JP3117635B2 - Superimposed wave filtering method and apparatus - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and an apparatus for filtering a superposed wave of an elastic wave propagating in concrete, soil, metal or the like.

[0002]

2. Description of the Related Art Conventionally, measurement of cracks in concrete, measurement of the position of underground structures, measurement of iron thickness, detection of fish schools, and the like have been performed by measuring elastic waves.

[0003]

However, the above-mentioned prior art has the following problems. That is, a wave existing in the natural world is formed by superimposing many waves, and considering a forced vibration wave due to a disturbance, many waves composed of a fundamental frequency and its higher-order components are superimposed. It was done. Therefore, although it is necessary to extract these waves from the superimposed waves, it is extremely difficult to accurately perform this extraction. Therefore, there is a problem that it is extremely difficult to accurately perform the above-described measurement.

The present invention has been made in view of the above problems, and provides a superimposed wave filtering method and apparatus capable of accurately determining a fundamental frequency of each of a large number of waves included in the superimposed waves. The purpose is to:

[0005]

According to the present invention, a superimposed wave filter according to the present invention is provided.
The filtering method uses elastic wave
An oscillation sensor and an elastic wave reception sensor
The elastic wave oscillated by the oscillation sensor is sent to the elastic wave receiving sensor.
Receive and filter the resulting superimposed wave
In the superimposed wave filtering processing method,Of the superimposed wave
Sweep the Fourier spectrum to get its integral multiple
Frequency with a spectrum peak at the frequency
A step of identifying the main frequency;The superimposed wave at time t
Expressed as a function f (t),SaidLet the fundamental frequency be f₀age,
Δt = m / 2f where m is a predetermined positive integer₀And a
And b are predetermined positive real numbers, respectively.Formula
{F (t) -af (t + Δt)} / bCalculationTo
ImplementationBy doing, F₀/ M and f₀/ M odd multiple vibration
Amplifying the number components, f₀/ M frequency component
Reduced or deletedFunction F ₁ A method to obtain a superimposed wave represented by (t)
And the function F ₁ Fourier of superimposed wave represented by (t)
Deriving a spectrum.Characterized by
You.

In another superposition wave filtering method according to the present invention, an elastic wave oscillation sensor and an elastic wave reception sensor are arranged on a substance through which an elastic wave propagates, and the elastic wave oscillated by the elastic wave oscillation sensor is subjected to the elastic wave oscillation. Received by the wave receiving sensor,
In a superposition wave filtering method for filtering the obtained superposition wave, a Fourier spectrum of the superposition wave is used.
By sweeping the vector, the frequency
The frequency at which the spectrum has a peak at
Identifying the superimposed wave as a function f (t) of time t
Expressed as, the number of the fundamental oscillation and f _0, where m is a predetermined positive integer, and Δt = m / 2f _0, the a and b, respectively, when a predetermined positive real number, equation {f ( t) + a
f (t + Δt)} / b to performing operations represented by
More, f ₀ / m and remove or reduce the odd multiple frequency components of f ₀ / m, function to amplify the even multiple frequency components of f ₀ / m
Obtaining a superimposed wave represented by the number F ₂ (t);
Deriving the Fourier spectrum of the superimposed wave represented by F ₂ (t)
And a step of outputting .

Note that the function F ₁ (t) or F ₂ (t) is
The function f of the superimposed wave received by the elastic wave receiving sensor
(T) and execute the operation represented by the above-described formula a plurality of times.
By applying, a new function F ₁ (t) or F ₂ (t)
And this may be repeated a plurality of times.

A superimposed wave filtering apparatus according to the present invention is an apparatus used for implementing the superimposed wave filtering method according to any one of claims 1 to 4, wherein the supersonic wave filtering sensor and the elastic wave receiving sensor are used. And a signal analyzer for filtering the superimposed wave received by the receiving sensor.

[0009]

The superposition wave filtering method according to the present invention
In addition,From the Fourier spectrum of the received superimposed wave
IdentifiedLet the fundamental frequency be f₀And m is a predetermined positive integer
Δt = m / 2f₀And further define a and b as
The superimposed waves received after each having been set to a predetermined real numberFunction
For f (t),Formula{F (t) -af (t + Δt)}
/ BCalculationImplementThus, the function F
₁ Get (t). Then, the wave of f (t)
Of the components, f₀/ M and f₀/ M odd multiple frequency (f₀
/ M, 3f₀/ M, 5f₀/ M, ...) increase
Width, f₀/ M even frequency (2f₀/ M, 4f₀/
m, 6f₀/ M, ...) are reduced or eliminated
It is. In this case, f₀/ M and f₀/ M odd frequency
(F₀/ M, 3f₀/ M, 5f₀/ M, ...)Success
MinuteLet X be the amplification factor and f₀/ M even frequency (2f₀/
m, 4f₀/ M, 6f₀/ M, ...)
When the rate is Y, it is indicated by a + b = X and a−b = Y
Calculate the simultaneous equations, and determine the values of a and b.
No. However, a and b are not limited to these values.
Also, m may be determined according to the purpose.
In the case of f₀And f₀Odd frequency (f₀, 3f₀, 5
f₀,...) Are amplified and f₀Even multiple vibration of
Number (2f₀, 4f₀, 6f₀, ... ・))
Or deleted. When m is 2, f₀/ 2
Odd multiple frequency (f₀/ 2, 3f₀/ 2,5f₀/ 2, ...
..) are amplified and f₀/ 2 even frequency
(2f₀/ 2, 4f₀/ 2, 6f₀/ 2, ...)
Components are reduced or eliminated. That is, f₀Integer multiple frequency of
(F₀, 2f₀, 3f₀, ... ・ ・)
Can be deleted.

In another superposition wave filtering method according to the present invention, the Fourier spectroscopy of a received superposition wave is performed.
The basic frequency identified from Torr and f _0, where m is a predetermined positive integer, is defined as Δt = m / 2f _0, a further a and b, respectively, after the set to a predetermined real number, is received was to superimposed wave function f (t), equation {f (t) + af ( t +
By performing the operation expressed by Δt)} / b, Seki
Obtain the number F ₂ (t) . Then, among the components of the wave constituting the _{f (t), f 0 /} m and f ₀ / odd multiple frequencies of the _{m (f 0 / m, 3f} 0 / m, 5f 0 / m, ····· ) Is deleted or reduced, and the even multiple frequency of f ₀ / m (2f ₀
/ M, 4f ₀ / m, 6f ₀ / m,...) Are amplified. In this case, the values of a and b can be determined by calculating the simultaneous equations as described above. However,
As in the above case, a and b are not limited to these values. In addition, m may be determined according to the purpose.
For the odd multiple frequencies of f ₀ and f ₀ (f _0, 3f _0, 5
The components of f ₀ ,... are deleted or reduced, and the components of even multiples of f ₀ (2f ₀ , 4f ₀ , 6f ₀ ,...) are amplified . In the case where the 2 m, f _0/2 odd multiple frequency _{(f 0 / 2,3f 0 / 2,5f} 0/2, ··
Components.) Is removed or reduced, f _0/2 even multiple frequency _{(2f 0 / 2,4f 0 / 2,6f} 0/2, ····
・) Is amplified. That is, an integral multiple frequency of _{f 0 (f 0, 2f 0} , 3f 0, ·····) can amplify a component of.

In any of the above-mentioned filtering methods, f (t) is Fourier-transformed, and each spectrum value of the obtained Fourier spectrum is increased or decreased at a predetermined rate for each frequency, and the filtering processing is performed. Is also good.
In this case, F ₁ (t) or F ₂ (t) is Fourier-transformed, and the above-mentioned predetermined ratio is calculated in advance for each frequency from the obtained spectrum value. Then, the calculation time is reduced as compared with the case where F ₁ (t) or F ₂ (t) is directly calculated and the filtering process is performed.

In any of the filtering processes,
The filtering process can be performed multiple times as needed. By using F ₁ (t) and F ₂ (t) a plurality of times, unnecessary wave components can be further removed from f (t), and necessary wave components can be further removed from f (t). Can be amplified.

A superimposed wave filtering apparatus according to the present invention includes an elastic wave oscillation sensor, an elastic wave reception sensor, and a signal analyzer for filtering a superimposed wave received by the receiver. Then, a superimposed wave filtering process is performed. Then, since the signal analysis unit is formed by a computer or the like, the filtering process is performed in a short time. Thereby, even if it is a complicated reception wave, the fundamental frequency of the wave which comprises a reception wave can be shown clearly in a short time.

[0014]

The present invention will be further described below. Results present inventors have conducted intensive studies on the nature of the wave and the wave the wave formed by superimposing a number having the higher frequency (superimposed wave) having an arbitrary number of basic vibration, the received superimposed wave Fu
Sweep the Rie spectrum to identify the fundamental frequency , amplify or reduce or delete the wave of the specific frequency from the superimposed wave with high precision, and for many waves included in the superimposed wave, multi-wave fundamental frequency Has been found out that a superimposed wave filtering processing method that can easily and clearly show the above.

Even if the superimposed wave f (t) has a very complicated shape, as long as the superimposed wave has a repetition period T (second), a simple sine wave as shown in the following equation 1 is obtained. Can be represented by the superposition of

[0016]

[Number 1] _{f (t) = a 0 +} {Σ (n = 1, k) a n cos (n
ωt)} + {Σ (n = 1, k) b n sin (nωt)} where, t: time (sec) omega: angular frequency _{a 0, a n, b n} : coefficient k, n: positive number.

Note that Σ (n = 1, k) is defined as changing n from 1 to k and taking the sum. For example, ｛Σ
(N = 1, k) X _n } represents X ₁ + X ₂ +... + X _k .

Using the above formula 1, the superimposed wave filtering method in the present invention will be described. First,
To simplify the discussion, the repetition period T is 1 second (the angular frequency ω in Equation 1 is 2π), k = 9, and a ₀ = a _1.
= A ₉ = 0 and b ₁ = b ₂ = ... b ₉
= 1, the superimposed wave f (t) and the period of the superimposed wave f (t) are shifted by Δt = 0.5 seconds, and f (t + Δ
The property of t) will be described.

