Electrochemical noise analysis to identify the corrosion type using the Stockwell transform and the Shannon energy

Journal of Electroanalytical Chemistry 836 (2019) 50–61

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Electrochemical noise analysis to identify the corrosion type using the Stockwell transform and the Shannon energy

T

O.J. Ramos-Negróna, J.H. Arellano-Péreza, R.F. Escobar-Jiménezb,*, J.F. Gómez-Aguilarc, D. Granados-Liebermand a

Posgrado del Tecnológico Nacional de México/CENIDET, Int. Internado Palmira S/N, Cuernavaca Palmira C.P. 62490, Morelos, Mexico Tecnológico Nacional de México/CENIDET, Int. Internado Palmira S/N, Cuernavaca Palmira C.P. 62490, Morelos, Mexico c CONACyT-Tecnológico Nacional de México/CENIDET, Int. Internado Palmira S/N, Cuernavaca Palmira C.P. 62490, Morelos, Mexico d Departamento de Ingeniería Electromecánica, Instituto Tecnológico Superior de Irapuato, Calle 43 No. 613 x C. 90, Irapuato Inalámbrica 97069, Guanajuato, Mexico b

ARTICLE INFO

ABSTRACT

Keywords: Corrosion Electrochemical noise Stockwell transform Shannon energy Wavelet transform.

In this research, a new method to identify the corrosion types (generalized, mixed, localized, and the passivation situation) is proposed. The proposed method is based on the electrochemical noise analysis using the Stockwell transform and Shannon energy. To develop the experimental analysis, the 6061-T6 aluminum was exposed to three different corrosive media: 15% H2SO4, 3.5% NaCl and diH2O. The experimental results using the Stockwell transform presented a better classification than the performed by Wavelet transform.

1. Introduction

2. Materials

The electrochemical noise (EN) technique is one of the best options for the in situ corrosion monitoring, especially because, it is a non-invasive technique. The EN measures the fluctuations of the electrochemical current noise (ECN) and the electrochemical potential noise (EPN) generated by the oxidation and reduction reactions when a metal is immersed in an electrolyte [1-3]. The EN analysis was usually carried out by visual inspections, statistical methods or using fast Fourier transform (FFT) for frequency domain analysis [4,5], and even chaos theory [6,7]. However, in the last years, applying methods based on the time-frequency domain, a better analysis has been obtained due to the non-stationary nature of the EN signals [8, 9], one of them is the Wavelet transform(WT) [10-14]. In this work, we propose a method based on the Stockwell transform (ST) and the Shannon energy (SSE) to identify the corrosion type by analyzing the EN signals. The EN signals considered for the analysis were taken from tests developed on the 6061-T6 aluminum (Al6061T6) exposed to three solutions (sulfuric acid, sodium chloride, and demineralized water) which generate different types of corrosion in the metal. A comparison between the proposed method and the WT analysis was developed to demonstrate that the ST-SSE offers better results for the identification of the type of corrosion from the EN signals analysis.

To measure the EN signals, three nominally identical Al6061T6 electrodes (see Fig. 1) in a cylindrical shape with a diameter of 6.34 mm and a length of 60 mm were developed. The electrodes were encapsulated in epoxy resin and sanding with sandpaper with a grain size of 6 μ m until achieving a mirror finish. The chemical composition of the Al6061T6 is Si 0.40–0.80, Fe 0.70 max., Cu 0.15–0.40, Mn 0.15 max., Mg 0.80–1.20, Cr 0.04–0.35, Zn 0.25 max. and Ti 0.15 max. wt.%. The solutions used to develop this work were 3.5% sodium chloride (NaCl), 15% sulfuric acid (H2SO4) and demineralized water (diH2O), the tests were carried out at a temperature between 20 and 25 °C. Fig. 1 shows the Al6061T6 electrodes before being used to develop the corrosion analysis. For the EPN signal measurement, a digital multimeter (DMM) Agilent 34410A was used, the instrument range is 1 V. On the other hand, for the ECN signal measurement, a DMM Keysight Technologies model 34461A was used, the instrument range is 100 μ A. Furthermore, a visual interface programmed in Labview 2012 for visualizing the electrochemical signals was developed. The data acquisition was carried out at a sampling frequency of 2 samples/s to develop records of 4096 samples each one. For the corrosion tests using NaCl and diH2O, 50 records were developed, equivalent to 28.44 h. And for the corrosion test using H2SO4, 1024 records were developed equivalent to 582.54 h.

*

Corresponding author. E-mail address: [email protected] (R.F. Escobar-Jiménez).

https://doi.org/10.1016/j.jelechem.2019.01.020 Received 23 October 2018; Received in revised form 19 December 2018; Accepted 9 January 2019 Available online 18 January 2019 1572-6657/ © 2019 Elsevier B.V. All rights reserved.

