System and method for determining railway vibration countermeasure locations using transmission path analysis

Abstract

To determine a railroad anti-vibration place by identifying a plate for determining sizes of railroad vibrations.SOLUTION: The railroad anti-vibration place determination system comprises: an analysis model generation unit that generates an analysis model of a railway structure and a foundation on which the structure is installed, and sets a plurality of attention points; a transmission path analysis unit that calculates displacement vectors of the attention points on the basis of the analysis model during train traveling, calculates transmission force vectors of the attention points on the basis of complex dynamic rigidity matrices and the displacement vectors of the attention points including the foundation impedance of the foundation during the train traveling, calculates transmission function vectors from the attention points to evaluation points, calculates the contribution degrees of vibration transmission paths from the attention points to the evaluation points from the transmission force vectors and the transmission function vectors, calculates the influence degree of each attention point on railroad vibrations of the evaluation points from the contribution degrees, and executes transmission path analysis; and an analysis result output unit that visualizes the influence degree on the analysis model.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] This disclosure relates to a system and method for determining railway vibration countermeasures using transmission path analysis. [Background technology]

[0002] Traditionally, vibrations caused by the movement of vehicles, which propagate through structures and ultimately reach the ground, can pose an environmental problem. Therefore, the need to implement countermeasures against railway vibrations is recognized. However, determining the locations where countermeasures should be implemented on structures above ground, i.e., the locations of countermeasures, is ultimately based on the judgment of engineers, although information such as vibration mode shapes and stress distribution is taken into consideration. This makes it difficult to determine the most effective locations for countermeasures.

[0003] However, techniques for determining locations for vibration and noise countermeasures using transfer functions have already been proposed (see, for example, Patent Documents 1 and 2). [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2009-059094 [Patent Document 2] Japanese Patent Publication No. 2006-185193 [Overview of the project] [Problems that the invention aims to solve]

[0005] However, the aforementioned conventional technology is designed for automobiles and does not take railway vibrations into consideration. Therefore, it has been difficult to obtain sufficient knowledge to determine the locations where countermeasures should be implemented on railway structures.

[0006] The objective here is to provide a railway vibration countermeasure location determination system and method using transmission path analysis, which solves the problems of the conventional technology described above. This system visualizes the degree of influence of each structural location on railway vibration at evaluation points using transmission path analysis, thereby identifying locations that determine the magnitude of railway vibration and determining locations for railway vibration countermeasures. [Means for solving the problem]

[0007] To this end, the railway vibration countermeasure location determination system using transmission path analysis includes: a countermeasure frequency determination unit that determines the countermeasure frequency when railway vibration at an evaluation point set on the ground along the railway line during train operation is input; an analysis model creation unit that creates an analysis model of the railway structure and the ground on which the structure is installed and sets multiple points of interest on the structure; a transmission path analysis unit that calculates the displacement vector of the points of interest during train operation based on the analysis model, calculates the transmission force vector of the points of interest during train operation from the complex dynamic stiffness matrix of the points of interest including the ground impedance of the ground and the displacement vector, calculates the transfer function vector from the points of interest to the evaluation point, calculates the contribution of the vibration transmission path from the points of interest to the evaluation point from the transmission force vector and the transfer function vector, calculates the influence of each point of interest on the railway vibration of the evaluation point from the contribution and performs a transmission path analysis; and an analysis result output unit that visualizes the influence on the analysis model.

[0008] In other systems for determining railway vibration countermeasure locations using transmission path analysis, the transmission path analysis unit further sets the positions of multiple rail fastening devices for fastening rails onto the structure as locations where excitation forces are input to the structure when a train is running, and calculates the displacement vector of the point of interest.

[0009] Furthermore, in a railway vibration countermeasure location determination system using other transmission path analysis, the countermeasure frequency determination unit further performs frequency analysis of the railway vibration at the evaluation point to determine the countermeasure frequency, and the transmission path analysis unit performs the transmission path analysis only for the countermeasure frequency.

