An illumination-robust edge detection method for nuclear fuel assembly deformation measurement

Fuel assemblies (FAs) are critical components of nuclear reactor cores. The excessive deformation of FAs can pose a serious risk of safety accidents in nuclear power plants. Hence, regular monitoring of the deformation of the FAs is necessary. To accomplish this task, the most critical challenge lies in accurately extracting the edges of FAs in the nuclear underwater environment with spatial variations in illumination. In this paper, a novel illumination-robust edge detection method is proposed. Firstly, tilt correction is applied to arrange the fuel rods vertically in the image. Then, the center of each fuel rod is located through grayscale projection and filtered by rod center spacing variance minimization. Subsequently, adaptive thresholding is employed to obtain a binary image. Finally, the edges are identified by searching in the vicinity of rod centers in the binary image. The effectiveness and robustness of the proposed method have been validated in experiments, and the approach has been successfully applied to the FA deformation measurement in nuclear power plants.


Introduction
Fuel assemblies (FAs) are pivotal components in nuclear power plants [1], serving as the primary fuel source to sustain nuclear fission reactions for electricity generation, as illustrated in Figure 1.Exposed to conditions of high temperature, pressure, and radiation, the FAs become irradiated and can become bowed and deformed due to differential growth [2].If excessive deformation in FAs is not promptly addressed, it may result in incomplete insertion of fuel rods or prevent accurate alignment with the lower core plate.This can lead to interference with adjacent components and, in extreme cases, make the rod insertion impossible, posing a serious threat to the safe operation of the nuclear reactor [3].Therefore, regular deformation inspection for all FAs in the nuclear reactor is essential.
To accomplish the procedure of deformation inspection, an orthogonal visual inspection system, as shown in Figure 2, is implemented within the nuclear plant.This system can capture videos of the FAs during the maintenance of the nuclear reactor core.However, relying on the human eyes to observe the deformation from videos is time-consuming and unreliable [4].Consequently, there is a significant need for the accurate edge detection of the fuel rods for deformation measurement.Moreover, edge detection can also be applied to measure grid width, fuel tilt, rod length, and other parameters.

Related work
Image edge detection has been extensively researched for decades [5].It aims to minimize data volume and eliminate irrelevant information while preserving crucial structural properties.The edge detection methods can be broadly classified into traditional methods and deep learning-based methods.
The traditional methods primarily utilize the discontinuity of gray values in the edges to segment the target region based on grayscale mutations [6].Some methods locate the edge by searching for the maximum and minimum values in the gradient image, such as the Sobel operator [7], the Prewitt's operator [8], and the Canny operator [9].Some methods locate the zero crossings in the second derivative of the image to find edges, such as the Laplacian operator, the LOG operator, and the DOG operator.These methods are simple and fast but are noise-sensitive and rely on parameter settings.They may not detect the desired edges or make it difficult to filter out the desired edges from the detected ones.
With the development of deep learning in recent years, a wide variety of convolutional neural network-based methods to implement edge detection have appeared.Bertasius et al. [10] claimed that recognizing objects and predicting contours are two mutually related tasks and proposed a multi-scale deep network DeepEdge.Yu et al. [11] proposed a multi-label learning framework CASE Net for semantic edge detection, which involves a deep semantic edge learning structure and an improved jump connection architecture based on ResNet.Pu et al. [12] proposed an edge detector network named RINDNet, which can simultaneously detect four types of edges.It can be seen that the performance of the current deep learning-based algorithms for edge detection is close to or even beyond the human visual level.However, deep learning-based methods typically require much well-annotated data for training.Moreover, when the network structure is complex, the detection time is much longer than traditional methods, making it hard to meet the real-time monitoring requirements.
Due to the harsh underwater environment of nuclear power plants, the FA video-capturing process is susceptible to nuclear radiation, uneven lighting, and capturing set-up.As a result, the FA videos suffer from radiation noise, illumination variations, and background structural interference, resulting in poor imaging quality, as illustrated in Figure 3. Whether using traditional methods or deep learningbased methods, accurately extracting the edges of fuel rods from the images is challenging work, which is essential for FA deformation measurement.This paper is inspired by the distribution of rod-gap-rod in the FA image, as shown in Figure 3, and proposes a fuel rod edge detection method for the FA deformation measurement based on this distribution.At first, the tilt of the FA is corrected to arrange this distribution in the horizontal direction.Then, the rod centers are obtained through grayscale projection.Finally, edge detection is achieved by searching the grayscale boundaries near the rod centers in the adaptive thresholding image, which is segmented based on the integral image.
The remaining parts of this paper are organized as follows.In Section 3, the proposed method is introduced in detail.In Section 4, the experiments are carried out to analyze the efficiency.Section 5 concludes this article.