Journal of Electroanalytical Chemistry 836 (2019) 50–61

O.J. Ramos-Negrón et al.

represents the initial value of each frequency range, and fmax represents the final value of each frequency range. 3.1.1. Lagrange interpolating polynomial Given a points set n + 1, (x 0 , y0 ), …, (xn , yn ) , the interpolator polynomial in the Lagrange form is a linear combination, that can be represented as follows: n

n

P (x ) = i=0

m = 0,

m i

x xi

xm y. xm i

(4)

3.2. Wavelet transform To evaluate the performance of the ST and ST-SSE, a comparison with the WT method is developed, in this sense in this section the related equations are presented. According to Ref. [26], considering xn(n = 1, 2, …, N ) as a time record, the wavelets approach consists of representing the term xn, by a linear functions combination ϕj,n and ψj,n which represent the father ϕ and the mother ψ wavelet functions, respectively, Eqs. (5) and (6). Fig. 1. Electrodes before the tests.

3. Methods This section presents the ST and ST-SSE methods to classify the type of corrosion on the alloy Al6061T6. Also shown is the Lagrange interpolation method, which will be used to propose polynomial series to approximate the energy behavior according to the corrosion type. Finally, the WT method is presented which will be used to develop a comparison with the proposed methods (ST and ST-SSE).

1 S [jT , 0] = N

N 1 m=0

N 1

=

G m =0

m+n e NT

2 2m2 i2 mj n2 e N ,

n

0

SSE (i ) =

(2 jt

n) = 2

j /2

t

j , n (t )

=2

j /2

(2 jt

n) = 2

j /2

t

n=0

fmaxi

j = 1 n = f min i

2j

(5)

2 jn 2j

(6)

SJ , n

x (t ) J*, n (t ) dt .

(7)

dj , n

x (t ) j*, n (t ) dt .

(8)

(1)

N

m g , NT

2 jn

where J*, n and j*, n are the complex conjugate of ϕJ,n and ψj,n, respectively. An alternative way to show the WT results is by the energy distribution diagrams, which show the energy of each crystal (frequency scales which for the work purpose are equivalent to the frequency ranges showed in Table 1). Eq. (9) describes the energy of each crystal.

E=

xd2

d = 1, 2, …, N

d=1

(2)

(9)

Moreover, Eqs. (10) and (11) correspond to the fraction of the coefficients for each crystal:

where G(kT) represents a discrete time series, N is the number of n jT , f and samples in each record (4096), NT j, m , n = 0, 1, …, N 1, finally, S is the obtained matrix from the ST calculation. For the purposes of this work, the code developed by Glenn Stockwell [21] was used. Once the DST has been calculated, the next step is to use the SSE for estimating the energy in a specific range of frequencies, previously obtained from the DST for each sample. As is referred in Ref. [22], the SSE is used to estimate the energy of the local spectrum for each sample, emphasizing the energy located at the medium of amplitudes, related works with the SSE use can be found in Refs.[23,24]. Therefore, to estimate the SSE, Eq. (3) is applied [25]. N

j /2

N

The Discrete Stockwell transform (DST) characteristics make it an excellent alternative for the digital signals processing of physical phenomena [15-20]. Therefore, in this work, the DST is used to propose a method that allows to classify the corrosion type of different solutions. The DST in discrete time series g(kT) can be written as follows (Eqs. (1) and (2)).

n NT

=2

where n = 1, 2, …, j and j = 1, 2, …, J ; J is often a small natural 2 number which depends mainly on ϕ,ψ and N, while 2j is a scale factor j and 2 n is as translation parameter. Therefore, from each basis function, the signal x(t) is transformed into wavelet coefficients Sj, n, dj, n, …, d1, n which are obtained from Eqs. (7) and (8). According to Ref. [26], these coefficients are computed as follows:

3.1. Discrete Stockwell transform

S [ , f ] = S jT ,

j , n (t )

E jd =

EJs =

1 E

1 E

N /2 j

x j2, n n= 1

j = 1, …, J

(10)

N /2 J

xJ2, n . n=1

(11)

4. Results In this section, the results of the EN analysis using the ST and ST-SSE to identify the corrosion type on the alloy Al6061T6 exposed to three different solutions are presented. Also, the Lagrange interpolation series coefficients used to approximate the energy behavior according to the corrosion type are shown. Finally, the comparison between the proposed method and the WT analysis is presented.

[|S (j, n)|]2 log [|S (j, n)|]2 (3)

where i is the number of each frequency range (see Table 1), fmin 51

Journal of Electroanalytical Chemistry 836 (2019) 50–61

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Table 1 Frequency ranges used for evaluating the ST-SSE method. 1

2

3

4

5

6

7

8

9

10

11

fmin and fmax (mHz)

500 to 1000

250 to 500

125 to 250

62.5 to 125

31.3 to 62.5

15.6 to 31.3

7.8 to 15.6

3.9 to 7.8

1.9 to 3.9

0.9 to 1.9

0.5 to 0.9

Potential (mV)

Number of range (i)

150

80

30

100

60

25

50

40 20

15

-50 0

-100

10 H SO 2

NaCl

4

diH O

2

100

Current ( A)

20

0

2

0

1 -0.01

0 0

-0.02

-100

-1

-200

-2 0

100

200

300

400

500

-0.03 5

10

15

20

25

5

10

15

20

25

Time (h)

Fig. 2. EPN and ECN signals of the Al6061T6 exposed to the three solutions.

