An integrated approach in the time, frequency and time-frequency domain for

the identification of corrosion using electrochemical noise

A.M. Homborga, R.A. Cottisb, J.M.C. Molc

aNetherlands Defence Academy, P.O. Box 505, 1780AM Den Helder, The

Netherlands, AM.Homborg@mindef.nl, tel. +31 223 65 75 58

bCorrosion and Protection Centre, School of Materials, University of Manchester,

Oxford Road, Manchester, M13 9PL, United Kingdom,

bob.cottis@manchester.ac.uk

cDelft University of Technology, Department of Materials Science and

Engineering, Mekelweg 2, 2628CD Delft, The Netherlands, J.M.C.Mol@tudelft.nl

Abstract

Transients in electrochemical noise (EN) signals that are associated with

localized corrosion typically contain frequency information that is quite localized

in time. The study of these transients is therefore preferably performed using

analysis procedures with high discrimination ability in both time and frequency

simultaneously. The present work studies the combination of the Hilbert-Huang

transform with the continuous wavelet transform, as data analysis methods that

operate in time as well as in frequency, for the identification of localized

corrosion. Additionally it incorporates fast Fourier transform as a technique to

determine the distribution of power over frequency. Finally, it integrates the

study of transient shape into the analysis of (time-) frequency properties. It is

1

shown that the maxima in instantaneous frequency amplitudes of transients with

otherwise different shapes can be similar. In the case of the presence of multiple

transients in the EN signal, the cut-off frequency obtained from power spectral

density plots is related to maxima in instantaneous frequency amplitudes of only

a limited number of transients.

Keywords

Electrochemical noise; Hilbert-Huang transform; Wavelet transform; Spectral

analysis; Transient shape

1 Introduction

Electrochemical noise (EN) measurements are principally intended to record

charge transfer that originates from spontaneous corrosion, while keeping

perturbation of the process to a minimum. Whereas measuring EN may appear

straightforward, in order to obtain meaningful mechanistic information from the

chemo-physical process it is essential to employ the appropriate data analysis

techniques [1, 2]. Amongst these, conceivably direct visual characterization of EN

transients in the raw data signal is the most straightforward. However, the

analysis of transient shape requires the possibility to visually locate and identify

transients individually. This necessity potentially decreases the suitability of

visual identification for this purpose. In the case of localized corrosion processes

that occur more or less at the same time, the resulting transient overlap may

impede the investigation of transient shape.

2

Operating in the frequency domain, for the analysis of EN signals fast Fourier

transform (FFT) is most often used to determine the distribution of power over

frequency, usually in the form of the power spectral density, or PSD [1]. An

important limitation of FFT is the requirement for a stationary signal, which is

often not met for EN signals.

The PSD shows specific characteristics that can indicate specific types of

corrosion: Firstly, the overall level of the PSD is reported to be related to the

intensity of the process [3, 4]. Secondly, the cut-off-, roll-off- or knee frequency,

which indicates the transition between the horizontal low-frequency part and

the slope at higher frequencies, can be used to discriminate between different

types of corrosion [4, 5]. As a third parameter, the slope in the higher frequency

part can be considered to differentiate between different corrosion types [3, 4, 6-

8]. It should however be noted that in some cases the discrimination ability of

the PSD can vary between the electrochemical current (ECN) or potential noise

(EPN) signal, and that it may be difficult to indicate the presence of a low-

frequency plateau or cut-off frequency [2].

A more recent development is the use of data analysis procedures operating in

the time-frequency domain for the investigation of EN [5, 9]. As an example,

corrosion studies using the Hilbert-Huang transform (HHT) have been reported

to effectively identify microbiologically influenced corrosion (MIC) [10] and

corrosion inhibition [11]. The HHT was first introduced by Huang et al. [12] and

is based on the extraction of characteristic scales, or intrinsic mode functions

from the EN signal, using a procedure called empirical mode decomposition

(EMD). After EMD, instantaneous frequencies are calculated from these intrinsic

oscillation modes [12]. The differentiation of those instantaneous frequencies in

3

time allows the analysis of nonlinear and non-stationary EN signals. To a certain

degree, it combines advantages of analysis procedures operating in the

frequency- as well as in the time domain. A different approach is to describe the

original EN signal using a linear combination of oscillations of a limited time

span, called wavelets. By scaling and translation of these wavelets, these allow

analysis of the signal at different timescales. The energy of each timescale can be

plotted in an energy distribution plot (EDP), where the dominant process is

associated with the timescale with the highest relative energy [5, 7]. Aballe et al.

