JP2023037329A - Derivation method, derivation device, derivation system and program - Google Patents

Abstract

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

Description

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

In recent years, many social infrastructures have deteriorated over time, and there is a need for a method of diagnosing the state of structures that constitute social infrastructures, such as railway bridges.
Patent Literature 1 discloses a method for investigating and evaluating the structural performance of a railway bridge, which makes it possible to appropriately investigate and evaluate the structural performance of a bridge using observation data of the acceleration response of the bridge during train travel. In the method for investigating the structural performance of a railway bridge in Patent Document 1, a train is assumed to be a moving load train, a bridge is a simple beam, and a theoretical analysis model for the dynamic response of the railway bridge when the train is running is formulated, and the acceleration of the bridge when the train is running. is measured, and unknown parameters of the theoretical analysis model are estimated from the acceleration data by inverse analysis.
Further, Patent Literature 2 discloses a method of obtaining an impact coefficient (dynamic response component) of a bridge using a vehicle vertical acceleration response of a running train, especially when passing over the bridge.

Patent No. 6543863 Patent No. 6467304

BACKGROUND ART There is a case where a set of moving bodies, such as a railway train, in which one or more moving bodies are organized moves on a structure such as a bridge. In such a case, there is a demand to obtain the amount of deflection at a specified position in the structure for the purpose of diagnosing the structure. When measuring the amount of deflection using a sensor or the like at an observation point on a structure, it was not possible to obtain the amount of deflection at a position other than the observation point. Also, in Patent Documents 1 and 2, the deflection amount at a position different from the observation point could not be obtained.

A derivation method for solving the above problems includes a physical quantity generated at a predetermined observation point in the structure as a response due to the organized moving body in which one or more moving bodies are organized moving through the structure, time series an acquisition step of acquiring data; a structure length that is the length of the structure; a moving body length that is the length of the moving body; an environmental information acquisition step of acquiring information as environmental information; a time derivation step of deriving an entry time and an exit time of the mobile organization with respect to the structure based on the time-series data; an amount of deflection of the structure occurring at the observation point based on a number acquisition step of acquiring the number of the organized mobile bodies, the number, the entry time, the exit time, and the environment information; an index value acquiring step of acquiring a first index value that is an index value of and a second index value that is an index value of the amount of deflection at a specified position in the structure; and a coefficient of a linear function that obtains an approximation of the amount corresponding to the time-series data by substituting the amount corresponding to the first index value for an argument between the entry time and the exit time, and An offset that is a portion of the deflection amount of the structure at the position that is not proportional to the first index value, and a third index value that is a value obtained by subtracting the offset from the time-series data, which is derived based on is the average value of the amplitude in a predetermined period of the second index value and the linear coefficient of the linear function, which is low-pass filtered to attenuate the frequency components equal to or higher than the fundamental frequency of the second index value Derivation of deflection for deriving the sum of the sum of the product of and the zeroth-order coefficient of the linear function divided by the average value as an estimated value of the deflection amount of the structure at the position and the offset is the product of the average value and the second index value, and the zeroth order of the linear function for elements whose absolute values are greater than the zeroth order coefficient of the linear function. is a value rounded to the value of the coefficient of, the amount corresponding to the time-series data is the amount after attenuating the frequency components equal to or higher than the fundamental frequency of the time-series data from the time-series data, and the The amount corresponding to the first index value is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value, and the predetermined period is the second index value. Before low-pass filtering that attenuates frequency components above the fundamental frequency of the index value It is a period in which the value of the second index value falls within the range of the predetermined width.
A derivation method for solving the above problems includes a physical quantity generated at a predetermined observation point in the structure as a response due to the organized moving body in which one or more moving bodies are organized moving through the structure, time series an acquisition step of acquiring data; a structure length that is the length of the structure; a moving body length that is the length of the moving body; an environmental information acquisition step of acquiring information as environmental information; a time derivation step of deriving an entry time and an exit time of the mobile organization with respect to the structure based on the time-series data; an amount of deflection of the structure occurring at the observation point based on a number acquisition step of acquiring the number of the organized mobile bodies, the number, the entry time, the exit time, and the environment information; an index value acquiring step of acquiring a first index value that is an index value of and a second index value that is an index value of the amount of deflection at a specified position in the structure; an average value between the entry time and the exit time of a ratio between a predetermined first amount according to a value and a predetermined second amount according to the second index value; and the first index. and a deflection derivation step of deriving an estimate of the amount of deflection of the structure at the location based on a value, wherein the first quantity is the first index value from the first index value. is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the value, and the second amount is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the second index value from the second index value is.
A derivation device for solving the above problems includes a physical quantity generated at a predetermined observation point in a structure as a response due to movement of an organized mobile body in which one or more mobile bodies are organized. An acquisition unit that acquires data, 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 with the structure on the moving body an environmental information acquisition unit that acquires information as environmental information; a time derivation unit that derives the entry time and exit time of the mobile organization from the structure based on the time-series data; a number acquiring unit that acquires the number of the organized moving bodies; an amount of deflection of the structure occurring at the observation point based on the number, the entering time, the leaving time, and the environmental information; an index value acquisition unit for acquiring a first index value that is an index value of and a second index value that is an index value of the amount of deflection at a specified position in the structure; and the first index and a coefficient of a linear function that obtains an approximation of the amount corresponding to the time-series data by substituting the amount corresponding to the first index value for an argument between the entry time and the exit time, and An offset that is a portion of the deflection amount of the structure at the position that is not proportional to the first index value, and a third index value that is a value obtained by subtracting the offset from the time-series data, which is derived based on is the average value of the amplitude in a predetermined period of the second index value and the linear coefficient of the linear function, which is low-pass filtered to attenuate the frequency components equal to or higher than the fundamental frequency of the second index value Derivation of deflection for deriving the sum of the sum of the product of and the zeroth-order coefficient of the linear function divided by the average value as an estimated value of the deflection amount of the structure at the position and the offset is the product of the average value and the second index value, and the zeroth order of the linear function for the element whose absolute value is larger than the zeroth order coefficient of the linear function is a value rounded to the value of the coefficient of, the amount corresponding to the time-series data is the amount after attenuating the frequency components equal to or higher than the fundamental frequency of the time-series data from the time-series data, and the The amount corresponding to the first index value is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value, and the predetermined period is the second index value. The value of the second index value that has been subjected to low-pass filtering that attenuates frequency components equal to or higher than the fundamental frequency of the index value is within a predetermined width range. It is a period that fits.
A derivation device for solving the above problems includes a physical quantity generated at a predetermined observation point in a structure as a response due to movement of an organized mobile body in which one or more mobile bodies are organized. An acquisition unit that acquires data, 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 with the structure on the moving body an environmental information acquisition unit that acquires information as environmental information; a time derivation unit that derives the entry time and exit time of the mobile organization from the structure based on the time-series data; a number acquiring unit that acquires the number of the organized moving bodies; an amount of deflection of the structure occurring at the observation point based on the number, the entering time, the leaving time, and the environmental information; an index value acquisition unit for acquiring a first index value that is an index value of and a second index value that is an index value of the amount of deflection at a specified position in the structure; and the first index an average value between the entry time and the exit time of a ratio between a predetermined first amount according to a value and a predetermined second amount according to the second index value; and the first index. and a deflection derivation unit for deriving an estimate of the amount of deflection of the structure at the location based on a value, wherein the first amount is the first index value from the first index value. is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the value, and the second amount is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the second index value from the second index value is.
A lead-out system for solving the above-mentioned problems is a lead-out system comprising a lead-out device and a sensor, wherein the lead-out device moves an organized moving body in which one or more moving bodies are organized to move a structure. an acquisition unit that acquires time-series data including the physical quantity measured via the sensor, which is a physical quantity generated at a predetermined observation point in the structure as a response to the movement of the structure, and the length of the structure. an environment information acquisition unit configured to acquire, as environment information, information on a structure length, a moving body length that is the length of the moving body, and an installation position of a contact portion of the moving body that contacts the structure; A time derivation unit for deriving the entry time and the exit time of the organized moving body to the structure based on the series data, a number acquiring unit for acquiring the number of the moving bodies organized in the organized moving body, Based on the number, the entry time, the exit time, and the environmental information, a first index value that is an index value of the amount of deflection of the structure occurring at the observation point, and an index value acquisition unit that acquires a second index value that is an index value of the amount of deflection at a specified position; the amount of deflection of the structure at the position, which is derived based on the coefficient of a linear function that provides an approximation of the amount corresponding to the time-series data when the amount corresponding to the first index value is substituted for the argument; and a third index value, which is a value obtained by subtracting the offset from the time-series data, as a frequency component equal to or higher than the fundamental frequency of the second index value. The sum of the product of the average value of the amplitude in the predetermined period of the second index value subjected to low-pass filtering to attenuate the first order coefficient of the first order function and the zeroth order coefficient of the first order function a deflection deriving unit that derives the sum of the value divided by the average value and the resulting value as an estimated value of the amount of deflection of the structure at the position; and the offset is the average value and the second index. A value rounded to the value of the 0th-order coefficient of the linear function for the element whose absolute value is greater than the 0th-order coefficient of the linear function, corresponding to the time series data The amount is an amount obtained by attenuating frequency components equal to or higher than the fundamental frequency of the time-series data from the time-series data, and the amount corresponding to the first index value is obtained by subtracting the first index value from the is the amount of attenuating frequency components equal to or higher than the fundamental frequency of the first index value, and the predetermined period is the second index value This is a period in which the value of the second index value, which has been subjected to low-pass filter processing for attenuating frequency components equal to or higher than the fundamental frequency of the reference value, falls within a predetermined width range.
A lead-out system for solving the above-mentioned problems is a lead-out system comprising a lead-out device and a sensor, wherein the lead-out device moves an organized moving body in which one or more moving bodies are organized to move a structure. an acquisition unit that acquires time-series data including the physical quantity measured via the sensor, which is a physical quantity generated at a predetermined observation point in the structure as a response to the movement of the structure, and the length of the structure. an environment information acquisition unit configured to acquire, as environment information, information on a structure length, a moving body length that is the length of the moving body, and an installation position of a contact portion of the moving body that contacts the structure; A time derivation unit for deriving the entry time and the exit time of the organized moving body to the structure based on the series data, a number acquiring unit for acquiring the number of the moving bodies organized in the organized moving body, Based on the number, the entry time, the exit time, and the environmental information, a first index value that is an index value of the amount of deflection of the structure occurring at the observation point, and a second index value that is an index value of the amount of deflection at a specified position; an index value obtaining unit that obtains a predetermined first amount and the second index according to the first index value; Deflection of the structure at the location based on the average value between the entry time and the exit time and the first index value of the ratio to a predetermined second amount depending on the value. a deflection deriving unit for deriving an estimated value of the amount, wherein the first amount is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value. , the second amount is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the second index value from the second index value.
A program for solving the above problem is stored in a computer as a response to movement of an organized moving body in which one or more moving bodies are organized, and physical quantities occurring at predetermined observation points in the structure, an acquisition step of acquiring time-series data, 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 with the structure on the moving body; as environment information, a time deriving step of deriving the entry time and the exit time of the moving body from the structure based on the time-series data, and the moving body organized into the moving body. an index of the amount of deflection of the structure occurring at the observation point based on the number, the entering time, the leaving time, and the environmental information; an index value obtaining step of obtaining a first index value that is a value and a second index value that is an index value of the amount of deflection at a specified position in the structure, the first index value; and a coefficient of a linear function that provides an approximation of the amount corresponding to the time-series data when the amount corresponding to the first index value is substituted for the argument between the entry time and the exit time. offset, which is a portion of the deflection amount of the structure at the position that is not proportional to the first index value, and a third index value, which is a value obtained by subtracting the offset from the time-series data, as the a product of the average value of the amplitude in a predetermined period of the second index value, which is low-pass filtered to attenuate the frequency components equal to or higher than the fundamental frequency of the second index value, and the first-order coefficient of the first-order function; a deflection derivation step of deriving the sum of the sum of the zero-order coefficient of the linear function and the average value divided by the average value as an estimated value of the deflection amount of the structure at the position; The offset is the product of the average value and the second index value, and the absolute value of the element whose absolute value is larger than the 0th order coefficient of the linear function is a rounded value, and the amount corresponding to the time-series data is an amount after attenuating frequency components equal to or higher than the fundamental frequency of the time-series data from the time-series data, and the first The amount corresponding to the index value is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value, and the predetermined period is the amount of the second index value. Low-pass filtering that attenuates frequencies above the fundamental frequency is a period in which the value of the second index value to which is applied falls within a predetermined width range.
A program for solving the above problem is stored in a computer as a response to movement of an organized moving body in which one or more moving bodies are organized, and physical quantities occurring at predetermined observation points in the structure, an acquisition step of acquiring time-series data, 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 with the structure on the moving body; as environment information, a time deriving step of deriving the entry time and the exit time of the moving body from the structure based on the time-series data, and the moving body organized into the moving body. an index of the amount of deflection of the structure occurring at the observation point based on the number, the entering time, the leaving time, and the environmental information; and a second index value that is an index value of the amount of deflection at a specified position in the structure; the average value between the entry time and the exit time of the ratio between the predetermined first amount and the predetermined second amount according to the second index value, and the first index value; a deflection derivation step of deriving an estimate of the amount of deflection of the structure at the position based on The second amount is an amount obtained by attenuating a frequency component equal to or higher than the frequency, and the second amount is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the second index value from the second index value.

It is a figure which shows the structure of a derivation|leading-out system. It is a figure which shows the cross section of a bridge. It is a figure which shows the dimension of a unit bridge girder. 1 is a diagram showing the dimensions of a railway vehicle; FIG. It is a figure which shows the outline|summary of a unit bridge girder. It is a figure explaining the bending moment in a unit bridge girder. It is a figure which shows the outline|summary of the bending of the unit bridge girder by a wheel. FIG. 4 is a diagram showing an outline of bending of a unit bridge girder due to a railway vehicle; It is a figure which shows the outline|summary of the bending of a unit bridge girder by a railroad train. It is a figure which shows the bending of a unit bridge girder by a railroad vehicle. It is a figure which shows the FFT result of the bending of a unit bridge girder. FIG. 10 is a diagram showing deflection of a unit bridge girder due to a railroad train after high-pass filtering; It is a figure which shows the bending of the unit bridge girder by each railroad vehicle. It is a figure which shows the deflection of the unit bridge girder by each railroad vehicle and railroad train. FIG. 2 shows details of each element of the derivation system; FIG. 4 is a diagram showing time-series data subjected to low-pass filter processing; It is a figure explaining the derivation|leading-out process of an approach time and an exit time. It is a figure explaining the derivation|leading-out process of an approach time and an exit time. 4 is a flowchart showing derivation processing; It is a figure which shows the estimated value of bending amount. FIG. 10 is a diagram showing amplitudes at designated positions; FIG. 4 is a diagram showing an amplitude ratio; FIG. 10 is a diagram showing offset; It is a figure which shows the estimated value of bending amount. It is a figure which shows the estimated value of bending amount.