Fig. 2 shows the EPN and ECN signals that correspond to an individual analysis made on different probes using H2SO4, NaCl, and diH2O solutions. At the top of Fig. 2, from left to right, the EPN signals of H2SO4, NaCl, and diH2O respectively, are shown, and in bottom of Fig. 2, from left to right, the ECN signals of H2SO4, NaCl, and diH2O respectively, are shown. The test carried out on the alloy Al6061T6 exposed to H2SO4 had a duration of 582.54 h, because the test purpose was to get the maximum pitting in the alloy. Meanwhile, for the NaCl and diH2O cases, the tests’ duration was 28.44 h because we reached the same corrosion behavior on the alloy, like the reported in the literature [2729]. As can be seen in Fig. 2, the EPN and ECN signals of H2SO4 have higher noise levels compared to NaCl and diH2O, while the EPN and ECN signals of diH2O have lower noise levels compared to H2SO4 and NaCl. Fig. 3 shows the Localization Index (LI) of NaCl and diH2O

calculated from the ECN signals. For the ST and ST-SSE analyses purposes, it is necessary to get the records of the EPN and ECN signals of NaCl in three different LI zones (in the border between mixed and localized corrosion, as well as, in the maximum and minimum LI values). So, we isolate three specific records of NaCl that correspond to the above-mentioned LI zones; from time 7.96 to 8.53 h, 11.95 to 12.52 h and from time 16.5 to 17.07 h. The last two records were considerate to develop the ST analysis of diH2O. Fig. 4 shows the LI analysis of H2SO4 using the ECN signal. For the ST and ST-SSE analyses purposes, it is necessary to get the records of the EPN and ECN signals of H2SO4. So, we consider the same two records chosen for diH2O. So, we isolate the specific records of H2SO4 that correspond from time 11.95 to 12.52 h and from time 16.5 to 17.07 h. The LI method gives us information about what type of corrosion is occurring in Al6061T6 due to exposure to the solutions. This index is the quotient of the standard deviation of the ECN signal between the root mean square (RMS) of the ECN signal. One of the main

100 Localized corrosion

NaCl diH2O

Localization Index

7.96 to 8.53 h

10-1

16.50 to 17.07 h

Mixed corrosion

11.95 to 12.52 h

10-2

Generalized corrosion

10-3

6

8

10

12

14

16

18

20

22

24

Time (h) Fig. 3. Localization index analysis developed on the 6061-T6 aluminum exposed to NaCl and diH2O. 52

26

Journal of Electroanalytical Chemistry 836 (2019) 50–61

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100 16.50 to 17.07 h

11.95 to 12.52 h 10-1

Localization Index

Localized corrosion

5

10-1

10

15

20

25

H2SO4

Mixed corrosion 10-2

Generalized corrosion

10-3

50

100

150

200

250

300

350

400

450

500

550

Time (h) Fig. 4. Localization index analysis developed on the 6061-T6 aluminum exposed to H2SO4.

Potential (mV)

controversies that have occurred in the evaluation of the type of corrosion using EN is the use of the LI, because different researchers have divided their opinions about this index, some researchers support the use of the index [30-33], while other researchers have disagreed to the use of this index [34-37]. In this sense, other techniques like the FFT and WT [26,38,39,11] have been used to identify different types of corrosion. Having reviewed the literature, in the present work, we will classify the corrosion type generated by each one of the solutions (NaCl, diH2O, and H2SO4) in the Al6061T6 using the ST and ST-SEE methods with the aim of proposing an alternative corrosion analysis. For analyzing the EN signals with the ST and ST-SSE methods, it is necessary to remove the linear trend of the signals. In this sense, to detrend the signals, the linear regression model based on the least squares approximation was used [40]. Fig. 5 shows the detrended signals. At top of Fig. 5, from left to right, the EPN signals of H2SO4, NaCl, and diH2O respectively, are shown. At bottom of Fig. 5, from left to right, the ECN signals of H2SO4, NaCl, and diH2O respectively, are shown. As can be seen in Fig. 5, the EPN and ECN of H2SO4 have higher noise levels compared to NaCl and diH2O, while the EPN and ECN of diH2O have lower noise levels compared to H2SO4 and NaCl. The EPN and ECN signals of NaCl have the biggest fluctuations.