[7] were the first to compare (discrete) wavelet transform (DWT) with FFT from

the perspective of their ability to identify different corrosion mechanisms. The

PSD was found to indicate the dominant timescale in the EN signal,

corresponding with observations from the EDP. However, it appeared that the

PSD could hardly discriminate between features in the EN signal related to

processes occurring in different timescales, whereas the DWT could. The PSD is

however closely related to the EDP determined by DWT [13]. Combined with the

apparently superior frequency resolution as provided by continuous wavelet

transform (CWT) with respect to DWT [13], it is interesting to investigate

whether information obtained by CWT can be confirmed by FFT. This is

therefore one of the primary objectives of the present work, together with the

comparison between the use of CWT- and Hilbert spectra for the analysis of EN

signals.

In this work, the combination of transient shape analysis, investigation of the

PSD and time-frequency spectra obtained from CWT and HHT is investigated.

Localized corrosion processes involving AISI304, carbon steel and AA2024-T3,

4

which were already analysed in detail by introducing transient analysis through

Hilbert spectra in earlier work [10, 11, 14], serve as case studies.

2 Experimental

All EN measurements involved a classical, open circuit configuration with two

working electrodes and a reference electrode. The experimental details are

identical to the ones described earlier for AISI304 [9], AA2024-T3 [11] and MIC

[10].

The AISI304 and AA2024-T3 working electrode surfaces were pre-treated

through wet grinding with up to 4000-grit SiC paper and rinsing with

demineralized water. Subsequently, the working electrodes were kept in a dry

environment at 20 °C for 1 day and analysed for imperfections prior to exposure.

Each working electrode covered an area of 0.05 cm2 and was either exposed to

an aqueous 10-4 M HCl (AISI304) or 10-1 M NaCl (AA2024-T3) electrolyte. The

electrolytes were produced from reagent of analytical quality, dissolved in

demineralized water. The experiments were carried out under aerated

conditions. A Red Rod REF201 reference electrode (Ag/AgCl/sat. KCl: 0.207 V vs.

SHE), from Radiometer Analytical, served as reference electrode.

The MIC experiments involved working electrodes that were made from carbon

steel, with working electrode areas of 19,6 mm2 each. Here, a platinum mesh

with an area of approximately 100 mm2 served as reference electrode. A

Postgate C solution [15] with additionally 2,5 wt.% NaCl, produced from reagent

of analytical quality that was dissolved in demineralized water, was used both as

electrolyte and as medium for the bacteria.

5

A Faradaic cage protected the measurement setup from electromagnetic

distortions. The atmospheric temperature of the surrounding area was regulated

at 20 °C. After each experiment, the working electrodes were analysed using an

optical microscope (Reichert MEF4 M) with a maximum magnification of 1000x.

Each experiment was repeated at least two times.

The ECN and EPN signals were measured using an Ivium Technologies

Compactstat potentiostat. For the experiments on AISI304 a sampling rate of 5

Hz was selected and for the measurements on AA2024-T3 and MIC 20 Hz was

used, all of which included the application of a low-pass filter of 10 Hz.

The CWT was computed with an analytic Morlet wavelet using the cwtft function

in Matlab, which uses the discrete Fourier transform algorithm [16]. Whatever

the algorithm used, a key decision when computing the CWT is the way in which

the signal is extended at the beginning and at the end of the time record (known

as ‘padding’). This is necessary because the wavelet must overlap the ends of the

time record by half its duration when computing the first and last points of the

spectrum. Various padding methods can be used (see [17] for the methods

available in Matlab) and the method chosen has a significant effect on the

artefacts produced at the beginning and at the end of the spectrum. For this work

symmetric padding was found to provide the best results. 32 Voices per octave

(i.e. 32 logarithmically spaced frequencies were computed for each factor of two

frequency range) were used to calculate the CWT. The Hilbert–Huang transform

was calculated by the application of a Matlab program developed by Rilling et al.

[18]. The analysis of transients was executed analogously to the procedure as

described in [11, 14]. In order to be able to calculate a reliable PSD, the DC drift

of each EN signal was first identified through discrete wavelet transform and

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subsequently removed from the signal before application of the FFT. Further

details on this trend removal procedure were published earlier in [19].

