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Strain and deformation angle for a steel pipe elbow using image measurement system under in-plane cyclic loading
Nuclear Engineering and Technology xxx (2017) 1e13
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Original Article
STRAIN AND DEFORMATION ANGLE FOR A STEEL PIPE ELBOW USING IMAGE MEASUREMENT SYSTEM UNDER IN-PLANE CYCLIC LOADING SUNG-WAN KIM a, HYOUNG-SUK CHOI a, BUB-GYU JEON a, *, DAE-GI HAHM b, MIN-KYU KIM b a
KOCED Seismic Simulation Test Center, Pusan National University, 49 Busandaehak-ro, Mulgeum, Yangsan, Kyungnam 50612, Republic of Korea Integrated Safety Assessment Division, Korea Atomic Energy Research Institute, 111 Daedeok-daero 989 Beon-gil, Yusung-gu, Daejeon 34057, Republic of Korea
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 April 2017 Received in revised form 9 November 2017 Accepted 9 November 2017 Available online xxx
Maintaining the integrity of the major equipment in nuclear power plants is critical to the safety of the structures. In particular, the soundness of the piping is a critical matter that is directly linked to the safety of nuclear power plants. Currently, the limit state of the piping design standard is plastic collapse, and the actual pipe failure is leakage due to a penetration crack. Actual pipe failure, however, cannot be applied to the analysis of seismic fragility because it is difficult to quantify. This paper proposes methods of measuring the failure strain and deformation angle, which are necessary for evaluating the quantitative failure criteria of the steel pipe elbow using an image measurement system. Furthermore, the failure strain and deformation angle, which cannot be measured using the conventional sensors, were efficiently measured using the proposed methods. © 2017 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Deformation Angle Failure Strain Image Measurement System Nuclear Power Plant Piping Steel Pipe Elbow
1. Introduction In a nuclear power plant in which a seismic isolation device has been installed, it is expected that there will be a considerable displacement, which does not apply to the existing nuclear power plants because the seismic load is managed by the seismic isolation device. Therefore, in a piping system that connects the structures in which a seismic isolation device has been installed and other general structures, the plastic deformation can be concentrated in specific parts, such as the elbows or tees, and cause piping failure. Therefore, it is necessary to review the seismic safety of such a piping system. A seismic safety evaluation of the piping system of a nuclear power plant is considered critical to the safety and operation of the nuclear power plant. Experimental and analytical studies have been conducted on piping systems to understand the possible fragility during a seismic event and to define the limit state. A shaking table was used to conduct a dynamic behavior analysis of a piping system made from different materials, considering the seismic load [1]. In the results, plastic deformation was observed in
* Corresponding author. E-mail address: [email protected] (B.-G. Jeon).
each pipe elbow. To analyze the dynamic behavior of a typical piping system subjected to a seismic load, the Japan Nuclear Energy Safety Organization (JNES) and the Nuclear Power Engineering Corporation (NUPEC) conducted cyclic loading tests on pipe elbows and shaking table tests on a piping system [2]. They conducted experiments to confirm the design method and limit state, and the experimental results indicated that the damage caused by the seismic load to the piping system was a result of low-frequency fatigue failure [3]. Overall, they determined the system to be safer than the individual components owing to factors such as the load redistribution [4]. Generally, the seismic safety review of a nuclear power plant includes a probabilistic seismic fragility analysis. The results of such an analysis vary drastically by failure criteria, and as such, it is critical to define the failure criteria with which severe accidents are actually expressed. Currently, the seismic design criteria for a piping system can identify only plastic collapse and cannot detect a rupture or leakage, which is the actual limit state. Therefore, the criteria cannot sufficiently reflect a critical accident. For a more reliable seismic fragility analysis, the definition of the limit state should be expanded. To confirm the limit state of a piping system, one study conducted an in-plane cyclic loading test at an elbow, which is one of the weakest points in the system. A crack was generated on the inside of the pipe elbow and propagated in the axis direction [5]. In
https://doi.org/10.1016/j.net.2017.11.001 1738-5733/© 2017 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Please cite this article in press as: S.-W. Kim, et al., STRAIN AND DEFORMATION ANGLE FOR A STEEL PIPE ELBOW USING IMAGE MEASUREMENT SYSTEM UNDER IN-PLANE CYCLIC LOADING, Nuclear Engineering and Technology (2017), https://doi.org/10.1016/j.net.2017.11.001
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addition, hoop strain and low-cycle ratcheting fatigue damage were observed. The limit state of the pipe elbow can be defined by calculating the damage index from the correlation between the load and the displacement of the in-plane cyclic loading test. As the design criteria and the experimental limit states do not match, Organization for Economic Co-operation and Development's Nuclear Energy Agency (OECD-NEA) launched the metallic component margins under a high seismic load (MECOS) benchmark initiative as a technical interchange to quantitatively evaluate the limit state of piping components and to include rupture or leakage under high seismic loads [6]. Prior studies have found the elbow to be a fragile element in the piping system with its failure triggered by low-cycle ratcheting fatigue. As the cause of failure is known, an analytical method can be used to anticipate the occurrence of failures during experimental studies. Although a damage or fatigue curve can be used to define the limit state of the pipe elbow, the results cannot be easily used in the probabilistic seismic fragility analysis. Therefore, this paper suggests a method of image signal processing to measure the failure strain and deformation angle (momentetheta relation), which are necessary for defining a reliable limit state. To measure the strain and deformation angle, which influence the deformation and damage of a structure, various reliable measurement techniques have been studied: use of a conventional sensor, numerical analysis using the finite element method, and image analysis using digital image processing. Generally, strain is an important factor in evaluating structural integrity. It is primarily measured using contact-type methods such as the use of an electric resistance strain gage. Such a sensor, however, is also sensitive to the external environment. Moreover, it cannot be relocated or reused, and it has a limited measurement range. Therefore, measuring a large strain is difficult. Measuring the deformation angle of pipe elbows, on the other hand, requires temporary installations for making the approach feasible and for affixing the sensor, which is not economical. In addition, as it is difficult to accurately install the temporary facility, the reliability of the measurement is low. Therefore, a method for measuring the strain and deformation angle from a remote distance, without attaching any sensor, is called for. In this study, we used an image measurement system to measure the failure strain and deformation angle of the steel pipe elbow and the zero-normalized sum of squared differences (ZNSSD) to measure the displacement, which is necessary for measuring the strain of the steel pipe elbow. Furthermore, the second-order shape function was used to measure the subpixels. In addition, to measure the failure strain in the hoop direction of the steel pipe elbow, we measured the average strain using the pixel-based displacement for a square area marked on the steel pipe elbow. For line recognition, which is needed to measure the deformation angle, the shape of the steel pipe elbow was enhanced using image signal processing, and the deformation angle was measured using the Hough transform of the enhanced image. Finally, an in-plane cyclic loading test was conducted to validate the method of measuring the failure strain in the hoop direction and deformation angle using an image measurement system for a steel pipe elbow, which is a weak part of a seismic isolation nuclear power plant piping system. Consequently, the deformation angle and failure strain in the hoop direction, which cannot be measured using the conventional sensors, were efficiently measured.
system, we used the gray level value of the image, which is a pattern analysis technique for measuring the difference between the two images [7e11]. The 8-bit gray level that is generally used in such an analysis expresses the information of an object with gray levels ranging from 0 to 255. The measurement conducted using the image correlation method separates the square-shaped image from both images to compare and measure the deformation. The small square-shaped image separated from the two images is called the “subset” or “window.” The window separated by the gray level value is used for comparing the correlations to measure the deformation. Fig. 1 shows the deformation measurement principle of the image correlation method, which registers a target window with an arbitrary template and finds the most similar target window from the region of interest (ROI) window, which changes over time. In Fig. 1, f ðxi ; yj Þ expresses the gray level pattern of the square separated from the reference image, and gðx0i ; y0j Þ expresses the gray level pattern of the square separated from the deformed image of an object by an external force. The size of the target window is that of a part image of the ð2M þ 1Þð2M þ 1Þsquare, where Mis half the size of the target window, which is a square. To measure the deformation of a structure, the correlation between the reference image and the deformed image was analyzed to find the coordinate with the highest correlation. In this study, the zero-normalized sum of squared differences (ZNSSD), as shown in Eq. (1), was used to compare the correlations of the two images. The coordinates with the minimum value ðCZNSSD Þ show the displacement of the object affected by the external force. In this regard, fm is defined as the mean values of the gray level of the target window. In addition, for an image that changes with time, gm is the mean value of gðx0i ; y0j Þ in the region that matches the current position of f ðxi ; yj Þ, and the calculation is carried out within the coordinates that are common to f ðxi ; yj Þ and gðx0i ; y0j Þ.
CZNSSD ¼
M M X X f ðx; yÞ fm gðx0 ; y0 Þ gm Df Dg i¼M j¼M
1
fm ¼
2
ð2M þ 1Þ
gm ¼
(1)
M M X X f xi ; y j ; i¼M j¼M
1
M M X X
ð2M þ 1Þ2
i¼M j¼M
g x0i ; y0j
(2)
2. Algorithm for measuring the strain and deformation angle 2.1. Strain measurement For the analysis of the correlation between the images obtained before and after the deformation using the image measurement
Fig. 1. Deformation measurement using the image correlation method.
