Export method, export device, export system, program

Abstract

This invention relates to a method, apparatus, system, and program for deriving the dynamic response of a structure. Previously, it was impossible to determine the dynamic response at a specified location. The dynamic response at a specified location is derived based on the standardized deflection caused by the vibration components of the dynamic response, the amplitude ratio (a first deflection representing the distribution of vibration amplitude at the observation point) to the standardized deflection representing the distribution of vibration amplitude at the specified location (a second deflection), the vibration components at the specified location derived from the vibration components and the amplitude ratio, and the static response at the specified location derived from time-series data and estimated values.

Description

Technical Field

[0001] This invention relates to export methods, export devices, export systems, and programs. Background Technology

[0002] In recent years, many social infrastructures have deteriorated over the years, prompting a search for methods to diagnose the condition of structures that constitute social infrastructure, such as railway bridges.

[0003] Patent Document 1 discloses a method for investigating the structural performance of railway bridges, which can appropriately investigate and evaluate the structural performance of bridges using observational data of the bridge's acceleration response during train travel. The method for investigating the structural performance of railway bridges in Patent Document 1 is characterized by treating the train as a moving load and the bridge as a simply supported beam, formalizing a logical analysis model of the dynamic response of the railway bridge during train travel, measuring the acceleration of the bridge during train travel, and using this acceleration data to deduce unknown parameters of the logical analysis model through inverse analysis.

[0004] Furthermore, Patent Document 2 discloses a method for determining the impact coefficient and dynamic response components of a bridge by using the vertical acceleration response of a train traveling on the bridge.

[0005] Patent Document 1: Japanese Invention Patent No. 6543863

[0006] Patent Document 2: Japanese Invention Patent No. 6467304

[0007] Similar to railway trains, multiple moving bodies sometimes move in formation on structures such as bridges. In such cases, the movement of these continuously moving bodies can sometimes cause vibrations in the structure. Depending on the structure's natural vibration frequency, the structure may resonate with the vibrations generated by the movement of the formation. For purposes such as structural diagnosis, there is a desire to determine the dynamic response at specified locations within the structure that have not been observed. However, in Patent Documents 1 and 2, it was previously impossible to determine the dynamic response at specified locations where the structure had not been observed. Summary of the Invention

[0008] The derivation method for solving the above-mentioned problem includes: an acquisition step, acquiring time-series data, the time-series data including physical quantities generated at a predetermined observation point in the structure due to the response caused by the movement of a group of mobile bodies, which are grouped together as one or more mobile bodies, on a structure; an environmental information acquisition step, acquiring information such as the length of the structure, the length of the mobile bodies, and the location of the contact points of the mobile bodies with the structure as environmental information; a time derivation step, deriving the entry and exit times of the grouped mobile bodies relative to the structure based on the time-series data; a number acquisition step, acquiring the number of mobile bodies grouped together as the grouped mobile bodies; and an estimated value acquisition step, acquiring the static response generated as the response based on the number, the entry and exit times, the environmental information, and a model of the deflection of the structure. The structure is provided with an estimated value for the deflection at the observation point; and a deflection derivation step, which derives the dynamic response at the specified location based on the deflection, amplitude ratio, vibration component at the specified location, and static response at the specified location. The deflection is a standardized deflection caused by the vibration component of the dynamic response derived from the model as the difference between the time series data and the estimated value. The amplitude ratio is the ratio of a first deflection representing the distribution of vibration amplitude at the observation point to a second deflection representing the distribution of vibration amplitude at the specified location of the structure. The vibration component at the specified location is derived based on the vibration component and the amplitude ratio, and the static response at the specified location is derived based on the time series data and the estimated value.

[0009] A derivation device for solving the above-mentioned problem includes: an acquisition unit for acquiring time-series data, the time-series data including physical quantities generated at a predetermined observation point in the structure due to the response caused by the movement of a group of mobile bodies formed by grouping one or more mobile bodies on a structure; an environmental information acquisition unit for acquiring environmental information such as the length of the structure, the length of the mobile bodies, and the setting position of the contact parts of the mobile bodies with the structure; a time derivation unit for deriving the entry time and exit time of the group of mobile bodies relative to the structure based on the time-series data; a number acquisition unit for acquiring the number of mobile bodies grouped into the group of mobile bodies; and an estimated value acquisition unit for acquiring a static response generated as the response based on the number, the entry time, the exit time, the environmental information, and a model of the deflection of the structure. The estimated value of the deflection at the observation point of the structure; and the deflection derivation unit, which derives the dynamic response at the specified location based on the deflection, amplitude ratio, vibration component at the specified location, and static response at the specified location, wherein the deflection is a standardized deflection caused by the vibration component of the dynamic response derived from the model as the difference between the time series data and the estimated value, the amplitude ratio is the ratio of a first deflection representing the distribution of the vibration amplitude at the observation point to a second deflection representing the distribution of the vibration amplitude at the specified location of the structure, the vibration component at the specified location is derived based on the vibration component and the amplitude ratio, and the static response at the specified location is derived based on the time series data and the estimated value.

[0010] A derivation system for solving the above-mentioned problems includes a derivation device and a sensor. The derivation device comprises: an acquisition unit for acquiring time-series data, the time-series data including physical quantities generated at predetermined observation points in the structure due to the response caused by the movement of a group of mobile bodies formed as one or more mobile bodies on a structure, and the physical quantities measured by the sensor; an environmental information acquisition unit for acquiring information such as the length of the structure, the length of the mobile bodies, and the placement positions of the contact parts of the mobile bodies with the structure; a time derivation unit for deriving the entry and exit times of the group of mobile bodies relative to the structure based on the time-series data; a number acquisition unit for acquiring the number of mobile bodies grouped as the group of mobile bodies; and an estimated value acquisition unit for calculating the estimated value based on the number, the entry and exit times, the environmental information, and the deflection mode of the structure. The model obtains an estimated value of the deflection at the observation point of the structure as a static response generated by the response; and a deflection derivation unit derives the dynamic response at the specified location based on the deflection, amplitude ratio, vibration component at the specified location, and static response at the specified location. The deflection is a standardized deflection caused by the vibration component of the dynamic response derived from the model as a difference between the time series data and the estimated value. The amplitude ratio is the ratio of a first deflection representing the distribution of vibration amplitude at the observation point to a second deflection representing the distribution of vibration amplitude at the specified location of the structure. The vibration component at the specified location is derived based on the vibration component and the amplitude ratio, and the static response at the specified location is derived based on the time series data and the estimated value.

[0011] The program for solving the above-mentioned problem causes a computer to perform the following steps: an acquisition step, acquiring time-series data, the time-series data including physical quantities generated at a predetermined observation point in the structure due to the response caused by the movement of a group of mobile bodies, which are grouped together as one or more mobile bodies, on a structure; an environmental information acquisition step, acquiring information such as the length of the structure, the length of the mobile bodies, and the location of the contact points of the mobile bodies with the structure as environmental information; a time derivation step, deriving the entry and exit times of the group of mobile bodies relative to the structure based on the time-series data; a count acquisition step, acquiring the number of mobile bodies grouped together as the group of mobile bodies; and an estimated value acquisition step, acquiring the physical quantities generated as the response based on the count, the entry and exit times, the environmental information, and a model of the deflection of the structure. The static response of the structure includes an estimated value of the deflection at the observation point; and a deflection derivation step, which derives the dynamic response at the specified location based on the deflection, amplitude ratio, vibration component at the specified location, and static response at the specified location. The deflection is a normalized deflection caused by the vibration component of the dynamic response derived from the model as the difference between the time series data and the estimated value. The amplitude ratio is the ratio of a first deflection representing the distribution of vibration amplitude at the observation point to a second deflection representing the distribution of vibration amplitude at the specified location of the structure. The vibration component at the specified location is derived based on the vibration component and the amplitude ratio, and the static response at the specified location is derived based on the time series data and the estimated value. Attached Figure Description

[0012] Figure 1 This is a block diagram showing the structure of the export system.

[0013] Figure 2 This is a diagram showing the cross-section of the bridge.

[0014] Figure 3 This is a diagram showing the dimensions of a unit bridge truss.

[0015] Figure 4 It is a diagram showing the dimensions of railway vehicles.

[0016] Figure 5 This is a diagram showing the outline of a unit bridge truss.

[0017] Figure 6 This is a diagram illustrating the bending moment in a unit bridge truss.

[0018] Figure 7This is a diagram showing a general outline of the deflection of a unit bridge truss caused by the wheels.

[0019] Figure 8 It is a diagram showing the general deflection of a unit bridge truss caused by railway vehicles.

[0020] Figure 9 It is a diagram showing the outline of the deflection of a unit bridge truss caused by a railway train.

[0021] Figure 10 This is a diagram showing the deflection of a unit bridge truss caused by railway vehicles.

[0022] Figure 11 This is a graph showing the FFT results of the deflection of a unit bridge truss.

[0023] Figure 12 This is a diagram showing the deflection of a unit bridge truss caused by a railway train after high-pass filtering.

[0024] Figure 13 It is a diagram showing the deflection of the unit bridge truss caused by each railway vehicle.

[0025] Figure 14 It is a diagram showing the deflection of the unit bridge truss caused by individual railway vehicles and trains.

[0026] Figure 15 This is a graph showing the estimated value of the deflection.

[0027] Figure 16 It is a graph showing the amplitude at the specified location.

[0028] Figure 17 This is a graph showing the amplitude ratio.

[0029] Figure 18 This is a diagram showing the offset.

[0030] Figure 19 This is a graph showing the estimated value of the deflection.

[0031] Figure 20 This is a diagram showing the amount of deflection caused by resonance.

[0032] Figure 21 This is a graph showing the FFT results of the deflection caused by resonance.

[0033] Figure 22 This is a diagram showing the first wave.

[0034] Figure 23 This is a diagram showing the third wave.

[0035] Figure 24 This is a graph showing the amplitude of the first wave.

[0036] Figure 25 This is a graph showing the amplitude of the first wave.

[0037] Figure 26 This is a graph showing the amplitude of the first wave.

[0038] Figure 27 This is a graph showing the amplitude of the third wave of the normalized deflection of a bridge-based structural formula.

[0039] Figure 28 This is a graph showing the amplitude of a third wave obtained by approximating it with a sine wave.

[0040] Figure 29 This is a diagram showing the derived first-order wave component.

[0041] Figure 30 This is a diagram showing the derived third wave components.

[0042] Figure 31 It is a graph showing the dynamic response at the observation point and the dynamic response at the derived specified location.

[0043] Figure 32 It is a diagram showing the details of the various elements of the derived system.

[0044] Figure 33 This diagram illustrates the export processing of entry and exit times.

[0045] Figure 34 This diagram illustrates the export processing of entry and exit times.

[0046] Figure 35 This is a flowchart illustrating the export process.

[0047] Explanation of reference numerals in the attached figures

[0048] 1: Measuring device; 2: Sensor device; 3: Server device; 4: Communication network; 5: Bridge; 6: Railway train; 7: Superstructure; 7a: Bridge deck; 7b: Support body; 7c: Guide rail; 7d: Sleeper; 7e: Gravel; F: Bridge deck; G: Main beam; 8: Substructure; 8a: Pier; 8b: Bridge seat; 10: Output system; 100: Control unit; 110: Storage unit; 120: Communication unit; 200: Control unit; 210: Accelerometer sensor; 220: Memory; 230: Communication unit; 300: Control unit; 301: Acquisition unit; 302: Environmental information acquisition unit; 303: Time output unit; 304: Count acquisition unit; 305: Estimated value acquisition unit; 306: Deflection output unit; 310: Storage unit; 320: Communication unit. Detailed Implementation

[0049] Hereinafter, embodiments of the present invention will be described in the following order.

[0050] (1) The composition of the export system:

[0051] (1-1) Exporting the system overview:

[0052] (1-2) Flexural model:

[0053] (1-3) Verification Experiment:

[0054] Details of elements (1-4):

[0055] (2) Export processing:

[0056] (3) Other implementation methods:

[0057] (1) The composition of the export system:

[0058] (1-1) Exporting the system overview:

[0059] Figure 1 This is a block diagram illustrating an example of the configuration of the derivation system 10 in this embodiment. The derivation system 10 is a system that, based on time-series data of physical quantities at predetermined observation points on a bridge 5 where a railway train 6, composed of one or more railway vehicles, moves, derives the dynamic response generated on the bridge 5 according to the passage of the railway train 6, at a designated location 9 different from the observation points on the bridge 5. The railway train 6 is an example of a assembled moving body. Each railway vehicle included in the railway train 6 is an example of a moving body. The bridge 5 is an example of a structure through which the moving bodies move. Each railway vehicle of the railway train 6 moves on the bridge 5 via wheels provided on its axles. The wheels are an example of the contact points between the railway vehicles and the bridge. In this embodiment, the railway vehicles assembled into the railway train 6 are structurally identical. Figure 1 As shown, the export system 10 includes a measuring device 1, at least one sensor device 2 installed on the superstructure 7 of the bridge 5, and a server device 3.

[0060] The measuring device 1 calculates the deflection, or displacement, of the superstructure 7 caused by the movement of the railway train 6 based on acceleration data output from each sensor device 2. The measuring device 1 is, for example, installed on the bridge abutment 8b. The measuring device 1 can communicate with the server device 3, for example, via a communication network 4 such as a mobile phone wireless network or the Internet. The measuring device 1 sends information about the displacement of the superstructure 7 caused by the movement of the railway train 6 to the server device 3. Based on the sent displacement data, the server device 3 derives the number of railway cars grouped into the railway train 6.

[0061] In this embodiment, bridge 5 is a railway bridge, such as a steel bridge, beam bridge, or RC bridge. RC is short for Reinforced-Concrete. Furthermore, in this embodiment, bridge 5 is a structure capable of applying BWIM (Bridge Weight in Motion). BWIM is a technique that compares a bridge to a "scale," measuring the weight, number of axles, etc., of vehicles passing on the bridge by measuring the bridge's deformation. A bridge that can analyze the weight of a moving object passing on it based on its deformation, strain, and other responses can be considered a structure capable of applying BWIM. Therefore, by applying the BWIM system, which describes the physical process between the action and response of the bridge, the weight of a moving object moving on the bridge can be measured. The correlation coefficient between displacement and load is determined in advance, and based on the measured displacement of the bridge when the moving object passes, the load of the passing moving object is derived using the correlation coefficient, thereby measuring the weight of the moving object.

