JPH0236911B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION (Technical Field) The present invention is a seismic wave dominant period detection device that calculates the dominant period of an earthquake from time to time in real time.

(Prior art) Methods for detecting the dominant period of seismic waves include the zero-crossing method, which estimates from the time interval at which the vibration crosses the zero line, and the FFT method, which calculates the spectrum by Fourier transforming waveform data within a certain period of time. . In the zero-crossing method, the period may not be known until the zero-crossing occurs, or when a high-period wave is superimposed on a low-period wave as shown in Figure 1, one may be confused by one of the periods and the intermediate It is inevitable that the period will be mistaken for the dominant period. In the FFT method,
Calculations take time, and the problem arises of how to calculate the dominant period from the calculated spectrum.In order to perform calculations in sections (see Figure 2), it is necessary to calculate continuously over time. The disadvantage is that it is difficult to

(Object of the Invention) An object of the present invention is to provide a device that uses the output signals of two types of seismometers with different natural periods to continuously calculate and output the dominant period of seismic waves. .

(Structure of the Invention) The present invention provides a seismometer device that outputs two types of waveforms that are equivalent to the observed waveforms of two types of seismometers with different natural periods, and noise such as variations and fluctuations included in each of the observation outputs. A means for calculating an exponential smoothing value to suppress the influence of the vibration component and continuously grasp the envelope shape (so-called amplitude fluctuation) of the vibration waveform, and a means for calculating the exponential smoothing value to suppress the influence of the vibration waveform, and to calculate the seismic wave by using the exponential smoothing value and the natural period of the seismometer. This is a seismic wave dominant period detection device characterized by comprising means for calculating a dominant period.

(Example) The present invention is based on the fact that when simultaneously observed using seismometers with different natural periods, completely different waveforms are obtained as shown in Fig. 3 because they are strongly sensitive to vibrations close to the natural periods. Depending on whether the amplitude of the waveform observed by a seismometer with a natural period is large, it can be estimated whether the waveform is close to that period, and the dominant period is calculated from the difference in amplitude and the natural period.

Examples will be described in detail with reference to the drawings.

FIG. 4 is a block diagram showing a first embodiment of the present invention. In Fig. 4, 1 and 2 are sensors that detect ground motion, and their respective natural frequencies are, for example, 0.2Hz for the first sensor 1 and 2Hz for the second sensor 2.
Different like Hz. 31 and 32 are the sensors 1,
an amplifier for amplifying the detection signal from 2, 41, 42;
is a buffer amplifier, 51 and 52 are A/D converters,
6 is a sampling means, 7 is an exponential smoothing means, 8 is a dominant period calculation means, 9 is a dominant period output means, and 10 is a D/
It is an A converter. A/D converters 51 and 52, sampling means 6, exponential smoothing means 7, dominant period calculation means 8, dominant period means 9, and D/A converter 10 constitute processing device 20. FIG. 5 is a flowchart illustrating the procedures performed in accordance with the embodiment.

Sensor 1 and sensor 2 constantly detect ground motion at the location where they are installed, convert this into an electrical signal, and send it to a processing device. The processing device 20 is the sensor 1
is detected by the sensor 2, and the amplifiers 31, 32, buffer amplifiers 41, 42, and A/D converters 51, 5
It takes in ground motion information that is constantly sent through 2. The sampling means 6 includes each of the sensors 1,
2 information at predetermined time intervals (for example, 1/50 to 1/15
The offset level, which is the DC component of the input data, is calculated from the average value of the past predetermined sampling information. This offset level is constantly updated based on sampling information obtained from time to time. Further, the sampling means 6 generates values x ₁ (t), x ₂ obtained by removing the offset level from the sampling values of the two ground motion information detected by the sensors 1 and 2 and sent from time to time.
(t) is calculated. Here, the sampling value is x _si
(t), and the offset level is x _pi , the value after removing the offset level is x _i (t) = x _si (t) - x _pi
(i=1, 2...). The sampling means 11 is x _i
(t) is sent to the exponential smoothing means 7.

The exponential smoothing means 7 suppresses the influence of noise components such as variations and fluctuations contained in the detected signal,
This is a means for calculating an exponential smoothing value for continuously grasping the envelope shape (so-called amplitude fluctuation) of the vibration waveform, and smoothing X _i (t). That is, the exponential smoothing value x _ai (t) is calculated using the following equation.

x _ai (t)=x _ai (t-1)×α _i +x _i ² (t) (1) α _i is a constant of about 0.9. Moreover, x _ai (t-1) is an exponentially smoothed value one sample before time t.
The exponential smoothing means 7 calculates the exponential smoothing value of the sampling value.
x _ai (t) is sent to the dominant period calculation means 8.