Please cite this article in press as: S.-W. Kim, et al., STRAIN AND DEFORMATION ANGLE FOR A STEEL PIPE ELBOW USING IMAGE MEASUREMENT SYSTEM UNDER IN-PLANE CYCLIC LOADING, Nuclear Engineering and Technology (2017), https://doi.org/10.1016/j.net.2017.11.001
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vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u M M h i2 uX X f xi ; y j f m ; Df ¼ t i¼M j¼M
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u uX M h i2 u M X g x0i ; y0j gm Dg ¼ t
(3)
the deformation was to be measured but the average strain in the square area. As shown in Fig. 2A, the slope was obtained using the pixel position in the hoop direction and the pixel-based displacement at an arbitrary time, and Fig. 2B shows the strain obtained using each slope measured over time.
i¼M j¼M
y0j ¼ yj þ h xi ; yj
ði; j ¼ M : MÞ
(4)
Assuming that the reference and deformed images are rigid body translations, the displacements of each point of the window become the same. Therefore, the zero-order shape function, as shown in Eq. (5), can be applied.
x0 xi ; yj ¼ u;
h0 xi ; yj ¼ v
(5)
However, as the zero-order shape function is insufficient for showing the shape change of the deformed image, the first-order shape function of Eq. (6), which is suitable for translation, rotation, and shear, is generally used.
x1 xi ; yj ¼ u þ ux Dx þ uy Dy;
h1 xi ; yj ¼ v þ vx Dx þ vy Dy (6)
The second-order shape function can be applied to a more complex deformation of the image, as shown in Eq. (7).
1 1 2 2 þ uxy Dy2 þ uxy DxDy 1 h2 xi ; yj ¼ v þ vx Dx þ vy Dy þ vxx Dx2 2 1 2 þ vyy Dy þ vxy Dy2 þ vxy DxDy 2
x2 xi ; yj ¼ u þ ux Dx þ uy Dy þ uxx Dx2 þ uyy Dy2
Dx/0
Du du 0 ¼ Dx dx
x axis displacement x axis pixel position
(8)
Fig. 3 gives the algorithm for measuring the average strain in the hoop direction for the steel pipe elbow using the image signal processing, which consists of six steps. The first step acquires image files and arranges them in chronological order for measuring the time history of the hoop strain of the steel pipe elbow. The second step designates the control points (9 9 points, a total of 81 points) within the square area in the obtained reference image where the strain needs to be identified. The third step identifies the coordinate with the maximum correlation through the calculation of the ZNSSD to find the control points at which the target window most optimally matches the ROI window. The fourth step rearranges and corrects for the location of the pixel using the second-order polynomial function to correct for the geometric distortion caused by the displacement and deformation and to calculate the subpixel of the displacement. The fifth step analyzes the pixel-based displacement using the pixel of the point with the optimal matching and the calculated subpixel information. The sixth step measures the average strain using the analyzed pixel-based displacement and the pixel position. After the sixth step, based
0.2
0.1
0.0
–0.1
–0.2 510
520
530
540
550
Hoop direction pixel position [pixel]
(7)
0.03
0.02
[
In Eqs. (5)e(7), Dx ¼ xi x0 , Dy ¼ yj y0 , uand v refer to the displacements toward the xand y directions from the center of the target window. The variables ux , uy , vx , and vy refer to the first-order displacement gradient of the target window, whereas uxx , uxy , uyy , vxx , vxy , and vyy refer to the second-order displacement gradient. In this study, the second-order shape function in Eq. (7) was used considering the bending and nonlinear behavior of an object due to an external force. In conducting the in-place cyclic loading test on the steel pipe elbow, the strain was measured using Eq. (8), considering the component characteristics. As shown in Eq. (8), the x-axis displacement along the x-axis pixel position was plotted for each image based on the pixel, and the x-axis strain was measured by calculating the slope using the linear function. The average strain that was used in this study was not the strain at the point in which
(A)
Hoop strain [ ε
x0i ¼ xi þ x xi ; yj ;
εx ¼ lim
Hoop direction displacement [pixel]
As object deformation by an external force occurs continuously, the displacement value around the surrounding points can be measured using a shape function. For a measurement using the image correlation method, zero through second-order shape functions is generally used, and to consider the effect of the object rotation and shearing by an external force, the first through secondorder shape function is used. Eq. (4) expresses the shape function using the image correlation method, where x is the shape function of the x-coordinate, h is the shape function of the y-coordinate, u and v are the displacement values at each location measured using the image correlation method, and M is half the size of the target window.
3
0.01
0.00
–0.01
–0.02 0
200
400
600
800
1,000
Time [sec]
(B) Fig. 2. Method for measuring the average strain. (A) Slope measured at an arbitrary time. (B) Measured strain.
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Image acquirement (Image file(JPEG)) Selecting control points (9× 9 points, total of 81 point)
ZNSSD calculation
ZNSSD calculation Reference image
Deformed image
Deformed image
ROI window Target window Target
Random target Initial coordinate ( x0 , y 0 )
Frame 1 (t 0 )
Coordinates of best match ( x2 , y2 )
Coordinates of best match ( x1 , y1 )
Frame 3 (t2 )
Frame 2 (t1 )
Subpixel estimation (Second-order shape function) Displacement analysis (Based on pixel)
t = t + Δt
Strain measurement (Average strain) Fig. 3. Summary of the algorithm.
on the calculated position as the standard, the strain is repeatedly calculated over time from the third step. As shown in Fig. 4, in this study, an automated program of the algorithm was coded and used with MATLAB. The left figure in Fig. 4 is the processed image over time, and the point marked in blue is
the control point designated in the reference image in step 2 of Fig. 3. The cyan point is the optimal-matching point in the deformed image in step 3 of Fig. 3. The right figure shows the hoop strain that was measured using the slope that was calculated over time.
Fig. 4. Program for measuring the average strain using MATLAB.
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2.2. Deformation angle measurement
The size of the second-order column vector is as shown in Eq. (13).
The purpose of image enhancement is to process the original image and then to convert it in accordance with a specific application purpose [12]. The region required for applying the image signal processing refers to the assembly of pixels that constitute the image. In this study, to enhance the shape of the steel pipe elbow, the Laplacian operator was applied as the isotropic differential operator. The bivariate function f ðx; yÞ is defined as shown in Eq. (9), and because the random-order differential is a linear calculation, the Laplacian operator becomes a linear operator as well [13].
V2 f ¼
v2 f v2 f þ vx2 vy2
(9)
The digitization of the second-order Laplacian operator is obtained by adding the two components of the second-order partial differential along the x and y directions, as shown in Eq. (10).
V2 f ¼ ½f ðx 1; y 1Þ þ f ðx; y 1Þ þ f ðx þ 1; y 1Þ þ f ðx 1; yÞ þ f ðx þ 1; yÞ þ f ðx 1; y þ 1Þ þ f ðx; y þ 1Þ (10) As the Laplacian operator is a differential operator, the importance of brightness, which emphasizes the discontinuity of the brightness within the image and changes gradually, is reduced. The basic principle for using the Laplacian operator for image enhancement is shown in Eq. (11), and it is used when the coefficient in the middle of the Laplacian mask is negative.
(11)
When substituting Eq. (10) for the right hand side of Eq. (11), the result obtained is as shown in Fig. 5. The shape of the steel pipe elbow was enhanced by weighting using the 3 3 convolution mask. The boundary of the steel pipe elbow with an enhanced shape refers to the detection of the boundary between the two regions with relatively different gray levels and can be realized by calculating the difference between the two neighboring regions. The boundary line provides information such as the object's location, shape, and size, and it is used in the pretreatment step to enhance the boundary of the steel pipe elbow. During image signal processing for enhancing the boundary line, the first derivation is realized using the size of the gradient, and it is defined by the second-order column vector, as shown in Eq. (12).
3 vf 6 vx 7 6 7 ¼6 7 4 vf 5 vy 2
Vf ¼
Gx Gy
" 2 #1=2 i1=2 h vf 2 vf 2 2 Vf ¼ magðVf Þ ¼ Gx þ Gy ¼ þ vx vy
(12)
Although the component of the gradient vector itself is a linear operator, it is not considered a linear operator owing to the squaring and square root calculation. The partial differential of Eq. (12) is not rotation invariant, but the size of the gradient vector is. As the execution of Eq. (13) on the entire image requires a huge calculation, the gradient size should generally be approximated using the absolute value instead of squaring and square root calculation, as in Eq. (14).
Vf ¼ jGx j þ Gy
Fig. 5. Sharpening filter.
(14)
Generally, the two different definitions, as suggested by Roberts [14], apply the differential method, whereas the 3 3 mask and approximation use the absolute value for image enhancement, as shown in Eq. (15).
