a response caused by a structured mobile body formed by one or more mobile bodies moving the structure; an environmental information acquisition unit that acquires information on the structure length which is the length of the structure, the mobile body length which is the length of the mobile body, and the installation position of the contact portion between the mobile body and the structure as environmental information; a time derivation unit that derives the entry time and the exit time of the structured mobile body with respect to the structure based on the time-series data; a number acquisition of the number of the mobile bodies formed in the structured mobile body Departmentan estimate acquisition unit that acquires an estimate of an amount of deflection of the observation point of the structure due to a static response occurring as the response based on the number, the entry time, the exit time, the environmental information, and a model of the deflection of the structure; and a deflection derivation unit that derives the dynamic response at the designated position based on a vibration component of a dynamic response that is the difference between the time series data and the estimate, a normalized deflection amount due to the vibration component of the dynamic response derived based on the model, an amplitude ratio that is the ratio between a first deflection amount that is the normalized deflection amount indicating a distribution of vibration amplitude at the observation point and a second deflection amount that is the normalized deflection amount indicating a distribution of vibration amplitude at a designated position that is a designated position of the structure, the vibration component of the designated position derived based on the vibration component and the amplitude ratio, and the static response of the designated position derived based on the time series data and the estimate. A derivation system for solving the above problem includes a derivation device and a sensor, and the derivation device includes 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 composed moving body, which is composed of one or more moving bodies, and the physical quantity 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, a time derivation unit that derives an entry time and an exit time of the composed moving body with respect to the structure based on the time series data, and a number acquisition unit that acquires the number of the moving bodies composed in the composed moving body. Departmentan estimate acquisition unit that acquires an estimate of an amount of deflection of the observation point of the structure due to a static response occurring as the response based on the number, the entry time, the exit time, the environmental information, and a model of the deflection of the structure; and a deflection derivation unit that derives the dynamic response at the designated position based on a vibration component of a dynamic response that is the difference between the time series data and the estimate, a normalized deflection amount due to the vibration component of the dynamic response derived based on the model, an amplitude ratio that is the ratio between a first deflection amount that is the normalized deflection amount indicating a distribution of vibration amplitude at the observation point and a second deflection amount that is the normalized deflection amount indicating a distribution of vibration amplitude at a designated position that is a designated position of the structure, the vibration component of the designated position derived based on the vibration component and the amplitude ratio, and the static response of the designated position derived based on the time series data and the estimate. A program for solving the above problem includes, on a computer, an acquisition step of acquiring time series data including physical quantities occurring at a predetermined observation point on a structure as a response to a structure movement of a composed moving body, which is composed of one or more moving bodies, through the structure; an environmental information acquisition step of acquiring 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; a time derivation step of deriving an entry time and an exit time of the composed moving body with respect to the structure based on the time series data; a number acquisition step of acquiring the number of moving bodies composed in the composed moving body; and calculating the response based on the number, the entry time, the exit time, the environmental information, and a model of the deflection of the structure. and a deflection derivation step of deriving the dynamic response at the designated position based on a normalized deflection due to the vibration component of the dynamic response derived based on a vibration component of the dynamic response which is the difference between the time series data and the estimated value and the model, an amplitude ratio which is the ratio between a first deflection which is the normalized deflection indicating a distribution of vibration amplitude at the observation point and a second deflection which is the normalized deflection indicating a distribution of vibration amplitude at a designated position which is a designated position of the structure, the vibration component of the designated position derived based on the vibration component and the amplitude ratio, and the static response of the designated position derived based on the time series data and the estimated 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. 13 is a diagram showing an estimated value of the amount of deflection. [Figure 16] FIG. 1 shows the amplitude at a specified position. [Figure 17] FIG. [Figure 18] FIG. [Figure 19] FIG. 13 is a diagram showing an estimated value of the amount of deflection. [Figure 20] FIG. 13 is a diagram showing the amount of deflection due to resonance. [Figure 21] FIG. 13 is a diagram showing an FFT result of the amount of deflection due to resonance. [Figure 22] FIG. 1 is a diagram showing a primary wave. [Diagram 23] FIG. 13 is a diagram showing a tertiary wave. [Figure 24] FIG. 13 is a diagram showing the amplitude of a primary wave. [Diagram 25] FIG. 13 is a diagram showing the amplitude of a primary wave. [Figure 26] FIG. 13 is a diagram showing the amplitude of a primary wave. [Figure 27] FIG. 13 is a diagram showing the amplitude of the tertiary wave according to the normalized deflection amount according to an equation based on the bridge structure. [Figure 28] FIG. 13 is a diagram showing the amplitude of a third wave approximated by a sine wave. [Figure 29] FIG. 11 is a diagram showing a derived primary wave component. [Diagram 30] FIG. 13 is a diagram showing derived third-order wave components. [Diagram 31] FIG. 13 is a diagram showing the dynamic response of an observation point and the derived dynamic response of a specified position. [Diagram 32] FIG. 2 is a diagram showing details of each element of the derivation system. [Diagram 33] 11A and 11B are diagrams for explaining a process of deriving an entry time and an exit time. [Diagram 34] 11A and 11B are diagrams for explaining a process of deriving an entry time and an exit time. [Diagram 35] 13 is a flowchart showing a derivation process. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

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

[0008] (1) Configuration of the derivation system: (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 dynamic response that occurs at a designated position 9, which is a designated position different from the observation point on the bridge 5, of a dynamic response that occurs on the bridge 5 due to the passage of the railway train 6 based on time-series data of physical quantities at a predetermined observation point on the bridge 5 on which the railway train 6, which is a train composed of one or more railway cars, moves. The railway train 6 is an example of a train of moving bodies. 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 the moving body moves. Each of the railway cars 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 the 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 truss bridge, an RC bridge, etc. RC is the abbreviation of Reinforced-Concrete. Further, in this embodiment, the bridge 5 is a structure to which BWIM (Bridge Weigh In Motion) can be applied. BWIM is a technology that measures the weight, the number of axles, etc. of a moving body passing through a bridge by regarding the bridge as a "scale" and measuring the deformation of the bridge. A bridge capable of analyzing the weight of a moving body passing through from responses such as the deformation and strain of the bridge is considered a structure to which BWIM can be applied. Therefore, it is possible to measure the weight of a moving body moving on the bridge by a BWIM system that applies the physical process between the action on the bridge and the response. The measurement of the weight of the moving body is performed by previously measuring the correlation coefficient between displacement and load, and deriving the load of the moving body passing through using the correlation coefficient from the measurement result of the displacement of the bridge when the moving body passes through.

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

[0012] The sensor device 2 is used 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 designated on the bridge 5 as a target for deriving the dynamic response that occurs in a unit girder of the bridge 5 due to the passage of a railway train 6 .