3 Results and discussion

This section starts with the analysis of single transients. Subsequently EN signals

containing transients that occur over different timescales and that in some cases

appear overlapped, are treated. Finally, a corrosion process that gradually

changes over time is discussed.

3.1 Single transient analysis

EN signals consisting of only one transient are perhaps the most straightforward

to investigate. Both transient shape and frequency characteristics are relatively

easy to analyse. In the absence of multiple (different) transients which all

contribute to the overall frequency spectrum, it is expected that the overall

frequency characteristics visible in the PSD are similar to those determined by

the HHT and CWT.

Figure 1 shows the ECN and EPN time signal of AISI304 exposed in a 10-4 M HCl

solution for a duration of 1000 s. Figures 2 and 3 show the CWT- and Hilbert

spectra, respectively.

Figure 1

Figure 2a

7

Figure 2b

Figure 3a

Figure 3b

One transient occurred, at approximately t = 800 s. The shape of a transient is

related to local kinetics of the associated corrosion process. In the case of pitting

corrosion, the characteristics of EN transients directly reflect processes

occurring in the associated pits [20]. Identification of an individual transient is

facilitated in cases where only one transient is present in the EN signal, or

otherwise when pits do not arise simultaneously and consequently their

associated transients do not overlap. For the ECN and EPN transients shown in

Figure 1 the gradually increasing amplitude reflects the metastable growth phase

of a pit. Subsequently, a rapid decay in the ECN transient indicates fast

repassivation and a slow decrease in magnitude of the EPN transient (i.e. a slow

recovery of the potential value in the positive direction) is associated with the

slow discharge of interfacial capacitance [20]. The increasing slope towards the

peak of the transients can be explained by an increase in the charge transfer rate:

apparently, the metastable growth phase is characterized by an increase in pit

growth rate. As a result of this, different steeper and shallower sloping regions

can be identified in the transients during the metastable growth phase.

The instantaneous frequency information provided by the Hilbert- and CWT

spectra of the ECN signal is comparable, with maxima around 6•10-2 Hz. The

Hilbert spectrum of the EPN signal shows a maximum at a lower frequency (2•10-

2 Hz), which can be attributed to the influence of the discharge of interfacial

8

capacitance in the overall EPN transient, which is a relatively slow process [9].

The increased amplitude of instantaneous frequencies around 4•10-3 Hz ahead of

the transient are likely to be artefacts arising from the empirical mode

decomposition that can be disregarded by the use of a proper transient analysis

procedure [14]. The CWT spectrum shows maxima around the lowest frequency

ranges of the spectrum (approximately 5•10-3 Hz).

As a comparison, Figure 4 shows a different kind of transient present in the ECN

and EPN time signal of again AISI304 working electrodes exposed in the same

10-4 M HCl solution for a duration of 1000 s. Figures 5 and 6 show the CWT- and

Hilbert spectra, respectively.

Figure 4

Figure 5a

Figure 5b

Figure 6a

Figure 6b

Although both working electrode sets were composed of AISI304 and received

similar pre-treatment, the transient visible in the ECN and EPN signal in Figure 4

lasts considerably longer than the one of the signal in Figure 1. The rate of the

repassivation phase is comparable, whereas the preceding metastable growth

phase is considerably longer in this case. In addition, the transient shown here

9

clearly indicates that, instead of a steady metastable growth, this phase is

characterized by consecutive bursts of charge. Each of those bursts generates a

fast increase of current locally, associated with steep parts in the slope of the

ECN transient. The accumulation of those processes however results in an

overall metastable growth phase that lasts considerably longer, and is in addition

slower than in the previous case. These differences in kinetics are visible in the

Hilbert- and CWT spectra. The Hilbert spectrum of the ECN signal shows a

maximum between 10-2 and 2•10-2 Hz, which is considerably lower than the 6•10-

2 Hz of the spectra of Figures 2a and 3a. The CWT spectrum of the ECN signal has

an overall maximum at 5•10-3 Hz, although here an additional peak is visible

between 10-2 and 2•10-2 Hz, at the time instant of the transient. The Hilbert- and

CWT spectrum of the EPN signal both show a maximum at 2•10-2 Hz, although the

overall maximum of the CWT spectrum is located at 5•10-3 Hz. It is worth noting

that, although the transients in Figure 1 and 4 share different durations, the

Hilbert- and CWT spectra of the EPN signals have local maxima in a similar

frequency range. Moreover, especially in the Hilbert spectra these maxima are

located at the same timeframe as the final part of their corresponding EPN

transient. By this way these spectra confirm the observation from transient

analysis that the rate of the repassivation phase is comparable in both cases,

regardless of the duration of the metastable growth phase.

