Natural frequency determination device and natural frequency determination method

Abstract

To facilitate theoretical solution fitting to a transfer function in which external factors relatively reduce a spectral amplitude ratio, and improve determination accuracy.SOLUTION: An eigenfrequency determination device 10 comprises a control part 20 receiving detection signals from sensors 11a, 11b. The control part 20 includes: a theoretical amplitude ratio calculation part 35 calculating a parameter when applying a ratio of Fourier transformation amplitude of vibration of a structure 1 calculated by an amplitude ratio calculation part 34 to Fourier transformation amplitude of vibration of ground 3 to a theoretical value of the ratio; an amplification factor calculation part 38 calculating a predetermined amplification factor A to be multiplied by the transfer function represented by the ratio; and an eigenfrequency determination part determining eigenfrequency on the basis of the parameter calculated by the theoretical amplitude ratio calculation part 35, the amplification factor A calculated by the amplification factor calculation part 38, and a determination coefficient calculated by a determination coefficient calculation part.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a natural frequency identifying device and a natural frequency identifying method for identifying the natural frequency of a structure (hereinafter simply referred to as a "structure") including a railway structure, a road structure, etc., installed on the ground. [Background technology]

[0002] In order to prevent train accidents caused by scouring due to the sudden rise and prolonged high water levels of rivers caused by typhoons or localized heavy rains, railway operators not only conduct regular general inspections, but also check bridge piers after the river rises to see if there are any abnormalities compared to before the rise, and carry out repairs and reinforcement as necessary.

[0003] However, in recent years, it has become difficult to reinforce all bridges against increasingly severe torrential rains, and it is unclear whether conventional measures will be effective against torrential rains that have never been experienced before.In addition, since it is extremely difficult to visually evaluate the ground conditions around bridge pier foundations located in rivers, it is important to have an evaluation method for constantly monitoring the condition of the foundations before and after flooding.

[0004] Impact vibration testing is known as a method for evaluating the soundness of bridge piers. In this method, the natural frequency of the pier is used as an index for evaluating the soundness of the pier, and the natural frequency is identified by directly vibrating the pier with a weight. This value is compared before and after the river floods, and the soundness of the pier is evaluated from the degree of decrease. However, this method has the problem that it is difficult to measure when the river is flooded, as it requires impact with a weight. Therefore, an evaluation method using constant microtremor measurement was developed with the aim of continuously measuring the natural frequency of the pier.

[0005] This method is an algorithm that identifies the natural frequency by installing sensors at two locations on the top end of a pier and measuring microtremors constantly, and it has been confirmed that it is possible to identify the natural frequency by applying it to model experiments and to some actual piers in service.By using this method to constantly monitor the soundness of the pier, it is possible to capture changes in the natural frequency from the early stages when the soil covering thickness decreases, or when minute deformations such as the pier's tilt or settlement occur, enabling more appropriate operation restrictions, and it is expected to contribute to improving the safety of the traffic transportation system.

[0006] Here, the principle of the method for identifying the natural frequency described above is outlined below, but a more detailed explanation will be given later. First, the microtremors in the direction perpendicular to the bridge axis and the vertical direction are measured by sensors installed at both ends of the bridge pier top. Next, the ground vibration is estimated from the difference in the vertical components of the microtremors measured by the two sensors at both ends of the bridge pier top and the geometric relationship of the sensor positions. At this time, based on the above assumptions, the difference in the vertical components of the microtremors cancels out the ground vibration, and the vertical component of the rocking vibration of the bridge pier can be extracted. Then, by plotting the microtremors in the direction perpendicular to the bridge axis and the difference in the vertical direction on a plane, the angle of the rocking vibration can be obtained geometrically, and the horizontal component of the rocking vibration can be calculated from the rocking angle and the vertical component of the rocking vibration. The horizontal component of the ground vibration can be obtained by subtracting the horizontal component of the rocking vibration calculated from the horizontal component of the microtremors measured on the bridge pier.

[0007] The Fourier amplitude ratio (transfer function) is calculated by dividing the horizontal component of the microtremors caused by the primary vibration of the pier measured on the pier by the estimated horizontal component of the ground vibration. The theoretical solution of the transfer function when forced vibration is applied from the ground to a one-degree-of-freedom vibration model with viscous damping is fitted to the calculated Fourier amplitude ratio, and the frequency at which the theoretical solution matches most closely is determined to be the natural frequency of the pier. In the prior art section "fitting the theoretical solution to identify (specify) the natural frequency," the transfer function (theoretical solution) used for fitting is calculated using the following formula (1). TIFF0007626729000001.tif34170 Where: JPEG0007626729000002.jpg1416 is the transfer function (theoretical solution), ω is the frequency (Hz), f(t) is the natural frequency of the pier at time t (Hz), and h(t) is the damping constant at time t.

[0008] The theoretical solution represents the Fourier amplitude ratio between the pier vibration when forced vibration is applied from the ground and the ground vibration at that time. Therefore, the transfer function obtained from the measurement data assumes that the ground vibration is input to the pier, causing the pier vibration, and is expressed as a theoretical solution in which the pier vibration and the ground vibration have the same magnitude, i.e. starting from 1. [Prior art documents] [Patent documents]

[0009] [Patent Document 1] Patent Publication No. 2019-132635 Summary of the Invention [Problem to be solved by the invention]

[0010] However, because actual measurement data includes not only pier vibration but also other external factors such as noise, if the influence is relatively large, the measurement data is buried in the noise and the transfer function becomes small. For example, when measurement data is generated that results in a transfer function that starts at 1 or less, as shown in the measured value (dotted line) in Figure 5, fitting to the theoretical solution is not successful (the solid line part (fitting result) and the dashed line part in Figure 5 do not match), and the accuracy of identifying the natural frequency drops significantly. Therefore, even though the actual transfer function shows a mountain-shaped shape and it is possible to identify the natural frequency (there is a prominent frequency), it is difficult to fit the theoretical solution to the relatively small transfer function, and it is not possible to improve the identification accuracy.