[0062] Bridge 5 has a movable part, namely the superstructure 7 and the substructure 8 that supports the superstructure 7. Figure 2 It is by Figure 1 The AA line provides a sectional view of the upper structure 7. (See figure.) Figure 1 as well as Figure 2 As shown, the superstructure 7 includes: a bridge deck 7a comprising a bridge deck F, main beams G, crossbeams (not shown), etc.; a support 7b; guide rails 7c; sleepers 7d; and aggregate 7e. Furthermore, as... Figure 1 As shown, the lower structure 8 includes piers 8a and abutments 8b. The upper structure 7 is a structure erected between adjacent abutments 8b and piers 8a, between two adjacent abutments 8b, or between two adjacent piers 8a. Hereinafter, abutments 8b and piers 8a will be collectively referred to as support parts. In this embodiment, a set of support parts, i.e., support bodies, and the portion of the upper structure 7 erected between these support parts are collectively considered as a single bridge truss. That is, a simply supported beam-like structure supported at both ends by two support parts is considered as a single bridge truss. Therefore, Figure 1 The bridge 5 shown comprises two trusses. Hereinafter, each truss of bridge 5 will be referred to as a unit truss.

[0063] The measuring device 1 and the sensor device 2 communicate via a wired or wireless connection, for example, through a communication network such as CAN (Controller Area Network).

[0064] The sensor device 2 is used in measuring a predetermined physical quantity for deriving the displacement (deflection) at an observation point set on the upper structure 7. In this embodiment, the predetermined physical quantity is acceleration. Furthermore, in this embodiment, the sensor device 2 is set at the observation point. In addition, the sensor device 2 includes an accelerometer, a MEMS (Micro Electro Mechanical Systems) accelerometer, or other accelerometer sensors. The sensor device 2 outputs data on the acceleration derived from the displacement of the upper structure 7 caused by the movement of the moving body, i.e., the railway train 6, at the observation point.

[0065] In this embodiment, the sensor device 2 is disposed at the center of the superstructure 7 along its length, specifically at the center of the main beam G along its length. However, the sensor device 2 is only required to detect the acceleration used to calculate the displacement of the superstructure 7, and its placement is not limited to the center of the superstructure 7. Furthermore, when the sensor device 2 is disposed on the bridge deck F of the superstructure 7, it may be damaged by the movement of the railway train 6, and the measurement accuracy may be affected by local deformation of the bridge deck 7a. Therefore, in… Figure 1 as well as Figure 2 In the example, sensor device 2 is installed on the main beam G of the superstructure 7.

[0066] The bridge deck F and main beam G of the superstructure 7 deflect vertically according to the load of the railway train 6 traveling on the superstructure 7. Each sensor device 2 measures the acceleration of the deflection of the bridge deck F and main beam G caused by the load of the railway train 6 traveling on the superstructure 7.

[0067] The designated position 9 is a position on bridge 5 that is specified as a derived object of the dynamic response generated by the unit truss of bridge 5 based on the passage of railway train 6.

[0068] (1-2) Flexural model:

[0069] Here, a model of bridge deflection in the case of a railway train moving on a unit bridge truss is explained. Here, the model consists of information such as formulas representing the correspondence between given information and derived results.

[0070] Furthermore, in the following, the number of railway cars (units) that will move on the bridge as a train is denoted as N. The time when the train enters the bridge, i.e., the entry time, is denoted as t. i Here, the entry of a railway train onto the bridge refers to the entry of the wheels of axle 1 of railway vehicle C1 (the first railway vehicle from the front of the train) onto the unit bridge truss. Furthermore, in the following, the moment when the railway train exits the unit bridge truss, i.e., the exit time, is denoted as t. oHere, the train exiting the unit bridge truss is the railway vehicle C. N The wheels of the very last axle of the last train (the last car in a train) are removed from the unit bridge truss. Furthermore, the following refers to the period during which the train passes over the unit bridge truss (from entry time t). i Exit time t o The period is set as t. s In the following, N and t will be... i t o t s The information is unified as observation information.

[0071] Furthermore, in the following, the length of the unit bridge truss, i.e., the bridge length, will be denoted as L. B Bridge length is an example of structural length. Furthermore, the distance from the end of a unit bridge truss along its length, on the side facing the direction from which the railway train approaches, to the observation point is denoted as L. x .exist Figure 3 L is shown in the middle B and L x In the following, the end of the unit bridge truss along its length that faces the direction in which the train is approaching is designated as the approach end. Furthermore, the end of the unit bridge truss along its length that faces the direction in which the train is retreating is designated as the exit end. Additionally, the length of the m-th train car from the front of the train is defined as L. c (m). Vehicle length is an example of the length of a moving body. In the following, L... c (1)~L c (N) are collectively referred to as L c Furthermore, the m-th railway car from the very front of the train is designated as C. m In addition, railway vehicles C m Let the number of axles in the vehicle be a. r (m). Below, a will be... r (1)~a r (N) are collectively referred to as a r In the following, from railway vehicle C m Starting from the front, the railway vehicles C are arranged in order. m a in r (m) axles are designated as axle 1, axle 2, axle 3, ..., a r (m) axis. Furthermore, from railway vehicle C... m Let L be the distance from the end of the forward direction in the middle to axis 1. a (a w (m、1)). Here, a w (α, β) represents the β axle of the α-th train in the railway system. Furthermore, from railway vehicle C... mLet L be the distance from the (n-1)th axis (n: an integer greater than 2) to the nth axis. a (a w (m, n)). That is, L a (a w (α, β) represents railway vehicle C α The distance between the β-axis and the (β-1)-axis in the equation, or the distance between the railway vehicle C and the (β-1)-axis. α The β-axis in the railway vehicle C α The distance at one end in the direction of travel. In the following, L... a (a w (1、1))~L a (a w (N、a r (N))) collectively referred to as L a L a These represent the positions of the corresponding axles in the corresponding railway vehicles. For example, L a (a w (m、1)) indicates that in railway vehicle C m From the front end in L a (a w There exists an axis 1 behind the distance (m, 1). Furthermore, L a (a w (m、2)) indicates that in railway vehicle C m From axis 1 in L a (a w There is a 2-axis behind the distance (m, 2)).

[0072] Here, railway vehicles with the same four axles are grouped together to form a railway train. That is, a r (m)(m=1, 2, ······, N) is 4. In Figure 4 Railway vehicle C is shown in the middle. m L in c (m), L a (a w (m、1)), L a (a w (m、2)), L a (a w (m、3)), L a (a w (m、4)).

[0073] In the following, L B L x L c a r L a It is unified as environmental information.

[0074] As shown in equation (1) below, ts As t o With t i The difference is calculated.

[0075] t s =t o -t i ···(1)

[0076] In addition, the total number of wheels T of the railway train can be calculated using the following formula (2). ar .

[0077]

[0078] From the first axle of the first railway car C1 to the mth railway car C m The distance along the n-axis is represented as D. wa (a w (m, n)). Calculate D according to the following formula (3). wa (a w (m, n)).

[0079]

[0080] From the first axle of railway car C1 at the very front of the railway car fleet to the last railway car C... N The last axis a r The distance (N) is D wa (a w (N、a r (N))). Using D wa (a w (N、a r (N))), as shown in equation (4) below, represents the average speed v of the railway train passing on the unit bridge truss. a .

[0081]

[0082] Based on equations (3) and (4), the following equation (5) holds true.

[0083]

[0084] Next, the deflection that occurs in the unit bridge truss when a load is applied will be explained.

[0085] exist Figure 5 A schematic diagram of a unit bridge truss is shown. Figure 5The diagram illustrates the condition where a load P is applied to a bridge. Here, the unit bridge truss is modeled as a simply supported beam supported at both ends. Furthermore, the distance between the location of the applied load P in the unit bridge truss and the entry end is denoted as a. Furthermore, the distance between the location of the applied load P in the unit bridge truss and the exit end is denoted as b. In this case, the bending moment at the location of the applied load P in the unit bridge truss is expressed by the following equation (6).

[0086]

[0087] exist Figure 6 The diagram shows the bending moments at various locations on a unit bridge truss, based on load P. For example... Figure 6 As shown, the bending moment generated by the load P in the unit truss is 0 at the entry end and increases proportionally as it approaches the position where the load P is applied, becoming the value shown in equation (6) at the position where the load P is applied. Furthermore, the bending moment generated by the load P in the unit truss decreases proportionally as it approaches the exit end from the position where the load P is applied, becoming 0 at the exit end. Therefore, the bending moment at any position X in the unit truss is expressed by the following equation (7).

[0088]

[0089] In equation (7), x represents the distance from the entry point in the direction of travel of the railway train to position X. Furthermore, H in equation (7) a It is the value shown by the following equation (8).

[0090]

[0091] The relationship between the deflection w and bending moment of a unit bridge truss at any location X is given by the following equation (9).

[0092]

[0093] In equation (9), θ is the angle between the horizontal line at position X and the deflected unit truss. Based on equations (7) and (9), the following equation (10) holds.

[0094]

[0095] By integrating both sides of equation (10) twice with x, we can obtain the following equation (11) which represents the deflection w at position X.

[0096]

[0097] In equation (11), g1 and g2 are constant terms. Here, since the unit bridge truss is supported at both the entry and exit ends, no deflection occurs at these locations. That is, in equation (11), at x = 0 and x = L... B In the case of , both ends become 0. Therefore, g1 and g2 are as shown in equations (12) and (13) below.

[0098] g1=ab(a+2b)···(12)

[0099] g2=0···(13)

[0100] Based on equations (11), (12), and (13), the following equation (14) is derived to represent the deflection w at position X.

[0101]

[0102] When a load P is applied at the center of the length direction of a unit bridge truss, the maximum deflection among the deflections generated by the unit bridge truss due to the application of load P occurs at the center of the length direction of the unit bridge truss. Let this maximum deflection be w. 0.51 Find the representation of w. 0.51 The formula is as follows: When the load P is applied at the center of the length of a unit bridge truss, a = b = 0.5L. B Furthermore, since the determined position X of the deflected object is the center of the length direction of the unit bridge truss, x = 0.5L. B Furthermore, in this case, since x ≤ a, therefore according to equation (8), H a =0. x = 0.5L B a = b = 0.5L B H a Substituting 0 into equation (14), we can obtain the value representing the deflection w. 0.51 The following formula (15).

[0103]

[0104] Use w 0.51 The deflection at any position in the unit bridge truss, expressed by equation (14), is standardized.

[0105] When the load P is located further into the end than the position X, i.e., x > a, according to equation (8), H a =1, as in equation (14) below (16).

[0106]

[0107] Let a = L Br. Here, r is a real number greater than 0 and less than 1. Since b = L B -a, therefore it can be expressed as b=L B (1-r). When a = L B r, b = L B Substitute (1-r) into equation (16) and divide by w 0.51 When standardizing, the standardized deflection w at position X, representing the case where x > a, is calculated. std The following formula (17).

[0108]

[0109] Similarly, when the load P is located further from the exit end than the location X, i.e., x ≤ a, according to equation (8), H a =0, as in equation (14) below (18).

[0110]

[0111] Let a = L B r. Here, r is a real number greater than 0 and less than 1. Since b = L B -a, therefore it can be expressed as b=L B (1-r). When a = L B r, b = L B Substitute (1-r) into equation (18) and divide by w 0.51 When standardizing, the standardized deflection w at position X, representing the case where x ≤ a, is calculated. std The following formula (19).

[0112]

[0113] L x Substituting x into equations (17) and (19), the standardized deflection w at the observation point of the deflection is obtained as shown in equation (20) below. std Represented as a function of r.

[0114]

[0115] The function R(r) in equation (20) is the function shown in equation (21) below.

[0116]

[0117] Here, using equations (20) and (21), we obtain the expression representing the condition based on any axle a. wThe time variation of the deflection at the observation point caused by the load (m, n) applied to the bridge by the wheels.

[0118] First, let t be the time it takes for a wheel of one axle of a railway train to travel from the entry point to the observation point. xn According to L x and v a t can be obtained using the following formula (22). xn .

[0119]

[0120] Furthermore, the time taken for one wheel of a railway train to traverse across a unit bridge truss, i.e., the time taken to travel from the entry end to the exit end, is denoted as t. ln According to L B and v a t can be obtained using the following formula (23). ln .

[0121]

[0122] In addition, the nth axle of the mth railway vehicle of the railway train will be... w Let t be the time when the wheels of (m, n) arrive at the entry end. o (m, n). According to t i v a and D wa (a w (m, n)), t is obtained using the following formula (24). o (m, n).

[0123]

[0124] According to equation (22), L is expressed as in equation (25) below. x .

[0125] L x =v a t xn ···(25)

[0126] Furthermore, according to equation (23), L is expressed as in equation (26) below. B .

[0127] L B =v a t ln ···(26)

[0128] axle w The positions of (m, n) represent the load positions. Therefore, axle a wThe position of (m, n) is a distance a = L from the entry end to the exit end. B The position of r. Furthermore, when the variable representing time is set to t, a at time t... w The distances (m, n) from the entry point and the distances of the railway vehicles from time t o The distances traveled by (m, n) to time t are equal. Therefore, the following equation (27) holds.

[0129] L B r = v a (t-t0(m,n))···(27)

[0130] According to equation (27), r is expressed as in equation (28) below.

[0131]

[0132] Using equations (25), (26), and (28), we can modify L in equations (20) and (21). x L B The values ​​of r are replaced, thus representing the value based on the axle a. w The model of the time variation of the deflection at the observation point caused by the load applied by the (m, n) wheels to the unit bridge truss is used to derive the function w of the following equation (29). std (a w (m, n), t). The function R(t) in equation (29) is the function shown in equation (30) below.

[0133]

[0134]

[0135] When the observation information and environmental information (t) i t o N, L B L x L c (1)~L c (N), a r (1)~a r (N), L a (a w (1、1))~L a (a w (N、a r When (N) is known, use this information to calculate w. std (a w (m, n), t). For example, according to t i t o Using equation (1), we can calculate t. s According to ts N, a r L a L c Using equation (5), we can calculate v. a According to v a L B and L x Using equations (22) and (23), t is calculated. xn t ln According to L a L c t i Using equations (3) and (24), t is calculated. o (m, n). Furthermore, the calculated t... xn t ln t o Substituting (m, n) into equations (29) and (30), we can obtain the function w of t. std (a w (m, n), t).

[0136] exist Figure 7 w is shown std (a w An example of the change in deflection at the observation point (m, n), t). Figure 7 The horizontal axis of the graph represents time, and the vertical axis represents deflection. Furthermore, based on a railway vehicle C... m The movement, and about a r Each of the (m) axles' respective wheel sets moves on the unit bridge truss. Therefore, w is the value of each axle. std (a w The sum of (m, n), and t is obtained as shown in equation (31) below, representing the sum of the sums ... m The function C of the model represents the time-varying deflection at the observation point caused by the movement of the object. std (m, t).

[0137]

[0138] exist Figure 8 The text appears to be a mix of Chinese characters and symbols, possibly related to a programming language or a specific language. A direct translation wouldn't be meaningful without further context or clarification. r When (m) is 4, that is, railway vehicle C m When the function C is composed of 4 axes std The diagram shows the change in deflection at the observation point (m, t). Figure 8 The horizontal axis of the graph represents time, and the vertical axis represents the deflection. Furthermore, Figure 8 The solid line in the graph represents C. std (m, t), the dashed curves represent w for each axle. std (aw (m, n), t).

