Method and system for identifying vibration modes of a structure

Abstract

To provide a structure vibration mode identification method capable of properly identifying the vibration modes of a structure by field tests.SOLUTION: The structure vibration mode identification method includes: vibrating multiple excitation points of a structure (step St1); measuring the excitation force at the excitation points (step St2); measuring the acceleration of waves propagating on the rail due to the excitation at the excitation points at the measurement points of structure (step St3); deriving a frequency response function of the acceleration at the measurement points based on the excitation force and the acceleration (step St4); identifying the vibrational mode shapes of the structure based on the frequency response function (step St6); and correcting a time synchronization error between the observed signals at the excitation points and the measurement points by phase standardization (step St7).SELECTED DRAWING: Figure 7

Description

[Technical field]

[0001] The present invention relates to a vibration mode identification method and a vibration mode identification system for a structure. [Background technology]

[0002] Steel railway bridges over which railway vehicles run can cause vibration and noise problems, such as rolling noise generated between the rails and wheels when trains pass, and structure-borne noise caused by vibration of components. Therefore, many studies have been conducted to identify the natural frequencies and vibration mode shapes of steel railway bridges as part of the performance evaluation of the steel railway bridges as structures.

[0003] Identification of such vibration mode shapes is generally performed by installing a large number of accelerometers (sensors) on a structure (steel railway bridge), as disclosed in, for example, Non-Patent Documents 1 and 2. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Hirohiro Matsuoka, Kiyoyuki Kaito, Tsutomu Watanabe, Masamichi Sogabe. (2011). Identification of vibration of RC railway viaduct members and understanding of dynamic behavior using running train load. Journal of Japan Society of Civil Engineers, Proceedings A1 (Structural and Earthquake Engineering), 67(3), 545-564. [Non-Patent Document 2] Matsuoka, K., Sogabe, M., Watanabe, T. (2018). Higher-order resonance behavior and acceleration evaluation of composite box girder bridge deck members for European high-speed railways. Journal of the Japan Society of Civil Engineers, Proceedings A1 (Structural and Earthquake Engineering), 74(1), 125-144. Summary of the Invention [Problem to be solved by the invention]

[0005] By the way, it has been found from past noise measurement results that the structure-borne sound of the steel railway bridge mentioned above has a high-frequency band of approximately 200 Hz or more. However, since the high-frequency vibration modes that contribute to such structure-borne noise generally have complex vibration mode shapes with many antinodes and nodes, in order to identify the vibration mode shapes using existing methods based on multi-point measurements, it is necessary to install a huge number of sensors on the steel railway bridge. For this reason, it has been practically difficult to identify the vibration mode shapes of steel railway bridges in on-site measurements with strict time and space constraints.

[0006] In addition, when identifying the vibration mode shape, the excitation force of the hammer that strikes the structure is obtained along with responses such as acceleration during vibration testing. However, in the frequency range of 200 Hz or more mentioned above, time synchronization errors between the excitation force and the response can cause large errors in identifying the vibration mode, and there are also significant limitations to the use of the excitation force.

[0007] The present invention has been made in consideration of the above circumstances, and has an object to appropriately identify the vibration mode of a structure by on-site testing. [Means for solving the problem]

[0008] The present invention for solving the above-mentioned problems is a method for identifying vibration modes of a structure, comprising the steps of: exciting a plurality of excitation points of the structure and measuring excitation forces at the excitation points; measuring acceleration of vibration of the structure caused by excitation at the excitation points at measurement points of the structure, the measurement points being set at least a number less than the excitation points; deriving a plurality of frequency response functions corresponding to each of the plurality of excitation points based on the excitation forces and the accelerations; identifying a vibration mode shape of the structure based on the plurality of frequency response functions; and performing phase normalization of the plurality of frequency response functions based on a time synchronization error occurring between observation signals of the excitation points and the measurement points. and identifying a natural frequency of the vibration mode based on a peak frequency of the frequency response function, wherein, in identifying the natural frequency, an envelope of a plurality of the frequency response functions is calculated, and the peak frequency is extracted based on the envelope. It is characterized by the following. According to another aspect of the present invention, there is provided a method for identifying a vibration mode of a structure, comprising the steps of: exciting a plurality of excitation points of the structure and measuring an excitation force at the excitation points; measuring an acceleration of the vibration of the structure caused by the excitation at at least measurement points of the structure set to a number smaller than the excitation points; deriving a plurality of frequency response functions corresponding to each of the plurality of excitation points based on the excitation force and the acceleration; identifying a vibration mode shape of the structure based on the plurality of frequency response functions; and performing phase normalization of the plurality of frequency response functions based on a time synchronization error occurring between observation signals of the excitation points and the measurement points, wherein the phase normalization step is characterized in that one of the plurality of excitation points is set as a reference point, and the phase of the frequency response function at the reference point when the reference point is excited is subtracted from the phases of the frequency response functions corresponding to all of the other excitation points. At this time, the reference point may be set to a point among the plurality of excitation points where the amplitude of a mode vector is maximum.

[0009] In the present invention, the vibration mode of a structure is identified by utilizing multi-point excitation and the reciprocity theorem. By using the reciprocity theorem, it is possible to interchange the excitation points and the measurement points. That is, instead of installing a large number of sensors as in the conventional method, by exciting the sensor installation points, information equivalent to that obtained by multi-point measurement can be obtained in a simulated manner. Specifically, in the present invention, a frequency response function of acceleration is derived based on the excitation forces at a plurality of excitation points and the accelerations at the measurement points, and this frequency response function resulting from multi-point excitation is equal to the frequency response function resulting from multi-point measurement. Then, the derived frequency response function makes it possible to identify the local vibration mode of the structure.

