Volume 1 Paper 10
The Preliminary Study for the Interpretation of Electrochemical Noise with Continuous Wavelet Transform
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)
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
, pointed out that the chaotic nature of corrosion process might require
different mathematical treatments, although they haven't gave any
§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
§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
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
§13 Table 1 Composition of Cements (Oxide content, wt-%)
§14 Table 2 Compositon of Steel
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
This work was founded by National Natural Science Foundation and the open
found of National Key Laboratory for Metal Corrosion and Protection of
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