JP6355095B1 - Estimation method of wave propagation time between two points - Google Patents
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Abstract
【課題】媒質に伝わる波動を測定することで、その測定した二点間の伝播時間をリアルタイムに推定することができる二点間の波動伝播時間の推定方法を提供する。【解決手段】二点間を波動が伝播することを考える。それぞれの位置をｘ、ｙとして、それぞれの点で観測された波形の相互相関関数を算定する。位置ｘにおけるある時点ｊの波形を基準として、この波形と位置ｙにおけるある時点ｊから時間ｉさかのぼった波形との相互相関関数を時間ｉをサンプル時間間隔を単位として変動させ、相互相関関数の絶対値が最大になる場合の時間ｉが、ある時点ｊにおける波動伝播時間となる。実際に処理を行うにあたっては、前述の位置ｘにおける波形を基準にした場合と、位置ｙにおける波形を基準にした場合の相互相関係数を、それぞれ時間差ｉをサンプル時間を単位として複数さかのぼって算出する。【選択図】図１An object of the present invention is to provide a method for estimating a wave propagation time between two points by measuring a wave propagating through a medium and estimating a propagation time between the two measured points in real time. Consider that a wave propagates between two points. The cross-correlation function of the waveform observed at each point is calculated with each position as x and y. Using the waveform at a certain time point j at the position x as a reference, the cross-correlation function between this waveform and the waveform that goes back from the certain time point j at the position y is varied with the time i as a sample time interval, and the absolute value of the cross-correlation function is obtained. The time i when the value is maximized is the wave propagation time at a certain time point j. In actual processing, the cross-correlation coefficient when the waveform at the position x described above is used as a reference and when the waveform at the position y is used as a reference is calculated by going back a plurality of time differences i in units of sample times. To do. [Selection] Figure 1
Description
本発明は波動を伝播する媒質の二点間の波動伝播時間の推定方法に関する。 The present invention relates to a method for estimating a wave propagation time between two points of a medium that propagates a wave.
波動の伝播時間を推定する方法としては、媒質中の二点で波動を観測し、他方の波動からもう一点で観測した波動を推定し、その差が最小になるサンプリング時間を波動の伝播時間とする方法（例えば特許文献１）や、波動の伝播時間を推定する方法としては、地震波の伝播時間を推定するＮＩＯＭ法（例えば、非特許文献１）や、ダムの波動伝播時間の推定方法（例えば、非特許文献２参照）が知られている。
波動の伝播時間を推定する方法としては、媒質中の二点で波動を観測し、他方の波動からもう一点で観測した波動を推定し、その差が最小になるサンプリング時間を波動の伝播時間とする方法（例えば特許文献１）や、地震波の伝播時間を推定するＮＩＯＭ法（例えば非特許文献１）、ダムの波動伝播時間の推定方法（例えば、非特許文献２参照）が知られている。
As a method for estimating the propagation time of a wave, the wave is observed at two points in the medium, the wave observed at the other point is estimated from the other wave, and the sampling time at which the difference is minimized is defined as the wave propagation time. As a method for estimating the propagation time of a wave (for example, Patent Document 1), a NIOM method for estimating the propagation time of a seismic wave (for example, Non-Patent Document 1), or a method for estimating a wave propagation time of a dam (for example, Non-Patent Document 2) is known.
As a method for estimating the propagation time of a wave, the wave is observed at two points in the medium, the wave observed at the other point is estimated from the other wave, and the sampling time at which the difference is minimized is defined as the wave propagation time. There are known methods (for example, Patent Document 1), NIOM method for estimating the propagation time of seismic waves (for example, Non-Patent Document 1), and methods for estimating the wave propagation time of a dam (for example, see Non-Patent Document 2).
まず特許文献１による方法であるが、この方法では媒質内の波動場が大きく乱された場合に誤差が大きくなり、例えば地盤などに適用する場合には液状化の影響を受けやすいという特徴がある。 The method according to Patent Document 1 is characterized in that the error increases when the wave field in the medium is greatly disturbed, and is susceptible to liquefaction when applied to the ground, for example. .
また、非特許文献１のＮＩＯＭ法は、波動を２点で観測し、それらの観測データに対して一定の時間間隔を取出しフーリエ変換を行い、その結果からその２点間の伝達関数を求めておき、パルス状の入力波形と出力波形の関係をこの伝達関数から求めることで、波動の伝播時間を求めるものである。 In addition, the NIOM method of Non-Patent Document 1 observes waves at two points, takes out a certain time interval for those observation data, performs Fourier transform, and obtains a transfer function between the two points from the result. The wave propagation time is obtained by obtaining the relationship between the pulsed input waveform and the output waveform from this transfer function.
