JP2009014697A - Wave direction calculating method of buoy-type wave height meter - Google Patents

Wave direction calculating method of buoy-type wave height meter Download PDF

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JP2009014697A
JP2009014697A JP2007203645A JP2007203645A JP2009014697A JP 2009014697 A JP2009014697 A JP 2009014697A JP 2007203645 A JP2007203645 A JP 2007203645A JP 2007203645 A JP2007203645 A JP 2007203645A JP 2009014697 A JP2009014697 A JP 2009014697A
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buoy
wave
wave direction
data
calculation method
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Katsuyoshi Shimizu
勝義 清水
Mineo Iwasaki
峯夫 岩崎
Shigeaki Adachi
重昭 安立
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KAIYO CHOSA KYOKAI
National Institute of Maritime Port and Aviation Technology
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KAIYO CHOSA KYOKAI
National Institute of Maritime Port and Aviation Technology
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Abstract

<P>PROBLEM TO BE SOLVED: To solve a problem in wave direction measurement by a GPS buoy wherein a wave direction cannot be stably measured at 360° by the covariance of the horizontal moving speed of the buoy and the vertical position of the buoy due to noncoincidence between the motion of water particles and the motion of the buoy. <P>SOLUTION: The method comprises carrying out wave direction calculation by dividing it into two calculations and combining the results thereof. First calculation is to determine the vibrating (reciprocating) direction (180° wave direction) of water particles. The vibrating direction of water particles can be determined by a method of carrying out coordinate conversion and determining the direction in which primary or secondary moment (power) is maximum. Second calculation is to determine the traveling direction of wave and the 360° wave direction. In the case of the buoy type, the 360° wave direction value of water particles by covariance is not stable but its code has stability. The code of the covariance value in the 180° wave direction obtained in the first method is obtained to determine the traveling direction. The stable 360° wave direction measurement of the buoy type is attained by utilizing the advantages of the two methods. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

本発明は、ブイの位置データを用いた波向計算手法に関する。  The present invention relates to a wave direction calculation method using position data of a buoy.

ブイに高精度のＧＰＳ（衛星測位システム）を搭載し、ブイの位置情報から、波高を測定することができる。しかし、ブイの位置情報の単純な処理では、精度の高い波向計測が難しい。この主な理由は、ブイには、縦方向の固有振動が存在し、垂直方向の水粒子運動とブイの垂直の動きが、必ずしも一致しなく、位相もずれる周波数領域がある。また、波による水平方向のブイの移動も位相がずれる周波数領域がある。すなわち、ＧＰＳブイ式波高計の場合は、直接水の粒子運動を計測するのではなく、ブイの位置を計測することで、水の粒子運動を推測することによるからである。  A high-precision GPS (satellite positioning system) is mounted on the buoy, and the wave height can be measured from the position information of the buoy. However, simple processing of buoy position information makes it difficult to measure the wave direction with high accuracy. The main reason for this is that the buoy has a natural frequency in the vertical direction, and there is a frequency region in which the water particle motion in the vertical direction and the vertical motion of the buoy do not always match and are out of phase. Further, there is a frequency region in which the phase of the movement of the buoy in the horizontal direction due to the wave is also shifted. That is, in the case of the GPS buoy wave altimeter, it is because the particle motion of water is estimated by measuring the position of the buoy rather than directly measuring the particle motion of water.