[0011] Therefore, an object of the present invention is to provide a natural frequency identifying device and a natural frequency identifying method that can facilitate fitting of a theoretical solution to a transfer function that has become relatively small, thereby improving the identification accuracy. [Means for solving the problem]

[0012] In order to solve the above-mentioned problems, one aspect of the natural frequency identifying device according to the present invention is a natural frequency identifying device that includes a pair of sensors that detect vibrations of a structure and a control unit that receives detection signals from the sensors, and identifies the natural frequency of a structure installed on the ground, wherein the control unit includes a ground vibration calculation unit that calculates the vibration of the ground based on the vibration of a predetermined frequency band of the structure detected by the pair of sensors and the height of the vibration center of the structure calculated by a vibration center position calculation unit, and a Fourier transform amplitude of the vibration of the structure detected by the pair of sensors and the ground vibration calculated by the ground vibration calculation unit. The vibration control device is characterized by having an amplitude ratio calculation unit that calculates a ratio with an amplitude of a Fourier transform, a theoretical amplitude ratio calculation unit that calculates a parameter when the ratio calculated by the amplitude ratio calculation unit is applied to a theoretical value of the ratio, an amplification factor calculation unit that calculates a predetermined amplification factor to be multiplied by a transfer function represented by the ratio, a determination coefficient calculation unit that calculates a determination coefficient between the ratio calculated by the amplitude ratio calculation unit and the theoretical value of the ratio, and a natural frequency identification unit that identifies a natural frequency based on the parameter calculated by the theoretical amplitude ratio calculation unit, the amplification factor calculated by the amplification factor calculation unit, and the determination coefficient calculated by the determination coefficient calculation unit.

[0013] Furthermore, another aspect of the natural frequency identifying device according to the present invention is characterized in that the amplification factor calculation unit calculates an amplification factor to be added as a variable parameter to the theoretical solution of the transfer function and to increase the magnification of the transfer function.

[0014] Moreover, one aspect of the natural frequency identification method according to the present invention is a method for identifying the natural frequency of a structure installed on the ground by a natural frequency identification device including a pair of sensors for detecting vibrations of the structure and a control unit for receiving detection signals from the sensors, in which a ground vibration calculation unit calculates ground vibration based on vibrations in a predetermined frequency band of the structure detected by the pair of sensors and the height of the vibration center of the structure calculated by a vibration center position calculation unit, and an amplitude ratio calculation unit calculates the amplitude of a Fourier transform of the vibration of the structure detected by the pair of sensors and the height of the vibration center of the structure calculated by the ground vibration calculation unit. a theoretical amplitude ratio calculation unit calculates a ratio between the amplitude of the vibration of the ground and an amplitude of a Fourier transform of the vibration of the ground measured by the amplitude ratio calculation unit, a theoretical amplitude ratio calculation unit calculates a parameter when the ratio calculated by the amplitude ratio calculation unit is applied to a theoretical value of the ratio, an amplification factor calculation unit calculates a predetermined amplification factor to be multiplied by a transfer function expressed by the ratio, a determination coefficient calculation unit calculates a determination coefficient between the ratio calculated by the amplitude ratio calculation unit and the theoretical value of the ratio, and a natural frequency identification unit identifies the natural frequency based on the parameter calculated by the theoretical amplitude ratio calculation unit, the amplification factor calculated by the amplification factor calculation unit, and the determination coefficient calculated by the determination coefficient calculation unit. Effect of the Invention

[0015] According to the present invention, it is possible to provide a natural frequency identifying device and a natural frequency identifying method that can improve the identification accuracy. [Brief description of the drawings]

[0016] [Figure 1] 1 is a block diagram showing a schematic configuration of a natural frequency identifying device according to an embodiment of the present invention; [Diagram 2] 1 is a diagram for explaining a method for identifying a natural frequency in the natural frequency identifying device according to the present embodiment; [Diagram 3] 1 is a diagram for explaining the principle of a natural frequency identifying device according to an embodiment of the present invention; [Figure 4] 4 is a flowchart showing an example of the overall operation of the natural frequency identifying device according to the present embodiment. [Diagram 5]FIG. 1 is a diagram showing a Fourier spectrum of microtremors measured using a conventional natural frequency identification device. [Figure 6] FIG. 1 is a diagram showing a Fourier spectrum of microtremors measured using the natural frequency identifying device according to the present embodiment. [Figure 7] FIG. 13 is a diagram showing an example of a result of whether or not a natural frequency can be identified when a conventional natural frequency identifying device is used. [Figure 8] FIG. 11 is a diagram showing an example of a result of whether or not a natural frequency can be identified when the natural frequency identifying device according to the present embodiment is used. [Figure 9] FIG. 11 is a diagram showing another example of the result of whether or not the natural frequency can be identified when the conventional natural frequency identifying device is used. [Figure 10] FIG. 11 is a diagram showing another example of the result of whether or not the natural frequency can be identified when the natural frequency identifying device according to the present embodiment is used. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017] (Overall configuration of the natural frequency identification device) DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, an embodiment of the present invention will be described with reference to the drawings. Fig. 1 is a block diagram showing a schematic configuration of a natural frequency identifying device according to the present embodiment.

[0018] The natural frequency identifying device (hereinafter simply referred to as identifying device) 10 according to the present embodiment identifies the natural frequency of a bridge pier 1, which is an example of a structure. As shown in FIG. 3, the bridge pier 1 is a part of a railway pier (not shown) erected over a river 4, and is erected on the ground 3.