[0139] Furthermore, based on the movement of the railway trains, N railway vehicles move on the unit bridge truss. Therefore, C is related to each railway vehicle. std The sum of (m, t) is used to obtain the function T, which represents the time variation of the deflection at the observation point caused by the movement of a railway train, as shown in equation (32) below. std (t).

[0140]

[0141] exist Figure 9 The diagram shows the function T when N is 16, i.e., when 16 railway vehicles are assembled into a railway train. std The graph (t) shows the change in deflection at the observation point. Figure 9 The horizontal axis of the graph represents time, and the vertical axis represents the deflection. Furthermore, Figure 9 The solid line in the graph represents T. std (t), the dashed curves represent C for each railway vehicle. std (m, t). For example... Figure 9 As shown in the curve, it can be seen that the waveform is obtained by adding the deflections of each passing railway vehicle, which generates the vibration of a continuous railway vehicle passing on a unit bridge truss under the cycle.

[0142] The following is an explanation of the deflection model in a unit bridge truss. Thus, the deflection model in this embodiment is based on the formula of a bridge structure represented by simply supported beams at both ends.

[0143] (1-3) Verification Experiment:

[0144] The inventors determined the deflection T under the condition that the observed information and environmental information are set to the values ​​shown below. std (t). That is, N = 4, t i =7.21 [seconds], t o = 8.777 [seconds], t s = 1.567 [seconds], L B =25[m], L x =12.5[m], L c = 25[m], a respectively r =4 respectively, regarding each m = 1 to N and L a (a w (m, 1)) = 2.5[m], regarding each m = 1 ~ N and L a (a w (m, 2)) = 2.5[m], regarding each m = 1 ~ N and La (a w (m, 3)) = 15[m], regarding each m = 1 ~ N and L a (a w (m、4))=2.5[m].

[0145] exist Figure 10 The value of the deflection T at this time is shown in the figure. std (t). Figure 10 The horizontal axis of the graph represents time, and the vertical axis represents deflection. Furthermore, the inventors, through the calculation of T... std T is obtained by performing a Fast Fourier Transform (FFT) on (t). std The intensity of each frequency component included in (t). Figure 11 The text shows the relationship between T and T. std The result of FFT of (t). Figure 11 The horizontal axis of the graph represents frequency, and the vertical axis represents the intensity of the corresponding frequency component. Furthermore, the inventors used T as the frequency of vibrations generated on the bridge due to the continuous movement of railway vehicles. std The FFT result of (t) is used to calculate T. std The fundamental frequency F of (t) f Here, the fundamental frequency is the frequency of the lowest frequency component included in the signal. Specifically, the inventors, based on T... std The FFT result of (t) removes sidelobes caused by the window function used in the FFT, determines the peak value corresponding to the lowest frequency, and uses the determined peak value as the fundamental frequency. Figure 11 In the example shown by the dashed line, two sidelobe peaks were found in the range less than 2 Hz, resulting from the influence of the window function used in the FFT. The inventors identified the peak in the portion enclosed by the dashed line as the lowest frequency peak among the remaining peaks after removing these peaks, and used the frequency corresponding to the identified peak as the fundamental frequency F. f Find it. The inventor based on Figure 11 The fundamental frequency of 3.1Hz was determined from the curve.

[0146] The inventors used the following formula (33) to calculate the passage period t. s The included fundamental frequency F f The wave number ν.

[0147] v = t s F f ···(33)

[0148] In this case, ν = 1.567 × 3.1 = 4.8577. Here, the number of railway cars in the moving train is 4. The inventors discovered the following feature: during the passage period t...s The included fundamental frequency F f The wave number ν is approximately 1 greater than N. This characteristic will be referred to as the first characteristic below. Therefore, the inventors discovered that using the number N of railway vehicles included in a railway train as the reference for the passage period t... s Included from the fundamental frequency F f The wave number ν is obtained by subtracting 1 and rounding it to an integer value, and is obtained using the following formula (34). The round function is a function that returns the value of the independent variable after rounding.

[0149] N = round(v-1)···(34)

[0150] Furthermore, the inventors used the following formula (35) based on the fundamental frequency F. f Find the fundamental period T. f .

[0151]

[0152] Moreover, the inventor used the fundamental period T f For the deflection T std (t) is used to perform a moving average, thereby adjusting T. std (t) Implement low-pass filtering to attenuate components at frequencies above the fundamental frequency. Low-pass filtering can also be other FIR filtering processes that attenuate components at frequencies above the fundamental frequency. The T frequency after low-pass filtering... std Let (t) be T. std_lp (t)=T std_lp (kΔt). Here, k represents the nth observation when the deflection is periodically observed at the observation point. That is, when the data period (time resolution) of the deflection observation is ΔT, t = kΔT.

[0153] As shown in equation (36) below, based on the fundamental period T f Given ΔT, calculate the moving average interval k adjusted to the time resolution of the data. mf .

[0154]

[0155] Use k mf According to the following equation (37), T is obtained. std_lp (t).

[0156]

[0157] The inventors obtained the deflection amount T from the data. std (t) minus T std_lp (t) and for T std(t) A high-pass filter was applied to attenuate components with frequencies lower than the fundamental frequency. This high-pass filtering could also be another FIR filter that attenuates components with frequencies lower than the fundamental frequency. The high-pass filtered T... std Let (t) be T. std_hp (t). Specifically, as shown in equation (38) below, the inventors obtain T std (t) minus T std_lp (t) and find T std_hp (t).

[0158] T std_hp (t)=T std (kΔT)-T std_lp (t)···(38) The calculated T std_hp (t) and T std (t) overlap, in Figure 12 As shown in the image. Figure 12 The horizontal axis of the graph represents time (t = kΔT), and the vertical axis represents the deflection. Figure 12 The solid line curve represents T std_hp (k), the dashed curve represents T std (t).

[0159] according to Figure 12 The curve, through the period t s (from entry time t) i Exit time t o During the period) T std_hp The number of positive peaks in (t) is 6. Here, the positive peak is T. std_hp The peak value of (t) is the one that bulges upwards towards the bridge. Furthermore, during period t... s T in std_hp The number of negative peaks in (t) is 5. Here, the negative peak is T. std_hp Among the peak values ​​of (t), there is a peak that bulges downwards towards the bridge. In view of this, the inventors discovered the following feature: during period t... s T in std_hp The number of positive peaks (6) of (t) is two more than the number of railway vehicles N(4) included in the railway train, and the number of negative peaks (6) is one more than N(4). Hereinafter, this feature will be referred to as the second feature.

[0160] The inventors changed the observed and environmental information to various values ​​and verified whether the first and second characteristics were valid. As a result, the inventors discovered that, when L is satisfied... c / 2<L B <3L cIn the case of / 2, the first and second features hold true. The inventors discovered that, based on the first and second features, the number of railway cars in a train 6 can be derived from the time-series data of the bridge's displacement (deflection) at the bridge's observation points. Hereinafter, the time-series data of the displacement at the bridge's observation points will be denoted as u(t). u(t) is data representing discrete values ​​of displacement measured at a predetermined period, and is data that establishes a correspondence between each discrete value and the measurement time.

[0161] The inventors, under the condition that the observed information and environmental information are as shown below, investigated the deflection C of a railway train composed of identical railway vehicles when it passes over a bridge. std (1、t)~C std (N, t), T std (t) was examined. That is, N=4, t i =7.21 [seconds], t o = 8.777 [seconds], t s = 1.567 [seconds], L B =25[m], L x =12.5[m], L c = 25[m], a respectively r =4 respectively, regarding each m = 1 to N and L a (a w (m, 1)) = 2.5[m], regarding each m = 1 ~ N and L a (a w (m, 2)) = 2.5[m], regarding each m = 1 ~ N and L a (a w (m, 3)) = 15[m], regarding each m = 1 ~ N and L a (a w (m、4))=2.5[m].

[0162] exist Figure 13 The figure shows the deflection C caused by the four railway vehicles included in the train at this time. std (1、t)~C std (4, t). Let T be the period of vibration generated on the bridge when railway vehicles continuously pass over it. f The vibrations produced on a bridge when railway vehicles continuously pass over it are the vibrations caused by the continuous passage of railway vehicles. Therefore, the period T f Let C be the time difference between the arrival times of consecutive railway vehicles crossing the bridge. Since the deflection caused by a railway vehicle on the bridge begins from the moment it enters the bridge, C... std The starting time of the deflection shown in (m, t) is related to C. stdThe time difference between the start times of the deflection shown in (m+1, t) is the period T. f .exist Figure 13 The diagram shows the deflection of a bridge as a train passes over it, caused by the passage of individual train cars. Figure 13 The horizontal axis of the graph represents time, and the vertical axis represents the deflection. For example... Figure 13 As shown, in T f The time difference causes the deflection of successive railway vehicles.

[0163] Due to period T f It is the time difference between the arrival times of consecutive railway vehicles passing on the bridge and entering the bridge. Therefore, as shown in the following equation (39), the vehicle length L can be expressed as... c (m) is considered to be at a velocity v a During the period of passage.

[0164]

[0165] Railway cars C of railway trains m Let t be the time spent traveling on the bridge. c (m). t c (m) is the moving body, i.e., the railway vehicle C. m An example of a moving body passing through a structure, i.e., a bridge. c (m) is from railway vehicle C m The moment when axle 1 arrives at the entry end of the railway vehicle C m a r The time interval during which the (m) axis reaches the exit end. That is, t c (m) represents railway vehicle C m The length of the moving bridge L B With railway vehicle C m The foremost axle, i.e., axle 1, to the last axle, i.e., axle 'a'. r The total distance of the distance along the (m) axis during the period. Therefore, t is expressed by the following equation (40). c (m).

[0166]

[0167] Let C be the number of railway cars in a train that are assembled when the train crosses a bridge, and the number of cars that have subsequent train cars. Tn Regarding the railway vehicles in a train, excluding the last vehicle, there are subsequent vehicles. Therefore, C Tn Let N be a number that is 1 less than N. That is, the following equation (41) holds.

[0168] ts =C Tn T f +t c (m)···(41) in Figure 14 C is shown in the middle. std (1、t)~C std (N, t), T std (t). Figure 14 The horizontal axis of the graph represents time, and the vertical axis represents the amount of deflection. Figure 14 The solid line curve represents T std (t), the dashed curves represent C respectively. std (1、t)~C std (4, t). For example... Figure 14 As shown, during period t s C Tn T f With a railway vehicle C m During the period t when passing on the bridge c The total of (m). That is, the following equation (42) holds.

[0169] N = C Tn +1···(42)

[0170] According to equations (41) and (42), the number N of railway vehicles grouped into a railway train is represented by the following equation (43).

[0171]

[0172] T f It is also the time it takes for a railway train to move the length of one railway vehicle. Therefore, the time t takes for a railway train to pass through is... s The distance traveled is the length of (N-1) railway vehicles and the distance traveled at a speed of v. a In t c The total distance traveled during the period (m). Therefore, the following equation (44) holds.

[0173]

[0174] According to equation (44), the following equation (45) holds. According to equation (45), it can also be confirmed that equation (43) holds.

[0175]

[0176] It can be considered that, as the fundamental frequency F f The component of the deflection T of the bridge when a railway train passes over it. std (t) includes the component of vibration generated on the bridge due to the continuous movement of railway vehicles. Because F fIt is also based on the frequency of vibrations generated on the bridge due to the continuous movement of railway vehicles, and therefore can be expressed as T as shown in the following equation (46). f The reciprocal of.

[0177]

[0178] According to equations (39) and (46), as in equation (47) below, F is used. f With L c The product of (m) represents the velocity v. a .

[0179] v a =F f L C (m)···(47) Therefore, t expressed in terms of equation (40) c (m), where L is the length of the bridge. B With railway vehicle C m The foremost axle, i.e., axle 1, to the last axle, i.e., axle 'a'. r The total distance of the (m) axis divided by F f With L c The value is obtained by producting (m).

[0180] According to equations (43) and (46), the number N of railway vehicles grouped into a railway train is expressed as the number of railway vehicles t during the time the railway train passes over the bridge. s Subtract one railway vehicle C m During the passage of the bridge t c The value after (m) and the fundamental frequency F f The value obtained by adding 1 to the product is expressed as shown in the following formula (48).

[0181] N=(t s -t c (m))F f +1···(48)

[0182] As shown in equation (47), the inventors discovered that the fundamental frequency F f With one railway vehicle C included in the railway train m The product of lengths represents the average speed v of the railway train. a Furthermore, as shown in equation (40), the inventors discovered that a railway vehicle C m During the period t when passing on the bridge c (m) is represented as railway vehicle C. m With velocity v a The length L of the moving bridge B With railway vehicle C m Axis 1 to a r(m) The total distance of the distance between axes during the period. Furthermore, as shown in equation (48), the inventors discovered that the number N of railway vehicles grouped into a railway train is expressed as the distance from t s Subtract t c The value after (m) and the fundamental frequency F f The value is obtained by adding 1 to the product.

[0183] Moreover, the inventors devised the following method: using time-series data of displacement at observation points on bridges where railway trains move, they derived the number of railway vehicles that make up the railway train.

[0184] The inventor's proposed method is as follows: Obtain the time-series data u(t) of the displacement at an observation point on a bridge where a railway train is moving, and obtain L... B L c and L a As environmental information, the fundamental frequency F of u(t) is obtained based on the time-series data u(t). f As the frequency of vibrations generated on the bridge due to the continuous passage of railway vehicles grouped as trains, the duration t of the train passing on the bridge is derived based on u(t). s Based on L B L c L a F f and t s Using the relationships shown in equations (40), (47), and (48), the number of railway vehicles included in a railway train can be derived.

[0185] In this embodiment, the derivation system 10 derives the value of the number N of railway vehicles that are assembled into a railway train 6 based on the time-series data u(t) of the deflection of the bridge 5 measured at the observation point and using insights obtained through experiments.

[0186] Furthermore, the inventors conceived of using the deflection amount T at that location derived from the deflection model. std (t) proportional deflection, and T that is disproportionate to the deflection derived from the deflection model. offset The sum of (t) approximates the actual deflection T(t) at a certain location in the bridge. That is, as in the following equation (49), the inventors conceived of using T(t) as a representation of T. std The equation (t) is approximated by a first-order function. c1 in equation (49) is a first-order coefficient. Here, the part proportional to the deflection derived from the deflection model is the displacement proportional to the load in the unit bridge truss to which BWIM can be applied.

[0187]

[0188] The inventors conceived that, as shown in the following equation (50), u, which has undergone low-pass filtering on the time series data measured at the observation point, is... lp (t) is T with respect to the first-order coefficient c1. std_R_lp Approximating T as a linear function of t. std_R_lp (t) represents the standardized deflection T at the observation point derived using the deflection model. std_R (t) is the value obtained by applying a low-pass filter to attenuate components above the fundamental frequency. c0 in equation (50) is a zero-order coefficient, representing displacement assumed to be independent of the position of the observation point.

