Power system insulator condition monitoring automation using mean ...

Int. J. Computer Aided Engineering and Technology, Vol. 5, No. 1, 2013

Power system insulator condition monitoring automation using mean shift tracker-FIS combined approach Velaga Sreerama Murthy Department of Computer Science and Engineering, GMR Institute of Technology, GMR Nagar, Rajam-532127, Srikakulam District, Andhra Pradesh, India E-mail: [email protected]

Dusmanta Kumar Mohanta* Department of Electrical and Electronics Engineering, Birla Institute of Technology, Mesra, Ranchi-835215, India E-mail: [email protected] E-mail: [email protected] *Corresponding author

Sumit Gupta Department of Computer Science and Engineering, M.V.G.R. College of Engineering, Vizianagaram-535005, India E-mail: [email protected] Abstract: Within the hierarchy of power system, distribution system automation plays a crucial role to provide reliable service to customers. Though initially computer aided automation started as substation monitoring system (SMS) just for monitoring some key parameters such as voltage and currents of different components in a substation, the technological advancement has enabled to have access to more features from components of the entire distribution system. Since the distribution system has expanded to cater power to even remote locations, thus for reliable power supply, insulator condition monitoring automation plays an important role because the failure of insulator either causes complete disruption of power or reduction of system voltage leading to heavy power losses. This paper presents a methodology for condition monitoring automation of insulators by a combined approach using mean shift tracker and fuzzy inference system (FIS) and the case studies validate the efficacy of the methodology. Keywords: mean shift tracker; fuzzy inference system; FIS; insulator condition monitoring; distribution system automation; DSA; video surveillance.

Copyright © 2013 Inderscience Enterprises Ltd.

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V.S. Murthy et al. Reference to this paper should be made as follows: Murthy, V.S., Mohanta, D.K. and Gupta, S. (2013) ‘Power system insulator condition monitoring automation using mean shift tracker-FIS combined approach’, Int. J. Computer Aided Engineering and Technology, Vol. 5, No. 1, pp.1–19. Biographical notes: Velaga Sreerama Murthy received his BE from Mepco Schlenk Engineering College, Sivakasi, TN, India in 2000 and PhD from Birla Institute of Technology, Mesra, Ranchi, India in 2011. He is currently working as an Associate Professor in GMRIT, Rajam, AP, India. His area of interest is image processing and video surveillance. Dusmanta Kumar Mohanta received his BSc Electrical Engineering from College of Engineering and Technology, Bhubaneswar, India and ME in Power Systems from Birla Institute of Technology (BIT), Ranchi, India. He received his PhD from Jadavpur University, Kolkata, India. His research topics are power quality analysis, power system planning and reliability analysis. He is currently a Professor in the Department of Electrical and Electronics Engineering in BIT, Ranchi. He has total experience of 21 years in teaching and industry. He has worked as an Electrical Engineer in captive power plant of National Aluminium Company (NALCO), Angul, India and has been involved as a Consultant for different problems in industry and for testing of different electrical equipments. He is a senior member of IEEE. He is a member of Editorial Board of Electric Power Components and Systems. Sumit Gupta received his BTech in IIT, Delhi in 1996 and PhD in NUS Singapore in 2003. He has worked as a faculty member in IIT Roorkee for two years and is currently heading the Department of Computer Science of M.V.G.R. College of Engineering, Vizianagaram, AP, India. His field of interest is image processing, video surveillance and 3D computations.

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Introduction

Research carried out in the field of power system insulator condition monitoring using image processing (IP) and machine learning techniques (MLTs) is very scarce. However, the well-being analysis of other equipments is enriched by a large number of research studies for example well-being analysis of safety critical software: a case study for computer relaying can found in Roy et al. (2010), ranging from psychology to engineering applications as found in Billinton et al. (1997) and Keyes et al. (2002). Therefore, an attempt is made in this paper a very innovative method using core techniques of IP and viable method of artificial intelligence for condition monitoring of insulators to give adequate emphasis on the paradigm shift in the area of power distribution system automation (DSA). With the advancement of digital IP techniques, there have been some applications related to aerial inspection of overhead power lines based on video surveillance (VS) for electric power distribution system monitoring and automation (Jones, 2000). A laboratory test-bed for an automated power line inspection system has also been proposed (Jones et al., 2005) which employs aerial inspection of transmission lines of England. In this case new difficulties arise due to the fast changing background, blurring of the images, camera sight control and so on. Jones and Earp