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

[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 train C 1 The wheel of one axle of the first railcar (the first railcar from the front of the railcar train) enters the unit bridge girder. In the following, the exit time, which is the time when the railcar exits the unit bridge girder, is defined as t o Here, the exit of a train from a unit bridge girder is defined as the exit of a train C N The wheel of the rear axle of the rearmost train car (the rearmost train car) exits the unit bridge girder. In the following, the period during which the train passes through the unit bridge girder (entrance time t i Exit 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, which is the length of the unit bridge girder, is referred to as L B The bridge length is an example of the length of a structure. The distance from the end of the unit bridge girder in the longitudinal direction on the side where the train is approaching to the observation point is defined as L x In Figure 3, B and L x In the following, the end of the unit girder in the longitudinal direction that is on the side where the train is approaching is referred to as the approach end. In the following, the end of the unit girder in the longitudinal direction that is on the side where the train is leaving is referred to as the exit end. In addition, the length of the m-th 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)~ar (N) to a r In 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 this case, from axis 1 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 the first axle of the leading railway vehicle C1 of the railway vehicle to the last axle a N of the last railway vehicle C r (N), the distance is D wa (a w (N, a r (N))). D wa (a w (N, a r (N))) is used to calculate the average speed v of the railway train passing through the unit bridge girder a which is expressed by the following formula (4).

[0025]

Number

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

[0027]

Number

[0028] Subsequently, the deflection occurring in the unit bridge girder when a load is applied to the unit bridge girder will be described. Fig. 5 shows a schematic diagram of the unit bridge girder. Fig. 5 shows a situation where a load P is applied to the bridge. Here, the unit bridge girder is modeled as a simple beam supported at both ends. Also, the distance between the position where the load P is applied to the unit bridge girder and the entry end is represented by a. Also, the distance between the position where the load P is applied to the unit bridge girder and the exit end is represented by b. In this case, the bending moment at the position where the load P is applied to the unit bridge girder is expressed by the following formula (6).

[0029]

Number

[0030] Figure 6 shows the bending moment at each position of a unit girder due to load P. As shown in Figure 6, the bending moment generated in a unit girder due to load P is zero 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 a unit girder due to load P decreases proportionally as it approaches the exit end from the position where load P is applied, reaching zero at the exit end. Therefore, the bending moment at any position X in a unit girder 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 a unit girder 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 unit girder 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] g1 and g2 in equation (11) are constant terms. Here, the unit girder is supported at the entrance end and exit end, so there is no deflection at the entrance end and exit end. 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 unit girder in the longitudinal direction, the maximum deflection of the unit girder due to the application of load P occurs at the center of the unit girder 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 unit girder 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 unit girder in the longitudinal direction, so x = 0.5L B In this case, since x≦a, from equation (8), Ha = 0. x = 0.5L B , a=b=0.5L B , H a By substituting =0 into equation (14), the deflection w 0.5l The following equation (15) is obtained.

[0046]

number

[0047] w 0.5l is used to normalize the deflection at any position in the unit girder expressed by equation (14). 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 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 position of the load P is on the retreat end side of the position X, that is, when x≦a, from equation (8), 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 amount 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 unit bridge girder, 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 unit girder through the wheel (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 wAn 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 a r A pair of wheels on each of the (m) axles moves along the unit bridge girder. 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, that is, 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 indicated.

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

[0081]

number

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

[0083] (1-3) Verification experiment: The inventors have determined that the deflection amount T std (t) was calculated. That is, N=4, t i =7.21[seconds], t o =8.777[seconds], 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. stdBy performing a fast Fourier transform (FFT) on (t), T std The intensity of each frequency component in (t) was calculated. T std The 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 fThe inventors have found that the wave number ν of the fundamental frequency F f It 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 mf Using 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 (Entry time t i Exit time t o T std_hpThe 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_hp The 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 the following, we will 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], LC = 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].

[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 m The 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)~C std (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 when 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 sBased 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 in a railway train 6 based on time-series data u(t) of the deflection of a bridge 5 measured at an observation point, using knowledge gained through experiments.

[0124] In addition, the inventors calculated the actual deflection amount T(t) at a certain position on the bridge based on the deflection amount T std The deflection amount is proportional to (t) and the deflection amount T that is not proportional to the deflection amount derived by the deflection model offset That is, the inventors came up with the idea of ​​approximating T(t) by adding T std The idea was to approximate it as a linear function of (t). 1 is a first-order coefficient. Here, the part proportional to the deflection derived from the deflection model is the displacement proportional to the load in the unit girder to which the BWIM is applicable.

[0125]

number

[0126] The inventors used u lp (t) is T with a linear coefficient of c1 as shown in the following equation (50). std_R_lp It was thought that it could be approximated as a linear function of (t). T std_R_lp (t) is the normalized deflection amount T at the observation point derived using the deflection model. std_R This is the value obtained by applying a low-pass filter process to (t) to attenuate components above the fundamental frequency. 0 is the zeroth order coefficient and indicates the displacement that is assumed to be independent of the position of the observation point.

[0127]

number

[0128] The error is calculated by subtracting the right side of equation (50) from the left side. The least squares method is used to minimize this error, c 1 , c 0 The derivation of Equation (51) and Equation (52) below results.

[0129]

number

[0130]

number

[0131] t in Equation (51) and Equation (52) 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 the formulas (51) and (52) is a value expressed by the following formula (53).

[0132]

number

[0133] As shown on the right side of equation (50), T std_R_lp (t), coefficient c 1 , c 0 The deflection amount restored using T Estd_R_lp (t) and so on. T Estd_R_lp (t) is as shown in the following equation (54). Here, t <t i , t>to During the period, since the train is not on the unit bridge girder, there is no deflection. 0 Set it to =0.

[0134]

number

[0135] T Estd_R_lp (t) and T std_R_lp (t) and the amplitude ratio R r is calculated as shown in the following equation (55). 0 is the deflection amount u lp n is a value indicating the number of observations of the earliest observed deflection amount during the period when the waveform of (t) is deflected and shifted. Also, n is the deflection amount u lp From the value indicating which observation value is the latest observed deflection value during the period in which the waveform of (t) shifts, k 0 That is, n is the value obtained by subtracting u lp The latest observed deflection during the shift of the waveform (t) is k 0 +nth observation.

[0136]

number

[0137] The inventors have determined the offset T offset_R_std (t) is expressed as R r and T std_R_lp (t) and its absolute value is c 0 For elements greater than c 0 We assume that the value is rounded to T offset_R_std (t) is the time lapse of the train from the entry of the bridge to the 0 and the value approaches c 0 After reaching c 0 and converges to zero over time as the rail train exits.

[0138]

number

[0139] The estimated deflection at the observation point, which is a static response caused by the passage of a railway train and is not due to resonance, is defined as T EO_R Here, the static response indicates the deflection caused by the load of a moving object passing over the bridge. The static response does not include the deflection caused by the resonance of the bridge excited by the passage of a moving object. The dynamic response is the sum of the static response and the deflection caused by resonance. From the relationship expressed in equation (50), the inventors have determined that T EO_R (t) as shown in the following equation (57), c 1 and the estimated value T using the deflection model std_R (t) and T offset_R_std (t) and .