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

(1) First embodiment (1-1) Configuration of derivation system:
(1-1-1) Overview of derivation system:
FIG. 1 is a diagram showing an example of the configuration of a derivation system 10 according to this embodiment. The derivation system 10 is based on the time-series data of the physical quantity at the predetermined observation point on the bridge 5 where the railway train 6 composed of one or more railway vehicles moves. 9 is a system for deriving the amount of deflection. The railroad train 6 is an example of a mobile organization. Each railroad vehicle included in the railroad train 6 is an example of a moving object. A bridge 5 is an example of a structure on which a moving object moves. Each railroad car of the railroad train 6 moves on the bridge 5 via wheels provided on the axles. A wheel is an example of a contact portion between a railroad vehicle and a bridge. In this embodiment, each of the railway vehicles organized into the railway train 6 has the same structure. As shown in FIG. 1 , the derivation system 10 comprises a measuring device 1 , at least one sensor device 2 provided on the superstructure 7 of the bridge 5 and a server device 3 .

Based on the acceleration data output from each sensor device 2 , the measuring device 1 calculates deflection, ie displacement, of the superstructure 7 due to the running of the railroad train 6 . The measuring device 1 is installed, for example, on the abutment 8b. The measuring device 1 and the server device 3 can communicate via a communication network 4 such as a mobile phone wireless network and the Internet, for example. The measuring device 1 transmits to the server device 3 information on the displacement of the superstructure 7 due to the running of the railroad train 6 . The server device 3 derives the number of railway vehicles organized into the railway train 6 based on the transmitted displacement data.

In this embodiment, the bridge 5 is a railway bridge, such as a steel bridge, a girder bridge, an RC bridge, or the like. RC is an abbreviation for Reinforced-Concrete. In this embodiment, the bridge 5 is a structure to which BWIM (Bridge Weigh In Motion) is applicable. BWIM is a technique for measuring the weight, number of axles, etc. of a moving object passing through a bridge by measuring the deformation of the bridge by using the bridge as a scale. A bridge that can analyze the weight of a moving object passing through from the response of deformation and strain of the bridge is considered to be a structure to which BWIM can be applied. Therefore, the BWIM system, which applies the physical process between action and response to the bridge, makes it possible to measure the weight of moving objects moving across the bridge. Measurement of the weight of a moving object involves measuring the correlation coefficient between displacement and load in advance, and using the correlation coefficient to derive the load of the passing moving object from the measurement results of the displacement of the bridge when the moving object passes. is done in

The bridge 5 includes an upper structure 7, which is a portion on which the moving body moves, and a lower structure 8 that supports the upper structure 7. As shown in FIG. FIG. 2 is a cross-sectional view of the upper structure 7 taken along line AA of FIG. As shown in FIGS. 1 and 2, the superstructure 7 includes a floor 7a including floor slabs F, main girders G, cross girders (not shown), bearings 7b, rails 7c, sleepers 7d, and ballast 7e. and including. Also, as shown in FIG. 1, the substructure 8 includes a bridge pier 8a and an abutment 8b. The superstructure 7 is a structure that spans between adjacent abutments 8b and piers 8a, between two adjacent abutments 8b, or between two adjacent piers 8a. Below, the abutment 8b and the pier 8a are generically called a support part. In the present embodiment, a pair of supporting portions and a bridge girder portion of the superstructure 7 spanning between the pair of supporting portions are collectively referred to as one bridge girder. In other words, a single bridge girder is a simple beam-like structure whose both ends are supported by two support portions. Therefore, the bridge 5 shown in FIG. 1 includes two bridge girders. Each bridge girder included in the bridge 5 is hereinafter referred to as a unit bridge girder.
The measuring device 1 and the sensor device 2 are, for example, wired or wirelessly connected, and communicate via a communication network such as CAN (Controller Area Network).

The sensor device 2 is used to measure predetermined physical quantities used to derive displacement (deflection) at observation points set on the superstructure 7 . In this embodiment, this predetermined physical quantity is acceleration. Moreover, in this embodiment, the sensor device 2 is installed at this observation point. The sensor device 2 also includes an acceleration sensor such as a crystal acceleration sensor or a MEMS (Micro Electro Mechanical Systems) acceleration sensor. The sensor device 2 outputs acceleration data for deriving the displacement of the superstructure 7 due to the movement of the railroad train 6, which is a moving object, at the observation point.

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. As shown in FIG. However, the sensor device 2 only needs to be able to detect the acceleration for calculating the displacement of the upper structure 7 , and its installation position is not limited to the central portion of the upper structure 7 . If the sensor device 2 is provided on the floor slab F of the superstructure 7, it may be destroyed by the running of the railroad train 6, and the measurement accuracy may be affected by local deformation of the bridge floor 7a. Therefore, in the example of FIGS. 1 and 2 the sensor device 2 is provided on the main girder G of the superstructure 7 .

A floor slab F, a main girder G, and the like of the superstructure 7 are vertically bent by the load of the railroad train 6 running on the superstructure 7 . Each sensor device 2 measures the acceleration of deflection of the floor slab F and the main girder G due to the load of the railroad train 6 running on the superstructure 7 .
A designated position 9 is a position designated as a target position for estimating the amount of deflection on the bridge 5 .

(1-1-2) Flexure model:
Here, a model of bridge deflection when a railroad train moves on one bridge will be described. Here, the model is information such as a formula indicating a correspondence relationship between predetermined information and an estimation result.

Moreover, below, the number (number) of the railroad vehicles organized into the railroad train which moves a bridge is set to N. Let the entry time, which is the time when the railroad train enters the bridge, be t _i . Here, entry of a railroad train into a bridge means that a wheel of one axle of the railroad vehicle C ₁ (the first railroad vehicle from the head of the railroad train) has entered the bridge. Also, hereinafter, the leaving time, which is the time when the railroad train leaves the bridge, is t ₀ . Here, the exit of the railroad train from the bridge means that the wheel of the rearmost axle of the railroad vehicle _CN (the rearmost railroad vehicle of the railroad train) has withdrawn from the bridge. Moreover, below, the period (period from the time t _i to the time t _o ) when a railroad train passes a bridge is set to _ts . Below, N, t _i , t _o , and t _s are collectively referred to as observation information.

Moreover, below, the bridge length which is the length of a bridge is set to _LB. A bridge length is an example of a structure length. Let _Lx be the distance from the end of the bridge in the direction in which the railway train enters to the observation point. FIG. 3 shows _LB and _Lx . Hereinafter, the end of the bridge in the direction in which the railroad train enters is referred to as the entry end. Also, hereinafter, the end of the bridge in the direction in which the railroad train is leaving will be referred to as the exit end. Also, let L _C (m) be the vehicle length of the m-th railway vehicle from the head of the railway train. The vehicle length is an example of the moving body length. Hereinafter, L _c (1) to L _c (N) are collectively referred to as L _c . Also, let C _m be the m-th railroad car from the head of the railroad train. Also, let the number of axles in the railway vehicle C _m be a _r (m). In the following, a _r (1) to a _r (N ₎ will be collectively referred to as a _r , and the a _r (m) axles in the railway vehicle C _m will be 1 axle, 2 axis, 3-axis, . . . , a _r (m)-axis.
In addition, let L _a ( _aw (m, 1)) be the distance from the front end of the railcar C _m in the traveling direction to the first axis. Here, a _w (α, β) indicates the β axis of the α-th railroad car in the railroad train. Let L _a ( _aw (m, n)) be the distance from the n−1 axis (where n is an integer equal to or greater than 2) to the n axis in the railway vehicle C _m . That is, L _a (a _w (α, β)) is the distance between the β axis and the (β-1) axis in the railway train C _α , or the traveling direction of the β axis in the railway train C _α and the railway train C _α Indicates the distance to the front edge. Hereinafter, L _a (a _w (1, 1)) to L _a (a _w (N, a _r (N))) are collectively referred to as L _a . Each L _a indicates the position of the corresponding axle in the corresponding railcar. For example, L _a (a _w (m, 1)) indicates that there is one axis behind the front end of the railcar C _m at a distance of L _a (a _w (m, 1)). In addition, L _a ( _aw (m, 2)) indicates that two axles exist behind the first axle by a distance of L _a ( _aw (m, 2)) in the railway vehicle C _m .
Here, the railway train is composed of railway vehicles having a similar four-axle configuration. That is, a _r (m) (m=1, 2, . . . , N) is 4. L _c ( _m ), La _{( aw} (m, 1)), La (aw (m, 2)), La _{( aw} (m, 3)), La _{( aw} (m, 3)), L _a (a _w (m, 4)) is shown.
Below, L _B , L _x , L _c , a _r , and L _a are collectively referred to as environmental information.

t _s is obtained as the difference between t _o and t _i as shown in the following equation (1).

Also, the total number of wheels T _ar of a railroad train is obtained by the following equation (2).

The distance from the _1st axis of the leading railroad vehicle C1 to the n-axis of the m-th railroad vehicle _Cm is represented as _Dwa ( _aw (m,n)). D _wa (a _w (m, n)) is obtained from the following equation (3).

The distance from one axis of the leading rail car _C1 to the last axis a _r (N) of the last rail car C _N is D _wa ( _aw (N, a _r (N ))). Using D _wa (a _w (N, a _r (N))), the average speed v _a of the railroad train passing through the bridge is represented by the following equation (4).

The following equation (5) holds from equations (3) and (4).

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

FIG. 6 shows the bending moment at each position of the bridge due to the load P. As shown in FIG. 6, the bending moment generated in the bridge by the load P is 0 at the entry end, and increases proportionally as the position where the load P is applied from the entry end approaches, and the load P is applied. At the position, it becomes the value indicated by equation (6). Further, the bending moment generated in the bridge by the load P decreases proportionally from the position where the load P is applied to the retracted end, and becomes 0 at the retracted end. Therefore, the bending moment at an arbitrary position X on the bridge is represented by the following equation (7).

x in the expression (7) indicates the distance from the entry end to the position X in the traveling direction of the railroad train. Also, Ha in Expression (7) is a value shown in Expression (8) below.

Between the deflection w of the bridge at an arbitrary position X and the bending moment, the relationship represented by the following formula (9) holds.

θ in equation (9) is the angle formed by the horizontal line at the position X and the bent bridge. The following equation (10) holds from equations (7) and (9).

By integrating both sides of equation (10) with x twice, equation (11) below, which expresses the deflection w at position X, is obtained.

g1 and g2 in equation (11) are constant terms. Here, since the bridge is supported at the entrance end and the exit end, no bending occurs at the entrance end and the exit end. That is, in equation (11), both sides are 0 when x=0 and x= _LB . Therefore, g1 and g2 are given by the following equations (12) and (13).

The following equation (14) representing the deflection w at the position X is obtained from equations (11), (12), and (13).

When the load P is applied to the center of the bridge in the longitudinal direction, the maximum deflection of the deflections caused in the bridge due to the application of the load P occurs at the center of the bridge in the longitudinal direction. Assuming that this maximum deflection is w _0.5l , an equation expressing w _0.5l is obtained. If the load P is applied to the longitudinal center of the bridge, a=b=0.5L _B. Also, since the target position X for which deflection is to be obtained is the center of the bridge in the longitudinal direction, x=0.5L _B. Also, in this case, since x<=a, H _a =0 from equation (8). By substituting x=0.5L _B , a=b=0.5L _B , and H _a =0 into the equation (14), the following equation (15) representing the deflection w _0.51 can be obtained.

w _0.5l is used to normalize the deflection at any position in the bridge represented by equation (14).
When the position of the load P exists on the approach end side of the position X, that is, when x>a, H _a =1 from formula (8), and formula (14) is transformed into the following formula (16). is represented by

Let a=L _B r. Here, r is a real number of 0 or more and 1 or less. Since b=L _B −a, it is expressed as b=L _B (1−r). Substituting a=L _B r and b=L _B (1−r) into equation (16) and normalizing by dividing by w _0.5l yields normalization at position X when x>a The following equation (17) representing the amount of deflection w _std is obtained.

Similarly, when the position of the load P exists on the withdrawal end side of the position X, i.e., when x<=a, H _a = 0 from formula (8), and formula (14) is the following formula ( 18).

Let a=L _B r. Here, r is a real number of 0 or more and 1 or less. Since b=L _B −a, it is expressed as b=L _B (1−r). Substituting a=L _B r and b=L _B (1−r) into equation (18) and normalizing by dividing by w _0.5l yields the standard at position X when x<=a The following equation (19) is obtained that indicates the normalized amount of deflection w _std .

By substituting L _x for x in equations (17) and (19), the normalized deflection amount w _std at the deflection observation point is expressed as the following equation (20) as a function of r. expressed.

Function R(r) in equation (20) is a function shown in equation (21) below.

Here, using equations (20) and (21), we show the time variation of the deflection caused at the observation point by the load applied to the bridge via the wheels of any one axle a _w (m, n). Find a function.
First, let t _xn be the time it takes for a wheel of one axle of a railroad train to travel from the approach end to the observation point. t _xn is obtained from L _x and v _a by the following equation (22).

Also, let t _ln be the time it takes for one wheel of the railroad train to cross the bridge, that is, the time it takes from the entry end to the exit end. t _ln is obtained from _LB and _va by the following equation (23).

Let t _o (m, n) be the time at which the wheels of the n-axis a _w (m, n) of the m-th rail car of the railroad train reach the entry end. t _o (m, n) is obtained from t _i , v _a , and D _wa (a _w (m, n)) by the following equation (24).

From Equation (22), L _x is expressed as in Equation (25) below.

Also, from equation (23), _LB is expressed as in equation (26) below.

The position of the axle a _w (m, n) is the load position. Therefore, the position of the axle a _w (m, n) is at a distance a=L _B r in the direction from the entry end to the exit end. Also, if a variable indicating time is t, the distance from the approach end of a _w (m, n) at time t is the distance traveled by the railcar from time t _o (m, n) to time t. equal. Therefore, the following formula (27) holds.

From Equation (27), r is expressed as in Equation (28) below.

By replacing L _x , L _B , and r in Equations (20) and (21) using Equations (25), (26), and (28), wheels of axle a _w (m, n) A function w _std (a _w (m, n), t) of the following equation (29) is obtained as a model showing the time variation of the deflection occurring at the observation point due to the load applied to the bridge via . Function R(t) in equation (29) is a function represented by equation (30) below.

Observation information and environmental information (t _i , t _o , N, L _B , L _x , L _c (1) to L c (N), a _r (1) to _{a r (} N), L _a (a _w (1, 1)) through L _a (a _w (N, a _r (N)))) are known, using these information, w _std (a _w (m, n), t) is sought. For example, t _s is obtained from t _i and t ₀ using equation (1). From t _s , N, a _r , L _a , and L _c , v _a is obtained using equation (5). From _va , _LB , and _Lx , txn _{and tln} are obtained using equations (22) and (23). From L _a , L _c , and ti, t _o (m, n) is obtained using equations (3) and (24). Then, by substituting the obtained t _xn , t _ln , t _o (m, n) into the equations (29) and (30), the function w _std (a _w (m, n), t) of t is sought.