[0010] Furthermore, according to the present invention, since at least one measurement point is sufficient, information equivalent to multi-point measurement can be obtained with a simple measurement system configuration. Another advantage is that the reduction in the number of measurement points reduces the amount of preparation work required for measurement.

[0011] Furthermore, according to the present invention, the time synchronization error that occurs between the observed signals at the excitation point and the measurement point is corrected by phase normalization of the frequency response function. In the high frequency band that contributes to structure-borne noise, the time synchronization error between the excitation force and the response generally causes errors in the identification of vibration modes, so there are restrictions on the use of excitation force. In this regard, the present invention corrects this time synchronization error by phase normalization of the frequency response function, making it possible to achieve mode identification by multi-point excitation at high frequencies.

[0013] The measurement point may be provided at one point on the structure.

[0015] The structure may be a bridge through which a moving object passes.

[0016] According to another aspect of the present invention, there is provided a system for identifying a vibration mode of a structure, the system comprising: an excitation force measuring device for measuring excitation forces at a plurality of excitation points of the structure; an acceleration measuring device for measuring, at the measurement points of the structure, an acceleration of vibration of the structure due to excitation at the excitation points; and a vibration mode identifying device for identifying a vibration mode type of the structure based on the excitation forces and the accelerations. The vibration mode identifying device comprises: a frequency response function derivation unit for deriving a plurality of frequency response functions corresponding to each of the plurality of excitation points based on the excitation force and the accelerations; a phase standardizing unit for performing phase standardization of the plurality of frequency response functions based on a time synchronization error occurring between observation signals at the excitation points and the measurement points; and a vibration mode type identifying unit for identifying a vibration mode type of the structure based on the plurality of frequency response functions after the phase standardization. The natural frequency of the vibration mode is identified based on a peak frequency of the frequency response function, and when identifying the natural frequency, an envelope of a plurality of the frequency response functions is calculated, and the peak frequency is extracted based on the envelope. It is characterized by the following. According to another aspect of the present invention, there is provided a system for identifying a vibration mode of a structure, the system comprising: an excitation force measuring device for measuring excitation forces at a plurality of excitation points of the structure; an acceleration measuring device for measuring, at a measurement point of the structure, an acceleration of vibration of the structure due to excitation at the excitation points; and a vibration mode identifying device for identifying a vibration mode shape of the structure based on the excitation forces and the accelerations, the vibration mode identifying device comprising a frequency response function for deriving a plurality of frequency response functions corresponding to each of the plurality of excitation points based on the excitation forces and the accelerations. The system includes a function derivation unit, a phase standardization unit that performs phase standardization of the plurality of frequency response functions based on a time synchronization error occurring between the observation signals of the excitation points and the measurement points, and a vibration mode type identification unit that identifies a vibration mode type of the structure based on the plurality of frequency response functions after the phase standardization, wherein the phase standardization unit sets one of the plurality of excitation points as a reference point, and subtracts the phase of the frequency response function at the time of excitation of the reference point from the phases of the frequency response functions corresponding to all of the other excitation points. Effect of the Invention

[0017] According to the present invention, the vibration modes of a structure can be appropriately identified by on-site testing. [Brief description of the drawings]