[0019] In the following explanation, the X-axis is taken from left to right on the page (perpendicular to the bridge axis: sleeper direction), and the Z-axis is taken from up to down on the page (vertical direction), with the right side of the page being the positive direction of the X-axis and the top of the page being the positive direction of the Z-axis. Also, river 4 flows from left to right on the page, so the left side is the upstream side of river 4 and the right side is the downstream side of river 4.

[0020] The natural frequency identifying device 10 of this embodiment has a pair of sensors 11a, 11b that measure vibrations of a bridge pier 1, and a main body 12 to which measurement signals from these sensors 11a, 11b are input.

[0021] As shown in Figures 1 and 3, sensors 11a and 11b are attached to the top (upper end) surface of pier 1, and are provided at the upstream and downstream ends of river 4, respectively, at a predetermined distance apart in the direction perpendicular to the bridge axis (X-axis direction) (see Figure 3(b)). Sensors 11a and 11b are preferably known speed sensors or acceleration sensors capable of detecting vibrations (speed or acceleration) in the X-axis and Z-axis directions. Sensors 11a and 11b output the detected vibrations of pier 1 as, for example, a potential difference.

[0022] The main body 12 is, for example, a personal computer, and includes a control unit 20, a storage unit 21, an input interface (I / F) 22, and an output interface (I / F) .

[0023] The control unit 20 includes a computing element such as a CPU. A control program (not shown) stored in the storage unit 21 is executed when the natural frequency identifying device 10 is started up, and based on this control program, the control unit 20 controls the entire natural frequency identifying device 10 including the storage unit 21, etc., and also executes functions as a frequency band setting unit 30, a vibration center position calculation unit 31, a vibration center position determination unit 32, a ground vibration calculation unit 33, an amplitude ratio calculation unit 34, a theoretical amplitude ratio calculation unit 35, a determination coefficient calculation unit 36, an amplification factor calculation unit 38, and a natural frequency identifying unit 37. The operation of each of these functional units will be described later.

[0024] The storage unit 21 includes a large-capacity storage medium such as a hard disk drive, and a semiconductor storage medium such as a ROM, a RAM, etc. The storage unit 21 stores the above-mentioned control programs, and also temporarily stores various data required for the control operation of the control unit 20.

[0025] The input interface 22 receives various inputs from the input device 13 connected to the main body 12, and outputs them to the control unit 20. The input device 13 in this embodiment is, for example, a keyboard or a mouse.

[0026] The output interface 23 receives the output signal output from the control unit 20 and outputs it to the display device 14. The display device 14 in this embodiment is, for example, a liquid crystal display device, and displays a display screen on a display surface (not shown) based on the display control signal output via the output interface 23.

[0027] (Principle of the natural frequency identification device) Hereinafter, the principle of the natural frequency identifying device 10 according to this embodiment, including the method disclosed in the above-mentioned Patent Document 1 by the same inventor as the present invention, will be described with reference to the flow charts of FIGS.

[0028] FIG. 3 is a diagram for explaining the principle of the natural frequency identifying device according to the present embodiment, where FIG. 3(a) is a side view and FIG. 3(b) is a plan view.

[0029] It is assumed that the pier 1 vibrates primarily, and point 1b, where the vibration center 1a is projected onto the bottom surface, is a point that divides points 1c and 1d, where the installation positions of sensors 11a and 11b are projected onto the bottom surface, in a ratio of a:b (both positive values), as shown in Figure 3(a). If the height from vibration center 1a to sensors 11a and 11b is h0, then the distance between the two sensors 11a and 11b is (a+b)h0.

[0030] In addition, the vibration waveform measured at the top of pier 1 is considered to be the sum of only the primary vibration of pier 1, which is the structure, (vibration of pier 1 only) and the vibration of ground 3, and higher-order vibrations and the effects of other structures such as girders are ignored here.

[0031] The waveform measured by sensor 11a installed at the upstream end of the top of pier 1 in the direction perpendicular to the bridge axis is denoted as xa(t), the vertical waveform is denoted as za(t), the waveform measured by sensor 11b installed at the downstream end in the direction perpendicular to the bridge axis is denoted as Xb(t) and the vertical waveform is denoted as Zb(t), the waveform of the vibration of ground 3 in the direction perpendicular to the bridge axis is denoted as Xg(t), and the vertical waveform is denoted as Zg(t).

[0032] The vibration waveforms measured by the sensors 11a and 11b may be either velocity waveforms or acceleration waveforms, as long as the same physical quantity is measured by each of the sensors 11a and 11b. The direction of the waveforms will be described here as positive from upstream to downstream in the direction perpendicular to the bridge axis, and positive from bottom to top in the vertical direction.

[0033] Among the components perpendicular to the bridge axis of the waveform detected by sensors 11a and 11b, the vibration components due to the primary vibration of pier 1 are denoted as Xas(t) and Xbs(t), and among the vertical components, the vibration components due to the primary vibration of pier 1 are denoted as Zas(t) and Zbs(t). Za(t) = Zas(t) + Zg(t) (2) Zb(t) = Zbs(t) + Zg(t) (3) It can be approximated as follows: Z as(t) = -a / b × Z b s(t) (4) From formulas (2) to (4), Zas(t)=a / (a+b)×{Za(t)-Zb(t)}···(5) We obtain the following geometrical Xas(t) = 1 / a × Zas(t) (6) Therefore, from equation (5) and equation (6), Xas(t)=1 / (a+b)×{Za(t)-Zb(t)}···(7) Also, from the above conditions, Xa(t) = Xas(t) + Xg(t) (8) Therefore, by using formula (7) and formula (8), Xg(t)=Xa(t)-1 / (a+b)×{Za(t)-Zb(t)}···(9) An estimated value (ground vibration) Xg(t) of the waveform of the ground vibration of the ground 3 is estimated based on the difference between the waveforms detected by the sensors 11a and 11b and the geometric relationship between the positions of the sensors 11a and 11b (see step S10 in FIG. 2).