4.1. Results of the analysis with the Stockwell transform-Shannon energy and the Wavelet transform This section presents the analyses to classify the type of corrosion using the ST-SSE and ST methods. Using the isolated EPN and ECN records, we established corrosion behavior according to each one of the solutions applying the ST-SSE method. To evaluate the ST-SSE method versus the WT, we use all the records to show that it is possible to distinguish the type of corrosion on the Al6061T6 according to the exposed solutions, obtaining satisfactory results. After considering the isolated records, the ST analysis was carried out, firstly on the NaCl solution, afterward on the three solutions H2SO4, NaCl and diH2O. Finally, in Section 4.1.2, based on experimental data and using the Lagrange interpolation algorithm, we present the energy threshold that corresponds to each corrosion type. 4.1.1. Corrosion type analysis using the EPN signals To determinate the corrosion type of NaCl based on the ST-SSE method, an analysis using three different records of the EPN signal of the Al6061T6 exposed to a NaCl solution was carried out (see Fig. 6). The first record (1R, green line) corresponds from time 7.96 h to 8.53 h, the second one (2R, blue line) was from time 11.95 h to 12.52 h, and the third record (3R, red line) corresponds from time 16.50 h to 17.07 h. These three records were selected because each one represents a

50

40

2

0

20

1

-50

0

0

-100

-20

-1

-150

-40

-2

H2SO4

diH2O

NaCl

150

0.01

2

100

0.005

Current ( A)

1 50

0 0

0 -50 100

200

300

400

500

-0.005 -0.01

-1 10

15

20

25

10

15

Time (h)

Fig. 5. Detrended EPN and ECN signals of the Al6061T6 exposed to the three solutions.

53

20

25

Journal of Electroanalytical Chemistry 836 (2019) 50–61

O.J. Ramos-Negrón et al.

0.04 −0.008 −0.01 −0.012 −0.014 −0.016 −0.018

0.03

12

Potential (V)

0.02

12.1

12.2

12.3

12.4

12.5

0.01 0 −0.01 −3

−0.02 −0.03

x 10 0 −5 −10 −15 16.5

0.03 0.025 0.02 8

8.1

−0.04

8.2

8.3

8.4

8.5

10

16.6

15

16.7

16.8

16.9

20

17

25

Time (h)

Fig. 6. EPN signals of the Al6061T6 exposed to the NaCl solution.

different type of corrosion according to LI criteria showed in Fig. 3. In this sense, these three isolated records were analyzed using the ST-SSE method, determining the energy levels that correspond to each corrosion type as shown in Fig. 7. The green line corresponds to the STSSE analysis made on the 1R record for mixed and localized corrosion. The blue line represents the corrosion analysis made on the 2R record for mixed corrosion. Finally, the red line represents the 3R record analysis for localized corrosion. Once the corrosion type was correlated according to the energy level criteria and denoted by the green, blue and red lines, the ST-SSE analysis was carried out on the records from 11 to 50 (from time 5.68 h to 28.44 h), this analysis is represented by the black boxplots of Fig. 7. It is possible to appreciate in the figure that in almost all frequencies the mixed corrosion prevails. However, some events of localized corrosion occur at all frequencies. Table 2 contains the obtained results from the ST-SSE analysis made on the records 1R, 2R, and 3R for each frequency range, the results correspond to the showed in Fig. 7. The records 1R, 2R, and 3R correspond to the isolated records above-mentioned in Section 4. The first, second and third rows of Table 2 show the energy behavior of the records 1R, 2R, and 3R, respectively. The yellow bar in the table means the contribution of energy of each record at each frequency range. The values of energy in 1R at high and medium frequencies are very similar to the 2R behavior, this is congruent since 1R and 2R contain mixed corrosion. However, from the 7.8–15.6 to 0.4 –0.9 mHz

frequency ranges, 1R has a higher energy level than 2R and 3R which is also congruent, since the 1R record was taken from the threshold between mixed and localized corrosion, so 1R contains localized corrosion. The energy behavior of the record 2R remained with the lowest energy levels in comparison with the 1R and 3R records in almost all frequency ranges, however, in the frequencies from 250 to 500, 125–250 mHz, and 62.5 –125 mHz, the 2R energy is slightly bigger than in 1R. The record 2R has slightly bigger energy than 3R only from 3.9 mHz to 7.8 mHz. It could mean that even when almost there is mixed corrosion, also there is localized corrosion. The record 3R has a higher energy level than the 1R and 2R records at the following frequencies 250–500 and 7.8 –15.6 mHz, which means that there is localized corrosion on the record 3R. In Fig. 8, the behavior of the corrosion type on the Al6061T6 due to the exposure to the three solutions (H2SO4, NaCl, and diH2O) using the ST-SSE method is established. Also, a comparison of the ST-SSE with the WT analysis is presented. In Fig. 8a) and b), the blue boxplots, the black boxplots, and the red boxplots represent the datasets corresponding to the ST-SSE and WT analyses made on the Al6061T6 exposed to H2SO4, NaCl, and diH2O, respectively. These analyses were carried out considering the EPN records corresponding from time 5.68 h to 28.44 h. Comparing both results from Fig. 8 a) and b), it is possible to see that by using the ST-SSE method, a defined Shannon energy behavior

1

NaCl (11.95 to 12.52 h) NaCl (16.5 to 17.07 h) NaCl (7.96 to 8.53 h)

10

Shannon Energy

100

10

-1

10

-2

10-3

10-4

500-1000

250-500

125-250

62.5-125

31.2-62.5

15.6-31.2

7.8-15.6

3.9-7.8

1.9-3.9

0.9-1.9

0.5-0.9

Frequency (mHz)