[0018] [Figure 1] FIG. 1 is a side view showing an outline of the configuration of a steel railway bridge to be identified according to the present embodiment. [Diagram 2] FIG. 1 is a cross-sectional view showing an outline of the configuration of a steel railway bridge to be identified according to the present embodiment. [Diagram 3] FIG. 1 is an explanatory diagram showing an example of the arrangement of vibration points on a steel railway bridge. [Figure 4A] FIG. 1 is an explanatory diagram showing an example of the arrangement of measurement points on a steel railway bridge. [Figure 4B] FIG. 11 is an explanatory diagram showing another example of the arrangement of measurement points on a steel railway bridge. [Diagram 5] 1 is an explanatory diagram showing an outline of a configuration of a vibration mode identification system according to an embodiment of the present invention; [Figure 6] FIG. 2 is an explanatory diagram showing an outline of the configuration of a calculation unit of the device according to the present embodiment. [Figure 7] FIG. 2 is a flowchart showing main steps of a vibration mode identification method according to the present embodiment. [Figure 8] FIG. 11 is an explanatory diagram showing a time synchronization error corrected by phase normalization. [Figure 9A] FIG. 11 is an explanatory diagram showing an example of a frequency response function and an envelope when the upper flange is vibrated. [Figure 9B] FIG. 4 is an explanatory diagram showing an example of a frequency response function and an envelope when a web is excited. [Figure 10A] 4A to 4C are explanatory diagrams showing an example of a natural frequency and a vibration mode shape identified by the identification method according to the present embodiment. [Figure 10B] 4A to 4C are explanatory diagrams showing an example of a natural frequency and a vibration mode shape identified by the identification method according to the present embodiment. [Figure 10C] 4A to 4C are explanatory diagrams showing an example of a natural frequency and a vibration mode shape identified by the identification method according to the present embodiment. [Figure 10D] 4A to 4C are explanatory diagrams showing an example of a natural frequency and a vibration mode shape identified by the identification method according to the present embodiment. [Figure 10E] 4A to 4C are explanatory diagrams showing an example of a natural frequency and a vibration mode shape identified by the identification method according to the present embodiment. [Figure 10F] 4A to 4C are explanatory diagrams showing an example of a natural frequency and a vibration mode shape identified by the identification method according to the present embodiment. [Figure 10G] 4A to 4C are explanatory diagrams showing an example of a natural frequency and a vibration mode shape identified by the identification method according to the present embodiment. [Figure 10H] 4A to 4C are explanatory diagrams showing an example of a natural frequency and a vibration mode shape identified by the identification method according to the present embodiment. [Figure 11A] FIG. 2 is an explanatory diagram showing a mode shape of a web identified by a conventional identification method. [Figure 11B] FIG. 2 is an explanatory diagram showing a mode shape of a web identified by a conventional identification method. [Figure 11C] FIG. 2 is an explanatory diagram showing a mode shape of a web identified by a conventional identification method. [Figure 12A]FIG. 4 is an explanatory diagram showing a mode shape of a lower flange identified by the identification method according to the present embodiment. [Figure 12B] FIG. 4 is an explanatory diagram showing a mode shape of a lower flange identified by the identification method according to the present embodiment. [Figure 12C] FIG. 4 is an explanatory diagram showing a mode shape of a lower flange identified by the identification method according to the present embodiment. [Figure 12D] FIG. 4 is an explanatory diagram showing a mode shape of a lower flange identified by the identification method according to the present embodiment. [Figure 13A] FIG. 10 is an explanatory diagram showing a mode shape of a lower flange identified by a conventional identification method. [Figure 13B] FIG. 10 is an explanatory diagram showing a mode shape of a lower flange identified by a conventional identification method. [Figure 13C] FIG. 10 is an explanatory diagram showing a mode shape of a lower flange identified by a conventional identification method. [Figure 13D] FIG. 10 is an explanatory diagram showing a mode shape of a lower flange identified by a conventional identification method. [Figure 14A] FIG. 11 is an explanatory diagram showing the identification result of a vibration mode shape when phase normalization is performed. [Figure 14B] FIG. 11 is an explanatory diagram showing the identification result of the vibration mode shape when phase normalization is not performed. [Figure 15A] FIG. 11 is an explanatory diagram showing a phase distribution of a vibration mode shape when phase normalization is performed. [Figure 15B] FIG. 11 is an explanatory diagram showing a phase distribution of a vibration mode shape when phase normalization is not performed. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0019] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In this specification and the drawings, elements having substantially the same functional configurations are denoted by the same reference numerals, and duplicated description will be omitted.

[0020] <Target structure> In this embodiment, the vibration mode of a steel railway bridge (bridge) as a structure is identified. Fig. 1 is a side view showing an outline of the configuration of a steel railway bridge 1 to be identified. Fig. 2 is a cross-sectional view showing an outline of the configuration of the steel railway bridge 1 to be identified.

[0021] The steel railway bridge 1 is a steel I-girder with a direct track located in a straight section, and includes an upper flange 11, a web 12, and a lower flange 13. The web 12 of the steel railway bridge 1 is divided in the bridge axis direction by stiffeners 14 installed on the inside of the girder. In the following description, each of the areas divided by the stiffeners 14 is referred to as a "panel P." A rail 3 is laid directly on the upper surface of an upper flange 11 of a steel railway bridge 1 via a fastening device 2 (for example, a spring-type fastening device). The rail 3 is a rail installed on an actual track on which railway vehicles run.

[0022] In this embodiment, one panel P is selected from the steel railway bridge 1 shown in FIG. 1, and the higher-order member vibration modes of each of the upper flange 11, web 12, lower flange 13, and stiffener 14 are identified.

[0023] In this embodiment, the vibration mode shape is identified by applying multi-point excitation to one panel P. That is, multiple excitation points M on the steel railway bridge 1 are excited, and the acceleration of the vibration caused by the excitation of the excitation points M is measured at measurement points L set on the steel railway bridge 1 in a number at least less than the number of the excitation points M. A plurality of excitation points M in the steel railway bridge 1 are set as shown in Fig. 3. That is, a plurality of excitation points M are arranged in an array with respect to the upper flange 11, the web 12, the lower flange 13, and the stiffeners 14. Specifically, one panel P is divided into eight in the bridge axis direction and the vertical direction, and the grid points are set as the excitation points M. The measurement points L on the steel railway bridge 1 are set as shown in Fig. 4A. That is, the measurement points L are set at a total of 13 points: one point (L1) on the rail 3, three points (L2 to L4) on the upper flange 11, three points (L5 to L7) on the web 12, and seven points (L8 to L13) on the lower flange 13.

[0024] By using a mode identification method using the reciprocity theorem described later, the higher-order component vibration mode can be identified with only one measurement point L1 set on the rail 3, for example, as shown in Fig. 4B. In other words, the measurement point L on the steel railway bridge 1 does not need to be set to multiple points as shown in Fig. 4A, and may be set to only one point as shown in Fig. 4B. However, in the following embodiment, multiple (13) measurement points L are set as shown in Fig. 4A for the purpose of verifying the accuracy of the present invention.

[0025] <Vibration mode identification system> 5 is an explanatory diagram showing an outline of the configuration of a vibration mode identification system 20 according to this embodiment. The vibration mode identification system 20 identifies the vibration mode of a steel railway bridge 1 by excitation at an excitation point M.

[0026] The vibration mode identification system 20 includes a hammer 30 , an amplifier 31 , an accelerometer 40 , a charge amplifier 41 , a preamplifier 42 , an AD converter 50 , a communication device 60 , and a device 70 .