[0189]

[0190] When the value obtained by subtracting the right side from the left side of equation (50) is taken as the error, and the least squares method is used to derive c1 and c0 in a way that minimizes the error, it becomes the following equations (51) and (52).

[0191]

[0192]

[0193] In equations (51) and (52), t a Use T std_R_lp (t) for u lp (t) is the start time of a predetermined period for the object being approximated. In this embodiment, t is... a Let's set the entry time as t. i In addition, t b Use T std_R_lp (t) for u lp (t) is the end time of a predetermined period for the object being approximated. In this embodiment, t is... b Set as exit time t o Furthermore, the value of k in equations (51) and (52) is expressed by the following equation (53).

[0194]

[0195] As shown on the right side of equation (50), T will be used. std_R_lp The deflection obtained by restoring (t) and coefficients c1 and c0 is denoted as T. Estd_R_lp (t). T Estd_R_lp (t) is as shown in equation (54) below. Here, when t < t i , t>t o During this period, since the railway train is not supported by the unit bridge truss, there is no deflection, and it is set as c0 = 0.

[0196]

[0197] As shown in equation (55) below, T is obtained. Estd_R_lp (t) and T std_R_lp The amplitude ratio of (t) to R r In equation (55), k0 represents the value of the deflection u. lp The earliest observed value of deflection during the period of waveform deflection and transformation of (t) is the nth observation. Furthermore, n is the value representing the deflection amount u. lp The latest observed value of deflection during the waveform transition of (t) is the value of the nth observation minus k0. That is, in u lp The latest observed value of the deflection during the waveform transition of (t) is the k0+nth observation.

[0198]

[0199] As in equation (56) below, the inventors will use the offset T at the observation point. offset_R_std (t) is assumed to be Rr and T std_R_lp The product of (t), and rounded to c0 for elements whose absolute value is greater than c0. That is, T offset_R_std (t) represents the component of deflection that approaches c0 as the railway train enters the bridge, remains constant after reaching c0, and converges to 0 as the railway train exits.

[0200]

[0201] The estimated value of the deflection at the observation point, and the deflection independent of resonance, based on the static response caused by the passing of a railway train, is set as T. EO_R (t). Here, the static response represents the deflection caused by the load of a moving body passing over the bridge. The static response does not include the deflection caused by the resonance of the bridge excited by the passing of the moving body. Furthermore, the dynamic response is the sum of the static response and the deflection caused by resonance. The inventors believe that, according to the relationship shown in equation (50), T can be expressed as follows in equation (57). EO_R (t) represents the sum of c1 and the estimated value T using the flexure model. std_R The product of (t) and T offset_R_std The sum of (t).

[0202] T EO_R (t)=c1T std_R (t)+T offset_R_std (t)···(57)

[0203] exist Figure 15The figure shows the time-series data u(t) of the actual deflection measured at the observation point on the bridge, and the standardized deflection T at the observation point derived from the deflection model. std_R (t) The deflection derived from equation (57) is the estimated value T of the static response. EO_R (t). Figure 15 The horizontal axis of the graph represents time, and the vertical axis represents the amount of deflection. Figure 15 The solid line curve represents T EO_R (t). Furthermore, the dashed line graph represents u(t). In Figure 15 The estimated value T is shown in the figure. EO_R (t) is an exact reconstruction of u(t). Furthermore, in Figure 15 In the example, since the bridge's natural vibration frequency is not near the frequency of vibrations generated on the bridge due to the passing of a railway train, no resonance is generated on the bridge caused by the passing of a railway train.

[0204] In addition, the inventors conceived of a method for deriving the deflection of the static response at a specified location other than the observation point in a unit bridge truss, as follows.

[0205] Here, the distance L from the entry end to the exit end on the unit bridge truss will be... B ×r x The location is specified as the location from which the deflection is derived. Here, it is set to r. x =0.05. Here, we will use the L of equations (20), (21), (22) and (25). x Replace with L B ×r x The standardized deflection at a specified location, derived from the deflection model, is denoted as T. std_rx (t). Furthermore, T was subjected to a low-pass filter that attenuated components above the fundamental frequency. std_rx Let (t) be T. std_rx_lp (t).

[0206] Here, using the coefficients c1 and c0 derived at the observation point location in the unit bridge truss, the result will be obtained by applying T... std_rx_lp The amount of deflection restored by adding c0 to the product of (t) and coefficient c1 is denoted as T. Estd_rx_lp (t). The inventor conceived of using T std_rx (t), T std_rx_lp A method for deriving the deflection amount representing the static response at a specified location using (t) and coefficients c1 and c0.

[0207] The following describes the sequence of the method performed by the inventor.

[0208] Inventor obtains T std_rx(t), regarding the obtained T std_rx (t), T is obtained by implementing a low-pass filter that attenuates components above the fundamental frequency. std_lp (t).

[0209] Furthermore, the inventors derived T using the following formula (58). std_rx_lp The amplitude h of (t) rx .exist Figure 16 The derived amplitude h is shown in the figure. rx .

[0210]

[0211] In equation (58), t1 and t2 are the start and end times of any period within the timeframe during which the bridge generates vibrations caused by the passage of a railway train, respectively. In this embodiment, t1 and t2 are respectively set as the start and end times of any period within the timeframe during which the bridge generates vibrations caused by the passage of a railway train. std_rx_lp (t) The start and end times of the period set within the transition period. That is, t1 and t2 are the start and end times of T, respectively. std_rx_lp The value of (t) converges within a given range of width centered on a value whose absolute value is greater than a given value. For example, t1 and t2 can also be obtained through periods t1 and t2 respectively. s (from entry time t) i Exit time t o The start and end times of a predetermined width (e.g., 1 second, 2 seconds, etc.) in the middle of a period. Furthermore, t1 and t2 can also be the start and end times from the entry time t1. i Only after a predetermined period has elapsed (e.g., through period t) s The time period of a predetermined proportion (10%, 30%, etc.) from the exit time t o Only the past given period (e.g., through period t) s The time period of a predetermined proportion (10%, 30%, etc.).

[0212] Thus, the inventor uses equation (58) to calculate T during the period from t1 to t2. std_rx_lp The average value of (t) is used as the amplitude h rx Export.

[0213] The inventors obtained u based on a low-pass filter applied to the time-series data u(t) to attenuate components above the fundamental frequency. lp (t), and the estimated value T of the standardized deflection at the observation point derived using the deflection model. std_R (t) T is obtained by performing a low-pass filter that attenuates components above the fundamental frequency. std_rx_lp (t), using equations (51) and (52), derive the coefficients c1 and c0.

[0214] For T Estd_rx_lp We will discuss the amplitude of (t). Estd_rx_lp (t) is a relation to T std_rx_lp The value of (t) plus the coefficient c1 plus c0. Therefore, it represents T. Estd_rx_lp (t) and T std_rx_lp The time function R of the amplitude ratio of (t) r_rx (t) is as shown in equation (59).

[0215]

[0216] exist Figure 17 The function R is shown in the figure. r_rx (t). Here, due to T std_rx_lp (t) changes during the period from t1 to t2, therefore the denominator and numerator on the right side of equation (59) are approximately constant during the period from t1 to t2, R r_rx The value of (t) is also approximately constant. That is, the period from t1 to t2 is R. r_rx The amplitude ratio values ​​at each time point (t) converge within a given width centered on a value whose absolute value is above a given value. Here, R during the period from t1 to t2... r_rx Let the average amplitude ratio of (t) be R. r_rx The amplitude ratio R is expressed as shown in equation (60) below. r_rx .

[0217]

[0218] In addition, T Estd_rx_lp The amplitude of (t) is relative to T std_rx_lp The amplitude h of (t) rx The value obtained by adding c0 to the product of c1 and c0. Therefore, the amplitude ratio R is also calculated as in equation (61) below. r_rx Represented as T Estd_rx_lp The amplitude of (t) and T std_rx_lp The amplitude h of (t) rx The ratio.

[0219]

[0220] The inventors based their work on t1, t2, and R. r_rx (t), using equation (60), the amplitude ratio R is derived. r_rx However, based on h rx c1 and c0 can also be used to determine the amplitude ratio R by using equation (61). r_rx The derivation of T. Furthermore, the inventors used equation (62) to derive the derivation of T. std_rx_lp (t) multiplied by R r_rx The obtained deflection Tr_rx (t).

[0221] T r_rx (t)=T std_rx_lp (t)R r_rx ···(62)

[0222] Furthermore, it is possible to use R of equation (62) r_rx Replace with T Estd_rx_lp (t)(for T) std_rx_lp The value of (t) plus the coefficient c1 plus c0 and T std_rx_lp The following equation (63) is derived from the ratio of (t) to the deflection T. r_rx (t).

[0223] T r_rx (t)=c1T std_rx_lp (t)+c0···(63)

[0224] Alternatively, it can be done earlier than the entry time t. i Later than exit time t o Let c0 = 0, and set T r_rx (t) is set as shown in equation (64).

[0225]

[0226] Moreover, the inventors used formula (65) based on the derived T r_rx (t), derives the offset T of the deflection at the specified location. offset_rx (t). That is, the inventor rounds T to c0 for elements whose absolute value is greater than c0. r_rx As T offset_rx (t) Export.

[0227]

[0228] exist Figure 18 The exported T is shown in the figure. offset_rx (t). Figure 18 The horizontal axis of the graph represents time, and the vertical axis represents the amount of deflection. Figure 18 The solid line curve represents T offset_rx (t). Furthermore, the dashed line graph represents T. r_rx (t). In Figure 18 T is shown offset_rx The value of (t) approaches c0 as the train enters the bridge, remains constant during the period when c0 is constant, and converges to 0 as the train leaves the bridge.

[0229] Furthermore, the inventors used the following formula (66) to compare the coefficients c1 and T.std_rx The product of (t) plus T offset_rx (t), thus deriving the estimated value T of the deflection at the specified location on the bridge. EO_rx (t). In Figure 19 The value T is shown in the figure. EO_rx (t) and the estimated value T of the deflection at the observation point derived in equation (57). EO_R (t). Figure 19 The horizontal axis of the graph represents time, and the vertical axis represents the amount of deflection.

[0230] T EO_rx =c1T std_rx (t)+T offset_rx (t)···(66)

[0231] In this way, the static response, i.e., the deflection, of the unit truss at a specified location 9 can be derived.

[0232] The inventor conceived of obtaining the vertical vibration component caused by the resonance generated in the bridge due to the passage of a railway train by subtracting the estimated value of the deflection (static response) at the observation point, derived using a deflection model, from the time-series data of the dynamic response measured at the observation point of the bridge. Hereinafter, the vertical vibration component caused by the resonance generated in the bridge due to the passage of a moving body will be considered as the vibration component of the dynamic response. Furthermore, the vibration component of the dynamic response generated in the bridge due to the passage of a railway train will be simply considered as the vibration component. The deflection caused by the vibration component of the dynamic response at the observation point will be denoted as u. nv (t).

[0233] That is, as in the following equation (67), the inventors conceived of subtracting the estimated value T of the static response at the observation point, i.e., the deflection independent of resonance, from the time-series data u(t) of the dynamic response measured at the observation point. EO_R (t), thus enabling the deflection (vibration component) u caused by resonance at the observation point to be derived. nv (t). In Figure 20 The diagram shows how to subtract T from u(t). EO_R (t) and the derived vibration component u nv An example of (t). Figure 20 The horizontal axis of the graph represents time, and the vertical axis represents the deflection. Furthermore, the observation point is located at the center of the bridge in the direction of the railway train's travel.

[0234] u nv (t)=u(t)-T EO_R (t)···(67)

[0235] In addition, the inventors conceived of the following method: based on the vibration component u derived in equation (67) nv (t), by means of the following, the amount of deflection of the dynamic response caused by resonance at a specified location in the bridge.

[0236] The following describes the sequence of the method performed by the inventor.

[0237] The inventor Figure 20 The vibration component u shown nv (t) performed an FFT. Figure 21 The text shows the relationship between u and u. nv The result of FFT of (t). Figure 21 The horizontal axis of the graph represents frequency, and the vertical axis represents the intensity of the corresponding frequency component.

[0238] The inventor based on u nv The FFT results of (t) identified the peak with the smallest frequency among the peaks whose intensity was above a given threshold (in Figure 21 (The example shows the peak value indicated by the solid arrow). Furthermore, the inventors determined the frequency corresponding to the determined peak value, 2.79167 Hz, as the fundamental frequency of the vibration component of the bridge's resonant dynamic response. Hereinafter, the fundamental frequency of the bridge's vibration component will be simply referred to as the fundamental frequency.

[0239] In addition, the inventor based on u nv The FFT results of (t) identified other peaks with intensities above a given threshold (in Figure 21 (The peak value shown by the dashed arrow in the example). Furthermore, the inventors determined the peak value corresponding to the third wave component of a frequency three times the fundamental frequency (2.79167Hz), based on the fact that the frequency corresponding to the determined peak value becomes approximately three times the fundamental frequency (8.3542Hz). Hereinafter, the fundamental frequency and its higher harmonics in the vibration components of the dynamic response generated in the bridge through resonance are transformed into the natural frequencies of the unit bridge truss. Furthermore, hereafter, the component of a frequency that is a natural number q times the fundamental frequency is taken as the qth wave.

[0240] In view of this situation, the inventor is identified as u. nv The main components of (t) are the fundamental frequency component and the component of the frequency three times the fundamental frequency (the third wave).

[0241] The inventor of u nv (t) Perform bandpass filtering to extract the fundamental frequency component, thereby extracting u nv (t) includes the fundamental frequency components. In the following, u nv Let the components of the q-th wave included in (t) be u. nv_q(t). For example, u nv The fundamental frequency components included in (t) become u nv_1 (t).

[0242] In addition, the inventors have made improvements to u nv (t) Perform bandpass filtering to extract the components of higher harmonic frequencies that are three times the fundamental frequency, thereby extracting u. nv The 3rd wave component u included in (t) nv_3 (t).

[0243] exist Figure 22 , Figure 23 The extracted u are shown in the figure. nv_1 (t), u nv_3 (t). Figure 22 , Figure 23 The horizontal axis of each graph represents time, and the vertical axis represents the amount of deflection.

[0244] When the load position *a* at the entry end of the bridge is located to the left of the observation point position *x* (here, denoted as the position at 1 / 2 of the bridge), since *x* > *a*, according to equation (8), H... a =1. Therefore, when x = 1 / 2, H a Substituting 1 into equation (14), and setting it as a+b=1, we can calculate the deflection w at the observation point caused by the load passing through the left side. L The following equation (68) is given. Here, l is a variable representing the length of the bridge.

[0245]

[0246] Furthermore, in the case where the load position 'a' at the entry end of the bridge exists further to the right than the observation point, since x < a, according to equation (8), H a =0. Therefore, when x = 1 / 2, H a Substituting 0 into equation (14), we can obtain the deflection w at the observation point, which represents the load passing through the right side. R The following formula (69) is given.