Fig. 7. ST-SSE analysis developed on the 6061-T6 aluminum exposed to a NaCl solution. The analysis shows three different NaCl records (green, blue, and red lines) and 40 records (black boxplot). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 54

Journal of Electroanalytical Chemistry 836 (2019) 50–61

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Table 2 Energy values of the ST-SSE analysis of the EPN signals of the 1R, 2R, and 3R NaCl records. 500 to 250 to 500 125 to 250 62.5 to 1000 mHz mHz mHz 125 mHz

Record

31.3 to 62.5 mHz

15.6 to 7.8 to 15.6 3.9 to 7.8 31.3 mHz mHz mHz

1.9 to 3.9 mHz

0.9 to 1.9 mHz

0.5 to 0.9 mHz

1R, Shannon Energy of EPN signal

0.4187

0.3493

0.2405

0.1607

0.1086

0.0638

0.0551

0.0576

0.0598

0.0374

0.3433

2R, Shannon Energy of EPN signal

0.3727

0.5144

0.3546

0.1716

0.0935

0.0492

0.0203

0.0170

0.0056

0.0026

0.0177

3R, Shannon Energy of EPN signal

2.5615

3.3153

2.6029

0.9215

0.5257

0.3321

0.0619

0.0142

0.0085

0.0284

0.0144

for each solution is obtained. While applying the WT analysis, it was not possible to separate the datasets with each other. Taking into account the criteria previously defined using the ST-SSE analysis shown in Fig. 7, we correlated the corrosion type on the Al6061T6 exposed to the three solutions as follows: the exposure to H2SO4 causes generalized corrosion, the exposure to NaCl causes mixed and localized corrosion, and the exposure to diH2O generates a passivation situation. Now, in Fig. 9, the ST analysis made on the 1R record (from time 7.96 h to 8.53 h) is presented. The proposed method classifies the type of corrosion according to the frequency amplitude of the analysis. According to aforementioned about Table 2 analysis, the record 1R is classified as follows: at high and medium frequencies there is mixed corrosion, and at low frequencies mostly there is localized corrosion. So, the values in Fig. 9 allow to establish the type of corrosion, as well as, the occurrence time. From Fig. 9, three amplitude scales have been proposed to determine the type of corrosion, from 1 × 10−6 to 1 × 10−5 it is considered a material passivation, from 1 × 10−5 to 1 × 10−4 it is considered that there is mixed corrosion, and from 1 × 10−4 to 1 × 10−3 it is considered localized corrosion when isolated events of high amplitudes occur, and generalized corrosion when the events are uniform and continuous. In this sense, Fig. 9 shows that at high and medium frequencies there is mixed corrosion. Also, the figure shows that at low frequencies there is localized corrosion. An important advantage of this analysis is the possibility of detecting the time of the localized corrosion occurrences, as shown in Fig. 9 at time 387 s approximately when an isolated event of corrosion occurs. Fig. 10 shows the results of the corrosion analysis made in two different records of EPN signals from the three different solutions, each record has 4096 EPN samples. These two records were taken from times 11.95 to 12.52 h and 16.5 to 17.07 h, respectively.

Cases a), c), and e) of Fig. 10 show the corrosion analysis from the 2R record made on the Al6061T6 exposed to diH2O, NaCl and H2SO4, respectively. Cases b), d), and f) of Fig. 10 show the corrosion analysis from the 3R record made on the Al6061T6 exposed to diH2O, NaCl and H2SO4, respectively. For the next analysis, the previous analysis presented in Fig. 9 is considered. In this sense, we have observed according to the results of cases a) and b) of Fig. 10, that there is an effect of passivation on the material at low and high frequencies. Now, regarding case c), the results show that at high frequencies, there is eventually localized corrosion, however, in medium and at low frequencies mixed and localized corrosion prevails. On the other hand, in case d), the results show that at high and medium frequencies localized corrosion occurs, and in the low frequencies mixed and localized corrosion occurs. Finally, regarding cases e) and f), the analyses show generalized corrosion at high and low frequencies. 4.1.2. Corrosion type analysis using the ECN signals In this section, the corrosion analysis using the ECN records is presented. The section is structured as Section 4.1.1. First, the analysis is developed using the ST-SSE method applied to the ECN records, the method is evaluated versus WT. Afterward, the ECN records are analyzed using the ST method. Finally, based on experimental data and using the Lagrange interpolation algorithm, we present the energy threshold that corresponds to each corrosion type. To determinate the corrosion type of NaCl based on the SSE, an analysis using three different records of the ECN signal of the NaCl solution (Fig. 11) was carried out. The first record (1RC) is from time 7.96 h to 8.53 h (green line), the second one (2RC) is from time 11.95 h

