Saeed Reza Allahkaram School of Metallurgy and Materials Engineering, University of Tehran, Tehran, Iran, and

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1 Applicatio of the iverse wavelet trasform o electrochemical curret sigals to demostrate the essece of high-frequecy variatios Mehdi Khodayari School of Metallurgy ad Materials Egieerig, Uiversity of Tehra, Tehra, Ira ad Departmet of Mechaical Egieerig, Uiversity of South Florida, Tampa, Florida, USA Saeed Reza Allahkaram School of Metallurgy ad Materials Egieerig, Uiversity of Tehra, Tehra, Ira, ad Alex A. Volisky Departmet of Mechaical Egieerig, Uiversity of South Florida, Tampa, Florida, USA Abstract Purpose Oe way to aalyze electrochemical sigals is the wavelet trasform, which trasforms a sigal ito aother represetatio whereby the sigal iformatio is preseted i a multi-scale maer. Usig the iverse wavelet trasform, it is also possible to split a sigal ito differet compoets of differet frequecy itervals. The iverse wavelet trasform is the cocept uderpiig this paper, the aim of which is to demostrate that high-frequecy variatios i curret sigals are as valuable as low-frequecy variatios. Desig/methodology/approach The set-up for the experimets carried out cosisted of two idetical carbo steel workig electrodes exposed to simulated cocrete pore solutio, sparged simultaeously with SO 2 ad CO 2. The correspodig electrochemical curret sigal was studied usig wavelet trasform. Fidigs High-frequecy compoets of curret sigals are as iformative as low-frequecy compoets. High-frequecy variatios could show some electrochemical activities that are ot obvious i the other parts. Origiality/value This paper shows that high-frequecy variatios ca be take ito cosideratio alog with low-frequecy variatios, sice both ca provide complemetary iformatio about electrochemical activities. Keywords Trasforms, Electrochemistry, Eergy techology, Frequecy distributio charts, Frequecies Paper type Research paper 1. Itroductio The curret issue ad full text archive of this joural is available at Ati-Corrosio Methods ad Materials 57/2 (21) q Emerald Group Publishig Limited [ISSN ] [DOI 1.118/ ] Electrochemical oise measuremet is used to ivestigate the corrosio behavior of metals i differet eviromets ad ca provide fudametal iformatio about the ature of corrosio processes. I several cases, this method provided useful iformatio about electrochemical activities that would have bee difficult to discer usig other covetioal methods (Zhag et al., 27; Kovač et al., 27; Lafrot et al., 27). Electrochemical curret oise is typically measured by moitorig the curret flowig betwee two symmetric electrodes usig a zero resistace ammeter, which maitais the two electrodes at the same electroic potetial (Iverso, 1968). Two mai methods ca be used to aalyze electrochemical oise, amely sequece-idepedet methods, usually referred to as statistical methods, ad sequecedepedet methods (Cottis, 21). The wavelet trasform is a relatively ew mathematical tool, which is classified as a sequece-depedet method ad was used i this study. Givig better approximatio to trasiet or localized pheomea tha covetioal methods (Resikoff ad Wells, 1997), the wavelet trasform appears to be appropriate for aalysis of electrochemical oise sigals due to their dyamic ature. The wavelet trasform was first applied to oise aalysis by Aballe et al. (1999). I this method, little wavelike fuctios referred to as wavelets are utilized. A wavelet is maipulated i two ways: a wavelet with a particular width moves to various locatios of the sigal ad is stretched or squeezed after which it agai spas the sigal (width of the sigal is a iteger multiplicatio of the maipulated wavelet). The largest wavelet is half the legth of the origial sigal ad the shortest oe is twice loger tha the distace betwee two cosequet data poits. The wavelet at a specific scale ad locatio is compared with the correspodig portio of the sigal ad if it matches the shape of the sigal well, a large trasform value is obtaied ad vice versa. The trasform values are computed at various locatios of the sigal ad for various scales of the wavelet so that all of the iformatio i the sigal is trasformed ito trasform values. 65

