JP6531984B2 - Displacement response calculation method using acceleration recording - Google Patents

Description

  The present invention calculates a displacement response calculation method using acceleration recording, in particular, calculates a displacement response of a structure when an external force is applied using an acceleration recording obtained by a central acceleration sensor. On the law.

For maintenance of structures such as bridges, it is important to identify the displacement of members causing local stress causing damage, especially because displacement response caused by external force is the dominant factor of fatigue damage. It is necessary to grasp this displacement response. At this time, when it is going to measure displacement directly using a laser displacement meter etc., there is a constraint such as securing the installation place and fixed point, so from the acceleration recording (acceleration data) measured by the central acceleration sensor, the response to external force A method of calculating is proposed. That is, by second-order numerical integration of the acceleration record, theoretically, the displacement response is calculated.
However, the measurement error included in the acceleration record measured by the central acceleration sensor greatly affects the numerical integration result, and the boundary conditions when performing numerical integration separately from the measurement error are also included in the numerical integration result. It has been shown to have a major impact.
Therefore, the "initial velocity estimation method" is disclosed, which calculates the displacement response of the bridge using the assumption that the time average value of velocity is 0 (zero) under boundary conditions in numerical integration. (See, for example, Non-Patent Document 1).

Ki-Tae Park, 3 others, "The determination of bridge displacement using measured acceleration", Engineering Structures, Vol. 27, pp. 371-378, 2005

The “initial velocity estimation method” in the bridge disclosed in Non-Patent Document 1 assumes that the initial displacement is zero and that it can detect the moment when the vehicle enters or leaves the bridge. Relatively accurate displacement responses can be calculated only if they hold.
However, since a structure such as a bridge in service always vibrates, the initial displacement does not always become 0, and there is a problem that the boundary condition of numerical integration is not appropriate.
In addition, the moment when the vehicle enters the bridge (hereinafter referred to as “vehicle entry time”), which corresponds to the start time and end time of the time zone during which external force acts on the structure (hereinafter referred to as “forced vibration section”) Since a method for detecting the moment of departure (hereinafter referred to as "vehicle leaving time") is not disclosed, there is a problem in specifying the integration interval of numerical integration.

  The present invention solves such a problem, and it is possible to accurately calculate the displacement response of the structure when an external force is applied, using the acceleration recording measured by the central acceleration sensor. It is to provide “a displacement response calculation method” that

The displacement response calculation method using acceleration recording according to the present invention is a displacement response calculation method using acceleration recording, which calculates a displacement response of a structure when an external force is applied,
Based on the original waveform which is an acceleration record measured by the central acceleration sensor installed in the structure, the initial time that is the time when the action of the external force on the structure starts and the action of the external force on the structure end A first step of specifying an end time which is a time to be performed, and setting a time zone from the initial time to the end time as a forced vibration section;
A second step of performing Fourier transform on the original waveform to calculate an acceleration waveform in a frequency domain;
A third step of removing a low frequency band of the acceleration waveform in the frequency domain and calculating an acceleration waveform corresponding to a free vibration in the frequency domain;
The inverse Fourier transform is performed on the acceleration waveform corresponding to the free vibration in the frequency domain to calculate the acceleration waveform corresponding to the free vibration in the time domain, and the acceleration waveform corresponding to the free vibration in the time domain is the initial time Specifying an integration start time at which acceleration becomes 0 (zero) at a time before time and an integration end time at which acceleration becomes 0 (zero) at a time later than the end time With 4 steps,
The acceleration waveform corresponding to the free vibration in the time domain is first-order numerically integrated with the integration interval from the integration start time to the integration end time to calculate a velocity waveform corresponding to the free vibration in the time domain, A fifth step of specifying the velocity at the initial time and the end time as an initial velocity and an end velocity, respectively, for the velocity waveform corresponding to the free vibration of the region;
The velocity waveform corresponding to the free vibration in the time domain is first-order numerically integrated with the integration interval from the integration start time to the integration end time, and the displacement waveform corresponding to the free vibration in the time domain is calculated. A sixth step of identifying displacements at the initial time and the end time as the initial displacement and the end displacement, respectively, for a displacement waveform corresponding to a free vibration of the region;
A seventh step of calculating a velocity waveform of a section including a forced vibration section by first-order numerical integration of the original waveform as an integral section from the initial time to the terminal time;
Among the velocity waveforms in the section including the forced vibration section, the drift component is subtracted from the velocity waveform in the forced vibration section, and the velocity at the initial time and the end time of the velocity waveform in the forced vibration section is respectively the initial velocity and the velocity. An eighth step of calculating a corrected velocity waveform of a section including a forced vibration section by performing correction so as to obtain an end velocity;
A ninth step of calculating a displacement waveform of a section including a forced vibration section by first-order numerical integration of the corrected velocity waveform of the section including the forced vibration section, with the interval from the initial time to the end time as an integral section;
Of the displacement waveform of the section including the forced vibration section, the drift component is subtracted from the displacement waveform of the forced vibration section, and the displacement at the initial time and the end time of the displacement waveform of the forced vibration section is respectively the initial displacement and the displacement correcting the so end-stage displacement, displacement response calculating method using the acceleration record and having a tenth step of calculating a correction displacement waveform of the forced vibration region.

In the displacement response calculation method using the acceleration recording according to the present invention, after the fourth step, instead of the fifth step and the sixth step,
21. A 21st step of integrating an acceleration waveform corresponding to free vibration in the frequency domain as an integration section from the integration start time to the integration end time to calculate a velocity waveform corresponding to free vibration in the frequency domain;
A speed step of integrating a velocity waveform corresponding to free vibration in the frequency domain as an integral section from the integration start time to the integration end time to calculate a displacement waveform corresponding to free vibration in the frequency domain;
The inverse Fourier transform is performed on the velocity waveform corresponding to the free vibration in the frequency domain, the velocity waveform corresponding to the free vibration in the time domain is calculated, and the velocity waveform corresponding to the free vibration in the time domain is the initial time And 23) specifying the velocity at the end time as an initial velocity and an end velocity, respectively.
The inverse Fourier transform is performed on the displacement waveform corresponding to the free vibration in the frequency domain, and the displacement waveform corresponding to the free vibration in the time domain is calculated, and the displacement waveform corresponding to the free vibration in the time domain is the initial time And 24th step for identifying the displacement at the end time as the initial displacement and the end displacement, respectively.
After the twenty-fourth step, the seventh to tenth steps are sequentially performed.

  The displacement response calculation method using the acceleration recording according to the present invention is characterized in that an acceleration waveform in the free vibration is obtained by removing the low frequency band from the acceleration recording.