[0027] The hammer 30 is, for example, an impulse hammer with a built-in sensor, and corresponds to the "excitation force measuring device" in the present invention. The hammer 30 is used to excite multiple excitation points M (see FIG. 3) set on the steel railway bridge 1. Specifically, excitation by the hammer 30 is performed intermittently for each excitation point M of the steel railway bridge 1, utilizing interval times other than when trains are passing. Furthermore, excitation of the excitation points M is performed in the vertical direction for the excitation points M set on the upper flange 11 and the lower flange 13, in the direction perpendicular to the bridge axis for the excitation points M set on the web 12, and in the bridge axis direction for the excitation points M set on the stiffener 14.

[0028] The hammer 30 measures the excitation force when the excitation point M is excited, and outputs an excitation force signal. The excitation force signal is amplified by the amplifier 31, and converted into a digital signal by the AD converter 50. In this embodiment, the hammer 30 is provided with a sensor to measure the excitation force, but the excitation force may be measured by a sensor outside the hammer 30. That is, the excitation means and the excitation force measuring means may be provided separately. In this embodiment, the hammer 30 is used as the excitation means, but is not limited to this as long as it can excite the excitation point M.

[0029] As described above, the amplifier 31 is connected to the hammer 30. The amplifier 31 is, for example, a charge amplifier. However, the type of the amplifier 31 is not limited to this.

[0030] The accelerometer 40 is, for example, a piezoelectric accelerometer, and corresponds to the "acceleration measuring device" in the present invention. The accelerometer 40 is provided at each measurement point L set on the steel railway bridge 1. As described above, the rail 3 is a rail of an actual line, and a train passes through it, so the accelerometer 40 is installed at the rail bottom, not the rail head, for the measurement point L1 corresponding to the rail 3. The accelerometer 40 measures the acceleration of the vibration generated in the steel railway bridge 1 by the vibration of the vibration point M by the hammer 30 at each measurement point L, and outputs an acceleration signal. The acceleration signal is amplified by the charge amplifier 41 and converted into a digital signal by the AD converter 50. In the present embodiment, a piezoelectric accelerometer is used as the accelerometer 40, but is not limited to this.

[0031] As described above, the charge amplifier 41 and the preamplifier 42 are each connected to the accelerometer 40. The type of amplifier connected to each accelerometer 40 can be arbitrarily selected from either the charge amplifier 41 or the preamplifier 42. That is, the type of accelerometer 40 may be different for each measurement point L. Note that the type of amplifier connected to the accelerometer 40 is not limited to this.

[0032] The AD converter 50 is connected to the amplifier 31 of the hammer 30, and the charge amplifier 41 and preamplifier 42 of the accelerometer 40, and is further connected to the device 70 via a communication device 60. The AD converter 50 converts the excitation force signal input from the hammer 30 and the acceleration signal input from the accelerometer 40 into digital signals, and outputs the excitation force signal (excitation force data) and acceleration signal (acceleration data) to the device 70.

[0033] The communication device 60 outputs the vibration force data and acceleration data output from the AD converter 50 to the device 70. The communication device 60 is not particularly limited as long as it can perform communication, and for example, a wireless LAN, a wired LAN, the Internet, etc. are used.

[0034] The device 70 is, for example, a notebook personal computer (PC), and the calculation unit of the device 70 corresponds to the vibration mode identification device in the present invention. The device 70 identifies the vibration mode of the steel railway bridge 1 based on the excitation force data and acceleration data input from the communication device 60. In this embodiment, a notebook PC is used as the device 70, but this is not limited thereto. For example, the device 70 may be a desktop PC, a tablet, or a smartphone.

[0035] As shown in FIG. 6, the device 70 includes a control unit 100, a storage unit 101, a frequency response function derivation unit 102, a phase normalization unit 103, a vibration mode shape identification unit 104, a communication unit 105, and a display unit .

[0036] The control unit 100 is a circuit (hardware) or a central processing unit such as a CPU. The control unit 100 controls the device 70 according to a program (software) stored in the storage unit 101. The storage unit 101 is composed of a RAM, a ROM, a flash memory, a HDD, an SDD, etc., and stores various programs and data.

[0037] The frequency response function derivation unit 102 derives a plurality of frequency response functions corresponding to each excitation point M based on the excitation force data and acceleration data output from the AD converter 50. The phase normalization unit 103 corrects the time synchronization error of the frequency response function derived by the frequency response function derivation unit 102 by performing phase normalization. The vibration mode type identification unit 104 identifies the vibration mode type of the steel railway bridge 1 based on the plurality of frequency response functions corresponding to each excitation point M.

[0038] The communication unit 105 is a communication interface that mediates communication with the communication device 60. Specifically, the communication unit 105 receives the excitation force data and the acceleration data output from the AD converter 50. The display unit 106 is, for example, a display, and displays various information related to the device 70.

[0039] <Vibration mode identification method> The vibration mode identification system 20 according to one embodiment is configured as described above. Next, a vibration mode identification method for a steel railway bridge 1 performed using the vibration mode identification system 20 will be described. Fig. 7 is a flow chart showing main steps of the vibration mode identification method according to this embodiment.

[0040] First, a plurality of excitation points M of the steel railway bridge 1 are excited by the hammer 30 (step St1 in FIG. 7). At this time, the excitation force at each excitation point M is measured by the hammer 30 (step St2 in FIG. 7). The measured excitation force data is amplified by the amplifier 31, converted into a digital signal by the AD converter 50, and then output to the communication unit 105 of the device 70 via the communication device 60 and stored in the memory unit 101.

