JP7732649B2 - Method, device, system, and program for calculating the time offset of multiple seismometers - Google Patents

Description

The present invention relates to a method, device, system, and program for calculating the time offset between multiple seismometers.

When installing seismometers such as acceleration sensors on the first and upper floors of a multi-story building and calculating building deformation from the measurement data collected during an earthquake, it is desirable to connect the seismometers on the first and upper floors via a wire and synchronize the time on both seismometers. However, connecting seismometers across floors via a wire poses challenges, including the complicated connection work, the inability to quickly adapt to changes in installation location, and wiring limitations.

On the other hand, by connecting seismometers wirelessly, the disadvantages of wired connections are eliminated, but this then creates another issue: the time on the seismometers cannot be synchronized, making it impossible to correctly calculate the deformation of each floor of the building at the same time.

Patent Document 1 proposes an analysis method that can correct for discrepancies in the time measurements of two seismometers to accurately calculate inter-story displacement. Specifically, the method uses first acceleration data in the X-axis, Y-axis, and Z-axis directions along a time history obtained from a first residential seismometer installed near the first floor or in the foundation below the floor of a wooden building to measure acceleration due to earthquake shaking, and second acceleration data in the X-axis, Y-axis, and Z-axis directions along a time history obtained from a second residential seismometer installed near the first floor ceiling or second floor of the wooden building to measure acceleration due to earthquake shaking, and calculates at least the inter-story displacement when the wooden building shakes using a predetermined analysis processing program. The method calculates a correlation coefficient between the first acceleration data in the Z-axis direction from the first residential seismometer and the second acceleration data in the Z-axis direction from the second residential seismometer, corrects for the discrepancy in the time history between the first acceleration data and the second acceleration data based on the calculation result, and then calculates the inter-story displacement.

JP 2018-100875 A

The analysis method described in Patent Document 1 calculates a correlation coefficient while gradually shifting the time of vertical acceleration waveforms measured by multiple seismometers, and determines the time shift when the correlation coefficient is at its maximum as the actual time shift. Therefore, calculating the correlation coefficient across the entire frequency band results in a high level of noise and low accuracy, which is particularly noticeable on the high-frequency side. Another issue is the need to shift the time slightly and perform calculations sequentially, resulting in a huge amount of calculation.

The present invention was made in consideration of the above-mentioned problems, and aims to provide a method, device, system, and program for calculating the time offset between multiple seismometers, which eliminates the need for sequential calculations, calculates the time offset between multiple seismometers with high accuracy, and enables the calculated time offset to be used for time offset correction.

In order to achieve the above object, one aspect of the method for calculating the time offset of a plurality of seismometers according to the present invention comprises:
A method for calculating the amount of time offset between multiple seismometers installed in a building, comprising:
Step A: calculating a transfer function based on measurement data measured by a plurality of the seismometers;
and step B of calculating the slope of the phase spectrum in a low frequency band in which the building does not resonate, and calculating the time offset amount based on the slope of the phase spectrum using the following formula (X).

According to this aspect, by calculating a transfer function based on measurement data measured by multiple seismometers, calculating the phase spectrum slope in the low-frequency band where the building does not resonate, and calculating the time offset between the multiple seismometers based on the phase spectrum slope, it is possible to calculate the time offset between the multiple seismometers with high accuracy without requiring sequential calculations. Here, "multiple seismometers" refers to, for example, when two or three or more seismometers are installed on the first floor (or foundation floor) and two or more floors above, the seismometer on the first or foundation floor that measures ground vibration input to the building, and one of the seismometers on the second or higher floors. This includes combinations such as seismometers on the first and second floors, seismometers on the first and third floors, and seismometers on the first floor and rooftop (RF) floor.

Furthermore, "low frequency bands where buildings do not resonate" refers to frequency bands where a multi-story building as a whole behaves in a translational manner, or frequency bands where the response is not amplified; for example, if all floors behave in a translational manner, the phase difference between seismometers on multiple floors will be zero.

The transfer function (phase) is a function of the ratio of response to input: response/input. For example, if measurement data from a seismometer on the first floor is used as input data related to ground vibration, and measurement data from a seismometer on an upper floor is used as response data for that floor, and taking into account that the phase difference between seismometers on multiple floors is zero as mentioned above in the low frequency band where the building does not resonate, the phase of the transfer function will be -ωΔt if there is a time lag: Δt in the waveforms (for example, sinusoidal waveforms) of the seismometers on multiple floors. In equation (X), the amount of time lag can be calculated using the phases: φ1, φ2 of any two frequencies f1, f2, and the angular frequencies ω1, ω2.

