1 NEW TIME-FREQUENCY METHOD OF DETECTION OF ... - CiteSeerX

NEW TIME-FREQUENCY METHOD OF DETECTION OF STRAY CURRENTS INTERFERENCE ON METAL STRUCTURES Kazimierz Darowicki, Krzysztof Zakowski Gdansk University of Technology, Department of Anticorrosion Technology, Narutowicza Str. 11/12, 80-952 Gdańsk, POLAND Summary: New method of detection of stray currents using the Short Time Fourier Transformation (STFT) is presented. This particular kind of signal analysis makes the determination of changes of the spectral power density of a signal (e.g. structure to electrolyte potential) in function of time possible. In this paper the results of joint time-frequency analysis of the potential of pipeline in the field of stray currents generated by tram-line are presented. Presented results unambiguously shows the possibility of accurate identification of source of stray currents and its interference on the underground metal construction. Introduction The corrosion rate of the outer surfaces of metal construction depends on many factors. One of them is the interference of stray currents fields [1]. The most important and the best known source of the stray currents fields is DC electric traction: tram-line or railway and underground tractions [2]. The stray currents leakance take place in tramlines which are an element of return circuit of traction currents. The extent of the stray currents leakance depends on the voltage drop in the rail (voltage drop is a function of intensity of flowing current and resistance of rail) and resistance of rail in relation to the ground [3]. The main source of stray currents can be transmission lines HVDC used for transmitting energy over long distances [4]. In many cases detection of influence of stray currents is usually being carried out on the basis of the measurement of potential [5]. The values and fluctuations of the structure to electrolyte potential and their range of fluctuation are the main criterions for assessing the electrolytic corrosion hazard [6]. IR component of registered potential values makes the results difficult to interpret. Typical methods of determination of the corrosion hazard caused by stray currents: ! Independent measurements of pipeline and tram-line potential [7]. The activity of stray currents is determined by the standard deviation and mean of potential values. ! Extrapolation of a functional interdependence of measured for a couple of minutes values of: structure to electrolyte potential and gradient of electric field [8]. The values of potential obtained in this way they consider as the real, IR-free component structure to electrolyte potential. ! Simultaneous measurement of potential of protected steel construction and the voltage between it and expected source of stray currents [9]. The main disadvantage of this method is a direct connection of investigated construction and expected source of stray currents by means of the meter (in this way the source and the analyzed object are physically connected by resistance of the meter) – the resistance of the layer consisted of the soil and isolation of the pipeline is comparable to resistance of the meter.

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All mentioned above methods of detection of stray currents consist in the measurement and the analysis of changes of potential in the time domain. As the rule of thumb, the analyzed changes of potential have stationary characteristics. However, stray currents are an examples of nonstationary signals because their mean value and the standard deviation change over time [9]. Joint time-frequency analysis make analysis of nonstationary signals possible [10]. Analysis of changes of voltage in joint time–frequency domain Let us assume, object A is a generator of stray currents. Measurement of the UA(t) voltage in a function of time between auxiliary electrode and the object from which the leakance of stray currents takes place allow to determine them. The registered changes of voltage characterize the object and are manifested in the form of frequency composition. In other words the frequency spectrum of registered voltage characterize the object. Performing of Fourier transformation of UA(t) voltage leads directly to frequency spectrum. This method of analysis is effective when voltage changes are stationary. The stray currents are not stationary signals. Their mean value and the standard deviation depend on the time of measuring. In case of nonstationary changes of voltage Fourier transform gives averaging results. Therefore the result of the analysis strongly depends on the time of measuring. It explains the luck of development of methods of stray currents analysis in the domain of time. The effective methods of nonstationary signals analysis are joint time-frequency methods. One of them is Short Time Fourier Transformation (STFT). STFT is described by the following relation: STFT {U (t )}= ∫ U A (τ ) γ (τ − t ) exp(− jϖτ )dτ

where: γ - window function, t - time of window location.

