JP2006329628A - Measuring method of deformation amount in structure - Google Patents
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Abstract
Description
本発明は、橋梁などの構造物における変形量計測方法に関する。 The present invention relates to a deformation measurement method for a structure such as a bridge.
従来、橋梁などの鋼構造物における撓み、すなわち変位（変形量ともいう）を計測する方法としては、３次元光波測定儀、歪ゲージや高精度の傾斜計を用いるものがあり（例えば、特許文献１参照）、また最近では、光ファイバーケーブルを用いて構造物の変位・形状などの状態変化を検知するものが提案されている（例えば、特許文献２参照）。
しかしながら、三次元光波測定儀、歪ゲージや高精度の傾斜計は、構造物のごく限られた範囲だけで変位を計測し得るものであり、例えば広範囲で変位を計測しようとすると、多くの計器を当該構造物に設置する必要があり、計測作業が煩雑になってしまう。 However, three-dimensional light wave measuring instruments, strain gauges, and high-precision inclinometers can measure displacement only within a very limited range of the structure. For example, when measuring displacement over a wide range, many instruments Must be installed in the structure, and the measurement work becomes complicated.
また、光ファイバーケーブルを用いたものでは、比較的、広範囲の変位を計測することができるが、構造物に設置するものであり、一度、設置すると長期間使用できるが、光ファイバーケーブル自体が高価であり、計測装置が高くつくという問題がある。 In addition, with a fiber optic cable, a relatively wide range of displacement can be measured, but it is installed in a structure, and once installed, it can be used for a long time, but the fiber optic cable itself is expensive. There is a problem that the measuring device is expensive.
そこで、本発明は、構造物の変位すなわち変形量を広範囲に亘って且つ安価な機器でしかも容易に計測し得る構造物における変形量計測方法を提供することを目的とする。 Therefore, an object of the present invention is to provide a deformation amount measuring method in a structure that can easily measure the displacement, that is, the deformation amount of the structure over a wide range and with an inexpensive device.
上記課題を解決するため、本発明の構造物における変形量計測方法は、構造物に力を付与した際の変形量を計測する方法であって、
力の付与前と力の付与後とにおける所定領域を光学式カメラ装置で撮影するステップと、このカメラ装置で撮影された少なくとも２枚の撮影画像にデジタル画像相関法を適用して両撮影画像上の所定領域における変形量を検出するステップと、上記検出された変形量に対して、上記光学式カメラ装置のレンズによる歪曲収差を補正する収差補正ステップとを具備し、
且つ上記収差補正ステップに、上記カメラ装置により構造物の所定領域に対してずれた位置で少なくとも２枚の撮影画像を得るステップと、この少なくとも２枚の撮影画像にデジタル画像相関法を適用して両撮影画像上での所定領域の移動量を検出するステップと、上記カメラ装置を構造物に対してずらした際の平面上での移動量算出式に、収差モデル量を加えてなる変位量算出式に上記移動量を代入し、最小二乗法を用いて当該変位量算出式における各係数を決定するステップと、上記各係数が決定された変位量算出式を用いて収差量を求めるステップとを有せしめた方法である。
In order to solve the above problem, the deformation amount measuring method in the structure of the present invention is a method of measuring the deformation amount when a force is applied to the structure,
A step of photographing a predetermined area before and after the application of force with an optical camera device, and applying a digital image correlation method to at least two photographed images taken with the camera device on both photographed images. Detecting a deformation amount in the predetermined region, and an aberration correction step of correcting distortion by the lens of the optical camera device with respect to the detected deformation amount,
In addition, in the aberration correction step, a step of obtaining at least two photographed images at positions shifted from a predetermined region of the structure by the camera device, and applying a digital image correlation method to the at least two photographed images. Detecting the amount of movement of a predetermined area on both captured images and calculating the amount of displacement by adding the aberration model amount to the equation for calculating the amount of movement on the plane when the camera device is displaced with respect to the structure Substituting the amount of movement into the equation, determining each coefficient in the displacement amount calculation formula using the least square method, and obtaining an aberration amount using the displacement amount calculation formula in which each coefficient is determined. This is the method that you have.
また、上記変形量計測方法における光学式カメラ装置のレンズとしてシフトレンズを用いた方法である。 In addition, a shift lens is used as a lens of the optical camera device in the deformation amount measuring method.
上記変形量計測方法によると、力を付与した構造物の変形量を光学式カメラ装置を用いて、力の付与前と付与後とにおいてそれぞれ撮影した撮影画像から、デジタル画像相関法を用いて計測し、しかも、この変形量に対し、レンズによる歪曲収差量を補正するようにしたので、例えば計測機器を構造物に設置する必要がなく、また光ファイバーケーブルなども用いる必要がないため、安価な計測機器を用いることができるとともに、簡単な計測作業にて、構造物の変形量を精度良く計測することができる。 According to the above deformation amount measurement method, the deformation amount of the structure to which force is applied is measured using the digital image correlation method from the captured images taken before and after the force is applied using the optical camera device. In addition, since the amount of distortion due to the lens is corrected for the amount of deformation, for example, there is no need to install a measuring instrument on the structure, and there is no need to use an optical fiber cable or the like. A device can be used, and the deformation amount of the structure can be accurately measured by a simple measurement operation.