Further, in the displacement response calculation method using the acceleration recording according to the present invention, after the first step, the second step to the sixth step are substituted,
Calculating an acceleration waveform corresponding to a free vibration by filtering the original waveform with a filter for removing a low frequency band;
The first-order numerical integration is performed corresponding to the acceleration waveform corresponding to the free vibration, the velocity waveform corresponding to the free vibration is calculated, and the velocity waveform at the initial time and the end time is calculated for the velocity waveform corresponding to the free vibration. A thirty-second step of identifying the initial velocity and the terminal velocity respectively;
The displacement waveform corresponding to the free vibration is calculated by first-order numerical integration of the velocity waveform corresponding to the free vibration, and the displacement at each of the initial time and the terminal time is calculated for the displacement waveform corresponding to the free vibration. And 33rd step identified as initial displacement and end displacement,
After the thirty-third step, the seventh to tenth steps are sequentially performed.

In the displacement response calculation method using the acceleration recording according to the present invention, in the 31st step, an integration start time which is a time when an acceleration becomes 0 (zero) at a time before the initial time, and the end time Identify the integration end time which is the time when the acceleration becomes 0 (zero) at a time later than the time,
The first-order numerical integration in the thirty-second step and the thirty-third step is characterized in that an interval from the integration start time to the integration end time is an integration interval.

  Further, the displacement response calculation method using the acceleration recording according to the present invention is characterized in that the initial time and the end time are respectively set to times at which the acceleration in the acceleration recording changes.

  Furthermore, in the displacement response calculation method using the acceleration recording according to the present invention, the central acceleration sensor specifies a central acceleration sensor that measures an acceleration recording for calculating the displacement waveform, and specifies the initial time and the end time. And a central acceleration sensor for measuring an acceleration record.

The displacement response calculation method using the acceleration recording according to the present invention specifies the forced vibration section based on the acceleration recording (original waveform), and an acceleration corresponding to the free vibration calculated based on the acceleration recording (original waveform). Based on the velocity boundary condition and the displacement boundary condition, and correcting the velocity waveform of the section including the forced vibration segment calculated from the original waveform to a corrected velocity waveform satisfying the velocity boundary condition; The displacement waveform of the section including the forced vibration section calculated from the corrected velocity waveform is corrected to a corrected displacement waveform satisfying the boundary of the displacement.
Therefore, in the structure to be measured, the displacement response of the part can be known only by installing the central acceleration sensor in the part where the displacement response is desired to be known. That is, since the installation of the displacement sensor and the strain gauge is unnecessary, the measurement is simplified and the restriction of the structure to be measured is alleviated.
Also, since the integration interval when calculating the velocity waveform and displacement waveform from the acceleration waveform is from the integration disclosure time when the acceleration corresponding to the free vibration is 0 (zero) to the integration end time, the integration accuracy is high. .
The corrected displacement waveform in the forced vibration section substantially includes a displacement waveform in free vibration, and is a displacement waveform close to an actual state. That is, since the displacement response due to the external force can be grasped with high accuracy, the estimation accuracy of the local stress due to the external force is improved, which contributes to the improvement of the accuracy of the maintenance information for the structure and the reliability for the structure.

It is a block diagram explaining the displacement response calculation device for enforcing the displacement response calculation method using acceleration recording concerning Embodiment 1 of the present invention. It is for demonstrating the displacement response calculation method using the acceleration recording which concerns on Embodiment 1 of this invention, Comprising: It is a displacement recording which shows the signal which the contact-type displacement meter detected. An acceleration recording indicating a high frequency component (25 Hz or more) of a signal (original waveform) detected by a central acceleration sensor, for explaining a displacement response calculation method using the acceleration recording according to the first embodiment of the present invention. It is. It is for describing the displacement response calculation method using the acceleration recording which concerns on Embodiment 1 of this invention, Comprising: It is an acceleration recording which shows the signal which the central acceleration sensor detected. It is for demonstrating the displacement response calculation method using the acceleration recording which concerns on Embodiment 1 of this invention, Comprising: It is an example of the displacement recording which shows the signal which the laser displacement meter detected. It is for demonstrating the displacement response calculation method using the acceleration recording which concerns on Embodiment 1 of this invention, Comprising: It is an example of the acceleration spectrum obtained by carrying out the second-order differentiation of displacement recording 12 seconds in several bridges. . It is a flowchart explaining the displacement response calculation method using the acceleration recording which concerns on Embodiment 1 of this invention. FIG. 8 is a correlation diagram showing the relationship between measurement records and calculation results for supplementarily explaining the flowchart shown in FIG. 7; It is an acceleration recording which shows the original waveform for supplementary explanation of the flowchart shown by FIG. It is an acceleration waveform in the frequency domain for supplementarily explaining the flowchart shown by FIG. It is an acceleration waveform corresponding to the free vibration in the frequency domain for supplementarily explaining the flowchart shown by FIG. It is an acceleration waveform corresponding to the free vibration in the time domain for supplementarily explaining the flowchart shown by FIG. It is a velocity waveform corresponding to the free vibration in the time domain for supplementarily explaining the flowchart shown by FIG. It is a displacement waveform corresponding to the free vibration in the time domain for supplementarily explaining the flowchart shown by FIG. It is a velocity waveform of the area including the forced oscillation area for supplementarily explaining the flowchart shown by FIG. FIG. 8 is a corrected velocity waveform of a section including a forced vibration section that satisfies a boundary condition for supplementarily describing the flowchart shown in FIG. 7. It is a displacement waveform of the area containing the forced oscillation area for supplementarily explaining the flowchart shown by FIG. It is a correction | amendment displacement waveform of the area including the forced oscillation area which satisfy | fills the boundary conditions for supplementarily explaining the flowchart shown by FIG. It is an Example explaining the displacement response calculation method using the acceleration recording which concerns on Embodiment 1 of this invention, Comprising: The displacement response calculation result (corrected displacement waveform) obtained using the original waveform by central acceleration sensor A It is. It is an Example explaining the displacement response calculation method using the acceleration recording which concerns on Embodiment 1 of this invention, Comprising: The displacement response calculation result (corrected displacement waveform) obtained using the original waveform by the central acceleration sensor B It is. It is an Example explaining the displacement response calculation method using the acceleration recording which concerns on Embodiment 1 of this invention, Comprising: The displacement response calculation result (corrected displacement waveform) obtained using the original waveform by the central acceleration sensor C It is. It is an Example explaining the displacement response calculation method using the acceleration recording which concerns on Embodiment 1 of this invention, Comprising: The displacement response calculation result (corrected displacement waveform) obtained using the original waveform by the central acceleration sensor D It is. It is a flowchart explaining the displacement response calculation method using the acceleration recording which concerns on Embodiment 2 of this invention. FIG. 24 is a relationship diagram showing a relationship between measurement records and calculation results for supplementarily explaining the flowchart shown in FIG. 23; It is a velocity waveform corresponding to the free vibration in the frequency domain for supplementarily explaining the flowchart shown in FIG. It is a displacement waveform corresponding to the free vibration in the frequency domain for supplementarily explaining the flowchart shown by FIG. It is a flowchart explaining the displacement response calculation method (Hereinafter, "the free vibration assumption method 3" is called) using the acceleration recording which concerns on Embodiment 3 of this invention. FIG. 28 is a relationship diagram showing a relationship between measurement records and calculation results for supplementarily explaining the flowchart shown in FIG. 27.