一般に、波がある状態では、水の粒子は、楕円運動をしている。水粒子の水平方向速度の絶対値は、水粒子が楕円の最も上にきたとき（時計で１２時の位置）と最も下にきたとき（時計で６時の位置）で大きくなる。波向は、水粒子の楕円運動の長軸方向と粒子の回転方向で定義されるが、簡単には、水粒子が楕円の最も上にきた時の水平方向流速の方向ということができる。したがって、波向計は、水粒子の楕円上の垂直位置と、水平方向流速（Ｘ，Ｙ方向）を計測する機能を有している。水粒子の楕円上の垂直位置は、水面の位置を計測することで求められる。これには、水圧計や、海底に設置した機器から水面までの距離を超音波で計測する手法がとられる。また、水平方向流速は、超音波を用いた流速計、超音波を用いたドプラー式流速計や電磁流速計が用いられる。  In general, in the presence of waves, water particles are in elliptic motion. The absolute value of the horizontal velocity of the water particles increases when the water particles come to the top of the ellipse (position at 12 o'clock on the clock) and when they reach the bottom (position at 6 o'clock on the clock). The wave direction is defined by the major axis direction of the elliptic motion of the water particles and the rotation direction of the particles, but can be simply referred to as the direction of the horizontal flow velocity when the water particles are on the top of the ellipse. Therefore, the wave direction meter has a function of measuring the vertical position of the water particle on the ellipse and the horizontal flow velocity (X and Y directions). The vertical position of the water particle on the ellipse can be obtained by measuring the position of the water surface. For this, a method of measuring the distance from a water pressure gauge or a device installed on the seabed to the water surface with ultrasonic waves is used. As the horizontal flow velocity, a flow velocity meter using ultrasonic waves, a Doppler flow velocity meter using ultrasonic waves, or an electromagnetic flow velocity meter is used.

波向は、水粒子の垂直位置最上点での水平方向流速（Ｘ，Ｙ方向）を計測し、その方向を波向とするか、水粒子の垂直位置最下点での水平方向流速（Ｘ，Ｙ方向）を計測し、その逆方向を波向とすればよいことになる。しかし、この方法は、波向きの考え方示すもので、実用的には共分散法が用いられている。共分散法は、水粒子運動楕円の中心をゼロとした座標系で水粒子の位置を表し、その位置に水平方向流速（Ｘ，Ｙ方向）を乗じたものの積分値を、Ｘ，Ｙ方向別々に求め、その合成成分の方向を波向とする方法である。この方法によれば、例えば、２０分間の平均波向を求めることができる。このような計算が可能であるのは、水粒子位置変動と水平流速変動の位相が一致しており、位相のずれはゼロか１８０度であるからである。すなわち、水粒子位置が最上点と最下点の位置で、水平流速の絶対値も最大となる。
「共分散法を用いた波向推定方式の数値的検討」港研報告、第２０巻 第３号、１９８１年９月、ｐｐ５３〜９２ 「波を測る」、沿岸開発技術センター、２００１年、ｐｐ１３４〜１３６、ｐ．６６、ｐ．６８ The wave direction is determined by measuring the horizontal flow velocity (X, Y direction) at the highest vertical position of the water particles and setting the direction as the wave direction or the horizontal flow velocity (X at the lowest vertical position of the water particles) , Y direction), and the opposite direction may be the wave direction. However, this method shows the idea of the wave direction, and the covariance method is practically used. The covariance method expresses the position of a water particle in a coordinate system in which the center of the water particle motion ellipse is zero, and the integrated value obtained by multiplying the position by the horizontal flow velocity (X, Y direction) is obtained separately for the X and Y directions. And the direction of the synthesized component is the wave direction. According to this method, for example, an average wave direction for 20 minutes can be obtained. Such a calculation is possible because the phase of the water particle position fluctuation and the horizontal flow velocity fluctuation coincide with each other, and the phase shift is zero or 180 degrees. That is, the absolute value of the horizontal flow velocity is maximized at the position of the water particle at the uppermost point and the lowermost point.
"Numerical examination of wave direction estimation method using covariance method" Minato Lab report, Vol. 20, No. 3, September, 1981, pp 53-92 “Measuring Waves”, Coastal Development Technology Center, 2001, pp 134-136, p. 66, p. 68

