A New Adaptive Threshold Algorithm for Narrow-band Interference Suppression in Partial Discharge Based on Improved Empirical Mode Decomposition and MDL

Criterion

Zhaoyan

Power transmission and transformation Technology College

Northeast Dianli University Jilin 132012 China

E-mail: zjb_112006@163.com

Abstract—According to the different characteristics of the spectra between the narrow-band and the PD signals, a new adaptive threshold algorithm using improved empirical mode decomposition (EMD) and Minimum Description Length (MDL) criterion is applied to extracting the PD signals from narrow-band noises. Firstly band-pass filter is designed to deal with the PD signals to reduce the amplitude of narrow-band interference in frequency. Then mid-signal after it is decomposed by EMD. The above method is called improved EMD. Finally the most appropriate coefficients are obtained by MDL criterion, and, therefore the corresponding coefficients are reconstructed to achieve de-noised PD. It not only retained the advantages of adaptive filtering by EMD but also features of adaptive threshold selection by MDL. Simulation shows that the algorithm has strong suppression capability of narrow-band interference and ultimately achieved optimal separation of PD signals and noise.

Keywords improved EMD； MDL criterion； partial discharge； narrow-band interference；

I. INTRODUCTION It is prevalent that insulation weak parts in the high

electric field occurs Partial Discharge (PD).Under certain conditions, it would lead to deterioration of the insulation, and even breakdown. PD signal is so weak that it occurs as form of a few to a few hundred nanoseconds’ pulse in the time domain, and it is buried in excessive electromagnetic noise. So, it is difficult to detect. The usual interference of PD signal is narrowband interference and Gaussian white noise. The key of detecting PD signals in excessive noise background is the suppression of the narrowband interference and Gaussian white noise. Noise and signal interference in the time and frequency domains were tested randomly distributed, which made the traditional digital signal processing techniques quite limited.

Empirical Mode Decomposition [1] which proposed by N.E. Huang et al. is a new nonlinear and non-stationary signal processing method. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to de-noising of PD signals. But there is intensive narrow-band interference of PD signals in addition to white noise. PD signal is totally submerged

because amplitude of narrow-band interference is several times bigger than the PD signals even more than tenfold times. Analysis and calculation of EMD is based on the upper and the lower envelopes of the signal. It is not ideal that de-noising results of PD signals by direct use of EMD. It will lead to large distortion although the PD signal can be extracted.

Therefore, in this article the method of combining band-pass filter with EMD is called the improved EMD. Firstly band-pass filter is designed to deal with the PD signals to reduce the amplitude of narrow-band interference in frequency, then mid-signal after it is decomposed by EMD, finally the most appropriate coefficients are obtained by MDL criterion, and therefore, the corresponding coefficients are reconstructed to achieve de-noised PD. Large mount of simulation proves that this method can suppress narrow band and white-noise interference efficiently. Denoising accuracy and efficiency was greatly improved.

II. EMPIRICAL MODE DECOMPOSITION The EMD is built on the assumption that any data set

consists of different, simple, intrinsic modes of oscillation that need not be sinusoidal. Based on this, each mode of oscillation from high frequency to low frequency is derived in an objective manner from the recorded complex data. Each of these oscillatory modes is called an intrinsic mode function (IMF).

First, identify all the local maxima. Connect all the local maxima by a cubic spline to produce upper envelop of X(t),and repeat the procedures for the local minima to produce the lower envelopes of X(t).The upper and lower envelopes should encompass all the data. The mean of these envelopes is designated as m1(t),and the difference between the data X(t)and m1(t)is the first Components h1(t),i.e.,

)()()( 11 tmtXth −= (1) Ideally, h1(t)should be an IMF. Yet, in practice, all the

conditions of an IMF cannot be achieved, called sifting process is repeated. In the subsequent sifting process, h1(t)is treated as the data, then

)()()( 11111 tmthth −= (2) Where m11(t)is the mean of the upper and lower

envelopes of h1(t).After repeated sifting, up to k times until h1k(t)is an IMF, given by

2010 International Conference on Intelligent Computation Technology and Automation

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DOI 10.1109/ICICTA.2010.324

203

)()()( )1(1)1(11 tmthth kkk −− −= (3) It is designated as the first IMF component c1(t)from the

data, or )()( 11 thtc k= (4)

c1(t)will contain the finest-scale or the highest frequency component of the signal. One then removes c1(t)from the rest of the data to obtain the residue r1(t),

)()()( 11 tctXtr −= (5) The residue r1(t),which contains longer-period

components, is treated as new data and subjected to the same sifting process as described above. This procedure can be repeated to obtain all the subsequent rj(t)

njtrtctr jjj ,3,2)()()(1 ==−− (6) The sifting process can be terminated on any of the

following predetermined criteria: a) either the component cn(t)or the residue rn(t)become so small that it is less than a predetermined value of consequence, or b)the residue rn(t)becomes a monotonic function, from which no more IMF can be extracted(Huang, et al,1998).Thus the original data is the sum of the IMF components plus the final residue:

)()()(1

trtctX n

n

jj +=∑

=

(7)

As decomposition process is not energy loss, original signal is accurately reconstructed by IMF components and residue.