FIG. 1 is a graph showing the relationship between the time t (second) on the horizontal axis and the superimposed wave f (t) on the vertical axis, and the time t (second) on the horizontal axis. The superimposed wave f (t + Δ
It is a graph which shows the relationship of both at the time of t). That is,
The upper part of FIG. 1 is a diagram showing Σ (n = 1, k) sin (2nπt). In the lower part of FIG. 1, the wave period Δt is shifted by 0.5 seconds {(n = 1, k) sin {(2nπ (t + Δt)}}.
FIG.

FIG. 2 shows time t (seconds) on the horizontal axis.
FIG. 4 is a diagram showing the relationship between the two, taking the amplitude on the vertical axis, the solid line represents each sin (2nπt) constituting f (t), and the broken line represents each sin ｛(2nπ (t +) constituting f (t + Δt).
Δt)｝. The obtained wave G ₁ (t) is shown in FIG. 3 by substituting each sine wave shown in FIG.

[0021]

G ₁ (t) = Σ (n = 1, k) sin (2nπt) −
{(N = 1, k) sin {(2nπ (t + Δt)}}

Further, each n component (frequency n) of G ₁ (t)
Is shown in FIG. The numbers on the right side in FIG. 4 indicate the maximum amplitude of each n component. Similarly, by substituting each sine wave shown in FIG. 2, the following equation 3 is calculated, and the obtained wave G
₂ (t) is shown in FIG.

[0023]

G ₂ (t) = Σ (n = 1, k) sin (2nπt) +
{(N = 1, k) sin {(2nπ (t + Δt)}}

Further, each n component of G ₂ (t) (frequency n)
Is shown in FIG. The numbers on the right side in FIG. 6 indicate the maximum amplitude of each n component.

The following can be seen from FIGS.
That is, the superimposed wave f (t) and the period T (T =
1.0 seconds) and a superimposed wave f (t + ΔT) shifted by a half cycle (ΔT = T / 2), the fundamental frequency f
The amplitude of the sine wave of ₀ (= 1 / T) and odd multiples of this fundamental frequency (3 / T, 5 / T, 7 / T and 9 / T) is doubled, and the frequency of an even multiple is (2 / T, 4 / T, 6
/ T and 8 / T), the amplitude of the sine wave is zero. Thus, the above equation (2) is obtained by calculating the fundamental frequency f
₀ even multiple frequency components of the removed, odd multiple frequency components of the fundamental frequency f ₀ can be said that the a filter for amplifying twice. FIG. 3 can be interpreted as a diagram showing the result of applying this filter to f (t).

On the other hand, as shown in FIG. 6, Equation 3 assumes that the amplitude of the odd multiple of the fundamental frequency f ₀ is 0 and the amplitude of the even multiple of the fundamental frequency f ₀ is twice. As a result, the above equation 2 is obtained by calculating the fundamental frequency f ₀ from the superimposed wave f (t).
It can be said that the filter removes the components of the odd-numbered frequencies and amplifies the components of the even-numbered frequencies twice.
FIG. 5 can be interpreted as a diagram showing the result of applying this filter to f (t).

Next, the fundamental frequency f _{0 is set} to 4 Hz, the cycle increment Δt in this case is determined to be 1 / (2f ₀ ) = 0.125 seconds, and k = 9, a ₀ = a ₁ =. ... = a ₉ =
0 and b ₁ = b ₂ =... = B ₉ = 1, the superimposed waves f (t) and f (t + Δ
The property of t) will be described. FIG. 7 shows the time t on the horizontal axis.
(Seconds), a graph showing the relationship between the superimposed waves f (t) on the vertical axis and time t (seconds) on the horizontal axis, and the superimposed waves f (t + Δt) on the vertical axis. It is a graph which shows the relationship of. FIG. 8 is a diagram showing the relationship between the time t (second) on the horizontal axis and the n-components (frequency n) of the superimposed waves f (t) and f (t + Δt) on the vertical axis, showing the relationship between the two. Is f
(T) shows each n component sin (2nπt), and the dashed line indicates f
Each of the n components sin ｛(2nπ (t + Δt) of (t + Δt)
t) indicates｝. The wave G ₁ (t) obtained by calculating the mathematical formula shown in the above mathematical formula 2 is shown in FIG. FIG. 10 shows each n component (frequency n) of G ₁ (t). The numbers on the right side in FIG. 10 indicate the maximum amplitude of each n component. As shown in FIG. 10, when the basic frequency f ₀ is 4 Hz, the above equation 2
Makes the amplitude of the odd multiple of the fundamental frequency f ₀ twice,
The amplitude of the even-number frequency is set to 0. Further, for a wave whose frequency is close to an odd-number frequency, the amplitude of the wave is amplified, while for a wave whose frequency is close to an even-number frequency, the amplitude of the wave is attenuated. FIG. 9 is a diagram showing waves obtained by applying such a filter.

Similarly, using each of the n-component waves shown in FIG.
₂ (t) is shown in FIG. FIG. 12 shows each n component (frequency n) of G ₂ (t). The numbers on the right side in FIG. 12 indicate the maximum amplitude of each n component. As shown in FIG. 12, the above equation 3 sets the amplitude of an odd multiple frequency of the fundamental frequency f ₀ to 0,
The amplitude of the even-number frequency is doubled. Further, for a wave whose frequency is close to an odd multiple frequency, the amplitude of the wave is attenuated, and for a wave whose frequency is close to an even multiple frequency, the amplitude of the wave is amplified. FIG. 11 is a diagram showing waves obtained by applying such a filter.

The above consideration is based on the above-mentioned equation 1, where k = 9, a ₀ = a ₁ =... = A ₉ = 0 and b ₁ =
b ₂ = for the case is ····· = b ₉ = 1, i.e., si
Although it was about n waves, a ₁ =... = a ₉ =
1 and a ₀ = b ₁ = b ₂ =... = B ₉ = 0, and co
The above considerations can be applied to the s-wave.

The properties of the above-described filter will be described using a Fourier spectrum. FIG. 13 shows Σ (n = 1, k) si
FIG. 9 is a graph showing the relationship between n (2nπt) by taking the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis. This spectrum has a constant spectrum value of 1.0. FIG. 14 is a diagram showing spectrum values obtained by applying Equation 2 to FIG.
FIG. 7 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis. Equation 2 is:
From the waveform represented by Σ (n = 1, k) sin (2nπt),
The waveform obtained by moving this waveform by the period Δt is subtracted. The operation of the above equation 2 will be examined from the relationship between the frequency and the spectrum value. As shown in FIG. 13, Δt = 1 / (2f
₀ ), that is, when f ₀ = 1 / (2Δt), the frequency is f ₀ , 3f ₀ , 5f ₀ ,... As shown in FIG.
Is amplified twice and the frequency is 2f ₀ , 4
The spectral values of f ₀ , 6f ₀ ,... Further, the spectrum values near the frequencies f ₀ , 3f ₀ , 5f ₀ ,... Are amplified, and the frequencies are 2f ₀ , 4f ₀ , 6f ₀ ,
... Attenuate nearby spectral values. Equation 2 means that such a filtering process is performed to extract a spectrum of an odd multiple of the fundamental frequency.

FIG. 15 shows the case where the above equation 3 is applied to FIG.
It is a figure which shows the obtained spectrum value, is a graph which shows frequency (Hz) on a horizontal axis and a spectrum value on a vertical axis | shaft, and shows the relationship between both. The above equation 3 is given by Σ (n = 1, k)
The waveform represented by sin (2nπt) and the waveform obtained by moving this waveform by the period Δt are added. Equation 3 above
When the effect of is viewed from the relationship between the frequency and the spectrum value, as shown in FIG. 15, the frequency is f ₀ , 3f ₀ , 5
The spectral value of f ₀ ,...
The spectrum values of f ₀ , 4f ₀ , 6f ₀ ,... are doubled. Further, the frequency is f ₀ , 3f ₀ , 5f ₀ ,.
... Attenuated nearby spectral values, frequency 2
f ₀ , 4f ₀ , 6f ₀ ,... Amplify nearby spectral values. Equation 3 means that such a filtering process is performed to extract a spectrum having an even multiple of the fundamental frequency.

The above-described filtering process is performed on an actual waveform. FIG. 16 is a graph showing the relationship between time t (seconds) on the horizontal axis and amplitude on the vertical axis. Δt = 30 μs, f ₀ = 1 / (2Δt) ≒ 16.6
kHz, as shown in FIG. 16, when the waveform is added and subtracted, F ₁ (t) = f (t) −f (t + Δ
t), a time-series wave represented by F ₂ (t) = f (t) + f (t + Δt) is obtained. Fourier transform is performed for each of F ₁ (t) and F ₂ (t).

FIGS. 17A and 17B respectively show f
(T), the Fourier spectrum of F ₁ (t), the horizontal axis frequency takes (Hz), is a graph showing the relationship between the two taking the spectral values on the vertical axis. The broken line in FIG. 17A shows the shape of the filter. f (t) is amplified by the filter indicated by the broken line, and the spectrum near f ₀ 016.6 kHz is amplified, and the spectrum having a frequency extremely different from f ₀ is attenuated.

FIGS. 18A and 18B show f and f respectively.
(T), the Fourier spectrum of F ₂ (t), the horizontal axis frequency takes (Hz), is a graph showing the relationship between the two taking the spectral values on the vertical axis. The broken line in FIG. 18A indicates the shape of the filter. f (t) is attenuated by the filter indicated by the broken line, and the spectrum near f ₀ ≒ 16.6 kHz is attenuated, and the spectrum having a frequency extremely different from f ₀ is amplified.

Consider what mathematical expressions the filters in FIGS. 17A and 18A can represent. A component in which nω in Expression 1 is R will be considered from f (t). f _R (t) and F ₁ for this f _R (t)
(T) and F ₂ (t) are shown in Equations 4 to 6 below.

[0036]

F _R (t) = a _R cos (Rt) + b _R sin (Rt)

[0037]

F _1R (t) = f _R (t) −f _R (t + Δt)

[0038]

## _EQU6 ## F _2R (t) = f _R (t) + f _R (t + Δt) Equation 4 is substituted into Equation 5 and arranged. The obtained result is shown in Formula 7 below.