[0041] At the measurement point L, the acceleration of the vibration caused by the excitation of the excitation point M by the hammer 30 is measured by the accelerometer 40 (step St3 in FIG. 7). The measured acceleration data is amplified by the charge amplifier 41 or the preamplifier 42, converted into a digital signal by the AD converter 50, and then output to the communication unit 105 of the device 70 via the communication device 60 and stored in the memory unit 101.

[0042] Next, in the frequency response function derivation unit 102, a frequency response function (FRF) of the acceleration at the measurement point L corresponding to each excitation point M is derived based on the excitation force and acceleration stored in the storage unit 101 (step St4 in FIG. 7). The derived frequency response function is output to and stored in the storage unit 101. In step St4, an acceleration G, which is one of the frequency response functions, is derived based on the excitation force and acceleration. lm (ω) is expressed by the following equation (1).

number

[0043] Here, if the above formula (1) is expanded to the frequency response of the acceleration of a multi-input multi-output system, it can be expressed as the following formula (2).

number

[0044] Further, according to Maxwell's reciprocity theorem, the frequency response function satisfies the following formula (3).

number

[0045] The frequency response function of the above formula (3) is a symmetric matrix. In other words, even if the excitation point M and the measurement point L are interchanged, the acceleration G lm (ω) means equal. In addition, the above equation (3) can be rewritten as follows when expressed as a vector with l = 1, 2, . . . , N.

number

[0046] In this way, by using the reciprocity theorem, it is possible to swap the excitation point M and the measurement point L, and by using multi-point excitation, it is possible to obtain information equivalent to that obtained by multi-point measurement. In other words, in the above formula (4), the left side corresponds to single-point excitation and multi-point measurement, and the right side corresponds to multi-point excitation and single-point measurement, and the frequency response functions in both cases are equivalent.

[0047] Next, the natural frequency ω of the vibration mode r (Step St5 in FIG. 7). That is, from the above formula (1), the natural frequency ω r Since the frequency response function shows a peak at , the natural frequency ω r is identified.

[0048] More specifically, the natural frequency ω r is identified by reading the spectrum peak frequency of the measured waveform. In this embodiment, the excitation force at the excitation point M is obtained as the measurement information as described above. In addition, since the frequency characteristic of the excitation force is relatively flat, the natural frequency ω r can be identified.

[0049] In addition, the natural frequency ω of the vibration mode in step St5 r The method of identifying the natural frequency ω is not limited to the method of reading the peak frequency of the frequency response function described above. Specifically, the natural frequency ω can be determined by a conventional method such as the Ritz method or the ERA method described later. r may be identified or may be calculated by referring to the theoretical analysis results of Leissa, for example.

[0050] In this embodiment, by multi-point excitation in which a plurality of excitation points M are excited, frequency response functions as many as the number of excitation points M can be obtained. These frequency response functions include points that are nodes of the mode shape and where the modal displacement is almost zero. In order to identify all high-order component vibration modes, it is necessary to extract the cases where the modal displacement is maximum across all points. Therefore, the natural frequency ω r When extracting the above-mentioned peak frequency in identifying the frequency response function, it is preferable to calculate the envelope of the frequency response function when all the excitation points M are excited (see FIG. 9 described later) and then extract the peak from this frequency response function envelope, rather than the frequency response function when a specific excitation point M is excited.

[0051] Next, the vibration mode type identifying unit 104 identifies the vibration mode type of the steel railway bridge 1 based on the frequency response function stored in the storage unit 101 (step St6 in FIG. 7). The identified vibration mode type is output to the storage unit 101 and stored therein.

[0052] The natural frequency of the rth mode of the frequency response function (ω = ω r Assuming that the coupling of adjacent modes can be ignored near the natural frequency (ω = ω r ) the frequency response function G lm (ω r ) and the mode vector φr, the following equation (5) is obtained.

number

[0053] Therefore, the vibration mode shape of the steel railway bridge 1 as the target structure is the spatial distribution of the imaginary term of the frequency response function measured at a single point when multiple points are excited, as in the case of multiple point measurement, and is identified by the following formula (6). In other words, the vibration mode shape can be identified from the frequency response function measured in step St4.

number

[0054] Here, to calculate the amplitude and phase of the vibration mode shape identified in step St6, it is necessary to calculate the absolute value and the argument of the above formula (4) using the following formulas (7) and (8).

number

number

[0055] In the above formulas (7) and (8), Im(·) represents the imaginary part, and Re(·) represents the real part. lr is the maximum value of the mode vector calculated by the above equation (7) normalized to 1.

[0056] Moreover, the positive or negative vibration mode shape is determined by the following formula (9) using the phase calculated by the above formula (8).

number

[0057] Here, when different types of amplifiers are used for each of the accelerometers 40 as described above, that is, when both the charge amplifier 41 and the preamplifier 42 are used in the vibration mode identification system 20, a time lag (time synchronization error) occurs in the measurement waveform upstream of the AD converter 50 due to the difference in the types of amplifiers in the measurement signal path. In other words, a time synchronization error exists between the observed signals of the hammer 30 and the accelerometer 40 due to the difference in signal processing time, as shown in FIG.

[0058] This time synchronization error is extremely small, for example, about 0.003 seconds, and does not have a significant effect on low-order mode identification. However, in high-order component vibration modes of 200 Hz or more, such as the structure-induced noise of steel railway bridge 1, the vibration period is 0.005 seconds or less, and so this can be reflected in the phase evaluation in the vibration mode type identification results. In particular, when a higher-order component vibration mode is to be identified as in this embodiment, the magnitude relationship of the higher-order component vibration mode with respect to the phase of π / 2 changes depending on the number of vibration nodes, resulting in a complex phase distribution that is prone to erroneous judgment.