Assuming that the natural frequency of the first sensor 1 is f ₁ Hz and the natural frequency of the second sensor 2 is f ₂ Hz, the dominant frequency f(t) of the seismic wave is calculated by the dominant period calculation means 8.

Here, calculation of the dominant frequency will be explained.
If the angular frequencies of sensors 1 and 2 are ω ₁ and ω ₂ (ω _i =2πf _i , f _i : natural frequencies), the damping constants are k ₁ and k ₂ , and the true acceleration waveform of ground vibration is y¨, (2 ), the output waveform is output as an electrical signal according to the equation of motion shown in equation (3).

x¨ ₁ +2h ₁ ω ₁ x〓 ₁ +ω ₁ ² x ₁ =2h _{1 ω} 1 y¨ (2) x¨ ₂ +2h ₂ ω ₂ x〓 ₂ +ω _{2 2} ^x ₂ =2h ₂ ω ₂ y¨ (3) In this case, the sensors 1 and 2 convert the vibration of the pendulum directly into an electrical signal and output it.
x ₁ , x ₂ are relative displacements, x〓 ₁ , x ₂ are relative velocities, x ¨
₁ , x¨2 is _the output waveform corresponding to relative acceleration.
The outputs of the sensors 1 and 2 can be various, but in this embodiment, outputs x ₁ and x ₂ corresponding to displacement are exemplified.

Now, y=ae ^j 〓 ^t (a＞0) (4) x ₁ ＝x ₁ e ^j( 〓 ^t+ 〓 ¹⁾ (x ₁ ＞0) (5) x ₂ ＝x ₂ e ^j( 〓 ^t+ 〓 ^{2 )} (x ₂ > 0) (6) Then, from equation (2), (ω ₁ ² −ω ² +j2h ₁ ω ₁ ω)x ₁ e ^j( 〓 ^t+ 〓 ¹⁾ = −2h ₁ ω ₁ aω ² e ^j 〓 ^t ∴x ₁ = −2h ₁ ω ₁ aω ² /ω ₁ ² −ω ² +j2h ₁ ω ₁ ω・e ^-j 〓 ¹ (7
) x ₁ is an output proportional to speed and is a real number (positive), so similarly The input speed amplitude is aω, and this is set as the unknown X.
Also, the input angular frequency is ω, which is also considered an unknown quantity, and ω
is derived from x ₁ and x ₂ .

From equations (8) and (9), x ₁ ² {(ω ₁ ² −ω ² ) ² + (2h ₁ ω ₁ ω) ² } =4h ₁ ² ω ₁ ² ω ² X ² (10) x ₂ ² {(ω ₂ ² − ω ² ) ² + (2h ₂ ω ₂ ω) ² }=4h ₂ ² ω ₂ ² ω
^{2 _} _{_} ^_ _{_} ^_ _{_} ^_ _{_} ^{_ _ _} _{_ _} ^_ _{_} ^_ ₁ ² x ₂ ² {(ω ₂ ² −ω ² ) ² + (2h ₂ ω ₂ ω) ² }=0 (h ₂ ² ω _{2 2} ^x ₁ ² −h ₁ ² ω ₁ ² x ₂ ² ) ω ⁴ +(−2h ₂ ² x ₁ ² +4h ₁ ² h ₂ ^{2 x} ₁ ² + _2h 1 2 _x ^{2 2} −4h ₂ ² h ₁ ² x ₂ ² )ω ₁ ² ω ₂ ² ω ² +h ₂ ² ω ₂ ² x ₁ ² ω ₁ ⁴ −h ₁ ² ω ₁ ² x ₂ ² ω ₂ ⁴ =0 (h ₂ ² ω ₂ ² x ₁ ² −h ₁ ² ω ₁ ² x ₂ ² )ω ⁴ +{−2h ₂ ² x ₁ ² (1−2h ₁ ² ) +2h ₁ ² x ₂ ² (1−2h ₂ ² )}ω ₁ ² ω ₂ ² ω ² +h ₂ ² ω ₂ ² x ₁ ² ω ₁ ⁴ −h ₁ ² ω ₁ ² x ₂ ² ω ₂ ⁴ =0 (12) Here, A=h ₂ ² ω ₂ ² x ₁ ² −h ₁ ² ω _{1 2} ^x ₂ ² (13) B={−h ₂ ² x ₁ ² (1 −2h ₁ ² )+h ₁ ² x ₂ ² (1−2h ₂ ² )}ω ₁ ² ω ₂ ² (14) C=h ₂ ² ω ₂ ² x ₁ ⁴ −h ₁ ω ₁ ² x ₂ ² ω ₂ ⁴ (15), equation (12) becomes Aω ⁴ +2Bω ² +C=0 (16). If we solve equation (13) for ω ² by considering ω ² >0, becomes. In order for ω ² >0, B ² −AC>0 and AC<0.