[0039]

## _EQU7 ## F _1R (t) = C ₁ ｛a _R cos (Rt + R · Δt)
/ 2) + b _R sin (Rt + R · Δt / 2)｝ where C ₁ is defined by the following equation (8).

[0040]

C ₁ = 2 cos (R · Δt / 2) Similarly, the above equation 4 is substituted into the equation 6 to arrange. The obtained result is shown in Formula 9 below.

[0041]

## _EQU9 ## F _2R (t) = C ₂ ｛a _R sin (Rt + R · Δt)
/ 2) + b _R cos (Rt + R ・ Δt / 2)｝ where C ₂ is defined by the following equation (10).

[0042]

## EQU10 ## C ₂ = ₂ sin (R · Δt / 2)

The filter indicated by a broken line in FIG. 17A is represented by the above equation (8).
The filter indicated by the broken line in FIG.
It is indicated by 0.

As described above, the superimposed wave can be filtered by adding or subtracting the superimposed wave obtained by shifting the period of the superimposed wave by Δt to the superimposed wave. Filter C ₂ shown in filters C ₁ and the equation 10 shown in above equation 8 is a basic form of the filter of the present invention, by combining the C ₁ and C _2, it can be obtained more meaningful filter.

The filter thus obtained is shown below. By using these filters,
The fundamental frequency of the wave constituting the superimposed wave can be easily determined.

FIGS. 19 to 22 show the frequency (Hz) on the horizontal axis.
FIG. 7 is a graph showing the relationship between the two, taking the spectrum value on the vertical axis. Each filter (filter 1-1, 1
-2, 1-3 and 1-4) are spectral components of an arbitrary frequency (f ₀ ) and odd multiples of this frequency (3f ₀ , 5)
f _0, it amplifies the spectral components .....). Each filter has an even multiple frequency (2f ₀ , 4f ₀ ,...)
..) Is deleted or reduced. Each of the filters shown in FIGS.
The C ₁ of those made in the base. That is, assuming that m is 1, Δt = m / 2f ₀ = 1 / 2f _0, and the filter is based on the calculation represented by the following Expression 11.

[0047]

F ₁ (t) = {f (t) −af (t + Δt)} / b

[0048] Among the filter shown in FIG. 19, the filter 81a is one obtained by multiplying a 1/2 C ₁ described above. That is, assuming that a in Equation 11 is 1 and b is 2, F ₁
Calculate (t). The obtained F ₁ (t) is obtained by applying a filter 81a to f (t). Filter 82a
Is a filter obtained by substituting the filter 81a for the filter 81a, and is a filter for applying the filter 81a twice. Similarly, the filter 83a is a filter that applies the filter 81a three times. That is,
If this filter 82a is expressed as F ₁ ² (t),
Luther 82a is a filter represented by the following equation (12).
Become. Similarly, to represent the filter 83a F ₁ ³ and (t)
Then, the filter 83a becomes a filter represented by the following Expression 13.
Become a filter.

(Equation 12)

(Equation 13)

[0049] Among the filter shown in FIG. 20, the filter 81b is C ₁ itself. That is, the above equation (11)
F ₁ (t) is calculated by setting a to 1 and b to 1. The obtained F ₁ (t) is obtained by applying a filter 81b to f (t). Also, the filter 82b is
This is a filter that applies b twice. Furthermore, filter 8
3b is a filter for applying the filter 81b three times.

The filter 81c among the filters shown in FIG. 21 was obtained as follows. Filter 81c
A and b are calculated from the following equations 14 and 15 so that the maximum value and the minimum value of are respectively 1.0 and 0.5.

[0051]

(14) (1 + a) /b=1.0

[0052]

[Number 15] (1-a) /b=0.5

From the above equations 14 and 15 , a = 0.333..., B = 1.333.
・ ・Substituting these a and b into Equation 11 above, F
₁ Calculate (t). The obtained F ₁ (t) is obtained by applying a filter 81c to f (t). The filter 82c is a filter that applies the filter 81c twice. Further, the filter 83c is a filter that applies the filter 81c three times.

The filter 81d among the filters shown in FIG. 22 was obtained as follows. In order to make the maximum value and the minimum value of the filter 81d 2.0 and 1.0, respectively, a and b are calculated from Expressions 16 and 17 below.

[0055]

[Number 16] (1 + a) /b=2.0

[0056]

[Number 17] (1-a) /b=1.0

From the above equations ( 16) and ( 17) , a and b are respectively a = 0.333..., B = 0.666.
・ ・Substituting these a and b into Equation 11 above, F
₁ Calculate (t). The obtained F ₁ (t) is obtained by applying a filter 81d to f (t). The filter 82d is a filter that applies the filter 81d twice. Further, the filter 83d is a filter that applies the filter 81d three times.

FIGS. 23 to 26 show the frequency (Hz) on the horizontal axis.
FIG. 7 is a graph showing the relationship between the two, taking the spectrum value on the vertical axis. Each filter (filters 2-1, 2
-2, 2-3 and 2-4) are spectral components of an arbitrary frequency (f ₀ ) and odd multiples of the frequency (3f ₀ ,
5f ₀ ,...) Or
Or reduce. Each filter has an even frequency (2
Amplify the spectral components of f ₀ , 4f ₀ ,... Each of the filters shown in FIGS.
A C ₂ are those made basic. That is, the filter is based on the calculation represented by the following Expression 18 , where m is 1, and Δt = m / 2f ₀ = 1 / 2f ₀ .

[0059]

Equation 18] _{F 2 (t) = {f} (t) + af (t + Δt)} / b

[0060] Among the filter shown in FIG. 23, the filter 81e is the one obtained by multiplying 1/2 to C _2.
That is, F ₂ (t) where a is 1 and b is 2 in Equation 18 above.
Is calculated. The obtained F ₂ (t) is obtained by applying a filter 81e to f (t). Also, the filter 82e
Is a filter that applies the filter 81e twice.
Further, the filter 83e is a filter that applies the filter 81e three times.

[0061] Among the filter shown in FIG. 24, the filter 81f is C ₂ itself. That is, the above equation ( 18)
F ₂ (t) is calculated by setting a to 1 and b to 1. The obtained F ₂ (t) is obtained by applying a filter 81f to f (t). Also, the filter 82f is
This is a filter that applies f twice. Furthermore, filter 8
3f is a filter for applying the filter 81f three times.

The filter 81g shown in FIG. 25 was obtained as follows. In order to make the maximum value and the minimum value of the filter 81g 1.0 and 0.5, respectively, when a and b are calculated from Expressions 14 and 15 , a and b are obtained.
Are a = 0.333..., B = 1.333, respectively.
... F ₂ (t) is calculated by substituting a and b into Equation 18 above. The obtained F ₂ (t) is f
(T) is obtained by applying a filter 81g. Also,
The filter 82g is a filter that applies the filter 81g twice. Further, the filter 83g is a filter that applies the filter 81g three times.

The filter 81h among the filters shown in FIG. 26 was obtained as follows. Filter 81h
When a and b are calculated from Expressions 16 and 17 so that the maximum value and the minimum value of are respectively 2.0 and 1.0, a and b are respectively a = 0.333 · ...
, B = 0.666... F ₂ (t) is calculated by substituting a and b into Equation 18 above. The obtained F ₂ (t) is obtained by applying a filter 81h to f (t). Also, the filter 82h is a filter 81
h is a filter that applies h twice. Furthermore, filter 8
3h is a filter that applies the filter 81h three times.

FIGS. 27 to 30 show frequency (Hz) on the horizontal axis.
FIG. 7 is a graph showing the relationship between the two, taking the spectrum value on the vertical axis. Each filter (filters 3-1, 3
-2, 3-3, and 3-4) are spectral components of an arbitrary frequency (f ₀ ) and integer multiples of the frequency (2f ₀ ,
3f ₀ ,...) Are amplified. These filters have Δt = m / 2f _{0 where} m is 2.
When = 1 / f ₀ , the filter is based on the filter expressed by the above equation ( 18 ).

Among the filters shown in FIG. 27, the filter 81i is a filter 81e when m is 2. Also, the filter 82i is the same as the filter 81i.
It is a filter that is applied 0 times. Further, the filter 83i
Is a filter that applies the filter 81i 50 times.

Of the filters shown in FIG. 28, a filter 81j is a filter 81f when m is 2. Also, the filter 82j has a filter 81j of 2
It is a filter to go around. Further, the filter 83j
Is a filter that applies the filter 81i three times.

Of the filters shown in FIG. 29, the filter 81k is a filter 81g when m is 2. Also, the filter 82k is equivalent to two filters 81k.
It is a filter to go around. Furthermore, filter 83k
Is a filter that applies the filter 81k three times.

Among the filters shown in FIG. 30, a filter 81m is a filter 81h when m is 2. Also, the filter 82m has two filters 81m.
It is a filter to go around. Furthermore, filter 83m
Is a filter that applies the filter 81m three times.

FIGS. 31 to 34 show frequency (Hz) on the horizontal axis.
FIG. 7 is a graph showing the relationship between the two, taking the spectrum value on the vertical axis. Each filter (filters 4-1 and 4
-2, 4-3, and 4-4) are spectral components of an arbitrary frequency (f ₀ ) and integer multiples of the frequency (2f ₀ ,
3f ₀ ,...) Are deleted or reduced. FIGS. 31 to 34 are obtained by continuously using the filters shown in FIGS. 19 to 22 and the filters shown in FIGS. 23 to 26, or by redefining 2f ₀ as f ₀ in the filters shown in FIGS. It was done. In other words, these filters are based on the filter expressed by the above equation 11 when m is 2 and Δt = m / 2f ₀ = 1 / f ₀ .

Of the filters shown in FIG. 31, a filter 81n is a filter 81a when m is 2. Also, the filter 82n has a filter 81n of 2
This is a filter that has been applied 0 times. Further, the filter 83n
Is a filter obtained by applying the filter 81n 50 times.

Of the filters shown in FIG. 32, a filter 81p is a filter 81b when m is 2. Also, the filter 82p has a filter 81p of 2
It is a filter to go around. Furthermore, filter 83p
Is a filter that applies the filter 81p three times.

Among the filters shown in FIG. 33, a filter 81q is a filter 81c when m is 2. Also, the filter 82q has the filter 81q
It is a filter to go around. Furthermore, the filter 83q
Is a filter that applies the filter 81q three times.