ＧＰＳブイ式波高計の場合は、ブイの位置を計測することで、水の粒子運動を推測することになる。ブイは、慣性質量を有し、水の抵抗があり、さらに固有振動を有している。固有振動は、ヒービング（上下動揺）、ローリング、ピッチングの動揺が存在する。例えば、ヒービングの場合、水粒子の上下運動の周波数が、ブイのヒービングの固有振周波数より大きい場合は、ブイの垂直位置は、水粒子の位置に追従できなく位相がおくれ、水粒子運動に対しブイの上下運動が小さく現れる。また、ブイの固有振動周波数に近い水粒子運動の場合、同調して、ブイが水粒子より大きく運動する場合があり、位相も大きくすれる。このブイの運動と水粒子運動のずれは、波高と共分散による波向の計算に障害となる。  In the case of a GPS buoy wave height meter, the particle motion of water is estimated by measuring the position of the buoy. The buoy has an inertial mass, is water resistant, and has a natural vibration. The natural vibration includes heaving (up-and-down shaking), rolling and pitching. For example, in the case of heaving, when the vertical motion frequency of the water particles is greater than the natural frequency of the buoy heaving, the vertical position of the buoy is unable to follow the position of the water particles, and the phase is set. The vertical movement of the buoy appears small. Further, in the case of water particle motion close to the natural vibration frequency of the buoy, the buoy may move more than the water particle in synchronism, and the phase is also increased. This deviation between buoy motion and water particle motion hinders the calculation of wave direction due to wave height and covariance.

ＧＰＳブイ式波高計の場合の共分散計算は、ブイのＺデータと、ブイの水平移動速度の共分散から計算される。ただし、ブイの水平移動速度は、ブイの水平位置から微分により求める。一般に、共分散計算が可能なのは、共分散計算に使う２つの物理量の位相ずれがゼロか１８０度である必要がある。上述したように、ブイの応答性のため、この関係が成立しない周波数領域が存在する。このため、この領域をフィルターで除去し、この周波数領域の波向きを求めなくすることが行われている。また、ブイの位置、または、速度のデータの位相補正を行う方法も試みられているが、ブイの垂直方向の固有運動は、波の運動と独立しているため、この補正は、難しい。従って、この領域での共分散計算単独による波向き計算は、困難である。また、ブイは、振れ回り運動等波と無関係な動きをするため、ある程度の波高がある場合にしか共分散法が適用できない問題点がある。すなわち、ＧＰＳブイ式波高計の場合は、共分散法だけでは、安定的に波向き計算ができない問題がある。  The covariance calculation in the case of the GPS buoy wave altimeter is calculated from the buoy Z data and the covariance of the horizontal movement speed of the buoy. However, the horizontal movement speed of the buoy is obtained by differentiation from the horizontal position of the buoy. In general, covariance calculation is possible when the phase shift between two physical quantities used for covariance calculation is zero or 180 degrees. As described above, there exists a frequency region where this relationship is not established due to the responsiveness of the buoy. For this reason, this region is removed by a filter so that the wave direction in this frequency region is not required. A method for correcting the phase of the buoy position or velocity data has also been attempted, but this correction is difficult because the vertical natural motion of the buoy is independent of the wave motion. Therefore, it is difficult to calculate the wave direction by covariance calculation alone in this region. In addition, since the buoy moves unrelated to the whirling motion and the like wave, there is a problem that the covariance method can be applied only when there is a certain wave height. That is, in the case of a GPS buoy type altimeter, there is a problem that the wave direction cannot be stably calculated only by the covariance method.