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(2001) discuss in detail the motivation for pursuing video inspection techniques and the accompanying problems which arise, especially in terms of the camera sightline pointing requirements for helicopter patrols. To avoid such practical difficulties, the present research aims at a comparatively easier approach for power system insulator condition monitoring automation using IP as delineated in the subsequent section. Insulator condition monitoring automation is to discern the health of insulators. Insulators can be in any one of the three states such as good, marginal or risk. In order to represent insulators in one of these three states, features (feature vectors) are extracted using Wavelet MRA, the details can be found in Murthy et al. (2010). These feature vectors can be used as training inputs, associated with their wellbeing labels, to employ MLTs for classifying a new and unknown insulator image into either good, marginal or risk states. Reddy and Mohanta (2009) presented a wavelet-support vector machine combined approach for location of transmission line faults. Combined wavelet-SVM approach for condition monitoring of insulators has been nicely depicted in Murthy et al. (2010). SVM approach is limited by labelling insulators into either good, marginal or risk states only. In order to find the degree of an insulator’s health (i.e., what degree it is good or marginal or risk), this paper employs fuzzy inference system (FIS). Different insulators having different degrees of damage for marginal or risky states which cannot be characterised by a simple and well defined deterministic mathematical model, but can be more easily handled in terms of the fuzzy-set theory, in which simple rules and a number of simple membership functions are used to derive the correct result. In general, fuzzy sets are efficient in various aspects of uncertain knowledge representation and are subjective and heuristic, while SVMs are capable of learning from examples, but have the shortcoming of implicit knowledge representation. The various applications based on fuzzy such as Fuzzy reliability evaluation of captive power plant maintenance scheduling incorporating uncertain forced outage rate and load representation by Mohanta et al. (2004), Performance evaluation of adaptive network-based FIS approach for location of faults on transmission lines using Monte Carlo simulation by Reddy and Mohanta (2008b), adaptive-neuro approach for transmission line fault classification and location incorporating effects of power swings by Reddy and Mohanta (2008a), fuzzy Markov model for determination of generating unit fuzzy state probabilities including the effect of maintenance scheduling (Mohanta et al., 2005) and A wavelet-neuro-fuzzy combined approach for digital relaying of transmission line faults by Reddy and Mohanta (2007) give wider applicability of fuzzy and its importance in various fields. In contrast to SVM that has the capability of classifying insulators into good, marginal and risk states only, FIS, is applied in the present paper to calculate the insulators health in terms of what degree they are in good or marginal or risk states. The main contribution of this paper is to extract the poles from video images using mean shift tracker and subsequently, well being analysis of insulators is done using FIS. The case studies demonstrate the efficacy of the proposed method using mean shift tracker-FIS combined approach. The organisation of the paper is as follows. Section 2 describes the overview of power system insulator detection and condition monitoring automation. Section 3 describes tracking of power system distribution poles using mean shift tracker with case studies. In Section 4, well-being analysis of insulators using wavelet-FIS combined approach is described. Section 5 describes the conclusion.

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Overview of power system insulator detection and condition monitoring automation

Figure 1 depicts the overall diagram of power system insulator condition monitoring automation using wavelet-MLT combined approach. The description is as follows. Initially images containing insulators have been acquired through either surface vehicular patrolling (SVP) approach or through remote terminal unit (RTU) approach. In order to acquire a streaming video of overhead distribution lines using SVP is inspired from a US patent (Peterson, 1990). The SVP approach consists of two stages. In the first stage, a streaming video containing all electric poles of 33 kV and 11 kV transmission and distribution lines of a specific area to be monitored is acquired using vehicular VS. The advantage of this approach is that any non-technical resource can go along with a camera which is mounted on a motor vehicle to acquire the input video. In order to track overhead power distribution system poles successfully from the acquired streaming video, the algorithm uses mean shift tracker. Figure 1

Image acquisition, pole extraction, insulator extraction and classification of insulators using combined wavelet-MLT techniques

Mean shift tracker extracts a clearly visible and a distinct pole from the video which is dealt in the second stage. In case of RTU approach the images have been acquired through RTU. The detailed information related to RTU method and the extraction of individual insulators from the images can be found in the reference (Murthy et al., 2010). In order to assess the well-being analysis of insulators, various MLTs can be employed. This paper employs FIS to discern the health of the insulators.