From equations (10) and (11), x ₁ ² = (2h ₁ ω ₁ ωX) ² / (ω ₁ ² −ω ² ) ² + (2h ₁ ω ₁ ω
) ² (18) x ₂ ² = (2h ₂ ω ₂ ωX) ² / (ω ₂ ² −ω ² ) ² + (2h ₂ ω ₂ ω
) ² (19) Substituting equations (18) and (19) into equation (13), A=4h ₁ ² h _{2 2} ^ω ₁ ² ω ₂ ² ω ² X ² / (ω ₁ ² −ω ² ) ² +(2h ₁ ω ₁
ω) ² −4h ₁ ² h ₂ ² ω ₁ ² ω ₂ ² ω ² X ² / (ω ₂ ² −ω ² ) ² + (2h ₂
ω ₂ ω) ² =4h ₁ ² h ₂ ² ω ₁ ² ω ₂ ² ω ² X ² / {(ω ₁ ² −ω ² ) ² + (2h ₁
ω ₁ ω) ² } {(ω ₂ ² −ω ² ) ² + (2h ₂ ω ₂ ω) ² } ・{(ω ₂ ² +ω ₁ ² )(ω ₂ ² −ω ₁ ² )−2(ω ₂ ² −ω ₁ ²
)ω ² +4(h ₂ ² ω ₂ ² −h ₁ ² ω ₁ ² )ω ² }…(20) Substituting equations (18) and (19) into equation (15), C=h ₂ ² ω ₂ ²・(2h ₁ ω ₁ ωX) ² / (ω ₁ ² −ω ² ) ² + (2h ₁
ω ₁ ω) ²・ω ₁ ⁴ −h ₁ ² ω ₁ ²・(2h ₂ ω ₂ ωX) ² / (ω ₂ ² −
ω ² ) ² + (2h ₂ ω ₂ ω) ²・ω ₂ ⁴ = 4h ₁ ² h ₂ ² ω ₁ ^{2 ω} 2 ₂ ^{ω 2} X ² / {(ω ₁ ² −ω ² ) ² + (2h ₁
ω ₁ ω) ² } {(ω ₂ ² −ω ² ) ² + (2h ₂ ω ₂ ω) ² } ・[(ω ₁ ⁴ {(ω ₂ ² −ω ² ) ² + (2h ₂ ω ₂ ω) ² }−ω ₂
⁴ {(ω ₁ ² −ω ² ) ² + (2h ₁ ω ₁ ω) ² }]…(21) (ω ₁ ² −ω ² ) ² + (2h ₁ ω ₁ ω) ² >0, (ω ₂ ² −ω ² )
²⁺
(2h ₂ ω ₂ ω) ² > 0 ω ₂ ² > ω ₁ ² , so in order for Equation (20) × Equation (21) = AC < 0, {(ω ₂ ² + ω ₁ ² ) ( ω ₂ ² −ω ₁ ² )−2(ω ₂ ² −ω ₁ ² )ω ₂ +4(h ₂ ² ω ₂ ² −h ₁ ² ω ₁ ² )ω ² } ・[ω ₁ ⁴ {(ω ₂ ² −ω ² ) ² + (2h ₂ ω ₂ ω) ² } −ω ₂ ⁴ {(ω ₁ ² −ω ² ) ² + (2h ₁ ω ₁ ω) ² }] <0. Rearranging the left side of the above equation, ω ² [(ω ₂ ² + ω ₁ ² ) (ω ₂ ² −ω ₁ ² )+2ω ² {ω ₁ ² (1−2h ₁ ² )−ω ₂ ² (1−2h ₂ ² )} ・[ω ² (ω ₁ ² +ω ₂ ² ) (ω ₁ ² −ω ₂ ² )−2ω ₁ ² ω ₂ ² {ω ₁ ² (1−2h ₂ ² )−ω ₂ ² (1−2h ₁ ² )}〕＜0 (22) Therefore, (1−2h ₁ ² )ω ₁ ² −(1−2h ₂ ² )ω ₂ ² 0 (1−2h ₂ ² )ω ₁ ² −(1−2h ₁ ² ) ω ₂ ² 0, then formula (22) is satisfied.