2 Iverse wavelet trasform o electrochemical curret sigals Mehdi Khodayari, Saeed Reza Allahkaram ad Alex A. Volisky There are two kids of the wavelet trasform icludig the cotiuous wavelet trasform (CWT) ad the discrete wavelet trasform (DWT) (Aballe et al., 1999). I the CWT, the trasform at various locatios of the sigal ad for various scales of the wavelet is computed i a smooth cotiuous fashio, while i the DWT it is computed i discrete steps. I geeral, DWT represets a sigal i the form of a hierarchical structure. A hierarchical structure orgaizes a sigal ito categories called levels so that the higher a level is, the fewer the umber of members (coefficiets) it cotais (Resikoff ad Wells, 1997). I classical DWT, orthogoal wavelet trasform (OWT) is the mathematical tool used i this study to aalyze electrochemical curret sigals. I this method, time record x(t) (t ¼ 1,..., N) is expressed by its correlatio degree with a basis composed of oscillatig fuctios of a limited time spa. The basis fuctios f j, ad c j, are geerated from a pair of fuctios called father wavelets (f) ad mother wavelets (c), through scalig ad traslatio, as follows: f j; ðtþ ¼2 2j=2 fð2 2j t 2 Þ ¼2 2j=2 f t 2 2j 2 j ð1þ c j; ðtþ ¼2 2j=2 cð2 2j t 2 Þ ¼2 2j=2 c t 2 2j 2 j ð2þ where N is the umber of recorded data samples, ¼ 1, 2,..., N/2, j ¼ 1, 2,..., J ( J is ofte a small atural umber that depeds maily o f, c ad ). I OWT, a sigal x(t) is trasformed ito J þ 1 sets of coefficiets (s J,, d J,,..., d 1, ), ad each set is called a crystal. Every coefficiet is the ier product of a wavelet (basis fuctio) ad the correspodig segmet of the sigal. Thus, each wavelet coefficiet measures the correlatio betwee the wavelet ad the correspodig portio of the sigal (Aballe et al., 1999). Eergy distributio (ED) correspodig to each crystal could be measured through equatios (3) ad (4). This quatity measures relative cotributio of fluctuatios with differet itervals of frequecies i the origial sigal: ED d j ¼ 1 E ED s J ¼ 1 E XN=2 j d 2 j; ¼1 XN=2 J s 2 J; ¼1 where E is the overall eergy of the sigal, ad is calculated as: E ¼ XN x 2 ¼1 The sigal ca be also recostructed by addig together the cotributig wavelets weighted by their correspodig coefficiets accordig to: X X xðtþ ¼ sj; f J; ðtþþ dj; c J; ðtþ X X ð6þ þ dj21; c J21; þ þ d1; c 1; ðtþ Furthermore, ew series of H j or H s, which are frequecy filtered sigals, ca be created accordig to equatios (7) ad (8). Each series is a filtered sigal, which resembles ð3þ ð4þ ð5þ fluctuatios of the mai sigal at a particular iterval of frequecies (e.g. H i represets all variatios of the iitial sigal betwee levels i ad i 2 1, ad H s represets all variatios above level J ): X H i ¼ di; c i; ðtþ ð7þ X H s ¼ sj; f J; ðtþ where i ¼ 1, 2,..., J. Here, the maipulated series from either equatios (7) or (8) is referred to as partial sigal (PS) (Allahkaram ad Khodayari, 28). I this study, the emphasis is o the importace of high-frequecy PS, which appears to be a domiat compoet of the curret sigal activities. For this aim, PSs with domiat activities are recogized from their ED values (higher ED amplitude shows more sigificat cotributio of the correspodig PS i the origial sigal), ad the they are recostructed usig the iverse wavelet trasform (Allahkaram ad Khodayari, 28). The iformatio that a PS could provide is discussed here. 2. Experimetal procedure Experimetal procedure i this study is exactly the same as i the earlier paper (Allahkaram ad Khodayari, 28), except that here the measuremets were carried out at ph values of 12.5, 11.6, 1.8, 8.6, ad 7.5, ad the stadard deviatio values of PSs were ot computed. 