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Tracking poles using mean shift tracker

The basic approach for tracking is to first represent the target object (based on colour, principal component analysis, etc.) and then try to find the same object in subsequent video frames. This section presents results obtained by implementing state of the art,

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kernel-based tracking algorithm using mean shift. In this approach, objects of interest are characterised by the probability density functions (PDFs) of their colour features. By masking the distribution with a monotonically decreasing kernel, a spatially-smooth similarity function is defined and mean-shift iterations can use the gradient of this similarity function as an indicator of the direction of target’s movement. The similarity is expressed in terms of Bhattacharyya coefficient. The algorithm focuses on a much smaller neighbourhood and can outperform the exhaustive search. Histograms are used for the representation of the objects’ colour PDFs, as they can satisfy the low-cost requirement of real-time tracking. The aim is to implement a mean-shift tracker to find pole occurrence and tracking that pole. The mean-shift tracker maximises the appearance similarity iteratively by comparing the histograms of the object, Q, and the window around the hypothesised object location, P. Histogram similarity is defined in terms of the Bhattacharya coefficient as given in equation (1) b

∑ P(u)Q(u)

(1)

u =1

where b is the number of bins. At each iteration, the mean-shift vector is computed such that the histogram similarity is increased. This process is repeated until convergence is achieved, which usually takes five to six iterations. For histogram generation, weighting scheme defined by a spatial kernel which gives higher weights to the pixels closer to the object centre is generally used. An obvious advantage of the mean-shift tracker over the standard template matching is the elimination of a brute force search, and the computation of the translation of the object patch in a small number of iterations. However, mean-shift tracking requires that a portion of the object is inside the circular region upon initialisation.

3.1 Mean shift concepts This paper presents results obtained by implementing state of the art, kernel-based tracking algorithm using mean shift that was introduced in Veenman et al. (2001).

3.1.1 The Kernel mask The object’s density estimates (i.e., histograms) are weighted by a monotonically decreasing Epanechnikov kernel function, given in equation (2) K E ( x) = 1/ 2cd−1 (d + 2) (1− || x ||2 )

( if || x ||< 1, 0

otherwise )

(2)

where cd is the volume of the unit d-dimensional sphere and x is the normalised pixel coordinates within the target, relative to the centre (i.e., || x ||2 is a squared Euclidean distance of each pixel from the centre of the target as shown in Figure 2). Since the algorithm deals with a two-dimensional image space, the kernel function can be represented as given in equation (3).

K E ( x) =

2

π

(1− || x ||2 )

(3)

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Figure 2

Epanechnikov monotonically decreasing kernel

The rationale for using a kernel to assign smaller weights to pixels farther from the centre is that those pixels are the least reliable, since they are the one which are most affected by occlusion or interference from the background (i.e., colour-bleeding due to low resolution, transmission errors and noise). A kernel with profile is essential for the derivation of the smooth similarity function between the distributions. Since Epanechnikov kernel derivative is constant the kernel masking lead to a function suitable for gradient optimisation, which gives the direction of the target’s movement. The search for the matching target candidate in that case is restricted to a much smaller area and therefore much faster than the exhaustive search.

3.1.2 Distance minimisation The probability of classification error is directly related to the similarity of the two distributions. So the choice of the similarity measure is supposed to maximise the Bayes error arising from the comparison of target pdf and candidate pdf. Bhattacharyya coefficient has been chosen as it is closely related entity to the Bayes error. The definition of Bhattacharyya coefficient of two statistical distributions is shown in equation (4).

ρ[ p( y ), q] =

∫

pz ( y )qz d z

(4)

where the distributions pz and qz are the histograms of the target and the candidate respectively.

3.1.3 Bhattacharyya coefficient The similarity function defines the distance between target model and the candidate. The distance between two discrete distributions is given in equation (5). d ( y ) = 1 − ρ [ pˆ ( y ), qˆ ]

(5)

where

ρˆ ( y ) = ρ [ pˆ ( y ), qˆ ] =

m

∑

pˆ u ( y )qˆu

u =1

is the sample estimate of the Bhattacharyya coefficient between p and q.

(6)

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3.2 Mean shift-based object tracker The mean shift tracker takes a series of image frames obtained from a digital camera as input. The tracker comprises of two main steps 1

target representation

2

target localisation.

Firstly, to characterise the target a feature space is chosen. The reference target model is represented by its pdf in the feature space which is shown in Figure 3. For target localisation, the localisation procedure starts from the position of the target in the previous frame (the model) and searches in its neighbourhood. The best candidate is selected by maximising the Bhattacharya coefficient. The same process is repeated for every next pair of frames. The procedure for target localisation is depicted in Figure 4. The mean shift procedure is implemented for the tracking of overhead power lines using their colour distribution. The main idea is to exploit the basin of attraction of the target, the estimated location of the target in the current frame being used to find the nearest mode in a confidence image derived from the subsequent frame. Figure 3

Target representation (see online version for colours)