[0140]

number

[0141] Figure 15 shows the time series data u(t) of the deflection actually measured at the bridge observation point and the normalized deflection T at the observation point derived from the deflection model. std_R (t) to the static response estimate T, which is the deflection calculated using equation (57) EO_R The horizontal axis of the graph in FIG. 15 indicates time, and the vertical axis indicates the amount of deflection. The solid line in FIG. 15 indicates T EO_R The dotted line graph shows u(t). In Fig. 15, the estimated value T EO_R It is shown that u(t) accurately restores u(t). In the example of Figure 15, the natural frequency of the bridge is not close to the frequency of the vibration caused on the bridge by the passage of a train, so no resonance occurs on the bridge due to the passage of a train.

[0142] The inventors also came up with the following method for deriving the amount of deflection of the static response at a specified position other than the observation point position in a unit bridge girder. Here, the position from which the deflection amount is derived is the distance L from the entry end to the exit end on the unit bridge girder. B ×r x Suppose the position of is specified, where r x = 0.05. Here, L in equations (20), (21), (22) and (25) x L B ×r x The normalized deflection amount at the specified position derived using the deflection model replaced by T std_rx Let (t) be the fundamental frequency and above. std_rx (t) to T std_rx_lp (t) Far away. Here, the coefficient c derived at the observation point position of the unit bridge girder 1 , c 0 Using T std_rx_lp (t) and coefficient c 1 and the product c 0 The deflection restored by adding Estd_rx_lp Let (t). The inventors define T std_rx (t), T std_rx_lp (t), coefficient c 1 , c 0 The inventors have come up with a method of deriving a deflection amount indicating a static response at a specified position using the above equation.

[0143] 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_rx For (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 use the following formula (58) to calculate T std_rx_lp Amplitude of (t) h rx The amplitude h rx Shows.

[0144]

number

[0145] In equation (58), t 1 , t 2 are the start time and end time of an arbitrary period during which vibration occurs on the bridge due to the passage of a railway train. 1 , t 2 are respectively, T std_rx_lp Let (t) be the start and end times of the period that is being shifted. That is, t 1 , t 2 are respectively, T std_rx_lp The period during which the value of (t) falls within a predefined range centered on a value whose absolute value is greater than a predefined value. For example, t 1 , t 2 are the transit period 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 t 1 , t 2 are the approach 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 (58) to calculate t 1 From 2 T in the period up to std_rx_lp The average value of (t) is taken as the amplitude h rx was derived as:

[0146] 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), the coefficient c is calculated using equations (51) and (52). 1 , c 0 was derived.

[0147] T Estd_rx_lp Let us consider the amplitude of (t). T Estd_rx_lp (t) is T std_rx_lp (t) and coefficient c 1 and the product c 0 Therefore, T Estd_rx_lp (t) and T std_rx_lp (t) is the amplitude ratio of the time function R r_rx is expressed as the following equation (59).

[0148]

number

[0149] Function R r_rx (t) is shown in FIG. 17. Here, T std_rx_lp (t) is t 1 From 2 Since the shift occurs in the period up to t 1 From 2 During the period up to , the denominator and numerator of the right-hand side of equation (59) are almost constant, and R r_rx The value of (t) is also almost constant. 1 From 2 The period until r_rx The period during which the absolute value of the amplitude ratio at each time indicated by (t) falls within a predetermined range centered on a value equal to or greater than a predetermined value. Here, t 1 From 2 R in the period up to r_rx The average amplitude ratio of (t) is R r_rx The amplitude ratio R r_rx is expressed as the following equation (60).

[0150]

number

[0151] Also, T Estd_rx_lp The amplitude of (t) is T std_rx_lp Amplitude of (t) h rx and c 1 and the product c 0 Therefore, 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 to the following equation (61):

[0152]

number

[0153] The inventors 1 , t 2 , R r_rx Based on (t), the amplitude ratio R r_rx Here, h rx , c 1 , c 0 Based on this, 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 (t) was derived.

[0154]

number

[0155] In addition, R in Eq. (62) r_rx , T Estd_rx_lp (t)(T std_rx_lp (t) and coefficient c 1 and the product c 0 (plus T std_rx_lp (t) and the deflection amount T r_rx can be derived.

[0156]

number

[0157] In addition, the approach time t i Before exit time t o later than c 0 = 0, T r_rx may be expressed as the following equation (64).

[0158]

number

[0159] Then, the inventors used Equation (65) 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 derived 0 For elements greater than c 0 Rounded to T r_rx , T offset_rx (t).

[0160]

number

[0161] Figure 18 shows the derived T offset_rx The horizontal axis of the graph in FIG. 18 indicates time, and the vertical axis indicates the amount of deflection. The solid line in FIG. 18 indicates T offset_rx (t). The dotted line graph shows T r_rx (t) is shown in Fig. 18. offset_rx The value of (t) changes with time from the train's entry onto the bridge. 0 Approaching c for a certain period of time 0 It is shown that the eigenvalue remains constant at 0 over time as the rail train exits. Then, the inventors use the following equation (66) to calculate the coefficient c 1 and T std_rx (t) and the product, Toffset_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 (57). EO_R 19. The horizontal axis of the graph in FIG. 19 represents time, and the vertical axis represents the amount of deflection.

[0162]

number

[0163] In this way, the amount of deflection, which is the static response of the unit girder at the specified position 9, can be derived.

[0164] The inventors came up with the idea of ​​obtaining the vertical vibration component due to resonance occurring on a bridge when a train passes by subtracting an estimated value of the amount of deflection (static response) at the observation point, derived using a deflection model, from the time series data of the dynamic response measured at the observation point of the bridge. Hereinafter, the vertical vibration component due to resonance occurring on a bridge when a moving object passes is referred to as the vibration component of the dynamic response. Hereinafter, the vibration component of the dynamic response of a bridge when a train passes is simply referred to as the vibration component. The amount of deflection due to the vibration component of the dynamic response at the observation point is referred to as u nv (t) Far away. That is, the inventors calculate an estimated value T of the amount of deflection not due to resonance, which is a static response at the observation point, from the time series data u(t) of the dynamic response measured at the observation point, as shown in the following equation (67). EO_R By subtracting (t), the deflection (vibration component) u due to resonance at the observation point is obtained. nv In Figure 20, we can derive T from u(t). EO_R The vibration component u derived by subtracting (t) nv 20 shows an example of (t). The horizontal axis of the graph in Fig. 20 shows time, and the vertical axis shows the amount of deflection. The observation point is located at the center of the bridge in the direction of travel of the train.

[0165]

number

[0166] In addition, the inventors have determined that the vibration component u nv Based on (t), we came up with a method to derive the amount of deflection of the dynamic response due to resonance at a specified position on a bridge by doing the following: The steps of this method carried out by the inventors are described below.

