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  1. 1. Elsayed M. Elrefaie, M. K. Abd Elrahman, Sherif Ghoneim, Ahmed Bakr / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1010-1015 Classification Of Partial Discharge Patterns Using Fractal GeometryElsayed M. Elrefaie1 M. K. Abd Elrahman2 Sherif Ghoneim3 Ahmed Bakr4 1,2 Faculty of Engineering Helwan University, Egypt 3,4 Faculty of Industrial Education Suez Canal University, EgyptABSTRACT Partial discharge (PD) pattern recognized need for condition monitoring andrecognition is an important diagnostic tool to get automated diagnostic systems in the electricalthe dielectric deterioration degree of electrical utilities. Such systems provide the ability to identifyinsulation. A PD pattern recognition approach of defects as they occur, allowing the scheduling ofartificial partial discharge sources based on maintenance, avoidance of equipment failure,neural networks is proposed in this paper. A optimizing the operation of the equipment andcommercial PD detector is used to measure the increasing reliability. Automated diagnostic systemsthree-dimension PD patterns. Two fractal features can only be successful if there exists a way of(fractal dimension and lacunarity) were extracted capturing information that indicates the health of thefrom the raw PD patterns. The box counting apparatus. Analysis of PD data provides one suchtechnique is used to generate the fractal features. indication [2]. Commercial PD detectors can measureFractal dimension is a constant value for each the electrical signal of electrical field variety in defectpattern. On the other hand, each pattern has model, and an experienced expert can use the PDseveral values for lacunarity depends upon the patterns to identify the defect types in the testedsize of the box. Therefore each PD pattern is object. The main parameters of the 3D PD patternscharacterized by several quantities. The are phase angle φ, discharge magnitude q, and theperformance of neural networks based recognition numbers of discharge n. Fractal has been verysystem depends upon the number of input features successfully used in description of naturallyas well as upon their contents of information. This occurring phenomena and complex shape, such aspaper is an attempt to improve the performance mountain ranges, coastlines, clouds, and so on,of PD recognition systems by minimizing number wherein traditional mathematical were found to beof input features. This can be done through inadequate[3, 4]. PD also is a natural phenomenonselecting the value of lacunarity which has the occurring in electrical insulation systems, whichmaximum ability to classify different PD sources. invariably contain tiny defects and non-uniformities,A wide range of lacunarity values were tested. The and gives rise to a variety of complex shapes andobtained results show that a very narrow range of surfaces, both in a physical sense as well as in thelacunarity values has the maximum ability for PD shape of PD patterns acquired using digital PDclassification. detector. This complex nature of the PD pattern shapes and the ability of fractal geometry to modelKeywords:- Partial Discharge, Fractal complex shapes have encouraged many authors toDimension, Lacunarity, and PD Recognition investigate the feasibility of fractal dimension for PDPatterns. pattern interpretation. The automated recognition of PD patternsI. INTRODUCTION has been widely studied recently. Various pattern PD is electrical discharges that do not recognition techniques have been proposed, includingcompletely bridge the distance between two expert systems [5], statistical parameters [6], fuzzyelectrodes under high voltage stress. It is small clustering [7], extension theory [8], PD-fingerprintselectrical sparks that occur within the electric [9], and neural networks (NNs) [10, 11]. The expertinsulation of electrical equipment. Although the system and fuzzy approaches require humanmagnitude of such discharges is usually small, it expertise, and have been successfully applied to thiscause progressive deterioration, ageing of insulation field. However, there are some difficulties inand may lead to ultimate failure of electrical acquiring knowledge and in maintaining the [1]. Occurrence of PD in electrical NNs can directly acquire experience from the traininginsulation is always associated with emission of data, and overcome some of the shortcomings of theseveral signals (i.e. electrical signal, acoustic pulses expert system. However, the raw values of 3-Dand chemical reactions). The main purpose of patterns were used with the NN for PD recognition ininsulation diagnosis for power apparatus is to give previous studies [12]; the main drawbacks are thatsystem operators the information on dielectric the structure of the NN has a great number of neuronsdeterioration degree of HV equipment. There is a with connections, and time-consuming in training. To 1010 | P a g e