If you choose h ₁ = h ₂ = 1/√2, then A=1/2 (ω ₂ ² x ₁ ² −ω ₁ ² x ₂ ² ) B=0 C=1/2ω ₁ ² ω ₂ ² (x ₁ ² ω ₁ ² −x _{2 2} ^ω ₂ ² ) Therefore, equation (17) is This equation (23) gives the dominant period. That is, ω={(x ₂ ² ω ₂ ² −x ₁ ² ω ₁ ² )/ (x ₁ ² ω ₂ ² −x ₂ ² ω ₁ ² )} ^1/4 (ω ₁ ω ₂ ) ^1/2 (24 ) f={(x ₂ ² f ₂ ² −x ₁ ² f ₁ ² )/ (x ₁ ² f ₂ ² −x ₂ ² f ₁ ² )} ^1/4 (f ₁ f ₂ ) ^1/2 dominant period The output means 9 outputs the dominant period f(t) at that time calculated by the dominant period calculating means 8 to the outside.

FIG. 6 is a block diagram showing the second embodiment. In Fig. 6, 1 is a sensor, 3 is an amplifier,
4 is a buffer amplifier, 60 is a characteristic conversion device, and the others are the same as those shown in FIG.

In the second embodiment, one sensor 1 is installed, and a characteristic conversion device 60 for converting the characteristics of the signal of the sensor 1 is installed between the buffer amplifier 4 and one input of the sampling means 6. are doing. The characteristic conversion device 60 provides the output to the sampling means 6 as if it were output from a sensor having a natural period different from that of the sensor 1. This characteristic conversion device 60 is disclosed in Japanese Patent Application Laid-Open No. 56-46479.
(Japanese Patent Application No. 54-122559). In other words, as shown in Fig. 7, the vibration waveform is input as an electrical signal, has arbitrarily settable frequency characteristics and damping characteristics, and there is a virtual seismograph function that simulates the sensor based on these, and a virtual seismometer function that simulates the sensor and the virtual A function that multiplies the output of the sensor by a constant determined by the format and characteristics of the seismograph function, and inputs this into the virtual seismograph function, and various outputs from the simulated results of the virtual seismograph function. This device has the function of multiplying the output signal of the sensor by a constant derived from the frequency characteristics and braking characteristics of the sensor, and adding these together.
In FIG. 7, 71 is a sensor, 72 is an n multiplier,
73 is a virtual seismograph, and 74 is an adder. By sending the output of the characteristic conversion device 10 obtained with such a configuration and the other output of the buffer amplifier 4 to the sampling means 6, the dominant period is obtained in the same manner as in the first embodiment. be able to.

(Effects of the Invention) According to the present invention, fluctuations in the dominant period of seismic waves can be calculated continuously over time.

[Brief explanation of drawings]

Figure 1 is a waveform diagram showing that high-frequency waves are superimposed on low-frequency waves, Figure 2 is a diagram showing calculation divisions using the FFT method, and Figure 3 is waveforms obtained by seismometers with different natural periods. 4 is a block diagram of the first embodiment of the present invention, FIG. 5 is a flowchart explaining the operation of FIG. 4, and FIG. 6 is a block diagram of the second embodiment of the present invention. , FIG. 7 is a block diagram illustrating the characteristic conversion device. 1, 2...Sensor, 6...Sampling means, 7...
Exponential smoothing means, 8... Predominant period calculation means, 9...
... dominant period output means, 60... characteristic conversion device.

Claims (1)

[Scope of Claims] 1. A seismometer device that outputs two types of waveforms equivalent to the observed waveforms of two types of seismometers having different natural periods; means for calculating an exponentially smoothed value of each of the observation outputs; 1. A seismic wave dominant period detection device comprising means for calculating a predominant period of seismic waves based on an exponential smoothing value and a natural period of a seismometer. 2. The seismic wave dominant period detection device according to claim 1, wherein the seismograph device outputting two types of observation outputs is a real seismograph device each having a different natural period. 3 As a seismograph that outputs two types of observation output, 1
2. The seismic wave dominant period detection device according to claim 1, further comprising an output from an actual seismometer and an output from a characteristic conversion device that converts the output from the actual seismometer.