Another aspect of the method for calculating the time offset of a plurality of seismometers according to the present invention is to
In the setting of the low frequency band,
The upper limit of the low frequency band is set to f ₀ /2 in consideration of the plastic region, where f ₀ is the primary natural frequency during structural calculation of the building,
The lower limit of the low frequency band is set to 0.5 Hz.

According to this aspect, by quantitatively setting the upper and lower limits of the low frequency band, it is possible to clarify the frequency band to which formula (X) can be applied.

Here, the basis for setting the upper limit is that the inter-story deformation angle in the elastic region during a normal earthquake is generally set to about 1/200, and the inter-story deformation angle in the plastic region during a large-scale earthquake is set to about 1/100 to 1/75. Therefore, the plastic region is about half the elastic region, and therefore the upper limit for the low frequency band is set to half the primary natural frequency: _f0 .

On the other hand, the lower limit was set at 0.5 Hz based on the performance (resolution) of seismometers currently in general use. In other words, since the lower limit can vary depending on the performance of the seismometer, it was decided to set it here based on the performance of currently used general seismometers.

Furthermore, one aspect of the apparatus for calculating the time offset of a plurality of seismometers according to the present invention is
A device for calculating the amount of time offset between multiple seismometers mounted on a building, comprising:
It has a calculation department,
In the calculation unit,
Calculating a transfer function based on measurement data measured by the plurality of seismometers;
Calculating the slope of the phase spectrum in a low frequency band where the building does not resonate;
The time offset is calculated based on the gradient of the phase spectrum using the following formula (X):

According to this aspect, the calculation unit calculates a transfer function based on measurement data measured by multiple seismometers, calculates the slope of the phase spectrum in the low-frequency band where the building does not resonate, and calculates the time offset between the multiple seismometers based on the slope of the phase spectrum. This makes it possible to calculate the time offset between the multiple seismometers with high accuracy while eliminating the need for sequential calculations.

Furthermore, one aspect of the system for calculating the time offset of a plurality of seismometers according to the present invention is
The building includes a plurality of seismometers and the calculation device,
The measurement data measured by the seismometer is received by the calculation device.

In this embodiment, measurement data collected by multiple seismometers is transmitted via wireless communication or other means to a calculation device located in a related department, such as the head office or branch office of the home builder or construction company that constructed the building. The calculation device that receives the measurement data quickly calculates the time offset of the target building, corrects the time offset of the multiple seismometers (synchronizes the time) based on the calculated time offset, and then calculates the building's deformation and inter-story deformation angle with high accuracy. Here, the calculation device can receive the measurement data via wireless communication over a network, or it can receive the measurement data via a method in which a resident of the target building or a home builder employee obtains the measurement data and inputs it into the calculation device.

Furthermore, one aspect of the program according to the present invention is
A program that causes a computer constituting a calculation device for calculating the amount of time offset of multiple seismometers mounted on a building to execute the following processing:
Calculating a transfer function based on measurement data measured by the plurality of seismometers;
Calculating the slope of the phase spectrum in a low frequency band where the building does not resonate;
The time offset is calculated based on the gradient of the phase spectrum using the following formula (X):

According to this aspect, by having the computer constituting the time offset calculation device execute a predetermined process, it is possible to calculate the time offset of multiple seismometers with high accuracy while eliminating the need for sequential calculations.

As can be understood from the above explanation, the method, device, system, and program for calculating the time offset between multiple seismometers of the present invention can calculate the time offset between multiple seismometers with high accuracy without requiring sequential calculations, and the calculated time offset can be used to correct the time offset.

1 is an overall configuration diagram showing an example of a system for calculating the amount of time offset between multiple seismometers according to an embodiment; FIG. 2 is a diagram illustrating an example of a hardware configuration of a time lag calculation device according to an embodiment. FIG. 2 is a diagram illustrating an example of a functional configuration of a time lag calculation device according to an embodiment. FIG. 10 is a diagram showing the relationship between frequency and phase spectrum in the case where there is no time lag, as measured in an experiment. FIG. 10 is a diagram showing the relationship between frequency and phase spectrum in the case where there is a time lag (+0.5 s) measured in an experiment. FIG. 10 is a diagram showing the relationship between frequency and phase spectrum in the case where there is a time lag (+2.0 s) measured in an experiment. FIG. 10 is a diagram showing the relationship between frequency and phase spectrum in the case where there is a time lag (−3.0 s) as measured in an experiment. FIG. 10 is a graph showing the relationship between the phase spectrum gradient (phase gradient) and the time lag amount (time lag), which was created based on experimental results.