SSE

100

10-5

a) Frequency (mHz) 500-1000

125-250

62.5-125

H2SO4 -5

10

31.2-62.5

15.6-32.2

7.8-15.6

3.9-7.8

1.9-3.9

0.9-1.9

0.5-0.9

d9

d10

s10

0

E d, E s

10

250-500

diH2O

NaCl

b) Crystals d1

d2

d3

d4

d5

d6

d7

d8

Fig. 8. EPN signals analysis with a) ST-SSE and b) WT. 55

Journal of Electroanalytical Chemistry 836 (2019) 50–61

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Fig. 9. ST analysis of the EPN signal of NaCl from 7.96 to 8.53 h.

to 12.52 h (blue line), and the third record (3RC) corresponds from time 16.50 h to 17.07 h (red line). These three records of ECN signals were selected because each one represents a different type of corrosion according to LI criteria showed in Fig. 3. As shown in the figure, the record 1RC is in the threshold between mixed and localized corrosion. The second record corresponds to mixed corrosion, and finally, the third record corresponds to localized corrosion, according to the LI criteria. These three records were analyzed using the ST-SSE method, determining the energy levels that correspond to each corrosion type as shown in Fig. 12. In green line, the ST-SSE analysis developed in the record 1RC is represented, the analysis developed on the record 2RC for mixed corrosion is represented in blue line, finally the record 3RC analysis for localized corrosion is shown in red line. Table 3 contains the numerical results showed in Fig. 12, both table and figure show the obtained results from the ST-SSE analysis made on the 1RC, 2RC, and 3RC records. The first, second and third rows of Table 3 show the energy behavior of the records 1RC, 2RC, and 3RC, respectively. The yellow bar in the table means the contribution of energy of each record at each frequency range. The results shown in Table 3 are explained below:

•

•

1RC register was taken from the threshold between mixed and localized corrosion. Therefore, 1RC contains localized corrosion, just as it occurs in the green region of Fig. 17, which corresponds to the localized corrosion presented at low frequencies, 1RC of Table 3. In the photo, it is shown that the size of the pitting in the green region is approximately 50 μ m. On the other hand, the energy behavior of 2RC is maintained with energy levels lower than 1RC and 3RC in almost all frequency ranges, however, at the frequency ranges 500–1000, and 250–500 it is slightly higher than 1RC, but its energy level is never higher than the 3RC energy level, it could mean that there is mixed corrosion and localized corrosion. Finally, the record 3RC has higher energy levels than the 1RC, and the 2RC at the frequency ranges from 500–1000 to 7.8 –31.3 mHz, as well as, in 0.9 –1.9 mHz, it confirms localized corrosion (see the red line of Fig. 12.)

In Fig. 13, the behavior of the corrosion type on the Al6061T6 due to the exposure to the three solutions (H2SO4, NaCl, and diH2O) is established using the ST-SSE method. Also, a comparison of the ST-SSE with the WT analysis is presented. In Fig. 13a) and b), the blue boxplots, the black boxplots, and the red boxplots represent the datasets corresponding to the ST-SSE and WT analyses made on the Al6061T6 exposed to H2SO4, NaCl, and diH2O, respectively. These analyses were carried out considering the ECN records corresponding from time 5.68 h to 28.44 h.

• The energy behavior of the record 1RC shows that at high and

medium frequencies it is very similar to the record 2RC, this is congruent since 1RC and 2RC contain mixed corrosion, however, from the frequency ranges 7.8–15.6 to 0.5 –0.9, 1RC has a higher energy level than 2RC and 3RC, which is also congruent because the

Fig. 10. ST analysis using the EPN signals of diH2O (top), NaCl (middle) and H2SO4 (bottom) from times 11.95 to 12.52 h, and 16.5 to 17.07 h. 56

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1.5

x 10

−7

−7

x 10

x 10 4 2

−2

1

0

−4

−2 8

8.1

8.2

8.3

8.4

8.5

−4 16.5

16.6

16.7

16.8

16.9

17

Current (A)

0.5

0 −7

x 10 4.5 4 3.5

−0.5

12

12.1

12.2

12.3

12.4

12.5

−1 10

15

20

25

Time (h)

Fig. 11. ECN signals of the Al6061T6 exposed to the NaCl solution. 10-6 NaCl (11.95 to 12.52 h) NaCl (16.5 to 17.07 h) NaCl(7.96 to 8.53 h)

-7

10

Shannon Energy

10-8 10-9 -10

10

-11

10

10-12 10-13

500-1000

250-500

125-250

62.5-125

31.2-62.5

15.6-31.2

7.8-15.6

3.9-7.8

1.9-3.9

0.9-1.9

0.5-0.9

Frequency (mHz)

Fig. 12. ST-SSE analysis of the ECN, showing three different NaCl records (green, blue, and red lines) and 40 records (black boxplots). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Comparing both results from Fig. 13 a) and b), it is possible to see that by using the ST-SSE method, a defined Shannon energy behavior for each solution is obtained. While applying the WT analysis, it was not possible to separate the datasets with each other. Taking into account the criteria previously defined using the ST-SSE analysis shown in Fig. 12, we correlated the corrosion type on the Al6061T6 exposed to the three solutions as follows: the exposure to H2SO4 causes generalized corrosion, the exposure to NaCl causes mixed and localized corrosion,

and the exposure to diH2O generates a passivation on the material. Once the behavior of the different types of corrosion were established by the ST-SSE analysis for each one of the three solutions, we use the experimental data (Table 4) to develop series approximation using Lagrange Polynomial Interpolation Eq. (4) of second order to define the energy thresholds for each one of the corrosion types, the results are shown in Fig. 14. Now, in Fig. 15, the ST analysis made on the record 1RC (from time