  2. 2. Elsayed M. Elrefaie, M. K. Abd Elrahman, Sherif Ghoneim, Ahmed Bakr / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1010-1015improve the performance, two fractal features that detector. The fractal features, fractal dimension andextract relevant characteristics from the raw 3-D PD lacunarity of phase windows are extracted topatterns are presented for the proposed NN-based highlight the more detailed characteristics of the rawclassifier. It can quickly and stably learn to categorize 3D PD patterns.input patterns and permit adaptive processes to accesssignificant new information. To demonstrate the II. A. FRACTAL DIMENSIONeffectiveness of the proposed method, 30 sets of PD The fractal dimension (FD) has been appliedpatterns from HV defect models are tested. in texture analysis and segmentation shape measurement and classification of image and graphicII. PRACTICAL PD FIELD and analysis in other fields. There are quite a fewMEASUREMENT definitions of FD making sense in certain situations. When the intensity of electric field exceeds Thus, different methods have been proposed tothe breakdown threshold value of a defective estimate the FD [15, 16].dielectric, PD occurs and results in a partial While the definition of fractal dimension bybreakdown in the surrounding dielectrics. PD is a self-similarity is straightforward, it is often difficultsymptom of insulation deterioration. Therefore, PD to compute for a given image data. However, the boxmeasurement and identification can be used as a good counting technique can be used for this purposeinsulation diagnosis tool to optimize both easily. In this work, the method suggested by Kellermaintenance and life-risk management for power [17] for the computation of fractal dimension from anapparatuses. image data has been followed. Let p(m, L) define the The new standard IEC60270 [13] for PD probability that there are m points within a box ofmeasurement has been published in 2001, which size L (i.e. cube of side L), which is centered about aestablishes an integral quality assurance system for point on the image surface. P(m, L) is normalized, asPD measurement instead of the old standard below, for all L [8].IEC60060-2 published in 1994. The standard nIEC60270 ensures accuracy of measuring results,  p(m.L)  1 (1) m 1comparability and consistency of different Where, N is the number of possible pointsinstruments and measuring methods. Moreover, the within the box. Let S be the number of image pointsnew standard provides digital PD measuring (i.e. pixels in an image). If one overlay the imagerecommendations as well as the analog measuring. In with boxes of side L, then the number of boxes withthis work, all PD experiments are based on the new m points inside the box is (S/m) p(m, L). Therefore,standard IEC60270. the expected total number of boxes needed to cover A PD experiment laboratory, including a set the whole image isof precious instrument has been used. The N S N 1constitution of the laboratory includes a PD analyzer N ( L)   p(m.L)  S  p(m.L) (2)(the computer aided measuring system LDD-6), a m 1 m m 1 mhigh-voltage control panel, a high-voltage The fractal dimension can be estimated bytransformer, a calibration capacitor, and a coupling calculating p(m, L) and N(L) for various values of L,capacitor. and by doing a least square fit on [log(L), -log(N(L))]. To estimate p(m, L), one must center the cube of sizeIII. EXTRACTION OF PD FEATURES FOR L around an image point and count the number ofRECOGNITION PURPOSES neighboring points m, that fall within the cube. Fractals have been very successfully used to Accumulating the occurrences of each number ofaddress the problem of modeling and to provide a neighboring points over the image gives thedescription of naturally occurring phenomena and frequency of occurrence of m. This is normalized toshapes, wherein conventional and existing obtain p(m,L). Values of L are chosen to be odd tomathematical methods were found to be inadequate. simplify the centering process. Also, the centeringIn recent years, this technique has increased attention and counting activity is restricted to pixels having allfor classification of textures and objects present in their neighbors inside the image. This will obviouslyimages and natural scenes and for modeling complex