［実施の形態］
以下、本発明の実施の形態に係る構造物における変形量計測方法を、図面に基づき説明する。
[Embodiment]
Hereinafter, a deformation measurement method for a structure according to an embodiment of the present invention will be described with reference to the drawings.
本実施の形態においては、例えば橋梁などの長尺物の構造物の老化状態を調べるために、当該構造物に荷重（力）を付与して、撓みなどの変形量をデジタル画像相関法を用いて計測するとともに、この計測に用いられる光学式カメラ装置における光学レンズによる撮影画像に生じている歪曲収差についても補正を行うようにしたものである。 In this embodiment, for example, in order to examine the aging state of a long structure such as a bridge, a load (force) is applied to the structure, and the amount of deformation such as bending is calculated using a digital image correlation method. In addition, the distortion aberration generated in the image taken by the optical lens in the optical camera device used for the measurement is also corrected.
すなわち、本実施の形態においては、光学レンズとしてシフトレンズが装着された光学式カメラ装置（具体的には、デジタルカメラである）を用いて、構造物を撮影するとともに、このカメラで撮影された構造物の撮影画像に基づき当該構造物の変形量を計測する際に、レンズの歪曲収差による誤差分（以下、歪曲収差量という）を除去するようにした変形量計測方法について説明する。 That is, in the present embodiment, an optical camera device (specifically, a digital camera) equipped with a shift lens as an optical lens is used to photograph a structure and the photograph is taken with this camera. A deformation amount measuring method for removing an error due to lens distortion (hereinafter referred to as distortion amount) when measuring the deformation amount of the structure based on a captured image of the structure will be described.
ここで、シフトレンズについて説明しておく。
通常、カメラの倍率は、レンズから被写体までの距離ａとレンズからフィルムまでの距離ｂとの比（ｂ／ａ）で決まる。このため、被写体とフィルムとの関係が平行である場合、相似の関係より被写体の両端の倍率は等しくなり、逆に、平行でない場合には、両端の倍率が異なってくる。つまり、シフトレンズとは、レンズを被写体と平行にずらせることによって、両端の倍率を保つことができるレンズをいう。
Here, the shift lens will be described.
Usually, the magnification of the camera is determined by the ratio (b / a) between the distance a from the lens to the subject and the distance b from the lens to the film. Therefore, when the relationship between the subject and the film is parallel, the magnifications at both ends of the subject are equal because of the similar relationship. Conversely, when the relationship between the subject and film is not parallel, the magnifications at both ends are different. That is, the shift lens is a lens that can maintain the magnifications at both ends by shifting the lens parallel to the subject.
本実施の形態に係る変形量計測方法は、構造物、すなわち撮影対象物の所定領域（以下、計算領域ともいう）を、荷重を付与しない変形前および荷重を付与した変形後を撮影した少なくとも２枚の撮影画像に、デジタル画像相関法を適用して、構造物での所定領域（例えば、荷重の付与部分）における変形量を計測するとともに、この変形量に対して歪曲収差量を補正するようにしたものである。 In the deformation amount measuring method according to the present embodiment, a predetermined area (hereinafter, also referred to as a calculation area) of a structure, that is, an object to be imaged, is imaged before and after deformation without applying a load. A digital image correlation method is applied to a single photographed image to measure the amount of deformation in a predetermined region (for example, a portion to which a load is applied) in the structure, and to correct the amount of distortion with respect to the amount of deformation. It is a thing.
まず、デジタル画像相関法を用いて、構造物の変形量を計測する方法について説明する。
デジタル画像相関法においては、計算領域の変形量を輝度値分布の相関を用いて検出する。これは、物体表面の乱反射像は物体表面と共に移動し、変形の前後でその特徴が保存されるということに基づくもので、変形前後の画像における輝度値の相関は下記（１）式で求められる。
First, a method for measuring the amount of deformation of a structure using the digital image correlation method will be described.
In the digital image correlation method, the deformation amount of the calculation region is detected using the correlation of the luminance value distribution. This is based on the fact that the diffuse reflection image of the object surface moves together with the object surface, and the feature is preserved before and after the deformation. The correlation of the luminance values in the image before and after the deformation is obtained by the following equation (1). .