[0010] Furthermore, in railway vibration countermeasure location determination systems using other transmission path analyses, the analysis result output unit further visualizes the degree of influence by displaying it as a vector at the points of interest in the analysis model.

[0011] The method for determining railway vibration countermeasure locations using transmission path analysis includes the steps of: determining the countermeasure frequency when railway vibration at an evaluation point set on the ground along the railway line during train operation is input; creating an analysis model of the railway structure and the ground on which the structure is installed, and setting multiple points of interest on the structure; calculating the displacement vector of the points of interest during train operation based on the analysis model, calculating the transmission force vector of the points of interest during train operation from the complex dynamic stiffness matrix of the points of interest including the ground impedance of the ground and the displacement vector, calculating the transfer function vector from the points of interest to the evaluation point, calculating the contribution of the vibration transmission path from the points of interest to the evaluation point from the transmission force vector and the transfer function vector, calculating the influence of each point of interest on the railway vibration of the evaluation point from the contribution, and performing a transmission path analysis; and visualizing the influence on the analysis model. [Effects of the Invention]

[0012] According to this disclosure, by visualizing the degree of influence of each structural location on railway vibration at evaluation points using transmission path analysis, it is possible to identify locations that determine the magnitude of railway vibration and determine locations for railway vibration countermeasures. [Brief explanation of the drawing]

[0013] [Figure 1] This is a block diagram showing the functional configuration of the railway vibration countermeasure location determination system in this embodiment. [Figure 2] This figure shows an example of an analytical model for reproducing railway vibrations in this embodiment. [Figure 3] This figure shows an example of the countermeasure frequency in this embodiment. [Figure 4] It is a diagram showing an example of a vibration force input to a structure in this embodiment. [Figure 5] It is a diagram showing an example of confirming the accuracy of contribution degree in this embodiment. [Figure 6] It is a diagram showing an example of railway vibration and contribution degree of evaluation points represented as vectors on the complex plane in this embodiment. [Figure 7] It is a diagram showing an example of influence degree visualized on an analysis model that reproduces railway vibration in this embodiment.

Embodiment for Carrying out the Invention

[0014] Hereinafter, the embodiments will be described in detail with reference to the drawings.

[0015] FIG. 1 is a block diagram showing the functional configuration of a railway vibration countermeasure location determination system in this embodiment.

[0016] In the figure, 10 is a railway vibration countermeasure location determination system using transmission path analysis in this embodiment. It is a type of computer system used to determine the locations that determine the magnitude of railway vibration for structures in a given section of a railway line by executing a railway vibration countermeasure location determination method using transmission path analysis, calculating and visualizing the degree of influence of evaluation points on the ground on railway vibration using transmission path analysis, and determining the locations for railway vibration countermeasures on the structures. The railway vibration countermeasure location determination system 10 is a computer system built within a computer equipped with a computing device such as a CPU or MPU, a storage device such as a magnetic disk or semiconductor memory, an input device such as a keyboard, mouse, touch panel, or data input port, an output device such as a CRT, liquid crystal display, printer, or data output port, and a communication interface. The computer may be, for example, a personal computer, workstation, server, or tablet computer, but it may be any type of computer that operates according to a program such as application software installed on a storage device, and it may be a single computer or a group of computers connected to each other via a network. Furthermore, the railway vibration countermeasure location determination system 10 may be connected to an external database or the like via a communication network or communication line not shown, such as the Internet, intranet, LAN, or WAN.

[0017] From a functional standpoint, the railway vibration countermeasure location determination system 10 comprises a countermeasure frequency determination unit 11 that determines the countermeasure frequency when numerical values ​​of railway vibration measured in advance on site are input, an analysis model creation unit 12 that creates an analysis model, a transmission path analysis unit 13 that performs a transmission path analysis (see, for example, Non-Patent Document 1), and an analysis result output unit 14 that visualizes the degree of influence of the point of interest.