First Embodiment
Next, a first embodiment according to the present invention will be specifically described with reference to the drawings, taking a bridge as an example of a structure. The following drawings are schematically drawn, and the present invention is not limited to the illustrated embodiment, and the order of executing the steps shown in the flowchart can be changed as appropriate. Furthermore, it may be a structure other than a bridge.

(Displacement response calculation device)
FIG. 1 is a block diagram for explaining a displacement response calculation device for implementing a displacement response calculation method using acceleration recording according to a first embodiment of the present invention.
In FIG. 1, a displacement response calculation apparatus 100 for implementing a displacement response calculation method using acceleration recording (hereinafter referred to as “free vibration method 1”) is a center installed on a bridge. An acceleration sensor 10 and a signal detected by the central acceleration sensor 10 (hereinafter referred to as "original waveform") are input, and a data recorder 20 for recording the original waveform, and an original waveform (A / D conversion) recorded in the data recorder 20 And a display unit 40 for displaying the calculation result of the calculation unit 30. The calculation unit 30 is the same as the CPU.

Although the central acceleration sensor 10 is a MEMS (Micro Electro Mechanical Systems) central acceleration sensor and is installed on the lower flange of the main girder at the center of the bridge axis (not shown), the present invention is limited to the MEMS It may be any central acceleration sensor, and the installation location may be any position where the user wishes to grasp the displacement response due to external force. Aside from the purpose of grasping the displacement response, a central acceleration sensor for vehicle detection may be installed, for example, on the bridge end vertical stiffener.
In addition, the bridge is not limited to the girder bridge structure, and may be a concrete structure.
Furthermore, the data recorder 20, the arithmetic unit (CPU) 30 and the display unit 40 do not need to be devices dedicated to the displacement response calculation device 100, and have versatility, respectively, and when performing the free vibration assumption method The displacement response calculation device 100 may be configured only in the above. Moreover, the transmission point of the signal (information) between each apparatus is not limited.

(Vehicle detection)
More than 70% of the road bridges in the country are girder bridges, with girder bridges measuring 30m to 40m in length. A central acceleration sensor is installed on the stiffener at the end of the bridge shaft of such a general girder bridge, and acceleration recording is obtained. Furthermore, a contact-type displacement gauge was installed on the lower flange of the central part of the bridge shaft, and a displacement record was obtained.
FIGS. 2 and 3 are for explaining the displacement response calculation method using the acceleration recording according to the first embodiment of the present invention, and FIG. 2 is below the center of the bridge shaft of a general girder bridge. A displacement record showing the signal detected by the contact type displacement gage installed on the flange, Fig. 3 is a signal (original waveform) detected by the central acceleration sensor installed on the stiffener at the end of the bridge shaft of a general girder bridge Acceleration recording showing a high frequency component (25 Hz or more) of
From FIG. 3, in 1013.17 [seconds] (shown as Ta), the change of acceleration occurs for the first time, and the approach of the vehicle is confirmed. A similar change in acceleration is then measured twice at intervals. In addition, after the acceleration changes twice at intervals, the change of the acceleration at 1015.82 [seconds] (indicated by Tb) is finally confirmed, and the change of the acceleration is not measured, so the departure of the vehicle is confirmed. Be done. The change in acceleration at time (corresponding to the initial time, hereinafter referred to as “vehicle entry time”) Ta and time (corresponding to the end time, hereinafter referred to as “vehicle exit time Tb”) Tb This occurs when passing directly above the vertical stiffener, and corresponds to the start time and end time of the displacement (deflection of the beam) in the detection result of the contact type displacement gauge shown in FIG.
Therefore, in the present invention, vehicle detection is performed by using a change in acceleration (a forced vibration section is specified).

(Frequency due to external force)
4 to 6 are for explaining the displacement response calculation method using the acceleration recording according to the first embodiment of the present invention, and FIG. 4 is a lower flange of a central bridge axis of a general girder bridge. An example of an acceleration record showing the signal (original waveform) detected by the central acceleration sensor installed in the center. Figure 5 shows the signal detected by a laser displacement meter installed on the lower flange of the central bridge axis of a general girder bridge. 6 shows an example of an acceleration spectrum obtained by second-order differentiation of 12 seconds of displacement records detected by a laser displacement meter installed at the lower flange of the central part of the bridge axis of a plurality of general girder bridges It is.
The deflection waveform by the vehicle is confirmed from the displacement recording shown in FIG. 5. The response waveform has a response time of about 2.0 seconds and a frequency of about 0.5 Hz. Also, from the acceleration spectrum shown in FIG. 6, the dominant frequency due to the external force can be confirmed in the vicinity of 0.4 Hz to 0.8 Hz.
Therefore, in the present invention, the vibration of the “low frequency band” of 1.0 Hz or less is the response vibration (forced vibration) by the external force. In the acceleration spectrum shown in FIG. 6, the dominant frequency in the vicinity of 2.0 Hz to 4.0 Hz is the natural frequency of the bridge, and the like.
The low frequency band is set to 1.0 Hz or less when the structure is a bridge, and the low frequency band is different for each structure.

(Free vibration assumption method 1)
FIGS. 7 to 19 illustrate the displacement response calculation method (free vibration assumption method 1) using the acceleration recording according to the first embodiment of the present invention, and FIG. 7 is a flowchart, and FIG. 9 is an acceleration record showing the original waveform, FIG. 10 is an acceleration waveform in the frequency domain, and FIG. 11 is a free vibration in the frequency domain. Fig. 12 is an acceleration waveform corresponding to free vibration in the time domain, Fig. 13 is a velocity waveform corresponding to free vibration in the time domain, Fig. 14 is a displacement waveform corresponding to free vibration in the time domain, 16 is the velocity waveform of the section including the forced vibration section, FIG. 16 is the corrected velocity waveform of the section including the forced vibration section satisfying the boundary condition, FIG. 17 is the displacement waveform of the section including the forced vibration section, FIG. 18 is a corrected displacement waveform of a section including a forced vibration section which satisfies the boundary condition.