Of the filters shown in FIG. 34, a filter 81r is a filter 81d when m is 2. Also, the filter 82r is the same as the filter 81r.
It is a filter to go around. Further, the filter 83r
Is a filter that applies the filter 81r three times.

In order to eliminate only the wave of the fundamental frequency and the wave of a frequency that is an integral multiple of the fundamental frequency, it is preferable to make the filter rise steeply. FIG. 35 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis. The solid line shows the steep filter 81u, and the broken line shows in FIG. This is a filter 81n (filter 4-1). As shown in FIG. 35, a filter having a steep rise and a maximum value near 1.0 is preferable. Such a filter can be obtained by combining the filters shown in FIGS.

The filter 81s shown in FIG.
Were obtained by continuously applying the filter shown in FIG. That is, the filters 81a, 81g and 8
After applying 1i and reading 2f ₀ as f ₀ (m = 2), the filter 81i is continuously applied. The filter 81i after reading 2f ₀ as f ₀ is represented by 82 in the figure.
i.

Also, after setting m = 2 for the filter 81s shown in FIG. 36, the filter 81s shown in FIG.
After applying h and then setting m = 4, the filter 81g shown in FIG. 25 is applied, and after setting m = 4, the filter 81k shown in FIG. 29 is applied to obtain the filter 81t shown in FIG. As shown in FIG. 38, the rise of the filter 81t is extremely steep.

Note that the wave obtained by applying the filter 81i n times to the wave f (t) is f _A (t), and f _B (t) =
by calculating the _{f (t) -f A (t} ), f B (t) is f
(T) is obtained by applying the filter of FIG. 35 itself. The steepness of the filter increases as the number of times n increases.

Next, an embodiment of the present invention will be described.

First Embodiment Method By using various filters obtained as described above, the fundamental frequency of each wave included in the superimposed wave can be easily and accurately extracted. To specifically show how to use each of the above-described filters, consider six waves having fundamental frequencies close to each other, superimpose these waves, perform a filtering process on the obtained superimposed wave, and perform individual filtering. This shows that the frequency of the wave can be extracted. The fundamental frequency of the six waves is
2.5, 3.6, 4.7, 5.8, 6.9 and 8.2 kHz, respectively.

First, the sampling interval Δt of this superimposed wave
_s is set to 1.0 μs, and the number of sampling points N is set to 40
96. FIG. 39 shows the frequency (Hz) on the horizontal axis,
FIG. 7 is a graph showing the relationship between the two by taking the spectrum value on the vertical axis and showing the Fourier spectrum of the obtained superimposed wave. The spectrum shown in FIG. 39 is subjected to a filtering process using each of the above-described filters, and respective waves are extracted from the superimposed waves, and the fundamental frequencies of these waves are obtained. In the spectrum shown in FIG. 39, the peak value of the spectrum is small on the lower and higher order frequency sides. Therefore, the peaks on the lower and higher order frequencies are amplified. With respect to the spectrum shown in FIG. 39, the fundamental frequency f ₀ is set to 26.367 kHz.
As z, the filtering process is performed twice using a filter 81g (filter 2-3) shown in FIG.
Next, the fundamental frequency f ₀ is set to 15.625 kHz, a filtering process is performed using a filter 81g (filter 2-3) shown in FIG.
₀ was set to 85.499 kHz, and the filtering process was performed twice using the filter 81h (filter 2-4) shown in FIG. FIG. 40 is a graph showing the relationship between the frequency and the frequency on the horizontal axis and the spectrum value on the vertical axis, showing the spectrum obtained by a series of filtering processes. As shown in FIG. 40, the lowest order frequency can be easily read from its peak position, and the lowest order frequency is 2.5 kHz. The broken lines in FIG. 40 indicate positions that are integral multiples of 2.5 kHz, and there are spectral peaks at these positions.
Thereby, the frequency of 2.5 kHz can be known as the fundamental frequency of the wave having the smallest fundamental frequency among the waves included in the superimposed wave. The basic frequency f _{0 is set} to 2.5 kHz, and the filter 81i (filter 3-
By performing the filtering process 100 times using 1), a spectrum having a frequency of 2.5 kHz and an integer multiple of this frequency can be extracted. FIG.
It is a graph which shows the spectrum obtained by this filtering processing. Note that this filtering process was performed after deleting the spectrum of 1.5 kHz or less and 80 kHz or more. The dotted line in FIG. 41 indicates the superimposed wave shown in FIG. 40, that is, the superimposed wave before the filtering process.

Further, by sweeping from 2.5 kHz to the higher frequency side, the position where the spectrum peak exists can be known, and from this peak, the fundamental frequency of other waves included in the superimposed wave can be lowered. It can be taken out in order of frequency. Specifically, the fundamental frequencies of 3.6, 4.7, 5.8, 6.9 and 8.2 kHz can be extracted.

FIG. 42 shows that the fundamental frequency f ₀ is set to 3.6 kHz.
The filter 81i shown in FIG.
It is a graph which shows the spectrum obtained by performing filtering process 100 times using 1). FIG.
FIG. 28 is a graph illustrating a spectrum obtained by performing a filtering process 50 times using a filter 81i (filter 3-1) illustrated in FIG. 27 with a fundamental frequency f ₀ of 4.7 kHz. FIG. 44 shows that the fundamental frequency f ₀ is 5.8 k
FIG. 28 is a graph illustrating a spectrum obtained by performing a filtering process 30 times using a filter 81i (filter 3-1) illustrated in FIG. 27 at Hz. FIG.
28 is a graph showing a spectrum obtained by performing a filtering process 50 times using a filter 81i (filter 3-1) shown in FIG. 27 with a fundamental frequency f ₀ of 6.9 kHz. FIG. 46 shows that the fundamental frequency f _{0 is set} to 8.8.
FIG. 28 is a graph illustrating a spectrum obtained by performing a filtering process 50 times using a filter 81i (filter 3-1) illustrated in FIG. 27 at 2 kHz. In each figure, the frequency is 1.5 kHz or less and 80 kHz.
It is obtained by performing a filtering process after deleting the spectrum of Hz or higher. The dotted line in each figure indicates the superimposed wave shown in FIG. 40, that is, the superimposed wave before the filtering process. As shown in FIGS. 41 to 46, the fundamental frequency of each wave can be known for a large number of waves included in the superimposed wave by the filtering processing of the method of the present embodiment.

[0083] When the second embodiment the method is low fundamental frequency (2.5 kHz in the first embodiment the method
And 3.6 kHz), the fundamental frequency of each wave can be extracted relatively easily from a large number of waves constituting the superimposed wave by the method of the first embodiment. However, when the fundamental frequency f ₀ is large, many higher-order spectrums of other fundamental frequencies stand, and the spectrum of f ₀ is buried in this higher-order spectrum, and the fundamental frequency f ₀
Is difficult to take out. The method of the second embodiment is a filtering processing method applicable to such a case.

The method of the second embodiment will be described using the same superimposed wave as in the method of the first embodiment. First, similarly to the method of the first embodiment, the spectra on the lower and higher order frequencies are amplified. The amplification conditions are the same as in the first embodiment. Next, low frequency fundamental frequencies (2.5 and 3.6 kHz) are found in advance by the method of the first embodiment. For each of the fundamental frequencies 2.5 and 3.6 kHz, FIG.
The filtering process was performed using the filter 81n (filter 4-1) shown in FIG. Note that this filtering process was performed after deleting the spectrum of 1.5 kHz or less and 80 kHz or more. FIG. 47 is a graph showing the relationship between the vibration frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectrum obtained by this series of processing. The dotted line in FIG. 47 indicates the superimposed wave shown in FIG. 40, that is, the superimposed wave before the filtering process. According to FIG. 47, there is a high peak at a position where the frequency is 4.7 kHz, and 4.7 kHz from this peak.
Is one of the fundamental frequencies. However, 4.7
There is a case where a peak does not exist at a position of an integral multiple of kHz or the peak value is small even if it exists. For example, 3
The next term (14.1 kHz), the sixth order (28.2 kHz), the seventh order (32.9 kHz), and the like. This is for the following reason.

The third-order term (14.1 kHz) is very close to the fourth-order term (14.4 kHz) of a wave having a fundamental frequency of 3.6 kHz, and the sixth-order term (28.2 kHz) has a fundamental frequency of 3.6 kHz.
Hz wave is very close to the 8th order term (28.8 kHz),
The next term (32.9 kHz) is a 13th-order term (32.5 kHz) and a fundamental frequency of 3.6 kHz of a wave having a fundamental frequency of 2.5 kHz.
It is very close to the 9th order term (32.4 kHz) of the Hz wave. For this reason, when filtering processing is performed for the fundamental frequencies of 2.5 and 3.6 kHz, respectively, the higher-order terms of the fundamental frequency of 4.7 kHz (third-order) together with the higher-order terms of 2.5 and 3.6 kHz are obtained. , 6th and 7th order) spectra are also deleted. However, 4.7 kHz
Since all of the higher-order spectrums are not deleted, as shown in FIG. 47, for 4.7 kHz and higher-order spectrums other than those described above, the fundamental frequencies of one or more waves have already been obtained. Even after removing this wave, it is still present in the spectrum. Thereby, 4.7 kHz
Is one of the fundamental frequencies.

According to the same procedure, the fundamental frequency can be determined sequentially from the low fundamental frequency. FIG.
Is a filter 81n (filter 4-
This is a spectrum obtained by using 1) and eliminating waves due to the fundamental frequencies of 2.5, 3.6, and 4.7 kHz and their higher-order spectra. As can be seen from FIG. 48, 5.8 kHz is one of the fundamental frequencies.

FIG. 49 is a spectrum from which waves at the fundamental frequencies of 2.5, 3.6, 4.7 and 5.8 kHz and their higher-order terms have been eliminated. The fundamental frequencies of 2.5, 3.6, and 4.7 kHz and the waves due to the higher-order terms are eliminated using the filter 81n (filter 4-1) shown in FIG. And the wave of the higher order spectrum was deleted using the filter (filter 4-5) shown in FIG. As can be seen from FIG. 49, 6.9 kHz is one of the fundamental frequencies.