[0167] The inventors have determined that the vibration component u nv We performed FFT on (t). Figure 21 shows u nv 21 shows the results of FFT for (t). The horizontal axis of the graph in Fig. 21 shows frequency, and the vertical axis shows the intensity of the corresponding frequency component. The inventors nv From the FFT results for (t), the peak with the smallest corresponding frequency (the peak indicated by the solid arrow in the example of FIG. 21) was identified among the peaks whose intensity is equal to or greater than a predetermined threshold. The inventors then identify 2.79167 Hz, which is the frequency corresponding to the identified peak, as the fundamental frequency of the vibration component of the dynamic response of the bridge's resonance. Hereinafter, the fundamental frequency of the vibration component of the bridge is simply referred to as the fundamental frequency. The inventors also nv From the results of FFT for (t), another peak (the peak indicated by the dotted arrow in the example of FIG. 21) whose intensity is equal to or greater than a predetermined threshold value was identified. The inventors then determined that the identified peak corresponds to a tertiary wave component with a frequency three times the fundamental frequency, since the frequency corresponding to the identified peak is 8.3542 Hz, which is approximately three times the fundamental frequency (2.79167 Hz). In the following, the fundamental frequency and its harmonics in the vibration components of the dynamic response generated in the bridge due to resonance are defined as the natural frequency of the unit bridge girder. In the following, the component with a frequency that is a natural number q times the fundamental frequency is defined as the qth wave. From this, the inventors nv The main components of (t) were identified as the fundamental frequency component and a component with a frequency three times the fundamental frequency (third-order wave).

[0168] The inventors performed a band-pass filter process to extract the component of the fundamental frequency for u nv (t), and extracted the component of the fundamental frequency included in u nv (t). In the following, the component of the q-th harmonic wave included in u nv (t) is denoted as u nv_q (t). For example, the component of the fundamental frequency included in u nv (t) is u nv_1 (t). Also, the inventors performed a band-pass filter process to extract the component of the harmonic frequency three times the fundamental frequency for u nv (t), and extracted the component of the third harmonic wave u nv (t) included in u nv_3 (t). Fig. 22 and Fig. 23 show the extracted u nv_1 (t) and u nv_3 (t), respectively. The horizontal axis of each graph in Fig. 22 and Fig. 23 represents time, and the vertical axis represents the amount of deflection.

[0169] When the load position a from the access end in the bridge exists on the left side of the observation point position x (here, the position of l / 2 of the bridge), from equation (8), H a = 1 because x > a. Therefore, substituting x = 1 / 2 and Ha = 1 into equation (14) and assuming a + b = l, the following equation (68) showing the deflection amount w L of the observation point caused by the left load is obtained. Here, l is a variable representing the length of the bridge.

[0170]

Equation

[0171] Also, when the load position a from the access end in the bridge exists on the right side of the observation point, from equation (8), H a = 0 because x < a. Therefore, substituting x = l / 2 and Ha = 0 into equation (14), the following equation (69) showing the deflection amount w R of the observation point caused by the right load is obtained.

[0172]

number

[0173] In addition, when the load position on the bridge is the position of the central observation point, H from equation (8) is obtained from x = a. a = 0. Therefore, by substituting x = l / 2 and Ha = 0 into equation (14), the deflection amount w P The following equation (70) can be obtained.

[0174]

number

[0175] In a model of a simple beam bridge supported at both ends, the deflection is maximum when the load is applied to the center of the bridge when the observation point is at the center. Therefore, the maximum deflection w of the bridge caused by the load is max Similarly to equation (70), it is expressed as the following equation (71).

[0176]

number

[0177] w shown in equation (68) L w shown in equation (71) max By dividing by w max When normalized by , the following equation (72) is obtained.

[0178]

number

[0179] In equation (72), if we set a / l=r and normalize the load position by the bridge length, we obtain the following equation (73).

[0180]

number

[0181] In addition, w shown in equation (69) R w shown in equation (71) max By dividing by w max When normalized by , the following equation (74) is obtained.

[0182]

number

[0183] Here, a / l=r, a+b=l, so b=l(1-r). Substituting b=l(1-r) into equation (74) and normalizing the bridge length to l=1, we obtain the following equation (75).

[0184]

number

[0185] When the bridge length is normalized to 1, the normalized deflection amplitude w observed at the center of the bridge when a load moves on the bridge is std is expressed as the following equation (76), which combines equations (73) and (75).

[0186]

number

[0187] In equation (76), r and (1-r) respectively indicate the ratio of the distance from the end of the bridge to the load position to the bridge length. As shown in the following equation (77), we define a variable A that combines r and (1-r).

[0188]

number

[0189] Using A shown in equation (77), equation (76) can be expressed as the following equation (78).

[0190]

number

[0191] In Figure 24, std In the graph of FIG. 24, the horizontal axis indicates r, and the vertical axis indicates normalized amplitude. FIG. 25 shows the waveform of a sine wave sin(rπ). In FIG. 25, the horizontal axis indicates r, and the vertical axis indicates amplitude. The inventors found that the waveforms shown in FIG. 24 and FIG. 25 are similar. The inventors then found that w std We found that it can be approximated as sin(rπ).

[0192] Due to resonance, the bridge generates vibration components of the dynamic response due to resonance, including the fundamental frequency component and harmonic components that are natural number multiples of the fundamental frequency of two or more. These components become sine wave vibrations with nodes at both ends of the bridge. Therefore, if a specified position on the bridge is a position at a distance lr from the approach end toward the exit end, the normalized deflection amount w, which indicates the distribution of vibration amplitudes that show the vibration amplitudes of the qth wave at the specified position, is q_std (r) can be approximated as sin(qrπ) as shown in the following equation (79).

[0193]

number

[0194] sin(rπ) and equation (78) are approximate. Therefore, the normalized deflection w, which shows the distribution of vibration amplitude including the fundamental frequency component and the harmonic frequency component, q_std In the range 0≦r≦1, (r) is expressed by the following equation (80).

[0195]

number

[0196] The model of the normalized deflection amount indicating the distribution of vibration amplitude in this embodiment is an equation based on the structure of a simple beam-like bridge. Here, the position of the observation point is set to a position at a distance lR from the entrance end to the exit end. Also, the position on the bridge designated as the target for deriving the deflection amount is set to a position at a distance lr x Located far away. By substituting q = 1 and r = R into equation (80), the inventors obtained the deflection amount w, which is the amplitude of the normalized primary wave (component of the fundamental frequency) at the observation point. 1_std (R). The inventors also found that q=1, r=r x By substituting into equation (80), the deflection amount w, which is the normalized amplitude of the primary wave at the specified position, is obtained. 1_std (r x ) was sought. The ratio Cr between the deflection amount, which is the amplitude of the qth wave at the observation point, and the deflection amount, which is the amplitude of the qth wave at the specified position q is expressed as follows: q_std (R) and w q_std (r x ) and is calculated as a ratio.