[0018] [Non-Patent Document 1] Koizumi, Tsujiuchi, Nakamura, Kido, Hashioka, "Extraction and Visualization of Vibration Transmission Characteristics of Structures with Multiple Transmission Paths," Transactions of the Japan Society of Mechanical Engineers (Series C), Vol. 76, No. 772 (2010-12), pp. 3301-3308, Paper No. 10-0246.

[0019] When the countermeasure frequency determination unit 11 receives numerical values ​​of railway vibration at evaluation points measured in advance on-site by an operator in a predetermined section of the railway line, it determines the numerical value of the countermeasure frequency based on a frequency analysis of the numerical values ​​of the railway vibration.

[0020] The aforementioned analysis model creation unit 12 creates an analysis model that reproduces railway vibrations in a predetermined section of the railway line, calculates the railway vibrations at evaluation points, and determines N (where N is the total number of points of interest) locations where countermeasures are possible.

[0021] The transmission path analysis unit 13 performs a transmission path analysis, calculates the displacement vector of the point of interest during train operation, outputs a complex dynamic stiffness matrix of the point of interest, and calculates the transmitted force vector of the point of interest during train operation from the displacement vector and the complex dynamic stiffness matrix. The complex dynamic stiffness matrix is ​​generally obtained during the vibration response calculation process. The transmission path analysis unit 13 further calculates the transfer function vector from the point of interest to the evaluation point, calculates the contribution of the railway vibration transmitted from each point of interest to the evaluation point from the transmitted force vector and the transfer function vector, checks the accuracy of the contribution by comparing the railway vibration at the evaluation point with the sum of the contributions, and calculates the influence of the point of interest on the railway vibration at the evaluation point from the contributions. The transmission path analysis unit 13 performs calculations for all six degrees of freedom: x, y, z, rx, ry, and rz.

[0022] The analysis result output unit 14 visualizes the degree of influence on the analysis model, enabling the operator to identify the location that determines the magnitude of the railway vibration.

[0023] Next, the operation of the railway vibration countermeasure location determination system 10 with the above configuration will be described.

[0024] Figure 2 shows an example of an analysis model that reproduces railway vibration in this embodiment, Figure 3 shows an example of a countermeasure frequency in this embodiment, Figure 4 shows an example of an excitation force input to a structure in this embodiment, Figure 5 shows an example of verifying the accuracy of the contribution in this embodiment, Figure 6 shows an example of railway vibration and contribution of evaluation points represented as vectors on the complex plane in this embodiment, and Figure 7 shows an example of the influence visualized on the analysis model that reproduces railway vibration in this embodiment.

[0025] The railway vibration countermeasure location determination system 10 in this embodiment is used to determine the locations where countermeasures should be applied to a structure, i.e., the locations for countermeasures, when considering or implementing countermeasures against railway vibration. It uses transmission path analysis to calculate and visualize the contribution of evaluation points to railway vibration, thereby identifying the locations that determine the magnitude of railway vibration and determining the locations for railway vibration countermeasures.

[0026] For the sake of explanation, the structure described here will be assumed to be a rigid-frame elevated bridge, but the structure can be any type of railway structure, such as a girder elevated bridge, a bridge, or a tunnel. Figure 2 shows an example of an analysis model that reproduces railway vibrations, and represents a part (1 set) of a cantilevered rigid-frame elevated bridge section. In the analysis model, each set has a span of 3 × 6 [m] + cantilevered section of 2 × 3 [m] = 24 [m]. In Figure 2, 20 is the elevated bridge as a rigid-frame elevated bridge, 21 is the bridge girder (elevated slab) on which rails (not shown) are laid on its upper surface, 22 is the bridge pier that supports the bridge girder 21 from below, 23 is the footing that protrudes laterally from the lower end of each bridge pier 22, and the × enclosed in a circle is the point of focus 24. Here, the bridge piers 22 are arranged side by side to form two rows of columns extending in the longitudinal direction of the bridge girder 21, and the point of interest 24 is described as being at a height of 1.3 m from the base of the bridge piers 22.