III. IMPROVED EMPIRICAL MODE DECOMPOSITION Yang J. N. and others [3 - 5] said that in which one of the

following situations, band-pass filter should be designed to deal with the data before EMD. That is,

1) IMF components are with higher frequency. 2) Signals were buried in high frequency noise. The EMD decomposes a signal into oscillating

components from the highest frequency component imf1 to the lowest frequency component imfn. Therefore, if the signal exists one of the above two situations, it will cause serious aliasing in the time-frequency distribution of the previous order IMF components.

PD signals in the narrow-band interference are with this characteristic. To deal with it, improve method is proposed. Improve EMD is divided into four sections: 1) Determine the peaks: Compute the spectral density using

FFT. Analyzes filtered data and picks out peaks via a complex downward scan of the FFT up-to a preset threshold value. 2） Filter Design: According to peaks of power spectrum. 3） Filter: Filters the raw data with band pass. 4） EMD: Signal is decompose using the EMD after filter.

IV. MINIMUM DESCRIPTION LENGTH CRITERION We begin with Kraft's inequality, which establishes the

equivalence between probability distributions and code lengths. The code lengths can determine probability distributions; on the contrary, the probability distribution reflects the code lengths.

According to Shannon source coding theory the shortest described length of sample is defined as the probability distribution of entropy.

∑=

−=N

iixpXL

1)(log)( Here, p denotes the

probability. In this way, the corresponding relationship between

probability and code length is established. That is, the length coding can be seen as probability distribution in another way.

Minimum Description Length (MDL) is the length in bits of the shortest possible code describing data. MDL criteria is the method by which the best model in the given model library can be found with the shortest code length.

MDL criterion approximate expression [6] )})(log

2log

23min{(),(AMDL

2)(22 m

k CINNkmk Θ−+= （8）

Where m is the index of transformation model, the variable k is the number of IMF coefficients retained, 0<k<N. )(kΘ indicates the threshold computing. Certain numbers (k) of great magnitude IMF coefficients are retained, the rest are replaced with zero. I indicate the same operator; Cm is IMF on the signal of the index m.

From the 8th formula we can see that AMDL has two parts: the former is the length coding of model. It can be described as subset of IMF coefficients of original signal after threshold operation )(kΘ . Collection capacity of k, recorded as )(ˆ kα , It is linear increasing with the increase of reservation of numbers (k).The latter is the deviation between actual signal and estimated signal which is increasing with the reduction of k.

A certain value ( ∗k ) can be minimized AMDL, so it can be found that the estimated optimization model ( )(ˆ kα ) of the signal. Therefore MDL criteria stress the best compromise between distortion and compression ratio of the signal.

Traditional wavelet threshold de-noising algorithms need pre-set threshold which is different due to different purposes or signals. Therefore, traditional method is lack of adaptability.

The choice of threshold according to the MDL criteria does not require parameters and thresholds set. It can change dynamically with the signal; and find balance between compression efficiency and fidelity of the signal. So, MDL method is adaptive, which can be used for PD signal denoised of different noise levels.

V. SIMULATION ANALYSES In this example, Single index and dual-index models of

vibration attenuation were used as simulation.

tfeAts c

t

πτ 2sin)( 11

−= （9）

tfeeAts c

tt

πττ 2sin)()(3.12.2

22

−−−= （10）

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Here, cf is the frequency of oscillation; τ is the attenuation coefficient; A is amplitude .In the simulation,

cf is 1 MHz, τ is 1μs, 2μs, 4μs, respectively, the amplitude is 0.2mV, 1mV, respectively, sampling frequency is 10 MHz. Gaussian white noise is with mean zero and constant variance 0.15. Intensive narrow-band interference includes the frequency of 34 kHz, 96 kHz, and 500 kHz and 1.3 MHz of the Figure 1.

The maximum amplitude of noise is almost two times larger than PD signals. Gaussian white noise and narrow-band interference totally submerged the PD signals. Power spectrum of PD signals with white noise and intensive narrow-band interference is showed in Figure 2.

Figure 1. Simulated PD signals

Figure 2. Power spectrum of PD signals

Figure 3. PD signals after band-pass filter

From Figure2, it shows that the amplitude and energy distribution in the frequency spectrum between intensive narrow-band interference and white noise after FFT is obviously different. Energy of narrow-band interference concentrates within a narrow frequency band which is almost an order of magnitude higher than that of PD signals. On basis of differences between them, 4th-order band pass (Butterworth filters) are designed to deal with the PD signals to reduce the amplitude of narrow-band interference in frequency. Table I shows cut-off frequency. [ωL ,ωH ] are cut-off frequency of band pass filter.