[0247]

[0248] Furthermore, when the load position in the bridge is the central observation point, since x = a, according to equation (8), H a =0. Therefore, when x = 1 / 2, H a Substituting 0 into equation (14), we can obtain the deflection w at the observation point when a load is applied. P The following formula (70) is given.

[0249]

[0250] In the model of a simply supported beam bridge supported at both ends, the deflection becomes maximum when the observation point is at the center and a load is applied at the center of the bridge. Therefore, similarly to equation (70), the maximum value w of the deflection caused by the load in the bridge is... max As in equation (71) below.

[0251]

[0252] When w as shown in equation (68) L Divide by w as shown in equation (71) max and through w max When standardizing, the following equation (72) is obtained.

[0253]

[0254] In equation (72), let a / l = r. When the load position is standardized by the length of the bridge, the following equation (73) is obtained.

[0255]

[0256] Furthermore, when w is shown in equation (69) R Divide by w as shown in equation (71) max and through w max When standardizing, the following equation (74) is obtained.

[0257]

[0258] Here, based on a / l=r, a+b=l, and b=l / (1-r), when b=l / (1-r) is substituted into equation (74) and the bridge length is standardized to l=1, the following equation (75) is obtained.

[0259]

[0260] With the bridge length standardized to 1, as the load moves on the bridge, the standardized deflection amplitude w observed at the center of the bridge is calculated as follows, as in equation (76) obtained by unifying equations (73) and (75). std .

[0261]

[0262] In equation (76), r and (1-r) represent the ratio of the distance from the end of the bridge to the load location to the length of the bridge. As shown in equation (77) below, a variable A is defined by unifying r and (1-r).

[0263]

[0264] When using A as shown in equation (77), equation (76) is expressed as in equation (78) below.

[0265] w std =3A-4A 3 ···(78)

[0266] exist Figure 24 w is shown std . Figure 24 The horizontal axis of the curve represents r, and the vertical axis represents the normalized amplitude. Furthermore, in Figure 25 The waveform of the sine wave sin(rπ) is shown in the figure. Figure 25 The horizontal axis represents r, and the vertical axis represents amplitude. The inventor discovered that... Figure 24 , Figure 25 The waveforms shown are similar. Furthermore, the inventors discovered that w... std It is approximated as sin(rπ).

[0267] The vibrational components, which are the dynamic response caused by resonance, generate components of the fundamental frequency and components of higher harmonics that are natural multiples of 2 or more of the fundamental frequency in the bridge through resonance. These components are sinusoidal vibrations with the two ends of the bridge as nodes. Therefore, when the specified position on the bridge is a distance lr from the entry end to the exit end, the normalized deflection w at the specified position, showing the distribution of the vibration amplitude of the q-th wave, is given by the following equation (79). q_std (r) can be approximated by sin(qrπ).

[0268] w q_std (r)=sin(qrπ)···(79)

[0269] sin(rπ) is approximately equal to equation (78). Therefore, in the interval 0 ≤ r ≤ 1, the normalized deflection w represents the distribution of the vibration amplitude, including the fundamental frequency component and the higher harmonic frequency components. q_std (r) becomes the following equation (80). Aw q_std (r)=(-1) [qr] (3A-4A 3 )

[0270] However,

[0271] The model for the standardized deflection representing the distribution of vibration amplitude in this embodiment is based on a formula for a simply supported beam bridge structure. Here, the observation point is set at a distance lr from the entry end to the exit end. Furthermore, the location specified for deriving the deflection on the bridge is also set at a distance lr from the entry end to the exit end. x The location.

[0272] The inventors substituted q = 1 and r = R into equation (80) to calculate the amplitude, i.e., the deflection w, of the normalized first-order wave (the component of the fundamental frequency) at the observation point. 1_std (R). Furthermore, the inventors set q = 1 and r = r x Substituting into equation (80), the normalized amplitude of the first wave, i.e., the deflection w, at the specified location is obtained. 1_std (r x ).

[0273] As shown in equation (81) below, the ratio Cr of the amplitude (i.e., deflection) of the q-wave at the observation point to the amplitude (i.e., deflection) of the q-wave at the specified location is Cr. q As w q_std (R) and w q_std (r x The ratio is calculated from the given ratio.

[0274]

[0275] Here, the deflection u caused by the vibration component at the observation point nv (t) mainly includes the first-order wave component and the third-order wave component. Therefore, the inventors used equation (81) to derive the ratio Cr1 of the amplitude (i.e., deflection) of the vibration component at the observation point to the amplitude (i.e., deflection) of the vibration component at the specified location. Figure 26 r is shown x w when R = 0.1 and R = 0.5 1_std (R), w 1_std (r x ). Figure 26 The horizontal axis represents r, and the vertical axis represents the normalized deflection, showing the distribution of the vibration amplitude. In this case, substituting q = 1 and R = 0.5 into equation (81), w 1_std (R) is found to be 1. Given q = 1 and r... x Substituting 0.1 into equation (81), we can determine the value of w. 1_std (r x The value is calculated to be 0.296. Therefore, setting Cr1 to 0.296 / 1, the value is calculated to be 0.296.

[0276] Let the q-th wave component of the deflection of the vibration component at the specified location be set as u. nv_q_rx(t). As in equation (82) below, the deflection u caused by resonance at the observation point is... nv The component u of the q-th wave included in (t) nv_q (t) multiplied by Cr q And find u nv_q_rx (t).

[0277] y nv_q_rx (t)=Cr q u nv_q (t)···(82)

[0278] As in equation (82), the inventor multiplied the calculated Cr1 by u nv_1 (t), where u is the component of the fundamental frequency of the dynamic response at the specified location. nv_1_rx (t) Export.

[0279] Furthermore, the inventors used equation (81) to derive the ratio Cr3 of the deflection of the third wave of the dynamic response at the observation point to the deflection of the third wave of the vibration component at the specified location. Figure 27 r is shown x w when R = 0.1 and R = 0.5 3_std (R), w 3_std (r x ). Figure 27 The horizontal axis represents r, and the vertical axis represents the amplitude of the normalized deflection, i.e., the deflection, which shows the distribution of the vibration amplitude. In this case, substituting q = 3 and R = 0.5 into equation (81), w 3_std (R) is calculated to be -1. Given q = 3 and r... x Substituting 0.1 into equation (81), we can determine the value of w. 3_std (r x The value is calculated to be 0.809. Therefore, setting Cr3 to 0.809 / 1, the result is 0.809. Furthermore, in... Figure 28 The text shows that in r x When R = 0.1 and R = 0.5, the w derived from equation (79) is used. 3_std (R), w 3_std (r x ). Figure 28 The horizontal axis represents r, and the vertical axis represents the amplitude of the normalized deflection, which shows the distribution of the vibration amplitude.

[0280] Moreover, as in equation (82), the inventor multiplied the calculated Cr3 by u nv_3 (t), the third wave component of the deflection of the vibration component of the dynamic response at the specified location is taken as u. nv_3_rx (t) Export.

[0281] exist Figure 29The exported u is shown in the figure. nv_1_rx (t). Figure 29 The horizontal axis of the graph represents time, and the vertical axis represents the deflection. Figure 30 The exported u is shown in the figure. nv_3_rx (t). Figure 30 The horizontal axis of the graph represents time, and the vertical axis represents the amount of deflection.

[0282] The inventor will derive u nv_1_rx (t) and u nv_3_rx The value obtained by adding (t) is used as the estimated value of the vibration component of the dynamic response at the specified location. That is, as in the following equation (83), based on the derived q-wave u nv_q_rx The sum of (t) gives the vibration component u at the specified location. nv_q_est (t).

[0283]

[0284] Furthermore, the inventors discovered that by using the deflection model, the estimated value T of the static response at a specified location can be obtained. EO_rx (t) and the estimated value u of the vibration component of the dynamic response. nv_q_est (t) are added together, and thus, as in equation (84) below, the estimated value T of the dynamic response at the specified location can be obtained. EST_rx (t).

[0285] T EST_rx (t)=T EO_rx (t)+u nv_q_est (t)···(84) in Figure 31 It is shown that T EO_rx (t), u nv_1_rx (t) and u nv_3_rx The deflection is obtained by adding (t) together. Figure 31 The horizontal axis of the graph represents time, and the vertical axis represents the amount of deflection. Figure 31 The solid line curve represents T EO_rx (t), u nv_1_rx (t) and u nv_3_rx The deflection is obtained by adding (t) together. Furthermore, Figure 31 The dashed line curve represents u(t).

[0286] The derivation system 10 of this embodiment derives the dynamic response at a specified position 9 of the unit bridge truss based on the method conceived by the inventors.

[0287] Details of elements (1-4):

[0288] Here, use Figure 32The details of the measuring device 1, sensor device 2, and server 3 of the export system 10 are described below. In this embodiment, the position of the designated position 9 in the unit bridge truss is a distance L from the entry end to the exit end. B ×r x The location. Here, r x It represents the distance from the entry end to the designated position 9 in the unit bridge truss relative to L. B The value of the proportion.

[0289] The measuring device 1 measures the deflection at the observation point via the sensor device 2. In this embodiment, the measuring device 1 is installed on the bridge base 8b, but it can also be installed in other locations. The measuring device 1 includes a control unit 100, a storage unit 110, and a communication unit 120. The control unit 100 includes a processor such as a CPU (Central Processing Unit), ROM (Read-Only Memory), RAM (Random Access Memory), etc. The control unit 100 expands various programs recorded in the ROM, etc., in the RAM and executes them via the CPU, thereby realizing the various functions of the measuring device 1. The storage unit 110 stores various programs, measured deflection data, etc. The communication unit 120 includes circuitry for wired or wireless communication with external devices.

[0290] As a predetermined physical quantity at the observation point, sensor device 2 detects acceleration. Sensor device 2 includes a control unit 200, an acceleration sensor 210, a storage unit 220, and a communication unit 230. The control unit 200 includes a processor such as a CPU, ROM, RAM, etc. The control unit 200 expands various programs recorded in the ROM, etc., in the RAM and executes them via the CPU, thereby realizing the various functions of sensor device 2.

[0291] Accelerometer 210 is an accelerometer such as a crystal accelerometer or a MEMS accelerometer capable of detecting accelerations generated in the directions of each of the three mutually orthogonal axes. In this embodiment, the accelerometer 210 is configured with one axis parallel to the vertical direction in order to more accurately detect acceleration in the vertical direction. However, the sensor device 2 in the upper structure 7 is sometimes installed at an angle. Even without combining the three detection axes of the accelerometer 210 which are set in the vertical direction, the measuring device 1 synthesizes the accelerations of the three axes and detects the acceleration in the vertical direction.

[0292] The control unit 200 of the sensor device 2 periodically detects the vertical acceleration at an observation point in the bridge 5 via the accelerometer 210 and sends the detected acceleration data to the measuring device. The control unit 100 of the measuring device 1 measures the vertical deflection of the bridge 5 at the observation point at the time of acceleration detection based on the acceleration data sent from the sensor device 2. In this embodiment, the control unit 100 integrates twice the acceleration shown in the data sent from the sensor device 2 with respect to time to calculate the vertical deflection of the bridge 5 at the observation point. Furthermore, the control unit 100 sends the measured deflection data to the server device 3. In addition, in this embodiment, the sensor device 2 detects acceleration at a predetermined period ΔT. Therefore, the measuring device 1 measures the time-series data of the deflection over the period ΔT. That is, the measured time-series data is data of discrete values ​​of variation measured over the period ΔT, and is data in which each discrete value corresponds to the measurement time.

[0293] Server device 3 derives the dynamic response at a specified location 9 based on the deflection of the observation point measured by measuring device 1. Server device 3 is an example of a derivation device. Server device 3 includes a control unit 300, a storage unit 310, and a communication unit 320. Control unit 300 includes a processor such as a CPU, ROM, RAM, etc. Control unit 300 expands various programs recorded in ROM, etc., in RAM and executes them via CPU, thereby realizing the functions of acquisition unit 301, environmental information acquisition unit 302, time derivation unit 303, count acquisition unit 304, estimated value acquisition unit 305, and deflection derivation unit 306. Storage unit 310 stores various programs, detected deflection data, etc. Communication unit 320 includes circuitry for wired or wireless communication with external devices.

[0294] The acquisition unit 301 functions as follows: it acquires timing data of the deflection at the observation point caused by the movement of the railway train 6 on the bridge 5. The control unit 300, based on the function of the acquisition unit 301, acquires the timing data u(t) of the deflection generated at the observation point from the measuring device 1.

[0295] The environmental information acquisition unit 302 has the following functions: acquiring environmental information including the length of the unit bridge truss, the length of the railway vehicles assembled into a railway train 6 (i.e., vehicle length), and the position of the axles of the railway vehicles equipped with wheels. Based on the functions of the environmental information acquisition unit 302, the control unit 300 acquires the bridge length L of the unit bridge truss. B The length L of each railway car in railway train 6 c , representing the distance L between the positions of each railway vehicle of railway train 6. aThe environmental information is used as environmental information. In this embodiment, the environmental information is stored in advance in the storage unit 310, and the control unit 300 obtains the environmental information from the storage unit 310. However, the control unit 300 may also obtain the environmental information using other methods, such as receiving environmental information from an external device.

[0296] The time-deriving unit 303 has the following function: based on the time-series data u(t), it derives the entry time t of the railway train 6 relative to the unit bridge truss. i and exit time t o The control unit 300 performs an FFT on u(t) according to the function of the time derivation unit 303. The control unit 300 detects peak values ​​based on the FFT results. The control unit 300 determines the peak value with the smallest frequency among the detected peak values ​​after removing the sidelobe peaks caused by the window function used in the FFT. The control unit 300 uses the frequency corresponding to the determined peak value as the fundamental frequency F of u(t). f Export.

[0297] The control unit 300 controls u(t) to set the fundamental frequency F as follows: f The above component attenuation is achieved through low-pass filtering. First, the control unit 300 performs low-pass filtering based on the acquired fundamental frequency F. f Similarly to equation (3), F is derived. f The reciprocal of the product, thus deriving the period T. f The control unit 300 is based on the derived T... f Given a fixed period ΔT, the interval k is derived using the following equation (85). mf .

[0298]

[0299] Regarding the values ​​of u(t), the control unit 300 uses the derived interval k mf The moving average in the equation is used to apply a low-pass filter to u(t). Let u(t) after low-pass filtering be denoted as u0. lp (t)=u lp (kΔT). Here, k represents the nth observation variable when the deflection is periodically observed at the observation point. The control unit 300 is based on the derived interval k. mf Using the following equation (86), u is derived. lp (t). Similarly, for data with multiple discrete values, u(t), u lp (t) represents data with multiple discrete values.