  In Figs. 7 and 8, the method of assuming free vibration No. 1 focuses on the fact that the bridge vibrates freely before entering the vehicle and after leaving the vehicle. (The same as in the vibration of That is, a first half step of specifying initial and final conditions (velocity and displacement of each of the vehicle entering time and leaving time of the vehicle will be collectively referred to as “boundary condition” hereinafter) of velocity and displacement in the forced vibration section And the latter half step of calculating the corrected displacement waveform from the original waveform so as to satisfy the boundary condition. Hereinafter, each step (hereinafter, abbreviated as “S”) will be described.

(S1: Identification of forced vibration section)
First, "vehicle detection" is performed using acceleration recording (hereinafter referred to as "original waveform") detected by the central acceleration sensor 10 (S1, see FIG. 3). That is, the vehicle approach time Ta and the vehicle exit time Tb of the vehicle are specified from the change of the acceleration, and the time from the vehicle approach time Ta to the vehicle exit time Tb is taken as a "forced vibration section". Therefore, the vehicle entry time Ta is the same as the start time (corresponding to the initial time) of the forced vibration section, and the vehicle exit time Tb is the same as the finish time (corresponding to the end time) of the forced vibration section. In addition, the area (Time to vehicle approach time Ta and time from vehicle exit time Tb) except this becomes a "free vibration area". (See Figure 9).

(S2, S3: Calculation of acceleration in frequency domain)
Next, Fourier transformation is performed on the original waveform (see FIG. 9) to calculate an acceleration waveform in the frequency domain (S2, see FIG. 10).
Then, in order to remove the influence of the response to the external force, the low frequency band (1.0 Hz or less) and the direct current component (gravity component) are removed from the acceleration in the frequency domain, and the acceleration waveform corresponding to the free vibration in the frequency domain is calculated S3, see FIG. 11).

(S4: Specify integration start time and integration end time)
Next, the inverse Fourier transform is performed on the acceleration waveform (see FIG. 11) corresponding to the free vibration in the frequency domain to calculate the acceleration waveform corresponding to the free vibration in the time domain (S5, see FIG. 12). Therefore, a time (hereinafter referred to as “integral start time”) T0 at which the acceleration becomes 0 (zero) at a time before the vehicle entry time Ta is specified. Further, a time (hereinafter referred to as “integral end time”) T1 at which the acceleration becomes 0 (zero) at a time after the vehicle leaving time Tb is specified.

(S5, S6: Identification of boundary conditions)
Next, an acceleration waveform (see FIG. 12) corresponding to the free vibration in the time domain is first-order numerically integrated to calculate a velocity waveform corresponding to the free vibration in the time domain (S5, see FIG. 13). Therefore, as the boundary condition of the velocity, the velocity of the vehicle entering time Ta and the velocity of the vehicle leaving time Tb in the velocity waveform corresponding to the calculated free vibration are specified, and are respectively defined as “initial velocity Va” and “end velocity Vb”.
Further, the velocity waveform corresponding to the free vibration in the time domain is subjected to first-order numerical integration, and a displacement waveform corresponding to the free vibration in the time domain is calculated (S6, see FIG. 14). Therefore, as the boundary conditions of displacement, the displacement of the vehicle approach time Ta and the displacement of the vehicle exit time Tb in the calculated displacement waveform are specified, and are respectively referred to as “initial displacement Ua” and “end stage displacement Ub”.
At this time, since the section of the first-order numerical integration is from the integration start time T0 to the integration end time T1, the calculation accuracy is high. That is, if first-order numerical integration is performed in an integration interval defined by a time when acceleration is not 0 (zero), data including an error is integrated, and accuracy is lost.
At this time, instead of one integral section from integration start time T0 to integration end time T1, a section from integration start time T0 to vehicle intrusion time Ta and a section from vehicle exit time Tb to integration end time T1 It may be two integration intervals.
The present invention does not limit the integration interval to the interval from integration start time T0 to integration end time T1, but from a predetermined time before vehicle intrusion time Ta to a predetermined time after vehicle exit time Tb. It may be

(S7, S8: Calculation of velocity of forced vibration section)
Next, first-order numerical integration is performed corresponding to the original waveform (acceleration recording, see FIG. 9) to calculate the velocity waveform of the section including the forced vibration section (S7, see FIG. 15). At this time, the section of the first floor numerical integration is a section from the vehicle entry time Ta to the vehicle exit time Tb, and although the speed at the vehicle entry time Ta is calculated as the initial velocity Va, it is affected by noise etc. The velocity at time Tb does not reach the terminal velocity Vb. That is, when the velocity waveform of the forced vibration segment calculated so as to be sandwiched by the velocity waveform of the free vibration segment (see FIG. 13) is drawn, the velocity waveform includes “drift component C” which is a linear component (FIG. 15). reference).
Therefore, the drift component C is subtracted from the calculated velocity waveform (see FIG. 15) to calculate a corrected velocity waveform of a section including a forced vibration section that satisfies the velocity boundary condition (see S8 and FIG. 16).

(S9, S10: Calculation of displacement of forced vibration section)
Next, first-order numerical integration is performed corresponding to the corrected velocity waveform (FIG. 16) of the section including the forced vibration section that satisfies the velocity boundary condition, and the displacement waveform of the section including the forced vibration section is calculated (S9, FIG. 17). At this time, although the section of the first floor numerical integration is a section from the vehicle entry time Ta to the vehicle exit time Tb, the displacement at the vehicle entry time Ta is calculated as the initial displacement Ua, but it is affected by noise etc. The displacement at time Tb does not become the terminal displacement Ub.
That is, when the displacement waveform of the forced vibration section calculated so as to be sandwiched by the displacement waveform of the free vibration section (see FIG. 14) is drawn, the displacement waveform includes “drift component D” which is a linear component (FIG. 17). reference).
Finally, the drift component D is subtracted from the calculated displacement waveform (see FIG. 17) to calculate a displacement waveform (corrected displacement waveform) of the forced vibration section that satisfies the boundary condition of displacement (S10, see FIG. 18).

In FIG. 13, the reason why the forced vibration section (time from vehicle entry time Ta to vehicle exit time Tb) is drawn by a dotted line is that only the free vibration component of the velocity in the forced vibration section is assumed. . Further, in FIG. 14, the reason why the forced vibration section (time from vehicle entry time Ta to vehicle exit time Tb) is drawn by a dotted line is that only the free vibration component of displacement in the forced vibration section is assumed. . The dotted lines in FIGS. 13 and 14 are drawn when the section of the numerical integration is a section from integration start time T0 to vehicle intrusion time Ta and a section from vehicle exit time Tb to integration end time T1. It will not be.
The velocity waveforms in the free vibration section in FIGS. 13, 15 and 16 are the same, and the displacement waveforms in the free vibration section in FIGS. 14, 17 and 18 are the same.