FIG. 7 shows an example of changes in the deflection amount at the observation point indicated by w _std (a _w (m, n), t). The horizontal axis of the graph in FIG. 7 indicates time, and the vertical axis indicates the amount of deflection. Also, according to the movement of one railroad vehicle C _m , the set of wheels for each of the a _r (m) axles will move on the bridge. Therefore, the function C _std (m, t) as a model representing the time variation of the amount of deflection caused at the observation point due to the movement of one railway vehicle C _m is w _std (a _w (m, n ) and t) are obtained by the following equation (31).

When a _r (m) is 4, that is, when the railway vehicle C _m has a four-axle configuration, FIG. 8 shows how the amount of deflection changes at the observation points indicated by the function C _std (m, t). The horizontal axis of the graph in FIG. 8 indicates time, and the vertical axis indicates the amount of deflection. Also, the solid line graph in FIG. 8 indicates C _std (m, t), and each dotted line graph indicates w _std (a _w (m, n), t) for each axle.

Also, according to the movement of the railway train, N railway vehicles move on the bridge. Therefore, the function T _std (t) as a model showing the time change of the amount of deflection caused at the observation point due to the movement of one railway train is the sum of C _std (m, t) for each railway vehicle, as follows: (32).

When N is 16, that is, when 16 railcars are organized in a railroad train, FIG. 9 shows how the amount of deflection changes at the observation points indicated by the function T _std (t). The horizontal axis of the graph in FIG. 9 indicates time, and the vertical axis indicates the amount of deflection. Further, the solid line graph in FIG. 9 indicates T _std (t), and each dotted line graph indicates C _std (m, t) for each railway vehicle. As shown in the graph of FIG. 9, the waveform is obtained by adding the deflection of each passing railroad vehicle, and it can be seen that vibration occurs at the period when successive railroad vehicles pass through the bridge.
The above is the explanation of the model of deflection in the bridge. Thus, the deflection model in this embodiment is a formula based on the structure of a simple beam-shaped bridge.

(1-1-3) Verification experiment:
The inventors obtained the deflection amount T _std (t) under the conditions that the observation information and the environmental information have the following values. That is, N = 4, t _i = 7.21 [seconds], t _o = 8.777 [seconds], t _s = 1.567 [seconds], _LB = 25 [m], L _x = 12.5 [m], L _C each = 25 [m], a _r each = 4, m = 1 to N respectively, L _a (a _w (m, 1)) = 2.5 [m], m = 1 to N L _a (a _w (m, 2)) = 2.5 [m] for each, m = 1 to N L _a (a _w (m, 3)) = 15 [m] for each, m = 1 to N L _a (a _w (m, 4))=2.5 [m] for each.

FIG. 10 shows the deflection amount T _std (t) at this time. The horizontal axis of the graph in FIG. 10 indicates time, and the vertical axis indicates the amount of deflection. In addition, the inventors determined the intensity of each frequency component included in T _std (t) by fast Fourier transforming (FFT) the determined T _std (t). The FFT results for T _std (t) are shown in FIG. The horizontal axis of the graph in FIG. 11 indicates the frequency, and the vertical axis indicates the intensity of the corresponding frequency component. Then, the inventors obtained the fundamental frequency F _f of T _std (t) from the FFT results of T _std (t) as the frequency of vibrations occurring in the bridge according to the continuous movement of railroad vehicles. Here, the fundamental frequency is the frequency of the lowest frequency component included in the signal. Specifically, the inventors identified the peak corresponding to the lowest frequency from the FFT result of T _std (t), excluding the sidelobes caused by the effect of the window function used in the FFT, and identified The resulting peak was obtained as the fundamental frequency. In the example of FIG. 11, as indicated by the dashed-dotted line, there are two sidelobe peaks in the range of less than 2 Hz caused by the window function used in the FFT. The inventors identified the peak surrounded by the dotted line as the lowest frequency peak among the peaks excluding these peaks, and obtained the frequency corresponding to the identified peak as the fundamental frequency _Ff . The inventors obtained the fundamental frequency of 3.1 Hz from the graph of FIG.

The inventors obtained the wavenumber ν of the fundamental frequency _Ff included in the transit period ts using the following equation (33).

In this case, ν=1.567×3.1=4.8577. Here, the number N of railcars of the moving railroad train is four. The inventors have found a feature that the wavenumber ν of the fundamental frequency _Ff included in the transit period ts is higher than N by about one. This feature is hereinafter referred to as the first feature. Therefore, the inventors assume that the number N of railroad vehicles included in the railroad train is obtained as a value obtained by subtracting 1 from the wavenumber ν of the fundamental frequency _Ff included in the transit period ts and rounded to an integer, It was found that it can be obtained using the following formula (34). A round function is a function that returns a rounded value of an argument.

Also, the inventors obtained the fundamental period _Tf from the fundamental frequency _Ff using the following equation (35).

Then, the inventors took a moving average of the amount of deflection T _std (t) at the fundamental period T _f to apply a low-pass filtering process to T _std (t) for attenuating frequency components equal to or higher than the fundamental frequency. The low-pass filtering process may be another FIR filtering process that attenuates frequency components equal to or higher than the fundamental frequency. Let T _std (t) subjected to low-pass filtering be T _{std_lp} (t)=T _{std_lp} (kΔT). Here, k is a variable that indicates the order of observation when the amount of deflection is periodically observed at an observation point. That is, if the data period (time resolution) of the deflection amount observation is ΔT, then t=kΔT.
As shown in Equation (36) below, the moving average interval _kmf adjusted to the time resolution of the data is obtained from the fundamental period _Tf and ΔT.

Using _kmf , T _{std_lp} (t) is obtained by the following equation (37).

The inventors subtracted T _{std_lp} (t) from the amount of deflection T _std (t), thereby performing high-pass filter processing for attenuating frequency components lower than the fundamental frequency to T _std (t). The high-pass filtering process may be any other FIR filtering process that attenuates frequency components below the fundamental frequency. Let T _std (t) subjected to high-pass filtering be T _{std_hp} (t). Specifically, the inventors obtained T _{std_hp} (t) by subtracting T _{std_lp} (t) from T _std (t) as shown in the following equation (38).

The calculated T _{std_hp} (t) is superimposed on T _std (t) and shown in FIG. In the graph of FIG. 12, the horizontal axis indicates time (t=kΔT), and the vertical axis indicates the amount of deflection. The solid line graph in FIG. 12 indicates T _{std — hp} (k), and the dotted line graph indicates T _std (t).
From the graph of FIG. 12, the number of positive peaks of T _{std_hp} (t) in transit period t _s (period from time t _i to time t _o ) is six. Here, the positive peak is the upward convex peak of the bridge among the peaks of T _{std_hp} (t). Also, the number of negative peaks of T _{std_hp} (t) in transit period t _s is five. Here, the negative peak is a downward convex peak of the bridge among the peaks of T _{std_hp} (t). From this, the inventors found that the number of positive peaks of T _{std_hp} (t) in the transit period t _s (6) is two more than the number of rolling stock N (4) included in the railway train, and the negative A feature was found that the number of peaks (5) was one more than N (4). This feature is hereinafter referred to as a second feature.

The inventors verified whether the first feature and the second feature hold while changing the observation information and the environment information to various values. As a result, the inventors found that the first feature and the second feature are satisfied when L _c /2 < _LB < 3L _c /2. Based on the first and second features, the inventors found that it is possible to derive the number of railway vehicles organized in the railway train 6 from the time-series data of the displacement (deflection) of the bridge at the observation point of the bridge. Found it. In the following, u(t) is the time-series data of displacement at the observation point of the bridge. u(t) is data of discrete values of displacement measured at a predetermined cycle, and is data in which each discrete value is associated with a measurement time.

The inventors have found that the amount of deflection C _std (1, t) ~ C _std (N, t) and T _std (t) were considered. That is, N = 4, t _i = 7.21 [seconds], t _o = 8.777 [seconds], t _s = 1.567 [seconds], _LB = 25 [m], L _x = 12.5 [m], L _C each = 25 [m], a _r each = 4, m = 1 to N respectively, L _a (a _w (m, 1)) = 2.5 [m], m = 1 to N L _a (a _w (m, 2)) = 2.5 [m] for each, m = 1 to N L _a (a _w (m, 3)) = 15 [m] for each, m = 1 to N L _a (a _w (m, 4))=2.5 [m] for each.

FIG. 13 shows deflection amounts C _std (1, t) to C _std (4, t) by each of the four railway vehicles included in the railway train at this time. Let T _f be the period of vibration that occurs in the bridge when railway vehicles pass continuously over the bridge. Vibration that occurs in a bridge when railroad vehicles continuously pass over the bridge is vibration that occurs when railroad vehicles pass the bridge in succession. Therefore, the cycle _Tf is the time difference between the entry times of successive railway vehicles passing through the bridge. Since the bridge is flexed by the railway vehicle from the time when the railway vehicle enters the bridge, the flexure start time indicated by C _std (m, t) and the flexure start time indicated by C _std (m+1, t) , is the period _Tf . FIG. 13 shows the deflection that occurs in the bridge due to the passage of each railcar of the railroad train as the railroad train passes over the bridge. The horizontal axis of the graph in FIG. 13 indicates time, and the vertical axis indicates the amount of deflection. As shown in FIG. 13, the bending caused by the rolling railcars occurs with a time difference of _Tf .

Since the period T _f is the time difference between the entry times of successive railway vehicles passing through the bridge, as shown in the following equation (39), the vehicle length L _C (m) passes at a speed _va can be considered a period

Let t _c (m) be the period during which a railroad vehicle C _m of a railroad train passes through the bridge. t _c (m) is an example of a moving object passage period during which the railway vehicle C _m that is a moving object passes through a bridge that is a structure. t _c (m) is the period from the time when the first axis of the railway vehicle C _m reaches the entry end to the time when the a _r (m) axis of the railway vehicle C _m reaches the exit end. That is, t _c (m) is the sum of the bridge length L _B of the railway vehicle C _m and the distance from the first axle, which is the front axle, to the a _r (m) axis, which is the rear axle of the railway vehicle C _m . It's time to move the distance. Therefore, t _c (m) is represented by the following equation (40).

When a railroad train passes over a bridge, let C _Tn be the number of railroad cars in which the following railroad cars are present among the railroad cars formed into the railroad train. Of the railroad vehicles organized into the railroad train, railroad vehicles other than the railroad vehicle at the end of the railroad train have subsequent railroad vehicles. Therefore, C _Tn is a number smaller than N by one. That is, the following formula (41) holds.

FIG. 14 shows C _std (1, t) to C _std (N, t) and T _std (t). The horizontal axis of the graph in FIG. 14 indicates time, and the vertical axis indicates the amount of deflection. The solid line graph in FIG. 14 indicates T _std (t), and the dotted line graphs indicate C _std (1, t) to C _std (4, t). As shown in FIG. 14, the passage period t _s is the sum of C _Tn T _f and the period t _c (m) during which one railway vehicle C _m passes through the bridge. That is, the following formula (42) holds.

From the equations (41) and (42), the number N of railway vehicles organized into the railway train is given by the following equation (43).

_Tf is also the time it takes for a railroad train to travel the length of one railroad car. Therefore, the distance traveled by the railroad train in transit period t _s is the sum of the length of (N−1) railcars and the distance traveled at speed v _a for t _c (m). Therefore, the following formula (44) holds.

The following equation (45) holds from equation (44). It can be confirmed from the equation (45) that the equation (43) holds.

It is considered that the amount of deflection T _std (t) that occurs in the bridge when a railroad train passes over the bridge includes, as a component of the fundamental frequency F _f , a vibration component that occurs in the bridge in response to the movement of successive railroad vehicles. be done. Since F _f is also the frequency of vibration that occurs in the bridge in response to the movement of successive railroad vehicles, it can be expressed as the reciprocal of T _f as shown in Equation (46) below.

From equations (39) and (46), the velocity v _a is represented by the product of F _f and L _C (m), as in equation (47) below.

Therefore, t _c (m) represented by Equation (40) is the distance from the first axle, which is the foremost axle, to the a _r (m) axle, which is the last axle, of the bridge length L _B and the railway vehicle C _m . , divided by the product of F _f and L _C (m).
From the equations (43) and (46), the number N of railway vehicles organized into a railway train can _be calculated from the bridge passage period t _s by a railway train to the bridge passage period t _c ( m) and the fundamental frequency Ff, plus 1, and is expressed as the following equation (48).

The inventors have found that the average speed v _a of a railroad train is expressed by the product of the fundamental frequency Ff and the length of one railcar _Cm included in the railroad train, as shown in Equation (47). Found it. Further, the inventors found that the period t _c (m) during which one railroad vehicle C _m passes over the bridge is determined by the length LB of the railroad vehicle C _m and the length _LB of the railroad vehicle We have found that the sum of the distances from one axis of C _m to the a _r (m) axis can be expressed as the period of movement at velocity v _a . In addition, as shown in Equation (48), the inventors added 1 to the product of the fundamental frequency Ff and the value obtained by subtracting _tc (m) from _ts when the number N of railway vehicles organized into a railway train is was found to be expressed as an added value.
The inventors then conceived of a method of deriving the number of rolling stock in a railway train using time-series data of displacement at observation points set on bridges on which railway trains move.

The method conceived by the inventors acquires time-series data u(t) of displacement at an observation point set on a bridge on which a railway train moves, and acquires _LB , _LC , and _La as environmental information. , based on the time-series data u(t), the fundamental frequency F _f of u(t) is obtained as the frequency of vibration generated in the bridge due to the passage of successive railway vehicles organized into railway trains, and u(t) Based on, the period t _s during which the railroad train passes the bridge is derived, and based on LB, _LC , L _{a ,} F _f and t _s , formula (40), formula (47), formula (48 ) is used to derive the number of railcars included in a railroad train.

In the present embodiment, the derivation system 10 uses the knowledge obtained in the experiment based on the time-series data u(t) of the deflection amount of the bridge 5 measured at the observation point. A value for the number N of vehicles is derived. Then, the derivation system 10 uses the derived N to derive the deflection amount at the observation point and the deflection amount of the bridge 5 at the specified position 9 using the bridge deflection model. . The derivation system 10 calculates the product of the ratio of the amount of deflection at the specified position to the derived amount of deflection at the observation point and the time-series data u(t) as an estimated value of the actual amount of deflection at the specified position 9. Ask as

(1-1-4) Element details:
Details of each of the measuring device 1, the sensor device 2, and the server device 3 of the derivation system 10 will now be described with reference to FIG.
In this embodiment, the derivation system 10 collects observation information (the number N of railway vehicles organized into the railway train 6, the time t _i when the railway train 6 enters the unit bridge girder, the time t when the railway train 6 exits the unit bridge girder, _o and the period t _s during which the railroad train 6 passes through the unit bridge girder are derived based on the data measured by the measuring device 1 .