3. Results Figures 1 ad 2 show the curret sigals at various ph values ad the resultig eergy distributio plot, respectively. I Figure 2(a), the highest ED value correspods to crystal s7, which is related to the low-frequecy variatios of the sigals. I order to gai some iformatio about highfrequecy variatios, the crystal s7 is left out ad the remaiig ED values are re-plotted, as show i Figure 2(b). Accordig to Figure 2(a) ad (b), it ca be observed that the highest values of ED were at s7 ad d1 crystals. These peaks must be represetative of prevailig electrochemical activities i the system. To examie these probable electrochemical activities, PSd 1 (PS with frequecies iterval correspodig to crystal d1) ad PSs 7 (PS with frequecies iterval correspodig to crystal s7) at all experimetal ph values were obtaied ad are show i Figure Discussio Ati-Corrosio Methods ad Materials Volume 57 Number PSs 7 shows low-frequecy compoets of a curret sigal, which ca be attributed to variatios of the electrodes potetial gradiets, causig the curret to flow i the closed circuit. For istace, at ph 12.5 util 9 s, PSs 7 shows fluctuatio i the curret sigal as a cosequece of successive potetial chage betwee the electrodes. After 9 s electrodes potetial differece is quite small, which has led to a miute curret flow betwee the electrodes. At ph 1.8 ad below, likewise, PSs 7 could idicate progressive deterioratio of the electrodes, resultig i potetial chage betwee the electrodes ad lack of PSs 7 stability. O the other had, PSd 1 shows high-frequecy compoets. PSd 1 could be attributed to the activity of ð8þ 66

3 Iverse wavelet trasform o electrochemical curret sigals Mehdi Khodayari, Saeed Reza Allahkaram ad Alex A. Volisky Ati-Corrosio Methods ad Materials Volume 57 Number Figure 1 Electrochemical sigals obtaied at various ph values Curret (ma).1 ph = Curret (ma).5.5 Curret (ma).2.4 ph = 1.8 Curret (ma) Curret (ma) Figure 2 ED values ED 1 ph = 12.6 ph = ED.4.2 ph = 12.6 ph = 1.8 d1 d2 d3 d4 d5 d6 d7 s7 Crystals (a) Notes: (a) At all crystals; (b) at crystals below s7 d1 d2 d3 d4 d5 d6 d7 Crystals (b) primary electrochemical couples o the electrodes. Primary electrochemical couples are geerated as a result of the differece i the structure ad chemical compositio of the grais i a ferrous metal (Legrad ad Leroy, 199). Formatio of such a couple is followed by curret flow betwee two poles of the couple, which are potetially differet. The aodic ad cathodic positios of the poles are iterchageable amog differet locatios o the electrodes ad chages i their positio occur quickly, leadig to simultaeous, immediate flow of the curret amogst differet locatios o the surfaces of the electrodes. I fact, PSd 1 portrays parts of the curret flowig amogst aodic ad cathodic areas of the primary electrochemical couples o the electrodes. From PSd 1 at ph 12.5 util 9 s, it ca be cocluded that the formatio of a uique passive layer o the electrodes is accompaied by relatively itese activity by the primary electrochemical couples. PSd 1 s after 9 s at ph 12.5 also shows that the itese activity of the primary couples has bee suppressed ad that a protective passive oxide layer has formed o the electrodes; PSd 1 at ph 11.6 shows similar behavior. Corrosio products were ot observed at ph 12.5 ad 11.6, which corroborates the hypothesis that there is a passive layer o the electrodes at these ph values. At ph 1.8 ad below, however, corrosio products were observed ad it is a sig of passive layer breakdow. At ph 1.8 ad below, PSd 1 registers similarly the activity of the primary couples, but here the activity itesity is lower tha was that observed durig the iitial stages of PSd 1 at ph A oteworthy poit is that i compariso to PSd 1 of curret sigals obtaied at ph 1.8 ad below, the variatio itesity of PSd 1 at ph 12.5, at the sigal portio before 9 s, is quite higher. This differece ca be attributed to the fact that whe a passive layer is to form o a aodic area, the extet of the curret flowig betwee the couple of aodic ad cathodic areas has to pass a threshold. I other words, at ph 12.5, it is the itese activity of the primary electrochemical couples that assures passage of the curret through the threshold value that leads to the passive layer formatio. At ph 1.8 or below, however, the primary couple s activity is ot sufficiet to guaratee the formatio of a passive layer o the electrodes, cosequetly leadig to cotiuig corrosio activity. 67