Below, an example of a method, calculation device, calculation system, and program for calculating the time offset of multiple seismometers according to an embodiment will be described with reference to the accompanying drawings. Note that in this specification and drawings, substantially identical components may be designated by the same reference numerals to avoid redundant explanation.

[Method, apparatus, system, and program for calculating the amount of time offset between multiple seismometers according to an embodiment]
First, an example of a method, a calculation device, a calculation system, and a program for calculating the amount of time deviation between multiple seismometers according to an embodiment will be described with reference to Figures 1 to 3. Here, Figure 1 is an overall configuration diagram showing an example of a system for calculating the amount of time deviation between multiple seismometers according to an embodiment.

The time lag calculation system 50 includes a multi-story building 10 (two stories in the illustrated example) equipped with multiple seismometers 15 on each floor, and a calculation device 40 according to an embodiment located at the home builder 30 that constructed the building 10. The seismometers 15 and calculation device 40 are connected via a network 20, and measurement data is transmitted to the calculation device 40. The calculation system may also be configured such that, without using the network 20, residents of the building 10 or a person in charge at the home builder obtains measurement data and inputs it into the calculation device 40, and this configuration is also included.

In the illustrated example, the two-story building 10 has seismometers 15A and 15B mounted on the first and second floors, respectively. The building 10 vibrates due to seismic motion E propagating through the ground G, and the resulting ground vibrations are measured by seismometer 15A on the first floor, which records the measured measurement data (acceleration data, for example, acceleration data for the X, Y, and Z axes). Meanwhile, the building vibrations (response vibrations) are measured by seismometer 15B on the second floor (upper floor), which similarly records the acceleration data. Both seismometers 15A and 15B are not time-synchronized via a wired connection, and the respective measurement data are transmitted to the calculation device 40 via network 20.

Network 20 includes public networks such as the Internet, wireless networks such as mobile phone networks, dedicated networks such as VPNs (Virtual Private Networks), LANs (Local Area Networks), etc.

Next, an example of the hardware configuration of the time lag calculation device 40 will be described with reference to Figure 2, and an example of the functional configuration of the time lag calculation device 40 will be described with reference to Figure 3.

As shown in Figure 2, the time lag calculation device 40 is composed of an information processing device (computer) such as a personal computer (PC).

The computer that constitutes the time lag calculation device 40 includes a CPU (Central Processing Unit) 41, a main memory device 42, an auxiliary memory device 43, an input/output IF (interface) 44, and a communication IF 45, all of which are interconnected via a connection bus 46. The main memory device 42 and the auxiliary memory device 43 are computer-readable recording media. Note that the above components may be provided separately, or some components may not be provided.

The CPU 41 is also called an MPU (Microprocessor) or processor, and may be a single processor or a multiprocessor. The CPU 41 is a central processing unit that controls the entire computing device 40, which is made up of a computer. The CPU 41, for example, deploys programs stored in the auxiliary storage device 43 in an executable form in the working area of the main storage device 42, and controls peripheral devices through the execution of the programs, thereby providing functions that meet specific purposes.

The main memory device 42 stores computer programs executed by the CPU 41, data processed by the CPU 41, and the like. The main memory device 42 includes, for example, flash memory, RAM (Random Access Memory), and ROM (Read Only Memory). The auxiliary memory device 43 stores various programs and data on a readable and writable recording medium, and is also called an external memory device. The auxiliary memory device 43 stores, for example, an OS (Operating System), various programs, various tables, and the like. The OS includes, for example, a communications interface program that exchanges data with external devices connected via the communications IF 45. External devices for the calculation device 40 include the seismometer 15 and other computers in related departments (various structural calculation computers), etc.

The auxiliary storage device 43 is used, for example, as a storage area that supports the main storage device 42, and stores computer programs executed by the CPU 41, data processed by the CPU 41, etc. The auxiliary storage device 43 may be a silicon disk including non-volatile semiconductor memory (flash memory, EPROM (Erasable Programmable ROM)), a hard disk drive (HDD), a solid state drive, etc. Examples of the auxiliary storage device 43 include drives for removable recording media such as CD drives, DVD drives, and BD drives, and examples of removable recording media include CDs, DVDs, BDs, USB (Universal Serial Bus) memory, and SD (Secure Digital) memory cards.