しかし、この方法によると一定の測定区間を用いてフーリエ変換を行うためデータ処理に遅れが生じ、また処理そのものも複雑になる。 However, according to this method, since the Fourier transform is performed using a fixed measurement interval, the data processing is delayed, and the processing itself is complicated.
さらに、非特許文献２の大町ほかによるダムの波動伝播速度の算出方法は、波動に含まれるある振動数が２点間を伝播する場合に位相が遅れることに着目したもので、フーリエ位相スペクトルを用いて振動数と位相差の関係を求めて、そこから伝播速度を算出する。 Furthermore, the calculation method of the wave propagation velocity of the dam by Omachi et al. In Non-Patent Document 2 focuses on the fact that the phase is delayed when a certain frequency included in the wave propagates between two points. The relationship between the frequency and the phase difference is obtained and the propagation velocity is calculated therefrom.
しかし、この方法の場合でも一定の測定区間を用いてフーリエ変換を行うためデータ処理に遅れが生じ、また処理そのものも複雑になる。さらに、この方法を双方向の伝播波動がほぼ等しい建物に適用した場合は、その建物内の上下２点では位相差が見かけ上なくなり、波動伝播時間の算定ができなくなるという問題もある。 However, even in this method, data processing is delayed because the Fourier transform is performed using a fixed measurement interval, and the processing itself is complicated. Furthermore, when this method is applied to a building where the two-way propagation waves are almost equal, there is a problem that the phase difference is apparently not observed at the two upper and lower points in the building, and the wave propagation time cannot be calculated.
本件発明が解決しようとする課題は、物性の変化や構造物などの劣化を評価するために波動伝播時間を求めようとする際に、用いるデータ個数に制限なくリアルタイム処理ができないことである。 The problem to be solved by the present invention is that real-time processing cannot be performed without limitation on the number of data used when trying to determine the wave propagation time in order to evaluate changes in physical properties or deterioration of structures.
二点間を波動が伝播することを考える。それぞれの位置をｘ、ｙとすると、ある時点ｊにおいてそれぞれの点で観測された波形はｆ（ｘ，ｊ）、ｆ（ｙ，ｊ）とあらわされる。このとき、これら二つの波形の相互相関関数ＴＲ（ｊ）は以下のように算定することができる。 Consider wave propagation between two points. Assuming that the respective positions are x and y, the waveforms observed at the respective points at a certain point in time j are represented as f (x, j) and f (y, j). At this time, the cross-correlation function TR (j) of these two waveforms can be calculated as follows.
ここで、演算子［Ｇ（ｘ）］はＧ（ｘ）のある時間にわたる平均演算を意味する。また、
Ｒ（ｉ，ｊ）=［ｆ（ｘ，ｊ）×ｆ（ｙ，ｊ−ｉ）］
Ｒｘ（ｊ）＝［ｆ（ｘ、ｊ）２］
Ｒｙ（ｊ）＝［ｆ（ｙ、ｊ）２］
であり、ｓｉｇｎ（）は符号関数である。
Here, the operator [G (x)] means an average operation over a certain time of G (x). Also,
R (i, j) = [f (x, j) × f (y, ji)]
Rx (j) = [f (x, j) 2 ]
Ry (j) = [f (y, j) 2 ]
And sign () is a sign function.
このとき、ｉは二つの波形の時間差を表しており、数１は位置ｘにおけるある時点ｊの波形を基準として、この波形と位置ｙにおけるある時点ｊから時間ｉさかのぼった波形との相互相関関数を算定するものである。この時間ｉをサンプル時間間隔を単位として変動させ、相互相関関数の絶対値が最大になる場合の時間ｉが、ある時点ｊにおける波動伝播時間となる。 At this time, i represents a time difference between the two waveforms, and Equation 1 is a cross-correlation function between this waveform and a waveform that goes back from the time point i at the position y to the time point i with reference to the waveform at the time point j at the position x. Is calculated. The time i when the absolute value of the cross-correlation function is maximized by varying the time i in units of the sample time interval is the wave propagation time at a certain time j.
実際に処理を行うにあたっては、前述の位置ｘにおける波形を基準にした場合と、位置ｙにおける波形を基準にした場合の相互相関係数を、それぞれ時間ｉをサンプル時間を単位として複数さかのぼって算出する。この処理を行うことでリアルタイムかつ時間遅れなく位置ｘと位置ｙの間の波動伝播時間を算出することができる。
In actual processing, the cross-correlation coefficient when the waveform at the position x described above is used as a reference and when the waveform at the position y is used as a reference is calculated by going back a plurality of times i with each sample time as a unit. To do. By performing this processing, the wave propagation time between the position x and the position y can be calculated in real time and without time delay.