Although less apparent, the part of the ECN transient in Figure 1 associated with

metastable growth also starts and ends with a steep part. It can be assumed that

this is generated by a comparable mechanism, as is the case for the transient in

Figure 4. Because the rate of the total metastable growth phase is higher than in

the case of the transient in Figure 4, the higher instantaneous frequencies

10

associated with these steep parts probably have a larger relative influence in the

Hilbert spectrum and, as a consequence, the dominating instantaneous

frequencies are in a higher range than compared to those in the Hilbert spectrum

of the ECN transient in Figure 4. Note that, with 16 nA, the absolute magnitude of

the brief transient in Figure 1 is even approximately 3 nA larger than that of the

longer lasting transient in Figure 4.

Figure 7 shows the PSDs of both the EN signals from Figure 1 (1) and 4 (2). By

this way, data analysis in the frequency domain can be combined with the

previous results from HHT and CWT. A vertical line indicates the cut-off

frequency of each PSD graph.

Figure 7a

Figure 7b

Comparing the cut-of frequencies visible in the PSD plots of Figure 7 reveals that

these correspond with the dominating instantaneous frequencies of the Hilbert

spectra and that, for the CWT spectra, these correspond only for the ECN signals

and for the EPN signal of Figure 4. In Figure 7a, the PSD of the transient from

Figure 1 shows a cut-off frequency of approximately 6•10-2 Hz and the PSD of the

transient from Figure 4 has a cut-off frequency of 10-2 Hz. The PSDs of the EPN

signals both show a cut-off frequency at 10-2 Hz.

3.2 Multiple transient analysis

11

Transient shape analysis can be useful to detect the nature of pitting corrosion.

In most cases, EN signals contain multiple transients. This subsection focuses on

the analysis of such signals. Figure 8 shows the ECN time signal of (a) again

AISI304 exposed in a 10-4 M HCl solution for a duration of 1000 s and (b) pitting

corrosion of carbon steel due to MIC after 13 days of immersion for a duration of

1000 s. In the case of the MIC experiments, detection of variations in EPN was

hindered by the use of a platinum mesh as reference electrode, which was

necessary for sterility considerations. Therefore, the EPN signal could only be

used for determination of the average open corrosion potential. In order to

facilitate transient analysis, Figure 9 shows an enlargement of the transients of

these signals, after a transient identification procedure as presented in earlier

work [11, 14]. Determination of transient duration can be achieved by

observation where the transient amplitude is nonzero. The procedure is based

on instantaneous frequency information in Hilbert spectra and is primarily

intended to avoid the influence of artefacts from those spectra [14]. Therefore,

differences with visual transient start and end points may occur. The transients

in the original ECN and EPN signal are indicated from left to right with 1-5

(Figure 9a) or 1-6 (Figure 9b).

Figure 8a

Figure 8b

Figure 9a

Figure 9b

12

Analogous to the transients from the EN signals in Figures 1 and 4, the transients

shown in Figure 9a exhibit an increasing slope towards their maximum absolute

value, which again indicates that the metastable growth phase is characterized

by an increase in pit growth rate. The duration of transient 3 is the largest,

approximately 23 s. This is the only transient in the positive direction in the

original time signal shown in Figure 8a. Transients 1, 2, 4 and 5 are in the range

of 8 to 15 s. For transient 3, the amplitude is almost 9 nA and transients 1, 2, 4

and 5 range between 3 and 6 nA. It appears here that a large transient duration is

not necessarily related to large amplitudes: the transient with the largest

timespan (transient 5, duration 15 s) shows a maximum amplitude of only 3 nA.

It is interesting to note the difference in transient shapes between Figures 9a and

9b. Where ECN transients in Figure 9a are related to initiation, slow metastable

growth and fast repassivation of a pit, those in Figure 9b are produced by

acidification at the interface between metal substrate and biofilm due to the

metabolism of SRB that causes a local corrosion attack [21, 22]. The SRB reduce

sulphate, which is present in the electrolyte and acts as terminal electron

acceptor [21, 23, 24]:

(1)

The resulting sulphide reacts with iron ions that are present due to the anodic

reaction, hence resulting in acidification of the anodic site along with the

production of iron sulphide [21, 22]:

13

(2)

Subsequently, migration of the H+ ions through the biofilm and away from the

substrate generates a decrease in transient magnitude [10]. All transients show a

similar characteristic shape with a more or less horizontal segment at the right

hand side, in which the decrease in charge transfer rate ceases for a moment.

