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A New Diagnosis Method on Insulators with Measuring ... - inass

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A <str<strong>on</strong>g>New</str<strong>on</strong>g> <str<strong>on</strong>g>Diagnosis</str<strong>on</strong>g> <str<strong>on</strong>g>Method</str<strong>on</strong>g> <strong>on</strong> <strong>Insulators</strong> <strong>with</strong> <strong>Measuring</strong> C<strong>on</strong>tact AnglesYan Liu 1, 3 , Kai Liu 3 , Wei-liang Tao 2 *, Ye Zhu 31 School of Electr<strong>on</strong>ic Informati<strong>on</strong>,Wuhan University, P.R.China2 Laboratory of System Integrated and Faults Diagnostics, Wuhan University, P.R.China3 State Grid Electric Power Research Institute ,Wuhan, P.R.China* Corresp<strong>on</strong>ding author’s Email: taowl2003@163.comAbstract: Compared to other methods, insulator’s c<strong>on</strong>tact angles detecti<strong>on</strong> can obtain more precise and moreaccurate hydrophobicity in parts of insulator, getting in-depth informati<strong>on</strong> like hydrophobicity of shed material,migrati<strong>on</strong> of the hydrophobicity after polluted insulator, attenuati<strong>on</strong> and recovery characteristics of the insulati<strong>on</strong>performance under certain c<strong>on</strong>diti<strong>on</strong>s, all of which are its particular advantages. A new detecti<strong>on</strong> method ofinsulator’s performance is proposed in this paper <strong>with</strong> measuring c<strong>on</strong>tact angles. With this method, the boundarycurve of water drop <strong>on</strong> insulator’s surface was extracted <strong>with</strong> image processing, then the polynomial fitting wasdeployed to fit the boundary curve, and c<strong>on</strong>tact angles of water drop were calculated by differentiate the polynomialdeduced from the polynomial fitting. So the performance of the insulator can be detected and the process doesn’tneed manual interventi<strong>on</strong> which makes the detect result accurate and objective. Experiments show that the root meansquare error of the measurement is below 2%.Keywords: insulator; hydrophobicity; c<strong>on</strong>tact angle; image processing;1. Introducti<strong>on</strong><strong>Insulators</strong> are widely used in the power system.The safe running of insulators is <strong>on</strong>e of the factors todetermine the investment budget and safety level ofthe power system. To ensure the safe electricitytransmissi<strong>on</strong>, it is necessary to seek an effective wayto measure insulator’s performance which determineswhether there is a need to maintain or replacethe insulators.There are many methods to measure the insulator’sperformance at present, of which the visualdetecti<strong>on</strong> [1] is widely adopted. However it not <strong>on</strong>lyrequest manipulators to observe insulators closely,but also need them to familiarize <strong>with</strong> various typesof insulators’ material, design and the frequentfailure modes. Resistance detecti<strong>on</strong> detects theleakage current to get the insulati<strong>on</strong> resistance whichcan reflect the performance of insulators. Themethod is simple and practical, but the informati<strong>on</strong>can be gained is limit. The effectiveness of theelectric field detecti<strong>on</strong> methods [ 2 - 5 ] has beenverified through experiments menti<strong>on</strong>ed by theliterature [ 6 ] . Meanwhile, it was found that thedetecti<strong>on</strong> precisi<strong>on</strong> is related to the fault locati<strong>on</strong>and whether the insulator is inundated will alsoaffect the results. Optical detecti<strong>on</strong> [ 7 , 8 ] estimatesinsulator’s discharge acti<strong>on</strong>s by observing thephot<strong>on</strong>s <strong>on</strong> insulator’s sur- face. This method mustavoid sunlight exposure, therefore requires thec<strong>on</strong>diti<strong>on</strong> of night. Thermal detecti<strong>on</strong> [9- 11] estimatesinsulator’s performance by the principles thatinsulator surface material degra- dati<strong>on</strong> is associated<strong>with</strong> the quantity of heat emitting from the insulatorin the electric field. The essence of this detecti<strong>on</strong>technology determines that it is sensitive to theinfluences from the wind, rain, sunshine and otherenvir<strong>on</strong>mental c<strong>on</strong>diti<strong>on</strong>. Acous- tic detecti<strong>on</strong>detects the noise produced by discha- rges <strong>with</strong>Internati<strong>on</strong>al Journal of Intelligent Engineering and Systems, Vol.2, No.2,2009 18