[0034] The value of a+b can be calculated geometrically when the vibration center 1a is located on the bottom surface of the pier 1. However, even when the vibration center 1a is not located on the bottom surface of the pier 1, it can be calculated based on the following formula (10). Xa(t)-Xg(t)=1 / a×{Za(t)-Zb(t)}···(10)

[0035] Next, a specific frequency band (for example, 20 Hz) is divided into n (n is a natural number) divided frequency bands each having a predetermined frequency band range using a band pass filter (see step S11 in FIG. 2). Specifically, in step S201 in FIG. 4, divided frequency bands ω1Hz to ω2Hz, ω2Hz to ω3Hz, ω n -1Hz~ω n Hz. And the divided frequency band ω k ~ω k+1 For each of (1≦k≦n), coefficient a k , b k Find the values ​​of a k , b k Using this, the ground vibration waveform Xg(t) is estimated using Equation (9). Next, the pier vibration waveform Xa(t) is divided by the estimated ground vibration waveform Xg(t) for each divided band to calculate a transfer function (see step S12 in Figure 2).

[0036] Here, the frequency at which the value of the Fourier amplitude ratio of the waveform Xa(t) and the waveform Xg(t) reaches a peak is the natural frequency of the pier 1 at time t. However, in actual waveform data, due to the influence of peak value fluctuations and noise, it may be difficult to determine the natural frequency from the value of the Fourier amplitude ratio of the Fourier spectrum obtained by Fourier transforming the actual waveform Xa(t) and the estimated waveform Xg(t). Therefore, a theoretical formula (theoretical solution) is fitted to the ratio (transfer function) of the actual waveform Xa(t) and the estimated waveform Xg(t), and the natural frequency f(t) at time t is specified (identified) based on the parameters (see step S13 in Fig. 2).

[0037] The Fourier amplitude ratio of Xa(t) and Xg(t) obtained by the Fourier transform ^Xa(t) and ^Xg(t) obtained by the formula (9) is theoretically expressed by the resonance curve expressed by the above formula (1). From a mathematically strict notational standpoint, the symbol (^) should be written above X, but due to notational limitations, the symbol (^) is written in front instead.

[0038] Here, before fitting the theoretical formula (theoretical solution) to the transfer function, a predetermined amplification factor A (variable: variable parameter) is further added to the fitting variables (frequency f, natural frequency f0, damping constant h) of the transfer function (see step S131 in FIG. 2 and step S206 in FIG. 4). That is, the entire transfer function (right side of formula (1)) is multiplied by the amplification factor A. Then, after multiplying the entire transfer function (right side of formula (1)) by the amplification factor A, the fitting process of the theoretical formula (theoretical solution) to the transfer function is performed.

[0039] After fitting with the theoretical solution described above, the narrowing down based on the vibration rotation center position, narrowing down based on the boundaries of the specific value (identification value) band, and narrowing down based on the coefficient of determination are performed, which will be described later, and finally, identification (specification) of the natural frequency is completed. Note that narrowing down based on the vibration rotation center position may be performed before fitting with the theoretical solution, and in the operation explanation described later, a case will be explained in which narrowing down based on the vibration rotation center position is processed before fitting with the theoretical solution, and narrowing down based on the boundaries of the specific value (identification value) band is processed after fitting with the theoretical solution.

[0040] (Filtering by vibration rotation center position) Normally, the vibration rotation center position in rocking vibration is said to be near the bottom of the pier, or slightly above the bottom if the pier is deeply embedded. Therefore, the height hc from the bottom of the foundation to the vibration center can be calculated from hc=hl / (a+b), where l is the distance between the sensors installed at the top end of the pier and h is the pier height. If the vibration center position of rocking vibration is significantly below the bottom or near the top of the pier, it cannot be considered to be the correct vibration center, so in such cases it can be determined that there is a high possibility that the natural frequency is not included, making it possible to narrow down the search.

[0041] (Refine based on specific value band boundaries) If the natural frequency f does not fit within the range of each frequency band, i.e., the boundary value ω set as the possible value of f k (1≦k≦n) and ω k+1 When the coefficient of determination for fitting is the best for (1≦k≦n), it can be determined that the natural frequency is not included, and it is possible to narrow down the search. This is because the parameter a related to height is used even though the natural frequency is not included in the set frequency band. k +b k If the value of is accidentally correct, the natural frequency is outside the range of the set frequency band in the fitting with the theoretical solution, so the lower limit ω of the boundary value close to that natural frequency side k Or the upper limit of the boundary value ω k+1 This is because it is expected that the coefficient of determination for the fitting of the theoretical solution will be the best.

[0042] <Refine by coefficient of determination> The narrowing down by the coefficient of determination is explained below. The natural frequency f(t) and the damping constant h(t) are provisionally set within the range of the divided frequency band, and a resonance curve is drawn. The coefficient of determination adjusted for the degrees of freedom or Coefficient of determination (hereafter referred to as the coefficient of determination) is calculated, and the optimum natural frequency f(t) and damping constant h(t) are determined as f(t) and h(t) when the highest coefficient of determination is obtained within the range of the divided frequency band. At this time, the range of possible values ​​for the damping constant h(t) should be slightly wider than the range of possible values ​​for a general damping constant, for example, about 0.01 to 0.40 for a railway pier.