Contrary to metastable pitting of AISI304, the largest transient also shows the

largest duration here, which can be explained by the activity of SRB. In case of a

thicker biofilm, the H+ production due to their metabolism can be high locally,

generating a larger pit in the metal substrate. The thick biofilm consequently

prevents fast migration of those H+ ions, thereby contributing to a larger

transient duration.

In order to be able to investigate the time-frequency characteristics, Figure 10

shows the CWT- (a) and Hilbert (b) spectrum of the ECN time signal of AISI304

exposed in a 10-4 M HCl solution for a duration of 1000 s and Figure 11 shows the

CWT- (a) and Hilbert (b) spectrum of the ECN time signal of pitting corrosion of

carbon steel due to MIC after 13 days of immersion for a duration of 1000 s.

Figure 10a

Figure 10b

Figure 11a

Figure 11b

14

Both the Hilbert- and CWT spectra of the ECN signal from Figure 10 show that

the largest transient, occurring after 200 s, is characterized by maxima in the

instantaneous frequency range between 2•10-2 and 3•10-2 Hz. In addition, the

remaining smaller transients are characterized by maxima in the order of 10-1 Hz

in both spectra, whereas those of the first transient are in a lower instantaneous

frequency region, around 4•10-2 Hz.

In Figure 11, the last transient (6 in Figure 9b), that was considerably longer

than the other five, is also associated with the lowest instantaneous frequencies

in the CWT- and Hilbert spectra. In the CWT spectrum, the largest amplitude for

this transient is at 4•10-2 Hz, whereas for the other transients maxima are

approximately present at 2•10-1 Hz. In the Hilbert spectrum, at 2•10-1 Hz local

maxima are also distinguishable, however the sharp transient peaks dominate

the spectrum to a larger extent, with maxima above 1 Hz for all transients. The

contribution of the longer second part of the last, large transient is visible in

increased instantaneous frequency amplitudes around 10-2 Hz.

Whether or not assisted by separate transient analysis figures, in the above cases

transient shapes can be relatively easily distinguished. This is however not

always the case. Figure 12 shows the ECN signal from a measurement on the

same measurement cell at the same day as the data presented in Figure 8b.

Figure 13 shows the CWT- (a) and Hilbert (b) spectra, respectively.

Figure 12

Figure 13a

15

Figure 13b

In the ECN signal of Figure 12, transients are increasingly overlapping. This is

made visible by a magnification of the transients occurring between 640 s and

660 s. The use of smaller working electrode surfaces can prevent this

phenomenon to a certain extent, however in most cases the semi-stochastic

nature of corrosion determines the amount of localized processes that occur

simultaneously. The sole use of transient shape analysis as identification

parameter for this specific type of localized corrosion becomes insufficient in

those cases. Despite the overlap in transients however, local frequency

characteristics remain largely preserved. The time-frequency techniques shown

in Figure 13 are therefore still able to visualize the instantaneous frequency

characteristics. The dominant instantaneous frequency ranges are comparable

with those of the spectra shown in Figure 11, which is expected since both ECN

signals originate from the same measurement cell under similar experimental

conditions.

Analogous to single transient analysis, also for the EN signals discussed here data

analysis in the frequency domain is combined with the results from HHT and

CWT. Figure 14a shows the PSD of the ECN signal from Figure 8a and Figure 14b

shows the PSDs of the ECN signals from Figure 8b (1) and 12 (2). A vertical line

again indicates the cut-off frequency of each PSD graph.

