Separation of Multiple Sources in PD Measurements Using an Intensity Based Clustering Algorithm

Hasan Al-Marzouqi D.E.E. The Petroleum Institute

Abu Dhabi, United Arab Emirates e-mail: haalmarzouqi@pi.ac.ae

Alfredo Contin D.E.E.I. University of Trieste

Trieste, Italy e-mail: contin@units.it

Abstract— Purpose of the paper is to present an application of a newly developed intensity based clustering algorithm in separating pulsating signals due to multiple PD sources and noise. It is applied to signals projected into a time-frequency plane which preserve information on the signal shapes thus, signals having different shape are grouped differently in the map. By using the proposed approach, the number and the optimum border between different groups can be obtained and the original Phase Resolved PD pattern can be split into the same number of sub-patterns. The application of the proposed algorithm to data obtained testing stator bars are reported and discussed to show its validity.

Keywords- Partial Discharges; signal classification; clustering; diagnostics; solid insulation;

I. INTRODUCTION Partial Discharge (PD) measurements are considered as an

important tool for diagnosis and continuous monitoring of insulation systems of HV machines and components. During a measurement session, different pulsating signal sources can be active due to the presence of either a plurality of defects or electrical noise or both. Consequently, the first step of the diagnostic procedure consists in the separation (classification) of the recorded signals in a set of groups each one pertinent to a specific noise or PD source typology, [1, 2]. One of the possible approaches is based on the assumption that the same source exhibit signals having similar shape, [3, 4]. The similarity among different pulse signals can be evaluated in the time or frequency domain and different types of classifiers have been proposed but the topic of the automatic separation, i.e., the efficient separation performed by algorithms without any human action, still remains under investigation. In fact, unsupervised classification algorithms are very often, time consuming (non-suitable for real-time applications) or not effective enough to guarantee reliable separation for any application, [5, 6]. Improvements could come from the use of density based clustering algorithms that are currently adopted in image processing to detect the edges and to extract objects from the global images, [7, 8].

Purpose of the paper is to present an employment of an intensity based clustering algorithm, for the automatic separation of signals due to multiple PD sources, disturbances and noise. In this paper, it is applied to signals projected into a time-frequency plane (T-F map) which preserve the information of the time- and frequency-features of the

recorded signals. Signals having different shape are grouped differently in the T-F map. By using the clustering approach, the optimum border between different groups of signals can be obtained and the original Phase Resolve PD (PRPD) pattern can be split into a set of sub-patterns each one pertinent to a specific signal source.

II. THE PROPOSED ALGORITHM The separation stage consists in the transformation of the

recorded pulse signals in groups homogeneous in terms of their shape on the basis of the assumption that the same signal source generate signals having similar shape while they differ when different signal sources are considered. In order to allow to the classifier to operate efficiently and in real time, the dimensionality of the recorded pulses (typically hundreds of signal samples) is reduced resorting to data projection techniques, [2, 3]. Among the different signal features, the use of the equivalent-time and –bandwidth, proposed in [3], is considered in this paper.

Let S(t) a given PD-pulse signal belonging to a set of N signals recorded during a PD measurement session, its equivalent time, T, and bandwidth, F, are defined as:

( ) ( )

( ) dttS

dttSttT 2

2202

∫∫

∞+

∞−

+∞

∞−−

= where ( )

( ) dttS

dttStt 2

2

0

∫∫

∞+

∞−

+∞

∞−= (1)

∫∫

∞+

∞−

+∞

∞−=dffS

dffSfF

2

222

)(

)( (2)

By means of this transformation, the N pulses are mapped in a two dimension plane (TF map). Proper pointers allow to maintain the connection between the original pulse and its projection in TF map.

A. Trasforming TF Map Data Points into Image Space Density based algorithms partition the data sets by assuming

that they consist of a number of high dense regions separated by regions of low density and/or surrounded by single points. Assuming the TF map as an image where the different density regions are associated to pixels having different gray levels, the different clusters can be identified considering cores where data density is relatively high. A quantization process maps

978-1-4244-6301-5/10/$26.00 @2010 IEEE

the data points from the TF domain to the discrete image domain as shown below.