[0300]

[0301] Furthermore, the control unit 300 according to u lp(t) for a given threshold C related to the deflection. L It is determined by two consecutive data points. Here, u lp Two consecutive data points of (t) are separated by a threshold C. L , indicating that in the case of u lp (t) includes the range between the values ​​of two continuously measured displacements, that is, the range above the smaller value and below the larger value of these displacements, including C. L In this embodiment, the threshold C L A given coefficient greater than or less than 1, and u during the period of deflection change. lp The product of the average values ​​of (t). Here, the period of deflection transition is the period during which the bridge deflection is maintained within a predetermined range while being supported by railway trains. More specifically, the period of deflection transition is the period during which the deflection converges within a predetermined width centered on a value whose absolute value is greater than a predetermined value. Control unit 300, for example, according to u lp (t) Data on the deflection amount is extracted over a predetermined period (e.g., 1 second, 2 seconds, etc.). If the absolute value of the average of the extracted data is above a predetermined threshold and the absolute value of the difference between the maximum and minimum values ​​among the extracted data is below a predetermined width, the extracted period is determined as the period of deflection change. Furthermore, the control unit 300 can also handle the specification of the start and end times of the deflection change period via the operation unit of the server device 300, etc. Moreover, regarding the period of deflection change, the control unit 300 calculates u... lp The average value of (t) is used as the threshold C, and the product of the calculated average value and the predetermined coefficient is used as the threshold C. L Export.

[0302] However, threshold C L It can also be other values. For example, the threshold C. L It can also be the value of the deflection at the observation point of a bridge in a situation where railway vehicles are arranged such that the leading axle of the railway vehicles is placed near the entry end. Furthermore, the threshold C... L It can also be the deflection at observation points of a bridge when a predetermined weight is applied near the approach end. Furthermore, the threshold C... L It can also be used as a predetermined percentage (e.g., 10%, 1%, etc.) of the maximum value of the deflection at the observation point of the bridge when a railway train passes over it.

[0303] exist Figure 33 u is shown lp (t) and threshold C L . Figure 33 The horizontal axis of the graph represents time (t = kΔT), and the vertical axis represents the deflection. Figure 33 The solid line curve represents u lp (t), the dashed curve represents u(t). Figure 33 In the part enclosed by the dashed circle, u lp (t) and threshold C L Intersection. Furthermore, in Figure 34 u is shown lp (t) and C L Intersecting parts ( Figure 33 An enlarged view of the circled portion of the dashed line on the left side of the curve graph. Figure 34 The horizontal axis of the graph represents time, and the vertical axis represents the amount of deflection. Figure 34 The black dots represent u respectively lp (t) includes discrete values ​​of data. Figure 34 In the example, u is shown lp The data k-1 included in (t) is separated from the data k by a threshold C. L It looks like that.

[0304] Control unit 300 pairs with the determined C L The later of two consecutive data points at two specific times is used to determine the time. Figure 34 In the example, the control unit 300 determines the time kΔT corresponding to the data k.

[0305] exist Figure 33 In the example, as separated by C L The control unit 300 also... Figure 33 The two data points in the circle of the dashed line on the right are determined, and the later of the two times corresponding to the two determined data points is determined.

[0306] Furthermore, the control unit 300 uses the earlier of the determined times as the entry time t of the railway train's six-way unit bridge truss. i Export. Furthermore, the control unit 300 will use the later of the determined times as the departure time t of the railway train 6 from the unit bridge truss. o Export. Figure 33 In the example, control unit 300 is derived as the entry time t i =7.2[s], Exit time t o =12.795[s]. Thus, in this embodiment, the control unit 300 will interact with u lp Any data included in (t) establishes the corresponding time as the entry time t. i Exit time t o Export.

[0307] Thus, in this embodiment, the control unit 300 will interact with ulp (t) includes, separated by C L The later of the two consecutive data points is taken as the entry time t. i Exit time t o Export. However, the control unit 300 can also use other times as the entry time t. i Exit time t o Export. For example, the control unit 300 can also be exported according to u. lp (t) for a given threshold C related to the deflection. L Determine two consecutive data points, and derive the entry time t from the period after the time of one of the determined data points and before the time of the other. i and exit time t o .exist Figure 34 In the example, the control unit 300 can also specify the time after time (k-1)ΔT corresponding to data k-1 and before time kΔT corresponding to data k (e.g., time (k-1)ΔT, and time before time kΔT corresponding to u). lp (t) and C L The time corresponding to the intersection point, etc., is used as the entry time t. i Export. Furthermore, the control unit 300 can also calculate the value for u. lp The curve obtained by interpolating the data included in (t) is then compared with the calculated curve and C. L The time corresponding to the intersection point is taken as t. i t o Find the answer.

[0308] In addition, regarding the distance between u lp C included in (t) L For two consecutive data points, one can be considered in relation to C. L The case of equality. For example, in Figure 34 In the example, one can consider the value of data k and C. L The case of equality. In this case, as separated by C L Two consecutive data points, control unit 300 and C L Equal data and the group of the previous data, and with C L The two groups of equal data and the group of the next data are used to determine the pair. Figure 34 In the example, in the data k and C L In the case of equality, as separated by C LGiven two consecutive data sets, the control unit 300 determines two groups: a group of data k-1 and data k, and a group of data k and data k+1. In this case, the control unit 300 can also select any one of the determined data groups and use the time interval between the two times corresponding to the two data sets in the selected group as t. i or t o Export.

[0309] In this embodiment, the control unit 300 will communicate with u lp Any data included in (t) establishes the corresponding time as the entry time t. i Exit time t o Export. Therefore, the control unit 300, by referring to u... lp (t) and can be easily obtained and flexibly used, including the entry time t. i Exit time t o The measurement times corresponding to the ΔT interval are u lp (t) data. In contrast, the control unit 300 will not be connected to u lp Any data included in (t) establishes the corresponding time as the entry time t. i Exit time t o In the case of exporting, it becomes through the original u lp The resampling of (t) and other methods are used to obtain the result including t. i t o The measurement times corresponding to the ΔT interval are u lp The data (t) increases the complexity of processing.

[0310] The control unit 300 uses u obtained by attenuating vibration components above the fundamental frequency. lp (t), which derives the entry and exit times, thereby reducing the influence of vibration components above the fundamental frequency and deriving the entry and exit times more accurately.

[0311] However, the control unit 300 may not need to export u. lp (t). In this case, the control unit 300 may, for example, also compare u(t) with the threshold C. L The moment of intersection is t i t o Export.

[0312] The counting unit 304 has the following function: to obtain the number of railway vehicles in the train 6. Based on the function of the counting unit 304, the control unit 300 derives the number of railway vehicles included in the train 6 based on a first feature. The control unit 300 then calculates the number of railway vehicles based on t... i and t oUsing equation (1), the passage time t of railway train 6 passing on the unit bridge truss is derived. s Furthermore, the control unit 300 is based on the derived t s and the fundamental frequency F derived from u(t) f Using equation (33), the passage period t is derived. s The included fundamental frequency F f The wave number ν. Based on the derived ν, the control unit 300 uses equation (34) to derive the number N of railway vehicles included in the railway train 6, thereby obtaining N. In this way, the control unit 300 will obtain N from t s With the fundamental frequency F of u(t) f The product minus 1 and rounded to the nearest integer is used to derive the value of N.

[0313] However, the control unit 300 can also obtain N through other methods. For example, the control unit 300 can also do so based on the second feature in the following manner. That is, the control unit 300 obtains N by subtracting u from u(t). lp (t), thus performing high-pass filtering on u(t) to attenuate components with frequencies lower than the fundamental frequency, deriving u(t) after high-pass filtering, i.e., u hp (t). Furthermore, the control unit 300, based on data from u... hp t in (t) i to t o The number of positive peaks is determined by the data during the period. The control unit 300 can also derive the value of N by subtracting 2 from the determined number of positive peaks.

[0314] In addition, the control unit 300 from u hp t in (t) i to t o The number of negative peaks is determined from the data during the period. The control unit 300 can also derive the value of N by subtracting 1 from the determined number of negative peaks.

[0315] Furthermore, the control unit 300 can also be implemented using a method conceived by the inventors, as follows: That is, the control unit 300 uses the vehicle length L of the railway car of the railway train 6, as shown by environmental information. c (m) and fundamental frequency F f Using equation (47), the average speed v of the railway train is derived. a The control unit 300 is based on the exported v a The environmental information shown by L B and L a Using equation (40), the duration t of a railway vehicle crossing a bridge is derived. c (m). Furthermore, the control unit 300 can also be based on the derived F.f t s and t c (m), using formula (48), derive the number N of railway vehicles grouped into railway train 6, and obtain N.

[0316] However, the control unit 300 may not necessarily derive the value of N. For example, the control unit 300 may accept the specification of N based on the user's operation of the operation unit of the server device 3, and obtain the accepted value as N. Alternatively, the control unit 300 may accept the specification of N from an external device and obtain the accepted value as N. Furthermore, the control unit 300 may also obtain a pre-defined value as N.

[0317] The estimated value acquisition unit 305 has the following functions: based on the number N and the entry time t i Exit time t o In conjunction with environmental information, obtain the estimated value T of the deflection. EO_R (t), where the deflection is the deflection of the structure generated at the observation point and is the deflection of the static response generated in the unit bridge truss due to the passage of the railway train 6.

[0318] Based on the function of the estimated value acquisition unit 305, the control unit 300 derives the estimated value T of the standardized deflection at the observation point caused by the passage of the railway train 6 when the number of railway vehicles shown as N are assembled into a railway train 6. std_R (t). Specifically, the control unit 300, based on t i t o Using equation (1), t is derived. s Control unit 300 according to t s N, a r L a L B L c Using equation (5), we can derive v a That is, v a As a train composed of N railway vehicles, from the first axle (axle 1 of the first railway vehicle) to the last axle (axle a of the last railway vehicle) in a train composed of N railway vehicles. r (N) axis distance and bridge length L B The sum divided by the sum from the entry time t i Exit time t o The period is the time through period t s The obtained value is then exported. Control unit 300 derives the value based on v. a L B and L x Using equations (22) and (23), t is derived. xn t lnFurthermore, the control unit 300 is based on L a L c t i Using equations (3) and (24), t is derived. o (m, n). Furthermore, the control unit 300 will export the t... xn t ln t o Substituting (m, n) into equations (29) and (30), we can derive the function w for each axle of each railway vehicle of railway train 6. std (a w (m, n), t).

[0319] Regarding the N railway vehicles of railway train 6, the control unit 300 uses formula (31) to determine the w of each axle. std (a w By adding (m, n), and t, we can derive C, which represents the deflection of a unit bridge truss caused by the passage of railway vehicles. std (m, t). Furthermore, the control unit 300 uses formula (32) to determine the C values ​​for N railway vehicles. std Adding (m and t) together, T is derived as the deflection of the unit bridge truss caused by the passage of railway vehicles. std (t). In this way, the control unit 300 will derive T. std (t) represents the standardized deflection T at the observation point. std_R (t) is used to obtain.

[0320] In addition, the control unit 300 controls T std_R (t) Implement low-pass filtering to attenuate components above the fundamental frequency, thereby determining T. std_R_lp (t). Specifically, the control unit 300 corresponds to T. std_R (t) An FFT is performed, and based on the FFT result, the peak value corresponding to the minimum frequency after removing the peak values ​​of the side lobes caused by the window function used in the FFT is determined. Furthermore, the control unit 300 sets the frequency corresponding to the determined peak value as the fundamental frequency F. f Using equation (36), the interval k is derived. mf The control unit 300 is based on the derived k. mf , will T std (t) is replaced by T std_R (t), and T std_lp (t) is replaced by T std_R_lp (t), using equation (37), derive T std_R_lp (t). However, the control unit 300 can also control T. std_R (t) Implement other FIR filters that attenuate components above the fundamental frequency, and calculate T.std_R_lp (t).

[0321] Control Unit 300 based on u lp (t) and T std_R_lp (t), using equations (51) and (52), derive the u shown in equation (50). lp (t) approximates T std_R_lp (t) represents the coefficients c1 and c0 of a linear function of the independent variable. Here, t... a As the entry time t i In addition, t b As the exit time t o .

[0322] As shown on the right side of equation (50), the control unit 300 will use T std_R_lp The deflection obtained by restoring (t) and coefficients c1 and c0 is taken as T. Estd_R_lp (t) is obtained. The control unit 300 derives T using equation (55). Estd_R_lp (t) and T std_R_lp The amplitude ratio of (t) to R r .

[0323] Control Unit 300 is based on R r and T std_R_lp Using equation (56), the offset T at the observation point is derived. offset_R_std (t).

[0324] Furthermore, the control unit 300 is based on c1, T std_R (t) and T offset_R_std (t), using equation (57), derive T EO_R (t).

[0325] The deflection derivation unit 306 has the following functions: based on the amplitude ratio, time series data u(t), and estimated value T, which is the ratio of the first deflection (the vibration component of the dynamic response generated at the observation point of the unit bridge truss as a result of the passage of the railway train 6) to the second deflection (the deflection at a specified position 9 caused by the vibration component of the vibration response). EO_R (t), which derives the vibration component of the dynamic response at a specified location 9.

[0326] Based on the function of the deflection derivation unit 306, the control unit 300 uses formula (67) to subtract T from u(t). EO_R (t), to obtain the vibration component u of the dynamic response at the observation point. nv (t). Control unit 300 pairs u nv (t) Perform FFT based on u nvThe FFT result of (t) determines the peak values ​​with intensity above a predetermined threshold. Furthermore, the control unit 300 determines the peak with the smallest corresponding frequency among the determined peak values ​​and uses the frequency corresponding to the determined peak value as the fundamental frequency of the unit bridge truss's natural frequency. In addition, for each of the other determined peak values, the control unit 300 also determines the corresponding frequency. Moreover, for each determined frequency, the control unit 300 derives a value obtained by dividing the frequency by the fundamental frequency and rounding it to a natural number. Furthermore, the control unit 300 uses the derived natural number plus 1 as a representation of u. nv (t) is the natural number of the frequencies of the components included (which are multiples of the fundamental frequency), that is, whether the components whose frequencies are multiples of the fundamental frequency are included in u. nv The natural numbers of (t) will be obtained. In the following, the number of times a natural number is obtained will be used as the number of times it is obtained.

[0327] The control unit 300 sets the number of acquisitions to q for each acquisition, and then controls u accordingly. nv (t) Perform bandpass filtering to extract the component of frequency q times the fundamental frequency, thereby extracting the component u of the qth wave. nv_q (t).