Distinct from regular Fourier transform in STFT the window function is applied. Window function located in time t cuts out fragment of analyzed signal UA(t). Then the regular Fourier transformation is performed for this fragment. Spectral power density spectrum of a signal is created and it corresponds to time t. In the next step the time window is moved to the next fragment of time and the new portion of analyzed signal is being cut out. By moving the time window on the time scale and repeating the process of performing Fourier transformation for cut out portions of the analyzed signal, we can obtain its spectral power density spectrum. The implementation of the window function γ(t) makes the analyzed signal U(t)γ(t) reaches zero beyond the window frame. This method of analysis allows determination of spectral power density in a functions of time. In practice a variety of types of window function are used: rectangular, Hanning, Hamming, Blackman, Gauss [11]. However, Gauss window function is crucial in STFT:  t2  1   − exp g (t ) = 1 2  (πσ 2 )4  2σ  where σ - parameter characterizing the width of window Applying the STFT for Gauss peak, which is determined in time domain, we can transfer its analysis to the joint time-frequency analysis. Time and frequency resolution of such analysis depends on the range of cut out portion of the signal, that is described by parameter σ. The relation between time σt and frequency σω resolution is described by: 2

1 σ2 1 = 2 2 2σ 4 The increase of σ is tantamount to the increase of the range of time window. It causes the increase of σt, thereby the deterioration of resolution of analyzed voltage in time domain and simultaneous improvement of resolution in frequency domain. Inversely: deterioration of time resolution entails (bring about, involve) improvement of time resolution.

σ t2σ ω2 =

Experimental The scheme of investigated system is presented in Fig.1. The generator of stray currents was electric tram-line. The investigated object was an underground steel pipeline φ300 with used bituminous isolation.

tram rails ER1 AD card

UA(t)

UB(t) ER2 pipeline

Fig. 1. Scheme of investigated system. ER1, ER2 – Cu/CuSO4 reference electrodes, UA(t) – voltage electric traction earthing-electrode, UB(t) – voltage pipeline-electrode. Two Cu/CuSO4 reference electrodes were used during the experimental. The voltage UA(t) was measured between the earthing of the tram-line and the electrode ER1. The ER1 electrode was placed in a distance of 5 meters from the earthing of the tram-line. Simultaneous measurement of voltage UB(t) between pipeline and electrode ER2 was carried out. This electrode was placed 1.5 meters over the pipeline. Because of great and variable in time share of ohmic IR drop in the registered voltage the authors decided not to use the term ‘potential’ in this case. Measurement set consisted of data acquisition card ADDIDATA APCI 3120 connected to PC computer. Sampling frequency was 10 Hz. The UA(t) and UB(t) voltage signals were analyzed by using Joint Time Frequency Analysis (JTFA) algorithm from LabView software package.

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Results and discussion

frequency

The carried out mathematical STFT analysis included continuous changes of voltage UA(t). In practice the discrete-time register is used for computer calculations. To perform a discrete STFT of the signal UA(t) the grid in the joint time-frequency domain is created. The STFT grid is presented on Fig.2. The energy of analyzed signal is included and represented by the nodes of this grid.

df

dt time

Fig. 2. Time-frequency grid of STFT. dt – time resolution, df – frequency resolution. Measurements of UA(t) and UB(t) voltage in time were carried out simultaneously. The fragment of time register of voltage signal UA(t) and corresponding time register of voltage signal UB(t) is presented in Fig.3. UA[V] 10

0

-10

UB[V] 0.0

-0.5

-1.0 60

120 [s]

Fig. 3. Fragment of time registers for voltage of tram rails versus reference electrode (UA) and pipeline versus reference electrode (UB).