The input/output IF 44 is an interface that inputs and outputs data between devices connected to the calculation device 40. Input devices such as a keyboard, a touch panel, a mouse, or other pointing device, and a microphone are connected to the input/output IF 44. The calculation device 40 receives operational instructions from an operator who operates the input device via the input/output IF 44.

In addition, the input/output IF 44 is connected to display devices such as liquid crystal displays (LCDs) and organic electroluminescence (EL) panels, as well as output devices such as printers and speakers. The calculation device 40 displays the transfer function and the time difference between the two seismometers 15A and 15B.

The communication IF 45 is an interface with the network 20 to which the calculation device 40 is connected. The communication IF 45 transmits measurement data from the seismometer 15 to the calculation device 40 via various networks 20, including the above-mentioned public networks such as the Internet.

As shown in FIG. 3, the calculation device 40 provides various functions of at least the communication unit 402, calculation unit 404, and storage unit 406 through program execution by the CPU 41. Here, at least some of the above processing functions may be provided by a DSP (Digital Signal Processor), GPU (Graphics Processing Unit), etc. Similarly, at least some of the above processing functions may be provided by dedicated LSIs (large scale integration) such as FPGAs (Field-Programmable Gate Arrays), numerical calculation processors, image processing processors, or other digital circuits.

After an earthquake occurs, the communication unit 402 receives measurement data transmitted from each seismometer 15 for a certain period of time and stores the data in the storage unit 406 as needed.

The calculation unit 404 calculates the amount of time difference between the two seismometers 15A and 15B based on the measurement data.

Here, the building vibration (response) of building 10 measured by seismometer 15B on the second floor and the ground vibration (input) measured by seismometer 15A on the first floor can be expressed by the following equations (Y1) and (Y2), respectively.

From equations (Y1) and (Y2), the transfer function (phase) can be expressed by the following equation (Y3):

In the low frequency band where building 10 does not resonate, the entire building 10 behaves in a translational manner, and the phase difference between the two seismometers 15A and 15B is zero, so β = α. By substituting this into equation (Y3), the phase of the transfer function when there is a time lag can be expressed by the following equation (Y4).

To calculate the time offset, the phase is calculated for multiple frequency bands and a simultaneous equation is solved. That is, the phase offsets φ1 and φ2 for the two frequencies f1 and f2 can be expressed by the following equations (Z1) and (Z2).

From equations (Z1) and (Z2), the time lag Δt can be expressed by the following equation (X):

The calculation unit 404 executes step A, which calculates a transfer function based on the measurement data measured by the two seismometers 15A and 15B, and then executes step B, which calculates the slope of the phase spectrum in the low-frequency band where the building 10 does not resonate, and calculates the time lag amount using equation (X) based on the slope of the phase spectrum. The calculated time lag amount Δt is stored in the storage unit 406. This series of processes in steps A and B by the calculation unit 404 constitutes the time lag calculation method according to the embodiment.

Here, the upper limit of the low frequency band is set to _f0 /2, taking into account the plastic _region , relative to the primary natural frequency: f0 during structural calculation of the building 10, and the lower limit of the low frequency band is set to 0.5 Hz based on the performance of currently commonly used seismometers.

The calculation device 40 executes the above processing in the calculation unit 404 by installing a program that causes a computer to execute the following processing. That is, processing based on this program calculates a transfer function based on measurement data measured by seismometers 15A and 15B, calculates the slope of the phase spectrum in the low-frequency band where building 10 does not resonate, and calculates the amount of time difference between seismometers 15A and 15B using the slope of the phase spectrum using the above formula (X).

The illustrated seismometer time offset calculation device, calculation system, and calculation method eliminate the need for sequential calculations and can directly calculate the time offset of multiple seismometers 15A, 15B from, for example, the phase gradient obtained in a single calculation, making it possible to calculate the time offset easily and quickly.

Furthermore, since the time offset is calculated for low frequency bands, the impact of noise (error) is minimal, allowing the time offset to be calculated with high accuracy.

The calculation device 40 may further include a structural calculation unit (not shown), which corrects the time difference between the measurement data of the seismometers 15A and 15B based on the calculated time difference, and then calculates the deformation of the first and second floors during an earthquake based on the time-synchronized measurement data from both floors, thereby calculating the inter-story deformation angle of the building 10. The safety and degree of damage of the building 10 can be evaluated based on the calculated inter-story deformation angle, etc.