[0197]

number

[0198] Here, the deflection amount u due to the vibration component at the observation point nv (t) mainly includes the first wave component and the third wave component. Therefore, the inventors used equation (81) to calculate the ratio Cr 1 Figure 26 shows the r x = 0.1, R = 0.5 1_std (R), w 1_std (r x ) in Fig. 26. The horizontal axis of Fig. 26 indicates r, and the vertical axis indicates the normalized deflection amount that shows the distribution of vibration amplitude. In this case, w 1_std (R) is calculated as 1 by substituting q = 1 and R = 0.5 into equation (81). 1_std (r x ) is q=1, r x= 0.1 into equation (81), we get 0.296. Therefore, Cr 1 is calculated as 0.296 / 1, which is 0.296.

[0199] The q-th wave component of the vibration component deflection at the specified position is expressed as u nv_q_rx (t) and far away. nv_q_rx (t) is the deflection amount u due to resonance at the observation point as shown in the following equation (82). nv The qth wave component u in (t) nv_q (t) Cr q This can be found by multiplying by

[0200]

number

[0201] The inventors calculated the Cr as shown in formula (82). 1 To,u nv_1 (t) to obtain the fundamental frequency component due to the dynamic response at the specified position, u nv_1_rx (t) was derived.

[0202] In addition, the inventors used Equation (81) to calculate the ratio Cr of the deflection due to the third wave of the vibration component of the dynamic response at the observation point to the deflection due to the third wave of the vibration component at the specified position. 3 Figure 27 shows the r x = 0.1, R = 0.5 3_std (R), w 3_std (r x ) in Fig. 27. The horizontal axis of Fig. 27 indicates r, and the vertical axis indicates the amount of deflection, which is the amplitude of the normalized amount of deflection that indicates the distribution of the vibration amplitude. In this case, w 3_std (R) is calculated as -1 by substituting q3 and R = 0.5 into equation (81). 3_std (r x ) is q3, r x = 0.1 into equation (81), we get 0.809. Therefore, Cr 1 is calculated as 0.809 / 1, which is 0.809. x= 0.1, R = 0.5, using equation (79) 3_std (R), w 3_std (r x 28, the horizontal axis represents r, and the vertical axis represents the amplitude of normalized deflection, which indicates the distribution of vibration amplitude. Then, the inventors calculated the Cr as shown in formula (82). 3 To,u nv_3 (t) to obtain the third wave component of the deflection of the vibration component of the dynamic response at the specified position, u nv_3_rx (t).

[0203] The u derived in Figure 29 nv_1_rx The horizontal axis of the graph in FIG. 29 indicates time, and the vertical axis indicates the amount of deflection. nv_3_rx 30. The horizontal axis of the graph in FIG. 30 represents time, and the vertical axis represents the amount of deflection.

[0204] The inventors derived u nv_1_rx (t) and u nv_3_rx The sum of (t) and (t) was calculated as an estimate of the vibration component of the dynamic response at the specified position. That is, as shown in the following equation (83), the derived qth wave u nv_q_rx From the sum of (t), the vibration component u at the specified position nv_q_est (t) was derived.

[0205]

number

[0206] The inventors then use the deflection model to estimate the static response at a specified location, T EO_rx (t) and the estimated vibration component of the dynamic response u nv_q_est (t) and the dynamic response T at the specified position is calculated as shown in the following equation (84). EST_rx (t) estimate T EST_rx We found that it is possible to obtain (t).

[0207]

number

[0208] In Figure 31, EO_rx (t) and u nv_1_rx (t) and u nv_3_rx The horizontal axis of the graph in FIG. 31 indicates time, and the vertical axis indicates the amount of deflection. The solid line graph in FIG. 31 indicates T EO_rx (t) and u nv_1_rx (t) and u nv_3_rx The dotted line in Fig. 31 indicates the amount of deflection u(t).

[0209] The derivation system 10 of this embodiment derives a dynamic response at a specified position 9 of a unit bridge girder due to the passage of a railway train 6, based on a method devised by the inventors.

[0210] (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. 32. In this embodiment, the position of the designated position 9 in the unit bridge girder is a distance L B ×r x Here, r x , L B This value indicates the ratio of the distance from the entry end to the designated position 9 in the unit bridge girder.

[0211] 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.

[0212] 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.

[0213] 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.

[0214] 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.

[0215] The server device 3 derives a dynamic response at the specified position 9 based on the deflection of the observation point measured by the measurement device 1. The server device 3 is an example of a derivation device. The server device 3 includes a control unit 300, a storage unit 310, and a communication unit 320. The control unit 300 includes a processor such as a CPU, a ROM, a RAM, and the like. 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 estimated 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 detected deflections, and the like. The communication unit 320 includes a circuit used for wired or wireless communication with an external device.

[0216] 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.

[0217] 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.

[0218] 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 o The 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:

[0219] 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 formula (85): mf Derive.

[0220]

number

[0221] 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, we use the following equation (86) to calculate u lp Derive (t). u lp (t) is data of multiple discrete values, just like u(t), which is data of multiple discrete values.

[0222]

number

[0223] 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, lpFrom (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:

[0224] However, the threshold C L may be other values. For example, the threshold C L may 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.

[0225] In Figure 33, u lp (t) and threshold C L The horizontal axis of the graph in FIG. 33 indicates time (t=kΔT), and the vertical axis indicates the amount of deflection. The solid line graph in FIG. 33 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 34, u lp (t) and C L The horizontal axis of the graph in FIG. 34 indicates time, and the vertical axis indicates the amount of deflection. Each black dot in FIG. 34 indicates the time lp (t) shows the discrete value data included in the lpThe 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 In the example of Fig. 34, 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. 33, 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. 33 are also identified, and the later of the two times corresponding to the identified two pieces of data is identified.

[0226] Then, the control unit 300 sets the earlier of the identified times as the entry time t i In addition, the control unit 300 derives the later of the identified times as the exit time t o In the example of FIG. 33, 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:

[0227] 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 LTwo 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. 34, 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:

[0228] Also, u lp C in (t) L For two consecutive data that sandwich the L For example, in the example of FIG. 34, 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. 34, 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:

[0229] In this embodiment, the control unit 300 lpThe 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.

[0230] 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:

[0231] 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 sand 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.

[0232] 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.

[0233] 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 aand 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.

[0234] The estimated value acquisition unit 305 receives the number N and the entry time t i and exit time t o Based on the environmental information, the deflection amount of the structure occurring at the observation point is calculated as an estimated value T EO_R This is a function to obtain (t). The control unit 300, by using the function of the estimated value acquisition unit 305, calculates an estimated value T std_R Specifically, the control unit 300 derives t 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 LB 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 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).

[0235] 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 The control unit 300 derives the derived T std (t) is the normalized deflection amount T std_R Obtained as (t).

[0236] 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_RThe 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 T based on the derived kmf. 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.