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The STFT spectrograms of registers from Fig.3 are presented in Fig.4. In accordance to the definition spectrogram is a square of a modulus of STFT, thus is defined in time and frequency domain. Therefore the spectrogram indirectly shows the rate of leakance of energy from electric traction. The spectrogram is a composition of spectral lines of defined frequency distribution. The localizations of spectral lines in Fig.4 correspond to time when tram passes. A good correlation of localization of spectral lines corresponding to voltage UA(t) and UB(t) in time domain is visible. For time t=70 s (see Fig.4) instantaneous spectral power density spectra of both measured voltage values were determined. These spectra are presented in Fig.5. Instantaneous spectral power density spectra have a very similar form. Two frequency peaks in a distance of 0,8 Hz from each other are distinctly visible. These peaks may be treated as a characteristic feature of tram passing. The comparison of time and frequency localization of peaks from spectrograms UA(t) and UB(t) is unambiguous evidence that the electric field generated by passing trams interfered on the investigated pipeline.

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electrode - rail

electrode - pipeline

Fig. 4. STFT spectrograms of signals from Fig. 3.

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rail - electrode

f [Hz] 0.0

1.0

2.0

3.0

4.0

5.0

4.0

5.0

pipe - electrode

f [Hz] 0.0

1.0

2.0

3.0

Fig. 5. Instantaneous spectral power density spectra corresponding to Fig. 4 (time t=70 s ).

Conclusions The proposed method of interference of stray currents detection has many advantages. The same time and frequency localization of peaks on spectrograms performed for voltage signals of source and investigated object versus reference electrode indicates the interference of electromagnetic field generated by passing trams. The measurement of voltage changes of the source and the analyzed object is carried out independently. In other existing methods the voltage between the source and the object is measured. Carrying out of such measurement causes the fact that the analyzed object and the source are physically connected by means of resistance of the meter. It may determine the changes of the potential of the object. When the STFT spectrograms performed for voltage of structure-electrode and voltage of rail–electrode differ from each other significantly (it is manifested by lack of characteristic spectral lines corresponding to time of tram passing and different shape of spectral power density spectra) it indicates the lack of interference of stray current on underground structure. References [1] [2] [3] [4]

S. Nikolakakos, Stray currents generation, interference effects and control, NACE CORROSION/98, Paper No. 559, 1998. K. Zakowski, K. Darowicki, Stray currents and pollution of the environment, Polish Journal of Environmental Studies 8 (4) (1999) 209. K. Moody, Stray current characteristics of DC transit systems, Materials Performance 33 (6) (1994) 15. J.H. Fitzgerald III, D.H. Kroon, Stray current interference control for HVDC earth currents, Materials Performance 34 (6) (1995) 19.

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[5]

K. Zakowski, K. Darowicki, Metods of evaluation of the corrosion hazard caused by stray surrents to metal structures containing agressive media, Polish Journal of Environmental Studies 9 (4) (2000) 237. [6] Polish Standard PN–90/E–05030/01: Corrosion protection. Electrochemical cathodic protection. Underground metallic structures. Requirements and tests. [7] K.W. Park, Y.B. Cho, K.S. Jeon, S.M. Lee, Y.T. Kho, Evaluation of Stray Current Effect on the Cathodic Protection of Underground Pipeline, Journal of the Corrosion Science Society of Korea 24 (3) (1995) 176. [8] B. Bazzoni, L. Lazzari, The Lateral Gradient Technique for Potential Measurements in Presence of Stray Current, NACE CORROSION/96, Paper No. 202, 1996. [9] K. Zakowski, W. Sokólski, 24-hour characteristic of interaction on pipelines of stray currents leaking from tram tractions, Corrosion Science 41 (1999) 2099. [10] R. Carmona, W-L. Hwang, B. Torresani, Wavelet Analysis and its Applications. Vol.9: Practical Time-Frequency Analysis. Ed.: Ch. Chui, Academic Press, USA, 1998. [11] R. Ramirez, The FFT Fundamentals and Concepts. Tektronix Inc., Englewood Cliffs, New Jersey, USA, 1985.

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