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

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

The acceleration sensor 210 is an acceleration sensor such as a crystal acceleration sensor, a MEMS acceleration sensor, or the like, which can detect acceleration occurring in each of three axial directions orthogonal to each other. 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 more accurately. However, the installation location of the sensor device 2 in the upper structure 7 may be tilted. Even if one of the three detection axes of the acceleration sensor 210 is not aligned in the vertical direction, the measuring device 1 combines the accelerations of the three axes to detect acceleration in the vertical direction.

The control unit 200 of the sensor device 2 periodically detects vertical acceleration at an observation point on the bridge 5 via the acceleration sensor 210 and transmits data of the detected acceleration to the measuring device 1 . The control unit 100 of the measurement device 1 measures the vertical deflection of the bridge 5 at the observation point at the acceleration detection time based on the acceleration data transmitted from the sensor device 2 . In 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 . Note that, in the present embodiment, the sensor device 2 detects acceleration at a predetermined cycle ΔT. Therefore, the measuring device 1 measures the time-series data of the deflection of the ΔT period. That is, the time-series data to be measured is data of discrete values of mutation measured at the ΔT period, and each discrete value is data associated with the measurement time.

The server device 3 derives the number of railcars included in the railroad train 6 based on the deflection at the observation point measured by the measuring device 1 . The server device 3 is an example of a derivation device. The server device 3 includes a control section 300 , a storage section 310 and a communication section 320 . The control unit 300 includes a processor such as a CPU, a ROM, a RAM, and the like. The control unit 300 develops various programs recorded in a ROM or the like into a RAM and executes them via a CPU, thereby obtaining an acquisition unit 301, an environment information acquisition unit 302, a time derivation unit 303, a number acquisition unit 304, Each function of the index value acquisition unit 305 and the deflection derivation unit 306 is realized. The storage unit 310 stores various programs, data of detected deflection, and the like. The communication unit 320 includes a circuit used for wired or wireless communication with an external device.

The acquisition unit 301 has a function of acquiring time-series data of deflection occurring at an observation point as a response when the railroad train 6 moves on each bridge in the bridge 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 .

The environment information acquisition unit 302 acquires environment information including information on the length of a unit bridge girder, the length of a railcar that is the length of a railroad vehicle organized in the railroad train 6, and the position of an axle on which wheels are installed in the railroad vehicle. is a function to obtain The control unit 300 uses the function of the environment information acquisition unit 302 to obtain the bridge length L _B of the unit bridge girder, the vehicle length L _c of each railroad vehicle of the railroad train 6, and the distance L _{a indicating the position of each railroad vehicle of the railroad train 6.} information as environment information. In this embodiment, environmental information is stored in the storage unit 310 in advance, and the control unit 300 acquires the environmental information from the storage unit 310 . However, the control unit 300 may acquire environment information using other methods such as receiving environment information from an external device.

The time derivation unit 303 has a function of deriving the entry time t _i and the exit time _{t 0} of the railroad train 6 with respect to the unit bridge girder based on the time-series data u(t). The control unit 300 uses the function of the time derivation unit 303 to perform FFT on u(t). The control unit 300 detects peaks from the FFT result. The control unit 300 identifies the peak corresponding to the minimum frequency among the detected peaks, excluding the peak of the side lobe caused by the window function used in the FFT. The control unit 300 derives the frequency corresponding to the specified peak as the fundamental frequency _Ff of u(t).

The control unit 300 applies a low-pass filter to u(t) to attenuate components of the fundamental frequency _Ff or higher as follows. First, based on the acquired fundamental frequency _Ff , the control unit 300 derives the period _Tf by deriving the reciprocal of _Ff in the same manner as in Equation (35). The control unit 300 derives the interval _kmf using the following equation (49) based on the derived _Tf and ΔT, which is the predetermined period.

The control unit 300 applies a low-pass filter to u(t) by taking a moving average of each value of u(t) in the derived interval _kmf . Let u(t) subjected to low-pass filtering be u _lp (t)=u _lp (kΔT). Here, k is a variable that indicates the order of observation when the amount of deflection is periodically observed at an observation point. The control unit 300 derives u _lp (t) using the following equation (50) based on the derived interval _kmf . u _lp (t) is data of multiple discrete values, similar to u(t), which is data of multiple discrete values. FIG. 16 shows the derived u _lp (t). The horizontal axis of the graph in FIG. 16 indicates time, and the vertical axis indicates the amount of deflection.

Then, from u _lp (t), the control unit 300 identifies two continuous data that sandwich a predetermined threshold value C _L regarding the amount of deflection. Here, two consecutive data of u _lp (t) sandwiching the threshold value C _L means a range sandwiched between values of two continuously measured displacement data included in u _lp (t), That is, it indicates that _CL is included in the range of the smaller value or more and the larger value or less of these displacement data. In the present embodiment, this threshold C _L is assumed to be the product of a predetermined coefficient between 0 and 1, and the average value of u _lp (t) during the period in which the amount of deflection is shifting. Here, the term "period in which the amount of deflection is shifting" refers to the period in which the amount of deflection of the bridge is maintained within a predetermined range due to railroad train rides. More specifically, the period during which the amount of deflection is shifted is the period during which the amount of deflection is within a predetermined width centered on a value whose absolute value is greater than the predetermined value. For example, from u _lp (t), the control unit 300 extracts deflection amount data for a period of a predetermined length (e.g., 1 second, 2 seconds, etc.), and the absolute value of the average value of the extracted data is set to the predetermined value. and the absolute value of the difference between the maximum value and the minimum value of the extracted data is equal to or less than a predetermined width, the extracted period is determined as the period in which the deflection amount is shifted. . Also, the control unit 300 may receive designation of the start time and end time of the period in which the bending amount is shifted via the operation unit of the server device 3 or the like. Then, the control unit 300 obtains the average value of u _lp (t) for the period in which the deflection amount is shifted, and derives the product of the obtained average value and a predetermined coefficient as the threshold value _CL .

However, the threshold _CL may be another value. For example, the threshold C _L may be the value of the deflection at the observation point of the bridge when the railway vehicle is arranged so that the front wheel of one axle of the railway vehicle is placed near the entry end. Also, the threshold C _L may be the deflection amount of the observation point of the bridge when a predetermined weight is applied near the entry end. Also, the threshold value _CL may be a value such as a predetermined ratio (eg, 10%, 1%, etc.) of the maximum value of the deflection amount at the observation point of the bridge when the railroad train passes over the bridge.

FIG. 17 shows u _lp (t) and the threshold C _L . The horizontal axis of the graph in FIG. 17 indicates time (t=kΔT), and the vertical axis indicates the amount of deflection. The solid line graph in FIG. 17 indicates u _lp (t), and the dotted line graph indicates u(t). u _lp (k) and the threshold C _L intersect in the portion surrounded by the dotted line circle in FIG. 17 . Further, FIG. 18 shows an enlarged view of the crossing point of u _lp (t) and _CL (left dotted circle portion in the graph of FIG. 17). The horizontal axis of the graph in FIG. 18 indicates time, and the vertical axis indicates the amount of deflection. Each black dot in FIG. 18 indicates discrete value data included in u _lp (t). In the example of FIG. 18, data k−1 and data k included in u _lp (t) sandwich the threshold C _L .
Control unit 300 identifies the later one of the two times corresponding to the two consecutive data sandwiching the identified _CL . In the example of FIG. 18, control unit 300 identifies time kΔT corresponding to data k.
In the example of FIG. 17, the control unit 300 also specifies two data circled by dotted lines on the right side of _FIG . Identify the later of the two times.

Then, the control unit 300 derives the earliest of the specified times as the entry time t _i of the railroad train 6 to the unit bridge girder. Further, the control unit 300 derives the later one of the specified times as the leaving time _t 0 of the railroad train 6 from the unit bridge girder. In the example of FIG. 17, the control unit 300 derives the entry time t _i =7.2 [s] and the exit time t _o =12.795 [s]. Thus, in the present embodiment, the control unit 300 derives the times associated with any data included in u _lp (t) as the entering time t _i and the leaving time t ₀ .

Thus, in the present embodiment, the control unit 300 selects the later one of the two times corresponding to the two consecutive data sandwiching C _L included in u _lp (t) as the entry time t i and the exit time t _i . Derived as time t _o . However, the control unit 300 may derive other times as the entry time t _i and the exit time t ₀ . For example, the control unit 300 identifies, from u _lp (t), two consecutive data sandwiching a predetermined threshold C _L regarding the deflection amount, and after one of the times corresponding to the identified two data, The time included in the period before the other time may be derived as the entering time t _i and the leaving time t ₀ . In the example of FIG. 18, the control unit 300 controls the time after the time (k-1)ΔT corresponding to the data k-1 and before the time kΔT corresponding to the data k (for example, the time (k-1)ΔT, such as the time corresponding to the intersection of u _lp (t) and C _L ) may be derived as the approach time t _i . Further, the control unit 300 obtains a curve obtained by interpolating between each data included in u _lp (t), and obtains the times corresponding to the intersections of the obtained curve and C _L as t _i and t _o . good.

Also, it is conceivable that one of two consecutive data sandwiching C _L contained in u _lp (t) is equal to C _L . For example, in the example of FIG. 18, the value of data k may be equal to _CL . In that case, the control unit 300 creates a set of the data equal to _CL and the data immediately before, and a set of the data equal to _CL and the data one after, as two consecutive data sandwiching _CL. , are identified. In the example of FIG. 18, when data k is equal to _CL , the control unit 300 generates two consecutive data sandwiching _CL , a set of data k−1 and data k, and a set of data k and data k+1. and . In such a case, the control unit 300 selects any one set from the specified set of data, and sets the time within the period between the two times corresponding to the two data included in the selected set to t It may be derived as _i or t _o .

In the present embodiment, the control unit 300 derives the times associated with any data included in u _lp (t) as the entering time t _i and the leaving time t ₀ . As a result, the control unit 300 can easily acquire the data of u _lp (t) corresponding to each measurement time of the ΔT interval including the entry time t _i and the exit time t ₀ by referring to u _lp (t). and can be used. On the other hand, when the control unit 300 derives times that are not associated with any data included in u _lp (t) as the entry time t _i and the exit _time t 0 , t _i , t ₀ are included. The data of u _lp (t) corresponding to each measurement time of the ΔT interval is obtained by resampling from the original u _lp (t) or the like, which increases the labor of processing.

The control unit 300 uses u _lp (t) in which the vibration component of the fundamental frequency or higher is attenuated to derive the entry time and the exit time, thereby reducing the influence of the vibration component of the fundamental frequency or higher and improving accuracy. Entry time and exit time can be derived.
However, the control unit 300 may not derive u _lp (t). In that case, the control unit 300 may derive, for example, the times at which u(t) and the threshold _CL intersect as t _i and t _o .

The number acquisition unit 304 is a function that acquires the number of railway vehicles organized into the railway train 6 . The control unit 300 derives the number of railcars included in the railroad train 6 based on the first feature using the function of the number acquisition unit 304 . Based on t _i and t _o , the control unit 300 uses Equation (1) to derive the passage period t _s during which the railroad train 6 passes through the unit bridge girder. Then, based on the derived t _s and the fundamental frequency F _f derived based on u(t), the control unit 300 uses Equation (33) to calculate the fundamental frequency F _f included in the transit period t _s to derive the wavenumber ν of The control unit 300 acquires N by deriving the number N of railroad vehicles included in the railroad train 6 using Equation (34) based on the derived ν. In this way, the control unit 300 derives the value of N by subtracting 1 from the product of _ts and the fundamental frequency _Ff of u(t) and rounding to an integer.

However, the control unit 300 may acquire N by another method. For example, the control unit 300 may perform the following based on the second feature. That is, the control unit 300 subtracts u _lp (t) from u(t), and performs high-pass filtering on u(t) to attenuate components of frequencies lower than the fundamental frequency. Derive u _hp (t), which is u(t). Then, the control unit 300 identifies the number of positive peaks from the data in the period from t _i to t _o in u _hp (t). The control unit 300 may acquire N by deriving the value of N by subtracting 2 from the number of identified positive peaks.
Also, the control unit 300 identifies the number of negative peaks from the data in the period from t _i to t _o in u _hp (t). The control unit 300 may acquire N by deriving the value of N by subtracting 1 from the number of identified negative peaks.

Further, the control section 300 may be configured as follows using a method conceived by the inventors. That _is , the controller ₃₀₀ calculates the average speed Derive v _a . Based on the derived v _a and L _B and L _a indicated by the environmental information, the control unit 300 uses Equation (40) to derive the period t _c (m) during which one railway vehicle passes through the bridge. do. Then, based on the derived F _f , t _s and t _c (m), the control unit 300 uses Equation (48) to derive the number N of railway vehicles organized into the railway train 6, and N can be obtained.
However, the control unit 300 does not have to derive the value of N. For example, the control unit 300 may receive designation of N based on the user's operation of the operation unit of the server device 3 and acquire the received value as N. Also, the control unit 300 may receive a designation of N from an external device and acquire the received value as N. Also, the control unit 300 may acquire a predetermined value as N.

The index value acquisition unit 305 calculates the amount of deflection of the structure occurring at the observation point based on the number N of railway vehicles organized in the railway train 6, the entry time t _i , the exit time t ₀ , and the environmental information. and a second index value that is the index value of the amount of deflection at the specified position 9 in the structure. In this embodiment, the position of the specified position 9 on the unit bridge girder is the position of the distance L _B ×rx from the entry end to the exit end. Here, rx is a value that indicates the ratio of the distance from the entry end to the specified position 9 in the unit bridge girder with respect to _LB. In this embodiment, rx is 0.05.
The control unit 300 uses the function of the index value acquisition unit 305 to calculate the standardized amount of deflection that occurs at the observation point due to the passage of the railway train 6 when the number of railway vehicles indicated by N is organized in the railway train 6. The estimated value is derived as the first index value, which is the index value of the amount of deflection at the observation point. Specifically, the control unit 300 derives t _s from t _i and t _o using Equation (1). The control unit 300 derives v _a from t _s , N, a _r , L _a , L _B , and L _c using Equation (5). That is, v _a is the distance from the foremost axle (the first axle of the foremost railway vehicle) to the last axle (the a _r (N) axis of the last railway vehicle) in a railway train composed of N railway vehicles. It is derived as a value obtained by dividing the sum of the distance and the bridge length _LB by the transit period _ts , which is the period from the entry time t _i to the exit time t _o . The control unit 300 derives t _xn and t ln from v _a , L _B and L _x using equations (22) and ( ₂₃ ). Further, the control unit 300 derives t _o (m, n) from L _a , L _c , and t _i using equations (3) and (24). Then, the control unit 300 substitutes the derived t _xn , t _ln , _to (m, n) into the equations (29) and (30) to obtain , to derive the function w _std (a _w (m, n), t).
The control unit 300 sums w _std (a _w (m, n), t) for each axle using Equation (31) for the N railway vehicles of the railway train 6 to obtain the Derive C _std (m, t) that indicates the deflection of the unit bridge girder due to passage. Then, the control unit 300 sums up C _std (m, t) for the N railway vehicles using Equation (32) to obtain T _std (t ). The control unit 300 thus acquires the normalized deflection amount T _std (t) at the observation point as the first index value. T _std (t) acquired as the first index value is hereinafter referred to as T _{std_R} (t).