ここで、Ｉｙ（ｘ，ｙ）は変形前画像の座標（ｘ，ｙ）における輝度値、Ｉｄ（ｘ＊，ｙ＊）は変形後画像の座標（ｘ＊，ｙ＊）における輝度値である。座標（ｘ，ｙ）と（ｘ＊，ｙ＊）との間には下記（２）式の関係がある。 Here, I y (x, y) is the luminance value at the coordinates (x, y) of the image before deformation, and I d (x * , y * ) is the luminance value at the coordinates (x * , y * ) of the image after deformation. It is. The relationship of the following formula (2) exists between the coordinates (x, y) and (x * , y * ).
ここで、図１に示すように、ｕｘおよびｕｙはそれぞれ計算領域画像の中心におけるｘ方向およびｙ方向の変位であり、ΔｘおよびΔｙは計算領域画像の中心から点（ｘ，ｙ）までの距離である。なお、図１は変形前後の計算領域の関係を表している。変形前のＰ点が変形後Ｐ′点に、Ｑ点がＱ′点に移動したとすると、Ｐ点の移動量が変位ｕｘ，ｕｙとなり、Ｑ′点の座標が上記（２）式で表される。 Here, as shown in FIG. 1, u x and u y are displacements in the x direction and y direction at the center of the calculation region image, respectively, and Δx and Δy are from the center of the calculation region image to the point (x, y). Is the distance. FIG. 1 shows the relationship between calculation areas before and after deformation. If the P point before deformation is moved to the P ′ point after deformation and the Q point is moved to the Q ′ point, the movement amount of the P point becomes displacement u x , u y , and the coordinates of the Q ′ point are expressed by the above equation (2). It is represented by
上記（１）式のＳを最小とする変位ｕｘ，ｕｙおよび変位勾配∂ｕｘ／∂ｘ，∂ｕｘ／∂ｙ，∂ｕｙ／∂ｘ，∂ｕｙ／∂ｙの６つの変数を探索することにより変位、すなわち変形量を決定することができる。このとき、１画素以下の解像度で変位を検出する場合には、双一次関数または３次のスプライン関数を利用して、輝度値を補間すればよい。また、計算速度を短縮するため、実際の相関演算方法としては、ニュートン・ラフソン法などが用いられる。すなわち、上記（１）式を６つの未知変数で偏微分して得られる６つの値が全てゼロになるように繰り返し演算を行う。 Six of displacement u x and u y and displacement gradient ∂u x / ∂x, ∂u x / ∂y, ∂u y / ∂x, and ∂u y / ∂y that minimize S in the above equation (1) The displacement, that is, the deformation amount can be determined by searching for the variable. At this time, when detecting a displacement with a resolution of one pixel or less, a luminance value may be interpolated using a bilinear function or a cubic spline function. In order to reduce the calculation speed, Newton-Raphson method or the like is used as an actual correlation calculation method. That is, the calculation is repeated so that the six values obtained by partial differentiation of the above equation (1) with six unknown variables are all zero.
上述したデジタル画像相関法により求められた変位すなわち変形量には、レンズの歪曲収差量が含まれており、以下、この歪曲収差量を補正する方法について説明する。
この歪曲収差量を求める際にも、上述したデジタル画像相関法が用いられる。
The displacement, that is, the deformation amount obtained by the digital image correlation method described above includes the distortion amount of the lens, and a method for correcting the distortion amount will be described below.
The digital image correlation method described above is also used when determining the amount of distortion.
なお、構造物の変形量を求める際には、計算領域の変形について考慮したが、ここでは、レンズによる歪曲収差量を求めだけであるため、すなわち荷重を付与することなく、カメラ装置にて所定距離ずれた位置で撮影して得られた２枚の撮影画像から歪曲収差量を求めるものであり、したがって変形させる必要がないため、剛体変位｛この変位には、剛体並進変位（剛体並行移動ともいう）と剛体回転変位（剛体回転移動ともいう）とがある｝という語句を用いて説明する。 Note that when calculating the deformation amount of the structure, the deformation of the calculation region was considered, but here, only the amount of distortion due to the lens is obtained, that is, a predetermined amount is not set by the camera device without applying a load. Since the amount of distortion is obtained from two captured images obtained by photographing at a position shifted from each other, and therefore, there is no need to deform the rigid body displacement {this displacement includes rigid body translational displacement (both rigid body parallel displacement and And a rigid body rotational displacement (also referred to as rigid body rotational movement)}.
次に、上述したデジタル画像相関法とほぼ同様の内容ではあるが、再度、所定領域（上述と同様に計算領域と称し、具体的には、数十画素×数十画素の範囲）を用いて移動量を計測する方法について説明しておく。この移動量を用いてレンズによる歪曲収差を補正するものである。 Next, the content is almost the same as that of the digital image correlation method described above, but again using a predetermined region (referred to as a calculation region as described above, specifically, a range of several tens of pixels by several tens of pixels). A method for measuring the movement amount will be described. This amount of movement is used to correct distortion aberration caused by the lens.
移動前後の画像における輝度値の相関は下記（３）式で求められる。 The correlation between the luminance values in the images before and after the movement is obtained by the following equation (3).