FIG. 50 shows 2.5, 3.6, 4.7, 5.
This is a spectrum from which waves due to the fundamental frequencies of 8 and 6.9 kHz and higher order spectra thereof have been deleted. 2.5,
The fundamental frequency of 3.6 and 4.7 kHz and the wave of the higher order spectrum are converted into the filter 81n shown in FIG.
(Filter 4-1) and then 5.8
The wave with the fundamental frequency of kHz and its higher-order spectrum is deleted using the filter (filter 4-5) shown in FIG. 36, and the wave with the fundamental frequency of 6.9 kHz and its higher-order spectrum is shown in FIG. Filter 81 shown
n (filter 4-1). As shown in FIG. 50, it can be seen that 8.2 kHz is one of the fundamental frequencies.

As described above, by sequentially performing the filtering process, the fundamental frequency of the wave included in the superimposed wave can be determined. Also, by performing a filtering process many times using the filter 81n (filter 4-1) shown in FIG. 31 at each fundamental frequency, only the fundamental frequency of this wave and its higher-order spectrum are extracted. The spectrum of other frequencies can be deleted. FIG. 51 shows that the fundamental frequency f ₀ is 8.2 kHz, and the filtering process is performed 100 times on the dotted spectrum shown in FIG. 50 using the filter 81n (filter 4-1) shown in FIG. FIG. 7 is a graph showing the obtained spectrum. As shown in FIG. 51, by using the filter shown in FIG. 31 many times, it is possible to extract only the spectrum of the fundamental frequency (8.2 kHz).

In FIGS. 49 and 50, the filter (filter 4) shown in FIG. 36 is used to delete the spectrum having the fundamental frequency of 5.8 kHz and the spectrum of the higher order terms.
-5) was used. This is for the following reason. FIG.
As shown in (1), there are many spectral peaks near the fundamental frequency of 5.8 kHz and the seventh order (40.6 kHz) of this frequency. For this reason, it is necessary to delete only the fundamental frequency and the spectrum of the higher-order term of this frequency, and to leave the nearby spectrum as much as possible. However,
In the filter 81n (filter 4-1) shown in FIG. 31, the fundamental frequency and the spectrum of the higher-order term of the frequency are deleted together with the spectrum in the vicinity thereof. Therefore, a filter 81s (filter 4-
5) was used. Because this filter is steep,
Only the fundamental frequency and the spectrum of the higher-order term of this frequency can be deleted, and the spectrum of the other part can be left.

The above two embodiments have been described. The functions of each filter are summarized below.

The filters shown in FIGS.
1-1, 1-2, 1-3, 1-42-1, 2-2,
2-3 and 2-4) The filters shown in FIGS. 19 to 26 are used to increase the spectral value having a small peak value or decrease the spectral value having a large peak value, as shown in FIG. . By performing such a filtering process in advance, the subsequent filtering process is facilitated.

The filters shown in FIGS.
3-1 and 3-2, 3-3 and 3-4) The filters shown in FIGS. 27 to 30 can be used for the same purpose as the filters shown in FIGS. In addition, the filters shown in FIGS. 27-30 can be used to extract the spectrum of the fundamental frequency and its higher order terms.

The filters shown in FIGS.
Tars 4-1 4-2, 4-3 and 4-4) The filters shown in FIGS. 31 to 34 can be used to eliminate or reduce the spectrum of the fundamental frequency and its higher order terms.

FIG . 35 (filter 4-7) and FIG.
Filter (filter 4-5) and the filter shown in FIG.
Filter (Filter 4-6) The filter shown in FIGS.
It has almost the same function as the filters shown in FIGS.
However, the filters shown in FIG. 35, FIG. 36 and FIG.
Even when the spectrum of the other fundamental frequency and the spectrum of the higher order term of this fundamental frequency exist near the spectrum of the fundamental frequency, the spectrum of the other fundamental frequency and the higher order term of this fundamental frequency The spectrum of the fundamental frequency and its higher-order terms can be deleted or reduced while preventing the spectrum from being reduced.

Although the functions of the filters shown in FIGS. 31 to 34 are as described above, the filtering process shown in FIG. 35 is not performed repeatedly on the time series wave shown in FIG. Is artificially created, and the Fourier spectrum of the time-series wave is directly filtered using this filter, so that the spectra shown in FIGS. 47 and 48 can be obtained. By directly filtering the spectrum instead of the time-series wave as described above, the filtering processing time can be reduced, and the filter shape can be arbitrarily set.

As shown in FIGS. 41 to 46, FIG.
By using the filter 81i (filter 3-1) shown in FIG. 7 and performing the filtering process 30 to 150 times continuously, the spectrum of each fundamental frequency and its higher-order terms can be extracted. The filter 81i (filter 3-1) shown in FIG. 27 or a filter similar to the filter 81i is applied about 150 times to create a new filter, and using this filter, FIG.
By directly filtering the spectrum of 0, spectra similar to the spectra shown in FIGS. 41 to 46 can be obtained. In this case, the operation time required for the filtering process can be significantly reduced.

The filter has been described with reference to a plurality of drawings. However, the filter is not limited to this, and various filters can be used as needed.

Next, a superimposed wave filtering processing device used for the above-described filtering processing will be described. FIG. 52 is a schematic diagram illustrating a superimposed wave filtering processing device according to an embodiment of the present invention. As shown in FIG. 52, the elastic wave reception sensor 71 is connected to the A / D converter 72. The elastic wave received by the receiving sensor 71 is converted into an electric signal, and the electric signal is converted into a digital signal by the A / D converter 72. A
The / D converter 72 is a personal computer or EW
Computer 73 such as S (Engineering Workstation)
, And a CRT (display device) 74 and a DISK (auxiliary storage device) 75 are connected to the computer 73. As a result, the digital signal is
3 and displayed on the CRT 74 and DI
It is stored in the SK75. The computer 73 is connected to a filtering device 76. The filtering device 76 includes a filtering CPU 77 and a memory 78. The filtering device 73 fetches a digital signal from the computer 73 by DMA (Direct Memory Access) transfer, and performs filtering processing of the digital signal at a very high speed by the filtering CPU 77. The elastic wave oscillation sensor (not shown) is provided at a predetermined location.

In the superimposed wave filtering processing apparatus thus configured, an elastic wave is oscillated from the elastic wave oscillation sensor, and this elastic wave is reflected by a target object or the like, and the reflected wave is received by the reception sensor 71 as the reception wave 79. I do. The reception sensor 71 converts the obtained reception wave 79 into an electric signal. The electric signal is converted into a digital signal by an A / D converter and transmitted to the computer 73. The computer 73 processes this digital signal and converts the received wave 79 to C
The data of the received wave 79 is displayed on the RT 75 and stored in the DISK 74. The data of the received wave 79 is sent to the filtering device 76, and the data is written to the memory 78. Under the control of the computer 73, the data is filtered at a very high speed by the filtering CPU 77, and the obtained result is returned to the computer 73. As a result, the fundamental frequency of each of many waves constituting the reception wave 79 is determined. As described above, by performing the filtering process, the filtering process can be performed at a high speed, and the filtering process of many received waves 79 can be performed.

Next, a case where the above-described filtering method is applied to reinforced concrete will be described. FIG. 53 is a schematic diagram showing a reinforced concrete model. As shown in FIG. 53, the width of the reinforced concrete 1 is 1
000 mm, and the distance from the upper surface 2 to the lower surface 8 is 300 mm. A crack 3 is formed at a substantially central portion of the upper surface 2 of the reinforced concrete 1 from the upper surface 2 in a depth direction. The depth of the crack 3 is 195 mm. A reinforcing bar 4 is embedded at a depth of 45 mm from the upper surface 2 so as to be perpendicular to the crack 3. Also, at a position 250 mm deep from the upper surface 2, the reinforcing bar 5 is cracked 3.
It is embedded so that it is perpendicular to. On both sides of the crack 3 on the upper surface 2, an elastic wave oscillation sensor 6 and a reception sensor 7
Is installed, and the oscillation sensor 6 and the reception sensor 7 are connected to the above-described filtering processing device (not shown).

In the reinforced concrete model thus configured, an elastic wave is oscillated from the oscillation sensor 6, an elastic wave caused by the elastic wave is received by the receiving sensor 7, and the received elastic wave is subjected to filtering processing. did. FIG.
4 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the relationship between the two. The oscillation wave oscillated by the oscillation sensor 6 and the superimposed wave obtained by the reception sensor 7 are shown. FIG. 4 is a diagram showing a Fourier spectrum of the. The oscillation wave is indicated by a dotted line, and the superimposed wave is indicated by a solid line. As shown in FIG. 54, the largest peak of the oscillating wave substantially matches the largest peak of the received wave, and the spectrum of the received superimposed wave is greatly affected by the spectrum of the oscillating wave. To amplify the low frequency and high frequency spectra using the filtering device described above, FIG.
The spectrum shown in FIG. 4 was filtered. FIG. 55 is a graph showing an oscillation wave and a reception wave after the filtering process. As in FIG. 54, the oscillating wave is indicated by a dotted line, and the received wave is indicated by a solid line. As shown in FIG. 55, when the oscillation wave shown by the dotted line is oscillated, the reception wave shown by the solid line is obtained. Table 1 below shows the history of this filtering process. In this filtering process, the order of each filtering process and the type of filter are arbitrary.

[0103]

[Table 1] The numbers in parentheses in Table 1 above indicate filter numbers and symbols.

Next, the received wave shown in FIG. 55 is subjected to filtering processing, and the fundamental frequency of each wave is determined for a large number of waves constituting the received wave. First, before performing the filtering process, the Fourier spectrum is swept from the low frequency side, and it is examined whether or not there is a peak at a position of the fundamental frequency and a frequency of an integral multiple thereof. FIG. 56 is a graph showing a frequency of 4.679 kHz and a position of a frequency that is an integral multiple of the frequency. As shown by the broken line in FIG. 56, a spectrum peak exists at a position of a frequency that is an integral multiple of 4.679 kHz. This gives 4.679
It can be seen that kHz is one of the fundamental frequencies. Similarly, by sweeping the Fourier spectrum, 6.1
Peaks can be found at frequencies of 42, 6.703 and 7.814 kHz and at integer multiples of these frequencies. Thereby, 6.142, 6.703, and 7.
It can be seen that 814 kHz is the fundamental frequency. Fig. 57
FIG. 4 is a graph showing the position of a frequency of 6.703 kHz and a frequency that is an integral multiple of the frequency. FIG. 58 is a graph showing the frequency of 7.814 kHz and the position of the frequency that is an integral multiple of this frequency.