[0043] The coefficient of determination is 1 if the theoretical value of the resonance curve and the Fourier amplitude ratio are perfectly in agreement, and the better the correlation, the larger the value becomes. Therefore, a high coefficient of determination means that the resonance curve and the Fourier amplitude ratio are in good agreement (fitted).

[0044] A fitting process is performed with the theoretical solution for all divided frequency bands, and f(t) with the best (largest) coefficient of determination is found, and this is taken as the natural frequency.

[0045] Frequency band ω k ~ω k+1 If does not include the natural frequency, a k +b k Therefore, the correct value of Xg(t) is not obtained, and the estimated ground vibration waveform Xg(t) is not correct. Therefore, the correct transfer function is not obtained, and the coefficient of determination becomes small in the fitting process with the theoretical solution. In addition, if the frequency band ω k ~ω k+1 Although the natural frequency is not included in a k +b k Even if the value of f(t) happens to be correct, if the natural frequency is not included in the range of possible values ​​of f(t) when fitting (i.e., the range of the divided frequency bands), the coefficient of determination is still likely to be small.

[0046] According to the above-mentioned process, even though the transfer function clearly shows a peak value with a mountain-shaped shape, the theoretical solution cannot adequately fit the transfer function, and the accuracy of identifying the natural frequency is improved. That is, in the prior art, the variable parameters of the theoretical solution of the transfer function are the natural frequency and the damping constant, whereas in the present embodiment, the amplification factor is additionally set as a variable parameter. Here, the natural frequency, which is a variable parameter, changes the position of the peak, and the damping constant changes the mountain-shaped shape. Since the Fourier amplitude ratio is expressed as the ratio between the pier vibration and the ground vibration, by adding the amplification factor as a variable parameter, the fitting accuracy can be improved without compromising the theoretical formula used in the prior art by mathematical processing that increases the magnification of the entire data.

[0047] Even when the accuracy of estimating bridge pier vibration and ground vibration decreases due to external factors such as noise (a state in which the effects of noise become prominent), and measurement data (dashed line) is generated that results in a transfer function that starts below 1, as shown in Fig. 6, it is possible to improve the fitting by forcibly amplifying the Fourier amplitude ratio (measured value) and increasing the consistency between the measured value and the theoretical solution. Therefore, the accuracy of identifying the natural frequency can be improved by performing mathematical processing that magnifies the entire data.

[0048] (Functional configuration of the control unit) Next, each functional unit constituting the control unit 20 will be described.

[0049] As described above, the frequency band setting unit 30 divides a specific frequency band, for example, within a range of 20 Hz, into n predetermined frequency bands (n is a natural number) each having a range of 3 Hz, for example, ω1 Hz to ω2 Hz, ω2 Hz to ω3 Hz, ω n-1 Hz~ω n The frequency bands are set by dividing the frequency bands into 100 Hz, and are output to the natural frequency identification unit 37. Note that the above-mentioned numerical values ​​are merely examples and can be changed as appropriate.

[0050] The vibration center position calculation unit 31 calculates the vibration center position in a specific divided frequency band ω k ~ω k+1 Assuming that there is a natural frequency within the bp xa(t), f bp By applying formulas (12) and (13) to za(t), the parameter a related to the height of the vibration center 1a of the pier 1 is obtained. k +b k and outputs it to the natural frequency identification unit 37.

[0051] The vibration center position determination unit 32 determines the parameter a relating to the height of the vibration center 1a of the bridge pier 1 calculated by the vibration center position calculation unit 31. k +b k Based on this, as shown in the above principle, it is determined whether or not the natural frequency exists within this divided frequency band. To repeat, if the vibration center 1a is significantly lower than the bottom surface or near the top edge, it is not considered to be the correct vibration center 1a, so the corresponding divided frequency band (ω k Hz~ω k+1 Hz) does not include the natural frequency of pier 1.

[0052] The ground vibration calculation unit 33 calculates a parameter a related to the height of the vibration center 1a calculated by the vibration center position calculation unit 31 in the divided frequency band that is determined by the vibration center position determination unit 32 to include the natural frequency. k +b k As shown in the above-mentioned formula (9), the waveform Xg(t) of the ground vibration is estimated from the waveforms Xa(t), Za(t), and Zb(t) of the vibration detected by the sensors 11a and 11b provided on the pier 1, and the waveform Xg(t) is output to the natural frequency identification unit 37.

[0053] The amplitude ratio calculation unit 34 performs a Fourier transform on the waveform Xa(t) of the vibration detected by the sensor 11a and the waveform Xg(t) of the ground vibration calculated by the ground vibration calculation unit 33, calculates the Fourier amplitude ratio of the Fourier spectrum, and outputs it to the natural frequency identification unit 37.

[0054] The theoretical amplitude ratio calculation unit 35 performs fitting processing with the above-mentioned theoretical solution, that is, calculates parameters when the ratio calculated by the amplitude ratio calculation unit 34 is applied to the theoretical value of the Fourier amplitude ratio (see formula (1)) in the divided frequency band that is determined to include the natural frequency by the vibration center position determination unit 32. The parameters here refer to the natural frequency f(t) and the damping constant h(t).

[0055] Before the theoretical amplitude ratio calculation unit 35 performs the fitting process of the theoretical equation (theoretical solution) to the transfer function, the amplification factor calculation unit 38 calculates an amplification factor A by which the fitting variables of the transfer function (frequency f, natural frequency f0, damping constant h) and the entire transfer function (the right side of formula (1)) are multiplied, and outputs the amplification factor A to the natural frequency identification unit 37.