Figure 14a

Figure 14b

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The cut-off frequency of the PSD graph of Figure 14a lies between 2•10-2 and

3•10-2 Hz. This corresponds with the transient characteristics of the large

transient occurring at 200 s in the CWT- and Hilbert spectrum of Figure 10. It

appears that this frequency information dominates the overall PSD to a large

extent, since the other transients show different frequency characteristics in the

CWT- and Hilbert spectrum that remain invisible in the PSD. The cut-off

frequencies of the PSD graphs of Figure 14b are approximately 10-1 Hz. This

value reflects the instantaneous frequency characteristics of the majority of the

transients: although the large transient at approximately t = 900 s in Figure 8b

has a lower dominant instantaneous frequency range (around 4•10-2 Hz), the

other five transients influence the PSD to a larger extent, resulting in an overall

PSD that is comparable with the one from the ECN signal in Figure 12, hence in a

loss of information. Contrary to the PSD in Figure 14a, in this case the largest

transient does not influence the PSD to the largest extent. This effect could be

explained by the smaller relative difference between transient sizes, and hence

the increased relative overall energy contribution of the smaller transients in

this case (compare the transients in Figure 9b with those in Figure 9a). It should

be noted that both PSD graphs of Figure 14b are similar, which reflects the

comparable corrosion characteristics in both cases, regardless of transient

overlap.

3.3 Overlapping transients and non-stationarity

17

In some cases, corrosion processes change significantly over time. Here, non-

stationarity is not only limited to the occurrence of transients, but transients also

change significantly in shape and duration over time. In addition, transients may

increasingly overlap as the corrosion process proceeds. As an example, Figure 15

shows the ECN and EPN time signal of AA2024-T3 exposed in a 10-1 M NaCl

solution for a duration of 1000 s.

Figure 15

Visual inspection of the ECN signal reveals a significant change in transient

characteristics, with larger transients of shorter duration occurring in an

increasing rate towards the end of the signal. Their number and overlapping

nature hinders clear visual identification. HHT and CWT both provide a means to

obtain clear time-frequency information in those cases, without the loss of time-

dependent features in the signal. Figures 16 and 17 show the CWT- and Hilbert

spectra of these EN signals, respectively.

Figure 16a

Figure 16b

Figure 17a

Figure 17b

The CWT spectrum in Figure 16a shows increasing contribution of frequencies

around 10-1 Hz in time, associated with the increasing number of short transients

18

in the signal. However, along the entire signal frequencies below 10-2 Hz

dominate the spectrum. The EPN CWT spectrum displayed in Figure 16b shows a

peak at 2•10-2 Hz. Compared to the CWT spectrum of Figure 16a, in the Hilbert

spectrum shown in Figure 17a the increasing magnitude of frequencies around

10-1 Hz in time is even more apparent. In addition, throughout the signal also a

considerable amount of low-frequency information is present, below 10-2 Hz.

Analogous to the EPN CWT spectrum in Figure 16b, in the EPN Hilbert spectrum

in Figure 17b each of the two large transients occurring after 550 s generates a

peak in instantaneous frequencies at 2•10-2 Hz. It must be appreciated here that

the resolution in time and frequency of the CWT are a function of the selected

wavelet. The selection of a Morlet wavelet with a lower sine frequency can

increase the resolution in time (while decreasing the resolution in frequency)

[13]. Also it must be appreciated that the Heisenberg Uncertainty Principle

implies a limitation on the simultaneous resolution in time and frequency.

Implicitly, the resolution of intrinsic mode functions (IMFs), resulting from the

empirical mode decomposition, is indeed decreasing with increasing IMFs. This

is a result from the interpolation between local maxima and minima that are

located further apart after each iteration, as the highest frequency components

are removed each time [9, 12].

Finally, data analysis in the frequency domain is again combined with the results

from HHT and CWT. Figure 18 shows the PSDs of the EN signals from Figure 15.

A vertical line indicates the cut-off frequency of each PSD graph.

Figure 18a

19

Figure 18b

For the ECN signal, the cut-off frequency is approximately 10-2 Hz, whereas for

the EPN signal the cut-off frequency is 2•10-2 Hz. This agrees well with

observations in the time-frequency spectra for the overall signals. Again, the lack

of differentiation in time is important to note in this case. Information like the

increasing magnitude of frequencies around 10-1 Hz in time that was observed in

the time-frequency spectra, originating from an increasing density of fast

transients, is lost in the PSD. Due to considerable transient overlap, this

phenomenon is also not obvious using visual identification. In addition, the

origin of the increased magnitude of the instantaneous frequencies around 2•10-2

Hz in the time-frequency spectra of the EPN signal, which could be associated

with the two large and slow transients occurring after 550 s, cannot be

determined using only the PSD.