また、時系列の振動波形において、連続するサンプリングデータを補間することで、サンプリング間隔よりも短い時間差の波動伝播時間を推定することができる。なお、補間の方法は、たとえば直線的に二つのサンプリングデータ間を補間するなど、その方法に限定はない。 In addition, by interpolating continuous sampling data in a time-series vibration waveform, it is possible to estimate a wave propagation time with a time difference shorter than the sampling interval. The interpolation method is not limited, for example, by linearly interpolating between two sampling data.
本発明の方法によれば、二点間を伝わる波動を測定することで、その二点間の波動伝播時間をリアルタイムに時間遅れなく推定することができる。このため、従来の方法では二点で観測を行い、限られたデータ長の波形を回収し、オフラインで複雑な処理を行う必要があったものを、非常に長いデータ長の観測波形であっても観測された波動を逐次処理し、連続的に波動伝播時間を算出することができる。また、振動場が乱された場合であっても波動伝播時間を算出することができる。 According to the method of the present invention, by measuring the wave transmitted between two points, the wave propagation time between the two points can be estimated in real time without a time delay. For this reason, in the conventional method, observation was performed at two points, a waveform with a limited data length was collected, and what was required to perform complicated processing offline was an observation waveform with a very long data length. The observed wave can be processed sequentially and the wave propagation time can be calculated continuously. Further, the wave propagation time can be calculated even when the vibration field is disturbed.
本発明の方法によれば、媒質に伝わる波動を測定することで、その測定した二点間の伝播時間をリアルタイムに推定することができる。このため非常に長いデータ長の観測波形であっても逐次処理し、連続的に算出することができる。 According to the method of the present invention, the propagation time between the two measured points can be estimated in real time by measuring the wave transmitted to the medium. Therefore, even an observation waveform having a very long data length can be sequentially processed and continuously calculated.
以下、本発明を実施するための形態を示す。 Hereinafter, modes for carrying out the present invention will be described.
本発明の手法を、東北大学工学部の人間・環境系研究棟で観測された東北地方太平洋沖地震の観測波形に適用した実施例を示す。 An example in which the method of the present invention is applied to the observed waveform of the off the Pacific coast of Tohoku Earthquake observed in the Human / Environmental Research Building of the Faculty of Engineering, Tohoku University is shown.
本発明の手法によると、図１に示すような波動伝播時間の時系列の変動をリアルタイムに得ることができる。なお、図１は特許文献１の方法により求められた波動伝播時間に、本発明の手法により求めた波動伝播時間を重ね書きしたものである。この図から、本発明の手法による波動伝播時間は特許文献１の方法による波動伝播時間とよく一致しており、本発明の手法の有効性を示している。 According to the method of the present invention, time-series fluctuations of wave propagation time as shown in FIG. 1 can be obtained in real time. In FIG. 1, the wave propagation time obtained by the method of the present invention is overwritten on the wave propagation time obtained by the method of Patent Document 1. From this figure, the wave propagation time according to the method of the present invention is in good agreement with the wave propagation time according to the method of Patent Document 1, indicating the effectiveness of the method of the present invention.
なお、本発明の実施例に用いた地震観測波形は独立行政法人建築研究所により提供された強震波形である。 Note that the seismic observation waveform used in the examples of the present invention is a strong earthquake waveform provided by the National Institute for Building Science.
二点間の波動伝播時間をリアルタイムに推定することができるので、例えば波動が伝播する媒質の物性の変化や、具体的には構造物の地震時の被害状況を、リアルタイムに把握することなどに資することができる。 Since the wave propagation time between two points can be estimated in real time, for example, to grasp in real time the change in physical properties of the medium in which the wave propagates, specifically the damage status of the structure during an earthquake Can contribute.