[0056] The coefficient of determination calculation section 36 calculates a coefficient of determination between the Fourier amplitude ratio calculated by the amplitude ratio calculation section 34 and the theoretical value of the Fourier amplitude ratio calculated by the theoretical amplitude ratio calculation section 35 .

[0057] Then, the natural frequency identification unit 37 multiplies the entire transfer function (the right side of formula (1)) by the amplification factor A, and then, based on the fitting process result of the theoretical formula (theoretical solution) to the transfer function, finds f(t) when the coefficient of determination is the best (largest) in all divided frequency bands, and identifies it as the natural frequency.

[0058] (Operation of the natural frequency identification device) Next, the operation of the natural frequency identifying device 10 according to the present embodiment will be described with reference to the flowcharts of Fig. 2 and Fig. 4. Fig. 2 is a flowchart for explaining the outline of the operation of the natural frequency identifying device 10, and Fig. 4 is a flowchart for explaining each process in Fig. 2 in more detail.

[0059] When the operation of the natural frequency identifying device 10 is started, first, in step S201, the frequency band setting unit 30 sets a plurality of divided frequency bands ω k ~ω k+1(k=1, 2, . . . n). In step S202, a specific (k=1) divided frequency band ω k ~ω k+1 is selected by the control unit 20.

[0060] In step S203, the vibration center position calculation unit 31 calculates a parameter a relating to the height of the vibration center 1a of the pier 1 in the divided frequency band selected in step S202. k +b k is calculated.

[0061] In step S204, the parameter a relating to the height of the vibration center 1a calculated in step S203 is k +b k is within a reasonable range, that is, whether the vibration center 1a is significantly lower than the bottom surface or near the top edge. If the judgment is affirmative (the vibration center 1a is not significantly lower than the bottom surface or near the top edge in step S204), the process proceeds to step S205, and if the judgment is negative, the process proceeds to step S211.

[0062] In step S205, the parameter a relating to the height of the vibration center 1a calculated by the vibration center position calculation unit 31 in step S203 is k +b k Using these, the ground vibration waveform Xg(t) is calculated by the ground vibration calculation unit 33. Then, using the waveform Xa(t) of the vibration of the pier 1 measured by the sensor 11a and the waveform Xg(t) of the ground vibration, the amplitude ratio calculation unit 34 calculates the Fourier amplitude ratio of these vibrations.

[0063] In step S206, the identification frequency ω j (The initial value is j=k) is selected by the control unit 20.

[0064] In step S207, the amplification factor calculation unit 38 calculates the amplification factor A to be multiplied by the entire transfer function (the right side of the formula (1)), and outputs the calculated amplification factor A to the natural frequency identification unit 37. That is, the calculated amplification factor A is added as a fitting variable of the transfer function.

[0065] In step S208, the theoretical amplitude ratio calculation unit 35 calculates the identifying frequency ω j By substituting into equation (1), a fitting process to the theoretical value of the Fourier amplitude ratio of the vibration is performed.

[0066] In step S209, the coefficient of determination is calculated by the coefficient of determination calculation unit 36 ​​using the Fourier amplitude ratio calculated in step S205 and the theoretical value of the Fourier amplitude ratio calculated in step S208. The narrowing down of the coefficient of determination has been described above, so its description will be omitted here. Note that the narrowing down process based on the rotation center position can be performed before or after the fitting process, and other processes (for example, the narrowing down process based on the boundary of the specific value (specific value) band) are performed after the fitting process in principle.

[0067] In step S210, the specific frequency ω j is the upper end of the split frequency band, i.e., ω k+1 The control unit 20 judges whether or not the current value of ω j =ω k+1 ), the process proceeds to step S211. If the determination is negative, the process proceeds to step S212, in which the control unit 20 determines the identifying frequency ω j A predetermined increment Δω is added to the value, and the process returns to step S206.

[0068] In step S211, it is determined whether the above-mentioned process has been performed for all the divided frequency bands, i.e., ω k =ω n The control unit 20 judges whether or not ω k =ω n), the process proceeds to step S213. If the determination is negative, the process proceeds to step S214, in which the next divided frequency band is selected by the control unit 20, that is, the divided frequency band is set to ω k =ω k+1 Then, the process returns to step S203. In step S213, the natural frequency of the pier 1 is specified (identified) by the natural frequency specifying unit 37.

[0069] (Experimental Example) A natural frequency identification task was carried out on an actual bridge pier using the natural frequency identifying device 10 of this embodiment. Here, in a 1 / 3 scale bridge pier model, the sides and bottom of the ground around the pier foundation were excavated, and using data from a model experiment simulating scouring conditions, the ability to identify the natural frequency was compared between a conventional example (see Fig. 5) and an experimental example using the natural frequency identifying device of this embodiment (see Fig. 6). A sensor was attached to the top of a spread foundation type pier model simulating a railway pier, and the Fourier amplitude ratio of the microtremors was calculated. In Fig. 5, the measured value (dashed line) is smaller than the possible range of the theoretical solution, so a good fitting was not possible, but in Fig. 6, fitting was possible.

[0070] The determination of whether or not it could be identified was mainly performed using the coefficient of determination (which indicates the consistency between the transfer function and the theoretical solution, with 1.0 being the maximum), and in this experiment, it was determined that a value of 0.7 or higher was identifiable. Sensor 1 is a speed sensor, and sensor 2 is an acceleration sensor, and an experiment was carried out to verify whether or not it was possible to identify the natural frequency of sensors 1 and 2, which detect different physical quantities.

[0071] <Experiment 1> First, the change in whether or not the natural frequency can be identified during side excavation is carried out using a speed sensor and an acceleration sensor, and compared. Figure 7 shows the results of whether or not the natural frequency can be identified in a conventional example, and Figure 8 shows the results of whether or not the natural frequency can be identified in an example using the natural frequency identifying device according to the present embodiment.

