[论文]英语小论文-MSJ.doc

The Calculation Method of the Thickness of Conductor Icing Based on Image Segmentation TechnologyDUAN Qi-chang1, MA Sai-jun1, DUAN Pan2,(1. Automation Department of Chongqing University, Chongqing, 400044, China 2. College of Electrical Engineering, Chongqing University, Chongqing, 400044 China)ABSTRACT: A new method to compute the thickness of ice accumulated on the transmission lines is presented in the paper, which is based on image segmentation method. It uses level set algorithm with mixed functional model to extract the image edge and uses calculus method to calculate the increased area by comparing the edges of two icing images, the final equivalent thickness and growth rate of the conductor icing can be gained by comparing with the intrinsic size of the conductor. Experimental results show that the method in the paper can obtain a good segmentation of icing image with the advantages of good anti-noise capability, high precision and low time cost, the method can correctly reflect the equivalent icing status of the conductor and forecast the thread of icing. The new calculation method is simple and feasible which can be used to calculate the actual thickness and growth rate of the conductor icing.KEYWORDS: conductor icing; icing thickness; image segmentation; Level Set algorithm (新方法简单可行，可用于实际的覆冰厚度和增长率计算,对摘要最后一句注释)1 IntroductionConductor icing is one of the main factors affecting the security of the transmission line. The overload and galloping of the conductor caused by the icing can lead to phase flashover, equipment damage, power failure, tower falling down, wire break and other serious accidents 1, so the early discovery and forecasting of conductor icing become important. The real-time calculation of the thickness and growth rate of icing can synthetically estimate the severity of the conductor and forecast the thread of icing where possible to make early warning before the disaster occurred, so as to make sure the safe operation of transmission lines can be guaranteed.At present icing image monitoring system 2 can only qualitatively observe the status of transmission line icing, but the ice thickness and the equivalent load should be known so as to find out whether it will destroy the electric networks. This paper proposes a new calculation method of the thickness of transmission line icing based on image segmentation so as to estimate the severity of the icing, it uses level set algorithm with mixed functional model to extract the image edge and calculates the increased pixel area, the final thickness and equivalent load of the conductor icing can be gained by comparing with the intrinsic size of the conductor pixel area and conductor diameter, also the growth rate of the conductor icing will be known by calculating the difference of two ice thickness in a certain period of time, thus the situation and trend of transmission line icing can be evaluated correctly.2 Computional MethodCalculation of icing thickness mainly considers two things: image segmentation and calculation of pixel area of icing. Principle diagram is shown in figure 1.Fig.1 The calculation of icing thickness Assume conductor icing is round or oval growth, if the total area of ice pixel area is St at time t and the inherent pixel area of wire is Sd; the measurement diameter value of conductor icing is H at point m, and measurement diameter value of wire is D, the actual diameter value of wire is d, the average ice thickness formula can be expressed as follows3:(1)The ice thickness formula of single-point can be expressed as:(2)Therefore, the growth rate of conductor icing in certain time can be expressed as:。(3)The calculation of the icing thickness of the insulator is similar to that of the conductor.3 Image Segmentation Algorithms3.1 Basic principle of level set AlgorithmImage segmentation is a classic problem in image processing computer vision. The icing image taken in bad weather is often with serious types of noise and its boundary is not obvious, so it is difficult to obtain accurate edge features of the conductor icing. Level set method proposed by the Osher and Sethian 4, the solution method is closer to human visual mechanism, and has been widely used in image segmentation 5.The basic idea is to represent contours as the zero level set of an implicit function defined in a higher dimension, usually referred as the level set function, and to evolve the level set function according to a partial differential equation (PDE).Variational level set method 6 is first to establish an energy model, and the evolution PDE of the level set function can be directly derived from the problem of minimizing a certain energy function defined on the level set function, such as C-V model 7 and Li model 8. Compared with pure PDE driven level set methods, the variational level set methods are more convenient and natural for incorporating additional information, such as region-based information 7 and shape-prior information 9, into energy function that are directly formulated in the level set domain, and therefore produce more robust results.3.2 C-V ModelChan and Vese 7 proposed a model based on Mumford-Shah and is a typical application of the variational level set method. This model assumes that the level set function divided the image into two regions: external region, and internal region. When the curve evolution into the edge of the two part regions, the energy function get a minimum value,The energy functional of the C-V model is defined by:(4)Using the Heaviside function and according to variational principle, the evolution equation of the level set function can be written as:in(0,)(5)and：However, the evolution of level set curve is slow when the initial level set curve in the smooth region or on the extreme depression region of the image for the model does not use local image gradient information, and signed distance function curves (SDF) need to re-initialization for every iteration of the level set method based on curve evolution model and the CV model, re-initialization is obey to the level set theory, so the calculation is time-consuming, and also with some errors.3.3 Level Set Evolution without Re-initializationIn order to overcome defect of the CV model to re-initialize the level set evolution function, Li 8 proposes variational level set method which does not need to re-initialization. The energy function is defined as:(6)Expression (6) compose with the internal energy and external energy terms, it is necessary to keep the evolving level set function close to a signed distance function, the standard re-initialization method is to solve the following re-initialization equation:(7)Where is the function to be re-initialized, and is the sign function. It is well known that a signed distance function must satisfy a desirable property of =1. Naturally, we propose