þ 2z4 þ z7 Þj (15) In this study, the detection of a steel pipe elbow's boundary was facilitated using the Sobel operator of a 3 3 size mask [15], as shown in Fig. 6. The sum of all the mask's coefficients is 0. The various theories that apply processing based on the shape of an object or a region inside an image for generating a new image required for interpretation are called “mathematical morphologies.” Among the algorithms of the mathematical morphology, the dilation algorithm expands the outermost pixels of the object [16]. Through this, the size of the object is expanded whereas the background is reduced. The expansion mask adds a pixel along the circumference of a white body. A region that has the same size is excluded from the calculation, while the white value is allocated to the central pixel of the mask, in case more than one different pixel exists. In this study, to facilitate line recognition by enhancing the shape of the steel pipe elbow, a 3 3 dilation structure, as shown in Fig. 7, was used to enhance the shape. For the shape of the steel pipe elbow that had been improved through the pretreatment process, the Hough transform was used to calculate the deformation angle by recognizing the line that changed with time [17e19]. The Hough transform refers to the process of finding specific shapes, such as lines and circles, from the image. It is a method of determining the association between specific points within the image and extracting their characteristics.
−1 −2 −1
−1
0
1
0 1
−2 −1
0 0
2 1
−1 −1 −1 −1 9 −1 −1 −1 −1
(13)
Vf zjðz7 þ 2z5 þ z9 Þ ðz1 þ 2z2 þ z3 Þj þ jðz3 þ 2z5 þ z9 Þ ðz1
þ f ðx þ 1; y þ 1Þ 8f ðx; yÞ
gðx; yÞ ¼ f ðx; yÞ V2 f ðx; yÞ
5
(A)
0 2
0 1 (B)
Fig. 6. Sobel operator. (A) Horizontal mask. (B) Vertical mask.
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0
1
0
1 0
1 1
1 0
Fig. 7. Dilation structure.
The Hough transform applies Eq. (16) to all the characteristic points of the x and y coordinates in the space to accumulate the Hough sequence values of the q and s coordinates from the converted coordinates, as shown in Fig. 8. After the execution of the Hough transform, the q and s coordinates of the maximum values in the region obtained from the Hough sequence are used to detect the straight line from the x and y coordinates of the space. The straight line passing through a certain point is expressed using Eq. (16). The polar coordinate system is obtained using the pixel information of x and y on the space coordinate system s and q. The pixel indicating the identical coordinate on the polar coordinate system becomes the line in the space coordinate system.
s ¼ x cos q þ y sin q
(16)
Here, s refers to the length of the normal line from the origin to the straight line, q refers to the angle between the normal line and the xaxis, and ðx; yÞ refers to the coordinate of the characteristic point in the space. When conducting the in-plane cyclic loading test, the minimum internal angle of the line, which is defined to be the line of each shape, is set to 30 , and any line whose internal angle is below 30 is removed using Eq. (17). This inner angle is identified to reduce the image noise caused by acquiring images and errors due to the line recognition generated by the other environments. Eq. (17) and lx , ly show the coordinates of the extracted line, and the angle is the internal angle of the line. As shown in Fig. 9, the information on the lines whose internal angle is 30 or larger based on the two parallel lines that are the closest to the upper and lower directions of the center of the image is stored.
q1 ¼ arctan
n X ly0n ly1n i¼0
jq1 j > 30
lx0n lx1n
! ; q2 ¼ arctan
n X ly00n ly01n lx0 lx00n i¼0 0n
!
q1 ¼ ðlx0 ; ly0 ; lx1 ; ly1 Þ;
q2 ¼ lx00 ; ly00 ; lx01 ; ly01 ;
jq2 j > 30 else ¼ remove Defomation Angle ¼ jq1 j þ jq2 j (17)
(A)
Fig. 9. Deformation angle measurement.
Fig. 10 shows the algorithm for measuring the deformation angle of the steel pipe elbow, and it is classified into five steps. An ROI window is extracted from the steel pipe elbow to measure the deformation angle. The shape of the steel pipe elbow is enhanced using the sharpening filter. The boundary of the steel pipe elbow is extracted using the Sobel operators on the enhanced shape. To facilitate line recognition, the dilation structure is applied to expand the outermost pixel. In addition, the deformation angle is measured through line recognition using the Hough transform of the shape of the steel pipe elbow. 3. In-plane cyclic loading test for the steel pipe elbow 3.1. Image measurement system The sensor comprising the image measurement system is both mobile and simple to install. The system includes a complementary metal oxide semiconductor (CMOS) camera (IMB-7050G, 2448 2048 pixels) and two laptop computers. The CMOS camera and laptop computers transmit data and control the operation through a local area network (LAN) communication. A lens (M5018MP2) was used to measure the strain and deformation angle of a remotely located steel pipe elbow. An image measurement system was installed to measure the strain and deformation angle of the steel pipe elbow, as shown in Fig. 11.
(B)
Fig. 8. Hough transform in s, q. (A) Straight line in an image space. (B) s, q parameter space.
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7
Fig. 10. Algorithm for measuring the deformation angle.
Fig. 11. Image measurement system.
Fig. 12. Manufacture of the steel pipe elbow.
3.2. Steel pipe elbow In this study, the steel pipe elbow was determined to be the vulnerable part. As shown in Fig. 12, an SA-106 3-inch SCH40 specimen of the American Society of Mechanical Engineers (ASME) B36.10M was manufactured. The specifications of the steel pipe elbow are listed in Table 1. To enable plastic behavior at the bend of the specimen, a direct pipe with a sufficient length over 3D (270 mm) was welded onto the elbow. The sufficient length of the direct pipe was considered in deriving the same experimental
Table 1 Specifications of the steel pipe elbow. Composition
Radius
Thickness
Outer diameter
Material
Elbow Pipe
114.3 mm N/A
5.49 mm
88.9 mm
SA-106
results as the series model. To represent the pin connection at both ends of the specimen, a fixture was manufactured and welded onto the specimen. As shown in Fig. 13, the fixture was connected to a universal testing machine (UTM). The fixtures and pin for connecting the respective fixtures were precisely manufactured so that they would not affect the accuracy of the experiment. To minimize the influence of external sources, a pipe manufactured by the same company that provides piping products to actual nuclear power plants was used. During the manufacture of the specimen, the joints connecting the parts were welded together. An internationally certified welding company that provides its products to nuclear power plants was requested to perform welding. 3.3. Experimental setup The installation positions of the sensors are shown in Fig. 14. Fig. 14A shows the steel pipe elbow installed in the UTM, and
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Fig. 13. Fixture for the UTM connection.
Fig. 14B shows the lighting installed to minimize optical noises. The in-plane cyclic loading test was conducted through displacement control. To compare the displacement with the linear variable differential transformer (LVDT) mounted inside the UTM, target 1 was installed in a jig for the UTM connection, as shown in Fig. 14C. Fig. 14C depicts that the circle-shaped targets were marked with 50-mm gaps on the steel pipe elbow to measure the deformation angle, and among the marked circles, targets 2e5 were used to measure the deformation angle. In addition, the deformation angle was measured with the line recognition of the steel pipe elbow shape, which was compared with the deformation angle measured with targets 2e5. Fig. 14D shows the randomly marked targets for measuring the failure strain in the hoop direction of the steel pipe elbow. The failure strain was measured using a total of 81 control points at the center of the elbow. As shown in Fig. 14E, the strain gage was installed at the center of the symmetry plane of the steel pipe elbow because installing the strain gage at the place where the image measurement system had been installed could interfere with the image analysis. The strain measured with this strain gage was compared with the hoop strain measured using image signal
Fig. 14. Location of sensor. (A) Steel pipe elbow. (B) Lighting. (C) Installed and marked targets. (D) Marked target. (E) Installed strain gage. (F) Air pump.
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processing. Fig. 14F shows the air pump that was used to provide internal pressure of the steel pipe elbow up to 3 MPa. During the experiment, the image measurement system was used to acquire 2448 2048 pixel images at two frames per second. The measurement using the UTM was conducted at a data acquisition speed of 1 Hz whereas that using the strain gage was conducted at a data acquisition speed of 0.25 Hz. To confirm the accuracy and precision of the responses measured by the conventional sensor through image analysis, the percent error of Eq. (18) and the root mean square (RMS) error of Eq. (19) were used to conduct error analysis. Here, dm refers to the response measured by the conventional sensor, dc to the response measured by the image signal processing, and n to the number of acquired data.