Assuming that the data points of TF map are given as a set of two features vectors X={x1, x2, x3,…..xn} and Y={x1, x2, x3,…..xn}, the pixel coordinates are computed as follow:

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎥⎦⎤

⎢⎣⎡

⋅⎥⎦

⎤⎢⎣

⎡ ⋅−⋅⋅−

=

YX

YrangeYY

XrangeXX

roundpixelCords

dimdim

)()min(1

)()min(1

(3)

where round () is the nearest integer function, (range (X)=max(X)-min(X)), 1 is a vector of all ones of size n, dimx and dimy the dimension of the image to be created. Values of dimx and dimy are specified based on the user’s choice of a discretization factor, discf, defined as:

discfYrangey

discfXrangex )(dim,)(dim == (4)

B. The Modified Kuwahara Filter In order to overcome the problem of over-classification, the

TF map is first processed by using a modified Kuwahara filter that is an edge preserving low-pass filter widely used in image processing applications, [9, 10]. It is based on placing a symmetric square neighborhood around each pixel of a gray level image and dividing it into four square sub-regions. The value of the central pixel is replaced by the gray level average over the most homogeneous sub-region, i.e., the sub-region with the lowest standard deviation. In the modified Kuwahara filter, the value of the central pixel is replaced by the density data points over the sub-region containing the maximum number of data points, multiplied by the number of data points in the chosen sub-region. Let x, y the coordinates of a given data in TF map considered as a pixel, the modified Kuwahara filter is described as:

),(),(),(),( yxfyxsumyxdensGyxK ii

ii ⋅⋅⋅= ∑ (7)

where densi(x,y) and sumi(x,y) are the density and the total number of data points in sub-region i, respectively while fi(x,y) is defined as:

⎩⎨⎧ =

=otherwise

yxsumindexiyxf i

i ,0)),(max(,1

),( (8)

The indexmax() function returns the index of the sub-region with the maximum number of data points and G is a factor specified by the user after the experimental validation. By using this digital filter, data points surrounding any dense center are smoothed in the direction of the dense centers thus generating connected groups and preserving their edges. As a consequence, the process of choosing suitable values for the input parameters becomes simpler.

C. Cluster Extraction The estimation of the number of clusters is performed

considering the cluster cores where the data density is

relatively high. The density level required in a cluster core is performed setting the value of G (Eq.7). G is computed with regard to a region of size LxL where L is the size of the filter used in creating the intensity map. Let n be the minimum number of data points in an LxL region needed to define a cluster core, the value of G will be set to equal

2

2

11⎟⎠⎞

⎜⎝⎛==

⋅=

nL

nLnsumdens

G (9)

Using this value for G, results in pixel values higher or equal to one in coordinates that have the density requirement satisfied. If we define filled-factor (ff) as the number of data points in an LxL region, then we get:

ff = ⎟⎠⎞

⎜⎝⎛

2Ln

= ⎟⎠⎞

⎜⎝⎛

nG1

The proposed algorithm needs two parameters as an input: Size of the filter L, and the filled factor (ff) that controls the number of pixels to be filled with data points in a square area of LxL to define a cluster core. The parameter ff takes values in the range 0-1.

The algorithm starts by sweeping through the intensity map looking for pixels with density values higher than one. Once such a pixel is found a search in the neighborhood of that pixel is done to locate all pixels connected to it. These points form a connected segment covering the data points in the core of the found cluster. The remaining data points are assigned to the appropriate cluster by using the minimum Euclidian distance metric to the closest intensity centroid coordinates of the intensity centroid are computed by using:

[ ]∑

∑−∈∀

−∈∀−

⋅=

isegyx

isegyxiseg yxI

yxyxIC

),(

),(

),(

,),( (10)

For a complete explanation of this clustering approach, the reader is referred to [10].