microph<strong>on</strong>e to estimates insulator’s perfor- mance,and its feasibility has been proved by Lundgaard[12] . The fault locati<strong>on</strong> and type of informati<strong>on</strong>can be obtained [13] through analyzing the amplitude,frequency and phase of acoustic wave. But the effectof the detecti<strong>on</strong> is determined by the material ofinsulator.Hydrophobicity detecti<strong>on</strong> technology is <strong>on</strong>e of themain detecti<strong>on</strong> methods as regards the evaluati<strong>on</strong> ofinsulator’s performance. The traditi<strong>on</strong>al methodmeasures the insulators’ hydrophobicity throughmeasuring the c<strong>on</strong>tact angle directly by photography[ 14 ] . However, this method can <strong>on</strong>ly becarried out in laboratory envir<strong>on</strong>ment. The restricti<strong>on</strong>is made up by STRI hydrophobicity classificati<strong>on</strong>method [ 15 , 16 ] . But it is dependent <strong>on</strong> theoperators’ subjective judgment, so the accuracy cannot be high. The method menti<strong>on</strong>ed in the Literature[17][18]estimates the average hydrophobicity usingdigital image processing. It is more objective andprecise, but it bases <strong>on</strong> the hydrophobicity classificati<strong>on</strong>and can not get the insulator’s partial hydrophobicity.It is obvious that the existing detecti<strong>on</strong> methodsare not satisfying and have some disadvantages. Soexperts nati<strong>on</strong>ally and internati<strong>on</strong>ally keep researching[19] in this field.This paper presents a detecti<strong>on</strong> method of insulator’sperformance through measuring the hydrophobicity.The method takes advantage of imageprocessing technology, such as extracting waterdroplets’ image from the background, fitting thewater droplets’ c<strong>on</strong>tour using the orthog<strong>on</strong>alpolynomial and measuring the c<strong>on</strong>tact angle, toestimate the insulator’s hydrophobicity. Comparing<strong>with</strong> other hydrophobicity detecti<strong>on</strong> methods, thismethod can detect the insulators which are stillrunning <strong>on</strong> the spot <strong>with</strong>out manual interventi<strong>on</strong>s,and the measurement results are more objective andprecise.2. Basic principleThe definiti<strong>on</strong> of c<strong>on</strong>tact angle is shown in Figure1. When the insulator’s surface is horiz<strong>on</strong>tal, thec<strong>on</strong>tact angles of water droplet <strong>on</strong> both sides are thesame, and is called static c<strong>on</strong>tact angle . Thedynamic c<strong>on</strong>tact angles a(advancing angle) andr(receding angle) can be defined when a droplet is<strong>on</strong> an inclined surface.The model of c<strong>on</strong>tact angle detecti<strong>on</strong> method isbased <strong>on</strong> image processing. Use drip device, dripappropriate water droplets <strong>on</strong> the insulator surface,then use CCD camera device to acquire images,image processing tools and curve fitting can beadopted to get c<strong>on</strong>tact angle.Figure 1 Diagram of c<strong>on</strong>tact anglesObviously, in the same water droplet capacity andtimes, the larger the static c<strong>on</strong>tact angle, the smallerthe interface that the water droplet c<strong>on</strong>tacting <strong>with</strong>the insulati<strong>on</strong> material, the better the hydrophobicity.It is generally believed that, when 90 insulatorsurface is hydrophobic. For inclined surface, bymeasuring the advancing angle and the recedingangle, the following formula can be used to researchhydrophobicity [20] .mg sin Lcosa cosr (1)where m is mass of water droplet, g is accelerati<strong>on</strong>of gravity, is incline angle, L is length of waterdroplet, is liquid surface tensi<strong>on</strong>, and r and a are the largest advancing angle and recedingangle of water droplet in inclined surface, respectively.Based <strong>on</strong> the liquid surface tensi<strong>on</strong> insulatorhydrophobic can be measured, the smaller thesurface tensi<strong>on</strong>, the better the hydrophobic.3. Image processingImage processing includes image preprocessing,image segmentati<strong>on</strong>, image feature extracti<strong>on</strong> andcurve fitting derivative about water