The edge detection method
The proposed method is shown in the flowchart in Figure 4.The tilt of the FA image is calculated and corrected, and then the rod centers are located and filtered.Finally, adaptive thresholding is applied to the FA image, and the edges are identified by searching the gray value transition position near the rod centers.

Tilt correction
It is natural to consider that correcting the light-dark-light distribution horizontally is equivalent to aligning the fuel rods vertically.Additionally, the inclination angle of the rods in the image aligns with the slopes of most linear features, as shown in Figure 3.To extract the line features in the FA image, we adopt a fast line detector to achieve this task.For a given FA image, we first apply the Canny operator to detect various edges in the image.Each edge pixel is connected to its neighboring pixels, and a straight line is fitted.The line is then extended to the next edge pixel.If the curvature after extension is significant and the length exceeds a set threshold, the current segment of the line is reserved, as shown in Figure 5.This process is repeated for all edge pixels, and all line segments in the image are acquired.The line-detected result for a tilted FA image is provided in Figure 6 (a).It can be seen that most of the detected lines are oriented in the same direction as the tilt of the rod, while there are some erroneous lines due to background interference.To mitigate the influence of the extraneous lines, the top 20% of line segments with the highest slopes and the bottom 20% with the lowest slopes are removed, as shown in Figure 6

Fuel rod center location
In the FA image, there exists a bright-dark-bright pattern along the transverse direction, as a result of the distribution of rod-gap-rod.To fully use this property, column grayscale projection is applied to the tilt-corrected image to identify the grayscale distribution of the FA image along the transverse direction.
The FA image I to be projected is the size of the rc  image, and the grayscale projection of the k-th column in I is defined as:  II To better extract the peaks on the grayscale projection curve, which represent the rod centers, a mean filter is applied to the projection curve: Due to the spatial variations in illumination, the extracted rod center number may be larger than the number of the real fuel rods.Therefore, it is necessary to select the actual rod centers from the above points.Considering that the fuel rods are uniformly distributed when inserted into the FA, an optimal set of centers can be selected by minimizing the variance of rod center spacings.The rod center spacings can be represented as:

Adaptive thresholding
After locating the fuel rod centers, we must segment the FA image into foreground (FA components) and background (gaps).To accommodate spatial variations in illumination, we adopt an adaptive thresholding method based on the integral image.The integral image ( ) Then, the threshold corresponding to the pixel at the center of the rectangle ( ) , , , x y x y can be computed as: , , , , 22 R x y x y x x y y Thr t x x y y ++  =  −−  where t is a thresholding adjustment factor, a higher value of t results in a smaller proportion of the foreground in the image, a satisfactory binary image segmented by Thr is shown in Figure 9. Finally, using the fuel rod centers extracted in Section 3.2 as the initial positions, a neighborhood search is performed in the binary image to identify the boundaries between the black and white pixels, which represent the rod edges.The detection result is shown in Figure 10.

Experiments and analysis
Two experiments are carried out to verify the effectiveness and robustness of the proposed method, including the FA sample deformation measurement experiment and the actual FA edge detection experiment for the videos captured from the spent fuel pool.The FA sample deformation measurement experiment verifies the effectiveness of the edge extraction proposed method by examining the accuracy of the deformation measurement, while the actual FA edge detection experiment verifies the robustness of the edge extraction method using actual FA videos.

FA sample deformation measurement experiment
In the FA sample deformation measurement experiment, an FA sample with a length of 4 was manufactured as the experimental object, as shown in Figure 11.It is mounted on the guide platform of a gantry milling machine, simulating the lifting process of the FA through the movement of the platform.The camera is fixed on the spindle of the milling machine to capture the video.Since the curvature of the FA sample is relatively small in its natural state, a jack is employed to compress the grid to generate a significant deformation.Additionally, a dial gauge with a precision of 0.01 mm is placed at the fuel rod edge as shown in Figure 12, by which the position of the fuel rod edge can be measured before and after compression to obtain the derivation.The jack is incrementally fed from 1 mm to 10 mm with a step of 1 mm, while the rod edges are measured by the indicator at each feed rate.The experiment results are shown in Table 1.Let the offset measured by the dial gauge be r b , the offset obtained by edge detection be m b , and the error e b is defined as m r b b − .As the jack feed rate increases from 1 mm to 10 mm, the fuel rod edge offset measured by the dial gauge increases from 0.95 mm to 8.67 mm.By calculating the difference between r b and m b , it can be seen that the calculation error of the fuel rod offset at all feed rates is less than 0.2 mm.The representative edge detection result is shown in Figure 13.The results are valid both visually and in terms of offset measurement accuracy, validating the effectiveness of the proposed method.