Percent Error ¼
n X
, 2
ðdm dc Þ
i¼1
n X
ðdm Þ2
(18)
i¼1
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n . uX ðdm dc Þ2 n RMS Error ¼ t
(19)
i¼1
3.4. In-plane cyclic loading test To verify the effectiveness of the algorithm for measuring the strain and deformation angle using image signal processing, an inplane cyclic loading test was conducted [20]. Table 2 lists the results for each load case on the steel pipe elbow. In this study, the failure mode of the steel pipe elbow was defined as a through-crack. Therefore, the in-plane cyclic loading test was conducted until the occurrence of a through-crack. Fig. 15 shows the elbow with a through-crack formed at the crown. Fig. 16 shows a graph comparing the responses measured from the LVDT installed inside the UTM in the in-plane cyclic loading test with those measured using image signal processing. The two responses matched each other well. In Table 3, because the percent error rate in each load case is within 0.1% and the RMS error is within 0.5 mm, we determined that the error was very small. Therefore, the reliability of the displacement response measured using image signal processing was good. Fig. 17 shows the comparison of the hoop strain measured using image signal processing and the strain response measured with the strain gage. When a through-crack occurred, as shown in Fig. 17, the nonlinear behavior of the elbow exceeded the measurement limit of the electric resistance strain gage. We found that the electric resistance strain gage could not measure the strain before the through-crack occurred because it already exceeded the performance limit after the nonlinear behavior started. In addition, at a load case over ± 50 mm, the strain gage exceeded the performance limit even in the first cycle. Table 4 lists the results of an error analysis conducted on the strain data obtained using the strain gage and through image signal processing before the performance limit of the strain gage was exceeded. As shown in Table 4, the error rate was within 10% and the RMS error was within 0.01, which indicates that the error Table 2 Load cases. Load case Loading amplitude (mm) Internal pressure (MPa) Leakage cycles 1 2 3 4 5 6
±20 ±30 ±40 ±50 ±60 ±70
3 3 3 3 3 3
76 30 13 9 8 5
9
Fig. 15. Elbow with a through-crack.
was somewhat large. This, however, is seemingly due to the local problem of installing the strain gage symmetrically. Although there was a difference between the response measured with the strain gage and that measured using image signal processing, the reliability was verified in the elastic region through a comparison with the results obtained with the use of the electric resistance strain gage. Fig. 18 shows a comparison of the deformation angle measured using the displacement measured using targets 2e5 and that measured using the Hough transform of the image obtained using image signal processing. In the figure, a phase difference can be seen at the starting point. This is because the circle-shaped target was not accurately positioned at the center of the steel pipe elbow. The deformation angle measured using the shape and that measured using targets 2e5 marked on the steel pipe elbow in Table 5 show an error rate of within 0.1% and an RMS error of within 0.6 . Therefore, the error was determined to be very small. In addition, when measuring the deformation angle, it is possible to obtain a reliable measurement by using the shape of the steel pipe elbow without the installation of targets. In addition, the method of measuring the deformation angle suggested in this study is expected to be useful when the failure criteria of the steel pipe elbow are expressed using the relationship between the moment and theta. 4. Conclusions This study proposed a noncontact-type measurement method using image signal processing based on an image measurement system that measured the failure strain and deformation angle during an in-plane cyclic loading test for a steel pipe elbow. The reliability of the image processing data was verified because the difference between the responses of the LVDT of the UTM obtained through the in-plane cyclic loading test and the responses measured using image signal processing was small. Even though there were differences between the responses measured using the strain gage and those measured using image signal processing due to the measurement position, the reliability was verified by comparing the results with the measurement result up to the performance limit of the electric resistance strain gage. Furthermore, the validity of the image processing data was confirmed because the deformation angle obtained by analyzing the image data through image signal processing showed an accuracy similar to the deformation angle derived using targets. It was found that the image signal processing algorithm can be used to measure the failure strain and deformation angle from a remote distance without installing the conventional sensors. Therefore, the measured failure strain and deformation angle are expected to be applicable in the future as important factors in defining the failure criteria for a seismic isolation nuclear power plant piping system. When the strain and deformation angle of a structure need to be measured using image signal processing, the measurement method suggested in this study can be applied. Using this method will enable simple and economical measurement in various fields.
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Time [sec]
(E)
(F)
Fig. 16. Comparison of the response measured from LVDT of the UTM. (A) Load case 1. (B) Load case 2. (C) Load case 3. (D) Load case 4. (E) Load case 5. (F) Load case 6.
Table 3 Error analysis of the response measured from the LVDT of the UTM. Load case
Percent error (%)
RMS error (mm)
1 2 3 4 5 6
0.032 0.065 0.0231 0.017 0.021 0.014
0.461 0.541 0.429 0.456 0.619 0.592
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S.-W. Kim et al. / Nuclear Engineering and Technology xxx (2017) 1e13
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Strain gage Average strain (image)
0
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500
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Time [sec]
(F)
(E)
Fig. 17. Comparison of the response measured by the strain gage. (A) Load case 1. (B) Load case 2. (C) Load case 3. (D) Load case 4. (E) Load case 5. (F) Load case 6.
Table 4 Error analysis of the response measured by the strain gage. Load case
Section (sec)
Percent error (%)
RMS error
1 2 3 4 5 6
All 0e2905 0e349 0e125 e e
2.145 7.349 1.145 1.832 e e
0.001 0.003 0.001 0.001 e e
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95 90 85 80
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Time [sec]
Time [sec]
(E)
(F)
Fig. 18. Comparison of the measured deformation angle. (A) Load case 1. (B) Load case 2. (C) Load case 3. (D) Load case 4. (E) Load case 5. (F) Load case 6.
Table 5 Error analysis of the measured deformation angle. Load case
Percent error (%)
RMS error ( )
1 2 3 4 5 6
0.001 0.002 0.002 0.001 0.003 0.004
0.208 0.348 0.403 0.183 0.526 0.416
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Conflicts of interest All authors have no conflicts of interest to declare. Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (NRF2017M2A8A4039749). Moreover, the authors would like to thank the KOCED Seismic Simulation Test Center for their assistance with the test equipment. References [1] F. Touboul, P. Sollogoub, N. Blay, Seismic behaviour of piping systems with and without detect: experimental and numerical evaluations, Nucl. Eng. Design 192 (1999) 243e260. [2] T. Zhang, F.W. Brust, G. Wikowski, D.J. Shim, J. Nie, C.H. Hofmayer, S.A. Ali, Analysis of JNES seismic tests on degraded piping, in: ASME 2010 Pressure Vessels and Piping Conference, Bellevue, Washington, USA, 2010. PVP2010e25333. [3] T. Otoyo, A. Otani, S. Fukushima, M. Jimbo, T. Yamamoto, T. Sakakida, S. Onishi, Development of an evaluation method for seismic isolation system of nuclear power facilities (Part 4) failure behavior of crossover piping for seismic isolation system, in: ASME 2014 Pressure Vessels and Piping Conference, Anaheim, California, USA, 2014. PVP2014-29011. [4] Y. Park, G. DeGrassi, C. Hofmayer, P. Bezler, N. Chokshi, Analysis of nuclear piping system seismic tests with conventional and energy absorbing supports, in: 14th International Conference on Structural Mechanics in Reactor Technology (SMiRT 14), Lyon, France, 1997. BNL-NUREG-64173. [5] K. Mizuno, H. Shimizu, M. Jimbo, N. Oritani, S. Onishi, Development of an evaluation method for seismic isolation systems of nuclear power facilities (Part 5) fatigue test of the crossover piping, in: ASME 2014 Pressure Vessels and Piping Conference, Anaheim, California, USA, 2014. PVP2014e29032.
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[6] http://www.mecosbenchmark.org. [7] H.A. Bruk, S.R. McNeil, M.A. Sutton, W.H. Perter, Digital image correlation using Newton-Raphson method of partial differential correlation, Exp. Mech. 29 (1989) 261e267. [8] J.P. Lewis, Fast normalized cross-correlation, Vision Interface (1995) 120e123. [9] S. Roux, F. Hild, Digital image mechanical identification (DIMI), Exp. Mech. 48 (2008) 495e508. [10] F. Hild, S. Roux, Comparison of local and global approaches to digital image correlation, Exp. Mech. 52 (2012) 1503e1519. [11] B. Pan, K. Qian, H. Xie, A. Asundi, Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review, Meas. Sci. Technol. 20 (2009) 1e17. [12] A. Young, Image enhancement and restoration, in: Handbook of Pattern Recognition and Image Processing, first ed., Academic Press, New York, 1986. [13] A. Rosenfeld, A.C. Kak, Digital Picture Processing, second ed., Academic Press, New York, 1982. [14] L.G. Roberts, Machine Perception of Three-Dimensional Solids, Optical and Electro-Optical Information Processing, Doctor's thesis of Massachusetts Institute of Technology, 1963. [15] O.R. Vincent, O. Folorunso, A Descriptive algorithm for Sobel image edge detection, in: Proceedings of Informing Science & IT Education Conference (InSITE 2009), Macon, GA, USA, 2009, pp. 97e107. [16] J. Wu, A. Paul, Y. Xing, Y. Fang, J. Jeong, L. Jiao, G. Shi, Morphological dilation image coding with context weights prediction, Signal Process. Image Commun. 25 (2010) 717e728. [17] D.H. Ballard, Generalizing the Hough transform to detect arbitrary shapes, Pattern Recognit. 13 (1981) 111e122. [18] N. Suetake, E. Uchino, K. Hirata, Generalized fuzzy Hough transform for detecting arbitrary shapes in a vague and noisy image, Soft Comput. 10 (2006) 1161e1168. [19] S. Zhou, Y. Jiang, J. Xi, J. Gong, G. Xiong, H. Chen, A Novel Lane Detection Based on Geometrical Model and Gabor Filter, Intelligent Vehicle Symposium, San Diego, CA, USA, 2010, pp. 59e64. [20] B.G. Jeon, S.W. Kim, H.S. Choi, D.U. Park, N.S. Kim, A failure estimation method of steel pipe elbows under in-plane cyclic loading, Nucl. Eng. Technol. 49 (2017) 245e253.