droplet, etc.3.1 Water droplet image preprocessing1) Gray value transformingFor the operati<strong>on</strong> in Gray Image is simpler thanColored Image, we often transfer Colored Imageinto Gray Image of 256 colors.2) Image smoothingMost pixels’ gray value of an image is of littledifference <strong>with</strong> the adjacent, existing large graycorrelati<strong>on</strong> degree, which leads the energy of theimage to c<strong>on</strong>centrate in the low-frequency regi<strong>on</strong>.Attenuating high-frequency comp<strong>on</strong>ents andenhancing low-frequency comp<strong>on</strong>ent can retain themain message of the image and filter high-frequencynoise.Image smoothing methods include: neighbor-Internati<strong>on</strong>al Journal of Intelligent Engineering and Systems, Vol.2, No.2,2009 19


hood average, median filter, Gaussian filter, frequencydomain method and so <strong>on</strong>. Particularly,median filter is suitable for extracting water dropletc<strong>on</strong>tours from the image, which has the followingadvantages: ○1 to preserve edge details while removingthe impulse noise, salt and pepper noise at thesame time. ○2 to eliminate pulse effectively <strong>with</strong>outaffecting the step functi<strong>on</strong> and the slope functi<strong>on</strong>. ○3to avoid fuzziness <strong>on</strong> image detail resulted by thelinear filter under certain c<strong>on</strong>diti<strong>on</strong>s. ○4 computingprocess is c<strong>on</strong>venient <strong>with</strong>out need of the statisticalcharacteristics of images. Experimental results showthat the average templates and Gaussian templateboth blur image, especially the average template,while the median template can preserver edge detailbetter, as shown in Figure 2. So in practice we choosemedian filtering method.Detailed practice: to use a sliding window <strong>with</strong>odd point to slide <strong>on</strong> the image, to arrange the oddpixels <strong>with</strong> the pixel gray value, which are c<strong>on</strong>tainedin the window, from small to large; then to replacethe pixel gray value of the window centre <strong>with</strong> themiddle gray value in the order, to move the windowfrom left to right till reaching the border, then tomove to the next row, from left to right again and gothrough the whole image in this way. After themedian filter transformati<strong>on</strong>, some pixel’s grayvalue is equivalent to the middle value of the grayvalues in the neighborhood.(a) original image(c) Gaussian template filter(b) average template filter(d) median template filterFigure 2 Images of three kinds of filtering templates3) Gray stretchSince water is translucent liquid, the c<strong>on</strong>trastbetween water droplet image and its background istoo little to distinguish. In order to highlight dropletand suppress the background, piecewise lineartransformati<strong>on</strong> is adopted here.The gray value of the water droplet in the imageis lower than the background, and the whole imagehas a low gray value. Therefore the high graysecti<strong>on</strong> is compressed and the low gray secti<strong>on</strong> isstretched.To be simple, we can choose a gray value M,stretch the secti<strong>on</strong> where gray value is less than M,and turn the secti<strong>on</strong> where gray value is more thanM to the highest gray value totally. If f i, jdenotespixel gray value of the original image, g i,jdenotes the gray value after gray transform, thelinear transformati<strong>on</strong> functi<strong>on</strong> would be:M/ Mfi,j 0f i,j gMgi, j(2)MgM f i,jMg4) Image Rotati<strong>on</strong>According to the need of image processing thatfollowed, we hope that the water droplet in theimage is at the horiz<strong>on</strong>tal level <strong>on</strong> the whole in thepicture. As the incline angle <strong>on</strong> the insulator surfaceis about 15°, the whole image should be rotated by15°.3.2 Image segmentati<strong>on</strong>1) Edge detecti<strong>on</strong>The water droplet’s transparency makes theboundary between water droplet and its backgroundless obvious, particularly <strong>on</strong> the light side of theborder. To detect and highlight the edge of the waterdroplet is the premise of extracti<strong>on</strong> of water dropletc<strong>on</strong>tour accurately.Edges mainly divide into step shape and roofshape. The water droplet image is step edge wherethe edge points’ first-order derivative has extremevalue. So detecting edge points can be