When the frequency is further swept to the higher frequency side of the Fourier spectrum, a higher-order term spectrum is established at an integer multiple of the above-mentioned fundamental frequency, and the spectrum having a higher fundamental frequency is buried. For this reason, it is difficult to find all of the fundamental frequencies by sweeping, and a great deal of trial and error and processing time is required. Therefore, the spectrum of the low frequency fundamental frequency and the spectrum of its higher order terms are deleted by the filtering process shown in the method 2 of the embodiment, and the fundamental frequency of the high frequency is determined. Figure 59
Is a 4.679kHz has already been determined the fundamental frequency f _0, filter 81n (filter shown in FIG. 31 4-
It is a graph which shows the spectrum of the wave obtained by performing a filtering process using 1) and this result . In addition,
Dotted lines indicate spectra before the filtering process is performed. As shown in FIG. 59, the frequency is 4.679 kHz.
The spectrum of z and the spectrum of the higher-order term are deleted, and the position of each peak in the spectrum after the filtering process is much clearer than the spectrum before the filtering process. Therefore, it is easy to find the fundamental frequency on the high frequency side, and by sweeping the high frequency side of the spectrum, the frequency becomes 10.094 k.
The fundamental frequency in Hz can be found. FIG. 60 is a graph showing the positions of a frequency of 10.094 kHz and a frequency that is an integral multiple of this frequency. As shown in FIG.
A spectrum peak exists at a frequency of 10.094 kHz and a frequency that is an integral multiple of this frequency.

As described above, the spectrum of the fundamental frequency having a low frequency and the spectrum of the higher-order terms thereof are sequentially deleted by the filtering process. FIGS. 61 to 64 are graphs showing spectra and fundamental frequencies obtained by this processing. As shown by the dotted lines in FIGS. 61 to 64,
11.721, 13.085, 35.726 and 45.
It can be seen that 003 kHz is one of the fundamental frequencies.
Table 2 below shows the history of the filtering process performed until the spectra shown in FIGS. 61 to 64 were obtained.

[0107]

[Table 2] The numbers in parentheses in Table 2 above indicate filter numbers and symbols.

Also, the spectrum of each fundamental frequency can be clarified by using the filter 81i (filter 3-1) shown in FIG. FIG. 65 is a graph showing a spectrum obtained by performing a filtering process 50 times with a fundamental frequency of 4.679 kHz. FIG.
6 is a graph showing a spectrum obtained by performing a filtering process 50 times with a fundamental frequency of 6.142 kHz. FIG. 67 shows that the fundamental frequency is 6.703 kHz.
FIG. 7 is a graph showing a spectrum obtained by performing filtering processing 50 times, where z is set. FIG. 68 shows that the fundamental frequency is 7.814 kHz and the filtering process is 50
It is a graph which shows the spectrum obtained by performing twice.
FIG. 69 is a graph showing a spectrum obtained by setting the fundamental frequency to 10.094 kHz and performing the filtering process 150 times. FIG. 70 shows that the fundamental frequency is set to 11.
FIG. 9 is a graph showing a spectrum obtained by performing filtering processing 150 times at 721 kHz. Figure 71
FIG. 4 is a graph showing a spectrum obtained by performing a filtering process 150 times with a fundamental frequency of 13.085 kHz. FIG. 72 is a graph showing a spectrum obtained by performing the filtering process shown in Table 3 below.

[0109]

[Table 3] The numbers in parentheses in Table 3 above indicate filter numbers and symbols.

As shown in FIGS. 65 to 71, the spectrum of each fundamental frequency can be clarified by performing a filtering process on each fundamental frequency. Also,
As shown in FIG. 72, the filter 81i shown in FIG.
After performing a filtering process using (filter 3-1), a filter 81j (filter 3-j) shown in FIG.
2), the spectral value of the fundamental frequency (35.726 kHz) is amplified,
The spectrum is easier to see.

By knowing the fundamental frequency of each of a large number of waves included in the superimposed wave by the method of the embodiment described above, various information can be obtained from the frequencies.
For example, in the case of the reinforced concrete model shown in FIG. 53, the position of the reinforcing bar in the concrete can be known from the fundamental frequency. When the elastic wave 14 oscillates from the oscillation sensor 6 and reaches the object in the concrete 1, for example, the reinforcing bar 4, a part of the wave is reflected by the reinforcing bar 4, and the reflected wave is received by the receiving sensor 7. You. Figure 73
FIG. 4 is a schematic diagram showing a state where a reflected wave is observed by a receiving sensor. As shown in FIG. 73, the oscillation sensor 6 and the receiving sensor 7 are set at a location away from the object 13. The distance between the oscillation sensor 6 and the reception sensor 7 and the object 13 is d. An elastic wave 14 is oscillated from the oscillation sensor 6,
A part of the elastic wave 14 is reflected by the object 13 and becomes the reflected wave 12. This reflected wave 12 is received by the reception sensor 7. When the medium between the oscillation sensor 6 and the receiving sensor 7 and the object 13 is a solid, the sound velocity of the solid (elastic body velocity)
Is V and the fundamental frequency of the reflected wave is f ₀ , d
Is represented by Equation 17 below.

[0112]

## EQU17 ## 2d = V / f ₀

In the above equation (17), the above fundamental frequency (4
5.003, 35.726, 10.094, 7.814
And 6.703 kHz), the position of an object such as a reinforcing bar in the concrete can be known.

FIG. 74 is a schematic diagram showing the relationship between each fundamental frequency and the position of an object in concrete. 74, the same components as those in FIG. 53 are denoted by the same reference numerals, and detailed description thereof will be omitted. A semicircle 21 (21a, 21b, 21c, 21c) centered on the oscillation sensor 6 and the reception sensor 7 in FIG.
21d, 21e) are drawn, and this semicircle 21 has a fundamental frequency of 45.00, 35.73, 10.09, 7.8.
1 and 6.70 kHz are each substituted into Expression 17 to show the obtained distance d. From the semicircles 21a and 21b, the depth and diameter of the reinforcing bar 4 can be known,
The depth of the tip 3a of the crack 3 can be known from c.
The depth of the reinforcing bar 5 can be known from the semicircle 21d, and the position of the lower surface of the concrete can be known from the semicircle 21e.

Next, as another example of the filtering process,
This shows a system for measuring the length of piles buried underground.
FIG. 75A is a schematic diagram showing this measurement system. As shown in FIG. 75 (a), a pile 31 is buried in the underground 33. The upper surface 32 of the pile 31 exists above the ground surface 34. The oscillation sensor 6 and the reception sensor 7 are installed on the upper surface 32, and are connected to a filtering processing device (not shown).

In the measuring system thus configured, an elastic wave is oscillated from the oscillation sensor 6, and when this wave reaches the tip 35 of the pile 31, a part of this wave is
The reflected wave is received by the reception sensor 7. The received wave (reflected wave) is filtered by the above-described filtering processing device, and for a number of waves constituting the received wave (reflected wave), these fundamental frequencies are derived from the received wave, and this fundamental frequency is calculated. By substituting into the above equation 17, the length d of the pile can be known.

FIG. 75 (b) is a schematic diagram showing a measuring system for measuring the position of the fractured surface when the pile buried in the ground is broken. In FIG. 75 (b), the same components as those in FIG. 75 (a) are denoted by the same reference numerals, and detailed description thereof will be omitted. As shown in FIG. 75 (b), the stake 31 has a broken portion 36 formed at a substantially central portion thereof, and the stake 31 allows the pile 31 to be connected to the upper stake 31a and the lower stake 31b. It is broken. In this case, an elastic wave is oscillated from the oscillation sensor 6, and this wave is generated by the fracture surface 36 of the pile 31a.
When the wave reaches a, a part of the wave is reflected by the fracture surface 36a, and the reflected wave is received by the reception sensor 7. The received wave (reflected wave) is subjected to filtering processing by the above-described filtering processing device, and for a large number of waves constituting the received wave (reflected wave), a fundamental frequency of each wave is derived. By substituting into 17, the length of the pile 31a, that is, the length d 'from the upper surface 32 of the pile 31 to the fracture surface 36a can be known.

FIG. 76 is a schematic diagram showing a measurement system for measuring the shape of a structure buried underground. FIG.
As shown in FIG. 6, a structure 41 is buried in the underground 44, and a large number of oscillation sensors 6 and receiving sensors 7 are installed on the ground surface 45. These oscillation sensor 6 and reception sensor 7 are connected to a filtering processing device (not shown).

In the measurement system thus configured, an elastic wave 43 is oscillated from the oscillation sensor 6, and when this wave reaches the outer surface 42 of the structure 41, a part of the wave is reflected by the outer surface 42. The reflected wave is received sensor 7
Is received by The received wave is filtered by the above-described filtering processing device, the fundamental frequency of the reflected wave is derived from the received wave, and the fundamental frequency is substituted into the above equation (17). Such measurement is performed by each oscillation sensor 6.
In addition, the shape of the structure 41 can be known by performing the operation on the reception sensor 7.

FIG. 77 is a schematic diagram showing a measuring system of a steel column shear breaking position. As shown in FIG.
1 is joined to the steel frames 52a and 52b by a welded portion 56. The steel frame 52a is fixed to the plate 54 by bolts 53a.
a is connected to the steel frame 52c through the
Is connected to a steel frame 52d by a bolt 53b via a plate 54b.
It is connected to the. The steel frame 51 is broken into a steel frame 51a and a steel frame 51b at a substantially central portion. However, although the fracture surface 55 is illustrated in an enlarged manner in the drawing, it is difficult to visually confirm the actual fracture surface 55. Steel frame 51
The oscillation sensor 6 and the reception sensor 7 are provided on the side surface of “a”. These oscillation sensor 6 and reception sensor 7
It is connected to a filtering processing device (not shown).