leave out image portions of width = (L −1) / 2 on thephysical processes. Fractal dimensions are allowed to borders. This reduced image is then considered fordepict surface asperity of complicated geometric the counting process. As it seen, large value of Lthings. Therefore, it is possible to study complex results in increased image areas from being excludedobjects with simplified formulas and fewer during the counting process, thereby increasingparameters [14]. PD also is a natural phenomenon uncertainty about counts near border areas of theoccurring in electrical insulation systems, which image. This is one of the sources of errors for theinvariably contain tiny defects and non-uniformities, estimation of p(m, L) and thereby FD. Additionally,and gives rise to a variety of complex shapes and the computation time grows with L value. Hencesurfaces, both in a physical sense as well as in the values from L = 2 to L = 40 were chosen for thisshape of 3D PD patterns acquired using digital PD 1011 | P a g e
  3. 3. Elsayed M. Elrefaie, M. K. Abd Elrahman, Sherif Ghoneim, Ahmed Bakr / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1010-1015work. Figure1 shows a sample plot of log (L) and Where N is the numbers of point in the data set of−log (N (L)). size L, the lacunarity becomes M 2 ( L)  M ( L) 2  ( L)  (5) M ( L)2 Figure 2: The sample plot of the variation ofFigure 1: The sample plot of the set [log (L), - log (N lacunarity with respect to box size L(L))] for different box size L Figure2 shows a sample plot of the variation of lacunarity with respect to box size L for differentII. B. LACUNARITY PD patterns. Figure3 shows the overall procedure for Theoretically, ideal fractal could confirm to extracting fractal features. The first step is to transferstatistical similarity for all scales. In other words, PD pattern to a 360×360 matrix and use boxes withfractal dimensions are independent of scales. different sizes to cover the matrix. In fractalHowever, it has been observed that fractal dimension dimension computation, we can obtain N (L). Inalone is insufficient for purposes of discrimination, lacunarity computation, M (L) and M2 (L) have to besince two differently appearing surfaces could have calculated and then by using equation (5) lacunaritythe same value of FD. To overcome this, Mandelbrot can be determined.[18] introduced the term called lacunarity Λ, whichquantifies the denseness of an image surface. Manydefinitions of this term have been proposed and thebasic idea in all these is to quantify the „gaps orlacunae‟ present in a given surface. As a result,lacunarity can be thought as a measure of „gappiness‟of a geometric structure. More precise definition wasgiven as a measure for the deviation of a geometricobject from translational invariance [19, 20]. Theconcept of lacunarity was established and developedfrom the scientific need to analyze multi-scalingtexture patterns in nature (mainly in medical andbiological research), as a possibility to associatespatial patterns to several related diagnosis.Regarding texture analysis of urban spaces registeredby satellite images, lacunarity is a powerful analyticaltool as it is a multi-scalar measure, that is to say, itpermits an analysis of density, packing or dispersionthrough scales. In the end, it is a measure of spatialheterogeneity, directly related to scale, density,emptiness and variance. It can also indicate the levelof permeability in a geometrical structure [21]. One Figure 3: Procedure for computing fractal dimensionof the useful definitions of this term as suggested by and lacunarityMandelbrot is NM ( L)   mp(m.L) (3) IV. PARTIAL DISCHARGE M 1 EXPERIMENTAL RESULTS N Using a conventional phase resolved PDM 2 ( L)   m 2 p(m.L) (4) analyzer (the computer aided measuring system M 1 LDD-6), 3-D PD patterns corresponding to different PD sources were acquired. These PD sources are due 1012 | P a g e
  4. 4. Elsayed M. Elrefaie, M. K. Abd Elrahman, Sherif Ghoneim, Ahmed Bakr / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1010-1015to the artificially introduced defects within carefullydesigned insulation models. Three types of partialdischarge generation source were used. The internaldischarge due to one void, three voids and five voidsin mica insulators as shown in Figure 4 weremeasured. In the testing process, all of the measuringdata are digitally converted in order to store them inthe computer. Then, the PD pattern classifier canautomatically recognize the different defect types ofthe testing objects. Typical measurement results ofeach partial discharge generation source areillustrated in Figure 