Figure 4

Target localisation

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3.3 Implementation of mean shift tracker for identifying distribution poles The biggest issues in visual tracking are the robustness of the algorithm under changing video conditions, including illumination and shape changes. So the first problem to be addressed is the choice of the colour space in which the tracking algorithm would operate. The easiest method is to choose the normalised rgb colour space, since it is invariant to viewpoint, illumination, and object shape changes (Gevers, 2001). It is assumed that the segmentation module has detected and localised the object of interest in the first video frame and it also knows exactly object’s position, shape and dimensions. Therefore, before starting with tracking, binary masks have been employed to extract the targets from the initial frames and find their colour histograms. For this implementation, colour histograms of the normalised rgb model have been employed. The input frames were first converted to the rgb space (since I = R + G + B, all pixel values were divided by the sum of their R, G, and B component values) which eliminates the intensity information from colour. Thus it eliminates the colour dependency on it. Subsequently, a weighted 3D histogram of each component has been computed (the number of bins in each dimension was restricted to 16, which is estimated to give enough discriminating power to the object’s colour distribution). A weight kernel has been adapted to the size of the target by the choice of the smoothing parameter h, which normalises the target’s ellipsoidal region, to a unit circle (by dividing each distance’s coordinates independently by hx and hy). Colour probability distribution functions can be used as a feature for object discrimination (Gevers, 2001). Colour is subjected to several variations, such as changes in intensity and saturation which are due to changes in the light source, the objects geometry and reflections (Valenti and Hageloh, 2003). So the algorithm should choose a colour system that is insensitive to these kinds of variations. Since, the video of overhead power lines lighting conditions are normally ideal, colour PDF (Comaniciu et al., 2003) q can be used in rgb space to represent the target object, q is also referred as target model. To find the target in subsequent frames, the pdf p is measured about different locations y, where p(y) is referred to as target candidate. To keep computational costs low, these pdfs are represented as m-bin histograms with only two rgb channels (the m-bin histogram size is 16 × 16 bin histogram). Hence the target model and the target candidate will be a two dimensional rgb histogram chosen over a specified region around a location y. The only problem with rgb is that it becomes unstable for low intensities, as we divide by very small numbers or potentially zero. This issue has been addressed during the implementation by using appropriate masks.

3.4 Mean-shift tracking The very basic idea of mean shift tracking is the same as brute force tracking, i.e., in subsequent video frames the target will not change much in position and appearance. Since target candidate is measured over a region, it is assumed that part of the target object will still fall under the region of the previous position. Hence, when measuring the pdf about the target’s previous position, the algorithm will detect at least some similarity with the target distribution. It is essential to include special information in the distance measure between the target distribution and current distribution. This way a gradient can be calculated which points towards the spatial direction where the two distributions are

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most similar and therefore it is most likely to find the target object. To link the colour pdf with spatial information a kernel can be used, which will define the target model as follows. In order to be able to estimate the most probable position of the target in the next frame, the following procedure is adopted. a

Finding of an appropriate metric: The proposed algorithm makes use of the Bhattacharyya coefficient here. Given two discrete and normalised distributions pˆ and qˆ the Bhattacharyya coefficient is defined as

ρ [ pˆ , qˆ ] =

m

∑

pˆ u qˆ

(7)

u =1

However, the algorithm expresses the distribution of the candidate object as a spatial function, so let pˆ ( y ) be the distribution of the candidate object at position y. Thus, the coefficient becomes

ρ [ pˆ ( y ), qˆ ] =

m

∑

pˆ ( y )u qˆ

(8)

u =1

b

Defining an appropriate kernel: The Epanechnikov kernel has been chosen as it defines an ellipsoidal region and gives more weights to pixels closer to the centre of the kernel. This is useful because pixels far from the centre of the object are more likely to be occluded or cluttered. The kernel function is defined by K ( x) = 1 / 2cd−1 (d + 2) (1− || x ||2 )

( if || x ||< 1, 0

otherwise )

(9)

Note that d is the number of dimensions and cd is the area of a unit circle in d-dimensions, so d =2 and cd = π in our case. c

Calculating the gradient with respect to y based on the choices are made for (a) and (b): Minimising the distance between target and candidate distribution is the same of maximising the Bhattacharyya coefficient. In essence, the mean shift procedure utilises the fact that for any density function the mean of a set of neighbouring samples is always biased towards a local mode (local maximum). This is quite intuitive since samples closer to the local mode will have bigger values thus ‘attract’ the mean towards them. So to estimate the gradient at a point x, first calculate the mean vector x from a sample set about x. Subsequently, calculate the mean-shift vector x − x. Using this technique, given the target object’s current position yˆ 0 its next position can be estimate by yˆ1

∑ = ∑

nh wx i =1 i i nh w i =1 i

where nh is the number of pixels under the kernel and

(10)

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wi =

∑ u =1

qˆu δ [ xi − u ] pˆ u ( yˆ 0 )

(11)

which is basically the square root of log-likelihood, but only for the values of the two distributions that correspond to the location (or pixel) xi inside the kernel. With the above information, the algorithm for tracking poles using mean-shift is as follows.