（３）式中、Ｉｙ（ｘ，ｙ）は移動前画像の座標（ｘ，ｙ）における輝度値、Ｉｄ（ｘ＊，ｙ＊）は移動後画像の座標（ｘ＊，ｙ＊）における輝度値である。座標（ｘ，ｙ）と（ｘ＊，ｙ＊）との間には下記（４）式の関係がある。 In equation (3), I y (x, y) is the luminance value at the coordinates (x, y) of the image before movement, and I d (x * , y * ) is the coordinates (x * , y * ) of the image after movement. The luminance value at. The relationship of the following formula (4) exists between the coordinates (x, y) and (x * , y * ).
図２に示すように、（４）式中のＵｘおよびＵｙはそれぞれ計算領域画像の中心におけるｘ方向およびｙ方向の移動量である。移動前のＰ点が移動後にＰ′点に移動したとすると、Ｐ点の移動量がＵｘ，Ｕｙになる。 As shown in FIG. 2, U x and U y in the equation (4) are movement amounts in the x and y directions at the center of the calculation area image, respectively. If the P point before the movement is moved to the P ′ point after the movement, the movement amounts of the P point are U x and U y .
そして、上記（３）式のＳを最小とする移動量Ｕｘ，Ｕｙを決定すればよい。なお、１画素以下の解像度で変位を検出する場合には、双一次関数または３次のスプライン関数を利用して、輝度値を補間すればよい。また、計算速度を短縮するため、実際の相関演算方法としては、ニュートン・ラフソン法などが用いられる。 Then, the movement amounts U x and U y that minimize S in the above equation (3) may be determined. When detecting displacement with a resolution of 1 pixel or less, a luminance value may be interpolated using a bilinear function or a cubic spline function. In order to reduce the calculation speed, Newton-Raphson method or the like is used as an actual correlation calculation method.
次に、歪曲収差について説明する。
歪曲収差とは、例えば直線である物体が曲線となって撮影される現象を言い、収差の中心（多くの場合は、画像の中心であるが、そうでない場合もある）からの距離を用いてモデル化することができる。
Next, distortion will be described.
Distortion refers to a phenomenon in which a straight object is photographed as a curve, for example, using the distance from the center of the aberration (in many cases the center of the image, but not always) Can be modeled.
例えば、図３に示すように、本来、Ａ点の位置に写るべき点が歪曲収差によりＢ点に写ったとする。
このＡ点とＢ点の距離（収差の量）は、半径方向（放射方向）歪曲収差αｒと円周方向歪曲収差αθとに分解することができる。
For example, as shown in FIG. 3, it is assumed that a point that should originally appear at the position of point A is reflected at point B due to distortion.
The distance between the points A and B (the amount of aberration) can be decomposed into a radial direction (radial direction) distortion alpha r and circumferential distortion alpha theta.
そして、円周方向歪曲収差αθは半径方向歪曲収差αｒに比べて十分に小さく、例えば円周方向歪曲収差αθを無視した場合、半径方向歪曲収差αｒは、収差の中心からの距離ｒの関数として、下記（５）式にて表される。 The circumferential distortion aberration α θ is sufficiently smaller than the radial distortion aberration α r . For example, when the circumferential distortion aberration α θ is ignored, the radial distortion aberration α r is a distance from the center of the aberration. As a function of r, it is expressed by the following equation (5).
ここで、ｋ１，ｋ２，ｋ３，・・・は収差の量を表す係数である。多くの場合、高次項を無視できるので、（５）式は下記（６）式にて近似することができる。 Here, k 1 , k 2 , k 3 ,... Are coefficients representing the amount of aberration. In many cases, higher-order terms can be ignored, so equation (5) can be approximated by equation (6) below.
すなわち、画像上の歪曲収差の量（幾何学的なずれ量）は収差の中心からの距離ｒの３乗に比例し、その係数ｋ１を決定することで歪曲収差の量を知ることができ、これに基づき補正を行うことができる。 That is, the amount of distortion of the image (geometric deviation amount) is proportional to the cube of the distance r from the center of the aberration, it is possible to know the amount of distortion by determining the coefficients k 1 Based on this, correction can be performed.
そして、上記半径方向歪曲収差αｒをｘ方向およびｙ方向に分解した場合、すなわち直交座標系における歪曲収差の量は、下記（７）式で表される。 When the radial distortion aberration α r is decomposed in the x direction and the y direction, that is, the amount of distortion aberration in the orthogonal coordinate system is expressed by the following equation (7).
ここで、θ＝arctan（ｘ，ｙ）である。
上述したように、デジタル画像相関法により、撮影対象物をそのまま移動させた場合、すなわち剛体変位をさせた場合の移動前後における撮影画像から、画像における輝度値の相関を用いて当該撮影対象物の移動量を検出することができる。言い換えれば、この方法を用いることにより、撮影対象物の剛体並進変位（以下、並行移動という）の分布を求めることができる。また、剛体回転変位（以下、回転移動という）の分布も求めることができる。
Here, θ = arctan (x, y).