(Action effect)
Since the free vibration hypothesis method 1 of the present invention includes the above-described steps, the following effects can be obtained.
(1) Since the vehicle is detected by using the change in acceleration, the grasp of the forced vibration section (time from the vehicle entry time Ta to the vehicle exit time Tb) on which the external force is acting becomes more accurate and the boundary condition The calculation of will be accurate.
(2) With regard to the acceleration waveform in the frequency domain calculated by Fourier transforming the original waveform, the low frequency band and the DC component are removed to calculate "acceleration corresponding to free vibration", and for the acceleration corresponding to such free vibration Inverse Fourier transform is performed to calculate “acceleration corresponding to free vibration in the time domain”, and the integration start time and integration end time at which the acceleration is 0 (zero) are specified. And since the section from the specified integration start time to the integration end time is made the section of the first-order numerical integration, the velocity waveform and displacement waveform corresponding to the free vibration can be accurately calculated, and furthermore, based on these Since the velocity and displacement boundary conditions are identified, accurate boundary conditions can be obtained. Therefore, while calculating the displacement response in the time during which the external force is acting (forced vibration section), attention is paid to the free vibration in which the external force is not acting, and the low frequency band causing the integration error is removed. Therefore, the integration error that would have occurred if the low frequency band were included is eliminated.
(3) The velocity waveform obtained by first-order numerical integration of the original waveform in the section including the forced vibration section is corrected to satisfy the boundary condition, and further, the first-order numerical integration of the corrected velocity waveform is performed The obtained displacement waveform is corrected so as to satisfy the boundary condition, and the corrected displacement waveform is calculated, so that a highly accurate displacement waveform (corrected displacement waveform) can be obtained.

(Example)
Next, a laser displacement meter and four types of MEMS (Micro Electro Mechanical Systems) central acceleration sensors A, B, C, D (hereinafter referred to as “central It is called “acceleration sensor A, B, C, D”. See Table 1), and vehicle detection (vehicle passage using the acceleration record (original waveform) measured by central acceleration sensors A, B, C, D) The time) was obtained, and the displacement response according to the "free vibration assumption method 1" of the present invention was determined.
That is, the central acceleration sensors A, B, C, and D are installed in an L-shaped steel jig, and the steel jig is fixed to the G2 girder central lower flange. At this time, noting that the horizontal acceleration of the central acceleration sensors A, B, C, and D is the gravity direction (not shown), attention is paid to the fact that the sensitivity differs depending on the direction.
Also, for comparison, the displacement response is determined by the “initial velocity estimation method” disclosed in Non-Patent Document 1, and a laser displacement meter target is installed at the same position as the central acceleration sensors A, B, C, D. The vertical displacement is measured at a sampling frequency of 500 Hz.

(Noise level of central acceleration sensor)
Table 1 shows the specifications of the four types of central acceleration sensors A, B, C, D by the manufacturer.
Also, the noise level is grasped by actually performing the "stationary test" under the same conditions. In the stationary test, the central acceleration sensors A, B, C, and D are fixed to an L-shaped steel jig placed on the floor and measured for 100 seconds, as in the case of installation on an actual bridge. did. At this time, by detecting a signal that should not be detected in the completely stationary state, noise as a central acceleration sensor system including external factors included in the stationary state and A / D conversion performance, Consider the noise level of each central acceleration sensor.

Then, the acceleration data obtained by the stationary test is subjected to Fourier transformation, and the power spectral density (μG / √Hz) representing the power value per unit frequency width is taken along the vertical axis so that the Fourier transformation result does not depend on the frequency resolution. (Not shown).
At this time, in the central acceleration sensors A, C, and D, the value of the power spectral density at a frequency of 1.0 Hz was substantially the same as the value (specification value) of the noise density in Table 1.
Also, in the low frequency band of 5.0 Hz or less, the noise levels of the central acceleration sensors A, B, C, D differ greatly, and the noise levels of the central acceleration sensor B are lower than those of the central acceleration sensors A, C, D , Was about 1/20 or less.
The reason why the noise density of the central acceleration sensor B shows a value larger than the noise density value (specification value) in Table 1 is considered to be because of the constant micromotion of the place where the measurement was performed.

19 to 22 show an embodiment for explaining the displacement response calculation method (free vibration assumption method 1) using the acceleration recording according to the first embodiment of the present invention, and FIG. The displacement response calculation result (corrected displacement waveform) obtained using the original waveform, FIG. 20 is the displacement response calculation result obtained using the original waveform by the central acceleration sensor B (corrected displacement waveform), FIG. The displacement response calculation result (corrected displacement waveform) obtained using the original waveform by the acceleration sensor C, FIG. 22 shows the displacement response calculation result (corrected displacement waveform) obtained using the original waveform by the central acceleration sensor D is there.
In FIGS. 19 to 22, for comparison, the vehicle passing time (same as the forced vibration section) obtained using the original waveform by the central acceleration sensors A, B, C, D is regarded as an integral section, The displacement response calculation result obtained by the "initial velocity estimation method" disclosed by the nonpatent literature 1 and the measurement result of the displacement which the laser displacement meter measured are shown.

  In FIG. 19, the displacement response result (shown by a broken line) calculated by the free vibration assumption method calculated using the original waveform measured by the central acceleration sensor A is the displacement response result calculated by the initial velocity assumption method ( The measurement results of the laser displacement meter (indicated by a solid line) are closer than those indicated by a dotted line). That is, it is shown that the effect of the measurement error is corrected by using the free vibration assumption method than in the case of using the initial velocity assumption method (this will be discussed later (the effect of the measurement error)).

In FIG. 20, a corrected displacement waveform (indicated by a broken line) calculated by the free vibration assumption method calculated using the original waveform measured by the central acceleration sensor B and a displacement response result calculated by the initial velocity assumption method (indicated by a dotted line) There is no big difference between the two), and they almost overlap the measurement results (shown by solid lines) of the laser displacement meter.
This is because the central acceleration sensor B was found to have a low noise level (in particular, a low noise level in a low frequency band of 5.0 Hz or less) by a stationary test. In addition to the fact that the time is the same and the initial displacement at the time of measurement is close to 0 (zero) and the measurement error is small, accurate values can be calculated without causing a large difference in the displacement response results by each method. It shows that it will be.

In FIGS. 21 and 22, a corrected displacement waveform (indicated by a broken line) calculated by the free vibration assumption method calculated using the original waveform measured by the central acceleration sensors C and D and a displacement response calculated by the initial velocity assumption method All the results (shown by dotted lines) are far from the measurement results (shown by solid lines) of the laser displacement meter. That is, the central acceleration sensors C and D have been found to have high noise levels also from the results of stationary tests, and each original waveform contains more components of the low frequency band.
This implies that it is necessary to use a central acceleration sensor with a relatively low noise level, even when using the free vibration assumption method (of course, also using the initial velocity estimation method).