Table 3 Energy values of the ST-SSE analysis of the ECN signals of the 1RC, 2RC, and 3RC NaCl records. Record

500 to 250 to 500 125 to 250 62.5 to 1000 mHz mHz mHz 125 mHz

31.3 to 62.5 mHz

15.6 to 7.8 to 15.6 3.9 to 7.8 31.3 mHz mHz mHz

1.9 to 3.9 mHz

0.9 to 1.9 mHz

0.5 to 0.9 mHz

1RC, Shannon Energy of ECN signal

4.76×10-08 1.73×10-08 7.34×10-09 3.34×10-09 1.58×10-09 8.15×10-10 7.81×10-10 3.50×10-10 2.66×10-10 1.62×10-10 1.76×10-09

2RC, Shannon Energy of ECN signal

5.01×10-08 1.79×10-08 7.67×10-09 2.24×10-09 7.36×10-10 2.45×10-10 7.76×10-11 2.03×10-11 5.89×10-12 5.43×10-12 3.41×10-11

3RC, Shannon Energy of ECN signal

2.90×10-07 1.95×10-07 7.46×10-08 2.35×10-08 6.25×10-09 3.47×10-09 3.05×10-10 1.33×10-10 1.56×10-10 1.63×10-10 3.70×10-10

57

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SSE

10

10-10

a) Frequency (mHz) 500-1000

250-500

125-250

62.5-125

31.3-62.5

15.6-31.3

7.8-15.6

3.9-7.8

1.9-3.9

0.9-1.9

0.5-0.9

d9

d10

s10

s

100

d

E ,E

H2SO4

NaCl

diH2O

10-10

b) Crystals d1

d2

d3

d4

d5

d6

d7

d8

Fig. 13. ECN signals analysis with a) ST-SSE and b) WT.

To develop this analysis, and to classify the type of corrosion, we propose three amplitude scales: from 1 × 10−9 to 1 × 10−8 it is considered a material passivation, from 1 × 10−8 to 1 × 10−7 it is considered that there is mixed corrosion, and from 1 × 10−7 to 1 × 10−6 it is considered localized corrosion when isolated events of high amplitudes occur, and generalized corrosion when the events are uniform and continuous. In this sense, Fig. 15 shows that at high and medium frequencies there is mixed corrosion. Also, the figure shows that at low frequencies there is localized corrosion. An important advantage of this analysis is the possibility of detecting the time of the localized corrosion occurrences, as shown in Fig. 15 at time 387 s approximately when an isolated event of corrosion occurs. Fig. 16 shows the results of the corrosion analysis made in the three different solutions using two different ECN records (2RC and 3RC), each one of the record has 4096 ECN samples. Cases a), c), and e) of Fig. 16 show the corrosion analysis from the record 2RC, made on the Al6061T6 exposed to diH2O, NaCl and H2SO4, respectively. Cases b), d), and f) of Fig. 16 show the corrosion analysis from the record 3RC, made on the Al6061T6 exposed to diH2O, NaCl and H2SO4, respectively. Taking into account the aforementioned about Fig. 15 analysis, we conclude that for cases a) and b) of Fig. 16 there is passivation of the material at low and high frequencies. Regarding case c), the analysis shows that at high frequencies, there is eventually localized corrosion, however, mixed corrosion prevails at medium and low frequencies. On the other hand, case d), the analysis shows that at high and low

Table 4 Minimum and maximum values of the Shannon energy for each type of corrosion at different frequency ranges. H2SO4

NaCl

diH2O

Minimum

Maximum

Minimum

Maximum

Minimum

Maximum

1.17E−07 3.86E−07 5.56E−07 4.61E−07 2.11E−07 1.20E−07 7.24E−08 2.64E−08 1.07E−08 1.97E−09 3.61E−09

9.23E−05 6.83E−05 5.92E−05 4.70E−05 3.24E−05 1.93E−05 9.30E−06 5.98E−06 3.59E−06 2.98E−06 9.17E−07

3.91E−08 1.34E−08 5.99E−09 1.87E−09 4.13E−10 1.52E−10 2.11E−11 8.99E−12 5.47E−12 4.08E−13 5.70E−13

3.17E−07 2.47E−07 1.15E−07 3.89E−08 1.55E−08 1.10E−08 2.52E−09 1.39E−09 1.48E−09 1.82E−09 1.29E−08

3.29E−14 1.07E−14 5.73E−15 4.53E−15 1.16E−15 5.99E−16 1.83E−16 6.19E−17 1.58E−17 1.52E−17 1.10E−18

7.83E−12 2.95E−12 3.73E−13 3.80E−13 3.01E−13 1.03E−13 7.20E−14 5.38E−14 2.27E−14 4.95E−15 2.93E−14

7.96 h to 8.53 h) is presented. The proposed method classifies the type of corrosion according to the frequency amplitude of the analysis. According to the aforementioned about Table 3 analysis, the record 1RC was classified as follows: at high and medium frequencies there is mixed corrosion, and at low frequencies mostly there is localized corrosion. So, using this knowledge, we carried out the ST analysis on the ECN record 1RC.