[0237] The control unit 300 lp (t) and T std_R_lp Based on (t), using equations (51) and (52), u shown in equation (50) is calculated. lp (t) approximation T std_R_lp Coefficient c of a linear function with (t) as an argument 1 , c 0 Here, t a is the approach time t i In addition, t b is the exit time t o Let us assume that. The control unit 300 calculates T std_R_lp (t), coefficient c 1 , c 0 The deflection amount restored using T Estd_R_lp The control unit 300 calculates T Estd_R_lp (t) and T std_R_lp (t) and the amplitude ratio R r Derive.

[0238] The control unit 300 is r and T std_R_lp Based on (t) and (56), the offset T offset_R_stdDerive (t). Then, the control unit 300 1 and T std_R (t) and T offset_R_std Based on (t) and (57), T EO_R Derive (t).

[0239] The deflection deriving unit 306 calculates an amplitude ratio, which is a ratio between a first deflection amount of a vibration component of a dynamic response at an observation point that occurs in a unit bridge girder in response to the passage of a railway train 6 and a second deflection amount that is a deflection amount at a specified position 9 due to the vibration component of this dynamic response, time series data u(t), and an estimated value T EO_R (t) and a function for deriving the vibration component of the dynamic response at a specified position 9 based on the above.

[0240] The control unit 300 calculates T from u(t) using the equation (67) by using the function of the deflection calculation unit 306. EO_R By subtracting (t), the vibration component u of the dynamic response at the observation point is nv The control unit 300 acquires u nv Perform FFT on (t) and nv From the results of the FFT for (t), the control unit 300 identifies peaks whose intensity is equal to or greater than a predetermined threshold. The control unit 300 then identifies the peak with the smallest corresponding frequency among the identified peaks, and identifies the frequency corresponding to the identified peak as the fundamental frequency of the natural frequency of the unit bridge girder. The control unit 300 also identifies the corresponding frequency for each of the other identified peaks. The control unit 300 then derives a value for each identified frequency by dividing the frequency by the fundamental frequency and rounding it to a natural number. The control unit 300 then calculates each derived natural number and 1 into u nv A natural number indicating the order of the frequency of the component in (t) (how many times the fundamental frequency it is), that is, how many times the frequency of the component in (t) is nv The degree is obtained as a natural number indicating whether the degree is included in (t). In the following, the natural number obtained here is referred to as the degree obtained.

[0241] The control unit 300 sequentially sets each acquisition order to q and nvBy applying a bandpass filter to (t) to extract the frequency components that are q times the fundamental frequency, the qth order component u nv_q Extract (t). The control unit 300 sequentially sets each acquired order to q, and calculates the deflection amount w, which indicates the amplitude distribution of the vibration of the q-th order wave on the unit bridge girder normalized at the observation point, using equation (80) based on q and r = R. q_std That is, the control unit 300 derives the first deflection amount w (R) as the first deflection amount. q_std (R). The control unit 300 sequentially derives each acquisition order as q and r=r x Based on this, the normalized deflection amount w due to the qth wave at the specified position 9 is calculated using equation (80). q_std (r x That is, the control unit 300 derives the amplitude of the designated position 9 of the deflection amount, which indicates the amplitude distribution on the unit girder of the vibration of the frequency that is a natural number q times the fundamental frequency among the vibration components of the dynamic response, as the second deflection amount w q_std (r x ) is derived as

[0242] The control unit 300 sequentially calculates the first deflection amount w q_std (R) and the second deflection w q_std (r x ) and the ratio Cr q Derive. Then, the control unit 300 sequentially sets each acquisition order to q and calculates the component u of the q-th wave as shown in equation (82). nv_q (t) and ratio Cr q The product of this and the q-th wave component u of the vibration component at the specified position 9 nv_q_rx The control unit 300 derives the u nv_q_rx (t) are added together using equation (83) to derive an estimate of the vibration component of the dynamic response at the specified position 9, and then the static response and vibration component at the specified position 9 are added together using equation (84) to derive an estimate of the dynamic response.

[0243] As described above, with the configuration of this embodiment, the deriving system 10 can derive the vibration component of the dynamic response at the specified position 9 in the structure. Depending on the position of the observation point, it may not be possible to measure the amplitude of some components contained in the vibration components of the dynamic response. For example, if the observation point is the center of the bridge, components of frequencies that are even multiples of the fundamental frequency (e.g., second-order waves, fourth-order waves, etc.) cannot be measured because the center of the unit bridge girder becomes a node of the waveform and no displacement occurs. In this way, for the q-th order wave component, the distance from the approach end to the exit end is L B The nodes of the waveform occur at the positions (n / q) (n is an integer from 0 to q). Therefore, the distance from the entrance end to the exit end is L B At the position (n / q), the qth wave component cannot be measured. Therefore, the control unit 300 calculates the q-th wave component u of the dynamic response at the specified position 9. nv_q_rx When deriving (t), the distance from the entrance end to the exit end is L B All we need to do is use time series data u(t) measured at a position different from the position of (n / q). Furthermore, the control unit 300 can derive more q-order wave components at the specified position 9 by using time-series data u(t) measured at a plurality of different observation points. In addition, when the vibration components of the dynamic response to be derived are determined in advance, the control unit 300 may use the time series data u(t) measured at a position where these components can be measured. For example, when the components to be derived are the first wave, second wave, and third wave components, the control unit 300 may use the distance L B (1 / 3) position, distance L from entrance end to exit end B (1 / 2) position, distance L from entrance end to exit end B All we need to do is use time series data u(t) measured at a location other than the (2 / 3) location.

[0244] (2) Derivation process: The process of deriving the vibration component of the dynamic response at the specified position 9 executed by the server device 3 will be described with reference to Fig. 35. The server device 3 starts the process of Fig. 35 in response to the transmission of displacement data at the observation point from the measurement device 1, but may start the process of Fig. 35 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 c Then, 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.

[0245] 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 lpFrom (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:

[0246] 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. i The 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.

[0247] 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.

[0248] In S120, the control unit 300 calculates t i , t o Using equation (1), ts 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 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).

[0249] 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 The control unit 300 derives the derived Tstd (t) is the normalized deflection amount T std_R Obtained as (t).

[0250] 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 The control unit 300 calculates u lp (t) and T std_R_lp Based on (t), using equations (51) and (52), u shown in equation (50) is calculated. lp (t) approximation T std_R_lp Coefficient c of a linear function with (t) as an argument 1 , c 0 Here, t a is the approach time t i In addition, t b is the exit time t o Let us assume that. The control unit 300 calculates T std_R_lp (t), coefficient c 1 , c 0 The deflection amount restored using T Estd_R_lp The control unit 300 calculates T Estd_R_lp (t) and T std_R_lp (t) and the amplitude ratio R r Derive:

[0251] The control unit 300 is r and T std_R_lp Based on (t) and (56), the offset T offset_R_std Derive (t). Then, the control unit 300 1 and T std_R (t) and T offset_R_std Based on (t) and (57), T EO_R (t) is derived. S120 is an example of an estimation value obtaining step.