3.5 Algorithm for mean shift tracker Given, the distribution of the target object qˆ and its location in the previous frame yˆ 0 , 1

Measure the distribution around the objects previous location yˆ 0 and check how well it matches the target distribution, by calculating the Bhattacharyya coefficient.

∑ = ∑

nh

wx i =1 i i nh w i =1 i

2

Estimate the objects next location yˆ1 using yˆ1

3

Measure the colour distribution around the new position and also check how well it matches the target distribution (Bhattacharyya again).

4

If the colour distribution at yˆ 0 matches qˆ better than at yˆ1 then the step calculated in 2 was too big. So keep measuring the colour distributions at locations closer to yˆ 0 by iteratively halving the step size until it is found a better match (or reaches yˆ 0 again).

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If the distribution at yˆ1 matches qˆ well enough (their distance is smaller than ε) then target object is found. Otherwise set yˆ 0 to yˆ1 and go back to 2.

.

3.6 SVP: mean shift tracker and case studies Here, using mean shift tracker method, the following case study with highly complex back ground is presented to extract poles from an input video. Using this method the number of poles available in the input video also found. In general, the mean-shift tracker works very well. The algorithm is tested on various portions of the video sequences which consist of overhead power lines (pole sequences). The algorithm is proved to be very robust to various changes in the target’s shape and size as well as to partial occlusions. Before testing the tracker, the algorithm requires to choose on which two rgb channels to use. The best channels should be the ones that give the best discriminative power in respect to the background. This can be investigated by comparing the target distribution to the distribution of the background (taken under the same kernel) with calculation of the Bhattacharya coefficient. The resulting video pole.avi is obtained by running the algorithm over several frames that contain changes in object’s shape and size, as well as several partial occlusions of the pole being tracked. As can be observed from the figures, the algorithm is robust to these conditions. Figure 5(a) shows the first frame in which the algorithm is tracking the pole

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of interest; Figure 5(b) is the 2nd frame, the next three frames [Figures 5(c) to 5(e)] show some characteristic frames in which a large amount of occlusion is present. Figure 5(f) shows the last frame in the sequence. Thus, using mean shift tracking algorithm over the given input video, the transmission poles are tracked successfully. The algorithm presented in this paper also outputs distinct poles as separate frames as well as pole count. Once the individual poles are extracted, the next stage is to extract insulators from the transmission pole image and in final stage the well-being will be assessed. Figure 5

(a) 1st frame (b) 2nd frame (c) 8th frame (d) 21st frame (e) 30th frame and (f) 34th frame (last frame)

(a)

(b)

(c)

(d)

(e)

(f)

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FIS for well-being analysis of insulators and case studies

Another significant contribution of this paper is that it extends the concept of well-being analysis of insulators for DSA for knowing the degree of damage of insulators for reliable and safety measures. In addition to, envisioning different possible degenerated states of insulators, fuzzy logic has been employed to characterise degraded state of insulator for DSA using the fuzzy well-being approach. The proposed methodology inherits the fundamental capability of a fuzzy model to deal with non-random uncertainties associated with vagueness and imprecision. In addition, it retains the property of a stochastic model to deal with random uncertainties. The insulator image properties have been adequately represented incorporating a fuzzy model and coherent conclusions in terms of fuzzy state probabilities have been identified in terms of the well-being indices. In order to assess the well-being analysis of insulators, first insulators have to be extracted; Murthy et al. (2009) vividly describes the extraction of insulators with various case studies. Murthy et al. (2010) provides with some indices that reflects to well-being analysis of insulators viz. good, marginal or risk only. But to know what degree an insulator is close to a risk state or marginal state or good state requires fuzzy approach. Thus fuzzy logic is an appropriate tool for well-being analysis, because it gives the range of values for which a system would be in good state, marginal state or risk state, leading to fuzzy well-being analysis. Although, the wavelet-MRA coefficients which are extracted from insulator images (Murthy et al., 2010) contain all information regarding the frequency components associated with the insulator type, yet these coefficients have inherent uncertainties as they are in a raw data form. This uncertainty is represented in expert system, where the analysis begins from the fundamental model of uncertainty based on fuzzy logic. Such an analysis leads the development of a rule-based expert system that effectively extracts information from available data for obtaining coherent conclusion with minimal overall uncertainty. This knowledge is represented by some rules so as to minimise the overall uncertainty. As in any rule-based system, the rules are chained together by what is called FIS. FIS has been successfully applied in the fields such as automatic control, data classification, decision analysis, expert systems, and computer vision. Because of its multidisciplinary nature, FISs are associated with a number of names, such as fuzzy rule-based systems, fuzzy expert systems, fuzzy modelling, fuzzy associative memory, fuzzy logic controllers, and simply fuzzy systems. Fuzzy inference is the process of formulating the mapping from a given input to an output using fuzzy logic. The mapping then provides a basis from which decisions can be made or patterns discerned. The process of fuzzy inference involves membership functions, fuzzy logic operators, and if-then rules. Mamdani’s fuzzy inference method (Mamdani and Assilian, 1975) is the most commonly seen fuzzy methodology. Mamdani’s method was among the first control systems built using fuzzy set theory. Mamdani’s effort was based on fuzzy algorithms for complex systems and decision processes (Zadeh, 1973). The block diagram for FIS is shown in Figure 6. The basic structure of FIS is a model that maps input characteristics to input membership functions, input membership function to rules, rules to a set of output characteristics, output characteristics to output membership functions and the output membership function to a single-valued output or a decision associated with the output. Usually membership functions are chosen somewhat