[0059] Therefore, in this embodiment, instead of the phase relationship between the input (hammer 30) and output (accelerometer 40) that is generally used in phase calculation, the output of any one accelerometer 40 (output at any one excitation point M) is assumed to be a reference point M0 with a zero phase to calculate the phase (phase standardization: step St7 in FIG. 7). That is, one excitation point M is set as the reference point M0, and the phase of the frequency response function at the time of excitation at the reference point M0 is subtracted from the phases of the frequency response functions of all other excitation points M to cancel the effect of the time synchronization error.

[0060] When an arbitrary degree of freedom p is set as the reference point M0, the phase normalization of the frequency response function of the excitation point M is expressed by the following formula (10). As an example, the reference point M0 can be selected to be a point where the amplitude of the mode vector is 1 (maximum amplitude).

number

[0061] In this embodiment, the time synchronization error of the frequency response function identified in step St6 is corrected in the above manner.

[0062] In calculating the frequency response function described above, it is physically impossible for the measured waveform to appear as a response before excitation of the excitation point M as shown in Figure 8, and depending on the method of extracting the measured waveform, the frequency response function may not be calculated appropriately. Therefore, in the vibration mode identification method according to this embodiment, as a pre-processing step, the time of the acceleration waveform (the measurement time by the accelerometer 40) may be corrected to be after the excitation time of the excitation point M by the hammer 30, as shown in FIG.

[0063] <Vibration mode identification results according to the embodiment> The vibration mode identification according to this embodiment is performed as described above. The vibration mode identification result by the above method will be shown below as an example.

[0064] 9A and 9B show an example of a frequency response function (step St4) calculated by extracting one second of the measured waveform, which shows each excitation force when the upper flange 11 and the web 12 are excited, and the mobility (velocity response per unit excitation force) calculated from each acceleration measured at the measurement point L1 on the rail 3, and their envelopes. That is, in this embodiment, the measurement point L1 on the rail 3 corresponds to the above-mentioned reference point M0. According to the reciprocity theorem described above, these are equivalent to the frequency response functions at each excitation point M on the upper flange 11 and the web 12 when the measurement point L1 on the rail 3 is excited.

[0065] As shown in Figures 9A and 9B, in the high frequency band exceeding 100 Hz, the amplitude of the frequency response function varies greatly depending on the excitation position even within the same member. It can also be seen that the envelope curve can comprehensively evaluate different peaks for each excitation point M. In other words, it can be seen that the frequency response function can be appropriately measured by the above method.

[0066] Next, the natural frequency was identified from the envelope of the frequency response function shown in Fig. 9 (step St5), and the vibration mode shape was identified from all the frequency response functions (step St6). As in the measurement of the frequency response function described above, the reference point M0 is the measurement point L1 on the rail 3. Moreover, the phase normalization (step St7) was set so that the phase at the point where the mode amplitude is maximum is zero.

[0067] 10A to 10H show the natural frequencies and vibration mode shapes of eight representative modes among the multiple identified natural frequencies and vibration mode shapes. The vibration mode shapes of the upper flange 11 and the lower flange 13 in the figures are interpolated so that the amplitude becomes zero at the joints between the web 12 and both flanges.

[0068] The vibration modes and natural frequencies of the modes shown in each of FIGS. 10A to 10H are as follows: That is, FIG. 10A shows a 1×1 vibration mode of the web with a natural frequency of 64 Hz. FIG. 10B shows a 2×1 vibration mode of the web with a natural frequency of 125 Hz. FIG. 10C shows a 1×2 vibration mode of the web with a natural frequency of 160 Hz. FIG. 10D shows a 2×3 vibration mode of the web with a natural frequency of 312 Hz and a 1×2 vibration mode of the web with a natural frequency of 312 Hz. FIG. 10E shows a 3×3 vibration mode of the web with a natural frequency of 404 Hz and a 2×3 vibration mode of the web with a natural frequency of 404 Hz. FIG. 10F shows a 3×3 vibration mode of the web with a natural frequency of 456 Hz and a 2×4 vibration mode of the web with a natural frequency of 470 Hz and a 2×4 vibration mode of the web with a natural frequency of 1st between the upper flange and the upper flange and a 2nd vibration mode of the auxiliary steel material. FIG. 10H shows a 7×2 vibration mode of the web with a natural frequency of 1145 Hz.

[0069] It can be seen that the vibration mode identification method according to this embodiment can identify not only well-known vibration modes such as 1×1 and 1×2 of the web 12 as shown in Figures 10A and 10C, but also higher-order member vibration modes such as 2×4 of the web 12 as shown in Figure 10G and 7×2 of the web 12 as shown in Figure 10H. In addition, it is believed that Figures 10E and 10F identify ring-shaped and X-shaped combined modes, the existence of which has been pointed out in plate vibration theory.

[0070] According to the vibration mode identification method of this embodiment, there are few restrictions on the number of accelerometers 40 (the number of excitation points M), so it is possible to grasp the vibration mode of not only one member such as the web 12, but also the entire panel P composed of multiple members such as the upper flange 11, the web 12, the lower flange 13, and the stiffener 14, and the coupling properties between the members. Specifically, it can be confirmed that the member that mainly vibrates in the steel railway bridge 1 changes as the vibration frequency changes, for example.