In addition, the control unit 300 calculates the normalized estimated value of the amount of deflection caused at the specified position 9 by the passage of the railroad train 6 when the number of railroad cars indicated by N is organized in the railroad train 6. It is derived as a second index value which is an index value of the amount of deflection in 9. Specifically, from v _a , L _B and rx, the control unit 300 replaces L _x with L _B ×rx, and uses equations (22) and (23) to obtain t _xn and t _ln derive Further, the control unit 300 derives t _o (m, n) from L _a , L _c , and t _i using equations (3) and (24). Then, the control unit 300 substitutes the derived t _xn , t _ln , _to (m, n) into the equations (29) and (30) to obtain , to derive the function w _std (a _w (m, n), t).
The control unit 300 sums w _std (a _w (m, n), t) for each axle using Equation (31) for the N railway vehicles of the railway train 6 to obtain the Derive C _std (m, t) that indicates the deflection of the unit bridge girder due to passage. Then, the control unit 300 sums up C _std (m, t) for the N railway vehicles using Equation (32) to obtain T _std (t ). The control unit 300 thus acquires the normalized deflection amount T _std (t) at the specified position 9 as the second index value. T _std (t) obtained as the second index value is hereinafter referred to as T _{std_rx} (t).

The deflection derivation unit 306 calculates the unit bridge girder at the specified position 9 based on the time-series data u(t), the first index value T _{std_R} (t), and the second index value T _{std_rx} (t). It is a function to derive an estimated value of the amount of deflection of .
By the function of the deflection deriving section 306, the control section 300 determines that the value of the deflection in T _{std_R} (t) and T _{std_rx} (t) begins to become larger than 0 as the period from when the deflection starts until it converges. A period from time t1 to time t2 when the deflection converges and the value converges to 0 is specified.
Further, the control unit 300 controls the ratio R rx_R (t) between the predetermined amount corresponding to the first index value T _{std_R} ( _t ) and the predetermined amount corresponding to the second index value T _{std_rx} (t). to derive In this embodiment, the predetermined amount corresponding to the first index value T _{std_R} (t) is the first index value T _{std_R} (t). Also, the predetermined amount corresponding to the second index value T _{std_rx} (t) is the second index value T _{std_rx} (t). Therefore _{, in the present embodiment, the control unit 300 calculates the ratio R rx_R ( t} ). However, as another example, the predetermined amount according to the first index value T _{std_R} (t) is from the first index value T _{std_R} (t) to the fundamental frequency of the first index value T _{std_R} (t) or higher. may be an amount obtained by attenuating the frequency component of . Further, the predetermined amount according to the second index value T _{std_rx} (t) is obtained by subtracting the frequency components equal to or higher than the fundamental frequency of the second index value T _{std_R} (t) from the second index value T _{std_R} (t). It may be an attenuated amount. In addition, the control unit 300 calculates, as the ratio R _{rx_R} (t), the amount obtained by attenuating the frequency components equal to or higher than the fundamental frequency of the second index value T _{std_R} (t) from the second index value T _{std_R} (t). , a value obtained by dividing the first index value T _{std_R} (t) by the amount of attenuation of the frequency component equal to or higher than the fundamental frequency of the first index value T _{std_R} (t).

Based on t ₁ , t ₂ and R _{rx_R} (t), _the control unit 300 _calculates the first index value T _{std_R} An average value Ravg of the ratio between (t) and the second index value T _{std_rx} (t) is derived.

However, the control unit 300 may derive, as Ravg, an average value of ratios of T _{std_R} (t) and T _{std_rx} (t) in a period different from the period from time _t1 to time _t2 . For example, the control unit 300 may derive the average value of the ratios of T _{std_R} (t) and T _{std_rx} (t) in the transit period t _s as Ravg. In that case, the control unit 300 may replace t ₁ and t ₂ in equation (52) with t _i and _to and derive Ravg using equation (52).

Then, the control unit 300 derives a value obtained by multiplying the time-series data u(t) by Ravg as an estimated value of the deflection amount at the designated position 9 . However, the control unit 300 may derive the estimated value of the deflection amount at the specified position 9 by multiplying each piece of data included in the time-series data u(t) by the corresponding R _{rx_R} (t).

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

(1-2) Derivation process:
Derivation processing of the deflection amount at the specified position 9 executed by the server device 3 will be described with reference to FIG. 19 . The server device 3 starts the processing of FIG. 19 in response to the transmission of the displacement data at the observation point from the measuring device 1, but starts the processing of FIG. 19 at an arbitrary timing such as a designated timing. may
In S<b>100 , 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 . S100 is an example of an acquisition step.
In S105, the control unit 300 uses the function of the environment information acquisition unit 302 to indicate the bridge length L _B of the unit bridge girder, the vehicle length L _c of each railroad vehicle of the railroad train 6, and the position of each railroad vehicle of the railroad train 6. Information on the distance La is acquired as environment information. S105 is an example of an environment information acquisition step.

In S110, the control unit 300 performs FFT on u(t) using the function of the time derivation unit 303, and detects a peak from the FFT result. The control unit 300 identifies the peak corresponding to the minimum frequency among the detected peaks, excluding the peak of the side lobe caused by the window function used in the FFT. The control unit 300 derives the frequency corresponding to the specified peak as the fundamental frequency _Ff of u(t). Based on the obtained fundamental frequency _Ff , the control unit 300 derives the period _Tf by deriving the reciprocal of _Ff in the same manner as in Equation (35). Control unit 300 derives interval _kmf using equation (49) based on derived _Tf and ΔT, which is the predetermined period. Control unit 300 derives u _lp (t) using equation (50) based on the derived interval k _mf .
Further, the control unit 300 extracts an interval of a predetermined value (for example, 1 second, 2 seconds, etc.) from u _lp (t), and extracts the absolute value of the difference between the maximum value and the minimum value of the amount of deflection in the extracted interval. If the value is equal to or less than the predetermined threshold, then the section in which the amount of deflection is shifted from the extracted section is determined. The control unit 300 obtains the average value of u _lp (t) for the section in which the deflection amount is shifted, and derives the product of the obtained average value and a predetermined coefficient as the threshold value C _L .

Then, the control unit 300 obtains an intersection point between u _lp (t) and the derived threshold C _L . Specifically, the control unit 300 obtains two values of t that satisfy u _lp (t)=C _L . Then, the control unit 300 derives the time indicated by the smaller one of the obtained values of t as the entry time t _i of the railroad train 6 into the unit bridge girder. In addition, the control unit 300 derives the time indicated by the larger one of the obtained values of t as the exit time t ₀ of the railroad train 6 from the unit bridge girder. S110 is an example of the time derivation step.

At S115, the control unit 300 uses the function of the number acquisition unit 304 to determine the passage period during which the railway train 6 passes through the unit bridge girder using the equation (1) based on t _i and t _o derived at S110. Derive _ts . Then, the control unit 300 derives the wavenumber ν of the fundamental frequency _Ff included in the transit period ts using Equation (33) based on the derived _ts and the _Ff derived in S110. The control unit 300 acquires N by deriving the number N of railroad vehicles included in the railroad train 6 using Equation (34) based on the derived ν. S115 is an example of the number acquisition step.

In S120, the control unit 300 uses the function of the index value acquisition unit 305 to derive v _a from t _s , N, a _r , L _a , and L _c using Equation (5). The control unit 300 derives t _xn and t ln from v _a , L _B and L _x using equations (22) and ( ₂₃ ). Further, the control unit 300 derives _{t o} (m, n) from L _a , L _c , and t _i using equations (3) and (24). Then, the control unit 300 substitutes the derived t _xn , t _ln , _to (m, n) into the equations (29) and (30) to obtain , to derive the function w _std (a _w (m, n), t).
The control unit 300 sums w _std (a _w (m, n), t) for each axle using Equation (31) for the N railway vehicles of the railway train 6 to obtain the Derive C _std (m, t) that indicates the deflection of the unit bridge girder due to passage. Then, the control unit 300 sums up the C _std (m, t) for the N railway vehicles using the equation (32) to obtain the standardized deflection amount T of the unit bridge girder due to the passage of the railway train. _std (t) is obtained as the first index value T _{std_R} (t).

Further, the control unit 300 derives t xn and t ln from v _a , L _B , _and rx by replacing L _x with L _B ×rx and using equations (22) and ( ₂₃ ). Further, the control unit 300 derives t _o (m, n) from L _a , L _c , and t _i using equations (3) and (24). Then, the control unit 300 substitutes the derived t _xn , t _ln , _to (m, n) into the equations (29) and (30) to obtain , to derive the function w _std (a _w (m, n), t).
The control unit 300 sums w _std (a _w (m, n), t) for each axle using Equation (31) for the N railway vehicles of the railway train 6 to obtain the Derive C _std (m, t) that indicates the deflection of the unit bridge girder due to passage. Then, the control unit 300 sums up C _std (m, t) for the N railway vehicles using Equation (32) to obtain T _std (t ). The control unit 300 thus acquires the normalized deflection amount T _std (t) at the designated position 9 as the second index value T _{std — rx} (t). S120 is an example of an index value obtaining step.

In S<b>125 , the control unit 300 uses the function of the deflection deriving unit 306 to determine whether the value of deflection is greater than 0 as the period from when the deflection starts to when it converges in T _{std_R} (t) and T _{std_rx} (t). A period from time _t1 at which the value starts to become 0 to time _t2 at which the deflection converges and the value converges to 0 is specified. Then, the control unit 300 derives the ratio R rx_R (t) between the first index value T _{std_R (} t) and the second index value T _{std_rx} (t) using equation (51). Based on t ₁ , t ₂ and R _{rx_R} (t), _the control unit 300 _calculates the first index value T _{std_R} (t ) and the second index value T _{std — rx} (t). The control unit 300 derives a value obtained by multiplying the time-series data u(t) by Ravg as an estimated value of the deflection amount at the designated position 9 . S125 is an example of a deflection derivation step.

(2) Second embodiment (2-1) Configuration of derivation system:
(2-1-1) Overview of derivation system:
The derivation system 10 of this embodiment has the same configuration as that of the first embodiment. However, the processing of the server device 3 is different from that of the first embodiment.
(2-1-2) Verification experiment:
The inventors have determined that the actual amount of deflection T(t) at a certain position on the bridge is the amount of deflection proportional to the amount of deflection T _std (t) at that position derived by the deflection model, and the amount of deflection derived by the deflection model The idea was to approximate by adding T _offset (t), which has no correlation with the quantity. That is, the inventors came up with the idea of approximating T(t) as a linear function of T _std (t), as shown in Equation (53) below. _c1 in equation (53) is a first-order coefficient. Here, the portion proportional to the amount of deflection derived from the deflection model is the displacement proportional to the load on the unit bridge girder to which BWIM is applicable.

The inventors found that u _lp (t) obtained by subjecting time-series data measured at an observation point to low-pass filter processing is obtained from an observation point derived using a bending model, as shown in Equation (54) below. is a linear function whose variable is T _{std_R_lp} (t) obtained by applying a low-pass filter process for attenuating components of the fundamental frequency or higher to the normalized amount of deflection T _{std_R} (t), where the first-order coefficient is c ₁ I came up with the idea that it can be approximated as a linear function where c ₀ in equation (54) is a coefficient of the 0th order and indicates a displacement that does not depend on the position on the bridge. Here, u _lp (t) is approximated as a linear function of T _{std_lp} (t) in the period from the entry time t _i to the exit time t ₀ .

Using the value obtained by subtracting the right side from the left side of Equation (54) as an error, using the least squares method to minimize this error, deriving c ₁ and c ₀ yields the following Equations (55) and (56) )become that way.

t _a in equations (55) and (56) is the start time of the predetermined period for which u _lp (t) is approximated by T _{std_R_lp} (t). In this embodiment, t _a is the entry time t _i . Also, t _b is the end time of the predetermined period for which u _lp (t) is approximated by T _{std_R_lp} (t). In this embodiment, _tb is the exit time _to . Also, K in the equations (55) and (56) is a value represented by the following equation (57).

As shown on the right side of equation (54), let T _{Estd_R_lp} (t) be the amount of deflection restored using T _{std_R_lp} (t) and coefficients c ₁ and c ₀ . T _{Estd_R_lp} (t) is as shown in Equation (58) below. Here, during the period of t<t _i , t>t ₀ , c ₀ =0, assuming that there is no deflection because the railroad train is not on the bridge.

The amplitude ratio _Rr between T _{Estd_R_lp} (t) and T _{std_R_lp} (t) is obtained by the following equation (59). k ₀ in Equation (59) is a value indicating the order of the observation of the amount of deflection performed earliest during the period in which the waveform of the amount of deflection u _lp (t) is shifting. In addition, N is a value obtained by subtracting _k0 from a value indicating the number of the latest observation of the amount of deflection during the period in which the waveform of the amount of deflection u _lp (t) is shifted. be. That is, N is the k ₀ +N-th observation of the deflection amount performed latest in the period in which the waveform of u _lp (t) is shifting.

We define the offset T _{offset_R_std} (t) at the observation point as the product of R _r and T _{std_R_lp} (t) with an absolute value greater than c ₀ as shown in equation (60) below. assumed to be values rounded to c ₀ for the elements. That is, T _{offset_R_std} (t) approaches c ₀ as time elapses after the railroad train enters the bridge, and after the value reaches c ₀ , it remains constant at c ₀ , and when the railroad train leaves the bridge. shows a component of deflection that converges to 0 with time.

Let T _{EO_R} (t) be the estimated value of the deflection amount at the observation point. The inventors derived T _{EO_R} (t) from the relationship expressed in Equation (54) by dividing c ₁ and the estimated value T _{std_R} (t) using the deflection model as shown in Equation (61) below. thought to be expressed as the sum of the product and T _{offset_R_std} (t).

FIG _. 20 shows the equation ( 61) and an estimated value T _{EO_R} (t) of the amount of deflection at the observation point derived by the method 61). The horizontal axis of the graph in FIG. 20 indicates time, and the vertical axis indicates the amount of deflection. The solid line graph in FIG. 20 indicates T _{EO_R} (t). Also, the dotted line graph indicates u(t). Checking FIG. 20 confirms that the estimated value T _{EO_R} (t) restores u(t) with good accuracy.