(Influence of measurement error)
Next, errors due to measurement errors in both the free vibration hypothesis method 1 of the present invention and the initial velocity estimation method disclosed in Non-Patent Document 1 will be examined.
Now, measurement for T seconds is performed at a sampling rate fs [Hz] (measurement interval dt = 1 / fs [seconds]), and it is assumed that acceleration is measured at a measurement point of n = T · fs. Then, the acceleration ai measured at the i-th measurement point is obtained by adding the measurement error Ei of the acceleration at the i-th measurement point to the true acceleration Ai at the i-th measurement point (ai = Ai + Ei , I = 1, 2, 3 ... n). The measurement error Ei is assumed to be random noise generated according to a normal distribution of the standard deviation σ.
Then, with respect to the acceleration ai measured at the i-th measurement point, second-order numerical integration is performed according to the rectangular law so as to satisfy the boundary conditions (initial conditions and terminal conditions) by the initial velocity estimation method or free vibration hypothesis method 1 And the displacement formula by each method is obtained. At this time, the calculation results include an error originating from noise contained in the acceleration, an error originating from the assumed boundary conditions, and an integration error generated at the time of numerical integration, but the integration error generated at the time of numerical integration is considered The numerical integration error is not taken into consideration, as this is not the purpose here.

And if the time from the vehicle entering and leaving the bridge is T seconds, the displacement will be maximum when the vehicle is at the center of the bridge (at T / 2 seconds), so measure at this time The error is also considered to be the largest.
Then, when the displacement formula obtained by each method is rewritten as the sum of independent variables and the variance of the error is determined, the variance of the error in the initial velocity estimation method is proportional to “T ³ / (192 · fs)”. An equation is obtained in which the variance of the error in the free vibration assumption method 1 is proportional to "T ³ / (48 · fs)" (description of the derivation process of the equation is omitted).
That is, since the error is the square root of the variance of the error, it becomes clear that the error in the initial velocity estimation method 1 becomes 1/2 (= √ (48/192)) of the error in the free vibration hypothesis method .

  Then, as compared with the initial velocity estimation method disclosed in Non-Patent Document 1, the free oscillation assumption method 1 of the present invention is more effective for the integration interval (forced vibration interval) and the boundary condition of numerical integration as described above. In addition to being accurate, the effects of measurement errors of the central acceleration sensor as discussed here can be said to be a better approach that is less susceptible.

Second Embodiment
Next, the displacement response calculation method using the acceleration recording according to the second embodiment of the present invention will be specifically described by taking a bridge as an example of a structure and referring to the drawings.
FIGS. 23 to 26 illustrate a displacement response calculation method using acceleration recording according to a second embodiment of the present invention (hereinafter referred to as “free vibration method 2”). FIG. 23 is a flowchart, FIG. 24 is a relationship diagram showing the relationship between measurement records and calculation results for supplementarily explaining the flowchart shown in FIG. 23, FIG. 25 is a velocity waveform corresponding to free vibration in the frequency domain, Reference numeral 26 denotes a displacement waveform corresponding to free vibration in the frequency domain.
The same reference numerals and reference numerals are given to steps and drawings having the same contents as the first embodiment (the free vibration assumption method 1), and the description will be partially omitted.

(S1: Identification of forced vibration section)
First, "vehicle detection" is performed using the original waveform detected by the central acceleration sensor 10 (S1, see FIG. 3). That is, the vehicle approach time Ta and the vehicle exit time Tb of the vehicle are specified from the change in acceleration, and divided into a forced vibration section and a free vibration section (see FIG. 9).

(S2, S3: Calculation of acceleration in frequency domain)
Next, Fourier transformation is performed on the original waveform (see FIG. 9) to calculate an acceleration waveform in the frequency domain (S2, see FIG. 10).
Then, the low frequency band (1.0 Hz or less) and the direct current component (gravity component) are removed, and an acceleration waveform corresponding to the free vibration in the frequency domain is calculated (S3, see FIG. 11).

(S4: Specify integration start time and integration end time)
Next, the inverse Fourier transform is performed on the acceleration waveform (see FIG. 11) corresponding to the free vibration in the frequency domain to calculate the acceleration waveform corresponding to the free vibration which is the vibration of the free vibration section in the time domain (S5, See Figure 12). Therefore, the integration start time T0 and the integration end time T1 are specified.

(S21, S22: Calculation of velocity and displacement in the frequency domain)
Next, the acceleration waveform (see FIG. 11) corresponding to the free vibration in the frequency domain is integrated to calculate the velocity waveform corresponding to the free vibration in the frequency domain (S21, see FIG. 25).
Then, the velocity waveform (see FIG. 12) corresponding to the free vibration in the frequency domain is integrated to calculate a displacement waveform corresponding to the free vibration in the frequency domain (S22, see FIG. 26).
At this time, since the section of the integration is a section from the integration start time T0 to the integration end time T1, the calculation accuracy is high. That is, if integration is performed in an integration interval defined by a time when acceleration is not 0 (zero), data including an error is integrated, and accuracy is lost.
At this time, instead of one section from the integration start time T0 to the integration end time T1, 2 of a section from the integration start time T0 to the vehicle intrusion time Ta and a section from the vehicle exit time Tb to the integration end time T1 It may be one section.
The present invention does not limit the integration interval to the interval from integration start time T0 to integration end time T1, but from a predetermined time before vehicle intrusion time Ta to a predetermined time after vehicle exit time Tb. It may be

(S23, S24: Identification of boundary conditions)
Next, inverse Fourier transform is performed on the velocity waveform (see FIG. 25) corresponding to the free vibration in the frequency domain to calculate the velocity waveform corresponding to the free vibration which is the vibration of the free vibration section in the time domain (S23, See Figure 13). Therefore, as the boundary condition of the velocity, the velocity of the entering time Ta and the velocity of the leaving time Tb in the calculated velocity waveform are specified, and are respectively defined as the “initial velocity Va” and the “end velocity Vb”.
Furthermore, the inverse Fourier transform is performed on the displacement waveform (see FIG. 26) corresponding to the free vibration in the frequency domain, and the displacement waveform corresponding to the free vibration in the time domain is calculated (S24, see FIG. 14). Therefore, as the boundary conditions of displacement, the displacement of the entering time Ta and the displacement of the leaving time Tb in the calculated displacement waveform are specified, and are respectively referred to as an “initial displacement Ua” and an “end displacement Ub”.