the following integral(8)as a metric to characterize how close a function is to a signed distance function. Minimizing equation (8), can approximate to 1 which ensures evolving level set function close to a signed distance function.External energy defines as：(9)Where;is edge detection function.Where the Dirac function, H is the Heaviside function The external energy drives the zero level set toward the object boundaries, while the internal energy penalizes the deviation of from a signed distance function during its evolution.3.4 Mixed functional modelThe experimental results shows, C-V model is based on a global optimization hypothesis, the evolution of level set curve is slow when the initial level set curve in the smooth region or on the extreme depression region of the image for the model does not use local image gradient information in term length and term area, whats more CV models need to initial signed distance function, so the calculation is time-consuming. Therefore we add re-initialization internal energy term and external energy term with gradient information to the C-V model, combining advantages of both CV model and the Li model, the mixed energy functional defined as follows: (10)The evolution equation of the level set function can be written as: (11)Where is the Laplace operator, the flow chart of level set algorithm based on mixed functional model is as follows:Fig.2 Flow chart of level set algorithm based on mixed functional model3.5 Icing Image Segmentation Algorithm Simulations and Performance AnalysisThe parameters set as follows: =2, 1=0.05，2=0.05，=0.04，=10，t=2，=1.5.C-V model uses the global information, the noise resisting ability is strong, but the signed distance function needs to re-initialize, so in the same number of iterations, the model takes more time, and the evolution curve is easy to separate which is not conducive to calculations. The segmentation results are shown in Figure 3(a) and Figure 3(b), in less number of iterations, the C-V model can get a good result.Li model only rely on local gradient information, the curve is difficult to quickly cross the local noise point, so it need larger number of iterations, the result in weak noise is shown in Figure 3(c), after 400 iterations, the result is dissatisfied, the result in strong noise is shown in Figure 3(d), after 1000 iterations, the result is essentially unchanged, the curve evolution is failed. We can see that the iterations of the Li model are much more than the iterations of the C-V model and the iterations of the mixed functional model. In addition the Li model hasnt global information; it is easy to get over-segmentation phenomenon in the local as shown in Figure 3(3) and Figure 3(d). (a) (b) (c) (d) (e) (f) Fig.3 Comparison of treatment effects of three algorithms. Fig.(a) 120 iterations, Fig.(b) 120 iterations, Fig.(c) 400 iterations, Fig.(d) 1000 iterations, Fig.(e) 100 iterations, Fig.(f) 100 iterations.Mixed functional model uses the global information, it is effectively to resist the interference of noise when the curve evolution, the noise almost has no effect to the evolution of the curve, and the curve is difficult to separate. The evolution of level set curve is quick when the initial level set curve in the smooth region or on the extreme depression region of the image for the model use local image gradient information. After 100 iterations, a good segmentation can be got as shown in Figure3(e) and Figure3(f). The curve doesnt have over-segmentation phenomenon for it use global information.Table 1 Comparison of image segmentation algorithmsComparison ObjectLi modelC-VmodelMixed functional modeliterations in weak noise400 iterations120 iterations100 iterationsiterations in strong noisefailed120 iterations100 iterationstime-consuming in 100 iterations6.3s10.2s7.1sKnown form the data in the table 1，the resistance to noise of mixed functional model is better than Li model for it uses the global information, but the calculation is larger than Li model, so the time-consuming is slightly more than the Li model in the same number of iterations. Li model needs more iterations to reach the ice edge affected by the strong noise, so its time-consuming is much larger the C-V model and mixed functional model. Besides, mixed functional model doesnt need to re-initialize the signed distance function meanwhile it adds a gradient-weighted information items, so the time-consuming and the number of iterations have some improvement compared with C-V model.4 Icing thickness calculationThe mixed functional model can quickly get a good segmentation of the image of the deep depression insulator and the image of the natural ice with icicle, as shown in Figure 4, Figure 5, Figure 6.Fig.4 Treatment of the conductor, unit (pixels)Fig.5 Treatment of the insulator, unit (pixels)Fig.6 Treatment of natural ice, unit (pixels)Using the formula (1), the solution process of the average thickness of conductor icing is as follows:Using different image segmentation algorithms to segment icing image, and the results of the various algorithms is shown in table 2. The external diameter is 7.3mm in Figure 4, the external diameter is 8.16mm in Figure 6.Table 2 The calculation and measurement results of ice thickness (mm)ObjectLi modelC-VmodelMixed functional modelMeasured valueErrorConductor icing in Fig.411.59.910.910.53.81%Insulator icing in Fig.56.95.35.86.26.10%Conductor icing in Fig.6 14.910.714.513.57.41%Known form the data in the table 2, it is not easy to split icing edge because the anti-noise capability of Li model is poor which led to larger calculated value, and due to internal separation, C-V model get a smaller calculated value, the calculated value of mixed functional model is closer to actual value by comparing with the measured value. According to Mokkon model 10，there will be lots of icicles under natural conditions, as shown in figure 6, because the growth rate of icicle is faster than the normal icing so the calculation value and the error is larger as shown is table 2.5 ConclusionsThis paper proposes a new calculation method of the thickness of conductor icing based on image segmentation, it uses level set algorithm with mixed functional model to extract the image edge, which has effective resistance to noise, it can get a good segmentation when the boundary is blur and the image is not smooth. By comparing the increased icing area with the natural size of the wire, we can get the equivalent icing thickness and the growth rate. Simulation and calculation results show that the method can effectively reflect the current conditions of the icing thickness and the trend of the icing, in the current conditions that lack of effective calculation methods, this method is a simple and practical approach.References1 Jiang Xinliang, Yi-Hui. Transmission Line Icing and the Protective