[0328] The control unit 300 sets the number of acquisitions to successive q. Based on q and r = R, it uses equation (80) to represent the deflection w of the amplitude distribution on the unit bridge truss, which represents the normalized vibration of the q-th wave at the observation point. q_std (R) is derived as the first deflection. That is, the control unit 300 takes the amplitude of the observation point of the deflection of the vibration distribution on the unit bridge truss at a frequency that is a natural number q times the fundamental frequency, which represents the vibration component of the dynamic response, as the first deflection w. q_std (R) Derivation. Furthermore, the control unit 300 sets the number of acquisitions to successive q, based on q and r = r x Using equation (80), the normalized q-wave deflection w at the specified location 9 is... q_std (r x The second deflection is derived as w. That is, the control unit 300 takes the amplitude of the deflection at a designated position 9, which represents the deflection of the vibration at a frequency that is a natural number q times the fundamental frequency among the vibration components representing the dynamic response, as the second deflection w. q_std (r x Export.

[0329] The control unit 300 sets the acquisition number to q for each successive acquisition and uses equation (81) to derive the first deflection amount w. q_std (R) and the second deflection w q_std (r x The ratio of Cr qFurthermore, the control unit 300 sets the acquisition number to successive q, as in equation (82), and sets the component u of the q-th wave. nv_q (t) and ratio Cr q The product of these components is the q-wave component u of the vibration component at the specified location 9. nv_q_rx (t) Derivation. The control unit 300 uses formula (83) to derive u for each acquisition number. nv_q_rx (t) are added together to derive the estimated value of the vibration component of the dynamic response at the specified location 9. Furthermore, using equation (84), the static response at the specified location 9 is added together with the vibration component to derive the estimated value of the dynamic response.

[0330] As described above, according to the structure of this embodiment, the deriving system 10 is able to derive the vibration component of the dynamic response at a specified location 9 in the structure.

[0331] Furthermore, depending on the location of the observation point, it is sometimes impossible to measure the amplitude of a portion of the vibration components included in the dynamic response. For example, when the center of the bridge is used as the observation point, components with frequencies that are even multiples of the fundamental frequency (e.g., second-order, fourth-order, etc.) cannot be measured because the center of the unit bridge truss becomes a node of the waveform and does not undergo displacement. Thus, the component with respect to the q-th order, at a distance L from the entry end to the exit end... B The node that generates the waveform is located at position (n / q) where n is an integer from 0 to q. Therefore, the node at which the waveform is generated is located at a distance L from the entry end to the exit end. B At the position (n / q), it is impossible to measure the q-th wave component.

[0332] Therefore, the control unit 300 derives the q-wave component u of the dynamic response at the specified location 9. nv_q_rx When (t), it is only necessary to use a distance L from the entry end to the exit end. B The time series data u(t) can be obtained by measuring at different positions of (n / q).

[0333] Furthermore, the control unit 300 uses time-series data u(t) measured at multiple different observation points to derive more q-wave components at a specified location 9.

[0334] Furthermore, when the vibration components of the dynamic response of the derived object are predetermined, the control unit 300 can simply use the time-series data u(t) measured at locations where these components can be measured. For example, if the derived object has three components—first, second, and third waves—the control unit 300 can simply use the time-series data u(t) measured at the two ends of the bridge, from the entry end to the exit end. B (1 / 3) position, distance L from the entry end to the exit end BThe position of (1 / 2) and the distance L from the entry end to the exit end. B The time series data u(t) can be obtained by measuring at different positions of (2 / 3).

[0335] (2) Export processing:

[0336] use Figure 3 The process of deriving the vibration components of the dynamic response at a specified location 9, performed by server device 3, is explained. Server device 3 begins processing based on the displacement data at the observation point sent from measuring device 1. Figure 35 However, it can also be processed at any time, such as a specified timer. Figure 35 The processing.

[0337] In S100, the control unit 300 acquires the timing data u(t) of the deflection generated at the observation point from the measuring device 1 according to the function of the acquisition unit 301. S100 is an example of the acquisition step.

[0338] In S105, the control unit 300 obtains the bridge length L of the unit bridge truss based on the function of the environmental information acquisition unit 302. B The length L of each railway car in railway train 6 c , representing the distance L between the positions of each railway vehicle of railway train 6. a The information is used as environmental information. S105 is an example of an environmental information acquisition step.

[0339] In S110, the control unit 300 performs an FFT on u(t) according to the function of the time derivation unit 303, and detects peak values ​​based on the FFT result. The control unit 300 determines the peak value that corresponds to the smallest frequency among the detected peak values ​​after removing the peak values ​​of side lobes caused by the window function used in the FFT. The control unit 300 uses the frequency corresponding to the determined peak value as the fundamental frequency F of u(t). f Export. The control unit 300 is based on the acquired fundamental frequency F. f Similarly to equation (35), F is derived. f The reciprocal of the product, thus deriving the period T. f The control unit 300 is based on the derived T... f Given a fixed period ΔT, we can derive the interval k using equation (49). mf The control unit 300 is based on the derived interval k. mf Using equation (50), derive u lp (t).

[0340] In addition, the control unit 300 according to u lp(t) Extracting a predetermined interval (e.g., 1 second, 2 seconds, etc.), if the absolute value of the difference between the maximum and minimum values ​​of the deflection in the extracted interval is below a predetermined threshold, the extracted interval is determined as the interval of deflection transition. Regarding the interval of deflection transition, the control unit 300 calculates u. lp The average value of (t) is used as the threshold C, and the product of the calculated average value and the predetermined coefficient is used as the threshold C. L Export.

[0341] Furthermore, the control unit 300 calculates u lp (t) and the derived threshold C L The intersection point. Specifically, the control unit 300 calculates u. lp (t)=C L The control unit 300 takes the smaller of the two values ​​of t as the entry time t of the railway train's six-way unit bridge truss. i Export. Furthermore, the control unit 300 will use the larger of the calculated values ​​of t as the time t at which the railway train 6 exits from the unit bridge truss. o Export. S110 is an example of a time-based export step.

[0342] In S115, the control unit 300 obtains the function of the unit 304 based on the number, according to t derived in S110. i and t o Using equation (1), the passage time t of railway train 6 passing on the unit bridge truss is derived. s Furthermore, the control unit 300 is based on the derived t s And F exported in S110 f Using equation (33), the passage period t is derived. s The included fundamental frequency F f The wave number ν. Based on the derived ν, the control unit 300 uses equation (34) to derive the number N of railway vehicles included in the railway train 6, thereby obtaining N. S115 is an example of a number acquisition step.

[0343] In S120, the control unit 300 acquires the function of the estimated value acquisition unit 305 based on t. i t o Using equation (1), t is derived. s Control unit 300 according to t s N, a r L a L B L c Using equation (5), we can derive v a That is, v aFrom the first axle of a train composed of N railway vehicles (axle 1 of the first railway vehicle) to the last axle of the train (axle a of the last railway vehicle)... r (N) axis distance and bridge length L B The sum divided by the sum from the entry time t i Exit time t o The period is the time through period t s The obtained value is then exported. Control unit 300 derives the value based on v. a L B and L x Using equations (22) and (23), t is derived. xn t ln Furthermore, the control unit 300 is based on L a L c t i Using equations (3) and (24), t is derived. o (m, n). Furthermore, the control unit 300 will export the t... xn t ln t o Substituting (m, n) into equations (29) and (30), we can derive the function w for each axle of each railway vehicle of railway train 6. std (a w (m, n), t).

[0344] Regarding the N railway vehicles of railway train 6, the control unit 300 uses formula (31) to determine the w of each axle. std (a w By adding (m, n), and t, we can derive C, which represents the deflection of a unit bridge truss caused by the passage of railway vehicles. std (m, t). Furthermore, the control unit 300 uses formula (32) to determine the C values ​​for N railway vehicles. std Adding (m and t) together, T is derived as the deflection of the unit bridge truss caused by the passage of railway vehicles. std (t). In this way, the control unit 300 will derive T. std (t) represents the standardized deflection T at the observation point. std_R (t) is used to obtain.

[0345] In addition, the control unit 300 controls T std_R (t) Implement low-pass filtering to attenuate components above the fundamental frequency, thereby determining T. std_R_lp (t). Control unit 300 based on u lp (t) and T std_R_lp (t), using equations (51) and (52), derive the u shown in equation (50). lp (t) approximates Tstd_R (t) represents the coefficients c1 and c0 of a linear function of the independent variable. Here, t... a As the entry time t i In addition, t b As the exit point.

[0346] As shown on the right side of equation (50), the control unit 300 will use T std_R_lp The deflection obtained by restoring (t) and coefficients c1 and c0 is taken as T. Estd_R_lp (t) is obtained. The control unit 300 derives T using equation (55). Estd_R_lp (t) and T std_R_lp The amplitude ratio of (t) to R r .

[0347] Control Unit 300 is based on R r and T std_R_lp Using equation (56), the offset T at the observation point is derived. offset_R_std (t).

[0348] Furthermore, the control unit 300 is based on c1, T std_R (t) and T offset_R_std (t), using equation (57), derive T EO_R (t). S120 is an example of the estimated value acquisition step.

[0349] In S125, the control unit 300, based on the function of the deflection derivation unit 306, uses equation (67) to subtract T from u(t). EO_R (t), to obtain the vibration component u of the dynamic response at the observation point. nv (t). Control unit 300 pairs u nv (t) Perform FFT based on u nv The FFT result of (t) determines the peak values ​​with intensity above a predetermined threshold. Furthermore, the control unit 300 identifies the peak with the smallest corresponding frequency among the identified peak values ​​and determines the fundamental frequency corresponding to the identified peak as the natural frequency of the unit bridge truss. Additionally, for each of the other identified peak values, the control unit 300 also determines the corresponding frequency. Moreover, for each determined frequency, the control unit 300 derives a value obtained by dividing the frequency by the fundamental frequency and rounding it to a natural number. Furthermore, the control unit 300 uses the derived natural number and 1 as the number of acquisitions.

[0350] The control unit 300 sets the number of acquisitions to q for each acquisition, and then controls u accordingly. nv (t) Perform bandpass filtering to extract the component of frequency q times the fundamental frequency, thereby extracting the component u of the qth wave. nv_q (t).

[0351] The control unit 300 sets the number of acquisitions to successive q, and r = R. Using equation (80), it derives the standardized q-th wave deflection w at the observation point. q_std (R). Furthermore, the control unit 300 sets the number of acquisitions to successive q, and sets r = r x Using equation (80), the normalized q-wave deflection w at the specified location 9 is derived. q_std (r x ).

[0352] The control unit 300 sets the number of acquisitions to q for each acquisition, and uses equation (81) to derive w. q_std (R) and w q_std (r x The ratio of Cr q .

[0353] Furthermore, the control unit 300 sets the acquisition number to successive q, as in equation (82), and sets the component u of the q-th wave. nv_q (t) and ratio Cr q The product of these components is the q-wave component of the vibrational response at a specified location 9. nv_q_rx (t) Derivation. The control unit 300 uses formula (83) to derive u with respect to the number of acquisitions. nv_q_rx (t) are added together to derive the estimated value u of the vibration component of the dynamic response at the specified location 9. nv_q_est (t). S125 is an example of a flexure derivation step.

[0354] (3) Other implementation methods:

[0355] The above-described embodiments are one example of implementing the present invention, and various other embodiments can also be adopted. As in the embodiments described above, the means of deriving the amount of deflection caused by resonance at a specified location based on the displacement at the observation point can also be implemented as an invention of a program or a method.

[0356] Furthermore, the functions of server device 3 can also be implemented using multiple devices. Alternatively, the functions of server device 3 can be distributed across multiple devices. Furthermore, the functions of server device 3 can be installed in other devices. For example, the functions of acquisition unit 301, environmental information acquisition unit 302, time derivation unit 303, count acquisition unit 304, estimated value acquisition unit 305, and deflection derivation unit 306 can be installed in measurement device 1. Alternatively, server device 3 can be distributed across multiple devices. Furthermore, the above-described embodiment is one example; embodiments that omit some components or add other components may also be used.

[0357] In the above-described embodiment, the deflection system 10 deflects the deflection of bridges crossed by railway trains 6 composed of one or more railway vehicles. However, the deflection system 10 can also deflect the deflection of bridges crossed by other types of moving bodies. For example, the deflection system 10 can also deflect the deflection of bridges crossed by swarms of handcarts consisting of one or more handcarts connected together, or by trailers with multiple vehicles connected together. Furthermore, the deflection system 10 can also deflect the deflection of structures different from bridges, such as the track support abutments.

[0358] Furthermore, in the above-described embodiments, the number of sensor devices 2 included in the export system 10 is two, but it can also be one, or it can be three or more.

[0359] Furthermore, in the above embodiment, as time-series data u(t), the control unit 300 acquires displacement (deflection) data measured based on the acceleration detected by the accelerometer 210. However, as u(t), the control unit 300 may also acquire bridge displacement data derived from physical quantities detected by sensors such as impact sensors, pressure sensors, strain gauges, image measuring devices, pressure measuring elements, and displacement gauges. For example, the control unit 300 may periodically photograph a predetermined target positioned at an observation point on the bridge 5 using an image measuring device, detect the displacement of the observation point, and acquire the detected displacement data. Furthermore, as u(t), the control unit 300 may also acquire data of physical quantities different from the bridge displacement. For example, as u(t), the control unit 300 may also acquire the number of pixels representing the displacement of a predetermined target positioned at an observation point on the bridge 5 within an image captured by the image measuring device.

[0360] Furthermore, in the above embodiment, the control unit 300, based on the result of the FFT of the timing data u(t) acquired by the acquisition unit 301, removes the peak values ​​of the side lobes caused by the influence of the window function used in the FFT, determines the peak value corresponding to the lowest frequency, and uses the determined peak value as the fundamental frequency F. f However, the control unit 300 can also consider the influence of noise generated by the FFT result of u(t) and calculate the fundamental frequency F. f For example, the control unit 300 can also, based on the result of the FFT on u(t), remove the peak values ​​of the side lobes caused by the window function used in the FFT, determine the peak values ​​above a predetermined threshold corresponding to the lowest frequency, and use the determined peak values ​​as the fundamental frequency F. f Find the answer.

[0361] Furthermore, in the above embodiment, the deriving system 10 derives the vibration component of the dynamic response at a specified location 9. However, the deriving system 10 can also further derive the dynamic response at the specified location 9, i.e., the deflection T. EO_rx (t), will be used to derive the vibration component u nv_q_est (t) and static response T EO_rx The deflection obtained by adding (t) is derived as the estimated value of the dynamic response at the specified position 9.

[0362] For example, the control unit 300 can also derive T in the following way. EO_rx (t). Control unit 300 acquires T std_R (t). Furthermore, the control unit 300 will take the standardized estimated value T of the deflection at a designated position 9 caused by the passage of the railway train 6 when the number of railway vehicles (N) is grouped into a railway train 6, as obtained by the function of the number acquisition unit 304. std_rx (t) is derived. Specifically, the control unit 300 is based on v a L B and r x , will L x Replace with L B ×r x Using equations (22) and (23), t is derived. xn t ln Furthermore, the control unit 300 is based on L a L c and t i Using equations (3) and (24), t is derived. o (m, n). Furthermore, the control unit 300 will export t. xn t ln t o Substituting (m, n) into equations (29) and (30), and considering each axle of each railway vehicle in railway train 6, the function w is derived. std (a w (m, n), t).