3.4 Overall discussion

In the case of the presence of only one transient or multiple similar transients in

an EN signal, the cut-off frequency obtained from the PSD plot corresponds well

with the highest amplitude instantaneous frequencies in CWT- or Hilbert

spectra. However, once differences in transient magnitude or duration emerge

within the signal (i.e. the corrosion process changes over time), this correlation

becomes less straightforward. Here, the time-frequency techniques are powerful

tools to locate differences in kinetics over time. The visual characterization of

transient shape can be a quite useful additional tool, provided that the transients

20

can be detected accurately. This is challenging, considering the semi-stochastic

nature of the underlying process and possible transient overlap. Provided that

transient start and end can be determined, its shape allows localization of the

anodic process in time, the (change in) charge transfer rate, peak current or

potential and duration of the first part towards the maximum amplitude and

from there towards the transient end. Together with time-frequency

information, this ability aids the understanding of the physicochemical process

that generated the transient.

4 Conclusions

In the time domain, transient shape analysis can be used as a first global

corrosion identification step with respect to its charge transfer kinetics, prior to

further data analysis. It is a suitable technique in order to enable the

differentiation of corrosion processes in a broad sense, without the necessity of

more sophisticated data analysis tools.

In the frequency domain, a certain agreement exists between the cut-off

frequency in a PSD plot and maxima observed in CWT- and Hilbert spectra. In

some cases however, only a small part of the EN signal can have a significant

impact on the PSD. This increases the risk of loosing essential details about the

corrosion process during a measurement. If a corrosion process is more or less

in a steady state this is acceptable, and the PSD can provide a good overall

impression of the frequency characteristics of the investigated EN signal.

However, for more dynamic systems that change over time, differentiation in

time is required.

21

Finally, in the time-frequency domain, CWT spectra as derived in this work

provided similar information as Hilbert spectra. The preference for the use of

either of both time-frequency techniques could depend on the required

application and further data analysis.

5 References

[1] R.A. Cottis, Corrosion, 57 (2001) 265-285.[2] A.M. Homborg, T. Tinga, E.P.M. van Westing, X. Zhang, G.M. Ferrari, J.H.W. de Wit, J.M.C. Mol, Corrosion, 70 (2014) 971-987.[3] T. Zhang, Y. Shao, G. Meng, F. Wang, Electrochim. Acta, 53 (2007) 561-568.[4] A.-M. Lafront, F. Safizadeha, E. Ghali, G. Houlachi, Electrochim. Acta, 55 (2010) 2505-2512.[5] A. Aballe, M. Bethencourt, F.J. Botana, M. Marcos, Electrochem. Commun., 1 (1999) 266-270.[6] K. Hladky, J.L. Dawson, Corros. Sci., 22 (1982) 231-237.[7] A. Aballe, M. Bethencourt, F.J. Botana, M. Marcos, Electrochim. Acta, 44 (1999) 4805-4816.[8] G. Du, J. Li, W.K. Wang, C. Jiang, S.Z. Song, Corros. Sci., 53 (2011) 2918-2926.[9] A.M. Homborg, E.P.M. van Westing, T. Tinga, X. Zhang, P.J. Oonincx, G.M. Ferrari, J.H.W. de Wit, J.M.C. Mol, Corros. Sci., 66 (2013) 97-110.[10] A.M. Homborg, C.F. Leon Morales, T. Tinga, J.H.W. de Wit, J.M.C. Mol, Electrochimica Acta, 136 (2014) 223-232.[11] A.M. Homborg, E.P.M. van Westing, T. Tinga, G.M. Ferrari, X. Zhang, J.H.W. de Wit, J.M.C. Mol, Electrochim. Acta, 116 (2014) 355-365.[12] N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.C. Yen, C.C. Tung, H.H. Liu, Proc. R. Soc. London, 454 (1998) 903-995.[13] R.A. Cottis, A.M. Homborg, J.M.C. Mol, Electrochimica Acta, 202 (2015) 277-287.[14] A.M. Homborg, T. Tinga, X. Zhang, E.P.M. van Westing, P.J. Oonincx, G.M. Ferrari, J.H.W. de Wit, J.M.C. Mol, Electrochim. Acta, 104 (2013) 84-93.[15] J.R. Postgate, The sulphate-reducing bacteria, Ed. Cambridge University Press, Cambridge, 1984.[16] The MathWorks, Inc., (2016). Wavelet Toolbox: User's Guide (R2016a). Retrieved July 1, 2016 from http://www.mathworks.com/help/pdf_doc/wavelet/wavelet_ug.pdf.[17] The MathWorks, Inc., (2016). Image Processing Toolbox: User's Guide (R2016a). Retrieved July 1, 2016 from http://www.mathworks.com/help/pdf_doc/wavelet/wavelet_ug.pdf.[18] G. Rilling, P. Flandrin, P. Goncalves, IEEE-EURASIP workshop on Nonlinear Signal and Image Processing NSIP-03, Grado, Italy, (2003) 1-5.