[0252] In S125, the control unit 300 calculates T from u(t) using the function of the deflection calculation unit 306 by using the formula (67). EO_RBy subtracting (t), the vibration component u of the dynamic response at the observation point is obtained. nv (t) is acquired. The control unit 300 performs FFT on u nv (t), and identifies peaks with an intensity equal to or greater than a predetermined threshold from the FFT result of u nv (t). Then, the control unit 300 identifies the peak with the smallest corresponding frequency among the identified peaks, and identifies the frequency corresponding to the identified peak as the fundamental frequency of the natural frequency of the unit bridge girder. In addition, the control unit 300 also identifies the corresponding frequency for each of the other identified peaks. Then, for each of the identified frequencies, the control unit 300 derives a value obtained by dividing the frequency by the fundamental frequency and rounding it to a natural number. Then, the control unit 300 acquires each of the derived natural numbers and 1 as the acquisition order.

[0253] The control unit 300 sequentially sets each acquisition order as q, and performs band-pass filter processing on u nv (t) to extract the component u nv_q (t) of the q-th wave by extracting the component of the frequency that is q times the fundamental frequency. The control unit 300 sequentially sets each acquisition order as q and r = R, and uses Equation (80) to derive the normalized deflection amount w q_std (R) due to the q-th wave at the observation point. In addition, the control unit 300 sequentially sets each acquisition order as q and r = r x , and uses Equation (80) to derive the normalized deflection amount w q_std (r x ) due to the q-th wave at the specified position 9.

[0254] The control unit 300 sequentially sets each acquisition order as q, and uses Equation (81) to derive the ratio Cr q_std between w q_std (R) and w x (r q ). Then, the control unit 300 sequentially sets each acquisition order as q, and as shown in Equation (82), the product of the component u nv_q (t) of the q-th wave and the ratio Cr q is used as the component u of the q-th wave of the vibration component of the dynamic response at the specified position 9.nv_q_rx The control unit 300 derives the u nv_q_rx (t) are summed using equation (83) to obtain the estimated value u nv_q_est S125 is an example of a step of deriving the deflection.

[0255] (3) Other embodiments: The above embodiment is an example for carrying out the present invention, and various other embodiments can be adopted. The method of deriving the amount of deflection due to resonance 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.

[0256] 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 estimated 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.

[0257] In the above-described embodiment, 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.

[0258] Also, in the above-described embodiment, the number of sensor devices 2 included in the derivation system 10 is assumed to be two, but it may be one, or may be three or more.

[0259] Also, in the above-described embodiment, the control unit 300 acquires, as the time-series data u(t), data of displacement (deflection) measured from the acceleration detected via the acceleration sensor 210. However, the control unit 300 may acquire, as u(t), data of the displacement of the bridge derived from physical quantities detected via sensors such as an impact sensor, a pressure sensor, a strain gauge, an image measurement device, a load cell, and a displacement meter. For example, the control unit 300 may detect the displacement of the observation point by periodically photographing a predetermined object arranged at the observation point of the bridge 5 via the image measurement device, and acquire the detected displacement data. Further, the control unit 300 may acquire, as u(t), data of a physical quantity different from the displacement of the bridge. For example, the control unit 300 may acquire, as u(t), the number of pixels indicating the displacement amount of a predetermined object arranged at the observation point of the bridge 5 in the image photographed via the image measurement device.

[0260] Also, in the above-described embodiment, the control unit 300 excludes the side lobes caused by the influence of the window function used in the FFT from the result of the FFT for the time-series data u(t) acquired by the function of the acquisition unit 301, and specifies the peak corresponding to the lowest frequency, and determines the specified peak as the fundamental frequency F f However, the control unit 300 may determine the fundamental frequency F f in consideration of the influence of the noise generated in the result of the FFT for u(t). For example, the control unit 300 excludes the side lobes caused by the influence of the window function used in the FFT from the result of the FFT for u(t), specifies the peak equal to or higher than a predetermined threshold corresponding to the lowest frequency, and determines the specified peak as the fundamental frequency F f as well.

[0261] In the above embodiment, the deriving system 10 derives the vibration component of the dynamic response at the specified position 9. However, the deriving system 10 further derives the amount of deflection T EO_rx (t) is derived, and the derived vibration component u nv_q_est (t) and static response T EO_rx The deflection amount obtained by adding (t) and (t) may be derived as an estimate of the dynamic response of the specified position 9. For example, the control unit 300 may perform the following: EO_rx (t) may be derived. The control unit 300 is std_R In addition, the control unit 300 acquires a standardized estimated value T std_rx Specifically, the control unit 300 derives 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 , 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 stdBy 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) to T std_rx Obtained as (t).

[0262] The control unit 300 is std_rx By applying a low-pass filter to (t), which attenuates the components above the fundamental frequency, 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 Similarly, the control unit 300 may obtain 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).

[0263] The control unit 300 uses the equation (58) to calculate T std_rx_lp Amplitude of (t) h rx Derive t 1 , t 2 are the transit period t s (Entry time t i Exit time t oThe 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.

[0264] The control unit 300 lp (t) and T std_R_lp Based on (t), the coefficient c is calculated using equations (51) and (52). 1 , c 0 That is, the control unit 300 derives u lp (t) is approximated by T std_R_lp Coefficient c of the linear function for (t) 1 , c 0 The control unit 300 derives c 1 and c 0 and rx Based on this, using equation (59), T std_rx_lp (t) and coefficient c 1 and the product c 0 The deflection T that is restored by adding Estd_rx_lp (t) and T std_rx_lp (t) and the amplitude ratio function R r_rx Then, the control unit 300 derives t 1 , t 2 , T std_rx_lp Based on (t), using equation (60), t 1 From 2 R in the period up to r_rx (t) Average amplitude ratio R r_rx However, the control unit 300 derives c 1 and c 0 and rx Based on this, the amplitude ratio R r_rx may be derived. The control unit 300 uses the equation (62) 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 (t) and c 1 and c 0 Based on this, the deflection amount T is calculated using equation (63). r_rx The control unit 300 may also derive the entry time t i Before exit time to later than c 0 = 0, T r_rx may be calculated as in equation (64).

[0265] 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 (65). offset_rx That is, the control unit 300 derives the absolute value of c 0 For elements greater than c 0 Rounded to T r_rx , offset T offset_rx (t). The control unit 300 derives the coefficient c 1 and T std_rx (t) plus offset T offset_rx (t) to obtain the estimated static response deflection T EO_rx Get (t). In this manner, the control unit 300 EO_rx (t) may be obtained.

[0266] However, the control unit 300 may use another method to estimate the estimated value T EO_rx For example, the control unit 300 may obtain the estimated value T EO_rx (t) may be obtained. The control unit 300 is 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 uses the following equation (87) to calculate T std_R (t) and T std_rx (t) and the ratio R rx_R Derive (t).

[0267]

number

[0268] The control unit 300 1 and 2 and R rx_R Based on (t), the following equation (88) is used to calculate the time t 1 From time t 2 During the period up to T std_R (t) and T std_rx The average value Ravg of the ratio with (t) is derived.