4 Iverse wavelet trasform o electrochemical curret sigals Mehdi Khodayari, Saeed Reza Allahkaram ad Alex A. Volisky Ati-Corrosio Methods ad Materials Volume 57 Number Figure 3 PSd 1 ad PSs 7 at differet ph values Curret (ma) Curret ( ma) Curret ( ma) Curret (ma) Curret (ma) PSd 1 at ph PSd 1 at ph 12.5 PSs 7 at ph PSd.5 1 at ph 11.6 PSs 7 at ph 11.6 PSd 1 at ph 1.8 Curret (ma) Curret (ma) Curret (ma) Curret (ma) Curret (ma).5.2 PSd 1 at ph PSs 7 at ph PSs 7 at ph 8.6 PSs 7 at ph 1.8 All of these results demostrate that high-frequecy compoets of curret sigals are as iformative as lowfrequecy compoets. Arguably, high-frequecy variatios could show some electrochemical activities that otherwise may ot be evidet. 5. Coclusio Whe evaluatig electrochemical curret sigals, while it is possible to gai iformatio pertiet to electrochemical activities from low-frequecy compoets, it is also feasible to observe additioal pheomea by scrutiizig highfrequecy compoets. To do so, the PSs of curret sigals ca be maipulated usig a wavelet trasform-based iverse trasform. I this study, the results of this methodology cofirmed that high-frequecy variatios could show some particular electrochemical activities that are quite differet to those observed from low-frequecy variatios. I cosequece, it is cosidered that high-frequecy variatios also should be take ito cosideratio as they ca provide further iformatio about the electrochemical activity. Refereces Aballe, A., Bethecourt, M., Botaa, F.J. ad Marcos, M. (1999), Usig wavelets trasform i the aalysis of electrochemical oise data, Electrochimica Acta, Vol. 44 No. 26, pp Allahkaram, S.R. ad Khodayari, M. (28), Electrochemical oise aalysis of carbo steel i simulated cocrete pore solutio affected by CO 2 ad SO 2 usig wavelet trasform, Ati-Corrosio Methods ad Materials, Vol. 55 No. 5, pp

5 Iverse wavelet trasform o electrochemical curret sigals Mehdi Khodayari, Saeed Reza Allahkaram ad Alex A. Volisky Cottis, R.A. (21), Iterpretatio of electrochemical oise data, Corrosio, Vol. 57 No. 3, pp Iverso, W.P. (1968), Trasiet voltage chages produced i corrodig metals ad alloys, Joural of Electrochemical Society, Vol. 115 No. 6, pp Kovač, J., Leba, M. ad Legat, A. (27), Detectio of SCC o prestressig steel wire by the simultaeous use of electrochemical oise ad acoustic emissio measuremets, Electrochimica Acta, Vol. 52 No. 27, pp Lafrot, A.M., Ghali, E. ad Morales, A.T. (27), Corrosio behavior of two bipolar plate materials i simulated PEMFC eviromet by electrochemical oise techique, Electrochimica Acta, Vol. 52 No. 15, pp Ati-Corrosio Methods ad Materials Volume 57 Number Legrad, L. ad Leroy, P. (199), Chapter 2: Water i Cotact with Ferrous Metals, Prevetio of Corrosio ad Scalig i Water Supply Systems, Ellis Horwood, Chichester, pp Resikoff, H.L. ad Wells, R.O. (1997), Chapter 3: Wavelets: A Positioal Notatio for Fuctios, Wavelet Aalysis ad the Scalable Structure of Iformatio, Spriger, New York, NY, pp Zhag, T., Shao, Y., Meg, G. ad Wag, F. (27), Electrochemical oise aalysis of the corrosio of AZ91D magesium alloy i alkalie chloride solutio, Electrochimica Acta, Vol. 53 No. 2, pp Correspodig author Saeed Reza Allahkaram ca be cotacted at: akaram@ut.ac.ir To purchase reprits of this article please reprits@emeraldisight.com Or visit our web site for further details: 69