[0027] Furthermore, the aforementioned evaluation point can be any location or point on the ground along the railway line, and may be singular or plural. However, here, from the perspective of preventing railway vibrations from becoming an environmental problem and for the sake of simplicity, it will be explained as a single point on the boundary of the railway site. In the analysis model shown in Figure 2, it is set to be located 11 [m] from the center of the column in a direction perpendicular to the bridge axis.

[0028] First, the operator sets up evaluation points along a designated section of the railway line in advance, and measures the railway vibration at these evaluation points on-site when a train is actually running along the line. For example, the acceleration of the railway vibration at the evaluation point is measured using a vibration level meter.

[0029] Next, when the operator inputs the measured railway vibration values ​​into the railway vibration countermeasure location determination system 10, the countermeasure frequency determination unit 11 performs frequency analysis and determines the countermeasure frequency. For example, as shown in Figure 3, a 1 / 3 octave band analysis is performed for the center frequency from 1 to 80 Hz to find the frequency band F with the highest vibration level, and then an FFT (Fast Fourier Transform) analysis is performed to determine the frequency with the largest amplitude within the frequency band F (20 Hz in the example shown in Figure 3) as the countermeasure frequency.

[0030] Furthermore, the analysis model creation unit 12 first creates an analysis model that reproduces railway vibrations. For example, it models the elevated bridge 20 shown in Figure 2 using the finite element method, and models the ground at the location where the elevated bridge 20 is installed using the thin-layer element method. This creates an analysis model that can perform dynamic coupled analysis. The analysis model is not necessarily limited to the one shown in Figure 2; for example, it is also possible to create an analysis model consisting of five consecutive sets of the one set of models shown in Figure 2. In this case, for example, it would include 15,385 nodes (45 of which are evaluation point nodes on the ground) and 13,280 elements. The analysis model can be created using, for example, SimcenterFemap Version 2021 2 MP1, software sold by Siemens PLM Software Co., Ltd. Furthermore, using this software, it is possible not only to create the analysis model but also to visualize the analysis results using the analysis model.

[0031] Next, the analysis model creation unit 12 sets N points of interest 24. Here, the points of interest 24 are locations that could be locations for countermeasures, that is, locations where countermeasures are possible, and in the example shown in Figure 2, these are locations at a height of 1.3 [m] from the base of the bridge pier 22.

[0032] Next, the transmission path analysis unit 13 calculates the displacement vector {X(f)} of the point of interest 24 during train operation based on the analysis model. In this case, the transmission path analysis unit 13 sets the positions of the multiple rail fastening devices installed on the bridge girder 21 as points where excitation forces are input to the elevated bridge 20, which is a structure, during train operation, and calculates the displacement vector {X(f)} of the point of interest 24. In the case of the analysis model consisting of five consecutive sets, there are 200 points on the left and right rail positions for the rail fastening devices, for a total of 400 points. The excitation force is the force input to each vibration source, i.e., each rail fastening device position, due to the movement of the train. In other words, when the transmission path analysis unit 13 calculates the displacement vector {X(f)} of the point of interest 24 during train operation, it inputs the excitation force calculated by a separate train operation analysis to each position of the multiple rail fastening devices. Figure 4 shows an example of the excitation force input to each position of the multiple rail fastening devices in the analysis model consisting of five consecutive sets. Figure 4 shows that the amplitude and phase of the excitation force applied at each position are divergent from each other.

[0033] Next, the transmission path analysis unit 13 outputs the complex dynamic stiffness matrix [K(f)] for the point of interest 24. This complex dynamic stiffness matrix [K(f)] is generally obtained during the vibration response calculation process.

