Superresolution Reconstruction of Electrical Equipment Incipient Fault

With the rapid development of industry and technology, the electrical power system becomes more complex and the electrical equipment becomes more diverse. Defective equipment is often the cause of industrial accidents and electrical injuries, which can result in serious injuries, such as electrocution, burns, and electrical shocks. In some cases, electrical equipment fault may result in death. However, in some special situation, some fault is very small even invisible, such as equipment aging, holes, and cracks, so the detection of these incipient faults is difficult or even impossible. These potential incipient faults become the biggest hidden danger in the electrical equipment and electricity power system. For these reasons, this paper proposes a superresolution reconstruction method for electrical equipment incipient fault to ensure complete detection in electrical equipment, which aims to guarantee the security of electrical power system operation and industry production. Experimental results show that this method can get a state-of-the-art reconstruction effect of incipient fault, so as to provide reliable fault detection of electrical power system.


Introduction
In the electrical power system, there is no doubt that the safety of electrical equipment is the basis for ensuring the stability and reliability [1].Aging and fine lines of electrical equipment components can be characterized as incipient fault of electrical equipment.In power system, fault of electrical equipment components may manifest themselves as abnormal deviations in system behavior and operation.However, due to their very slow evolution, their effects may be confused with noise and uncertainty, which constitutes the characteristic that incipient fault is difficult to detect.Because it is not easy to be discovered, incipient fault is often regarded as precursors in significant accidents.Earlier detected type and exact location of the fault can cause faster detection and repairing of the fault, which is very important for the stable operation of the power system [2].In recent years, there are many researchers who focus on fault detection of the electrical power system.Huang D et al. developed a transformer fault information pattern recognition and diagnosis model using the objective entropy weight method [3].Taha I B M et al. designed a conditional probability scheme to inspect transformer incipient fault [4].And Huang D et al. presented an improved hidden Markov model (HMM) algorithm for fault diagnosis of urban rail transit motors equipment; they also used a back-propagation neural network for multiple fault of complex equipment bearings [5,6].However, these methods can only be targeted at minor devices, failing to accurately determine potential incipient fault, which is a limitation in fault detection application.At present, it seems that few works are concerned with the topic of incipient fault detection [7][8][9].In view of the above situation, this paper proposes a preprocessing method based on superresolution (SR) reconstruction, which can helpfully detect the incipient fault by improving the resolution of the electrical equipment image.In this method, a deep network structure is combined with sparse prior information, so as to obtain the highresolution (HR) version by mapping from low-resolution (LR) input.Finally the SR reconstruction result of incipient fault can be obtained to improve the subjective visual effect, which can help detect and analyze the electrical equipment fault.
This paper is organized as follows.The basic framework and methods of SR are discussed in Section 2. In Section 3, we evaluate our model on some electrical equipment images containing electrical fault and give a detailed analysis of these results.Finally, Section 4 draws a conclusion.

Basic Framework of SR.
In some special electrical situations where it is difficult to produce HR monitoring video (images), SR reconstruction is an efficient method to improve the resolution of the captured monitoring video (images).SR is a problem of obtaining a HR image from multiple or single LR images [10], which is an inverse problem of imaging process.In imaging process, the LR image is acquired through various imaging devices which are corrupted by noise and other degraded effect [11][12][13], and the imaging process is shown in Figure 1(a).It is worthwhile to improve the resolution of LR images in some special situations.The observation model of imaging process is mathematized as (1) and shown in Figure 1(b).
(, ) = ℎ (, , , ) ⋅  (, ) +  (, ) where f(x,y) represents the original real HR continuous natural scene, g(x,y) is the output digital LR image, h(x,y,,) is the point-spread function (PSF), which represents blurring matrices and downsampling matrices, and n(x,y) is the additive noise from different environment and device [14].From this observation model, SR is an ill-posed inverse problem of reconstructing a HR image from an observed LR image.Figure 1(a) is the basic illustration of the colorful imaging process of a natural scene, which can obtain R, G, and B channel of an image, respectively, by CCD array.Figure 1(b) is the image degraded model; it corresponds to (1).SR is an inverse process of Figure 1(b), so it is an ill-posed inverse problem which estimates a HR version closed to an original real HR scene.
In recent image processing area, the type of SR reconstruction can be divided into single-image SR, single-video SR, and multiple-video SR.This paper focuses on singleimage SR; it is more useful in the incipient fault detection of electrical equipment.Single-image SR also can be divided into classical method [15,16] and learning-based method [17][18][19].Figure 2(a) shows the classical multiframe image to achieve single-image SR; there are 4 LR images with subpixel translation; the complementary information can be fused to reconstruct a HR image with higher resolution.In Figure 2(a), all of the small circulars, rhombuses and triangles represent subpixel different sample points in HR grid, respectively.
The other recently popular method is learning-based SR reconstruction, one of which is illustrated in Figure 2(b) [20].All of these methods use single-scale or multiscale information to get learning network, so as to achieve HR reconstruction from LR input.In this paper, we adopt the second SR framework to reconstruct detailed information of incipient fault on electrical equipment.