As described above, when the subject is moved as it is by the digital image correlation method, that is, from the taken images before and after the movement when the rigid body is displaced, the correlation of the luminance value in the image is used. The amount of movement can be detected. In other words, by using this method, the distribution of the rigid translational displacement (hereinafter referred to as parallel movement) of the object to be imaged can be obtained. Further, a distribution of rigid body rotational displacement (hereinafter referred to as rotational movement) can also be obtained.
図４は、ｘ方向（水平方向）に撮影対象物を移動させた場合にデジタル画像相関法で得られた変位分布を示す。レンズに歪曲収差が無い場合には、変位に分布は現れずに一様な値となる。一方、収差がある場合には、図４に示すような変位分布が現れる。この分布を用いて歪曲収差を検出することになる。なお、図４の（ａ）はｘ方向変位を示し、（ｂ）はｙ方向変位を示している。 FIG. 4 shows the displacement distribution obtained by the digital image correlation method when the object to be photographed is moved in the x direction (horizontal direction). When there is no distortion in the lens, the distribution does not appear in the displacement and becomes a uniform value. On the other hand, when there is aberration, a displacement distribution as shown in FIG. 4 appears. Distortion is detected using this distribution. 4A shows the displacement in the x direction, and FIG. 4B shows the displacement in the y direction.
ここで、収差を含む点の座標値をｘ′，ｙ′、収差の無い理想的な場合の点の座標をｘ，ｙ、ｘ方向およびｙ方向の収差の量をαｘ，αｙとすると、それらの関係は下記（８）式で表される。 Here, if the coordinate value of the point including the aberration is x ′, y ′, the coordinate of the ideal point without aberration is x, y, the amount of aberration in the x direction and the y direction is α x , α y. Their relationship is expressed by the following equation (8).
デジタル画像相関法により得られる移動量、すなわち収差を含んだｘ方向およびｙ方向の移動量ｕ′ｘ，ｕ′ｙは下記（９）式で表される。 The amount of movement obtained by the digital image correlation method, that is, the amounts of movement u ′ x and u ′ y in the x direction and y direction including aberration are expressed by the following equation (9).
ここで、ｘ′ｕは移動前のｘ座標（収差を含む）、ｙ′ｕは移動前のｙ座標（収差を含む）、ｘ′ｄは移動後のｘ座標（収差を含む）、ｙ′ｄは移動後のｙ座標（収差を含む）、αｘｕは点（ｘｕ，ｙｕ）におけるｘ方向収差、αｙｕは点（ｘｕ，ｙｕ）におけるｙ方向収差、αｘｄは点（ｘｄ，ｙｄ）におけるｘ方向収差、αｙｄは点（ｘｄ，ｙｄ）におけるｙ方向収差、ｘｕは移動前のｘ座標（収差を含まず）、ｙｕは移動前のｙ座標（収差を含まず）、ｘｄは移動後のｘ座標（収差を含まず）、ｙｄは移動後のｙ座標（収差を含まず）、ｕｘはｘ方向移動量（収差を含まず）、ｕｙはｙ方向移動量（収差を含まず）である。 Here, x ′ u is the x coordinate before movement (including aberration), y ′ u is the y coordinate before movement (including aberration), x ′ d is the x coordinate after movement (including aberration), y ′ d (including aberration) y-coordinate after movement, alpha xu is the point (x u, y u) x-direction aberration in, alpha yu is the point (x u, y u) y-direction aberration in, alpha xd is the point ( x direction aberration at x d , y d ), α yd is the y direction aberration at point (x d , y d ), x u is the x coordinate before movement (excluding aberration), and yu is the y coordinate before movement. (Without aberration), x d is the x coordinate after movement (without aberration), y d is the y coordinate after movement (without aberration), and u x is the amount of movement in the x direction (without aberration) , U y are y-direction movement amounts (not including aberrations).
ところで、撮影対象物が剛体並行移動および剛体回転移動（剛体変位である）した場合を考えてみると、その移動量については、平面を表す方程式（移動量算出式）でもって近似し得るという知見を得た。 By the way, considering the case where the object to be imaged is a rigid body parallel movement and a rigid body rotational movement (rigid body displacement), the knowledge that the movement amount can be approximated by an equation representing a plane (movement amount calculation formula). Got.
すなわち、撮影対象物が剛体並行移動した場合には、移動量ｕｘおよびｕｙは、下記（１０）式にて表すことができる。 That is, when the object to be imaged is moved in parallel with the rigid body, the movement amounts u x and u y can be expressed by the following equation (10).