[0034] Next, the transmission path analysis unit 13 calculates the transmission force vector {R(f)} at point 24 during train operation, expressed by the following equation (1), from the displacement vector {X(f)} at point 24 and the complex dynamic stiffness matrix [K(f)]. {R(f)}=[K(f)]{X(f)}...Equation (1)

[0035] Furthermore, Non-Patent Document 1 provides an equation for representing the transmission force vector {R(f)}, as shown in equation (2) below, for use in calculating the transmission force in vibration transmission path analysis in structures such as automobiles. {R(f)}=(-ω 2 [M]+[K]){X(f)}...Equation (2)

[0036] Here, ω is the angular frequency, [M] is the mass matrix of the structure, and [K] is the stiffness matrix of the structure.

[0037] However, when dealing with railway vibrations as in the railway vibration countermeasure location determination system 10, the object of analysis includes not only the structure but also the ground at the location where the structure is installed. Therefore, in addition to the structure information (-ω 2 [M] + [K]), the ground impedance [K G (f)] as ground information needs to be considered.

[0038] Therefore, the transfer force vector {R(f)} is represented by the following equation (3) that takes into account the ground impedance [K G (f)] instead of the above equation (2). {R(f)} = (-ω 2 [M] + [K] + [K G (f)]){X(f)} ··· Equation (3)

[0039] Here, substituting (-ω 2 [M] + [K] + [K G (f)]) = [K(f)] into the above equation (3), the above equation (1) can be obtained.

[0040] Note that the calculation of the displacement vector {X(f)} of the point of interest 24 and the ground impedance [K G (f)] can be performed using, for example, SuperFLUSH / 3D, software sold by Structure Planning Laboratory Co., Ltd. Also, arithmetic operations such as determinants can be performed using, for example, MATLAB R2022b, software sold by MathWorks, Inc. in the United States.

[0041] Subsequently, the transfer path analysis unit 13 calculates the transfer function vector {H(f)} from the point of interest 24 to the evaluation point. The transfer function vectors {H(f)} from all points of interest 24 to the evaluation point can be obtained at once by applying a unit excitation to the evaluation point.

[0042] Next, the transmission path analysis unit 13 calculates the vibration Q(f) transmitted from each point of interest 24 to the evaluation point from the transmission force vector {R(f)} and the transfer function vector {H(f)}. The vibration Q(f) at the evaluation point is the sum of the contributions C(f) of each vibration transmission path from each point of interest 24 to the evaluation point, and is expressed by the following equation (4).

[0043]

number

[0044] Here, H i (f) is the transfer function of vibration from the i-th point of interest 24 to the evaluation point, R i (f) is the transmission force vector of the i-th point of interest 24, C i (f) is the contribution of the vibration transmission path from the i-th point of interest 24 to the evaluation point, i is the point of interest number, and N is the total number of points of interest.

[0045] Next, the transmission path analysis unit 13 analyzes the vibration Q(f) of the evaluation point, which is the sum of the contributions C(f), and the railway vibration Q of the evaluation point obtained from prior field measurements. original By comparing this with (f), we can confirm the accuracy of the contribution C(f) as shown in Figure 5.

[0046] Next, the transmission path analysis unit 13 analyzes the railway vibration Q at the evaluation point. original The influence I(f) of the contribution C(f) to (f) is calculated according to the following equation (5). I(f) = |C(f)|cosθ ... Equation (5)

[0047] Here, θ is the railway oscillation Q. original This is the phase difference between (f) and the contribution C(f).

[0048] Figure 6 shows the railway vibration Q with a phase difference of θ. original This is an example of representing (f) and its contribution C(f) as vectors on the complex plane.