From this, the inventors came up with the following method for deriving the deflection amount at the specified position.
Here, it is assumed that the position of the distance L _B r _x from the entrance end to the exit end on the bridge is designated as the position for deriving the amount of deflection. Here, let r _x =0.05. Let T _{std_rx} (t) be the normalized amount of deflection at a specified position derived using the deflection model. Also, T _{std_rx} (t) subjected to low-pass filter processing for attenuating frequency components equal to or higher than the fundamental frequency is denoted by T _{std_rx_lp} (t).
That is, given the deflection amount T _{Estd_rx_lp} (t) restored by adding c ₀ to the product of T _{std_rx_lp} (t) and the coefficient c ₁ , the inventors obtain T _{std_rx_lp} (t), the coefficient c ₁ , Using c ₀ , the amplitude ratio between T _{Estd_rx_lp} (t) and T _{std_rx_lp} (t) is obtained in the same manner as in Equation (59), and from the obtained amplitude ratio and T _{std_rx_lp} (t), Equation (60) and By similarly obtaining the offset and adding the obtained offset to the product of T _{std_rx} (t) and c ₁ in the same manner as in Equation (61), the inventors have come up with a method of deriving the amount of deflection at the specified position.

In the following, the steps of this method performed by the inventors are described.
The inventors obtained T _{std_rx} (t), and obtained T _{std_rx_lp} (t) by applying a low-pass filter process for attenuating components of the fundamental frequency or higher to the obtained T _{std_rx} (t).
Then, the inventors derived the amplitude h _rx of T _{std_rx_lp} (t) using the following equation (62). FIG. 21 shows the derived amplitude h _rx .

t ₁ and t ₂ in equation (62) are the start time and end time, respectively, of an arbitrary period within the period during which the bridge is vibrating due to the passage of a railroad train. In this embodiment, t ₁ and t ₂ are respectively the start time and end time of a period set within the period in which T _{std_rx_lp} (t) is shifted. That is, t ₁ and t ₂ are respectively the periods during which the value of T _{std_rx_lp} (t) falls within a predetermined width around a value whose absolute value is greater than the predetermined value. For example, t ₁ and t ₂ are the start times of a period of a predetermined width (eg, 1 second, 2 seconds, etc.) in the middle of the transit period t _s (the period from the entry time t _i to the exit time t _o ). , end time. In addition, t ₁ and t ₂ are respectively the time when a predetermined period (for example, the length of a predetermined ratio (10%, 30%, etc.) of the passage period t _s ) has elapsed from the entry time t _i , and the exit time. It may be a time in the past from the time t ₀ by a predetermined period (for example, a period having a length of a predetermined ratio (10%, 30%, etc.) of the transit period t _s ).
Thus, the inventors derived the average value of T _{std_rx_lp} (t) in the period from t ₁ to t ₂ as the amplitude h _rx using equation (62).

The inventors obtained u _lp (t), which is the time-series data u(t) subjected to low-pass filter processing that attenuates components above the fundamental frequency, and normalized data at the observation point derived using the deflection model. Equations (55) and (56) are used based on T _{std_R_lp} (t) obtained by applying a low-pass filter process that attenuates components of the fundamental frequency or higher to the estimated deflection amount T _{std_R} (t). , the coefficients c ₁ and c ₀ were derived.

Consider the amplitude of T _{Estd_rx_lp} (t). T _{Estd_rx_lp} (t) is a value obtained by substituting T _{std_rx_lp} (t) instead of T _{std_R_lp} (t) as an argument in the linear function shown in Equation (53), that is, T _{std_rx_lp} (t), coefficient c ₁ and is the value obtained by adding _c0 to the product of Therefore, the time function R _{r_rx} (t) representing the amplitude ratio between T _{Estd_rx_lp} (t) and T _{std_rx_lp} (t) is given by Equation (63) below.

The function R _{r_rx} (t) is shown in FIG. Here, since T _{std_rx_lp} (t) shifts in the period from t ₁ to t ₂ , the denominator and numerator on the right side of equation (63) are almost constant in the period from t ₁ to t ₂ , and the value of _{Rr_rx} (t) is also substantially constant. That is, during the period from t ₁ to t ₂ , the value of the amplitude ratio at each time represented by R _{r_rx} (t) falls within a predetermined width centered on a value whose absolute value is equal to or greater than the predetermined value. period. Here, let _{Rr_rx} be the average amplitude ratio of _{Rr_rx} (t) in the period from _t1 to _t2 . The amplitude ratio _{Rr_rx} is expressed as in Equation (64) below.

Also, the amplitude of T _{Estd_rx_lp} (t) is a value obtained by adding c ₀ to the product of the amplitude h _rx of T _{std_rx_lp} (t) and c ₁ . Therefore, the amplitude ratio R _{r_rx} is also expressed as the following equation (65) as a ratio between the amplitude of T _{Estd_rx_lp} (t) and the amplitude h _rx of T _{std_rx_lp} (t).

The inventors derived the amplitude ratio R _{r_rx} using Equation (64) based on t ₁ , t ₂ and R _{r_rx} (t). However, it is also possible to derive the amplitude ratio R _{r_rx} by using Equation (65) based on h _rx , c ₁ , and c ₀ . Then, the inventors derived the deflection amount T _{r_rx} by multiplying T _{std_rx_lp} (t) by R _{r_rx} using the following equation (66).

Also, R _{r_rx} in equation (65) is replaced by the ratio of T _{Estd_rx_lp} (t) (value obtained by adding c ₀ to the product of T _{std_rx_lp} (t) and coefficient c ₁ ) and T _{std_rx_lp} (t). The deflection amount _{Tr_rx} can be derived using the following equation (66) derived by

Alternatively, before the entry time t _i and after the exit time t ₀ , c ₀ =0 may be set, and _{Tr_rx} may be expressed by the following equation (68).

Then, the inventors derived the deflection amount offset T _{offset_rx} (t) at the designated position based on the derived T _{r_rx} using Equation (69). That is, the inventors derived T _{r_rx} rounded to c ₀ for elements whose absolute values are greater than c ₀ as T _{offset_rx} (t).

FIG. 23 shows the derived T _{offset_rx} (t). The horizontal axis of the graph in FIG. 23 indicates time, and the vertical axis indicates the amount of deflection. The solid line graph in FIG. 23 indicates T _{offset_rx} (t). Also, the dotted line graph indicates T _{r_rx} (t). FIG. 23 shows that the value of T _{offset_rx} (t) approaches c ₀ as time elapses after the railroad train enters the bridge, remains constant at c ₀ for a certain period of time, and becomes constant over time when the railroad train leaves the bridge. is shown to converge to 0 as time passes.
Then, using the following equation (70), the inventors add T _{offset_rx} (t) to the product of the coefficient c ₁ and T _{std_rx} (t) to obtain the deflection at the specified position on the bridge An estimate of the quantity T _{EO_rx} (t) was derived. FIG. 24 shows the derived value T _{EO — rx} (t) and the estimated deflection amount T _EO (t) at the observation point derived from Equation (61). The horizontal axis of the graph in FIG. 24 indicates time, and the vertical axis indicates the amount of deflection.

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

(2-1-3) Element details:
The measuring device 1 and the sensor device 2 of this embodiment are the same as those of the first embodiment. Also, the server device 3 of the present embodiment is the same as that of the first embodiment except for the function of the deflection derivation section 306 . The details of the deflection lead-out portion 306 of the present embodiment will be described below.

Similar to the first embodiment, the deflection derivation unit 306, based on the time-series data u(t), the first index value T _{std_R} (t), and the second index value T _{std_rx} (t), It is a function of deriving an estimated value of the deflection amount of the unit bridge girder at the specified position 9.
Using the function of the deflection derivation unit 306, the control unit 300 performs low-pass filtering for attenuating components of the fundamental frequency or higher on the second index value T _{std_rx} (t). A second index value T _{std_rx_lp} (t) is obtained. Specifically, the control unit 300 performs FFT on T _{std_rx} (t), and from the result of FFT, the peak of the side lobe caused by the effect of the window function used in the FFT is removed, and the minimum frequency corresponding to Identify peaks. Then, the control unit 300 sets the frequency corresponding to the identified peak as the fundamental frequency _Ff , and derives the section _kmf using the equation (36). Based on the derived _kmf , the control unit 300 replaces T _std (t) with T _{std_rx} (t), replaces T _{std_lp} (t) with T _{std_rx_lp} (t), and uses equation (37) to obtain , T _{std_rx_lp} (t). However, the control section 300 may obtain T _{std_rx_lp} (t) by applying another FIR filter that attenuates components of the fundamental frequency or higher to T _{std_rx} (t).

In addition, the control unit 300 obtains T _{std_R_lp} (t) by applying low-pass filter processing for attenuating components of the fundamental frequency or higher to T _{std_R} (t). Specifically, the control unit 300 performs FFT on T _{std_R} (t), and from the result of the FFT, corresponds to the minimum frequency excluding the peak of the side lobe caused by the window function used in the FFT. Identify peaks. Then, the control unit 300 sets the frequency corresponding to the identified peak as the fundamental frequency _Ff , and derives the section _kmf using the equation (36). Based on the derived _kmf , the control unit 300 replaces T _std (t) with T _{std_R} (t), replaces T _{std_lp} (t) with T _{std_R_lp} (t), and uses equation (37) to obtain , T _{std_R_lp} (t). However, the control section 300 may obtain T _{std_R_lp} (t) by applying another FIR filter that attenuates components of the fundamental frequency or higher to T _{std_R} (t).

The control unit 300 derives the amplitude h _rx which is the average value of T _{std_rx_lp} (t) in the period from t ₁ to t ₂ using equation (62). t ₁ and t ₂ are the start and end times of a period of a predetermined width (for example, 1 second, 2 seconds, etc.) in the center of the transit period t _s (the period from the entry time t _i to the exit time t _o ), respectively. It is assumed that it is the time, but it may be another period of time.

The control unit 300 uses equations (55) and (56) based on u _lp (t), T _{std_R_lp} (t), t _a (t _i ), and t _b (t _o ). to derive coefficients c ₁ and c ₀ . That is, the control unit 300 takes T _{std_R_lp} (t) as an argument and derives coefficients c ₁ and c ₀ of a linear function that returns u _lp (t), which is shown in Equation (54). T _{std_R_lp} (t) is an example of a quantity corresponding to the first index value T _{std_R} (t). u _lp (t) is an example of a quantity corresponding to the time-series data u(t). Based on c ₁ , c ₀ and h _rx , the control unit 300 uses equation (63) to provide the linear function shown in equation (53) with an argument T _{std_rx_lp} (t) instead of T _{std_R_lp} (t) A function R _{r_rx} (t) of the amplitude ratio between T _{Estd_rx_lp} (t), which is a value obtained by substituting , and T _{std_rx_lp} (t) is derived. _{That is ,} the control unit ₃₀₀ controls the amplitude _ratio function Derive R _{r_rx} (t). Then, based on t ₁ , _{t 2} , and T _{std_rx_lp} (t), the control unit 300 uses equation ( ₆₄ ) to calculate the average _amplitude ratio R Derive _{r_rx} . R _{r_rx} derived using equation (64) is obtained by using T _{std_rx_lp} (t), which is the second index value subjected to low-pass filtering, as an argument of a linear function with a first-order coefficient c ₁ and a zero-order coefficient c ₀ It is the average value of the amplitude ratio of the assigned value and T _{std_rx_lp} (t) during the period in which the value of the amplitude ratio falls within the predetermined width.
However, the control unit 300 may derive the amplitude ratio R _{r_rx} using equation (65) based on c ₁ , c ₀ and h _rx . R _{r_rx} , derived using equation (65), is the average amplitude during the period in which the value of the low-pass filtered second index T _{std_rx_lp} (t) is within a predetermined width. be.
The control unit 300 derives the deflection amount T _{r_rx} by multiplying T _{std_rx_lp} (t) by R _{r_rx} using Equation (66). However, based on T _{std_rx_lp} (t) and c ₁ and c ₀ , the control unit 300 may derive the amount of deflection T _{r_rx} using equation (67). Further, the control unit 300 may obtain T _{r_rx} as in equation (68) with c ₀ =0 before the entry time t _i and after the exit time t ₀ .

Then, the control unit 300 derives the deflection amount offset T _{offset_rx} (t) at the specified position 9 using Equation (69) based on the derived _{Tr_rx} . That is, the control unit 300 derives T _{r_rx} rounded to c ₀ for elements whose absolute values are greater than c ₀ as the offset T _{offset_rx} (t). The control unit 300 adds the offset T _{offset_rx} (t) to the product of the coefficient c ₁ and T _{std_rx} (t) using equation (70), thereby estimating the deflection amount at the specified position on the bridge. Derive the value T _{EO_rx} (t).

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

(2-2) Derivation process:
The processing of the derivation system 10 of this embodiment is the same as that of the first embodiment except for the processing of S125 among the processing of FIG. 19 in the first embodiment. Among the processes of the present embodiment, points different from those of the first embodiment will be described.
In S<b>125 , the control unit 300 obtains T _{std_rx_lp} (t) by performing low-pass filter processing for attenuating components of the fundamental frequency or higher on T _{std_rx} (t) using the function of the deflection deriving unit 306 . In addition, the control unit 300 obtains T _{std_R_lp} (t) by applying low-pass filter processing for attenuating components of the fundamental frequency or higher to T _{std_R} (t).

The control unit 300 derives the amplitude h _rx of T _{std_rx_lp} (t) using equation (62). The control unit 300 uses equations (55) and (56) based on u _lp (t), T _{std_R_lp} (t), t _a (t _i ), and t _b (t _o ). to derive coefficients c ₁ and c ₀ . Based on T _{Estd_rx_lp} (t), ie c ₁ T _{std_rx_lp} (t)+c ₀ and T _{std_rx_lp} (t), the control unit 300 derives the amplitude ratio function R _{r_rx} (t) using equation (63). . Control unit 300 then derives R _{r_rx} using equation (64).
The control unit 300 derives the deflection amount T _{r_rx} by multiplying T _{std_rx_lp} (t) by R _{r_rx} using Equation (66). The control unit 300 derives the deflection amount offset T _{offset_rx} (t) at the specified position 9 using Equation (69) based on the derived _{Tr_rx} . Then, the control unit 300 adds T _{offset_rx} (t) to the product of the coefficient c ₁ and T _{std_rx} (t) using equation (70) to obtain the deflection amount at the specified position on the bridge. Derive an estimate of T _{EO_rx} (t).

(3) Third embodiment:
(3-1) Overview of derivation system:
The derivation system 10 of this embodiment has the same configuration as that of the second embodiment. However, the processing of the server device 3 is different from that of the second embodiment.
(3-2) Verification experiment:
An amount u _of (t) obtained by subtracting the offset T _{offset_R_std} (t) at the observation point from the time-series data u(t) shown in the following equation (71) is set as a third index value.

The inventors divided the third index value u _of (t) by the amplitude ratio R _{r_rx} derived using the equation (65), as represented by the following equation (72). A method of estimating a value obtained by adding the offset T _{offset_rx} (t) at the specified position as an estimated value of the deflection at the specified position was devised.