ここで、移動量ｕｘおよびｕｙは撮影画像上で一様の値（定数）となる。一方、撮影対象物が剛体回転移動した場合には、移動前座標と移動後座標との関係は回転行列を用いて、下記（１１）式にて表される。 Here, the movement amounts u x and u y are uniform values (constants) on the captured image. On the other hand, when the object to be imaged is rotated and rotated rigidly, the relationship between the coordinates before movement and the coordinates after movement is expressed by the following equation (11) using a rotation matrix.
したがって、撮影対象物が剛体回転移動した場合の移動量ｕｘおよびｕｙは、下記（１２）式で表すことができる。 Therefore, the movement amounts u x and u y when the object to be imaged is rotationally moved by a rigid body can be expressed by the following equation (12).
ここで、θは回転角度であるので、撮影した特定の画像に対して定数となる。
すなわち、剛体並行移動を測定した場合には、上記（９）式におけるｕｘおよびｕｙは一定値（測定領域内で一様）となる。一方、剛体並行移動と剛体回転移動の両者を測定した場合には、ｕｘおよびｕｙは２次元の平面として表すことができるため、測定した移動量は下記（１３）式で示す変位量算出式にて表される。
Here, since θ is a rotation angle, it is a constant for a specific photographed image.
That is, when measured rigid body parallel movement, u x and u y in the above equation (9) becomes a constant value (uniform in the measurement region). On the other hand, when measured both rigid translational movement and the rigid rotation movement, since u x and u y may be represented as a two-dimensional plane, the movement amount measured displacement amount calculation represented by the following formula (13) It is expressed by a formula.
収差のモデルは収差を含まない座標の関数として表されているが、測定結果は収差を含む座標の関数として得られる。
ところで、デジタル画像相関法により得られる移動量は、収差を含む点（ｘ′，ｙ′）の関数として得られるが、（１３）式の収差のモデルは当該収差を含まない点（ｘ，ｙ）の関数として与えられている。そのため、各係数を直接決定することはできない。そこで、最小二乗法と繰返し演算を組み合わせて各係数を決定する。
Although the aberration model is expressed as a function of coordinates including no aberration, the measurement result is obtained as a function of coordinates including aberration.
By the way, the movement amount obtained by the digital image correlation method is obtained as a function of the point (x ′, y ′) including the aberration, but the aberration model of the equation (13) does not include the aberration (x, y ) As a function. Therefore, each coefficient cannot be determined directly. Therefore, each coefficient is determined by combining the least square method and the iterative calculation.
まず、収差を含む座標値（ｘ′，ｙ′）を（ｘ，ｙ）に初期値として代入し、最小二乗法により各係数の近似値を決定する．すなわち、下記（１４）式にて計算することができる。勿論、最小二乗法を用いる場合には、複数の画素について計算が行われる。 First, a coordinate value (x ′, y ′) including aberration is substituted as an initial value for (x, y), and an approximate value of each coefficient is determined by a least square method. That is, it can be calculated by the following equation (14). Of course, when the least square method is used, calculation is performed for a plurality of pixels.
ここで、 here,
上記式中、下付添字の１・・・ｎはデータ点のインデックスを示す。以上の計算により得られた各係数の近似値を用い、収差を含まない座標（ｘ，ｙ）の近似値を計算する。その座標値（ｘ，ｙ）を用い、再び、同様の最小二乗法により各係数を計算する。これを各係数の値が収束するまで繰り返すことにより、各係数を決定することができる。 In the above formula, subscripts 1... N indicate data point indexes. Using the approximate value of each coefficient obtained by the above calculation, the approximate value of coordinates (x, y) not including aberration is calculated. Using the coordinate value (x, y), each coefficient is calculated again by the same least square method. By repeating this until the value of each coefficient converges, each coefficient can be determined.
なお、収差の中心を求める必要がある場合には、収差の中心座標を未知数とし、非線形最小二乗法を用いればよい。
そして、上述したように、収差モデル量すなわち収差量が決定されると、この収差量を用いて、デジタル画像相関法にて計測された構造物における変形量の補正が行われる。なお、撮影画像の歪みを補正する場合、例えば画像の輝度値補間法などが用いられる。
If it is necessary to determine the center of aberration, the center coordinate of the aberration is set as an unknown and a nonlinear least square method may be used.
As described above, when the aberration model amount, that is, the aberration amount is determined, the deformation amount of the structure measured by the digital image correlation method is corrected using the aberration amount. In addition, when correcting distortion of a captured image, for example, an image luminance value interpolation method or the like is used.
上述した各事項を踏まえて、構造物、例えば橋梁における変形量計測方法について、簡単に説明する。
まず、図５および図６の模式図に示すように、橋梁１から或る距離だけ離れた位置に光学式カメラ装置２を配置した後、荷重Ｗを付与する位置の橋梁部分を所定範囲（所定領域、計算領域でもある）に亘って撮影する。
Based on the above items, a method for measuring the amount of deformation in a structure, for example, a bridge, will be briefly described.