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arbitrarily and are fixed in nature. Also fuzzy inference is employed for modelling of systems whose rule structure is essentially predetermined by the user’s interpretation of the characteristics of the variables in the model. For the fuzzy input variables, the universe of discourse spans over zero to one because normalised values are used for sake of computational simplicity. Each input variable is quantised into linguistic variables such as good, marginal &risk for further operation using FIS. Similarly, the universe of discourse for the output variable is also spans over zero to one. This universe of discourse is divided into linguistic variables according to different fault zones. For the case study, universe of discourse is quantised into three linguistic variables, namely, Z1, Z2 and Z3 corresponding to good, marginal and risk states respectively. The inputs have been combined together based on the expert opinion, all through possible rules have been framed and then the output has been defuzzified using centriod rule to get the crisp value of D. Figure 6

Block diagram of FIS

The universal set is divided into various membership functions accordingly. The point of fuzzy logic is to map an input space to an output space, and the primary mechanism for doing this is a list of if-then statements called rules. All rules are evaluated in parallel, and the order of the rules is unimportant. The rules themselves are useful because they refer to variables and the adjectives that describe those variables. Before building a system that interprets rules, it is required to define all the terms which are planned to use and the adjectives that describe them. The extracted statistical wavelet MRA coefficients from insulator images constitute the feature vectors for representing their respective states good, marginal or risk. The feature vector consists of four features, namely, standard deviations σL1, σL2 and σL3 which are obtained from first, second and third level horizontal detail coefficients of the bior2.2 mother wavelet for the given input image (insulator) and finally index beta (β) is computed by subtracting the summation of minimum horizontal detail wavelet coefficients of the first three levels (MaxL1 + MaxL2 + MaxL3) from the summation of maximum horizontal detail wavelet coefficients of first three levels (MinL1 + MinL2 + MinL3). Since, the feature vector forms the basis for well-being analysis

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of insulators; therefore these values are used as inputs to the FIS as shown in Figure 6. The variable (D) is considered as output. The standard fuzzy membership numbers, called trapezoidal fuzzy numbers are used to represent the uncertain parameters such as input variables σL1, σL2, σL3, β and output variable D. This type is more similar to human thinking, which defines the possibility as a range rather than a point. For example, a linguistic declaration such as “β will surely not below 1,100 or above 1,500 for healthy insulator, and the best estimate is between 1,100 to 1,500” will be translated into a trapezoidal fuzzy number, [1,000, 1,100, 1,500, 1,600] instead of a crisp value of something like 1,300. In this paper, both Mamdani-type and Sugeno-type inference systems have been applied for wellbeing analysis of insulators and finally the results are compared. Mamdani-type inference, expects the output membership functions to be fuzzy sets. After the aggregation process, there is a fuzzy set for each output variable that needs defuzzification. It is possible, and in many cases much more efficient, to use a single spike as the output membership functions rather than a distributed fuzzy set. This is sometimes known as a singleton output membership function, and it can be thought of as a pre-defuzzified fuzzy set. It enhances the efficiency of the defuzzification process because it greatly simplifies the computation required by the more general Mamdani method, which finds the centroid of a two-dimensional function. Rather than integrating across the two-dimensional function to find the centroid, we use the weighted average of a few data points. Sugeno-type systems support this type of model. In general, Sugeno-type systems can be used to model any inference system in which the output membership functions are either linear or constant. Sugeno (1985) or Takagi-Sugeno-Kang, method of fuzzy inference is similar to the Mamdani method in many respects. The first two parts of the fuzzy inference process, fuzzifying the inputs and applying the fuzzy operator, are exactly the same. The main difference between Mamdani and Sugeno is that the Sugeno output membership functions are either linear or constant. A typical rule in a Sugeno fuzzy model has the form If Input 1 = x and Input 2 = y, then Output is z = ax + by + c or a zero-order Sugeno model, the output level z is a constant (a = b = 0). The output level zi of each rule is weighted by the firing strength wi of the rule. For example, for an AND rule with Input 1 = x and Input 2 = y, the firing strength is wi = AndMethod(F1(x), F2(y)) where F1, F2 (.) are the membership functions for Inputs 1 and 2. The final output of the system is the weighted average of all rule outputs, computed as N