[Experiment to verify the validity of the calculation formula for time lag]
The inventors conducted an experiment to verify the validity of the above formula (X). In this experiment, based on the actual measurements of two seismometers, the relationship between frequency and phase spectrum was determined for four cases: no time lag, a time lag of +0.5 seconds, a time lag of +2 seconds, and a time lag of -3 seconds. Here, the ± time lag indicates that the seismometer on the first floor is used as the reference and that the seismometer on the second floor is delayed and has a time lag of +.

Figures 4, 5, 6, and 7 show the relationship between frequency and phase spectrum in the cases of no time lag, time lag (+0.5 s), time lag (+2.0 s), and time lag (-3.0 s), respectively, as measured in experiments. Figure 8 also shows a graph created based on the experimental results, showing the relationship between the slope of the phase spectrum (phase slope) and the amount of time lag (time lag).

Figure 4 demonstrates that in the case of no time lag, the phase spectrum slope is zero in frequency bands below 3 Hz, and that as the frequency increases, the phase spectrum becomes more randomly dispersed.

Furthermore, comparing the slope of the phase spectrum in the low frequency band (e.g., 0.5 to 1 Hz) in Figures 5 to 7 demonstrates that the slope of the phase spectrum increases as the time lag increases.

The slope of the phase spectrum for each time shift can be calculated using methods such as finding an approximate straight line, which is a statistical process, or using the median of multiple values obtained by moving average.

Summarizing the results of these experiments, the relationship between phase gradient and time lag can be expressed by the approximate straight line shown in Figure 8, which coincides with equation (X) above.

In this way, in the low-frequency band, where the influence of buildings does not need to be considered, if there is no time lag between the two seismometers, the phase slope is zero, but if there is a time lag, the phase will have a slope. By calculating this slope using a formula, it is possible to calculate the amount of time lag easily and quickly, eliminating the need for sequential calculations.

Note that other embodiments may be possible in which other components are combined with the configurations described in the above embodiments, and the present invention is in no way limited to the configurations shown here. In this regard, changes can be made without departing from the spirit of the present invention, and can be determined appropriately depending on the application form.

10: Building (two-story building)
15, 15A, 15B: Seismometer 20: Network 30: House builder 40: Calculation device (time lag calculation device)
50: Calculation system (time deviation calculation system)
402: Communication unit 404: Calculation unit 406: Storage unit G: Ground E: Earthquake motion

Claims (5)

A method for calculating the amount of time offset between multiple seismometers installed in a building, comprising:
Step A: based on measurement data measured by the plurality of seismometers, calculating a transfer function, which is the ratio of response to input when measurement data measured by the seismometer on the first floor is used as input data related to ground vibration and measurement data measured by the seismometer on an upper floor is used as response data for the upper floor ;
and step B of calculating the slope of the phase spectrum in a low frequency band in which the building does not resonate, and calculating the time offset based on the slope of the phase spectrum using the following formula (X):
In the setting of the low frequency band,
The upper limit of the low frequency band is set to f ₀ /2 in consideration of the plastic region, where f ₀ is the primary natural frequency during structural calculation of the building,
2. The method for calculating the time offset of a plurality of seismometers according to claim 1, wherein the lower limit of the low frequency band is 0.5 Hz. A device for calculating the amount of time offset between multiple seismometers mounted on a building, comprising:
It has a calculation department,
In the calculation unit,
Based on the measurement data measured by the plurality of seismometers , a transfer function is calculated, which is the ratio of the response to the input when the measurement data from the seismometer on the first floor is used as input data related to ground vibration and the measurement data from the seismometer on the upper floor is used as response data for the upper floor;
Calculating the slope of the phase spectrum in a low frequency band where the building does not resonate;
A device for calculating the amount of time deviation of a plurality of seismometers, characterized in that the device calculates the amount of time deviation based on the slope of the phase spectrum using the following formula (X):
a plurality of seismometers provided in the building; and the calculation device according to claim 3;
A system for calculating the amount of time offset between a plurality of seismometers, characterized in that the system is configured so that measurement data measured by the seismometers is received by the calculation device. A program that causes a computer constituting a calculation device for calculating the amount of time offset of multiple seismometers mounted on a building to execute the following processing:
Based on the measurement data measured by the plurality of seismometers , a transfer function is calculated, which is the ratio of the response to the input when the measurement data from the seismometer on the first floor is used as input data related to ground vibration and the measurement data from the seismometer on the upper floor is used as response data for the upper floor;
Calculating the slope of the phase spectrum in a low frequency band where the building does not resonate;
Calculating the time lag amount based on the slope of the phase spectrum using the following formula (X):