First, as shown in the schematic diagrams of FIGS. 5 and 6, after the
次に、その位置に荷重Ｗを付与した状態で、所定範囲を撮影する。
そして、荷重Ｗの付与前と付与後との撮影画像に、デジタル画像相関法を適用して、その変形量を求める。
Next, a predetermined range is photographed with a load W applied to the position.
Then, the digital image correlation method is applied to the photographed images before and after the application of the load W to obtain the deformation amount.
次に、上記光学式カメラ装置２を用いて、荷重Ｗを付与しない状態で、上記所定領域を撮影した後、所定距離Ｌ（例えば、Ｕｘに相当）だけずれた位置で、同じく、カメラ装置２にて上記所定領域（計算領域）を撮影する。
Next, after photographing the predetermined area with the
次に、これらの撮影画像にデジタル画像相関法を用いて、所定領域についての移動量を検出する。
次に、この移動量を、最小二乗法の（１４）式に代入して、（１３）式の変位量算出式における各係数を決定した後、この変位量算出式を用いて、所定領域における歪曲収差量を求める。
Next, the amount of movement for a predetermined region is detected using a digital image correlation method for these captured images.
Next, after substituting this amount of movement into the equation (14) of the least square method and determining each coefficient in the equation (13) for calculating the amount of displacement, using this equation for calculating the amount of displacement, Determine the amount of distortion.
そして、この歪曲収差量を用いて、上記求められた変形量に対して補正を行うことにより、歪曲収差の影響を受けない、すなわち橋梁の変形量を精度良く計測することができる。 Then, by correcting the obtained deformation amount using the distortion amount, it is possible to accurately measure the deformation amount of the bridge without being affected by the distortion aberration.
ここで、上述した変形量計測方法をステップ様式にて記載しておく。
すなわち、この変形量計測方法は、構造物に力を付与した際の変形量を計測する方法であって、力の付与前と力の付与後とにおける所定領域を光学式カメラ装置で撮影するステップと、このカメラ装置で撮影された少なくとも２枚の撮影画像にデジタル画像相関法を適用して両撮影画像上の所定領域における変形量を検出するステップと、上記検出された変形量に対して、上記光学式カメラ装置のレンズによる歪曲収差を補正する収差補正ステップとを具備し、
且つ上記収差補正ステップに、上記カメラ装置により構造物の所定領域に対してずれた位置で少なくとも２枚の撮影画像を得るステップと、この少なくとも２枚の撮影画像にデジタル画像相関法を適用して両撮影画像上での所定領域の移動量を検出するステップと、上記カメラ装置を構造物に対してずらした際の平面上での移動量算出式に、収差モデル量を加えてなる変位量算出式に上記移動量を代入し、最小二乗法を用いて当該変位量算出式における各係数を決定するステップと、上記各係数が決定された変位量算出式を用いて収差量を求めるステップとを有せしめた方法である。
Here, the deformation amount measuring method described above is described in a step format.
That is, this deformation amount measuring method is a method of measuring a deformation amount when a force is applied to a structure, and is a step of photographing a predetermined area before and after the application of force with an optical camera device. And applying a digital image correlation method to at least two captured images captured by the camera device to detect a deformation amount in a predetermined region on both captured images, and for the detected deformation amount, An aberration correction step for correcting distortion by the lens of the optical camera device,
In addition, in the aberration correction step, a step of obtaining at least two photographed images at positions shifted from a predetermined region of the structure by the camera device, and applying a digital image correlation method to the at least two photographed images. Detecting the amount of movement of a predetermined area on both captured images and calculating the amount of displacement by adding the aberration model amount to the equation for calculating the amount of movement on the plane when the camera device is displaced with respect to the structure Substituting the amount of movement into the equation, determining each coefficient in the displacement amount calculation formula using the least square method, and obtaining an aberration amount using the displacement amount calculation formula in which each coefficient is determined. This is the method that you have.
さらに、上記収差補正ステップをより詳しく説明すれば、当該収差補正ステップに、カメラ装置にてしかも構造物の所定領域に対してずれた位置で少なくとも２枚の撮影画像を得るステップと、これら少なくとも２枚の撮影画像にデジタル画像相関法を適用して両撮影画像上での所定領域の移動量（ｕ′ｘ，ｕ′ｙ）を検出するステップと、収差を表す収差モデル量（αｘ，αｙ）にずれによる回転移動および並行移動を考慮した平面の式で表される移動量算出式を加えて得られる下記（Ａ）式および（Ｂ）式で示される変位量算出式に、上記ステップで検出された移動量を代入し、最小二乗法を用いて当該変形量算出式の少なくとも収差モデル量を表す係数を決定するステップと、上記各係数が決定された変位量算出式を用いて収差量を求めるステップとを有せしめた方法である。 Further, the aberration correction step will be described in more detail. In the aberration correction step, at least two shot images are obtained at a position shifted by the camera device and with respect to a predetermined region of the structure, and at least two of these A step of detecting a movement amount (u ′ x , u ′ y ) of a predetermined region on both captured images by applying a digital image correlation method to the captured images, and an aberration model amount (α x , α representing aberration) In addition to the displacement amount calculation formula shown by the following formulas (A) and (B) obtained by adding a movement amount calculation formula expressed by a plane formula in consideration of rotational movement and parallel movement due to deviation to y ), the above step Substituting the amount of movement detected in step (2), determining a coefficient representing at least an aberration model amount of the deformation amount calculation formula using the least square method, and using the displacement amount calculation formula in which each coefficient is determined amount A method of the steps was allowed chromatic seeking.