5, Figure 6, and Figure7. Figure 7: Partial discharge pattern due to five voids Obviously, differences in patterns of partial discharge measurement results were obtained. Each partial discharge generation source generated individual partial discharge pattern. These measurement data are used to test the purpose technique. Characteristics ofFigure 4: Test samples partial discharge data were calculated by using fractal features to apply for pattern recognition and classification. The individual 3-D PD patterns are plotted. The x and y axes correspond to the phase and amplitude (or charge), respectively. The matrix elements correspond to the pulse count data (or the z axis of the 3-D pattern). Fractal features are computed for all the available patterns recorded. Figure 8 is a plot of fractal dimension and lacunarity for different discharge sources. It is obvious that patterns belonging to a particular defect type gather together.Figure 5: Partial discharge pattern due to one void Figure 8. Fractal dimension and lacunarity of different discharge sources V. RECOGNITION RESULTS AND CLASSIFICATION The main objective of this paper is how to determine the box size which acquires the lacunarity the maximum ability to classify different types of defect that produce PD data. In this aim, a multilayerFigure 6: Partial discharge pattern due to three voids artificial NN could appear as a suitable possible solution to classify PD patterns. A back propagation 1013 | P a g e
  5. 5. Elsayed M. Elrefaie, M. K. Abd Elrahman, Sherif Ghoneim, Ahmed Bakr / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1010-1015neural network (BPNN) has been chosen because it is VI. CONCLUSIONSsimple and easy to change the number of hidden Analysis of PD patterns and identification oflayers and the number of neurons. The neuron discharge sources are important tools for thenumber of its input is determined by the number of diagnosis of HV insulation system. Through the lastfractal features. The number of neurons in the hidden decades, several features including the fractallayer depends on the number of the input data. The geometry have been used to characterize the PDneuron number of output layer is determined by the patterns. Calculating the fractal features like thenumber of defects to be identified, which are three in fractal dimension and lacunarity depends on the boxthis study. To demonstrate the recognition ability, 30 counting technique. This technique is based onsets of PD patterns are used to test the proposed PD covering the PD pattern with boxes having differentrecognition system. The NN-based PD recognition sizes. Increasing the box size leads to increasing thesystem randomly chooses 20 sets from the data as the computational time. Therefore this paper is antraining data set, and the rest of the sets as testing attempt to investigate the effect of box size on thedata. In order to determine the optimum value of ability of fractal features to discriminate betweenlacunarity which has the maximum ability to different PD sources. A NN-based PD patterndiscriminate between different PD sources, recognition method was used for this purpose. Thecombinations of fractal dimension and lacunarity obtained results show that the fractal dimension alonewere used for the training of the neural network. is not sufficient to discriminate between different PDTable I shows the accuracy of classification of the sources. On the other hand, lacunarity is moreproposed system with the different combinations. efficient for this purpose. But the ability of lacunarity It is obvious that the ability of NN-based PD depends upon the size of the box which used toclassification system depends upon the length of the calculate the value of lacunarity. Classificationbox side. The classification accuracy starts to accuracy increases with increasing the box size toincrease with increasing the box size that has been certain length and then starts to decrease. It isused to determine the lacunarity. The classification important to note that the value of box size whichaccuracy reaches maximum at L = 10 and then started acquires the lacunarity its maximum ability ofto decrease. This result emphasizes that the using of classification is very small compared to total size oflarge value of L will increase the computation time the full PD pattern. Based on this result a limitedwithout any improvement to the classification value of box size could be used to generate the fractalaccuracy. Therefore limited values of L can be used features which will reduce the computational timeto calculate the fractal dimension and lacunarity. significantly.TABLE I Accuracy of Classification According to REFERENCESDifferent Values of Lacunarity which Have Been [1] E. Kuffel, W.S. Zaengl and J. Kuffel, “HighUsed in Combination with Fractal Dimension Voltage Engineering Fundamentals”. 