[0071] According to this embodiment, as shown in FIG. 10, the coupled properties with other components are clarified by detailed mode identification, and the predominant properties of the web 12 when the measurement point L is a node can be estimated to some extent from the predominant properties and vibration frequency of the upper flange 11, so that at least underestimation of the influence of the web 12 can be avoided.

[0072] <Effects of the vibration mode identification method according to this embodiment> The following shows the results of vibration mode identification according to this embodiment, compared with existing identification methods and theories and analyses. Note that in the following, to facilitate comparison with theories, the comparison results are shown focusing on two members, the web 12 and the bottom flange 13. Note that the Eigensystem Realization Algorithm (ERA), an identification method based on multi-point measurement that has been widely used in the past, was selected as the existing identification method for comparison.

[0073] 11A to 11C show the identification results of the web 12 by the ERA method, which correspond to the identification results according to the present embodiment shown in Fig. 10B, Fig. 10D, and Fig. 10F, respectively. Note that, for the mode identification results of the web 12 according to the present embodiment used as a comparison subject, vibration modes (Fig. 10B, Fig. 10D, and Fig. 10F) in which the center in the bridge axis direction of the panel P of the web 12 is not a node were extracted for comparison with existing methods and theories. 12A to 12D and 13A to 13D show the identification results of the bottom flange 13 by the identification method according to this embodiment and the ERA method, respectively.

[0074] It was confirmed that the natural frequency identified by the ERA method coincided with the identification result by multi-point excitation according to the present embodiment within an error of 5%. In addition, the vibration mode shape identified by the ERA method generally coincided with the identification result by multi-point excitation (identification method according to the present embodiment) in Fig. 10 at the same position. The identification result of the lower flange 13 by the ERA method shown in Fig. 13 also showed the same tendency as the web 12, and it was confirmed that it coincided with the natural frequency and vibration mode shape identified by multi-point excitation (identification method according to the present embodiment) in Fig. 12 with high accuracy.

[0075] From the above, it has been found that the vibration mode identification method according to the embodiment of the present invention is capable of identifying natural frequencies with the same level of accuracy as existing identification methods, and is also capable of identifying high-order component vibration modes with very complex vibration mode shapes with a small number of sensors (accelerometers 40).

[0076] In addition, although it is qualitative, the identification method according to the present embodiment using multi-point excitation requires much less work and time compared to conventional multi-point measurement, especially when there are many measurement points L. For example, in the case of conventional multi-point measurement, it takes about two hours to prepare even for the 13 measurement point arrangement shown in Fig. 4A due to the installation of accelerometers 40, cable wiring, sensor testing, etc., whereas in the case of multi-point excitation with the same number of points, the preparation and testing can be completed in less than one hour. On the other hand, if the huge number of excitation points M shown in Fig. 3 were to be measured by the accelerometers 40 instead of excitation, it would take more than two days just to install the accelerometers 40, and it would be practically impossible to wire a large amount of cables on-site. This shows that the identification method according to the embodiment is highly effective in identifying higher-order member vibration modes by on-site measurement of the steel railway bridge 1 as a structure.

[0077] In this way, the vibration mode identification method according to the present invention makes it possible to identify local vibration modes of a structure by on-site multipoint measurement, which was previously difficult in practice. These vibration modes are important information, especially for identifying the source of structure-borne sound. Furthermore, according to the vibration mode identification method of the present invention, the number of measurement points L (the number of installed accelerometers 40) needs to be at least one, so that the preparation work for measurement can be significantly reduced.

[0078] Next, a comparison of mode identification results when the above-mentioned phase normalization process (step St7) is performed and when it is not performed is shown. Note that since it is difficult to grasp the effect of phase normalization in the case of a complex vibration mode shape, an example of a web (vertical second order x horizontal first order) mode with a vibration frequency of 125 Hz, which is a relatively simple and well-known vibration mode shape, is shown here. For the same reason, the identification results focusing only on the web 12 are also shown.

[0079] Fig. 14 shows a comparison result showing the influence of phase normalization on the identification result of the vibration mode shape of the web 12. Fig. 14A shows the case with phase normalization, and Fig. 14B shows the case without phase normalization. The "●" in the figure indicates the excitation point.

[0080] As described above, the web 12 has a vertical second order horizontal first order vibration mode, but the vibration mode shape in Fig. 14B without phase normalization has a positive / negative inversion in a part of the lower part of the web 12, and appears to have a second order vibration mode shape in the horizontal direction as well. Therefore, it can be seen that the mode order cannot be accurately evaluated because the positive / negative of the vibration mode shape is inverted by phase normalization. Although we have shown an example here of a vertical secondary horizontal primary vibration mode, which is relatively easy to determine the vibration mode, the effect of positive / negative reversal of the vibration mode shape is even greater in higher-order component vibration modes with more complex mode shapes.

[0081] Figure 15 shows the difference in phase distribution of the mode with and without phase standardization. Figure 15A shows the case with phase standardization, and Figure 15B shows the case without phase standardization. The phase is shown by contours from 0 to π. The "●" in the figure indicates the excitation point.

[0082] In Fig. 15B, where phase normalization is not performed, measurement points L showing a phase close to π / 2, which is the boundary between positive and negative determination in the above formula 10, are widely distributed, particularly in the lower part of the web 12, and it can be seen that a slight difference in phase causes the vibration mode shape to appear to be inverted in positive and negative. On the other hand, by performing phase normalization as shown in Fig. 15A, measurement points L having a phase close to π / 2 almost disappear, and it can be seen that the positive and negative determination is performed more clearly. Although a typical example is shown here, this effect is more pronounced in higher modes.