一般に、波向き計算は、計算過程を分割することなく、行われている。このため、上述の課題を解決できなかった。しかし、波向き計算を、２つの計算に分割して計算し、結果を合わせる手法を発明し、課題を解決した。この計算の１つの計算は、水粒子の振動（往復運動）方向を求めることである。この振動方向が示す波向きを１８０度波向きと呼ぶことにする。なぜなら、この波向きは、波の進行方向が分からず、０度〜１８０度の範囲で定義される波向きである。もう１つの計算は、波の進行方向を求めることである。この進行方向が分かると、０度〜３６０度の範囲で定義される波向きが求められる。これを３６０度波向きと呼ぶことにする。一般には、３６０度波向きが要求される。  In general, the wave direction calculation is performed without dividing the calculation process. For this reason, the above-mentioned subject was not able to be solved. However, the wave direction calculation was divided into two calculations and the method of combining the results was invented to solve the problem. One calculation of this calculation is to determine the vibration (reciprocating) direction of the water particles. The wave direction indicated by the vibration direction is referred to as a 180-degree wave direction. This is because the wave direction is a wave direction defined in the range of 0 degrees to 180 degrees without knowing the traveling direction of the waves. Another calculation is to determine the direction of wave travel. When this traveling direction is known, the wave direction defined in the range of 0 to 360 degrees is obtained. This is referred to as a 360-degree wave direction. Generally, a 360 degree wave direction is required.

水粒子の振動（往復運動）方向の平均波向は、次の手法で計算できる。ブイの水平移動動揺の中心を中心とする座標で、ブイの位置（Ｘｉ，Ｙｉ）がｎ個の時系列データで示されているとする。このとき、数式１で示される１次モーメントＭｘ１（θ）が最大となるθの方向が平均波向の方向となる。

Figure 2009014697
ただし、Ｘｉ（θ）は、θ回転した座標系上のブイの位置のＸ方向成分で、回転前の座標値（Ｘｉ，Ｙｉ）を用いて数式２で求められる。
Figure 2009014697
 The average wave direction in the vibration (reciprocating) direction of water particles can be calculated by the following method. It is assumed that the position of the buoy (X i , Yi) is indicated by n pieces of time-series data with the coordinates centering on the center of the buoy's horizontal movement. At this time, the direction of θ at which the first moment Mx 1 (θ) expressed by Equation 1 is the maximum is the direction of the average wave direction.
Figure 2009014697
 However, X i (θ) is the X direction component of the position of the buoy on the coordinate system rotated by θ, and is obtained by Equation 2 using the coordinate values (X i , Y i ) before rotation.
Figure 2009014697

さらに、水粒子の振動（往復運動）方向の主波向は、次の手法で計算できる。数式３で示す２次モーメント（パワー）Ｍｘ２（θ）が最大となるθの方向が主波向の方向となる。

Figure 2009014697
また、数式４の関係式をもちいると、
Figure 2009014697
 モーメントが最大になる方向である主波向きの方向θｐは、数式５で表される。非特許文献１を参照。
Figure 2009014697
 Furthermore, the main wave direction in the direction of vibration (reciprocating motion) of water particles can be calculated by the following method. The direction of θ at which the second moment (power) Mx 2 (θ) shown in Formula 3 is the maximum is the direction of the main wave direction.
Figure 2009014697
 Also, using the relational expression of Equation 4,
Figure 2009014697
 The direction θ p in the main wave direction, which is the direction in which the moment is maximized, is expressed by Equation 5. See Non-Patent Document 1.
Figure 2009014697

波の進行方向を求めるには、まず、上述の手法で平均波向または主波向の方向θを求めておく。この場合の波の進行方向の符号は、数式６の共分散値Ｓ１（θ）の符号を用いる。式中のＶｘｉ（θ）は、波向き方向のブイの速度で、数式２でθ方向の位置の時系列データＸｉ（θ）を求め、これを微分して求める。また、Ｚｉは、ブイの垂直位置データで、波向き方向のブイの速度Ｖｘｉ（θ）と同時刻のデータである。

Figure 2009014697
In order to obtain the traveling direction of the wave, first, the direction θ of the average wave direction or the main wave direction is obtained by the above-described method. In this case, the sign of the wave traveling direction is the sign of the covariance value S 1 (θ) of Equation 6. V xi (θ) in the equation is the speed of the buoy in the wave direction, and the time series data X i (θ) at the position in the θ direction is obtained by Equation 2 and obtained by differentiating it. Z i is vertical position data of the buoy and is data at the same time as the speed V xi (θ) of the buoy in the wave direction.
Figure 2009014697

