Ding Hong-bo, Pan Zhong-xiao, Yu Xing-zeng, Zheng Fu-yang and Renato Seeber
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JCSE Volume 1 Paper 10 Submitted 24 January 1999 The Preliminary Study for the Interpretation of Electrochemical Noise with Continuous Wavelet Transform Ding Hong-bo1, Pan Zhong-xiao1, Yu Xing-zeng2, Zheng Fu-yang2, Renato Seeber3 1Department of Applied Chemistry, University of Science and Technology of China,230026, Hefei, P.R.China; 2Corrosion Branch, Fujian Institute of Research on the Structure of Matters, Chinese Academy of Sciences, 361012, Xiamen, P.R. China; 3Departimento di Chimica, Universita di Modena, 41100, Modena, Italy) §1 Abstract Random fluctuations of the electrical quantities (electrode potential and cell current) in electrochemical systems commonly are referred to as electrochemical noise (ECN). The ECN signal for the corrosion of mild steel in reinforced concrete specimen was analyzed with the Continuous Wavelet Transform (CWT). The original signal was transformed into a time-frequency phase plane with colors representing the coefficients of the CWT. The signal shows a self-similarity structure in the phase plane. Through this way, the chaotic nature of corrosion process is manifested. §2 Keywords: Corrosion, ECN, CWT, time-frequency phase plane, reinforced concrete specimen, chaos, fractals comment(3) 1. Introduction Electrochemical noise (ECN) [1-6] is a generic term used to describe the spontaneous fluctuations of potential or current which occur at an electrode interface. The stochastic process giving rise to the noise signals is related to the electrode kinetics, and in the case of a corroding system, may be related to the corrosion rate and mechanism. §4 Because of the simplicity of the test method, the ECN method has attracted much attention in the field of electrochemistry, especially for the monitoring of metal corrosion. However, due to the non-stationary nature of the ECN signal, data analysis has been a barrier to its wide application. Researchers have proposed many methods. Unfortunately, it seems that none of them can satisfactorily solve the problem. So, Legat and Delecek have, in their paper [3], pointed out that the chaotic nature of corrosion process might require different mathematical treatments, although they haven't gave any identification. §5 Wavelets [7-11] are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. Wavelet analysis has been widely used in the field of digital signal processing. §6 Based on the above, the Wavelet Transform was tried to solve the problem. Unlike the common used "Mallat Algorithm", our attention was given to the Continuous Wavelet Transform (CWT). comment(7) 2. Theory We can define a family of functions = as continuous wavelets, with as its "mother wavelet" if is in the space of square integrable functions, and fulfills the equation Here, refers to the Fourier Transform of . §8 Therefore, we can define the continuous wavelet transform of a function as Wf(a,b) = We find that the analysis produces wavelet coefficients Wf(a,b) which are a function of scale and position, where scale represents the constant by which the wavelet is uniformly stretched or compressed and where position represents the constant by which the onset of wavelets is shifted (delayed or accelerated). This can be shown in the time-frequency phase plane which is illustrated as below: §9 Fig1 Basis functions and the corresponding time-frequency resolution of Wavelet Transform: (a) basis functions, (b) the relevant representation of time-frequency phase plane map §10 The Continuous Wavelet Transform both has a deep mathematical background and is a practical algorithm with wide application in various fields. The above is just a very brief introduction. §11 3. Experimental setup Electrochemical current noise was measured in a freely corroding system. The probe consisted of two identical reinforcing mild steel rods in a concrete specimen submerged in tap water. §12 The basis of the measuring system was a multi-meter connected to a personal computer using an IEEE 488 bus. Input impedance was 100Ω. Resolution was 1nA and the sampling rate was 1Hz. In one test period,1024 current values were collected. CWT computer program was written with Matlab programming language. §13 Table 1 Composition of Cements (Oxide content, wt-%) CaO SiO2 Al2O3 Fe2O3 SO3 MgO Na2O K2O Ignition loss 63.4 20.2 7.3 2.3 3.1 1.2 0.4 0.5 0.9 §14 Table 2 Compositon of Steel C Si Mn P S Cr Mo Ni 0.14 0.20 0.87 0.018 0.028 0.2 0.05 0.18 comment(15) 4. Results and discussion The original ECN signal was shown as Fig.2 as below. §16 Fig.2 The ECN signal recorded for the corrosion of steel in reinforced concrete specimen in tap water §17 From Fig.2,We can see that due to the complicated and non-stationary nature of corrosion process, the recorded ECN signal is very complicated. It was very difficult to get any useful information from it. §18 Fig.3 The time-frequency phase plane representation for the recorded ECN signal of Fig.2 §19 Fig.3 is the time-frequency phase plane representation for the recorded ECN signal of Fig.2. Here, the x axis represents time (scaled as 1, standing for 1024 seconds), y axis represents frequency (scaled as log(1/a), with a high value standing for high frequency). The coefficients of CWT were represented as colors: black, yellow, red and white accorded with increasing values. §20 From figure 3, it is seen that, when the scale is large, there are only few frequency components; while zoomed in, the frequency components of the noise signal add up increasingly, and show complicated bifurcation structure [12,13]; and in the end, infinite frequency components appear and the system enters a chaotic state. There are only few bifurcation undergoing from large-scale periodic state to small-scale chaotic state. §21 On the other hand, from figure 3, it is also seen that the signal has a self-similarity structure [7,14]. It's a kind of fractal structure. Any local structure was the same as that of the whole. From this, we can further infer that the changing of those state parameters has a "chaotic attractor [12,13] " characteristic. §22 From the above, we can see that corrosion process is most complicated, the changing of its state parameters are random, seemed non-deterministic. However, behind the randomness, there are inner rules and determinacy. comment(23) 5. Conclusion The Continuous Wavelet Transform is a promising method for the data analysis of ECN signal. With this, we can draw information from the non-stationary signal because of its time-frequency trade-offs. The results showed that the process of metal corrosion has a chaotic characteristic and determinacy. It is deterministic random. Further work is now under consideration. comment(24) Acknowledgements This work was founded by National Natural Science Foundation and the open found of National Key Laboratory for Metal Corrosion and Protection of P.R.China. comment(25) References 1. U. Bertrocci and F. 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Sparow, The Lorenz equations, bifurcations, chaos and strange attractors, Appl. Math. Sci., 38, 1982. 14. B.B. Mandelbrot, The fractal geometry of nature, Freeman Company, California, 1982.