10

-4

10

-6

H SO 2

Shannon Energy

10

4

max NaCl min NaCl max H SO

-8

2

min H SO 2

10

-10

4

4

max diH2 O

NaCl

min di H O 2

10

-12

10

-14

max LPI H2 SO 4 min LPI H 2 SO 4 max LPI NaCl min LPI NaCl max LPI diH2 O

diH O

min LPI diH O

2

10

-16

10

-18

1

2

3

4

5

6

7

2

8

9

10

11

Frequency Ranges

Fig. 14. Areas formed by the minimum and maximum values of each one of the solutions behaviors and their approximation. 58

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Fig. 15. ST analysis of the ECN signal of NaCl from 7.96 to 8.53 h.

Fig. 16. ST analysis using the ECN signals of diH2O (top), NaCl (middle) and H2SO4 (bottom) from times 11.95 to 12.52 h and 16.5 to 17.07 h.

frequencies localized corrosion occurs, and in low frequencies mixed corrosion prevails. Finally, regarding cases e) and f), the analyses show generalized corrosion at high and low frequencies. Finally, Fig. 17 shows the effect of H2SO4, NaCl, and diH2O solutions on the Al6061T6. From left to right of Fig. 17, the electrodes exposed to H2SO4, NaCl, and diH2O are shown. As can be seen in the figure, the electrodes exposed to the H2SO4 solution had generalized corrosion since aggressive pitting in all material surfaces can be seen. The electrodes exposed to the NaCl solution had mixed and localized corrosion. In almost all material surfaces, events of corrosion around 23 μm can be seen, however, in some specific area, there was pitting events around 50 μm. Finally, the electrodes exposed to the diH2O solution had no corrosion effects since the metal had passivation.

analysis, it is clear that these behaviors can be identified better with the ST-SSE, Figs. 8a) and 13a). Using the WT analysis, it was difficult to identify the corrosion behaviors of each one of the solutions, Figs. 8b) and 13b). 6. Conclusions In this paper, a method to analyze the corrosion type in Al6061T6 exposed to three different solutions are presented. This strategy consisted of analyzing the EN signals by using the ST-SEE method. The results of the analysis allowed to find a correlation between the type of corrosion and the SSE, as well as with the amplitude of the ST frequency. The SSE analysis showed that the material passivation is related to the low SSE, the energy levels vary depending on the analyzed frequency. In the ST analysis, passivation corresponds to low amplitudes. Also, it is shown that the localized corrosion is related to high SSE energy and high amplitudes. In this work, the regions for the corrosion type (passivation material, mixed corrosion, and localized corrosion) were established. The WT analysis didn’t give relevant information about the Al6061T6 corrosion type, which justifies the proposed method. The ST has the advantages of a good time-frequency resolution (better than the Fourier transform, the Short-Time Fourier transform and also the WT) and the possibility of filtering the signals. ST showed to be a useful technique in EN signals analysis due to nonstationary nature. In addition, compared to the WT, the ST provides

5. Discussion After developing the analysis of the EPN and ECN signals with the LI, ST-SSE, WT, and ST methods, it is concluded that the ST-SSE method has advantages compared to the LI and the WT. Although the LI method can determine the type of corrosion in the analysis using the acid solution, the test had to be extended more than 245 h to reach LI values which specify generalized corrosion on the metal, Fig. 4. But, applying the ST-SSE analysis, the first 28 h of the test was sufficient to determine the presence of generalized corrosion. Also, comparing the corrosion type behaviors obtained using the WT analysis versus the ST-SSE 59

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2

4

2

Fig. 17. Surfaces of the Al6061T6 electrodes before and after the tests.

values of magnitude and not only the decompositions by frequency ranges. However, a disadvantage of ST transformation is that it requires a high computational cost.

[9]

Acknowledgments

[10]

Oscar Jaime Ramos Negrón would like to thank to CONACyT (Consejo Nacional de Ciencia y Tecnología de México), and ITSCH (Instituto Tecnológico Superior de Las Choapas) for the support given during the development of their Ph.D.’s thesis. José Hugo Arellano Pérez would like to thank to CONACyT (Consejo Nacional de Ciencia y Tecnología de México) for the support given during the development of their Ph.D.’s thesis. The authors would like to thank PRODEP, Tecnológico Nacional de México and CENIDET for the support to develop this work. José Francisco Gómez Aguilar acknowledges the support provided by CONACyT: cátedras CONACyT para jóvenes investigadores 2014.

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