The inventors obtained the offset T _{offset_R_std} (t) at the observation point under the same conditions as the verification experiment of the second embodiment. Then, the inventors derived the third index value u _of (t) by subtracting T _{offset_R_std} (t) from the time-series data u(t) using Equation (71). Also, the inventors derived the amplitude h _rx , the coefficient c ₁ , and the coefficient c ₀ as in the verification experiment of the second embodiment. The inventors derived the amplitude ratio R _{r_rx} using Equation (65) based on the derived h _rx , c ₁ , and c ₀ . Also, the inventors derived the offset T _{offset_rx} (t) at the specified position, as in the verification experiment of the second embodiment.
Then, the inventors determined the estimated value u _{est_rx} (t) using Equation (72) based on the determined u _of (t), R _{r_rx} and T _{offset_rx} (t).
FIG. 25 shows the estimated value u _{est_rx} (t) obtained and the time-series data u(t) measured at the observation point. The horizontal axis of the graph in FIG. 25 indicates time, and the vertical axis indicates the amount of deflection. It can be seen that u _{est_rx} (t) in FIG. 25 and T _{EO_rx} (t) in FIG. 24 show similar waveforms. Therefore, it was confirmed that the estimated value of the bending amount at the designated position can be derived even by the method conceived by the inventors.

(3-3) Element details:
The measuring device 1 and the sensor device 2 of this embodiment are the same as those of the second embodiment. Also, the server device 3 of the present embodiment is the same as that of the second embodiment except for the function of the deflection deriving section 306 . The details of the deflection lead-out portion 306 of the present embodiment will be described below.

Similar to the second embodiment, the deflection derivation unit 306, based on the time-series data u(t), the first index value T _{std_R} (t), and the second index value T _{std_rx} (t), It is a function of deriving an estimated value of the deflection amount of the unit bridge girder at the specified position 9.
The control unit 300 uses the function of the deflection derivation unit 306 to obtain T _{std_rx_lp} (t), which is the second index value subjected to low-pass filter processing for attenuating components of the fundamental frequency or higher, as in the second embodiment. However, the control section 300 may obtain T _{std_rx_lp} (t) by applying another FIR filter that attenuates components of the fundamental frequency or higher to T _{std_rx} (t).

Also, the control unit 300 obtains T _{std_R_lp} (t) that has been subjected to low-pass filter processing that attenuates components of the fundamental frequency or higher, as in the second embodiment. However, the control section 300 may obtain T _{std_R_lp} (t) by applying another FIR filter that attenuates components of the fundamental frequency or higher to T _{std_R} (t).

As in the second embodiment, the control unit 300 derives the amplitude h _rx that is the average value of T _{std_rx_lp} (t) in the period from t ₁ to t ₂ using equation (62). t ₁ and t ₂ are the start and end times of a period of a predetermined width (for example, 1 second, 2 seconds, etc.) in the center of the transit period t _s (the period from the entry time t _i to the exit time t _o ), respectively. It is assumed that it is the time, but it may be another period of time.

As in the second embodiment, the control unit 300 calculates equation (55) based on u _lp (t), T _{std_R_lp} (t), _ta (t _i ), and t _b (t _o ). , to derive the coefficients c ₁ and c ₀ using equation (56).
Then, based on the derived _c1 , _c0 and _hrx , the control unit 300 derives the amplitude ratio _{Rr_rx} using equation (65).

Based on T _{std_R_lp} (t) and c ₁ and c ₀ , control unit 300 derives T _{Estd_R_lp} (t) using equation (58).
The control unit 300 extracts the deflection amount data for a period of a predetermined length (for example, 1 second, 2 seconds, etc.) from u _lp (t), and the absolute value of the average value of the extracted data is set to a predetermined threshold value. If the above is satisfied and the absolute value of the difference between the maximum value and the minimum value of the extracted data is equal to or less than the predetermined width, the extracted period is determined as the period during which the deflection amount is shifted. Also, the control unit 300 may receive designation of the start time and end time of the period in which the bending amount is shifted via the operation unit of the server device 3 or the like. Then, the control unit 300 sets k ₀ as the earliest order of observation of the amount of deflection during the period in which the amount of deflection is shifting. Further, the control unit 300 sets N to a value obtained by subtracting _k0 from the order of observation of the latest deflection amount during the period in which the deflection amount is shifted. Then, the control unit 300 derives the amplitude ratio R _r using equation (59) based on k ₀ , N, T _{std_R_lp} (t), and T _{Estd_R_lp} (t).

Control section 300 derives offset T _{offset_R_std} (t) at the observation point using equation (60) based on amplitude ratio R _r and T _{std_R_lp} (t). Then, the control unit 300 derives the third index value u _of (t) by subtracting T _{offset_R_std} (t) from the time-series data u(t) using Equation (71).
Then, the control unit 300 derives the third index value u _of (t) by subtracting T _{offset_R_std} (t) from the time-series data u(t) using Equation (71).

The control unit 300 derives the deflection amount T _{r_rx} (t) by multiplying T _{std_rx_lp} (t) by R _{r_rx} using Equation (66). However, based on T _{std_rx_lp} (t) and c ₁ and c ₀ , the control unit 300 may derive the deflection amount T _{r_rx} (t) using Equation (67). Further, the control unit 300 may obtain T _{r_rx} (t) as in Equation (68) with c ₀ =0 before the entry time t _{i and} after the exit time t 0 . The control unit 300 derives the deflection amount offset T _{offset_rx} (t) at the designated position 9 using Equation (69) based on the derived T _{r_rx} (t).

Then, based on _uof (t), _{Rr_rx} , and _{Toffset_rx} (t), the control unit 300 derives the estimated value _{uest_rx} (t) using Equation (72).

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

(3-2) Derivation process:
The processing of the derivation system 10 of this embodiment is the same as that of the first embodiment except for the processing of S125 among the processing of FIG. 19 in the first embodiment. Among the processes of the present embodiment, points different from those of the first embodiment will be described.
In S<b>125 , the control unit 300 uses the function of the deflection deriving unit 306 to obtain T _{std_rx_lp} (t), which is a second index value that has been subjected to low-pass filter processing that attenuates components of the fundamental frequency or higher. The control unit 300 also obtains T _{std_R_lp} (t) that has been subjected to low-pass filter processing that attenuates components of the fundamental frequency or higher.

The control unit 300 derives the amplitude h _rx which is the average value of T _{std_rx_lp} (t) in the period from t ₁ to t ₂ using equation (62). The control unit 300 uses equations (55) and (56) based on u _lp (t), T _{std_R_lp} (t), t _a (t _i ), and t _b (t _o ). to derive coefficients c ₁ and c ₀ .
Then, based on the derived _c1 , _c0 and _hrx , the control unit 300 derives the amplitude ratio _{Rr_rx} using equation (65).

Based on T _{std_R_lp} (t) and c ₁ and c ₀ , control unit 300 derives T _{Estd_R_lp} (t) using equation (58).
The control unit 300 extracts the deflection amount data for a period of a predetermined length (for example, 1 second, 2 seconds, etc.) from u _lp (t), and the absolute value of the average value of the extracted data is set to a predetermined threshold value. If the above is satisfied and the absolute value of the difference between the maximum value and the minimum value of the extracted data is equal to or less than the predetermined width, the extracted period is determined as the period during which the deflection amount is shifted. Then, the control unit 300 sets k ₀ as the earliest order of observation of the amount of deflection during the period in which the amount of deflection is shifting. Further, the control unit 300 sets N to a value obtained by subtracting _k0 from the order of observation of the latest deflection amount during the period in which the deflection amount is shifted. Then, the control unit 300 derives the amplitude ratio R _r using equation (59) based on k ₀ , N, T _{std_R_lp} (t), and T _{Estd_R_lp} (t).

Control section 300 derives offset T _{offset_R_std} (t) at the observation point using equation (60) based on amplitude ratio R _r and T _{std_R_lp} (t). Then, the control unit 300 derives the third index value u _of (t) by subtracting T _{offset_R_std} (t) from the time-series data u(t) using Equation (71).
Then, the control unit 300 derives the third index value u _of (t) by subtracting T _{offset_R_std} (t) from the time-series data u(t) using Equation (71).

The control unit 300 derives the deflection amount T _{r_rx} (t) by multiplying T _{std_rx_lp} (t) by R _{r_rx} using Equation (66). The control unit 300 derives the deflection amount offset T _{offset_rx} (t) at the designated position 9 using Equation (69) based on the derived T _{r_rx} (t).

Then, based on _uof (t), _{Rr_rx} , and _{Toffset_rx} (t), the control unit 300 derives the estimated value _{uest_rx} (t) using Equation (72).

(4) 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 at a specified position from the displacement at the observation point as in the above embodiment can be realized as an invention of a program or an invention of a method.

Furthermore, a configuration may be adopted in which the functions of the server device 3 are realized by a plurality of devices. Each function of the server device 3 may be distributed and implemented in a plurality of devices. Also, each function of the server device 3 may be implemented in another device. For example, the functions of the acquisition unit 301 , the environment information acquisition unit 302 , the time derivation unit 303 , the number acquisition unit 304 , the index value acquisition unit 305 , and the deflection derivation unit 306 may be implemented in the measuring device 1 . A configuration or the like in which the server device 3 is distributed among a plurality of devices may also be used. Furthermore, the above-described embodiment is an example, and an embodiment in which some configurations are omitted or other configurations are added may be adopted.

In Embodiments 1 and 2 described above, the derivation system 10 derives the amount of deflection of a bridge through which a railroad train 6 composed of one or more railcars passes. However, the derivation system 10 may derive the amount of deflection of a bridge on which other moving bodies move. For example, the derivation system 10 may derive the amount of deflection of a bridge through which a train train with one or more connected trucks, a trailer with a plurality of vehicles connected to each other, or the like passes. Further, the derivation system 10 may derive the amount of deflection of a structure other than a bridge, such as a foundation supporting a railroad track.

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

In the first and second embodiments described above, the control unit 300 acquires displacement (deflection) data measured from acceleration detected via the acceleration sensor 210 as the time-series data u(t). However, the control unit 300 uses, as u(t), bridge displacement data derived from physical quantities detected via sensors such as impact sensors, pressure sensors, strain gauges, image measuring devices, load cells, and displacement gauges. may be obtained. For example, the control unit 300 detects the displacement of the observation point by periodically photographing a predetermined object placed at the observation point of the bridge 5 via the image measuring device, and acquires the data of the detected displacement. You may Also, the control unit 300 may acquire data of a physical quantity different from the displacement of the bridge as u(t). For example, the control unit 300 may obtain, as u(t), the number of pixels indicating the amount of displacement of a predetermined object placed at the observation point of the bridge 5 in the image captured through the image measuring device. .

Further, in the above-described first and second embodiments, the control unit 300 determines from the result of the FFT on the time-series data u(t) acquired by the function of the acquisition unit 301 that the side effect caused by the window function used in the FFT. Excluding the lobe, the peak corresponding to the lowest frequency was identified and the identified peak was taken as the fundamental frequency _Ff . However, the control unit 300 may obtain the fundamental frequency _Ff considering the influence of noise generated in the FFT result on u(t). For example, the control unit 300, from the FFT result for u (t), excludes side lobes caused by the influence of the window function used in the FFT, and identifies a peak above a predetermined threshold corresponding to the lowest frequency, The identified peak may be determined as the fundamental frequency _Ff .

_In the first embodiment described above, the control unit 300 adds the _time -series data u(t ) is derived as an estimated value of the amount of deflection at the specified position 9 . However, the control unit 300 may derive the estimated value of the deflection amount at the specified position 9 by another method.
For example, the control unit 300 may derive a value obtained by multiplying the first index value T _{std — R} (t) by Ravg as the estimated value of the deflection amount at the specified position 9 .

Also, the control unit 300 may derive an estimated value of the deflection amount at the specified position 9 as follows. The control unit 300 derives T _{std_R_lp} (t) and coefficients c ₁ and c ₀ as in the second embodiment. Then, based on T _{std_R_lp} (t), c ₁ and c ₀ , control unit 300 derives T _{Estd_R_lp} (t) using equation (58).
The control unit 300 extracts the deflection amount data for a period of a predetermined length (for example, 1 second, 2 seconds, etc.) from u _lp (t), and the absolute value of the average value of the extracted data is set to a predetermined threshold value. If the above is satisfied and the absolute value of the difference between the maximum value and the minimum value of the extracted data is equal to or less than the predetermined width, the extracted period is determined as the period during which the deflection amount is shifted. Also, the control unit 300 may receive designation of the start time and end time of the period in which the bending amount is shifted via the operation unit of the server device 3 or the like. Then, the control unit 300 sets k ₀ as the earliest order of observation of the amount of deflection during the period in which the amount of deflection is shifting. Further, the control unit 300 sets N to a value obtained by subtracting _k0 from the order of observation of the latest deflection amount during the period in which the deflection amount is shifted. Then, the control unit 300 derives the amplitude ratio R _r using equation (59) based on k ₀ , N, T _{std_R_lp} (t), and T _{Estd_R_lp} (t).
Control section 300 derives offset T _{offset_R_std} (t) at the observation point using equation (60) based on amplitude ratio R _r and T _{std_R_lp} (t). Based on c ₁ , T _{std_R} (t), and T _{offset_R_std} (t), the control unit 300 uses Equation (61) to derive the estimated value T _{EO_R} (t) of the amount of deflection at the observation point. Then, the control section 300 may derive a value obtained by multiplying T _{EO_R} (t) by Ravg as an estimated value of the deflection amount at the designated position 9 .

Further, the control unit 300 may obtain Ravg as a value different from the average value of the ratios of the first index value T _{std_R} (t) and the second index value T _{std_rx} (t). For example, here, a predetermined amount corresponding to the first index value T _{std_R} (t) is added to T _{std_R} (t) as an amount T _{std_R_lp} ( t). Further, the predetermined amount corresponding to the second index value T _{std_rx} (t) is the amount T _{std_rx_lp} (t) obtained by performing low-pass filtering for attenuating the frequency components equal to or higher than the fundamental frequency to T _{std_rx} (t). Suppose there is In this case, the control unit 300 may derive the average value of the ratios of T _{std_R_lp} (t) and T _{std_rx_lp} (t) as Ravg. For example, based on T _{std_R_lp} (t) and T _{std_rx_lp} (t), the control unit 300 obtains R _{rx_R} (t) using the following equation (73).