TABLE I. BAND-PASS FREQUENCY OF BAND PASS FILTER (MHZ)

Signal ωL ωH

IMF1 0.032 0.036

IMF2 0.49 0.51

IMF3 0.093 0.099

IMF4 1.2 1.5

So, the amplitude of narrow-band interferences is

suppressed after band pass filter. However, both spectra of white noises and of PD signals have broad-band frequency distribution which overlaps in frequency. There is also some noise after the processing .Figure 3 is PD signals after pretreated. After the processing, most intensive narrow-band interference is denoised while there is still some white noise. Signal to noise ratio is by up-19.0362dB to-0.19384dB.

The following program compares results of by EMD with by improved EMD. The nine IMF components and the residual component decomposed by the EMD as shown in Figure 4.

The twelve IMF components and the residual component decomposed by the improved EMD as shown in Figure 5. Due to space limitations, the several IMF components and the residual have been omitted for they do not reflect the signal characteristics.

Figure 4. EMD of the PD signals

Figure 5. Result of improved EMD

Figure 6. processing result of the PD signal

Comparing Figure 4 with Figure5 ， c2- c4 components in Fig 5 show characteristics of four partial discharge signals, while Fig4 is almost totally ignored . Correlation coefficient

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of c2- c3 ， c2- c4 and original data is respectively 0.7644 ，0.7678 in Figure 5. These IMF components are the main components of the original data. Correlation coefficient of c2- c3，c2- c4 and original data is respectively 0.1824 ，0.17091 in Figure 4. High-amplitude narrow-band interference covers the PD completely. EMD process enables flexible representation of a dynamic signal by revealing its time-dependent amplitude. So, it will cause serious aliasing in the time-frequency distribution of the previous order IMF components.

Then, we use the MDL Criterion to deal with signals after improved EMD. Results were showed in Figure 6.

By MDL Criterion, the result of automatic search which retained the number of coefficients is 159, AMDL=-3002.25, Compression ratio is 24.8%.

Comparison results of two methods are obtained in table2. All indicators of Improved EMD are superior to EMD results, as can be seen in Table II.

TABLE II. INDICATORS OF IMPROVED EMD AND EMD

SNR/dB

root mean square error

(RMSE)

Cross-Correlation Coefficient

original data -19.0362 0.1048 0.1662

EMD and

MDL -0.0234 0.0368 0.6801

Improved EMD and

MDL 1.5301

0.0161

0.8159

VI. CASE STUDIES In order to further verify the validity of the algorithm,

PD signals of windings of hydroelectric power is analyzed by Improved EMD and MDL. In this example, sampling frequency is 2.165MHz.

PD signals showed in Figure 7(a). have intensive narrow-band interference and white noise. PD signals are totally submerged. Result by Improved EMD and MDL is showed in Figure 7(b).

Figure 7. Processing result of real PD signals

The comparison of pre and post processing can be seen that our method not only eliminated noise but also preserved the features of signals. So our method is effective and feasible.

Because of limitations, this paper will not repeat the comparison of dealing with results of various methods.

VII. CONCLUSION The problem has been resolved by improved EMD and

MDL that aliasing in the time-frequency distribution of the previous order IMF components of narrow-band interference in PD. A new adaptive threshold algorithm of Improved EMD and MDL is a fully data-driven technique. It has strong suppression capability of narrow-band interference of PD signals, and ultimately achieved optimal separation of PD signals and noise.

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[2] Wei Huang , Zheng Shen , Norden E Huang. “Engineering analysis of biological variables : an example of blood pressure over 1 day,” . Proc. Natl Acad Sci USA ,95 (9) , pp.4816 – 4821, 1998 .

[3] Yang J N , Lei Y. “Identification of natural frequencies and damping ratios of linear structures via Hilbert transform and empirical mode decomposition,” Proceedings of the IASTED International Conference on Intelligent Systems and Control , Santa Barbara :IASTED/ Acta Press ,1999 , pp.310 - 315.

[4] Yang J N, Lei Y. “System identification of linear structures using Hilbert transform and empirical mode decomposition,” Proceedings of the 18th International Modal Analysis Conference. San Antonio, Texas: 2000 ,pp.213 - 219.

[5] Yang J N , Lei Y, Huang N. “Damage identification of civil engineering structures using Hilbert-Huang transform ,” Proceedings of the 3rd International Workshop on Structural Health Monitoring: New York, 2001, pp.544.

[6] Saito N．“Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum description length criterion,”San Diego,Academic Press，1994．

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