achieved bycalculating each pixel's gray gradient.The digital image’s first-order partial derivativeswould approximately be: f x f x1,yf x,y(3)f y f x,y 1f x,yTo simplify the calculati<strong>on</strong> of gradient, thefollowing approximate formula is used frequently:gradxy f x f y, (4)Generally, the gradient operator is sensitive inlevel or vertical directi<strong>on</strong> <strong>on</strong> the edge, while Robertsacross operator detects the gradient which crossal<strong>on</strong>g <strong>with</strong> the image coordinate axis 45° and 135°.The Operator is:gradx,y f f x y(5)f x,y f x 1,y 1 f x 1,y f x,y 1 Internati<strong>on</strong>al Journal of Intelligent Engineering and Systems, Vol.2, No.2,2009 20


Other comm<strong>on</strong> operators include Prewittoperator, Sobel operator, and Laplace operator. Asshown in Figure 3, it is indicated from the four edgedetecti<strong>on</strong> experimental results that Laplace operatoris more affected by noise, Prewitt and Sobeloperator detecti<strong>on</strong> edge are wider and its accuracy islow, and Robert operator results turn up satisfactorily.(a) Laplace operator(c) Sobel operatorFigure 3 Images of four edge detecting algorithms2) Binary processingBinary processing makes the image pixel grayvalue either 0 or 255 <strong>with</strong> certain rules, so focusedareas are apart from background completely. Am<strong>on</strong>gbinary processing methods threshold segmentati<strong>on</strong> iseffective and easy to implement.(a) OTSU methodFigure 4 Binarizati<strong>on</strong> images of dropletSuppose <strong>on</strong>e image is defined as followingmapping: f x, yG, and x,yis the space coordinates,f x,yis the gray value <strong>on</strong> the positi<strong>on</strong> ofx, y, G is a positive integer set which denotes graylevels. Segment image <strong>with</strong> threshold T, the resultwould be x, y0,255, which is:f t(b) Prewitt operator(d) Roberts operator(b) Iterative methodf 255f ( x,y) T( x,y)t 0 f ( x,y ) T(6)Therefore, those pixels <strong>with</strong> gray value 255corresp<strong>on</strong>d to the objects and the others corresp<strong>on</strong>dto the background.The key of threshold segmentati<strong>on</strong> is how todetermine the optimal threshold value. As noises,such as facular noise, exist in water droplet image,segmentati<strong>on</strong> results <strong>with</strong> fixed threshold would beextensively affected by the noise. OTSU method anditerative method are the main methods to achieve theoptimal dynamic threshold value. As shown inFigure 4, when the gray value between object andbackground is close, OTSU method will lose theobject informati<strong>on</strong>, while iterative method resultsare better, so iterative method is adopted.The approach can be described as follows.Firstly, to calculate image gray value histogram,to select the median of the whole image gray rangeas an initial threshold T (suppose there are L gradesof gray value in all). Then to use T to segment image,this will generate two sets of pixels. G1 set is madeup of all pixels whose gray value is larger than orequal to T, and G2 set is made up of all the pixelswhose grey value is less than the T value. Calculatethe average gray value of all the pixels in G1 andG2:T 1 (cm m)cm, 2 (cm m)m0Tm0L1mT1L1cmmT1Sec<strong>on</strong>dly, to calculate the new thresholdT=0.5( 1+ 2); then to calculate the new averagegray value 1, 2<strong>with</strong> this new threshold, and to repeatthe steps above until the iterati<strong>on</strong> value is equalto T.3.3 C<strong>on</strong>tour extracti<strong>on</strong>1) Thinning of binary imageThinning algorithm is stripping the border pixelsfrom binary image repeatedly, until the width ofborder turns to a pixel. During thinning processing,the c<strong>on</strong>nectivity of the object must be maintained.Thinning algorithm deployed in this paper isiterative algorithm for extract skelet<strong>on</strong>. It's a methodto judge if a border point should be eliminated fromthe binary structural c<strong>on</strong>tour according to therelati<strong>on</strong>ship <strong>with</strong> adjacent points, to realize c<strong>on</strong>tourthinning.Iterative algorithm is as follows: Firstly, it needsto detect the whole image, and to search the structuralelements p1 to compute n(p1) and s(p1).Judging by the following four c<strong>on</strong>diti<strong>on</strong>s:C<strong>on</strong>diti<strong>on</strong> 1: 2 n ( p1 ) 6 If p1 <strong>on</strong>ly has <strong>on</strong>eneighborhood point, p1 is pixels string’s end point,can’t be deleted. If p1 has seven neighborhoodpoints, to delete p1that will delete <strong>on</strong>e regi<strong>on</strong> willlead a secti<strong>on</strong> split.C<strong>on</strong>diti<strong>on</strong> 2: s (p1) = 1. If there have more than<strong>on</strong>e adjacent point transiti<strong>on</strong> 0 to 1, delete p1 willlead a secti<strong>on</strong> split.C<strong>on</strong>diti<strong>on</strong> 3: p 2 p4 p6 0 .C<strong>on</strong>diti<strong>on</strong> 4: p 8 p4 p6 0 .If four c<strong>on</strong>diti<strong>on</strong>s are met, as said p1 locates inthe West, North or Southeast border of the objects asInternati<strong>on</strong>al Journal of Intelligent Engineering and Systems, Vol.2, No.2,2009 21


shown, P1 will be marked as "delete," after thepoints are all dealing <strong>with</strong> in images then deletereunificati<strong>on</strong>.Then, repeat the above process to the processedimage, but c<strong>on</strong>diti<strong>on</strong>s 3 and c<strong>on</strong>diti<strong>on</strong>s 4 arechanged as follows:C<strong>on</strong>diti<strong>on</strong> 3: p2 p4 p8 0C<strong>on</strong>diti<strong>on</strong> 4: p2 p4 p8 0Similarly, if four c<strong>on</strong>diti<strong>on</strong>s are met at the sametime, P1 will be marked as "delete," after the point isall dealing <strong>with</strong> in images then delete reunificati<strong>on</strong>.Then start a new iterative algorithm after completi<strong>on</strong>until no pixel was marked as "delete."2) C<strong>on</strong>tour trackingBesides getting the c<strong>on</strong>tour, some disorderednoises still exist in the local area after thinningprocess. It is needed to extract water droplet bordersmore accurately. 8-neighborhood c<strong>on</strong>tour trackingalgorithm can track and extract water droplet bordereffectively.Eight directi<strong>on</strong> codes <strong>on</strong> edge points are shownin Figure 5.Figure 5 Eight directi<strong>on</strong> codes <strong>on</strong> edge pointsSuppose x, yis a border point of the object,the next border point must lie in the 8-neighborhoodarea. So we can track outside border according tothe 8-neighborhood informati<strong>on</strong>: Firstly, to locate aborder point in the top left corner of the object areaas a beginning for the search and then to search its8-neighborhood for the next border pointanti-clockwise, from top to bottom, from left to right,then to c<strong>on</strong>tinue searching <strong>with</strong> the point as currentstarting point. This searching process will berepeated till we reach the first starting point back.3)Vertical ScanningFor water is transparent, the aspect of waterdroplet towards the light side will be projected <strong>on</strong>the insulator and there is a "false border" in theimage. So the lower part of the water dropletc<strong>on</strong>tour we get before is not the real border, but theprojecti<strong>on</strong> <strong>on</strong> the insulator. We should take the mostleft droplet border point as the left point c<strong>on</strong>tactingthe insulator, and the most right <strong>on</strong>e as the rightpoint c<strong>on</strong>tacting the insulator. Set the points whichare above the line between two points as the graybackground and <strong>on</strong>ly retain the true border which is<strong>on</strong> the top.3.4 C<strong>on</strong>tact angle detecti<strong>on</strong>1) Polynomial FittingAccording to the definiti<strong>on</strong> of c<strong>on</strong>tact angle, tocalculate it needs tangent slope at the c<strong>on</strong>tact point<strong>on</strong> the droplet border <strong>with</strong> the insulator. Therefore itis necessary fitting the discrete points in bordercurve, and working out the derivative of theendpoint in the curve functi<strong>on</strong>.Generally, the least squares fitting algorithmwhich takes polynomial as basis functi<strong>on</strong> is adoptedto march the curve fitting. But coefficient matrix ofpolynomial fitting (Gelanmu matrix) is a seriouspathological matrix, which has an effect <strong>on</strong>computati<strong>on</strong>al stability.Orthog<strong>on</strong>al polynomial fitting c<strong>on</strong>structs a groupof orthog<strong>on</strong>al polynomials as the basis functi<strong>on</strong> andmakes their linear combinati<strong>on</strong> as curve equati<strong>on</strong>. Itsadvantage is: the Gelanmu matrix is diag<strong>on</strong>al matrix,the result is stable and of less fitting distorti<strong>on</strong>. Soorthog<strong>on</strong>al polynomials are adopted as the basicfuncti<strong>on</strong> to fit.2) C<strong>on</strong>tact angle calculati<strong>on</strong>By curve fitting we have attained the fittingpolynomial of original data points, from itsderivative, the slopes of the endpoints can becalculated to obtain the advancing angle a andthe receding angle r .4. Experimental analysesFigure 6JPEG color image of water dropletInternati<strong>on</strong>al Journal of Intelligent Engineering and Systems, Vol.2, No.2,2009 22