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[19] A.M. Homborg, T. Tinga, X. Zhang, E.P.M. van Westing, P.J. Oonincx, J.H.W. de Wit, J.M.C. Mol, Electrochim. Acta, 70 (2012) 199-209.[20] G. Berthomé, B. Malki, B. Baroux, Corros. Sci., 48 (2006) 2432-2441.[21] B.W.A. Sherar, I.M. Power, P.G. Keech, S. Mitlin, G. Southam, D.W. Shoesmith, Corros. Sci., 53 (2011) 955-960.[22] W.A. Hamilton, Biofouling, 19 (2003) 65-76.[23] T. Gu, K. Zhao, S. Nesic, Corrosion, (2009) 1-12.[24] T. Gu, D. Xu, Demystifying MIC Mechanisms, in: NACE International, 2010.

Figure captions

Figure 1 ECN and EPN time signal of AISI304 exposed in a 10-4 M HCl solution for

a duration of 1000 s

Figure 2 CWT spectrum of the ECN (a) and EPN (b) signal of AISI304 exposed in

a 10-4 M HCl solution for a duration of 1000 s

Figure 3 Hilbert spectrum of the ECN (a) and EPN (b) signal of AISI304 exposed

in a 10-4 M HCl solution for a duration of 1000 s

Figure 4 ECN and EPN time signal of AISI304 exposed in a 10-4 M HCl solution for

a duration of 1000 s

Figure 5 CWT spectrum of the ECN (a) and EPN (b) signal of AISI304 exposed in

a 10-4 M HCl solution for a duration of 1000 s

Figure 6 Hilbert spectrum of the ECN (a) and EPN (b) signal of AISI304 exposed

in a 10-4 M HCl solution for a duration of 1000 s

23

Figure 7 PSDs of the ECN (a) and EPN (b) signals of Figure 1 (1) and 4 (2) of

AISI304 exposed in a 10-4 M HCl solution for a duration of 1000 s

Figure 8 ECN time signal of (a) AISI304 exposed in a 10-4 M HCl solution for a

duration of 1000 s and (b) pitting corrosion of carbon steel due to MIC after 13

days of immersion for a duration of 1000 s

Figure 9 Transients of the ECN signal of (a) AISI304 exposed in a 10-4 M HCl

solution for a duration of 1000 s and (b) pitting corrosion of carbon steel due to

MIC after 13 days of immersion for a duration of 1000 s, from left (1) to right (5

or 6)

Figure 10 CWT- (a) and Hilbert (b) spectrum of the ECN signal of AISI304

exposed in a 10-4 M HCl solution for a duration of 1000 s

Figure 11 CWT- (a) and Hilbert (b) spectrum of the ECN signal of pitting

corrosion of carbon steel due to MIC after 13 days of immersion for a duration of

1000 s

Figure 12 ECN time signal of pitting corrosion of carbon steel due to MIC after 13

days of immersion for a duration of 1000 s

Figure 13 CWT- (a) and Hilbert spectrum (b) of the ECN signal of pitting

corrosion of carbon steel due to MIC after 13 days of immersion for a duration of

1000 s

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Figure 14 (a) PSD of the ECN signal of AISI304 exposed in a 10-4 M HCl solution

for a duration of 1000 s and (b) PSDs of the ECN signals of pitting corrosion of

carbon steel due to MIC after 13 days of immersion for a duration of 1000 s

Figure 15 ECN and EPN time signal of AA2024-T3 exposed in a 10-1 M HCl

solution for a duration of 1000 s

Figure 16 CWT spectrum of the ECN (a) and EPN (b) signal of AA2024-T3

exposed in a 10-1 M HCl solution for a duration of 1000 s

Figure 17 Hilbert spectrum of the ECN (a) and EPN (b) signal of AA2024-T3

exposed in a 10-1 M HCl solution for a duration of 1000 s

Figure 18 PSDs of the ECN (a) and EPN (b) signal of Figure 15 of AA2024-T3

exposed in a 10-1 M HCl solution for a duration of 1000 s

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