(S7, S8: Calculation of velocity of forced vibration section)
Next, first-order numerical integration is performed corresponding to the original waveform (acceleration recording, see FIG. 9) of the forced vibration section, and the velocity waveform of the section including the forced vibration section is calculated (S7, see FIG. 15).
Furthermore, the drift component C is subtracted from the calculated velocity waveform (see FIG. 15) to calculate a corrected velocity waveform of a section including a forced vibration section that satisfies the velocity boundary condition (see S8 and FIG. 16).

(S9, S10: Calculation of displacement of forced vibration section)
Next, first-order numerical integration is performed corresponding to the corrected velocity waveform (FIG. 16) of the section including the forced vibration section that satisfies the velocity boundary condition, and the displacement waveform of the section including the forced vibration section is calculated (S9, FIG. 17).
Finally, the drift component D is subtracted from the calculated displacement waveform (see FIG. 17) to calculate a displacement waveform (corrected displacement waveform) of the forced vibration section that satisfies the boundary condition of displacement (S10, see FIG. 18).

(Action effect)
As described above, the free vibration assumption method 2 differs in the points (S21, S22) for calculating the velocity and displacement in the frequency domain from the free vibration assumption method 1 in which the velocity and displacement are not calculated in the frequency domain. The points except for are the same as the free vibration assumption method 1.
Therefore, according to the free vibration assumption method 2, as with the effect of the free vibration assumption method 1, a highly accurate displacement waveform (corrected displacement waveform) is obtained.
Note that the calculation result by the free vibration assumption method 2 is the same as the calculation result by the free vibration assumption method 1 (it may be strictly different), so the figure showing the calculation result by the free vibration assumption method 1 12 to 18 are used.

Third Embodiment
Next, a displacement response calculation method using acceleration recording according to the third embodiment of the present invention will be specifically described with reference to the drawings, taking a bridge as an example of a structure.
FIG. 27 and FIG. 28 illustrate the displacement response calculation method using acceleration recording according to the third embodiment of the present invention (hereinafter referred to as “the free vibration assumption method 3”). FIG. 27 is a flowchart, and FIG. 28 is a relationship diagram showing the relationship between measurement records and calculation results for supplementarily explaining the flowchart shown in FIG.

In FIGS. 27 and 28, the free vibration assumption method 3 has the following steps. In the free vibration assumption method 3, as in the free vibration assumption method 1 described in the first embodiment, the first half step of specifying the boundary conditions for the velocity and displacement in forced vibration and the boundary conditions are satisfied. And the second half step of calculating the corrected displacement waveform from the original waveform.
However, in the first half step of specifying the boundary conditions in the third embodiment, although the point of filtering the original waveform is different from that of the first embodiment using the Fourier transform and the inverse Fourier transform, the steps other than this are the steps. Since the steps are the same as in the first embodiment, the same steps and drawings have the same reference numerals and reference numerals, and a part of the description will be omitted.

(S1: Identification of forced vibration section)
First, the vehicle detection time Ta and the vehicle exit time Tb are specified together with "vehicle detection" using the original waveform detected by the central acceleration sensor 10 (S21), and divided into a forced vibration section and a free vibration section (See Figure 9).

(S31: Calculation of acceleration of free vibration and identification of integration start time and integration end time)
Then, the original waveform (see FIG. 9) is filtered by a filter (highpass filter) that removes low frequency bands (passes over 1.0 Hz), and an acceleration waveform corresponding to free vibration is calculated (S31, see FIG. 12) ). Therefore, at integration start time T0 at which the acceleration becomes 0 (zero) at a time before vehicle entry time Ta (corresponding to the initial time) and at a time later than vehicle exit time Tb (corresponding to the end time) The integration end time T1 at which the acceleration becomes 0 (zero) is specified.

(S32, S33: Identification of boundary conditions)
Next, the acceleration waveform (see FIG. 9) corresponding to the free vibration is first-order numerically integrated to calculate the velocity waveform corresponding to the free vibration (S32, see FIG. 13). Therefore, the speeds at the vehicle entry time Ta and the vehicle exit time Tb are specified as the initial speed Va and the end speed Vb, respectively, as the speed boundary conditions.
Further, the velocity waveform corresponding to the free vibration is subjected to first-order numerical integration, and a displacement waveform corresponding to the free vibration is calculated (S33, see FIG. 14). Therefore, the displacement at the vehicle entry time Ta and the vehicle exit time Tb is specified as an initial displacement Ua and an end displacement Ub, respectively, as boundary conditions of displacement.
At this time, since the integration interval of the first-order numerical integration is from the integration start time T0 to the integration end time T1, the calculation accuracy is high. It should be noted that instead of one section from integration start time T0 to integration end time T1, two sections from integration start time T0 to vehicle intrusion time Ta and two sections from vehicle exit time Tb to integration end time T1 It may be a section.
The present invention does not limit the integration interval to the interval from integration start time T0 to integration end time T1, but from a predetermined time before vehicle intrusion time Ta to a predetermined time after vehicle exit time Tb. It may be

(S7, S8: Calculation of velocity of forced vibration section)
Next, first-order numerical integration is performed corresponding to the original waveform (acceleration recording, see FIG. 9) of the forced vibration section, and the velocity waveform of the section including the forced vibration section is calculated (S7, see FIG. 15).
Furthermore, the drift component C is subtracted from the calculated velocity waveform (see FIG. 15) to calculate a corrected velocity waveform of a section including a forced vibration section that satisfies the velocity boundary condition (see S8 and FIG. 16).

(S9, S10: Calculation of displacement of forced vibration section)
Next, first-order numerical integration is performed corresponding to the corrected velocity waveform (see FIG. 16) of the section including the forced vibration section satisfying the velocity boundary condition, and the displacement waveform of the section including the forced vibration section is calculated (S9, See Figure 17).
Finally, the drift component D is subtracted from the calculated displacement waveform (see FIG. 17) to calculate a displacement waveform (corrected displacement waveform) of the forced vibration section that satisfies the boundary condition of displacement (S10, see FIG. 18).

(Action effect)
As described above, the free vibration assumption method 3 executes the step of calculating the acceleration of free vibration by filtering (S31), the step of calculating the acceleration of free vibration by Fourier transform and inverse Fourier transform (S2 to S2) The free vibration hypothesis method for carrying out S4) is the same as step 1 except for the free vibration hypothesis method 1 except for this.
Therefore, since the free vibration assumption method 3 does not perform the Fourier transform and the inverse Fourier transform, the calculation is simple, and it has an operation effect that the displacement waveform (corrected displacement waveform) can be obtained quickly, and the free vibration assumption It produces the same effect as the first part of the law.
Note that the calculation result by the free vibration assumption method No. 3 is the same as the calculation result by the free vibration assumption method No. 1 (it may be strictly different), so the figure showing the calculation result by the free vibration assumption method no. 12 to 18 are used.