[0072] In the conventional example, the identification accuracy was high for the speed sensor, but low for the acceleration sensor (see Table 1). On the other hand, in the embodiment, the identification accuracy was high for both the speed sensor and the acceleration sensor (see Table 1). Therefore, when the natural frequency identification device according to the present embodiment is used, it is possible to significantly improve the identification accuracy even when an acceleration sensor is used. Therefore, the identification accuracy is improved and a high capture rate is obtained for both micromotion sensors of different physical quantities such as the speed sensor and the acceleration sensor, which is expected to lead to an expansion of the types of sensors that can be used in the identification method. This makes it possible to reduce the cost of the sensors used. [Table 1] TIFF0007626729000003.tif31170

[0073] <Experiment 2> Next, the change in whether or not the natural frequency can be identified during bottom excavation is carried out using a speed sensor and an acceleration sensor, and compared. Note that bottom excavation differs from side excavation in that it includes conditions in which the pier foundation tilts and displaces. Figure 9 shows the results of whether or not the natural frequency can be identified in a conventional example, and Figure 10 shows the results of whether or not the natural frequency can be identified in an example using the natural frequency identifying device of this embodiment.

[0074] In the conventional example, the identification accuracy was not high for both the speed sensor and the acceleration sensor (see Table 2). On the other hand, in the embodiment, the identification accuracy was high for both the speed sensor and the acceleration sensor (see Table 2). It was found that when the natural frequency identification device according to the present invention was used, the identification accuracy was significantly improved even when an acceleration sensor was used. [Table 2] TIFF0007626729000004.tif32170

[0075] In other words, even in the early stages when displacement and inclination of the bridge pier are occurring, by using the natural frequency identification device of this embodiment, it is possible to improve the identification accuracy of both the speed sensor and the acceleration sensor. Therefore, when the natural frequency identifying device according to the present embodiment is used, it is possible to easily fit a theoretical solution to a transfer function whose spectrum amplitude ratio has become relatively small due to an external factor, whether the micro-motion sensor is a speed sensor or an acceleration sensor having a different physical quantity, thereby improving the identifying accuracy. This improves the degree of freedom of the micro-motion sensor used in implementing the natural frequency identifying method, and reduces the cost of the sensor used.

[0076] Although the embodiments of the present invention have been described in detail above with reference to the drawings, the specific configurations are not limited to these embodiments and examples, and design changes that do not deviate from the gist of the present invention are included in the present invention.

[0077] For example, in the above-mentioned embodiment of the natural frequency identification device 10, the operation of identifying the natural frequency of the bridge pier 1 has been explained, but the identification device of the present invention is capable of identifying the natural frequency of not only bridge piers but also any structure installed on the ground.

[0078] In the above-mentioned embodiment, the program for operating the natural frequency identifying device 10 is stored in the storage unit 21 and provided, but it is also possible to use an optical disk drive (not shown) or the like to connect a DVD (Digital Versatile Disc), a USB external storage device, a memory card, or the like in which the program is stored, and to read the program from the DVD or the like into the natural frequency identifying device 10 to operate it. Also, the program may be stored in a server device on the Internet, and a communication unit may be provided in the natural frequency identifying device 10 to read the program into the natural frequency identifying device 10 to operate it. Furthermore, in the above-mentioned embodiment, the natural frequency identifying device 10 is configured with a plurality of hardware elements, but it is also possible for the control unit 20 to realize the operation of some of these hardware elements by the operation of a program.

[0079] [Summary of effects] The natural frequency identifying device 10 according to the present embodiment includes a pair of sensors 11a, 11b for detecting vibrations of a structure, and a control unit 20 for receiving detection signals from the sensors 11a, 11b, and identifies the natural frequency of the structure installed on the ground. The control unit 20 a ground vibration calculation unit 33 that calculates the vibration of the ground 3 based on the vibration of the structure 1 in a predetermined frequency band detected by the pair of sensors 11a and 11b and the height of the vibration center of the structure 1 calculated by a vibration center position calculation unit 31; an amplitude ratio calculation unit 34 that calculates a ratio between the amplitude of a Fourier transform of the vibration of the structure 1 detected by the pair of sensors 11a, 11b and the amplitude of a Fourier transform of the vibration of the ground 3 calculated by a ground vibration calculation unit 33; a theoretical amplitude ratio calculation unit 35 that calculates parameters when the ratio calculated by the amplitude ratio calculation unit 34 is applied to a theoretical value of the ratio; an amplification factor calculation unit 38 that calculates a predetermined amplification factor A to be multiplied by a transfer function expressed as a ratio; a coefficient of determination calculation unit 36 ​​that calculates a coefficient of determination between the ratio calculated by the amplitude ratio calculation unit 34 and a theoretical value of the ratio; and a natural frequency identification unit that identifies the natural frequency based on the parameters calculated by the theoretical amplitude ratio calculation unit 35, the amplification factor A calculated by the amplification factor calculation unit 38, and the determination coefficient calculated by the determination coefficient calculation unit. Therefore, even when measurement data is generated that results in a transfer function that starts at less than 1 due to a decrease in the accuracy of estimating bridge pier vibration and ground vibration due to external factors such as noise, the consistency between the measurement value and the theoretical solution can be improved by forcibly amplifying the Fourier amplitude ratio (measured value), thereby improving the accuracy of identifying the natural frequency.