また、共分散法による符号の決定は、ブイの水平位置とブイの垂直方向速度の共分散値Ｓ２（θ）でも可能である。この場合は、数式７で示される。ただし、Ｖｚｉは、ブイの垂直方向速度である。これは、Ｚｉを微分して求める。

Figure 2009014697
Further, the sign can be determined by the covariance method based on the covariance value S 2 (θ) of the horizontal position of the buoy and the vertical speed of the buoy. In this case, it is expressed by Equation 7. Where V zi is the vertical speed of the buoy. This is obtained by differentiating Z i .
Figure 2009014697

本発明により、ＧＰＳを用いたブイの位置を計測するブイシステムで、高精度な３６０度波向きの計測が可能になる。  According to the present invention, a buoy system that measures the position of a buoy using GPS enables highly accurate measurement of a 360-degree wave direction.

ブイの形状として、筒形を用いる。これは、ローリングとピッチングをおさえる働きがある。また、ブイのヒービングの固有振動数を計測したい波の周波数より下になるようブイを設計してある。このブイにＲＴＫ（リアルタイムキネマチック）ＧＰＳの位置出し装置と、得られたブイの３次元位置（Ｘ，Ｙ，Ｚ）を陸上局に送くる送信装置が搭載されている。陸上にある観測局には、データ受信装置、データ処理装置と表示装置が設けられている。  A cylindrical shape is used as the shape of the buoy. This has the function of suppressing rolling and pitching. In addition, the buoy is designed to be below the frequency of the wave for which the natural frequency of buoy heaving is to be measured. This buoy is equipped with an RTK (real-time kinematic) GPS positioning device and a transmitter for sending the obtained three-dimensional position (X, Y, Z) of the buoy to the land station. The observation station on land is provided with a data receiving device, a data processing device, and a display device.

データ処理装置は、受信したブイのＸ方向水平位置の時系列データ、ブイのＹ方向水平位置の時系列データと、ブイの垂直（Ｚ方向）位置の時系列データとをディジタルフィルターを通過させ、周期帯分離また、ノイズ処理を行う。次に、周期帯分離されたブイの位置データから、数式５を用いその周期帯の主波向きを求める。この時点では、この主波向きは、波の振動方向で、１８０度の範囲で定義される波向きである。つぎに、数式６または、数式７を用いて、波の進行方向を決定し、３６０度の範囲で定義される波向きを求める。  The data processing apparatus passes the time-series data of the received buoy in the X-direction horizontal position, the time-series data of the buoy in the Y-direction horizontal position, and the time-series data of the buoy in the vertical (Z direction) position through the digital filter, Periodic band separation and noise processing are performed. Next, from the position data of the buoys separated by the periodic band, the main wave direction of the periodic band is obtained using Equation 5. At this time, the main wave direction is a wave direction defined by a range of 180 degrees in the vibration direction of the wave. Next, the traveling direction of the wave is determined using Equation 6 or Equation 7, and the wave direction defined in the range of 360 degrees is obtained.

Claims (7)