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Original Article
STRAIN AND DEFORMATION ANGLE FOR A STEEL PIPE ELBOW USING IMAGE MEASUREMENT SYSTEM UNDER IN-PLANE CYCLIC LOADING SUNG-WAN KIM a, HYOUNG-SUK CHOI a, BUB-GYU JEON a, *, DAE-GI HAHM b, MIN-KYU KIM b a
KOCED Seismic Simulation Test Center, Pusan National University, 49 Busandaehak-ro, Mulgeum, Yangsan, Kyungnam 50612, Republic of Korea Integrated Safety Assessment Division, Korea Atomic Energy Research Institute, 111 Daedeok-daero 989 Beon-gil, Yusung-gu, Daejeon 34057, Republic of Korea
b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 11 April 2017 Received in revised form 9 November 2017 Accepted 9 November 2017 Available online xxx
Maintaining the integrity of the major equipment in nuclear power plants is critical to the safety of the structures. In particular, the soundness of the piping is a critical matter that is directly linked to the safety of nuclear power plants. Currently, the limit state of the piping design standard is plastic collapse, and the actual pipe failure is leakage due to a penetration crack. Actual pipe failure, however, cannot be applied to the analysis of seismic fragility because it is difficult to quantify. This paper proposes methods of measuring the failure strain and deformation angle, which are necessary for evaluating the quantitative failure criteria of the steel pipe elbow using an image measurement system. Furthermore, the failure strain and deformation angle, which cannot be measured using the conventional sensors, were efficiently measured using the proposed methods. © 2017 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Deformation Angle Failure Strain Image Measurement System Nuclear Power Plant Piping Steel Pipe Elbow
1. Introduction In a nuclear power plant in which a seismic isolation device has been installed, it is expected that there will be a considerable displacement, which does not apply to the existing nuclear power plants because the seismic load is managed by the seismic isolation device. Therefore, in a piping system that connects the structures in which a seismic isolation device has been installed and other general structures, the plastic deformation can be concentrated in specific parts, such as the elbows or tees, and cause piping failure. Therefore, it is necessary to review the seismic safety of such a piping system. A seismic safety evaluation of the piping system of a nuclear power plant is considered critical to the safety and operation of the nuclear power plant. Experimental and analytical studies have been conducted on piping systems to understand the possible fragility during a seismic event and to define the limit state. A shaking table was used to conduct a dynamic behavior analysis of a piping system made from different materials, considering the seismic load [1]. In the results, plastic deformation was observed in
* Corresponding author. E-mail address: [email protected] (B.-G. Jeon).
each pipe elbow. To analyze the dynamic behavior of a typical piping system subjected to a seismic load, the Japan Nuclear Energy Safety Organization (JNES) and the Nuclear Power Engineering Corporation (NUPEC) conducted cyclic loading tests on pipe elbows and shaking table tests on a piping system [2]. They conducted experiments to confirm the design method and limit state, and the experimental results indicated that the damage caused by the seismic load to the piping system was a result of low-frequency fatigue failure [3]. Overall, they determined the system to be safer than the individual components owing to factors such as the load redistribution [4]. Generally, the seismic safety review of a nuclear power plant includes a probabilistic seismic fragility analysis. The results of such an analysis vary drastically by failure criteria, and as such, it is critical to define the failure criteria with which severe accidents are actually expressed. Currently, the seismic design criteria for a piping system can identify only plastic collapse and cannot detect a rupture or leakage, which is the actual limit state. Therefore, the criteria cannot sufficiently reflect a critical accident. For a more reliable seismic fragility analysis, the definition of the limit state should be expanded. To confirm the limit state of a piping system, one study conducted an in-plane cyclic loading test at an elbow, which is one of the weakest points in the system. A crack was generated on the inside of the pipe elbow and propagated in the axis direction [5]. In
https://doi.org/10.1016/j.net.2017.11.001 1738-5733/© 2017 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
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addition, hoop strain and low-cycle ratcheting fatigue damage were observed. The limit state of the pipe elbow can be defined by calculating the damage index from the correlation between the load and the displacement of the in-plane cyclic loading test. As the design criteria and the experimental limit states do not match, Organization for Economic Co-operation and Development's Nuclear Energy Agency (OECD-NEA) launched the metallic component margins under a high seismic load (MECOS) benchmark initiative as a technical interchange to quantitatively evaluate the limit state of piping components and to include rupture or leakage under high seismic loads [6]. Prior studies have found the elbow to be a fragile element in the piping system with its failure triggered by low-cycle ratcheting fatigue. As the cause of failure is known, an analytical method can be used to anticipate the occurrence of failures during experimental studies. Although a damage or fatigue curve can be used to define the limit state of the pipe elbow, the results cannot be easily used in the probabilistic seismic fragility analysis. Therefore, this paper suggests a method of image signal processing to measure the failure strain and deformation angle (momentetheta relation), which are necessary for defining a reliable limit state. To measure the strain and deformation angle, which influence the deformation and damage of a structure, various reliable measurement techniques have been studied: use of a conventional sensor, numerical analysis using the finite element method, and image analysis using digital image processing. Generally, strain is an important factor in evaluating structural integrity. It is primarily measured using contact-type methods such as the use of an electric resistance strain gage. Such a sensor, however, is also sensitive to the external environment. Moreover, it cannot be relocated or reused, and it has a limited measurement range. Therefore, measuring a large strain is difficult. Measuring the deformation angle of pipe elbows, on the other hand, requires temporary installations for making the approach feasible and for affixing the sensor, which is not economical. In addition, as it is difficult to accurately install the temporary facility, the reliability of the measurement is low. Therefore, a method for measuring the strain and deformation angle from a remote distance, without attaching any sensor, is called for. In this study, we used an image measurement system to measure the failure strain and deformation angle of the steel pipe elbow and the zero-normalized sum of squared differences (ZNSSD) to measure the displacement, which is necessary for measuring the strain of the steel pipe elbow. Furthermore, the second-order shape function was used to measure the subpixels. In addition, to measure the failure strain in the hoop direction of the steel pipe elbow, we measured the average strain using the pixel-based displacement for a square area marked on the steel pipe elbow. For line recognition, which is needed to measure the deformation angle, the shape of the steel pipe elbow was enhanced using image signal processing, and the deformation angle was measured using the Hough transform of the enhanced image. Finally, an in-plane cyclic loading test was conducted to validate the method of measuring the failure strain in the hoop direction and deformation angle using an image measurement system for a steel pipe elbow, which is a weak part of a seismic isolation nuclear power plant piping system. Consequently, the deformation angle and failure strain in the hoop direction, which cannot be measured using the conventional sensors, were efficiently measured.
system, we used the gray level value of the image, which is a pattern analysis technique for measuring the difference between the two images [7e11]. The 8-bit gray level that is generally used in such an analysis expresses the information of an object with gray levels ranging from 0 to 255. The measurement conducted using the image correlation method separates the square-shaped image from both images to compare and measure the deformation. The small square-shaped image separated from the two images is called the “subset” or “window.” The window separated by the gray level value is used for comparing the correlations to measure the deformation. Fig. 1 shows the deformation measurement principle of the image correlation method, which registers a target window with an arbitrary template and finds the most similar target window from the region of interest (ROI) window, which changes over time. In Fig. 1, f ðxi ; yj Þ expresses the gray level pattern of the square separated from the reference image, and gðx0i ; y0j Þ expresses the gray level pattern of the square separated from the deformed image of an object by an external force. The size of the target window is that of a part image of the ð2M þ 1Þð2M þ 1Þsquare, where Mis half the size of the target window, which is a square. To measure the deformation of a structure, the correlation between the reference image and the deformed image was analyzed to find the coordinate with the highest correlation. In this study, the zero-normalized sum of squared differences (ZNSSD), as shown in Eq. (1), was used to compare the correlations of the two images. The coordinates with the minimum value ðCZNSSD Þ show the displacement of the object affected by the external force. In this regard, fm is defined as the mean values of the gray level of the target window. In addition, for an image that changes with time, gm is the mean value of gðx0i ; y0j Þ in the region that matches the current position of f ðxi ; yj Þ, and the calculation is carried out within the coordinates that are common to f ðxi ; yj Þ and gðx0i ; y0j Þ.
CZNSSD ¼
M M X X f ðx; yÞ fm gðx0 ; y0 Þ gm Df Dg i¼M j¼M
1
fm ¼
2
ð2M þ 1Þ
gm ¼
(1)
M M X X f xi ; y j ; i¼M j¼M
1
M M X X
ð2M þ 1Þ2
i¼M j¼M
g x0i ; y0j
(2)
2. Algorithm for measuring the strain and deformation angle 2.1. Strain measurement For the analysis of the correlation between the images obtained before and after the deformation using the image measurement
Fig. 1. Deformation measurement using the image correlation method.