2nd, Box length to calculate the Recognition Butterworth – Heinemann, 2000 lacunarity rate (%) [2] S. Rudd, S. D. J. McArthur and M. D. Judd 2 30 "A Generic Knowledge-based Approach to 4 50 the Analysis of Partial Discharge Data", 6 60 IEEE Transactions on Dielectrics and 8 80 Electrical Insulation Vol. 17, No. 1; 10 100 February 2010. 12 90 [3] Z. Zhao, Y. Qiu, and E. Kuffel, “Application 14 70 of Fractal to PD Signal Recognition,” IEEE International Symposium on Electrical 16 80 Insulation, April 2002, pp. 523-526. 18 70 [4] L. Jian, T. Ju, S. Caixin, L. Xin, and D. Lin, 20 60 “Pattern Recognition of Partial Discharge 22 50 with Fractal Analysis to Characteristic 24 50 Spectrum,” International Conference on 26 60 Properties and Application of Dielectric 28 60 Materials, Vol. 2, June 2000, pp. 21-26. 30 50 [5] K. Zalis, “Applications of expert systems in 32 40 evaluation of data from partial discharge 34 40 diagnostic measurement,” in Proc. 7th 36 40 International Conf. Properties and 38 40 Applications of Dielectric Materials, pp. 40 30 331-334, June 2003. [6] Muhamad Mansor, Prodipto Sankar Ghosh & Ahmad Basri Abdul Ghani ," PD Patterns 1014 | P a g e
  6. 6. Elsayed M. Elrefaie, M. K. Abd Elrahman, Sherif Ghoneim, Ahmed Bakr / InternationalJournal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, Issue 5, September- October 2012, pp.1010-1015 Recognition In XLPE Cable Under Various [17] J.M. Keller, S. Chen, R.M. Crownover, Thermal Conditions Using Statistical Texture description and segmentation Technique ", IJRRAS 5 (2) ,November, through fractal geometry, J. Comput. Vis. (2010),p.p. 171-181. Graphics Image Process. 45 (1989) 150–[7] S. Boonpoke and B. Marungsri" Pattern 160. Recognition of Partial Discharge by Using [18] B. B. Mandelbrot, The Fractal Geometry of Simplified Fuzzy ARTMAP", World Nature, New York, Freeman, 1983. Academy of Science, Engineering and [19] Gefen et al., 1984. Phase transitions on Technolog China, pp 212-219, September fractals: III infinitely ramified lattices. 2010. Journal of Physics A, 17, pp.1277-1289.[8] Hung-Cheng Chen, Feng-Chang Gu, Chun- [20] Y. Malhi, R.M. Román-Cuesta"Analysis of Yao Lee "A New Method Based on lacunarity and scales of spatial homogeneity Extension Theory for Partial Discharge in IKONOS images of Amazonian tropical Pattern Recognition", Wseas Transactions forest canopies", Remote Sensing of on Systwms, Issue 12, Volume 7, pp.1402- Environment 112 (2008) 2074–2087. 1411, December 2008. [21] M. N. Barros Filho a, F. J. A. Sobreira[9] PO-Hung Cheni, Hung-Cheng Chen, An "Accuracy Of Lacunarity Algorithms In Liu, Li-ming Chen "Pattern Recognition Texture Classification Of High Spatial For Partial Discharge Diagnosis Of Power Resolution Images From Urban Areas" The Transformer", Proceedings of the Ninth International Archives of the International Conference on Machine Photogrammetry, Remote Sensing and Learning and Cybernetics, Qingdao, Vol. Spatial Information Sciences. Vol. XXXVII. 4493, pp. 2996-3001, July 2010. Part B3b.,p.p 417-422, Beijing 2008.[10] Hung-Cheng Chen, PO-Hung Chen, and Meng-Hui Wang " Partial Discharge Classification Using Neural Networks and Statistical Parameters", International Conference on Instrumentation, Measurement, Circuits & Systems, April 15- 17, 2007,p.p 84-88.[11] Karthikeyan, B., Gopal, S., & Venkatesh, S. (2006). "ART 2 – An unsupervised neural network for PD pattern recognition and classification", International Journal on Expert Systems with Applications, 31, 345– 350.[12]. Salama, M.M.A., Bartnikas, R.: Determination of Neural Network Topology for Partial Discharge Pulse Pattern Recognition. IEEE Trans. on Neural Networks 13 (2002) 446-456.[13] IEC, High-Voltage Test Techniques-Partial Discharge Measurements, IEC 60270, 2001.[14] L. Satish, W. S. Zaeng, “Can Fractal Features Be Used for Recognizing 3-D Partial Discharge Patterns? ” IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 2, June 1995, pp. 352-359.[15] Jian Li, QianDu, CaixinSun " An improved box-counting method for image fractal dimension estimation", Contents lists available at Science Direct, Pattern Recognition 42 (2009) 2460 – 2469.[16] B. S. Raghavendra, and D. Narayana Dutt "Computing Fractal Dimension of Signals using Multiresolution Box-counting Method", International Journal of Information and Mathematical Sciences 6:1, p.p 50-65, 2010. 1015 | P a g e