In the measuring system thus configured, an elastic wave is oscillated from the oscillation sensor 6, and when this wave reaches the fracture surface 55, a part of this wave is reflected by the fracture surface 55 and is reflected. The waves are received by the receiving sensor 7. The received wave is filtered by the above-described filtering processing device, the fundamental frequency of the reflected wave is derived from the received wave, and the fundamental frequency is substituted into the above equation (17). The length d _{2 up} to the fracture surface 55 can be known, and the fracture surface 55
Can be specified.

FIG. 78 is a schematic diagram showing a system for searching for an underground structure. In the underground 65, a manhole 61 and a cave 62 are buried. As shown in FIG. 78, on the ground 66, a pair of oscillation sensors 6 and a reception sensor 7a are installed.
b, 7c and 7d are provided. These oscillation sensor 6 and reception sensor 7 (7a, 7b, 7c, 7d) are connected to a filtering processing device (not shown).

In the exploration system configured as described above, an elastic wave 63 is oscillated from the oscillation sensor 6, and when this wave reaches the manhole 61 or the sinus 62, a part of the wave is reflected by these structures. The reflected wave 64 is received by the receiving sensor 7 (7a, 7b, 7c, 7d). Each received wave is subjected to a filtering process by the above-described filtering processing device to derive a fundamental frequency of each received wave. Based on the fundamental frequency of each reception wave obtained by each reception sensor 7 (7a, 7b, 7c, 7d), each reception sensor 7 (7a, 7
b, 7c, 7d) and the distance between the manhole 61 and the tunnel 62 are calculated. Since the receiving sensors 7 are provided at a plurality of locations, each receiving sensor 7 and the manhole 61 and the sinus 62
The positions of the manhole 61 and the cave 62 can be specified from the distance to.

As described above, the filtering processing method according to the present embodiment can be used for position measurement, but the application of the filtering processing method is not limited to this. Can be used for For example, it can be used for internal see-through of porous materials such as reinforced concrete and ground, internal see-through of quasi-porous materials such as pottery, and internal see-through of homogeneous materials such as iron, aluminum and other metal materials. Further, it can be used for extracting a signal such as voice buried in noise.

[0125]

As described above, according to the superimposed wave filtering processing method according to the present invention, of the components constituting the received superimposed wave, the component having the predetermined frequency and the component of the odd multiple of this frequency are used. Is amplified, and the components of even multiples of this frequency are reduced or deleted, so even if the superimposed wave has a complicated shape, for each of the plurality of waves constituting the superimposed wave, The fundamental frequency can be accurately determined, and the accuracy of position measurement and the like using elastic waves can be improved.

According to another superimposed wave filtering method according to the present invention, of the components constituting the received superimposed wave, the component of the predetermined frequency and the frequency of an odd multiple of this frequency are deleted or reduced. Since the component of the even-numbered frequency of this frequency is amplified, even when the superimposed wave has a complicated shape, the fundamental frequency of the wave constituting the superimposed wave can be accurately determined, Accuracy such as position measurement using an elastic wave can be improved.

The superimposed wave filtering processing device according to the present invention comprises an elastic wave oscillation sensor, an elastic wave reception sensor,
Since there is a signal analyzer for filtering the superimposed wave received by the receiving sensor, the superimposed wave can be filtered in an extremely short time.

[Brief description of the drawings]

FIG. 1A is a graph showing the relationship between the time t (second) on the horizontal axis and the superimposed wave f (t) on the vertical axis, and FIG. 1B shows the time t (second) on the horizontal axis. FIG. 10 is a graph showing the relationship between the two, with the superimposed wave f (t + Δt) being plotted on the vertical axis, taking (seconds).

FIG. 2 is a diagram showing the relationship between the time t (second) on the horizontal axis and the amplitude on the vertical axis, where the solid line indicates each sin (2nπt) constituting f (t), and the broken line indicates f (t + Δt)
Are represented by sin {(2nπ (t + Δt)}.

FIG. 3 is a graph showing G ₁ (t).

FIG. 4 is a graph showing each n component of G ₁ (t).

FIG. 5 is a graph showing G ₂ (t).

FIG. 6 is a graph showing each n component of G ₂ (t).

7A is a graph showing the relationship between the time t (second) on the horizontal axis and the superimposed wave f (t) on the vertical axis, and FIG. 7B is a graph showing the time t on the horizontal axis. FIG. 10 is a graph showing the relationship between the two, with the superimposed wave f (t + Δt) being plotted on the vertical axis, taking (seconds).

FIG. 8 shows time t (seconds) on the horizontal axis and superimposed wave f on the vertical axis.
It is a figure which shows each relationship by taking each n component (frequency n) of (t) and f (t + (DELTA) t), the solid line shows the fundamental frequency wave sin (2n (pi) t) of f (t), and the broken line shows f (t). (T + Δ
t) shows the fundamental frequency wave sin {(2nπ (t + Δt)}).

FIG. 9 is a graph showing G ₁ (t).

FIG. 10 is a graph showing each n component of G ₁ (t).

FIG. 11 is a graph showing G ₂ (t).

FIG. 12 is a graph showing each n component of G ₂ (t).

FIG. 13 shows Σ (n = 1, k) sin (2nπt)
FIG. 7 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis.

FIG. 14 is a diagram showing spectrum values obtained by applying Equation 2 to FIG. 13, and a graph showing the relationship between the two by taking the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis. FIG.

FIG. 15 is a diagram showing spectrum values obtained by applying Equation 3 to FIG. 13. FIG. 15 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis. FIG.

FIG. 16 is a graph showing the relationship between time t (seconds) on the horizontal axis and amplitude on the vertical axis.

17 (a) and (b) show f (t) and F, respectively.
₁ is a Fourier spectrum of (t), a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis.

FIGS. 18A and 18B show f (t) and F, respectively.
₂ is a Fourier spectrum of FIG. ₂ (t), in which a horizontal axis indicates a frequency (Hz) and a vertical axis indicates a spectrum value, showing a relationship between the two.

FIG. 19 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the odd number of this frequency. Amplify the spectral components of the over-multiplied frequencies (3f ₀ , 5f ₀ ,...), And obtain the even-multiplied frequencies (2f ₀ , 4f ₀ ,.
It is a figure which shows the filter which deletes or reduces the spectrum component of ()).

FIG. 20 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the odd number of this frequency. Amplify the spectral components of the over-multiplied frequencies (3f ₀ , 5f ₀ ,...), And obtain the even-multiplied frequencies (2f ₀ , 4f ₀ ,.
It is a figure which shows the filter which deletes or reduces the spectrum component of ()).

FIG. 21 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the odd number of this frequency. Amplify the spectral components of the over-multiplied frequencies (3f ₀ , 5f ₀ ,...), And obtain the even-multiplied frequencies (2f ₀ , 4f ₀ ,.
It is a figure which shows the filter which deletes or reduces the spectrum component of ()).

FIG. 22 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the odd number of this frequency. Amplify the spectral components of the over-multiplied frequencies (3f ₀ , 5f ₀ ,...), And obtain the even-multiplied frequencies (2f ₀ , 4f ₀ ,.
It is a figure which shows the filter which deletes or reduces the spectrum component of ()).

FIG. 23 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the odd number of this frequency. The spectral components of the multiple frequencies (3f ₀ , 5f ₀ ,...) Are deleted or reduced, and the even multiple frequencies (2f ₀ , 4f ₀ ,
FIG. 7 is a diagram illustrating a filter that amplifies the spectral components of...

FIG. 24 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the odd number of this frequency. The spectral components of the multiple frequencies (3f ₀ , 5f ₀ ,...) Are deleted or reduced, and the even multiple frequencies (2f ₀ , 4f ₀ ,
FIG. 7 is a diagram illustrating a filter that amplifies the spectral components of...

FIG. 25 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the odd number of this frequency. The spectral components of the multiple frequencies (3f ₀ , 5f ₀ ,...) Are deleted or reduced, and the even multiple frequencies (2f ₀ , 4f ₀ ,
FIG. 7 is a diagram illustrating a filter that amplifies the spectral components of...

FIG. 26 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the odd number of this frequency. The spectral components of the multiple frequencies (3f ₀ , 5f ₀ ,...) Are deleted or reduced, and the even multiple frequencies (2f ₀ , 4f ₀ ,
FIG. 7 is a diagram illustrating a filter that amplifies the spectral components of...

FIG. 27 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing a spectrum component of an arbitrary frequency (f ₀ ) and an integer of this frequency. times frequency _{(2f 0, 3f 0, ·····} ) is a diagram illustrating a filter for amplifying the spectral components.

FIG. 28 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing a spectrum component of an arbitrary frequency (f ₀ ) and an integer of this frequency. times frequency _{(2f 0, 3f 0, ·····} ) is a diagram illustrating a filter for amplifying the spectral components.

FIG. 29 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the integer of this frequency. times frequency _{(2f 0, 3f 0, ·····} ) is a diagram illustrating a filter for amplifying the spectral components.

FIG. 30 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing a spectrum component of an arbitrary frequency (f ₀ ) and an integer of this frequency. times frequency _{(2f 0, 3f 0, ·····} ) is a diagram illustrating a filter for amplifying spectral components.

FIG. 31 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing a spectrum component of an arbitrary frequency (f ₀ ) and an integer of this frequency. times frequency _{(2f 0, 3f 0, ·····} ) is a diagram illustrating a filter for or reduce to remove spectral components.

FIG. 32 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the integer of this frequency. times frequency _{(2f 0, 3f 0, ·····} ) is a diagram illustrating a filter for or reduce to remove spectral components.

FIG. 33 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing a spectrum component of an arbitrary frequency (f ₀ ) and an integer of this frequency. times frequency _{(2f 0, 3f 0, ·····} ) is a diagram illustrating a filter for or reduce to remove spectral components.

FIG. 34 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the spectral component of the arbitrary frequency (f ₀ ) and the integer of this frequency. times frequency _{(2f 0, 3f 0, ·····} ) is a diagram illustrating a filter for or reduce to remove spectral components.

FIG. 35 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis. The solid line indicates the steep filter, and the broken line indicates the filter shown in FIG. It is.

FIG. 36 is a graph showing a filter obtained by continuously applying the filter shown in FIG. 37.