III. EXPERIMENTAL APPLICATION The proposed algorithm was applied to analyze results of

PD measurements performed in laboratory on frames simulating complete stator coils. A waveform analyzer that digitally records the complete signal shapes in vectors of Nc=256 digital samples has been used to record PD pulse signals. The instrumentation has large bandwidth (from 0 to 200 MHz) and operates at sampling rate high enough to avoid frequency aliasing (up to 500 Msa/s). The measuring system is remote controlled by a lap-top via IEEE-488 bus. The instrumentation was connected to a R=50 Ω resistor used as measuring impedance. An high-pass filter (150 kHz cut-off) was adopted to suppress the low-frequency components of the test voltage. The output of each acquisition session consists in a time-series of signals, having a wide number of signals to enable their stochastic analysis, which constitutes the input data for the separation stage. Some examples having TF maps

with scattered, separated or partially overlapped groups, are here discussed to show the validity of the method.

The first example refers to degradation processes occurred on end-arm corona suppressing system of a coil for HV induction motors rated 11 kV, during a multifactor aging test (cycles of combined electric and thermal stresses). The insulation system is based on mica tape layers impregnated with epoxy resin, completed with polyester-graphite tape (slot-grading tape) and with polyester-semiconductive tape as the end-arm corona suppressing system (corona-grading tape). The stator coil was cured using the VPI technology. The multifactor aging procedure is composed by 6 days of thermal and electrical stresses, followed by 3 ours of mechanical vibration.

Figure 1: A stator coil after 500 hour of aging.

After about 500 hours, a detachment between the end-arm

stress-grading tape and the surface of the ground-wall insulation, due to the combined action of thermal and mechanical stresses, was found. An image of the aged coil is reported in Figure 1. A new PD activity was detected during PD tests and localized in the stress grading area by hearing the acoustic emission of PD. When the new degradation process occurred, a new PD phenomenon added its own pulse signals to the existing one (due to distributed micro-voids), and a mixed PD-pulse sequence was recorded during the PD measurement session. The PRPD pattern and the TF map, relevant to PD measurements performed at 6 kV (phase-to-ground) and composed by N=4000 pulses, are reported in Figure 2. As can be seen, from Fig.2B, two groups of high density data appear partially overlapped and surrounded by low density and rarefied data. The TF map has been processed to extract the clusters, according to the proposed procedure. Different values of L and ff parameters were evaluated to select those that allow the best separation. Figure 3 shows the effect of the filter applied to the TF map transformed in an image. The intensity map generated by selecting L=7, ff=0.7 is reported in Fig.3A. As can be seen, the original TF map of Fig.2B is transformed in an image where the higher brigthtness is indicative of an higher concentration of data points. The appearance of these regions demonstrate the advantage of the proposed approach. Data points surrounding the dense center of each group are smoothed in the direction of the dense center thus generating the two connected segments. By increasing the ff value, spread pixels are concentrated and the “granularity” of the image appearrs more evident (L=5, ff=0.9, see Fig.3B). The connection between the different

segments can be restored by increasing the order of the Kuwahara filter (L=7, ff=0.8, Fig.3C). Two groups appear more evident and the relevant centroids can be evaluated according to Eq.(10). The remaining data points are assigned to the appropriate clusters using the Euclidean distance. The PRPD sub-patterns and the relevant centroids are reported in Fig.4. In particular, the identification system assigned to a prevalent surface activity the sub-pattern of Fig.4C (group #1, black color in the TF map of Fig.3D) and to distributed microvoids PD the sub-pattern of Fig.4D (group #2, gray color of Fig.3D).

A B

Figure 2: Results of PD measurements performed at 6 kV on the coil of Fig.1, after about 500 h of aging. A) the PRPD pattern and B) the

relevant TF map.

A B

C D

Figure 3: The effect of the application of the proposed algorithm to the TF map of Fig.2B. Bright segments indicate cluster cores

generated by (A) G=5, ff=0.7; (B) G=5, ff=0.8; (C) G=7, ff=0.8; (D) the clusterized TF map obtained using G=7 and ff=0.8.