  The present invention has been described based on the first to third embodiments, taking a bridge as an example of a structure as an example, but these are exemplifications, and the selection of the structure and the respective components thereof It will be understood by those skilled in the art that various modifications can be made by combining the respective steps) and such modifications are also within the scope of the present invention.

  The displacement response calculation method using the acceleration recording according to the present invention can grasp the displacement response due to the external force acting on the structure with high accuracy, so the displacement response due to the external force of various structures is not limited to the bridge. It can be widely used as a method of calculating

10 central acceleration sensor 20 data recorder 30 arithmetic unit (CPU)
40 Display Unit 100 Displacement Response Calculation Device

Claims (7)

A displacement response calculation method using acceleration recording, which calculates a displacement response of a structure when an external force acts,
Based on the original waveform which is an acceleration record measured by the central acceleration sensor installed in the structure, the initial time that is the time when the action of the external force on the structure starts and the action of the external force on the structure end A first step of specifying an end time which is a time to be performed, and setting a time zone from the initial time to the end time as a forced vibration section;
A second step of performing Fourier transform on the original waveform to calculate an acceleration waveform in a frequency domain;
A third step of removing a low frequency band of the acceleration waveform in the frequency domain and calculating an acceleration waveform corresponding to a free vibration in the frequency domain;
The inverse Fourier transform is performed on the acceleration waveform corresponding to the free vibration in the frequency domain to calculate the acceleration waveform corresponding to the free vibration in the time domain, and the acceleration waveform corresponding to the free vibration in the time domain is the initial time Specifying an integration start time at which acceleration becomes 0 (zero) at a time before time and an integration end time at which acceleration becomes 0 (zero) at a time later than the end time With 4 steps,
The acceleration waveform corresponding to the free vibration in the time domain is first-order numerically integrated with the integration interval from the integration start time to the integration end time to calculate a velocity waveform corresponding to the free vibration in the time domain, A fifth step of specifying the velocity at the initial time and the end time as an initial velocity and an end velocity, respectively, for the velocity waveform corresponding to the free vibration of the region;
The velocity waveform corresponding to the free vibration in the time domain is first-order numerically integrated with the integration interval from the integration start time to the integration end time, and the displacement waveform corresponding to the free vibration in the time domain is calculated. A sixth step of identifying displacements at the initial time and the end time as the initial displacement and the end displacement, respectively, for a displacement waveform corresponding to a free vibration of the region;
A seventh step of calculating a velocity waveform of a section including a forced vibration section by first-order numerical integration of the original waveform as an integral section from the initial time to the terminal time;
Among the velocity waveforms in the section including the forced vibration section, the drift component is subtracted from the velocity waveform in the forced vibration section, and the velocity at the initial time and the end time of the velocity waveform in the forced vibration section is respectively the initial velocity and the velocity. An eighth step of calculating a corrected velocity waveform of a section including a forced vibration section by performing correction so as to obtain an end velocity;
A ninth step of calculating a displacement waveform of a section including a forced vibration section by first-order numerical integration of the corrected velocity waveform of the section including the forced vibration section, with the interval from the initial time to the end time as an integral section;
Of the displacement waveform of the section including the forced vibration section, the drift component is subtracted from the displacement waveform of the forced vibration section, and the displacement at the initial time and the end time of the displacement waveform of the forced vibration section is respectively the initial displacement and the displacement correcting the so end-stage displacement, displacement response calculating method using the acceleration record and having a tenth step of calculating a correction displacement waveform of the forced vibration region. After the fourth step, instead of the fifth step and the sixth step,
21. A 21st step of integrating an acceleration waveform corresponding to free vibration in the frequency domain as an integration section from the integration start time to the integration end time to calculate a velocity waveform corresponding to free vibration in the frequency domain;
A speed step of integrating a velocity waveform corresponding to free vibration in the frequency domain as an integral section from the integration start time to the integration end time to calculate a displacement waveform corresponding to free vibration in the frequency domain;
The inverse Fourier transform is performed on the velocity waveform corresponding to the free vibration in the frequency domain, the velocity waveform corresponding to the free vibration in the time domain is calculated, and the velocity waveform corresponding to the free vibration in the time domain is the initial time And 23) specifying the velocity at the end time as an initial velocity and an end velocity, respectively.
The inverse Fourier transform is performed on the displacement waveform corresponding to the free vibration in the frequency domain, and the displacement waveform corresponding to the free vibration in the time domain is calculated, and the displacement waveform corresponding to the free vibration in the time domain is the initial time And 24th step for identifying the displacement at the end time as the initial displacement and the end displacement, respectively.
The displacement response calculation method using acceleration recording according to claim 1, wherein the seventh step to the tenth step are sequentially executed after the twenty-fourth step.   The displacement response calculation method using acceleration recording according to claim 1, wherein an acceleration waveform in the free vibration is obtained by removing a low frequency band from the acceleration recording. After the first step, instead of the second step to the sixth step,
Calculating an acceleration waveform corresponding to a free vibration by filtering the original waveform with a filter for removing a low frequency band;
The first-order numerical integration is performed corresponding to the acceleration waveform corresponding to the free vibration, the velocity waveform corresponding to the free vibration is calculated, and the velocity waveform at the initial time and the end time is calculated for the velocity waveform corresponding to the free vibration. A thirty-second step of identifying the initial velocity and the terminal velocity respectively;
The displacement waveform corresponding to the free vibration is calculated by first-order numerical integration of the velocity waveform corresponding to the free vibration, and the displacement at each of the initial time and the terminal time is calculated for the displacement waveform corresponding to the free vibration. And 33rd step identified as initial displacement and end displacement,
The displacement response calculation method using acceleration recording according to claim 1, wherein the seventh step to the tenth step are sequentially executed after the thirty-third step. In the 31st step, an integration start time at which the acceleration becomes 0 (zero) at a time before the initial time, and a time at which the acceleration becomes 0 (zero) at a time after the end time Identify an integration end time,
5. The displacement response calculation method using acceleration recording according to claim 4, wherein the first-order numerical integration in the 32nd step and the 33rd step takes an integration interval from the integration start time to the integration end time. .   The displacement response calculation method using the acceleration recording according to any one of claims 1 to 5, wherein the initial time and the end time are respectively set to times at which the acceleration in the acceleration recording changes.   The central acceleration sensor is configured by a central acceleration sensor that measures an acceleration record for calculating the displacement waveform, and a central acceleration sensor that measures an acceleration record for identifying the initial time and the end time. The displacement response calculation method using the acceleration recording according to any one of claims 1 to 5, characterized in that

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