Actual FA edge detection experiment
To verify the robustness of the proposed edge detection method, actual FA videos captured from an actual nuclear power plant reactor environment are gathered for rod edge detection.For over 400 FA videos collected from the spent fuel pool in the underwater nuclear power plant, four representative FA images are tested by the proposed method for edge detection.The results are shown in Figure 14.It can be seen that for normal images, such as images with light source variations, images with significant radiation noise, and images with severely eroded fuel rods, the proposed method can effectively extract the fuel rod edges, which validates the robustness of the proposed method.It is worth noting that the proposed method has been applied to the deformation monitoring of the FAs during the downtime of nuclear power plants.

Conclusions
This paper proposes a novel illumination-robust edge detection method for nuclear FA deformation measurement.In the proposed method, the tilt angle of the FA image is obtained by line detection and is corrected by bilinear interpolation.Then, a column grayscale projection is applied to get rod center candidates, which will be selected by rod center spacing variance minimization.Subsequently, an adaptive thresholding method based on the integral image is utilized to separate the fuel rod foreground and background.Finally, the rod edges can be acquired by searching the grayscale boundaries near the rod centers in the binary image.To verify the effectiveness and robustness of the proposed method, both the FA sample deformation measurement experiment and the actual FA edge detection experiment are carried out.In the FA sample deformation measurement experiment, the absolute error of edge derivation calculated by edge detection is less than 0.2 mm.In the actual FA edge detection experiment, the edges of the fuel rods in four representative FA images are extracted using the proposed method, achieving visually satisfactory results.Furthermore, due to the effectiveness and robustness of the proposed method, it has been applied to FA deformation monitoring in nuclear power plants.The proposed illumination-robust edge detection method can also provide a new idea for edge detection for some other periodically distributed components.

Figure 1 .
Figure 1.The FAs working in a nuclear reactor.Figure 2. Orthogonal visual inspection system.

Figure 2 .
Figure 1.The FAs working in a nuclear reactor.Figure 2. Orthogonal visual inspection system.

Figure 4 .
Figure 4.The flowchart of the proposed method.

Figure 5 .
Figure 5. Two situations when extending lines.If the line extension encounters a high curvature, as in (a), the extension stops; otherwise, as in (b), it continues the extension.

Figure 6 .
Figure 6.Images in the process of tile correction.(a) Raw detected lines.(b) Detected lines after selected.(c) Tilt-corrected image.

Figure 7 .
Figure 7. Grayscale projection curves.The thin red curve represents the original column projection curve, while the thick blue curve represents the curve after filtering.

1 ,
m center candidates and the expected n rod centers can be selected by the following:The rod centers before and after filtering by spacing variance minimization are illustrated in Figure8.

Figure 8 .
Figure 8. Results of the fuel rod centers localization.The blue points represent erroneously extracted centers, and the red points represent the centers after filtering by fuel rod center spacing variance minimization.
xy T is defined as the sum of grayscale values of all pixels to the left and above a given pixel ( )

Figure 9 .
Figure 9.The binary image is segmented based on the integral image.

Figure 10 .
Figure 10.Result of edge detection.Blue lines represent the rod edges, and the rod points represent the rod centers.

Figure 11 .
Figure 11.FA Sample and experimental facility.Figure 12.The jack is used to induce a derivation which can be measured by the dial gage.

Figure 12 .
Figure 11.FA Sample and experimental facility.Figure 12.The jack is used to induce a derivation which can be measured by the dial gage.

Figure 13 .
Figure 13.The edge detection result of the FA sample.The image on the left represents the overall edge detection results, while the image on the right shows the corresponding details.

Figure 14 .
Figure 14.Edge detection results of four representative FA images collected from the spent fuel pool.(a) Normal FA image.(b) Image with light source appearing in view.(c) Image with a lot of noise.(d) Image with severely eroded fuel rods.

Table 1 .
The derivation results of reference and calculation.