[0080] In the natural frequency identifying device 10 according to this embodiment, the amplification factor calculation unit 38 calculates the amplification factor A for increasing the magnification of the transfer function by adding it as a variable parameter to the theoretical solution of the transfer function. Therefore, by performing mathematical processing to magnify the entire data, the Fourier amplitude ratio (measured value) is forcibly amplified, which improves the consistency between the measured value and the theoretical solution, resulting in a better fitting. This improves the accuracy of identifying the natural frequency.

[0081] The method for identifying a natural frequency according to the present embodiment is a method for identifying a natural frequency of a structure 1 installed on the ground 3 by a natural frequency identifying device 10 including a pair of sensors 11a, 11b for detecting vibrations of the structure 1 and a control unit 20 for receiving detection signals from the sensors 11a, 11b, A ground vibration calculation unit 33 calculates the vibration of the ground 3 based on the vibration of the structure 1 in a predetermined frequency band detected by the pair of sensors 11a, 11b and the height of the vibration center of the structure 1 calculated by the vibration center position calculation unit 31; an amplitude ratio calculation unit calculates a ratio between the amplitude of the Fourier transform of the vibration of the structure 1 detected by the pair of sensors 11a, 11b and the amplitude of the Fourier transform of the vibration of the ground 3 calculated by the ground vibration calculation unit 33; A theoretical amplitude ratio calculation unit 35 calculates parameters when the ratio calculated by the amplitude ratio calculation unit 34 is applied to a theoretical value of the ratio, The amplification factor calculation unit 38 calculates a predetermined amplification factor A to be multiplied by the transfer function expressed as a ratio, A coefficient of determination calculation unit 36 ​​calculates a coefficient of determination between the ratio calculated by the amplitude ratio calculation unit 34 and a theoretical value of the ratio, The natural frequency identification unit 37 identifies the natural frequency based on the parameters f(t) and h(t) calculated by the theoretical amplitude ratio calculation unit 35, the amplification factor A calculated by the amplification factor calculation unit 38, and the determination coefficient calculated by the determination coefficient calculation unit 36. Therefore, even when measurement data is generated that results in a transfer function that starts at less than 1 due to a decrease in the accuracy of estimating bridge pier vibration and ground vibration due to external factors such as noise, the consistency between the measurement value and the theoretical solution can be improved by forcibly amplifying the Fourier amplitude ratio (measured value), thereby improving the accuracy of identifying the natural frequency. [Explanation of symbols]

[0082] 1. Bridge pier (structure) 1a Vibration center 3 Ground 4. Rivers 10 Natural frequency identification device 11a, 11b Sensor 12 Main body 20 Control section 30 Frequency band setting section 31 Vibration center position calculation section 32 Vibration center position determination section 33 Ground vibration calculation section 34 Amplitude ratio calculation section 35 Theoretical amplitude ratio calculation section 36 Coefficient of determination calculation section 37 Natural frequency identification part 38 Amplification factor calculation section

Claims

1. A natural frequency identification device that includes a pair of sensors that detect vibrations of a structure and a control unit that receives detection signals from the sensors, and that identifies the natural frequency of the structure installed on the ground, The control unit is a ground vibration calculation unit that calculates the vibration of the ground based on the vibration of the structure in a predetermined frequency band detected by the pair of sensors and the height of the vibration center of the structure calculated by a vibration center position calculation unit; an amplitude ratio calculation unit that calculates a ratio between an amplitude of a Fourier transform of the vibration of the structure detected by the pair of sensors and an amplitude of a Fourier transform of the vibration of the ground calculated by the ground vibration calculation unit; an amplification factor calculation unit that calculates a predetermined amplification factor to be multiplied by the transfer function represented by the ratio; a theoretical amplitude ratio calculation unit that calculates a natural frequency when the ratio calculated by the amplitude ratio calculation unit is multiplied by the amplification factor and the product is applied to a theoretical value of the ratio; A coefficient of determination calculation unit that calculates a coefficient of determination between the ratio calculated by the amplitude ratio calculation unit and a theoretical value of the ratio; a natural frequency specification unit that specifies the natural frequency when the coefficient of determination is the largest based on the natural frequency calculated by the theoretical amplitude ratio calculation unit and the coefficient of determination calculated by the coefficient of determination calculation unit, A natural frequency identification device characterized by the above.

2. The amplification factor calculation unit calculates an amplification factor for increasing a magnification of the transfer function by adding the amplification factor as a variable parameter to a theoretical solution of the transfer function.

2. The device for identifying natural vibration frequency according to claim 1.

3. A method for identifying a natural frequency of a structure installed on the ground by a natural frequency identifying device having a pair of sensors for detecting vibration of the structure and a control unit for receiving detection signals from the sensors, comprising: a ground vibration calculation unit that calculates the vibration of the ground based on the vibration of the structure in a predetermined frequency band detected by the pair of sensors and the height of the vibration center of the structure calculated by the vibration center position calculation unit; an amplitude ratio calculation unit calculates a ratio between an amplitude of a Fourier transform of the vibration of the structure detected by the pair of sensors and an amplitude of a Fourier transform of the vibration of the ground calculated by the ground vibration calculation unit; an amplification factor calculation unit calculates a predetermined amplification factor to be multiplied by the transfer function represented by the ratio; a theoretical amplitude ratio calculation unit calculates a natural frequency when the ratio calculated by the amplitude ratio calculation unit is multiplied by the amplification factor and applied to a theoretical value of the ratio; A coefficient of determination calculation unit calculates a coefficient of determination between the ratio calculated by the amplitude ratio calculation unit and a theoretical value of the ratio, a natural frequency specifying unit specifying the natural frequency when the coefficient of determination is largest based on the natural frequency calculated by the theoretical amplitude ratio calculating unit and the coefficient of determination calculated by the coefficient of determination calculating unit; A method for identifying a natural frequency comprising the steps of:

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