[0269]

number

[0270] However, the control unit 300 sets Ravg at time t 1 From time t 2 T for a period different from the period up to 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 derive the average value of the ratio of t 1 and 2 and i and o and Ravg may be derived using equation (88).

[0271] Then, the control unit 300 multiplies the time series data u(t) by Ravg to obtain an estimated value T EO_rx However, the control unit 300 may obtain the time series data u(t) as R rx_R The value multiplied by the corresponding data included in (t) is the estimated deflection amount T at the specified position 9. EO_rx It may also be derived as (t).

[0272] 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.

[0273] 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]

[0274] 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...estimated 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 estimation value acquisition step of acquiring an estimate of a deflection amount of the structure at the observation point due to a static response occurring as the response, based on the number, the entry time, the exit time, the environmental information, and a model of the deflection of the structure; a deflection derivation step of deriving the dynamic response at the designated position based on a normalized deflection amount due to the vibration component of the dynamic response derived based on a vibration component of the dynamic response which is a difference between the time series data and the estimated value and the model, an amplitude ratio which is a ratio between a first deflection amount which is the normalized deflection amount indicating a distribution of vibration amplitude at the observation point and a second deflection amount which is the normalized deflection amount indicating a distribution of vibration amplitude at a designated position which is a designated position of the structure, the vibration component of the designated position derived based on the vibration component and the amplitude ratio, and the static response of the designated position derived based on the time series data and the estimated value; A derivation method including:

2. The derivation method according to claim 1, wherein the static response of the designated position is an estimate of a deflection amount which is a part of the deflection amount of the structure occurring at the designated position based on the number, the entry time, the exit time, and the environmental information, and which is a static response of the designated position which occurs in the structure in response to the passage of the train moving body.

3. 2. The method according to claim 1, wherein the amplitude ratio is a ratio between the first deflection amount in a standardized deflection amount indicating a distribution of vibration amplitudes derived based on a multiple of the fundamental frequency of the frequency of the vibration component and the position of the observation point, and the second deflection amount in a standardized deflection amount indicating a distribution of vibration amplitudes derived based on a multiple of the fundamental frequency of the frequency of the vibration component and the specified position.

4. In the deflection deriving step, deriving the vibration component at the observation point which is a difference between the time series data and the estimated value which is the static response at the observation point; determining one or more frequencies from the fundamental frequency and harmonic frequencies of the vibrational component, and extracting components of each of the determined frequencies from the vibrational component; deriving the amplitude ratio, which is a ratio between the first deflection amount and the second deflection amount, for each of the frequencies based on the normalized deflection amount of the order of the frequency; deriving, for each of the frequencies, a value obtained by multiplying the component corresponding to the frequency by the corresponding amplitude ratio as the vibration component of the frequency at the specified position; deriving a sum of the vibration components at each of the derived frequencies and the static response at the specified position as the dynamic response at the specified position; A method according to any one of claims 1 to 3.

5. In the deriving of the amplitude ratio in the deflection deriving step, 5. The method according to claim 4, further comprising the steps of: deriving the first deflection amount using equation (1) for a normalized deflection amount in which the order of the frequency is q and the observation point on the structure when the length of the structure is 1 is R for the determined frequency; deriving the second deflection amount using equation (2) for a normalized deflection amount in which the order of the frequency is q and the specified position on the structure when the length of the structure is 1 is r; and deriving a ratio between the derived first deflection amount and the derived second deflection amount as the amplitude ratio. [0010] [0025]

6. In the deriving of the amplitude ratio in the deflection deriving step, For the determined frequency, the first deflection amount is derived using Equation (3) for a normalized deflection amount in which the order of the frequency is q and the observation point on the structure is R when the length of the structure is 1; 5. The method according to claim 4, further comprising the steps of: deriving the second deflection amount using equation (4) for a normalized deflection amount in which the order of the frequency is q and the specified position in the structure when the length of the structure is 1 is r; and deriving a ratio between the derived first deflection amount and the derived second deflection amount as the amplitude ratio. [0030] [0045]

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

8. The method according to any one of claims 1 to 7, wherein the moving body is a railway vehicle that moves the structure via wheels.

9. The method according to claim 1 , wherein the model of the deflection of the structure is an equation based on a structure of the structure.

10. The derivation method according to any one of claims 1 to 9, wherein the equation based on the structure of the structure, including the normalized deflection amount which is the static response and the normalized deflection amount which indicates the distribution of the vibration amplitude, is a simple beam supported at both ends.

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 estimate acquisition unit that acquires an estimate of a deflection amount of the structure at the observation point due to a static response occurring as the response, based on the number, the entry time, the exit time, the environmental information, and a model of the deflection of the structure; a deflection derivation unit that derives the dynamic response at the designated position based on a vibration component of the dynamic response that is a difference between the time-series data and the estimated value and the model, a normalized deflection amount due to the vibration component of the dynamic response, an amplitude ratio that is a ratio between a first deflection amount that is the normalized deflection amount indicating a distribution of vibration amplitude at the observation point and a second deflection amount that is the normalized deflection amount indicating a distribution of vibration amplitude at a designated position that is a designated position of the structure, the vibration component of the designated position derived based on the vibration component and the amplitude ratio, and the static response of the designated position derived based on the time-series data and the estimated 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 estimate acquisition unit that acquires an estimate of a deflection amount of the structure at the observation point due to a static response occurring as the response, based on the number, the entry time, the exit time, the environmental information, and a model of the deflection of the structure; a deflection derivation unit that derives the dynamic response at the designated position based on a vibration component of the dynamic response that is a difference between the time-series data and the estimated value and the model, a normalized deflection amount due to the vibration component of the dynamic response, an amplitude ratio that is a ratio between a first deflection amount that is the normalized deflection amount indicating a distribution of vibration amplitude at the observation point and a second deflection amount that is the normalized deflection amount indicating a distribution of vibration amplitude at a designated position that is a designated position of the structure, the vibration component of the designated position derived based on the vibration component and the amplitude ratio, and the static response of the designated position derived based on the time-series data and the estimated 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 estimation value acquisition step of acquiring an estimate of a deflection amount of the structure at the observation point due to a static response occurring as the response, based on the number, the entry time, the exit time, the environmental information, and a model of the deflection of the structure; a deflection derivation step of deriving the dynamic response at the designated position based on a normalized deflection amount due to the vibration component of the dynamic response derived based on a vibration component of the dynamic response which is a difference between the time series data and the estimated value and the model, an amplitude ratio which is a ratio between a first deflection amount which is the normalized deflection amount indicating a distribution of vibration amplitude at the observation point and a second deflection amount which is the normalized deflection amount indicating a distribution of vibration amplitude at a designated position which is a designated position of the structure, the vibration component of the designated position derived based on the vibration component and the amplitude ratio, and the static response of the designated position derived based on the time series data and the estimated value; A program for executing the above.

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