ブイの位置を計測する波向計測手法において、波の振動する方向と、その符号（進行・逆行）を個別に求め、その２つの結果を合わせることにより、３６０度の範囲で定義される波向きを求めることを特徴とする波向き計算手法。  In the wave direction measurement method for measuring the position of the buoy, the wave direction defined in the range of 360 degrees is obtained by individually obtaining the direction of wave vibration and its sign (travel / reverse) and combining the two results. Wave direction calculation method characterized by obtaining ブイの位置を計測する波向計測手法において、ブイの水平移動動揺の中心を中心とする座標で、ブイの位置を示し、波の振動する方向を、ブイの水平位置の（Ｘ，Ｙ）の２次モーメント（パワー）が最大になる方向とすることを特徴とする請求項１で規定する波向き計算手法。  In the wave direction measurement method for measuring the position of the buoy, the position of the buoy is indicated by coordinates centered on the center of the buoy's horizontal movement, and the direction in which the wave vibrates is determined by the horizontal position of the buoy (X, Y). The wave direction calculation method defined in claim 1, wherein the second moment (power) is maximized. ブイの位置を計測する波向計測手法において、ブイの水平移動動揺の中心を中心とする座標で、ブイの位置を示し、波の振動する方向を、ブイの水平位置の（Ｘ，Ｙ）の１次モーメントが最大になる方向とすることを特徴とする請求項１で規定する波向き計算手法。  In the wave direction measurement method for measuring the position of the buoy, the position of the buoy is indicated by coordinates centered on the center of the buoy's horizontal movement, and the direction in which the wave vibrates is determined by the horizontal position of the buoy (X, Y). The wave direction calculation method defined in claim 1, wherein the first moment is set to a maximum direction. ブイの位置を計測する波向計測手法において、波の振動する方向の符号（進行・逆行）を波の振動する方向のブイの水平方向移動速度とブイの垂直方向変位の共分散値の符号、または、波の振動する方向のブイの水平方向位置とブイの垂直方向移動速度の共分散値の符号により決定することを特徴とする請求項１で規定する波向き計算手法。  In the wave direction measurement method for measuring the position of the buoy, the sign of the direction of wave vibration (travel / reverse) is the sign of the covariance value of the horizontal movement speed of the buoy and the vertical displacement of the buoy, Alternatively, the wave direction calculation method defined in claim 1, wherein the wave direction calculation method is defined by a sign of a covariance value of a horizontal position of the buoy in a direction of wave vibration and a vertical movement speed of the buoy. ブイの位置を計測する波向計測手法において、ブイの水平位置データ（Ｘ，Ｙ）と垂直位置データＺの時系列データから波向を計算する時に悪い影響を与える周波数帯を、あらかじめディジタルフィルターで削除するノイズ除去処理を行い、ノイズ除去処理されたＸ，Ｙ，Ｚデータを求めておき、そのデータを用いて波向きを求めることを特徴とする請求項１、請求項２、請求項３、請求項４で規定する波向き計算手法。  In the wave direction measurement method to measure the position of the buoy, the frequency band that has a bad influence when calculating the wave direction from the time series data of the horizontal position data (X, Y) of the buoy and the vertical position data Z is digitally filtered in advance. The noise removal processing to be deleted is performed, the X, Y, Z data subjected to the noise removal processing is obtained, and the wave direction is obtained using the data. The wave direction calculation method prescribed | regulated in Claim 4. ブイの位置を計測する波向計測手法において、ブイの水平位置データ（Ｘ，Ｙ）と垂直位置データＺの時系列データをそれぞれ、あらかじめローパス、バンドパス、ハイパス等のディジタルフィルターを通し、周期帯別に分離しておき、そのデータを用いて、周期帯波向きを求める請求項１、請求項２、請求項３、請求項４で規定する波向き計算手法。  In the wave direction measurement method for measuring the position of the buoy, the time series data of the horizontal position data (X, Y) and vertical position data Z of the buoy are passed through digital filters such as a low pass, a band pass, and a high pass in advance, respectively. The wave direction calculation method prescribed | regulated by Claim 1, Claim 2, Claim 3, and Claim 4 which isolate | separates separately and calculates | requires a period band wave direction using the data. ブイの移動速度をブイの位置データを微分して求めることを特徴とする請求項４で規定する波向き計算手法  5. The wave direction calculation method defined in claim 4, wherein the moving speed of the buoy is obtained by differentiating the position data of the buoy.
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JPH03262990A (en) * 1990-03-13 1991-11-22 Tech Res & Dev Inst Of Japan Def Agency Wave observation radar
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