[0363] Regarding the N railway vehicles of railway train 6, the control unit 300 uses formula (31) to determine the w of each axle. std (a w By adding (m, n), and t, we can derive C, which represents the deflection of a unit bridge truss caused by the passage of railway vehicles. std (m, t). Furthermore, the control unit 300 uses formula (32) to determine the C values ​​for N railway vehicles. std Adding (m and t) together, T is derived as the deflection of the unit bridge truss caused by the passage of railway vehicles. std(t). In this way, the control unit 300 will specify the standardized deflection T at location 9. std (t) as T std_rx (t) is obtained.

[0364] Control unit 300 pairs T std_rx (t) Implement low-pass filtering to attenuate components above the fundamental frequency, thereby determining T. std_rx_lp (t). Specifically, the control unit 300 corresponds to T. std_rx (t) An FFT is performed, and based on the FFT result, the peak value corresponding to the minimum frequency after removing the peak values ​​of the side lobes caused by the window function used in the FFT is determined. Furthermore, the control unit 300 sets the frequency corresponding to the determined peak value as the fundamental frequency F. f Using equation (36), the interval k is derived. mf The control unit 300 is based on the derived k. mf , will T std (t) is replaced by T std_rx (t), and T std_lp (t) is replaced by T std_rx_lp (t), using equation (37), derive the interval T. std_rx_lp (t). However, the control unit 300 can also control T. std_rx (t) Implement other FIR filters that attenuate components above the fundamental frequency, and calculate T. std_rx_lp (t). Furthermore, similarly, the control unit 300 pairs T std_R (t) Implement low-pass filtering to attenuate components above the fundamental frequency, thereby determining T. std_R_lp (t).

[0365] Control unit 300 uses formula (58) to derive T std_rx_lp The amplitude h of (t) rx t1 and t2 are the time intervals t1 and t2, respectively. s (from entry time t) i Exit time t o The period is defined by a predetermined width (e.g., 1 second, 2 seconds, etc.) in the center of the period, which is the start and end time of the period, but it can also be other periods.

[0366] Control Unit 300 based on u lp (t) and T std_R_lp (t), using equations (51) and (52), derive the coefficients c1 and c0. That is, the control unit 300 derives the coefficients c1 and c0 for u. lp (t) approximates with respect to T std_R_lp The coefficients c1 and c0 of a linear function of (t). The control unit 300 is based on c1, c0, and h. rxUsing equation (59), we derive the result by applying T std_rx_lp The deflection T restored by adding c0 to the product of (t) and coefficient c1. Estd_rx_lp (t), and T std_rx_lp The function R of the amplitude ratio of (t) r_rx (t). Furthermore, the control unit 300 is based on t1, t2, and T. std_rx_lp Using equation (60), R(t) is derived for the period from t1 to t2. r_rx The average amplitude ratio of (t) to R r_rx However, the control unit 300 can also be based on c1, c0, and h. rx Using equation (61), the amplitude ratio R is derived. r_rx .

[0367] The control unit 300 uses formula (62) to derive the T std_rx_lp (t) multiplied by R r_rx The obtained deflection T r_rx However, the control unit 300 can also be based on T. std_rx_lp Using equation (63), we derive the deflection T from (t), c1, and c0. r_rx Furthermore, the control unit 300 can also operate earlier than the entry time t. i Later than exit time t o Let c0 = 0, and calculate T as in equation (64). r_rx .

[0368] Furthermore, the control unit 300 is based on the derived T r_rx Using equation (65), the offset T of the deflection at the specified location 9 is derived. offset_rx (t). That is, the control unit 300 rounds T to c0 for elements whose absolute value is greater than c0. r_rx As offset T offset_rx (t) Derivation. The control unit 300 uses equation (66) to compare the coefficients c1 and T. std_rx The product of (t) plus the offset T offset_rx (t), thereby obtaining the estimated value T of the static response, i.e., the deflection, at a specified location on the bridge. std_rx (t).

[0369] In the manner described above, the control unit 300 can also obtain T. EO_rx (t).

[0370] However, the control unit 300 can also obtain the estimated value T through other methods. EO_rx (t). For example, the control unit 300 can also obtain the estimated value T as described above. EO_rx (t).

[0371] Control unit 300 in Tstd_R (t) and T std_rx In (t), the period from the moment t1 when the value of the deflection begins to increase beyond 0 to the moment t2 when the deflection converges to 0 is determined, which is the period from the moment the deflection begins to increase beyond 0. Furthermore, the control unit 300 derives T using the following equation (87). std_R (t) and T std_rx The ratio R of (t) rx_R (t).

[0372]

[0373] Control unit 300 is based on t1, t2 and R rx_R Using the following equation (88), we derive T(t) from the period from time t1 to time t2. std_R (t) and T std_rx The average value of the ratio of (t) is Ravg.

[0374]

[0375] However, as a Ravg, the control unit 300 can also derive T during a period different from the period from time t1 to time t2. std_R (t) and T std_rx The average value of the ratio of (t). For example, as Ravg, control unit 300 can also derive the average value of the ratio ... s T in std_R (t) and T std_rx The average value of the ratio of (t). In this case, the control unit 300 can also replace t1 and t2 in equation (88) with t i and t o Using equation (88), derive Ravg.

[0376] Furthermore, the control unit 300 can also use the value obtained by multiplying the timing data u(t) by Ravg as the estimated value T of the deflection at the specified position 9. EO_rx (t) is acquired. However, the control unit 300 may also multiply each value of the time-series data u(t) by R. rx_R The value obtained from the corresponding data included in (t) is used as the estimated value T of the deflection at the specified position 9. EO_rx (t) is used for export.

[0377] Timing data can be obtained at a data rate that is at least twice the frequency of vibrations in the structure caused by the movement of the group of moving bodies.

[0378] Furthermore, the present invention can also be applied as a computer-executable program or method. In addition, while such programs and methods are sometimes implemented as a single device, they are sometimes implemented using components of multiple devices, including various methods. Furthermore, appropriate modifications can be made, such as making some parts software and others hardware. Furthermore, the invention also exists as a program recording medium. Of course, the program recording medium can be a magnetic recording medium, a semiconductor memory, or the like, and this can also be considered in any recording medium developed in the future.

Claims

1. A method for deriving, characterized in that, include: The acquisition step involves acquiring time-series data, which includes physical quantities generated at a predetermined observation point in the structure in response to the movement of a group of mobile bodies, which are grouped together as one or more mobile bodies, on the structure. The environmental information acquisition step involves acquiring information such as the length of the structure, the length of the moving body, and the location of the contact points between the moving body and the structure. The time-deriving step involves deriving the entry and exit times of the grouped moving body relative to the structure based on the time-series data. The number acquisition step involves acquiring the number of mobile bodies grouped into the grouped mobile bodies. The estimated value acquisition step involves obtaining, based on the number of instances, the entry time, the exit time, the environmental information, and the deflection model of the structure, an estimated value of the deflection at the observation point of the structure, which is the static response generated by the response; and The deflection derivation step derives the dynamic response at the specified location based on the deflection amount, amplitude ratio, vibration component at the specified location, and static response at the specified location. The deflection amount is the standardized deflection caused by the vibration component of the dynamic response derived from the model, which is the difference between the time-series data and the estimated value. The amplitude ratio is the ratio of the first standardized deflection amount representing the distribution of vibration amplitude at the observation point to the second standardized deflection amount representing the distribution of vibration amplitude at the specified location of the structure. The vibration component at the specified location is derived based on the vibration component and the amplitude ratio, and the static response at the specified location is derived based on the time-series data and the estimated value.

2. The export method according to claim 1, characterized in that, The static response at the specified location is a portion of the deflection of the structure at the specified location based on the number of units, the entry time, the exit time, and the environmental information, and is an estimated value of the deflection at the specified location of the static response generated by the group of moving bodies.

3. The export method according to claim 1, characterized in that, The amplitude ratio is the ratio of the first deflection in the standardized deflection representing the distribution of vibration amplitude, derived from the frequency of the vibration component being a multiple of the fundamental frequency and the location of the observation point, to the second deflection in the standardized deflection representing the distribution of vibration amplitude, derived from the frequency of the vibration component being a multiple of the fundamental frequency and the specified location.

4. The derivation method according to any one of claims 1 to 3, characterized in that, In the flexure derivation step. The vibration component at the observation point is derived as the difference between the time-series data and the static response at the observation point, i.e., the estimated value. One or more frequencies are determined based on the fundamental frequency and higher harmonic frequencies of the vibration components, and components of each determined frequency are extracted from the vibration components. For each of the aforementioned frequencies, based on the deflection amount after the frequency has been standardized, the amplitude ratio, which is the ratio of the first deflection amount to the second deflection amount, is derived. For each of the aforementioned frequencies, the value obtained by multiplying the component corresponding to the frequency by the corresponding amplitude ratio is derived as the vibration component of the frequency at the specified location. The sum of the vibration components at each of the specified frequencies and the static response at the specified location is used to derive the dynamic response at the specified location.

5. The export method according to claim 4, characterized in that, In the derivation of the amplitude ratio in the deflection step, Regarding the determined frequency, the first deflection is derived using equation (1) of the standardized deflection at the observation point R in the structure with the frequency order set to q and the structure length set to 1. The second deflection is derived using equation (2) of the standardized deflection at the specified position r in the structure with the frequency order set to q and the structure length set to 1. The ratio of the derived first deflection to the second deflection is then derived as the amplitude ratio. 。 6. The export method according to claim 4, characterized in that, In the derivation of the amplitude ratio in the deflection step, Regarding the determined frequency, the first deflection is derived using equation (3) of the standardized deflection at the observation point R in the structure with the frequency order set to q and the structure length set to 1. Using equation (4) of the standardized deflection at the specified position r in the structure with the frequency set to q and the structure length set to 1, the second deflection is derived. The ratio of the derived first deflection to the second deflection is then derived as the amplitude ratio. 。 7. The export method according to claim 1, characterized in that, The structure in question is a bridge.

8. The export method according to claim 1, characterized in that, The moving body is a railway vehicle that moves on the structure via wheels.

9. The export method according to claim 1, characterized in that, The model of the deflection of the structure is based on the formula of the structure.

10. The export method according to claim 1, characterized in that, The deflection model of the structure is based on the formula of a bridge structure shown as a simply supported beam supported at both ends, the formula of which includes the standardized deflection as the static response and the standardized deflection representing the distribution of the vibration amplitude.

11. The export method according to claim 1, characterized in that, The time-series data is data detected by at least one of an accelerometer, an impact sensor, a pressure sensor, a strain gauge, an image measuring device, a pressure measuring element, and a displacement gauge.

12. The export method according to claim 1, characterized in that, The structure is capable of applying dynamic weighing of bridges.

13. A dispensing device, characterized in that, have: The acquisition unit acquires time-series data, which includes physical quantities generated at a predetermined observation point in the structure as a result of the response caused by the movement of a group of mobile bodies, which are grouped together as one or more mobile bodies, on the structure. The environmental information acquisition unit acquires information such as the length of the structure, the length of the moving body, and the location of the contact parts of the moving body with the structure. The timing derivation unit, based on the timing data, derives the entry and exit times of the grouped moving body relative to the structure; The number acquisition unit acquires the number of the mobile bodies grouped into the grouped mobile bodies; The estimation value acquisition unit acquires an estimated value of the deflection of the structure at the observation point as a static response generated by the response, based on the number, the entry time, the exit time, the environmental information, and the model of the structure's deflection. as well as The deflection derivation section derives the dynamic response at the specified location based on the deflection amount, amplitude ratio, vibration component at the specified location, and static response at the specified location. The deflection amount is a standardized deflection caused by the vibration component of the dynamic response derived from the model, which is the difference between the time-series data and the estimated value. The amplitude ratio is the ratio of a first deflection amount representing the distribution of vibration amplitude at the observation point to a second deflection amount representing the distribution of vibration amplitude at the specified location of the structure. The vibration component at the specified location is derived based on the vibration component and the amplitude ratio, and the static response at the specified location is derived based on the time-series data and the estimated value.

14. An export system, characterized in that, Equipped with an export device and sensors, The export device includes: The acquisition unit acquires time-series data, which includes physical quantities generated at a predetermined observation point in the structure in response to the movement of a group of moving bodies that are grouped together as one or more moving bodies on the structure, and the physical quantities are measured by the sensor. The environmental information acquisition unit acquires information such as the length of the structure, the length of the moving body, and the location of the contact parts of the moving body with the structure. The timing derivation unit, based on the timing data, derives the entry and exit times of the grouped moving body relative to the structure; The number acquisition unit acquires the number of the mobile bodies grouped into the grouped mobile bodies; The estimation value acquisition unit acquires an estimated value of the deflection of the structure at the observation point as a static response generated by the response, based on the number, the entry time, the exit time, the environmental information, and the model of the structure's deflection. as well as The deflection derivation section derives the dynamic response at the specified location based on the deflection amount, amplitude ratio, vibration component at the specified location, and static response at the specified location. The deflection amount is a standardized deflection caused by the vibration component of the dynamic response derived from the model, which is the difference between the time-series data and the estimated value. The amplitude ratio is the ratio of a first deflection amount representing the distribution of vibration amplitude at the observation point to a second deflection amount representing the distribution of vibration amplitude at the specified location of the structure. The vibration component at the specified location is derived based on the vibration component and the amplitude ratio, and the static response at the specified location is derived based on the time-series data and the estimated value.

15. A program product, characterized in that, Includes a program that causes a computer to perform the following steps: The acquisition step involves acquiring time-series data, which includes physical quantities generated at a predetermined observation point in the structure in response to the movement of a group of mobile bodies, which are grouped together as one or more mobile bodies, on the structure. The environmental information acquisition step involves acquiring information such as the length of the structure, the length of the moving body, and the location of the contact points between the moving body and the structure. The time-deriving step involves deriving the entry and exit times of the grouped moving body relative to the structure based on the time-series data. The number acquisition step involves acquiring the number of mobile bodies grouped into the grouped mobile bodies. The estimated value acquisition step involves obtaining, based on the number of instances, the entry time, the exit time, the environmental information, and the deflection model of the structure, an estimated value of the deflection at the observation point of the structure, which is the static response generated by the response; and The deflection derivation step derives the dynamic response at the specified location based on the deflection amount, amplitude ratio, vibration component at the specified location, and static response at the specified location. The deflection amount is the standardized deflection caused by the vibration component of the dynamic response derived from the model, which is the difference between the time-series data and the estimated value. The amplitude ratio is the ratio of the first standardized deflection amount representing the distribution of vibration amplitude at the observation point to the second standardized deflection amount representing the distribution of vibration amplitude at the specified location of the structure. The vibration component at the specified location is derived based on the vibration component and the amplitude ratio, and the static response at the specified location is derived based on the time-series data and the estimated value.

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