Control unit 300 may derive Ravg using equation (52) based on the obtained R _{rx_R} (t). Here, control unit ₃₀₀ uses t _i and to as t ₁ and t ₂ in equation (52), but other values may be used.
Then, the control unit 300 calculates the product of the estimated value T _{EO_R (t) derived based on the first index value T std_R (} t) and the derived Ravg as the estimated value of the deflection amount at the designated position 9. derived as Further, the control unit 300 may derive the product of the first index value T _{std_R} (t) or the time-series data u(t) and the derived Ravg as an estimated value of the deflection amount at the specified position 9. good.
In this way, the control unit 300 uses T _{std_R_lp} (t) and T _{std_rx_lp} (t) that have been subjected to low-pass filtering, thereby reducing the effect of high-frequency noise on T _{std_R_lp} (t) and T _{std_rx_lp} (t). can derive Ravg with reduced As a result, the control unit 300 can derive the estimated value of the deflection amount at the designated position 9 with higher accuracy.

The time-series data may be data acquired at a data rate that is at least twice the frequency of vibrations that are assumed to occur in structures due to movement of the moving body.

Furthermore, the present invention is also applicable as a computer-executed program or method. Moreover, the above programs and methods may be implemented as a single device or may be implemented using components provided in a plurality of devices, and include various modes. In addition, it can be changed as appropriate, such as a part of which is software and a part of which is hardware. Furthermore, the invention is established as a program recording medium. Of course, the recording medium for the program may be a magnetic recording medium, a semiconductor memory, or the like, and any recording medium that will be developed in the future can be considered in exactly the same way.

DESCRIPTION OF SYMBOLS 1... Measuring device, 2... Sensor device, 3... Server device, 4... Communication network, 5... Bridge, 6... Railroad train, 7... Superstructure, 7a... Bridge floor, 7b... Bearing, 7c... Rail, 7d... Sleeper , 7e... ballast, F... floor slab, G... main girder, 8... lower structure, 8a... bridge pier, 8b... abutment, 10... derivation system, 100... control unit, 110... storage unit, 120... communication unit, 200... Control unit 210 Acceleration sensor 220 Storage unit 230 Communication unit 300 Control unit 301 Acquisition unit 302 Environment information acquisition unit 303 Time derivation unit 304 Number acquisition unit 305 Index Value Acquisition Unit 306 Deflection Derivation Unit 310 Storage Unit 320 Communication Unit

Claims (14)

an acquisition step of acquiring time-series data including physical quantities occurring at a predetermined observation point in a structure in response to movement of an organized mobile body in which one or more mobile bodies are organized;
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 with the structure on the moving body is acquired as environment information. an environmental information acquisition step;
a time derivation step of deriving an entry time and an exit time from the structure of the mobile organization based on the time-series data;
a number acquisition step of acquiring the number of the moving bodies organized in the organized moving body;
Based on the number, the entry time, the exit time, and the environmental information, a first index value that is an index value of the amount of deflection of the structure occurring at the observation point, and an index value acquisition step of acquiring a second index value that is an index value of the amount of deflection at the specified position;
A linear function that approximates the amount corresponding to the time-series data by substituting the amount corresponding to the first index value for an argument between the first index value and the entry time and the exit time. an offset, which is the portion of the amount of deflection of the structure at the position that is not proportional to the first index value, derived based on a coefficient of , and a value obtained by subtracting the offset from the time-series data The third index value is the average value of the amplitudes of the second index value in a predetermined period and the linear function, which is subjected to low-pass filtering that attenuates frequency components equal to or higher than the fundamental frequency of the second index value. The sum of the sum of the product of the first-order coefficient and the zeroth-order coefficient of the linear function divided by the average value, and the sum of the divided value and the estimated amount of deflection of the structure at the position a deflection derivation step of deriving as
including
The offset is the product of the average value and the second index value, and the elements whose absolute values are larger than the 0th order coefficient of the linear function are rounded to the value of the 0th order coefficient of the linear function. is the value obtained by
The amount corresponding to the time-series data is the amount after attenuating the frequency components equal to or higher than the fundamental frequency of the time-series data from the time-series data,
The amount corresponding to the first index value is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value,
The predetermined period is a period in which the value of the second index value, which has been subjected to low-pass filtering for attenuating frequency components equal to or higher than the fundamental frequency of the second index value, falls within a predetermined width. Method. an acquisition step of acquiring time-series data including physical quantities occurring at a predetermined observation point in a structure in response to movement of an organized mobile body in which one or more mobile bodies are organized;
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 with the structure on the moving body is acquired as environment information. an environmental information acquisition step;
a time derivation step of deriving an entry time and an exit time from the structure of the mobile organization based on the time-series data;
a number acquisition step of acquiring the number of the moving bodies organized in the organized moving body;
Based on the number, the entry time, the exit time, and the environmental information, a first index value that is an index value of the amount of deflection of the structure occurring at the observation point, and an index value acquisition step of acquiring a second index value that is an index value of the amount of deflection at the specified position;
an average value between the entry time and the exit time of the ratio of the predetermined first amount corresponding to the first index value and the predetermined second amount corresponding to the second index value; a deflection derivation step of deriving an estimated value of the amount of deflection of the structure at the position based on the first index value;
including
the first amount is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value;
The derivation method, wherein the second amount is an amount obtained by attenuating, from the second index value, frequency components equal to or higher than the fundamental frequency of the second index value. In the time deriving step, the time series data corresponds to two consecutive data sandwiching a predetermined threshold, which are included in the time series data subjected to low-pass filter processing for attenuating vibration components with frequencies equal to or higher than the fundamental frequency of the time series data. The entry time and the exit time are obtained by performing, for each of the entry time and the exit time, a time within a period after one of the two times and before the other time. 3. The derivation method according to claim 1, wherein the time is derived. 2. In the number acquisition step, a value obtained by subtracting 1 from the product of the period from the entry time to the exit time and the fundamental frequency of the time-series data and rounding to an integer is acquired as the number. 4. The derivation method according to any one of 3. 5. The derivation method according to any one of claims 1 to 4, wherein the structure is a bridge. 6. The derivation method according to any one of claims 1 to 5, wherein the moving object is a railway vehicle that moves the structure via wheels. The time-series data is based on data detected through 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. 7. A derivation method according to any one of claims 1 to 6, which is data. The derivation method according to any one of claims 1 to 7, wherein BWIM (Bridge Weigh in Motion) is applicable to the structure. an acquisition unit that acquires time-series data including physical quantities that occur at a predetermined observation point in a structure in response to movement of an organized mobile body in which one or more mobile bodies are organized;
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 with the structure on the moving body is acquired as environment information. an environmental information acquisition unit;
a time derivation unit for deriving an entry time and an exit time to the structure of the mobile organization based on the time-series data;
A number acquisition unit that acquires the number of the moving bodies organized in the organized moving body;
Based on the number, the entry time, the exit time, and the environmental information, a first index value that is an index value of the amount of deflection of the structure occurring at the observation point, and an index value acquisition unit that acquires a second index value that is an index value of the amount of deflection at the designated position;
A linear function that approximates the amount corresponding to the time-series data by substituting the amount corresponding to the first index value for an argument between the first index value and the entry time and the exit time. an offset, which is the portion of the amount of deflection of the structure at the position that is not proportional to the first index value, derived based on a coefficient of , and a value obtained by subtracting the offset from the time-series data The third index value is the average value of the amplitudes of the second index value in a predetermined period and the linear function, which is subjected to low-pass filtering that attenuates frequency components equal to or higher than the fundamental frequency of the second index value. The sum of the sum of the product of the first-order coefficient and the zeroth-order coefficient of the linear function divided by the average value, and the sum of the divided value and the estimated amount of deflection of the structure at the position and a deflection derivation part that derives as
with
The offset is the product of the average value and the second index value, and the elements whose absolute values are larger than the 0th order coefficient of the linear function are rounded to the value of the 0th order coefficient of the linear function. is the value obtained by
The amount corresponding to the time-series data is the amount after attenuating the frequency components equal to or higher than the fundamental frequency of the time-series data from the time-series data,
The amount corresponding to the first index value is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value,
The predetermined period is a period in which the value of the second index value, which has been subjected to low-pass filtering for attenuating frequency components equal to or higher than the fundamental frequency of the second index value, falls within a predetermined width. Device. an acquisition unit that acquires time-series data including physical quantities that occur at a predetermined observation point in a structure in response to movement of an organized mobile body in which one or more mobile bodies are organized;
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 with the structure on the moving body is acquired as environment information. an environmental information acquisition unit;
a time derivation unit for deriving an entry time and an exit time to the structure of the mobile organization based on the time-series data;
A number acquisition unit that acquires the number of the moving bodies organized in the organized moving body;
Based on the number, the entry time, the exit time, and the environmental information, a first index value that is an index value of the amount of deflection of the structure occurring at the observation point, and an index value acquisition unit that acquires a second index value that is an index value of the amount of deflection at the designated position;
an average value between the entry time and the exit time of the ratio of the predetermined first amount corresponding to the first index value and the predetermined second amount corresponding to the second index value; a deflection derivation unit that derives an estimated value of the deflection amount of the structure at the position based on the first index value;
with
the first amount is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value;
The derivation device, wherein the second amount is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the second index value from the second index value. A derivation system comprising a derivation device and a sensor,
The derivation device is
A physical quantity generated at a predetermined observation point in a structure in response to movement of an organized mobile body in which one or more mobile bodies are organized, the physical quantity being measured via the sensor. , an acquisition unit that acquires time-series data;
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 with the structure on the moving body is acquired as environment information. an environmental information acquisition unit;
a time derivation unit for deriving an entry time and an exit time to the structure of the mobile organization based on the time-series data;
A number acquisition unit that acquires the number of the moving bodies organized in the organized moving body;
Based on the number, the entry time, the exit time, and the environmental information, a first index value that is an index value of the amount of deflection of the structure occurring at the observation point, and an index value acquisition unit that acquires a second index value that is an index value of the amount of deflection at the designated position;
A linear function that approximates the amount corresponding to the time-series data by substituting the amount corresponding to the first index value for an argument between the first index value and the entry time and the exit time. an offset, which is the portion of the amount of deflection of the structure at the position that is not proportional to the first index value, derived based on a coefficient of , and a value obtained by subtracting the offset from the time-series data The third index value is the average value of the amplitudes of the second index value in a predetermined period and the linear function, which is subjected to low-pass filtering that attenuates frequency components equal to or higher than the fundamental frequency of the second index value. The sum of the sum of the product of the first-order coefficient and the zeroth-order coefficient of the linear function divided by the average value, and the sum of the divided value and the estimated amount of deflection of the structure at the position and a deflection derivation part that derives as
The offset is the product of the average value and the second index value, and the elements whose absolute values are larger than the 0th order coefficient of the linear function are rounded to the value of the 0th order coefficient of the linear function. is the value obtained by
The amount corresponding to the time-series data is the amount after attenuating the frequency components equal to or higher than the fundamental frequency of the time-series data from the time-series data,
The amount corresponding to the first index value is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value,
The predetermined period is a period in which the value of the second index value, which has been subjected to low-pass filtering for attenuating frequency components equal to or higher than the fundamental frequency of the second index value, falls within a predetermined width. system. A derivation system comprising a derivation device and a sensor,
The derivation device is
A physical quantity generated at a predetermined observation point in a structure in response to movement of an organized mobile body in which one or more mobile bodies are organized, the physical quantity being measured via the sensor. , an acquisition unit that acquires time-series data;
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 with the structure on the moving body is acquired as environment information. an environmental information acquisition unit;
a time derivation unit for deriving an entry time and an exit time to the structure of the mobile organization based on the time-series data;
A number acquisition unit that acquires the number of the moving bodies organized in the organized moving body;
Based on the number, the entry time, the exit time, and the environmental information, a first index value that is an index value of the amount of deflection of the structure occurring at the observation point, and an index value acquisition unit that acquires a second index value that is an index value of the amount of deflection at the designated position;
an average value between the entry time and the exit time of the ratio of the predetermined first amount corresponding to the first index value and the predetermined second amount corresponding to the second index value; a deflection derivation unit that derives an estimated value of the deflection amount of the structure at the position based on the first index value;
with
the first amount is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value;
The derivation system, wherein the second quantity is a quantity obtained by attenuating frequency components equal to or higher than the fundamental frequency of the second index value from the second index value. to the computer,
an acquisition step of acquiring time-series data including physical quantities occurring at a predetermined observation point in a structure in response to movement of a structure by an organized mobile body in which one or more mobile bodies are organized;
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 with the structure on the moving body is acquired as environment information. an environmental information acquisition step;
a time derivation step of deriving an entry time and an exit time to the structure of the mobile organization based on the time-series data;
a number acquisition step of acquiring the number of the moving bodies organized in the organized moving body;
Based on the number, the entry time, the exit time, and the environmental information, a first index value that is an index value of the amount of deflection of the structure occurring at the observation point, and an index value acquisition step of acquiring a second index value that is an index value of the amount of deflection at the specified position;
A linear function that approximates the amount corresponding to the time-series data by substituting the amount corresponding to the first index value for an argument between the first index value and the entry time and the exit time. an offset, which is the portion of the amount of deflection of the structure at the position that is not proportional to the first index value, derived based on a coefficient of , and a value obtained by subtracting the offset from the time-series data The third index value is the average value of the amplitudes of the second index value in a predetermined period and the linear function, which is subjected to low-pass filtering that attenuates frequency components equal to or higher than the fundamental frequency of the second index value. The sum of the sum of the product of the first-order coefficient and the zeroth-order coefficient of the linear function divided by the average value, and the sum of the divided value and the estimated amount of deflection of the structure at the position A deflection derivation step, which derives as
and
The offset is the product of the average value and the second index value, and the elements whose absolute values are larger than the 0th order coefficient of the linear function are rounded to the value of the 0th order coefficient of the linear function. is the value obtained by
The amount corresponding to the time-series data is the amount after attenuating the frequency components equal to or higher than the fundamental frequency of the time-series data from the time-series data,
The amount corresponding to the first index value is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value,
The predetermined period is a period in which the value of the second index value, which has been subjected to low-pass filter processing that attenuates frequency components equal to or higher than the fundamental frequency of the second index value, falls within a predetermined width range. . to the computer,
an acquisition step of acquiring time-series data including physical quantities occurring at a predetermined observation point in a structure in response to movement of a structure by an organized mobile body in which one or more mobile bodies are organized;
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 with the structure on the moving body is acquired as environment information. an environmental information acquisition step;
a time derivation step of deriving an entry time and an exit time to the structure of the mobile organization based on the time-series data;
a number acquisition step of acquiring the number of the moving bodies organized in the organized moving body;
Based on the number, the entry time, the exit time, and the environmental information, a first index value that is an index value of the amount of deflection of the structure occurring at the observation point, and an index value acquisition step of acquiring a second index value that is an index value of the amount of deflection at the specified position;
an average value between the entry time and the exit time of the ratio of the predetermined first amount corresponding to the first index value and the predetermined second amount corresponding to the second index value; a deflection derivation step of deriving an estimated value of the amount of deflection of the structure at the position based on the first index value;
and
the first amount is an amount obtained by attenuating a frequency component equal to or higher than the fundamental frequency of the first index value from the first index value;
The program according to claim 1, wherein the second amount is an amount obtained by attenuating frequency components equal to or higher than the fundamental frequency of the second index value from the second index value.

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