FIG. 37 is a graph showing a filter obtained by continuously applying the filters shown in FIGS. 19 to 34;

FIG. 38 is a graph showing a filter obtained by continuously applying the filter shown in FIG. 36.

FIG. 39 is a graph showing the relationship between the vibration frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the Fourier spectrum of the obtained superimposed wave.

FIG. 40 is a graph showing the relationship between the vibration frequency and the spectrum value on the horizontal axis and the spectrum value on the vertical axis, showing the spectrum obtained by a series of filtering processes.

FIG. 41 is a graph showing a spectrum obtained by the filtering process.

FIG. 42 shows a case where the fundamental frequency f ₀ is set to 3.6 kHz and FIG.
Use the filter shown in
It is a graph which shows the spectrum obtained by performing 0 times.

FIG. 43 shows a case where the fundamental frequency f ₀ is set to 4.7 kHz;
Use the filter shown in
It is a graph which shows the spectrum obtained by performing twice.

FIG. 44 shows a case where the fundamental frequency f ₀ is 5.8 kHz;
Filtering is performed using the filter shown in
It is a graph which shows the spectrum obtained by performing twice.

FIG. 45: The fundamental frequency f ₀ is set to 6.9 kHz, and FIG.
Use the filter shown in
It is a graph which shows the spectrum obtained by performing twice.

FIG. 46 shows a case where the fundamental frequency f ₀ is 8.2 kHz and FIG.
Use the filter shown in
It is a graph which shows the spectrum obtained by performing twice.

FIG. 47 is a graph showing the relationship between the vibration frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing a spectrum obtained by a series of filtering processes.

FIG. 48: Using the filter shown in FIG.
It is a graph which shows the spectrum from which the fundamental frequency of 3.6 and 4.7 kHz was deleted.

FIG. 49 is a graph showing a spectrum from which fundamental frequencies of 2.5, 3.6, 4.7 and 5.8 kHz have been deleted.

FIG. 50: 2.5, 3.6, 4.7, 5.8 and 6.9
It is a graph which shows the spectrum from which the fundamental frequency of kHz was deleted.

FIG. 51 shows a case where the fundamental frequency f ₀ is 8.2 kHz;
32 is a graph showing a spectrum obtained by performing a filtering process 100 times on the spectrum shown in FIG. 31 using the filter shown in FIG. 31.

FIG. 52 is a schematic diagram showing a superimposed wave filtering processing device according to an embodiment of the present invention.

FIG. 53 is a schematic view showing a reinforced concrete model.

54 is a graph showing the relationship between the frequency (Hz) on the horizontal axis and the spectrum value on the vertical axis, showing the relationship between the oscillation wave oscillated by the oscillation sensor 6 and the reception obtained by the reception sensor 7. FIG. It is a figure showing the Fourier spectrum of a wave.

FIG. 55 is a graph showing an oscillating wave and a received wave after the filtering processing.

FIG. 56 is a graph showing a frequency of 4.679 kHz and a position of a frequency that is an integral multiple of the frequency.

FIG. 57 is a graph showing a frequency of 6.703 kHz and a position of a frequency that is an integral multiple of the frequency.

FIG. 58 is a graph showing a frequency of 7.814 kHz and a position of a frequency that is an integral multiple of the frequency.

FIG. 59: 4.679k for which basic frequency f ₀ has already been determined
Hz and the filter shown in FIG.
1 is a graph showing a spectrum obtained by performing a filtering process using reference numeral 81n).

FIG. 60 is a graph showing a frequency of 10.094 kHz and a position of a frequency that is an integral multiple of the frequency.

FIG. 61 is a graph showing a spectrum and a fundamental frequency obtained by the filtering process.

FIG. 62 is a graph showing a spectrum and a fundamental frequency obtained by a filtering process.

FIG. 63 is a graph showing a spectrum and a fundamental frequency obtained by the filtering process.

FIG. 64 is a graph showing a spectrum and a fundamental frequency obtained by a filtering process.

FIG. 65 is a graph showing a spectrum obtained by performing a filtering process 50 times with a fundamental frequency of 4.679 kHz.

FIG. 66 is a graph showing a spectrum obtained by performing a filtering process 50 times with a fundamental frequency of 6.142 kHz.

FIG. 67 is a graph showing a spectrum obtained by performing a filtering process 50 times with a fundamental frequency of 6.703 kHz.

FIG. 68 is a graph showing a spectrum obtained by performing a filtering process 50 times with a fundamental frequency of 7.814 kHz.

FIG. 69 is a graph showing a spectrum obtained by performing a filtering process 150 times with a fundamental frequency of 10.094 kHz.

FIG. 70 is a graph showing a spectrum obtained by performing a filtering process 150 times with a fundamental frequency of 11.721 kHz.

FIG. 71 is a graph showing a spectrum obtained by performing a filtering process 150 times with a fundamental frequency of 13.085 kHz.

FIG. 72 is a graph showing a spectrum obtained by performing the filtering processing shown in Table 3 above.

FIG. 73 is a schematic view showing a state in which a reflected wave is observed by a reception sensor.

FIG. 74 is a schematic diagram showing the relationship between each fundamental frequency and the position of an object in concrete.

FIG. 75 (a) is a schematic diagram showing a measurement system for measuring the length of a pile buried in the ground, and when the pile buried in the ground is broken, It is a schematic diagram which shows the measurement system which measures a position.

FIG. 76 is a schematic diagram showing a measurement system for measuring the shape of a structure buried underground.

FIG. 77 is a schematic diagram showing a measurement system for a steel column shear fracture position.

FIG. 78 is a schematic diagram showing an underground structure exploration system.

[Explanation of symbols]

1; reinforced concrete 2; upper surface 2a; reference line 3; cracks 4, 5; reinforcing bar 6; oscillation sensor 7; receiving sensor 8; lower surface 12, 64; reflected wave 13; object 14; elastic waves 21a, 21b, 21c, 21d, 21e; semicircle 31, 31a, 31b; pile 32; upper surface 33, 44, 65; underground 34, 45; ground surface 35; tip 36; rupture portion 36a; rupture surface 41; structure 42; outer surface 43; , 52b, 52a, 52b, 52c, 52d; steel frame 53a, 53b; bolt 54a, 54b; plate 55; fractured surface 56a; welded portion 61; manhole 62; sinus passage 63; elastic wave 64; reflected wave 71; Converter 72; signal processing unit 72a; CPU 72b; DSP 72c; memory 73; GP-IB interface 74; SOKKI A 75b; Instrument B 81a, 81b, 81c, 81d, 81e, 81f, 8
1g, 81h, 81i, 81j, 81k, 81m, 81
n, 81p, 81q, 81r, 81s, 81t, 81
u, 82a, 82b, 82c, 82d, 82e, 82
f, 82g, 82h, 82i, 82j, 82k, 82
m, 82n, 82p, 82q, 82r, 83a, 83
b, 83c, 83d, 83e, 83f, 83g, 83
h, 83i, 83j, 83k, 83m, 83n, 83
p, 83q, 83r; filter

Continued on the front page (51) Int.Cl. ⁷ identification code FI G01N 29/22 501 G01N 29/22 501 G01S 7/526 G01S 7/52 J (58) Investigated field (Int.Cl. ⁷ , DB name) G01H 1/14 G01B 17/00 G01B 17/02 G01H 3/08 G01N 29/10 G01N 29/22 501 G01S 7/526

Claims (5)

(57) [Claims] 1. An elastic wave oscillation sensor and an elastic wave reception sensor are arranged on a material through which an elastic wave propagates, and the elastic wave oscillated by the elastic wave oscillation sensor is received by the elastic wave reception sensor. In a superimposed wave filtering method for filtering a wave, a Fourier transform of the superimposed wave is provided.
Sweep the spectrum to get an integer multiple of its frequency
The frequency with the spectrum peak at the position
As a function of time t
Expressed as (t), the number of the fundamental oscillation and f _0, where m is a predetermined positive integer, and Δt = m / 2f _0, a and b
The, respectively, when a predetermined positive real number, equation {f
Performs the operation represented by (t) −af (t + Δt)｝ / b
By doing so , the components of f ₀ / m and odd multiples of f ₀ / m are amplified, and the components of even multiples of f ₀ / m are reduced or deleted , and represented by a function F ₁ (t). Step of obtaining superimposed waves
And the Fourier of the superimposed wave represented by the function F ₁ (t)
Deriving a spectrum . 2. An elastic wave oscillating sensor and an elastic wave receiving sensor are arranged on a material through which an elastic wave propagates, and the elastic wave oscillated by the elastic wave oscillating sensor is received by the elastic wave receiving sensor. In a superimposed wave filtering method for filtering a wave, a Fourier transform of the superimposed wave is provided.
Sweep the spectrum to get an integer multiple of its frequency
The frequency with the spectrum peak at the position
As a function of time t
Expressed as (t), the number of the fundamental oscillation and f _0, where m is a predetermined positive integer, and Δt = m / 2f _0, a and b
The, respectively, when a predetermined positive real number, equation {f
Performs the operation represented by (t) + af (t + Δt)｝ / b
By doing so , the components of f ₀ / m and odd multiples of f ₀ / m are deleted or reduced, and the components of even multiples of f ₀ / m are amplified and represented by a function F ₂ (t). Step of obtaining superimposed waves
And the Fourier of the superimposed wave represented by the function F ₂ (t)
Deriving a spectrum . Wherein said acoustic wave receiving cell said function F ₁ (t)
Considering the function f (t) of the superimposed wave received by the sensor,
By a plurality of times exemplary child the operation expressed by the equation,
A step of obtaining a new function F ₁ (t).
The superimposed wave filtering method according to claim 1. Wherein said acoustic wave receiving cell the function F ₂ (t)
Considering the function f (t) of the superimposed wave received by the sensor,
By performing the operation represented by the above formula a plurality of times,
A step of obtaining a new function F ₂ (t).
The superimposed wave filtering method according to claim 2. 5. An apparatus used for implementing the superimposed wave filtering processing method according to claim 1, wherein the elastic wave oscillation sensor, the elastic wave reception sensor, and the reception signal are received by the reception sensor. And a signal analyzer for filtering the superimposed wave.