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S.-W. Kim et al. / Nuclear Engineering and Technology xxx (2017) 1e13
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u M M h i2 uX X f xi ; y j f m ; Df ¼ t i¼M j¼M
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u uX M h i2 u M X g x0i ; y0j gm Dg ¼ t
(3)
the deformation was to be measured but the average strain in the square area. As shown in Fig. 2A, the slope was obtained using the pixel position in the hoop direction and the pixel-based displacement at an arbitrary time, and Fig. 2B shows the strain obtained using each slope measured over time.
i¼M j¼M
y0j ¼ yj þ h xi ; yj
ði; j ¼ M : MÞ
(4)
Assuming that the reference and deformed images are rigid body translations, the displacements of each point of the window become the same. Therefore, the zero-order shape function, as shown in Eq. (5), can be applied.
x0 xi ; yj ¼ u;
h0 xi ; yj ¼ v
(5)
However, as the zero-order shape function is insufficient for showing the shape change of the deformed image, the first-order shape function of Eq. (6), which is suitable for translation, rotation, and shear, is generally used.
x1 xi ; yj ¼ u þ ux Dx þ uy Dy;
h1 xi ; yj ¼ v þ vx Dx þ vy Dy (6)
The second-order shape function can be applied to a more complex deformation of the image, as shown in Eq. (7).
1 1 2 2 þ uxy Dy2 þ uxy DxDy 1 h2 xi ; yj ¼ v þ vx Dx þ vy Dy þ vxx Dx2 2 1 2 þ vyy Dy þ vxy Dy2 þ vxy DxDy 2
x2 xi ; yj ¼ u þ ux Dx þ uy Dy þ uxx Dx2 þ uyy Dy2
Dx/0
Du du 0 ¼ Dx dx
x axis displacement x axis pixel position
(8)
Fig. 3 gives the algorithm for measuring the average strain in the hoop direction for the steel pipe elbow using the image signal processing, which consists of six steps. The first step acquires image files and arranges them in chronological order for measuring the time history of the hoop strain of the steel pipe elbow. The second step designates the control points (9 9 points, a total of 81 points) within the square area in the obtained reference image where the strain needs to be identified. The third step identifies the coordinate with the maximum correlation through the calculation of the ZNSSD to find the control points at which the target window most optimally matches the ROI window. The fourth step rearranges and corrects for the location of the pixel using the second-order polynomial function to correct for the geometric distortion caused by the displacement and deformation and to calculate the subpixel of the displacement. The fifth step analyzes the pixel-based displacement using the pixel of the point with the optimal matching and the calculated subpixel information. The sixth step measures the average strain using the analyzed pixel-based displacement and the pixel position. After the sixth step, based
0.2
0.1
0.0
–0.1
–0.2 510
520
530
540
550
Hoop direction pixel position [pixel]
(7)
0.03
0.02
[
In Eqs. (5)e(7), Dx ¼ xi x0 , Dy ¼ yj y0 , uand v refer to the displacements toward the xand y directions from the center of the target window. The variables ux , uy , vx , and vy refer to the first-order displacement gradient of the target window, whereas uxx , uxy , uyy , vxx , vxy , and vyy refer to the second-order displacement gradient. In this study, the second-order shape function in Eq. (7) was used considering the bending and nonlinear behavior of an object due to an external force. In conducting the in-place cyclic loading test on the steel pipe elbow, the strain was measured using Eq. (8), considering the component characteristics. As shown in Eq. (8), the x-axis displacement along the x-axis pixel position was plotted for each image based on the pixel, and the x-axis strain was measured by calculating the slope using the linear function. The average strain that was used in this study was not the strain at the point in which
(A)
Hoop strain [ ε
x0i ¼ xi þ x xi ; yj ;
εx ¼ lim
Hoop direction displacement [pixel]
As object deformation by an external force occurs continuously, the displacement value around the surrounding points can be measured using a shape function. For a measurement using the image correlation method, zero through second-order shape functions is generally used, and to consider the effect of the object rotation and shearing by an external force, the first through secondorder shape function is used. Eq. (4) expresses the shape function using the image correlation method, where x is the shape function of the x-coordinate, h is the shape function of the y-coordinate, u and v are the displacement values at each location measured using the image correlation method, and M is half the size of the target window.
3
0.01
0.00
–0.01
–0.02 0
200
400
600
800
1,000
Time [sec]
(B) Fig. 2. Method for measuring the average strain. (A) Slope measured at an arbitrary time. (B) Measured strain.
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Image acquirement (Image file(JPEG)) Selecting control points (9× 9 points, total of 81 point)
ZNSSD calculation
ZNSSD calculation Reference image
Deformed image
Deformed image
ROI window Target window Target
Random target Initial coordinate ( x0 , y 0 )
Frame 1 (t 0 )
Coordinates of best match ( x2 , y2 )
Coordinates of best match ( x1 , y1 )
Frame 3 (t2 )
Frame 2 (t1 )
Subpixel estimation (Second-order shape function) Displacement analysis (Based on pixel)
t = t + Δt
Strain measurement (Average strain) Fig. 3. Summary of the algorithm.
on the calculated position as the standard, the strain is repeatedly calculated over time from the third step. As shown in Fig. 4, in this study, an automated program of the algorithm was coded and used with MATLAB. The left figure in Fig. 4 is the processed image over time, and the point marked in blue is
the control point designated in the reference image in step 2 of Fig. 3. The cyan point is the optimal-matching point in the deformed image in step 3 of Fig. 3. The right figure shows the hoop strain that was measured using the slope that was calculated over time.
Fig. 4. Program for measuring the average strain using MATLAB.
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S.-W. Kim et al. / Nuclear Engineering and Technology xxx (2017) 1e13
2.2. Deformation angle measurement
The size of the second-order column vector is as shown in Eq. (13).
The purpose of image enhancement is to process the original image and then to convert it in accordance with a specific application purpose [12]. The region required for applying the image signal processing refers to the assembly of pixels that constitute the image. In this study, to enhance the shape of the steel pipe elbow, the Laplacian operator was applied as the isotropic differential operator. The bivariate function f ðx; yÞ is defined as shown in Eq. (9), and because the random-order differential is a linear calculation, the Laplacian operator becomes a linear operator as well [13].
V2 f ¼
v2 f v2 f þ vx2 vy2
(9)
The digitization of the second-order Laplacian operator is obtained by adding the two components of the second-order partial differential along the x and y directions, as shown in Eq. (10).
V2 f ¼ ½f ðx 1; y 1Þ þ f ðx; y 1Þ þ f ðx þ 1; y 1Þ þ f ðx 1; yÞ þ f ðx þ 1; yÞ þ f ðx 1; y þ 1Þ þ f ðx; y þ 1Þ (10) As the Laplacian operator is a differential operator, the importance of brightness, which emphasizes the discontinuity of the brightness within the image and changes gradually, is reduced. The basic principle for using the Laplacian operator for image enhancement is shown in Eq. (11), and it is used when the coefficient in the middle of the Laplacian mask is negative.
(11)
When substituting Eq. (10) for the right hand side of Eq. (11), the result obtained is as shown in Fig. 5. The shape of the steel pipe elbow was enhanced by weighting using the 3 3 convolution mask. The boundary of the steel pipe elbow with an enhanced shape refers to the detection of the boundary between the two regions with relatively different gray levels and can be realized by calculating the difference between the two neighboring regions. The boundary line provides information such as the object's location, shape, and size, and it is used in the pretreatment step to enhance the boundary of the steel pipe elbow. During image signal processing for enhancing the boundary line, the first derivation is realized using the size of the gradient, and it is defined by the second-order column vector, as shown in Eq. (12).
3 vf 6 vx 7 6 7 ¼6 7 4 vf 5 vy 2
Vf ¼
Gx Gy
" 2 #1=2 i1=2 h vf 2 vf 2 2 Vf ¼ magðVf Þ ¼ Gx þ Gy ¼ þ vx vy
(12)
Although the component of the gradient vector itself is a linear operator, it is not considered a linear operator owing to the squaring and square root calculation. The partial differential of Eq. (12) is not rotation invariant, but the size of the gradient vector is. As the execution of Eq. (13) on the entire image requires a huge calculation, the gradient size should generally be approximated using the absolute value instead of squaring and square root calculation, as in Eq. (14).
Vf ¼ jGx j þ Gy
Fig. 5. Sharpening filter.
(14)
Generally, the two different definitions, as suggested by Roberts [14], apply the differential method, whereas the 3 3 mask and approximation use the absolute value for image enhancement, as shown in Eq. (15).
þ 2z4 þ z7 Þj (15) In this study, the detection of a steel pipe elbow's boundary was facilitated using the Sobel operator of a 3 3 size mask [15], as shown in Fig. 6. The sum of all the mask's coefficients is 0. The various theories that apply processing based on the shape of an object or a region inside an image for generating a new image required for interpretation are called “mathematical morphologies.” Among the algorithms of the mathematical morphology, the dilation algorithm expands the outermost pixels of the object [16]. Through this, the size of the object is expanded whereas the background is reduced. The expansion mask adds a pixel along the circumference of a white body. A region that has the same size is excluded from the calculation, while the white value is allocated to the central pixel of the mask, in case more than one different pixel exists. In this study, to facilitate line recognition by enhancing the shape of the steel pipe elbow, a 3 3 dilation structure, as shown in Fig. 7, was used to enhance the shape. For the shape of the steel pipe elbow that had been improved through the pretreatment process, the Hough transform was used to calculate the deformation angle by recognizing the line that changed with time [17e19]. The Hough transform refers to the process of finding specific shapes, such as lines and circles, from the image. It is a method of determining the association between specific points within the image and extracting their characteristics.