(a) gray transform (b) median filter (c) gray stretch (d) Image rotati<strong>on</strong>(e) Roberts edge detecti<strong>on</strong>(f) binary processing (g) thin processing (h) c<strong>on</strong>tour tracking (i) vertical scanning (j) polynomial fittingFigure 7 The processing images of water dropletIn this paper Can<strong>on</strong>'s digital camera “ixus60” isdeployed to capture the water droplet image <strong>on</strong>insulator, whose resoluti<strong>on</strong> is 1600×1200 pixels andwhich is saved as the BMP format. Figure 6 showsthe image.Figure 7 shows images processing of the insulatorc<strong>on</strong>tact angle detecti<strong>on</strong>. Since our attenti<strong>on</strong> isfocused <strong>on</strong> the area near the endpoints, removing themid-points which influence the fitting results andchoosing a number of points near the endpoints to fitis likely to increase fitting accuracy.90.0°80.0°70.0°60.0°50.0°40.0°30.0°20.0°70.0°65.0°60.0°55.0°50.0°45.0°40.0°35.0°30.0°25.0°20.0°8 11 14 17 20 23 26 29 32 35 38 41quadratic cubic quartic quintic photographyFigure 8 Precisi<strong>on</strong> analysis of advancing angle8 11 14 17 20 23 26 29 32 35 38 41quadratic cubic quartic quintic photographyFigure 9 Precisi<strong>on</strong> analysis of receding angleChoose different numbers of points near endpointsand polynomials degree <strong>with</strong> sec<strong>on</strong>d, third,fourth or fifth to fit curve many times, the results areshown in Figure 8 and Figure 9.The results show that when the polynomialsdegree is low, the fitting error is large, the c<strong>on</strong>tactangle has great fluctuati<strong>on</strong> <strong>with</strong> fitting pointsnumber changing, and experiment reproducibility ispoor. When polynomial degree is a higher number(more than four), the fitting effect is better. Thecalculated results are similar to photography measurementresults. The less the fitting points are, thegentler the curve is, which illuminates that properlyreduced sample points near the endpoints helps toenhance the accuracy. But when the number ofpoints is less than 10, the results has a largefluctuati<strong>on</strong>, which shows that there are not enoughpoints, so the fitting accuracy is reduced and thedetecti<strong>on</strong> accuracy is reduced either. All c<strong>on</strong>sidered,we select 28 points near the endpoints to carry <strong>on</strong>five polynomial fitting.Table 1 Result of c<strong>on</strong>tact angles measurementSequenceAdvancinganglemeansdifferenceRecedinganglemeansdifference1 74.0° 1.0° 54.6° 0.0°2 71.6° 1.4° 56.0° 1.4°3 73.8° 0.8° 53.6° 1.0°4 72.0° 1.0° 53.0° 1.6°5 73.5° 0.5° 55.8° 1.2°Average 73.0° 0.94° 54.6° 1.04°Using this whole process to measure the sameinsulator many times, we can get the results asshown in Table 1, from which it is proved thatmeasurement variance is less than 2%. Thus themethod is accurate, effective and has a certainInternati<strong>on</strong>al Journal of Intelligent Engineering and Systems, Vol.2, No.2,2009 23


perspective of practice.5. C<strong>on</strong>clusi<strong>on</strong>In this paper, the detecti<strong>on</strong> method of hydrophobicity<strong>on</strong> insulator surface based <strong>on</strong> imageprocessing could detect the c<strong>on</strong>tact angle <strong>with</strong>digital image processing techniques automatically.But further work should be d<strong>on</strong>e to make thismethod realized, such as how the image are gottenand how the image processing are taken in anembedded system. In additi<strong>on</strong>, how the partialhydrophobicity is synthesized to evaluate the performanceof an insulator and how the estimati<strong>on</strong> ofc<strong>on</strong>tact angles are affected when many water droplets<strong>with</strong> different sizes are present should bec<strong>on</strong>sidered. 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