SR Reconstruction Method for Incipient Fault Detection.
For what is detailed above, in order to accurately detect the incipient fault and guarantee safety of electricity power system, improving the resolution of monitoring images of electrical equipment is an effective pathway.A SR reconstruction method is introduced in this paper, which adopt the idea of deep learning network model [21] shown in Figure 3.This model combines the traditional sparse coding model  into deep learning so as to obtain HR result, which extends the conventional sparse coding model using several key ideas from deep learning, and complements large learning capacity to improve SR reconstruction performance.
Firstly, we implement a feed-forward neural network whose layers strictly correspond to each step in the processing flow of sparse coding based image SR; the framework is shown in Figure 3.In this way, the sparse representation prior is effectively encoded in our deep network structure; all the coded components are trained jointly through backpropagation.This method includes three stages as shown in Figure 3.The first stage S 1 is a convolutional process, which is patch extraction and representation.LR image I y is the Bicubic-upscaled version of input real LR image, and this layer extracts feature for each LR patch of size 5 × 5.In this stage, the size of our input patch y must be the same as the filter spatial size as s y × s y .This process can be represented as S 1 (y) = max (0,w 1 * y+b 1 ); here w 1 and b 1 are convolution filter and deviation, respectively.In this paper, we extract 100-dimension feature in this stage.The middle stage of this model S 2 is a high-dimension mapping process, which includes three linear layers shown in Figure 4 [22].The sparse code  is multiplied with HR dictionary D x in the last linear layer to reconstruct HR patch.This stage is : Process of middle mapping stage S 2 [22].
equal to a filter with simple spatial support 1 × 1; it also can be mathematized as Here w 2 and b 2 are also filter and deviation, respectively, just like in stage S 1 .The final stage S 3 in this model is reconstruction, which is also a convolution similar to S 1 .In this stage, all the recovered patches are placed back to the corresponding positions in the HR grid through a convolutional filter, so as to get the HR output result.This model combined with the focal points of sparse coding and the strong points of deep learning to achieve SR reconstruction.As a result, HR version of the incipient fault on electrical equipment can be more visible and helpful in achieving easier fault detection.The recurrent middle stage adopted the idea referred in [22], which is mathematized as Eq. ( 2) where y is the input signal and h  is an coordinatewise shrinkage function defined as with positive threshold .W is the transpose of the dictionary matrix D y , and S is D Y T ⋅ D y .The matrices W and S are learned so as to minimize the approximation error to the optimal sparse coding on a given dataset.The final convolution stage S 3 producing HR reconstruction result is described as S 3 (y) = w 3 * S 2 (y)+b 3 , b 3 is a vector, and w 3 project the coefficients to image spatial domain to get averaged HR result [22,23].
On the other hand, loss function is also needed in this model, which can be obtained by minimizing reconstruction result S 3 (y) and corresponding original HR version I x .In this paper, mean squared error (MSE) is adopted as loss function in this model, which is shown in Here SSE is the sum of squared error, n is the number of samples, weight w i > 0, I i is the original HR image, and y i is the estimated SR reconstruction HR result.

Experiment
In order to show the efficiency of the proposed method for incipient fault SR reconstruction of electrical equipment, we give two experiments to straightly verify the effective result.
One is simulation incipient fault image SR, and some good electrical equipment is manually added and some incipient fault on the surface.The other is electrical equipment images with real incipient fault on the surface.
In these experiments, we firstly perform incipient fault extraction on images captured by high-definition (HD) camera, and then a degraded processing is applied to change the resolution to be 256 * 256, which is referred to as original HR image.For SR model, the resolution of LR input is 128 * 128 by Bicubic interpolation.In our SR reconstruction process, the upscaling factor is 2. In order to clearly show the efficiency of the detailed method in this paper, the result of Bicubic interpolation, SR reconstruction of SRCNN [24], SR result by proposed method in this paper, and the ground-truth HR image are all provided to give a complete subjective comparable effect.At the same time, we also provide the objective quantitative metric peak-signal-noise-ratio (PSNR) [25,26] and structural similarity index metric (SSIM) [25,27] to evaluate all of these results, so as to further validate efficiency of the detailed method in this section.PSNR is a classical objective metric for image quality evaluation, which is widely used in many real applications.SSIM is a popular image quality assessment based on computing the structure similarity; it also provides superior performance.