[0083] As described above, according to the identification method of this embodiment, the previously unexplored higher-order component vibration modes up to about 1000 Hz of a steel railway bridge 1 with a directly connected track have been empirically clarified by a newly proposed method based on multi-point excitation and reciprocity theorem.

[0084] Although the embodiment of the present invention has been described above, the present invention is not limited to such examples. It is clear that a person skilled in the art can come up with various modified or altered examples within the scope of the technical ideas described in the claims, and it is understood that these also naturally belong to the technical scope of the present invention.

[0085] Further, for example, in the above embodiment, the structure to be identified is the steel railway bridge 1, but the structure to be identified is not limited to this. [Industrial Applicability]

[0086] The present invention is useful for identifying the vibration mode of a structure, for example, when evaluating the performance of the structure. [Explanation of symbols]

[0087] 1. Steel Railway Bridge 2 Fastening device 3. Rail 11 Upper flange 12. Web 13 Lower flange 14 Stiffeners 20 Vibration mode identification system 30 Hammer 31 Amplifier 40 accelerometer 41 Charge Amplifier 42 Preamplifier 50 A / D converter 60 Communication Equipment 70 Devices 100 Control section 101 Storage section 102 Frequency response function derivation section 103 Phase standardization section 104 Vibration mode shape identification section 105 Communications Department 106 Display section L measuring point M Excitation point

Claims

1. 1. A method for identifying vibration modes of a structure, comprising: A step of exciting a plurality of excitation points of the structure and measuring the excitation forces at the excitation points; measuring an acceleration of vibration of the structure caused by excitation at the excitation points at measurement points of the structure set in a number less than that of the excitation points; Deriving a plurality of frequency response functions corresponding to each of the plurality of excitation points based on the excitation force and the acceleration; identifying a vibration mode shape of the structure based on a plurality of said frequency response functions; performing phase normalization of the plurality of frequency response functions based on a time synchronization error occurring between the observation signals of the excitation point and the measurement point; identifying a natural frequency of the vibration mode based on a peak frequency of the frequency response function; The vibration mode identifying method, wherein, when identifying the natural frequency, an envelope of a plurality of the frequency response functions is calculated, and the peak frequency is extracted based on the envelope.

2. 1. A method for identifying vibration modes of a structure, comprising: vibrating a plurality of excitation points of the structure and measuring the excitation forces at the excitation points; measuring an acceleration of vibration of the structure caused by excitation at the excitation points at measurement points of the structure set in a number less than that of the excitation points; Deriving a plurality of frequency response functions corresponding to each of the plurality of excitation points based on the excitation force and the acceleration; identifying a vibration mode shape of the structure based on a plurality of said frequency response functions; and performing phase normalization of the plurality of frequency response functions based on a time synchronization error occurring between the observation signals of the excitation point and the measurement point; In the step of performing phase normalization, One of the plurality of excitation points is set as a reference point; A vibration mode identification method, comprising: subtracting a phase of the frequency response function at the time of excitation of the reference point from phases of the frequency response functions corresponding to all of the other excitation points.

3. 3. The vibration mode identification method according to claim 2, wherein the reference point is set to a point among the plurality of excitation points at which an amplitude of a mode vector is maximum.

4. 4. The vibration mode identifying method according to claim 1, wherein the measurement point is provided at one point on the structure.

5. 5. The vibration mode identifying method according to claim 1, wherein the structure is a bridge over which a moving object passes.

6. 1. A system for identifying vibration modes of a structure, comprising: An excitation force measuring device that measures excitation forces at a plurality of excitation points of the structure; an acceleration measuring device that measures an acceleration of vibration of the structure caused by excitation at the excitation point at a measurement point of the structure; a vibration mode identifying device that identifies a vibration mode shape of the structure based on the excitation force and the acceleration; Equipped with The vibration mode identification device includes: a frequency response function derivation unit that derives a plurality of frequency response functions corresponding to each of the plurality of excitation points based on the excitation force and the acceleration; a phase normalization unit that performs phase normalization of the plurality of frequency response functions based on a time synchronization error occurring between the observation signals of the excitation point and the measurement point; a vibration mode shape identifying unit that identifies a vibration mode shape of the structure based on the plurality of frequency response functions after the phase normalization; Equipped with identifying a natural frequency of the vibration mode based on a peak frequency of the frequency response function; The vibration mode identification system, wherein, when identifying the natural frequency, an envelope of a plurality of the frequency response functions is calculated, and the peak frequency is extracted based on the envelope.

7. 1. A system for identifying vibration modes of a structure, comprising: An excitation force measuring device that measures excitation forces at a plurality of excitation points of the structure; an acceleration measuring device that measures an acceleration of vibration of the structure caused by excitation at the excitation point at a measurement point of the structure; a vibration mode identifying device that identifies a vibration mode shape of the structure based on the excitation force and the acceleration; Equipped with The vibration mode identification device includes: a frequency response function derivation unit that derives a plurality of frequency response functions corresponding to each of the plurality of excitation points based on the excitation force and the acceleration; a phase normalization unit that performs phase normalization of the plurality of frequency response functions based on a time synchronization error occurring between the observation signals of the excitation point and the measurement point; a vibration mode shape identifying unit that identifies a vibration mode shape of the structure based on the plurality of frequency response functions after the phase normalization; Equipped with the phase standardization unit sets one of the plurality of excitation points as a reference point, and subtracts a phase of the frequency response function at the time of excitation of the reference point from phases of the frequency response functions corresponding to all of the other excitation points.

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