−1 −2 −1
−1
0
1
0 1
−2 −1
0 0
2 1
−1 −1 −1 −1 9 −1 −1 −1 −1
(13)
Vf zjðz7 þ 2z5 þ z9 Þ ðz1 þ 2z2 þ z3 Þj þ jðz3 þ 2z5 þ z9 Þ ðz1
þ f ðx þ 1; y þ 1Þ 8f ðx; yÞ
gðx; yÞ ¼ f ðx; yÞ V2 f ðx; yÞ
5
(A)
0 2
0 1 (B)
Fig. 6. Sobel operator. (A) Horizontal mask. (B) Vertical mask.
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0
1
0
1 0
1 1
1 0
Fig. 7. Dilation structure.
The Hough transform applies Eq. (16) to all the characteristic points of the x and y coordinates in the space to accumulate the Hough sequence values of the q and s coordinates from the converted coordinates, as shown in Fig. 8. After the execution of the Hough transform, the q and s coordinates of the maximum values in the region obtained from the Hough sequence are used to detect the straight line from the x and y coordinates of the space. The straight line passing through a certain point is expressed using Eq. (16). The polar coordinate system is obtained using the pixel information of x and y on the space coordinate system s and q. The pixel indicating the identical coordinate on the polar coordinate system becomes the line in the space coordinate system.
s ¼ x cos q þ y sin q
(16)
Here, s refers to the length of the normal line from the origin to the straight line, q refers to the angle between the normal line and the xaxis, and ðx; yÞ refers to the coordinate of the characteristic point in the space. When conducting the in-plane cyclic loading test, the minimum internal angle of the line, which is defined to be the line of each shape, is set to 30 , and any line whose internal angle is below 30 is removed using Eq. (17). This inner angle is identified to reduce the image noise caused by acquiring images and errors due to the line recognition generated by the other environments. Eq. (17) and lx , ly show the coordinates of the extracted line, and the angle is the internal angle of the line. As shown in Fig. 9, the information on the lines whose internal angle is 30 or larger based on the two parallel lines that are the closest to the upper and lower directions of the center of the image is stored.
q1 ¼ arctan
n X ly0n ly1n i¼0
jq1 j > 30
lx0n lx1n
! ; q2 ¼ arctan
n X ly00n ly01n lx0 lx00n i¼0 0n
!
q1 ¼ ðlx0 ; ly0 ; lx1 ; ly1 Þ;
q2 ¼ lx00 ; ly00 ; lx01 ; ly01 ;
jq2 j > 30 else ¼ remove Defomation Angle ¼ jq1 j þ jq2 j (17)
(A)
Fig. 9. Deformation angle measurement.
Fig. 10 shows the algorithm for measuring the deformation angle of the steel pipe elbow, and it is classified into five steps. An ROI window is extracted from the steel pipe elbow to measure the deformation angle. The shape of the steel pipe elbow is enhanced using the sharpening filter. The boundary of the steel pipe elbow is extracted using the Sobel operators on the enhanced shape. To facilitate line recognition, the dilation structure is applied to expand the outermost pixel. In addition, the deformation angle is measured through line recognition using the Hough transform of the shape of the steel pipe elbow. 3. In-plane cyclic loading test for the steel pipe elbow 3.1. Image measurement system The sensor comprising the image measurement system is both mobile and simple to install. The system includes a complementary metal oxide semiconductor (CMOS) camera (IMB-7050G, 2448 2048 pixels) and two laptop computers. The CMOS camera and laptop computers transmit data and control the operation through a local area network (LAN) communication. A lens (M5018MP2) was used to measure the strain and deformation angle of a remotely located steel pipe elbow. An image measurement system was installed to measure the strain and deformation angle of the steel pipe elbow, as shown in Fig. 11.
(B)
Fig. 8. Hough transform in s, q. (A) Straight line in an image space. (B) s, q parameter space.
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Fig. 10. Algorithm for measuring the deformation angle.
Fig. 11. Image measurement system.
Fig. 12. Manufacture of the steel pipe elbow.
3.2. Steel pipe elbow In this study, the steel pipe elbow was determined to be the vulnerable part. As shown in Fig. 12, an SA-106 3-inch SCH40 specimen of the American Society of Mechanical Engineers (ASME) B36.10M was manufactured. The specifications of the steel pipe elbow are listed in Table 1. To enable plastic behavior at the bend of the specimen, a direct pipe with a sufficient length over 3D (270 mm) was welded onto the elbow. The sufficient length of the direct pipe was considered in deriving the same experimental
Table 1 Specifications of the steel pipe elbow. Composition
Radius
Thickness
Outer diameter
Material
Elbow Pipe
114.3 mm N/A
5.49 mm
88.9 mm
SA-106
results as the series model. To represent the pin connection at both ends of the specimen, a fixture was manufactured and welded onto the specimen. As shown in Fig. 13, the fixture was connected to a universal testing machine (UTM). The fixtures and pin for connecting the respective fixtures were precisely manufactured so that they would not affect the accuracy of the experiment. To minimize the influence of external sources, a pipe manufactured by the same company that provides piping products to actual nuclear power plants was used. During the manufacture of the specimen, the joints connecting the parts were welded together. An internationally certified welding company that provides its products to nuclear power plants was requested to perform welding. 3.3. Experimental setup The installation positions of the sensors are shown in Fig. 14. Fig. 14A shows the steel pipe elbow installed in the UTM, and
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S.-W. Kim et al. / Nuclear Engineering and Technology xxx (2017) 1e13
Fig. 13. Fixture for the UTM connection.
Fig. 14B shows the lighting installed to minimize optical noises. The in-plane cyclic loading test was conducted through displacement control. To compare the displacement with the linear variable differential transformer (LVDT) mounted inside the UTM, target 1 was installed in a jig for the UTM connection, as shown in Fig. 14C. Fig. 14C depicts that the circle-shaped targets were marked with 50-mm gaps on the steel pipe elbow to measure the deformation angle, and among the marked circles, targets 2e5 were used to measure the deformation angle. In addition, the deformation angle was measured with the line recognition of the steel pipe elbow shape, which was compared with the deformation angle measured with targets 2e5. Fig. 14D shows the randomly marked targets for measuring the failure strain in the hoop direction of the steel pipe elbow. The failure strain was measured using a total of 81 control points at the center of the elbow. As shown in Fig. 14E, the strain gage was installed at the center of the symmetry plane of the steel pipe elbow because installing the strain gage at the place where the image measurement system had been installed could interfere with the image analysis. The strain measured with this strain gage was compared with the hoop strain measured using image signal
Fig. 14. Location of sensor. (A) Steel pipe elbow. (B) Lighting. (C) Installed and marked targets. (D) Marked target. (E) Installed strain gage. (F) Air pump.
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S.-W. Kim et al. / Nuclear Engineering and Technology xxx (2017) 1e13
processing. Fig. 14F shows the air pump that was used to provide internal pressure of the steel pipe elbow up to 3 MPa. During the experiment, the image measurement system was used to acquire 2448 2048 pixel images at two frames per second. The measurement using the UTM was conducted at a data acquisition speed of 1 Hz whereas that using the strain gage was conducted at a data acquisition speed of 0.25 Hz. To confirm the accuracy and precision of the responses measured by the conventional sensor through image analysis, the percent error of Eq. (18) and the root mean square (RMS) error of Eq. (19) were used to conduct error analysis. Here, dm refers to the response measured by the conventional sensor, dc to the response measured by the image signal processing, and n to the number of acquired data.