[0049] In this embodiment, the transmission path analysis unit 13 performs various calculations for all six degrees of freedom: x, y, z, rx, ry, and rz. Regarding frequency, the transmission path analysis is performed only for the countermeasure frequency determined by the countermeasure frequency determination unit 11, thus shortening the analysis time. For example, ground impedance [K G (f) is a complex dynamic stiffness matrix, which has frequency dependence. Normally, this would require calculation for each frequency, which would take a long time. However, in this embodiment, calculation only needs to be performed for the countermeasure frequency, so the calculation can be completed in a short time.

[0050] Next, the analysis result output unit 14 visualizes the influence I(f) calculated by the transmission path analysis unit 13 on the analysis model. For example, as shown in Figure 7, the influence I(f) can be visualized by displaying it as a vector at the point of interest 24 of the analysis model.

[0051] Then, when the analysis result output unit 14 outputs the influence I(f) visualized on the analysis model in this way, for example on a liquid crystal display, the operator can identify the location that determines the magnitude of the railway vibration based on the displayed content and decide that location to be the location for railway vibration countermeasures.

[0052] As described above, the railway vibration countermeasure location determination system 10 using transmission path analysis in this embodiment, when input of railway vibration at evaluation points set on the ground along the railway line during train operation, includes a countermeasure frequency determination unit 11 that determines the countermeasure frequency, an analysis model creation unit 12 that creates an analysis model of the railway structure, the elevated bridge 20 and the ground on which the elevated bridge 20 is installed, and sets multiple points of interest 24 on the elevated bridge 20, and calculates the displacement vector {X(f)} of the points of interest 24 during train operation based on the analysis model and the ground impedance [K GThe system includes a transmission path analysis unit 13 that performs a transmission path analysis by calculating the transmission force vector {R(f)} of the 24 points of interest during train operation from the complex dynamic stiffness matrix [K(f)] including (f) and the displacement vector {X(f)} of the 24 points of interest, calculating the transfer function vector {H(f)} from the 24 points of interest to the evaluation point, calculating the contribution C(f) of the vibration transmission path from the 24 points of interest to the evaluation point from the transmission force vector {R(f)} and the transfer function vector {H(f)}, and calculating the influence I(f) of each point of interest 24 to the railway vibration at the evaluation point from the contribution C(f), and an analysis result output unit 14 that visualizes the influence I(f) on the analysis model.

[0053] Furthermore, the method for determining railway vibration countermeasure locations using transmission path analysis in this embodiment involves the following steps: when railway vibration at evaluation points set on the ground along the railway line during train operation is input, the countermeasure frequency is determined; an analysis model of the elevated bridge 20, which is a railway structure, and the ground on which the elevated bridge 20 is installed is created, and multiple points of interest 24 are set on the elevated bridge 20; and based on the analysis model, the displacement vector {X(f)} of the points of interest 24 during train operation is calculated, and the ground impedance [K G The process includes the steps of: calculating the transmission force vector {R(f)} of point 24 during train operation from the complex dynamic stiffness matrix [K(f)] and displacement vector {X(f)} of point 24 including (f); calculating the transfer function vector {H(f)} from point 24 to the evaluation point; calculating the contribution C(f) of the vibration transmission path from point 24 to the evaluation point from the transmission force vector {R(f)} and transfer function vector {H(f)}; and calculating the influence I(f) of each point 24 on the railway vibration at the evaluation point from the contribution C(f) to perform a transmission path analysis; and visualizing the influence I(f) on the analysis model.

[0054] This visualizes the influence I(f) of each of the 24 points of interest on railway vibration at the evaluation points, making it possible to identify the locations that determine the magnitude of railway vibration, determine where railway vibration countermeasures would be most effective, and decide on the locations for railway vibration countermeasures.

[0055] Furthermore, the transmission path analysis unit 13 sets the positions of multiple rail fastening devices for fastening rails onto the elevated bridge 20 as points where excitation forces are input to the elevated bridge 20 during train operation, and calculates the displacement vector {X(f)} at the point of interest 24. Therefore, it is possible to more accurately grasp railway vibrations and perform vibration transmission path analysis.