Simulation Incipient Fault Experiment.
In the following simulation experiment, we simulate the incipient fault of common four types of electrical equipment in substations.In Figures 5-8, we simulate the gaps and the oil pillow's leakage of insulator marked by gray part; we also simulate the 35kv transformer's crack with a black broken line, and a painted brown part on the circuit breaker is the simulated rust stain.All of these artificially added parts are simulated fault on the electrical equipment, which are very small or invisible in natural scene, because the size of electrical equipment is usually large or huge.Note that, in order to better display the visual results, we select detailed information of the fault for each image and enlarge them to show better display.All the following experiments also follow this rule.
From the different SR reconstruction results in Figures 5-8, the details of Bicubic reconstruction in Figures a1-a4      information is not sufficient enough to make accurate fault judgments.It is clearly shown that the image c1-c4 has a fine edge structure; the image feature structure is closer to the HR image (d1-d4).In the image detected by our method, the edge portion of the electrical device has more zigzag texture, and the image sharpening effect is better, so that the shape and angle of the notch and crack can be clearly observed to help diagnose electrical equipment incipient fault.All of the objective evaluation values are included in Table 1, which also proves the efficient SR reconstruction of the proposed method in this paper.

Real Incipient Fault Experiment.
Although the simulation incipient fault SR experiment is effective and credible, we further provide real incipient fault SR experiment to validate the proposed method.Similar to the above experiments, we detect the actual fault commonly found in substations.In the same way, we also give objective evaluation and subjective     evaluation indicators based on human vision in this SR reconstruction experiment.In the power system, once incipient fault such as cracks and gaps occur in electrical equipment, which are difficult to be discovered by human, they even lead to a huge accident crisis for the whole system.In Figures 9-12, the Bicubic interpolation reconstruction (a5-a8) has the most blurring fault edge information and the highest distortion, which is helpless for the detection of incipient fault.The SR reconstruction results (b5-b8) by SRCNN are relatively acceptable.In Table 2 and Figure 13 (average value of these three methods of PSNR and SSIM), the results of the proposed method in this paper (c5-c8) are absolutely superior to Bicubic and SRCNN, the edges and lines of the fault are more clear, and the crack length and shape are more obvious.So it is shown that the proposed method is the effective way to make the incipient fault more visible.

Low-Resolution Actual Incipient Fault Experiment.
In this subsection, the incipient fault images are captured by LR imaging device (such as cellphone with LR shot camera); some of them are also captured in special conditions such as dim environments.In this case, the original LR image is 128 * 128, and the upscaled factor is 2. Because there is not a HR version for objective quality evaluation, the blind image quality metric (BRISQUE) [28,29] is adopted in this experiment.BRISQUE is a widespread no-reference image quality metric; it extracts mean subtracted contrast normalized (MSCN) coefficients to fit asymmetric generalized Gaussian distribution (AGGD), so as to estimate the image quality.
Figures 14 and 15 are electrical equipment LR images captured in a dim environment; most of the incipient fault is difficult to detect under such circumstance.The burr sparked by insulator in Figure 14 and the soldering position on the switch blade in Figure 15 are easy to be recognized by SR reconstruction.Comparable fine structure SR results in Figure c9-10 are more vivid than other results.Furthermore, the objective evaluation metric of BRISQUE also proves the proposed method is higher than the SR results by other    methods (lower BRISQUE value means more quality or higher resolution of the image) in Table 3.

Conclusion
A SR reconstruction method combining sparse coding and deep learning is used in this paper, so as to achieve preprocessing for accurate incipient fault detecting of electrical equipment.It can be seen from the subjective and objective results compared with other methods that the proposed SR   detection of a series of initial defect incipient fault, such as incompleteness, cracks, and blemishes, this method can obtain relatively clear effect and retain most of fine edge information.Applying this method for practical incipient fault detection can improve fault resolution and achieve accurate fault location and judgment, so as to ensure the safe operation of electrical equipment and electricity power system.For actual application, our further work will combine this method in fault diagnosis and other areas, to ensure the reliability of electrical system operation.

Figure 1 :
Figure 1: Imaging process and image degraded model.

Figure 2 :
Figure 2: The relation of LR samples mapped on HR grid.

Figure 5 :
Figure 5: Simulated gaps fault in the ceramic insulators.
are the most obscured and ambiguous.Although the results of SRCNN shown in Figures b1-b4 are slightly clear, the detailed 67dB/0.8756) (c2) Our method (28.95dB/0.8793)(d2) Original HR image

Figure 6 :
Figure 6: Simulated oil leaking in the transformer's oil pillow.

Figure 8 :
Figure 8: Simulating the rust in the circuit breaker.

Table 1 :
The objective comparison (PSNR / SSIM) of simulation incipient fault by three methods.Bold indicates the best performance.

Figure 10 :
Figure 10: Oil leak in the transformer's oil pillow.

Table 3 :
The objective comparison (BRISQUE) of actual incipient fault by three methods.Bold indicates the best performance.

Figure 11 :Figure 12 :
Figure 11: Cracks on the body of transformer.

Figure 13 :
Figure 13: Average value of PSNR and SSIM of actual fault detection by three methods.Red indicates the best performance.

Table 2 :
The objective comparison (PSNR / SSIM) of actual incipient fault by three methods.Bold indicates the best performance.