ｕ′ｘ＝ａ１ｘ＋ａ２ｙ＋ａ３＋αｘ ・・・（Ａ）
ｕ′ｙ＝ａ４ｘ＋ａ５ｙ＋ａ６＋αｙ ・・・（Ｂ）
上述したように、荷重を付与した構造物の変形量をシフトレンズを有する光学式カメラ装置を用いて、荷重の付与前と付与後とにおいてそれぞれ撮影した撮影画像から、デジタル画像相関法を用いて計測し、しかも、この変形量に対し、レンズによる歪曲収差量を補正するようにしたので、例えば計測機器を構造物に設置する必要がなく、また光ファイバーケーブルなども用いる必要がないため、安価な計測機器を用いることができるとともに、簡単な計測作業にて、構造物の変形量を精度良く計測することができる。延いては、構造物の経年状態を精度良く計測することができる。
u ′ x = a 1 x + a 2 y + a 3 + α x (A)
u ′ y = a 4 x + a 5 y + a 6 + α y (B)
As described above, the digital image correlation method is used to calculate the amount of deformation of a structure to which a load is applied from an image photographed before and after the application of the load using an optical camera device having a shift lens. Measurement is performed and the amount of distortion due to the lens is corrected for the amount of deformation. For example, it is not necessary to install a measuring instrument on the structure, and it is not necessary to use an optical fiber cable. A measuring device can be used, and the deformation amount of the structure can be accurately measured by a simple measuring operation. As a result, the aged state of the structure can be accurately measured.
なお、上記実施の形態においては、構造物に荷重を付与した際の変形量を検出するステップを説明した後に、収差補正ステップを説明したが、逆に、収差補正ステップを先に行い、後から、荷重を付与した際の変形量を検出するステップを行うようにしてもよい。 In the above embodiment, the aberration correction step is described after the step of detecting the deformation amount when the load is applied to the structure, but the aberration correction step is performed first. The step of detecting the deformation amount when the load is applied may be performed.
Ｗ 荷重
１ 橋梁
２ カメラ装置
W load 1
Claims (2)
力の付与前と力の付与後とにおける所定領域を光学式カメラ装置で撮影するステップと、
このカメラ装置で撮影された少なくとも２枚の撮影画像にデジタル画像相関法を適用して両撮影画像上の所定領域における変形量を検出するステップと、
上記検出された変形量に対して、上記光学式カメラ装置のレンズによる歪曲収差を補正する収差補正ステップとを具備し、
且つ上記収差補正ステップに、
上記カメラ装置により構造物の所定領域に対してずれた位置で少なくとも２枚の撮影画像を得るステップと、
この少なくとも２枚の撮影画像にデジタル画像相関法を適用して両撮影画像上での所定領域の移動量を検出するステップと、
上記カメラ装置を構造物に対してずらした際の平面上での移動量算出式に、収差モデル量を加えてなる変位量算出式に上記移動量を代入し、最小二乗法を用いて当該変位量算出式における各係数を決定するステップと、
上記各係数が決定された変位量算出式を用いて収差量を求めるステップと
を有せしめたことを特徴とする構造物における変形量計測方法。 A method for measuring the amount of deformation when a force is applied to a structure,
Photographing a predetermined area before and after applying force with an optical camera device; and
Applying a digital image correlation method to at least two photographed images photographed by the camera device to detect a deformation amount in a predetermined region on both photographed images;
An aberration correction step for correcting distortion by the lens of the optical camera device with respect to the detected deformation amount,
And in the aberration correction step,
Obtaining at least two photographed images at positions displaced from a predetermined region of the structure by the camera device;
Applying a digital image correlation method to the at least two captured images to detect a movement amount of a predetermined region on both captured images;
The displacement is calculated by adding the aberration model amount to the displacement amount calculation formula obtained by adding the aberration model amount to the movement amount calculation equation on the plane when the camera device is displaced with respect to the structure, and the displacement is calculated using the least square method. Determining each coefficient in the quantity formula,
A method for measuring a deformation amount in a structure, comprising: calculating an aberration amount using a displacement amount calculation formula in which each coefficient is determined.
2. The deformation amount measuring method for a structure according to claim 1, wherein a shift lens is used as a lens of the optical camera device.
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