[0056] Furthermore, the countermeasure frequency determination unit 11 performs frequency analysis of railway vibrations at the evaluation point to determine the countermeasure frequency, and the transmission path analysis unit 13 performs transmission path analysis only for the countermeasure frequency. Therefore, the calculation time can be reduced.

[0057] Furthermore, the analysis result output unit 14 visualizes the influence I(f) by displaying it as a vector at the point of interest 24. Therefore, the operator can easily identify the location that determines the magnitude of railway vibration and decide that location to be designated as a location for railway vibration countermeasures.

[0058] This specification describes features relating to preferred and exemplary embodiments. Various other embodiments, modifications, and variations within the scope and spirit of the claims attached herein will be readily apparent to those skilled in the art by reviewing this specification. [Industrial applicability]

[0059] This disclosure can be applied to a system and method for determining railway vibration countermeasure locations using transmission path analysis. [Explanation of Symbols]

[0060] 10. Railway Vibration Countermeasure Location Determination System 11 Countermeasure frequency determination unit 12. Analysis Model Creation Department 13 Transmission Path Analysis Unit 14. Analysis Result Output Section 20 viaduct 24 points of focus

Claims

1. When railway vibrations at evaluation points set on the ground along the railway line are input during train operation, the countermeasure frequency determination unit determines the countermeasure frequency, An analysis model creation unit creates an analysis model of the railway structure and the ground on which the structure is installed, and sets multiple points of focus on the structure. A transmission path analysis unit performs a transmission path analysis by calculating the displacement vector of the point of interest during train operation based on the analysis model, calculating the transmission force vector of the point of interest during train operation from the complex dynamic stiffness matrix of the point of interest including the ground impedance of the ground and the displacement vector, calculating the transfer function vector from the point of interest to the evaluation point, calculating the contribution of the vibration transmission path from the point of interest to the evaluation point from the transmission force vector and the transfer function vector, and calculating the influence of each point of interest on the railway vibration of the evaluation point from the contribution, based on the analysis model, A system for determining railway vibration countermeasure locations using transmission path analysis, characterized by comprising an analysis result output unit that visualizes the degree of influence on the analysis model.

2. The railway vibration countermeasure location determination system using transmission path analysis according to claim 1, wherein the transmission path analysis unit sets the positions of a plurality of rail fastening devices for fastening rails onto the structure as locations where an excitation force is input to the structure when a train is running, and calculates the displacement vector of the point of interest.

3. The countermeasure frequency determination unit performs a frequency analysis of the railway vibration at the evaluation point to determine the countermeasure frequency. The system for determining railway vibration countermeasure locations using the transmission path analysis described in claim 1, wherein the transmission path analysis unit performs the transmission path analysis only for the countermeasure frequency.

4. The railway vibration countermeasure location determination system using transmission path analysis according to claim 1, wherein the analysis result output unit visualizes the degree of influence by displaying it as a vector at the point of focus of the analysis model.

5. When railway vibrations at evaluation points set on the ground along the railway line are input during train operation, the process involves determining the countermeasure frequency. The process involves creating an analytical model of the railway structure and the ground on which the structure is installed, and setting multiple points of focus on the structure. Based on the aforementioned analysis model, the displacement vector of the point of interest during train operation is calculated; the transmission force vector of the point of interest during train operation is calculated from the complex dynamic stiffness matrix of the point of interest, including the ground impedance of the ground, and the displacement vector; the transfer function vector from the point of interest to the evaluation point is calculated; the contribution of the vibration transmission path from the point of interest to the evaluation point is calculated from the transmission force vector and the transfer function vector; and the influence of each point of interest on the railway vibration at the evaluation point is calculated from the contribution, thereby performing a transmission path analysis. A method for determining railway vibration countermeasures locations using transmission path analysis, characterized by including the step of visualizing the degree of influence on the analysis model.

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