Percent Error ¼
n X
, 2
ðdm dc Þ
i¼1
n X
ðdm Þ2
(18)
i¼1
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n . uX ðdm dc Þ2 n RMS Error ¼ t
(19)
i¼1
3.4. In-plane cyclic loading test To verify the effectiveness of the algorithm for measuring the strain and deformation angle using image signal processing, an inplane cyclic loading test was conducted [20]. Table 2 lists the results for each load case on the steel pipe elbow. In this study, the failure mode of the steel pipe elbow was defined as a through-crack. Therefore, the in-plane cyclic loading test was conducted until the occurrence of a through-crack. Fig. 15 shows the elbow with a through-crack formed at the crown. Fig. 16 shows a graph comparing the responses measured from the LVDT installed inside the UTM in the in-plane cyclic loading test with those measured using image signal processing. The two responses matched each other well. In Table 3, because the percent error rate in each load case is within 0.1% and the RMS error is within 0.5 mm, we determined that the error was very small. Therefore, the reliability of the displacement response measured using image signal processing was good. Fig. 17 shows the comparison of the hoop strain measured using image signal processing and the strain response measured with the strain gage. When a through-crack occurred, as shown in Fig. 17, the nonlinear behavior of the elbow exceeded the measurement limit of the electric resistance strain gage. We found that the electric resistance strain gage could not measure the strain before the through-crack occurred because it already exceeded the performance limit after the nonlinear behavior started. In addition, at a load case over ± 50 mm, the strain gage exceeded the performance limit even in the first cycle. Table 4 lists the results of an error analysis conducted on the strain data obtained using the strain gage and through image signal processing before the performance limit of the strain gage was exceeded. As shown in Table 4, the error rate was within 10% and the RMS error was within 0.01, which indicates that the error Table 2 Load cases. Load case Loading amplitude (mm) Internal pressure (MPa) Leakage cycles 1 2 3 4 5 6
±20 ±30 ±40 ±50 ±60 ±70
3 3 3 3 3 3
76 30 13 9 8 5
9
Fig. 15. Elbow with a through-crack.
was somewhat large. This, however, is seemingly due to the local problem of installing the strain gage symmetrically. Although there was a difference between the response measured with the strain gage and that measured using image signal processing, the reliability was verified in the elastic region through a comparison with the results obtained with the use of the electric resistance strain gage. Fig. 18 shows a comparison of the deformation angle measured using the displacement measured using targets 2e5 and that measured using the Hough transform of the image obtained using image signal processing. In the figure, a phase difference can be seen at the starting point. This is because the circle-shaped target was not accurately positioned at the center of the steel pipe elbow. The deformation angle measured using the shape and that measured using targets 2e5 marked on the steel pipe elbow in Table 5 show an error rate of within 0.1% and an RMS error of within 0.6 . Therefore, the error was determined to be very small. In addition, when measuring the deformation angle, it is possible to obtain a reliable measurement by using the shape of the steel pipe elbow without the installation of targets. In addition, the method of measuring the deformation angle suggested in this study is expected to be useful when the failure criteria of the steel pipe elbow are expressed using the relationship between the moment and theta. 4. Conclusions This study proposed a noncontact-type measurement method using image signal processing based on an image measurement system that measured the failure strain and deformation angle during an in-plane cyclic loading test for a steel pipe elbow. The reliability of the image processing data was verified because the difference between the responses of the LVDT of the UTM obtained through the in-plane cyclic loading test and the responses measured using image signal processing was small. Even though there were differences between the responses measured using the strain gage and those measured using image signal processing due to the measurement position, the reliability was verified by comparing the results with the measurement result up to the performance limit of the electric resistance strain gage. Furthermore, the validity of the image processing data was confirmed because the deformation angle obtained by analyzing the image data through image signal processing showed an accuracy similar to the deformation angle derived using targets. It was found that the image signal processing algorithm can be used to measure the failure strain and deformation angle from a remote distance without installing the conventional sensors. Therefore, the measured failure strain and deformation angle are expected to be applicable in the future as important factors in defining the failure criteria for a seismic isolation nuclear power plant piping system. When the strain and deformation angle of a structure need to be measured using image signal processing, the measurement method suggested in this study can be applied. Using this method will enable simple and economical measurement in various fields.
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20
UTM Target1
40 30
Cycling loading [mm]
Cycling loading [mm]
50
UTM Target1
10
0
–10
–20
20 10 0 –10 –20 –30 –40
–30
–50 0
2,000
4,000
6,000
8,000
10,000
0
1,000
2,000
Time [sec]
(A)
5,000
60
UTM Target1
6,000
30
0
–30
UTM Target1
40
Cycling loading [mm]
Cycling loading [mm]
4,000
(B)
60
20
0
–20
–40
–60
–60 0
1,000
2,000
3,000
4,000
0
5,000
1,000
2,000
3,000
4,000
5,000
Time [sec]
Time [sec]
(C)
(D)
80
100
UTM Target1
60
UTM Target1
80 60
40
Cycling loading [mm]
Cycling loading [mm]
3,000
Time [sec]
20 0 –20 –40 –60
40 20 0 –20 –40 –60 –80 –100
–80 0
500
1,000
1,500
2,000
2,500
3,000
3,500
0
4,000
Time [sec]
500
1,000
1,500
2,000
2,500
3,000
3,500
Time [sec]
(E)
(F)
Fig. 16. Comparison of the response measured from LVDT of the UTM. (A) Load case 1. (B) Load case 2. (C) Load case 3. (D) Load case 4. (E) Load case 5. (F) Load case 6.
Table 3 Error analysis of the response measured from the LVDT of the UTM. Load case
Percent error (%)
RMS error (mm)
1 2 3 4 5 6
0.032 0.065 0.0231 0.017 0.021 0.014
0.461 0.541 0.429 0.456 0.619 0.592
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0
2,000
4,000
6,000
8,000
0
10,000
(A)
1,000
11
2,000
3,000
4,000
5,000
6,000
(B)
0
(C)
1,000
2,000
3,000
4,000
5,000
(D)
Hoop strain [ε]
Strain gage Average strain (image)
0
1,000
2,000
3,000
4,000
0
500
1,000
1,500
2,000
2,500
3,000
3,500
Time [sec]
(F)
(E)
Fig. 17. Comparison of the response measured by the strain gage. (A) Load case 1. (B) Load case 2. (C) Load case 3. (D) Load case 4. (E) Load case 5. (F) Load case 6.
Table 4 Error analysis of the response measured by the strain gage. Load case
Section (sec)
Percent error (%)
RMS error
1 2 3 4 5 6
All 0e2905 0e349 0e125 e e
2.145 7.349 1.145 1.832 e e
0.001 0.003 0.001 0.001 e e
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S.-W. Kim et al. / Nuclear Engineering and Technology xxx (2017) 1e13 100
100
Target Shape
95
Angle [degree ]
95
Angle [degree ]
Target Shape
90
90
85
85
80
80 0
2,000
4,000
6,000
8,000
0
10,000
1,000
2,000
(A)
5,000
110
Target Shape
100
6,000
Target Shape
100
Angle [degree ]
Angle [degree ]
4,000
(B)
110
90
80
90
80
70
70 0
1,000
2,000
3,000
4,000
5,000
0
1,000
Time [sec]
2,000
3,000
4,000
5,000
Time [sec]
(C)
(D)
110
110
Target Shape
Target Shape
105 100
Angle [degree ]
100
Angle [degree ]
3,000
Time [sec]
Time [sec]
90
95 90 85 80
80
75 70
70 0
1,000
2,000
3,000
0
4,000
1,000
2,000
3,000
4,000
Time [sec]
Time [sec]
(E)
(F)
Fig. 18. Comparison of the measured deformation angle. (A) Load case 1. (B) Load case 2. (C) Load case 3. (D) Load case 4. (E) Load case 5. (F) Load case 6.
Table 5 Error analysis of the measured deformation angle. Load case
Percent error (%)
RMS error ( )
1 2 3 4 5 6
0.001 0.002 0.002 0.001 0.003 0.004
0.208 0.348 0.403 0.183 0.526 0.416
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Conflicts of interest All authors have no conflicts of interest to declare. Acknowledgments This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (NRF2017M2A8A4039749). Moreover, the authors would like to thank the KOCED Seismic Simulation Test Center for their assistance with the test equipment. References [1] F. Touboul, P. Sollogoub, N. Blay, Seismic behaviour of piping systems with and without detect: experimental and numerical evaluations, Nucl. Eng. Design 192 (1999) 243e260. [2] T. Zhang, F.W. Brust, G. Wikowski, D.J. Shim, J. Nie, C.H. Hofmayer, S.A. Ali, Analysis of JNES seismic tests on degraded piping, in: ASME 2010 Pressure Vessels and Piping Conference, Bellevue, Washington, USA, 2010. PVP2010e25333. [3] T. Otoyo, A. Otani, S. Fukushima, M. Jimbo, T. Yamamoto, T. Sakakida, S. Onishi, Development of an evaluation method for seismic isolation system of nuclear power facilities (Part 4) failure behavior of crossover piping for seismic isolation system, in: ASME 2014 Pressure Vessels and Piping Conference, Anaheim, California, USA, 2014. PVP2014-29011. [4] Y. Park, G. DeGrassi, C. Hofmayer, P. Bezler, N. Chokshi, Analysis of nuclear piping system seismic tests with conventional and energy absorbing supports, in: 14th International Conference on Structural Mechanics in Reactor Technology (SMiRT 14), Lyon, France, 1997. BNL-NUREG-64173. [5] K. Mizuno, H. Shimizu, M. Jimbo, N. Oritani, S. Onishi, Development of an evaluation method for seismic isolation systems of nuclear power facilities (Part 5) fatigue test of the crossover piping, in: ASME 2014 Pressure Vessels and Piping Conference, Anaheim, California, USA, 2014. PVP2014e29032.
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Please cite this article in press as: S.-W. Kim, et al., STRAIN AND DEFORMATION ANGLE FOR A STEEL PIPE ELBOW USING IMAGE MEASUREMENT SYSTEM UNDER IN-PLANE CYCLIC LOADING, Nuclear Engineering and Technology (2017), https://doi.org/10.1016/j.net.2017.11.001