１ 波動伝播時間を示す軸（単位：１／１００秒）
２ 時間軸（単位：秒）
１１ 本発明の手法による波形伝播時間
１２ 特許文献１の手法による波形伝播時間
1 Axis indicating wave propagation time (unit: 1/100 second)
2 Time axis (unit: second)
11 Waveform propagation time by the method of the present invention 12 Waveform propagation time by the method of Patent Document 1
Claims (1)
空間的に離れた二点間を波動が伝播する場合に、
おのおのの点において該波動を時系列の振動波形として計測し、
一方の点において計測された時系列の振動波形についてサンプリング時間をさかのぼった時系列の振動波形と、
他方の点において計測された時系列の振動波形と、
の相互相関関数を、
各測定時点について該サンプリング時間をさかのぼって連続的に算出したものを第一の相互相関関数群とし、
また、
一方の点において計測された時系列の振動波形と、
他方の点において計測された時系列の振動波形についてサンプリング時間をさかのぼった時系列の振動波形と、
の相互相関関数を、
各測定時点について該サンプリング時間をさかのぼって連続的に算出したものを第二の相互相関関数群とし、
該第一の相互相関関数群と該第二の相互相関関数群との中で、
相互相関係数の絶対値が最大になる該サンプリング時間のさかのぼり量を測定時点ごとにリアルタイムに算出し、
算出された相互相関係数の絶対値が最大になるサンプリング時間の該さかのぼり量を、
該測定時点における該二点間の波動伝播時間とする、
ことを特徴とする、
二点間の波動伝播時間の推定方法。
In the method of estimating the wave propagation time between two points,
When waves propagate between two spatially separated points,
Measure the wave as a time-series vibration waveform at each point,
A time series vibration waveform that goes back the sampling time for a time series vibration waveform measured at one point, and
A time-series vibration waveform measured at the other point;
The cross-correlation function of
The first cross-correlation function group is obtained by continuously calculating the sampling time for each measurement time point,
Also,
Time series vibration waveform measured at one point,
A time series vibration waveform that goes back the sampling time for a time series vibration waveform measured at the other point, and
The cross-correlation function of
What was continuously calculated by going back the sampling time for each measurement time point as a second cross-correlation function group,
Among the first cross-correlation function group and the second cross-correlation function group,
Calculate the retroactive amount of the sampling time that maximizes the absolute value of the cross-correlation coefficient in real time for each measurement point,
The amount of retroactive sampling that maximizes the absolute value of the calculated cross-correlation coefficient is
The wave propagation time between the two points at the time of measurement,
It is characterized by
A method for estimating the wave propagation time between two points.
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Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS6035284A (en) * | 1983-08-08 | 1985-02-23 | Fujitsu Ltd | Varying time difference detecting system |
| JPH11201812A (en) * | 1998-01-08 | 1999-07-30 | Mitsui Eng & Shipbuild Co Ltd | Method for measuring sound velocity in fluid piping |
| JP2006003311A (en) * | 2004-06-21 | 2006-01-05 | Mitsubishi Electric Corp | Abnormality part detecting device |
| JP2008544260A (en) * | 2005-06-21 | 2008-12-04 | ナショナル リサーチ カウンシル オブ カナダ | Nondestructive inspection of pipes |
| JP2011133410A (en) * | 2009-12-25 | 2011-07-07 | Tokyo Electric Power Services Co Ltd | Deformed-state monitoring method of tunnel lining |
| WO2015141129A1 (en) * | 2014-03-17 | 2015-09-24 | 日本電気株式会社 | Speed-of-sound calculation device, speed-of-sound calculation method, and speed-of-sound calculation program |
| JP6024012B1 (en) * | 2015-12-18 | 2016-11-09 | 株式会社システムアンドデータリサーチ | Estimation method of wave propagation time between two points |
| WO2017175692A1 (en) * | 2016-04-06 | 2017-10-12 | 株式会社Ｓｕｂａｒｕ | Ultrasonic inspection system, ultrasonic inspection method, and aircraft structure |
-
2017
- 2017-10-30 JP JP2017208958A patent/JP6355095B1/en active Active
Patent Citations (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPS6035284A (en) * | 1983-08-08 | 1985-02-23 | Fujitsu Ltd | Varying time difference detecting system |
| JPH11201812A (en) * | 1998-01-08 | 1999-07-30 | Mitsui Eng & Shipbuild Co Ltd | Method for measuring sound velocity in fluid piping |
| JP2006003311A (en) * | 2004-06-21 | 2006-01-05 | Mitsubishi Electric Corp | Abnormality part detecting device |
| JP2008544260A (en) * | 2005-06-21 | 2008-12-04 | ナショナル リサーチ カウンシル オブ カナダ | Nondestructive inspection of pipes |
| JP2011133410A (en) * | 2009-12-25 | 2011-07-07 | Tokyo Electric Power Services Co Ltd | Deformed-state monitoring method of tunnel lining |
| WO2015141129A1 (en) * | 2014-03-17 | 2015-09-24 | 日本電気株式会社 | Speed-of-sound calculation device, speed-of-sound calculation method, and speed-of-sound calculation program |
| JP6024012B1 (en) * | 2015-12-18 | 2016-11-09 | 株式会社システムアンドデータリサーチ | Estimation method of wave propagation time between two points |
| WO2017175692A1 (en) * | 2016-04-06 | 2017-10-12 | 株式会社Ｓｕｂａｒｕ | Ultrasonic inspection system, ultrasonic inspection method, and aircraft structure |
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