∑w z

i i

Final output =

i =1 N

∑w

(12)

i

i =1

4.1 Case studies In order to assess the well-being analysis of insulators, insulators must be extracted from the transmission pole image. Extraction of transmission pole frames from streaming video was discussed in Section 3. Murthy et al. (2009) vividly describes the various case studies to extract insulators from the different types of pole images. Murthy et al. (2010) gives the methodology to extract wavelet-MRA features from the extracted insulator

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images. The chosen mother wavelet is bior2.2. Figure 7 shows the sample of six good insulator images and Figure 8 shows the sample of five bad insulator images. The wavelet features (σL1, σL2, σL3 and β) considered for good insulators for FISare shown in Table 1. The wavelet features considered for bad insulators for are shown in Table 2. FIS works with the help of simple if-then rules. In order to achieve better outputs, rules must be framed with the help of expert opinion. Since the input variables are four in number, the total number of rules for this FIS system is 81 in number. Table 3 shows 12 rules out of 81 framed for Mamdani FIS. In Table 3, the possible states of insulator are denoted with G, M and R where G stands for good, M stands for marginal and R stands for risk states. The interpretation of rules is explained as follows. For example, rule number 1 says if (SD1 is G) and (SD2 is G) and (SD3 is G) and (Beta is G) then (D is G). That means if standard deviation of level 1(SD1) falls in the range of good insulator, standard deviation of level 2 (SD2) falls in the range of good insulator, if standard deviation of level 3(SD3) falls in the range of good insulator and if index beta also falls in the range of good insulator, then the output variable D is good. Similarly other rules can also be made. The partial list (14) of 81 rules is shown in Table 3. Table 4 depicts the condition indices obtained for good insulator using FIS. Insulators 1–6 provided in Table 4 are correspondent to the insulators given in Figure 7, which are in good state. In Table 4, Insulator 1 has SD1 = 3.825, SD2 = 23.63, SD3 = 88.7 and Beta = 1,166.55. The actual health of insulator 1 is healthy. FIS (Mamdani type) gives condition indices as 80.6 and FIS (Sugeno) type gives condition indices as 95.1. Similarly remaining five insulators health condition can be verified by FIS. Table 4 shows that the outputs of Sugeno type are superior to Mamdani type, because Sugeno type results are closer to 100, as 100 indicates that the insulator is good. For Insulator 3, FIS (Mamdani) and FIS (Sugeno) both gives the health value as 50, which is a wrong condition indices generated by FIS. Figure 7

Good insulator images

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V.S. Murthy et al.

Figure 8

Damaged insulators

Table 5 gives feature vectors for three marginal type insulators [Figure 8 (damaged 1–3)] and for two risky type insulators [Figure 8 (damaged 4-5)]. Condition indices given by FIS (Mamdani) for Figure 8 (1–3) are 34.4, 46.8 and 42.3 respectively. Condition indices given by FIS (Sugeno) for Figure 8 (1–3) are 36.2, 48.9 and 47.3 respectively. In case of marginal type insulators, both FIS (Mamdani) and FIS (Sugeno) produce almost same results. Condition indices given by FIS (Mamdani) for Figure 8 (4–5) are 22.4 and 23.5 respectively, indicating that insulators damaged condition is deeper. Condition indices given by FIS (Sugeno) for Figure 8 (4–5) are 0 and 2.5 respectively. These values (0 and 2.5 ≅ 0) indicating that damaged insulators belongs to risk state. In this case, though the outputs of FIS (Sugeno) do not give the degree of damage but it does classify the insulator correctly. Table 1 Wavelet features→ Insulator number↓ Good insulator 1 Good insulator 2 Good insulator 3 Good insulator 4 Good insulator 5 Good insulator 6

Mother wavelet (bior 2.2) features for good insulators

σL1

σL2

Beta (β)