The L and ff values selected to separate the mixed PRPD

pattern of Fig.2, have been adopted to analyze a quite complex TF map reported in Fig.5B. The experimental data of Fig.5 refers to PD measurements performed at 6 kV on a coil belonging to the same set of coils of HV induction motors, before the application of the aging procedure described above (new coil). The TF map of Fig.5B shows many groups partially overlapped. The smoothing filter of Eq.7 was able to reduce the number of potential groups in two, preserving a clear border between them (Fig.6A). The classification

algorithm grouped the data in two classes (groups #1 and #2, black and gray colors in Fig.6B, respectively). The PRPD sub-patterns are reported in Fig.7. These patterns can be due to distributed microvoids (Fig.7A) and surface discharges (Fig.7B). Different values of L and ff factors allowed a more detailed separation (not discussed here) but they must be set manually.

A B

C D

Figure 4: The centroids and the PRPD sub-patterns relevant to group #1, A) and C) (black color in Fig.3D) and group #2, B) and C) (gray

color in Fig.3D).

IV. CONCLUSIONS A new clustering algorithm for the separation of pulsating

signals due to multiple PD sources or noise, has been presented. Pulse signals are clustered in an image space obtained transforming the TF map and filtered by using a modified Kuwahara low-pass filter. In this framework, the user controls the density level required to define a cluster core. Points not belonging to cluster cores are clustered using a defined function. This should make the algorithm easily adaptable to other kinds of planes obtained selecting different features of PD signals. The proposed algorithm is fast enough to be used in real time applications and does not require the number of clusters as input. More investigations are required to find out optimum values of L and ff factors and to reach the important result of an effective automatic separation.

REFERENCES [1] A. Cavallini, A. Contin, G. C. Montanari, F.Puletti, “Application of a

New Methodology for Identification of PD in Electrical Apparatus”, IEEE Trans. Dielectr. Electr. Insul., Vol. 12, pp. 203-215, 2005.

[2] R. Heinrich, S. Schaper, W. Kalkner, R. Plath, A. Bethge, “Synchronous Three Phase Partial Discharge Detection on Rotating Machines”. Proc. of XIIIth Int. Symp. On High Voltage Eng., Delft (The Netherlands), pp.507-510, 2003.

[3] A. Contin, A. Cavallini, G. C. Montanari, G. Pasini and F. Puletti, “Digital Detection and Fuzzy Classification of Partial Discharge Signals”, IEEE Trans. Dielectr. Electr. Insul., Vol. 9, pp. 335-348, 2002.

[4] P. Morshuis, “Assessment of Dielectric Degradation by Ultrawide-Band PD Detection”, IEEE Trans. Dielectr. Electr. Insul., Vol. 2, pp. 744-760, 1995.

[5] N.C.Sahoo, M.M.Salama and R.Bartnikas, “Trends in PD Pattern Classification: a Survey”, IEEE Trans. Dielectr. Electr. Insul., vol.12, pp.248-264, 2005.

[6] A.Contin and S.Pastore, “Classification and Separation of Partial Discharge Signals by Means of their Auto-Correlation Function Evaluation”, IEEE Trans. Dielectr. Electr. Insul., vol.16, pp1609.1622, 2009.

[7] R. Xu and D.Wunch, “Survey of Clustering Algorithms”, IEEE Trans. Neural Net., vol.16, pp.645-678, 2005.

[8] A.K. Jain and R.C. Dubes, Algorithms for Data Clustering, Pretice Hall, Englewood Cliffs, New York, 1988.

[9] M. Kuwahara, K. Hakimura, S. Ehiu and M. Kinoshita, “Processing of Ri-Angiocardiographic Images”, in Digital Processing of Biomedical Images, pp.187-203, New York Plenum, 1976.

[10] H. Al-Marzouqi, “Data Clustering Using a Modified Kuwahara Filter”, IEEE Proc. Int. Conf. on Neural Net., pp.128-131, Atlanta (USA), 2009.

A B

Figure 5: Results of PD measurements performed at 6 kV on a coil after about 500 h of aging. A) the PRPD pattern and B) the relevant

TF map.

A B

Figure 6: The effect of the application of the proposed algorithm to the TF map of Fig.4B. A) Bright segments indicate cluster cores

generated by G=7 and ff=0.8. B) the clusterized TF map.

A B

Figure 7: The PRPD sub-patterns obtained after the separation stage. sub-pattern of (A) group #1 (black) and (B) group #2

(gray) of Fig.5B.