σL3

MaxL1 MaxL2 MaxL3 MinL1 MinL2 MinL3

88.7

18.69

132.9

418.8

33.6

–165

–397

1,166.55

3.407 20.86 74.87

25.38

100.3

487.2

–41.7

–200

–270

1,125.07

5.094

31.6

80.01

39.06

137.5

311.7

–50.3

–308

–497

1,343.47

3.41

19.69 64.39

27.94

100.1

268.1

–34.1

–146

–338

913.5

20

132.1

255

–30.6

–133

–710

1,280.33

37.94

180.7

205.6

–49.8

–235

–690

1,398.59

3.825 23.63

3.851 22.54 96.92 5.541

30.8

91

Power system insulator condition Table 2

17

Mother wavelet (bior 2.2) features for bad insulators

Wavelet features→

σL1

Insulator number↓ Damaged insulator 1 Damaged insulator 2 Damaged insulator 3 Damaged insulator 4 Damaged insulator 5 Table 3

σL2

σL3

MaxL1 MaxL2 MaxL3

MinL1

MinL2

Beta (β)

MinL3

3.528 18.48

73.67 24.63

111.5

303.6

–44.88 –100.5 –423.2 1,008.31

3.128 18.89

75.41 29.06

148

236.1

–26.25 –131.6 –463.3 1,034.31

3.409 14.017 63.44 35.44

93.36

236.2

–24.06 –95.57 –369.2

3.595 18.47

67.5

28.69

91.09

222.4

–25.19 –176.3 –513.5 1,057.17

3.161 12.76

32.36 27.94

78.43

108.7

–27.81 –103.7 –141.7

853.3

488.28

Rule base for FIS

S. no

Rules

1

If (SD1 is G) and (SD2 is G) and (SD3 is G) and (Beta is G) then (D is G)

2

If (SD1 is G) and (SD2 is G) and (SD3 is G) and (Beta is M) then (D is G)

3

If (SD1 is G) and (SD2 is G) and (SD3 is G) and (Beta is R) then (D is M)

4

If (SD1 is G) and (SD2 is G) and (SD3 is M) and (Beta is G) then (D is G)

5

If (SD1 is G) and (SD2 is G) and (SD3 is M) and (Beta is M) then (D is M)

6

If (SD1 is G) and (SD2 is G) and (SD3 is M) and (Beta is R) then (D is M)

7

If (SD1 is G) and (SD2 is G) and (SD3 is R) and (Beta is G) then (D is G)

8

If (SD1 is G) and (SD2 is G) and (SD3 is R) and (Beta is M) then (D is M)

9

If (SD1 is G) and (SD2 is G) and (SD3 is R) and (Beta is R) then (D is R)

10

If (SD1 is G) and (SD2 is M) and (SD3 is G) and (Beta is G) then (D is G)

11

If (SD1 is G) and (SD2 is M) and (SD3 is G) and (Beta is M) then (D is M)

12

If (SD1 is G) and (SD2 is M) and (SD3 is G) and (Beta is R) then (D is M)

Table 4

Condition indices for good insulators using FIS

Insulator no.

SD1

SD2

SD3

Beta

Actual condition indices

Condition indices (Mamdani)

Condition indices (Sugeno)

Insulator 1

3.825

23.63

88.7

1,166.55

Good

80.6

95.1

Insulator 2

3.407

20.86

74.87

1,125.07

Good

72.7

84.7

Insulator 3

6.575

30.7

90.77

1,431.78

Good

50

50

Insulator 4

5.663

27.57

86.12

1,200.37

Good

73.8

93.8

Insulator 5

5.094

31.6

80.01

1,343.47

Good

83.7

100

Insulator 6

3.851

22.54

96.92

1,280.33

Good

77.7

97.3

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V.S. Murthy et al.

Table 5

The condition indices for bad insulators using FIS

Insulator no.

SD1

SD2

SD3

Beta

Actual condition indices

Condition indices (Mamdani)

Condition indices (Sugeno)

Insulator 1

3.083

17.8

57.12

823.74

Marginal

34.4

36.2

Insulator 2

4.173

16.07

64

847.85

Marginal

46.8

48.9

Insulator 3

3.409

14.017

63.44

853.3

Marginal

42.3

47.3

Insulator 4

3.293

9.837

27

450.68

Risk

22.4

0

Insulator 5

4.97

16.75

41.12

678.18

Risk

23.5

2.5

5

Conclusions

The power system insulator condition monitoring using IP and MLT seems to be promising for automation purposes. Compared to template matching involving a complete video frame leading to greater computational time for tracking of poles in the subsequent frame, mean shift tracker has the ability to extract clearly and a distinctly pole from a streaming video in a lesser time, reducing computational burden as the total number of poles for distribution system as a whole is very large. Due to inherent ability of getting inference from a uncertain database, FIS has been employed for well-being analysis of insulators having different degrees of damages. FIS helps not only to detect an insulator is in good, marginal or risk state, but also gives information about the degree of damage for alarming the maintenance crew according to the degree of severity when incorporated as a part of power system automation.

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