Electrochemical noise techniques have been used to study corrosion related processes since the early 1980's. Preliminary studies of the electrochemical characteristics of localised corrosion phenomena, in particular pitting and cavitation attack, established the sensitivity of the technique for the detection of spontaneous changes in corrosion processes. Throughout the last sixteen years, the fundamental principles and methodology behind the measurements has changed little, but with the advent of the computer age, improved data acquisition, signal processing, and fast analysis techniques have enabled the technique to be routinely used in the field. The evolution of electrochemical noise monitoring techniques is reviewed with relation to the development of electrochemical noise measurement for metallic corrosion, and the analysis and interpretation of the observed noise response. Practical site applications have been an intrinsic part of the evolutionary process, and the development of the technology is discussed with relation to the database obtained for a wide variety of corrosion circumstance.

Keywords: Electrochemical noise, localised corrosion, general corrosion, corrosion monitoring.

"Every truth passes through three stages before it is recognised. In the first it is ridiculed, in the second it is opposed, in the third it is regarded as self evident." Arthur Schopenhauer.

Acceptance of the electrochemical noise technique is by no means universal, although in practical terms it has been successfully used for many years to help mitigate corrosion problems in situations where the rather more conventional electrochemical techniques are not applicable. In the stages of recognition it is somewhere between the second and third hurdles.

It was observed many years ago, that certain types of corrosion processes, in particular localised corrosion phenomena, had characteristic signatures. Changes in the free corrosion potential could be observed and correlated with localised attack. In itself, this proved to be a practically useful tool, and could be used to identify changes in the behaviour of materials in particular environments. However, it could only be used to monitor changes in the corrosion mechanism, and gave little indication of the kinetics of the processes involved. The term "electrochemical noise" was coined to describe the spontaneous fluctuations in the potential with time. This terminology has inevitably led to certain mis-interpretation, since the "noise" is usually measured at relatively low frequencies, and is not an acoustic signal. Enhancement of the measurement techniques, resulted in the simultaneous measurement of current and potential noise signals associated with the evolving corrosion processes. It was discovered that the response observed in certain circumstances could be analysed and correlated with other electrochemical techniques such as polarisation resistance, electrochemical impedance and harmonic analysis. This, in itself, has led to a wider acceptance and use of the technique in the last few years.

Unfortunately classical electrochemical theory does not take into account the dynamic nature of naturally evolving electrochemical processes such as corrosion, and much of the development of the measurement techniques was based upon an empirical understanding of the fundamental processes involved. In short the theory behind the observations of particular types of corrosion processes and kinetics was particularly lacking. This, in itself, is perhaps more understandable from an experimentalists viewpoint, where the observations he makes either fall neatly into some particular pattern, or alternatively, do not. It does not mean that the observations are useless, rather that the understanding of the system behaviour is incomplete. It is perhaps much a fault of classical education that we often attempt to reduce our observations to a series of simple equations in an attempt to classify certain types of behaviour. There are parallels to this situation in all areas of the sciences, and there is much recently published material regarding phenomena similar to electrochemical noise. The study of probability, random variables, stochastic processes, fractal dimensions, percolation theory, & etc. all have some relevance to the overall interpretation of the observed electrochemical noise signals, and may be used to provide information about the system being studied.

HISTORICAL

The foundations of electrochemical noise technology lie in original work undertaken by Iverson(1), who studied transient voltage changes produced in corroding metals and alloys using fairly rudimentary instrumentation, and who subsequently published in 1968. At the time it was seen to be more of a scientific curiosity than a technique which would find use as a corrosion monitoring tool. Interest in the use of electrochemical techniques in the late 1970's led to a flurry of activity in the field of electrochemical impedance and harmonic analysis, which were seen as natural extensions to polarisation studies. In part this activity was due to changes in instrumentation (the onset of digital electronics) and to the newly available desk top computers. Blanc et al(5,6) undertook some fundamental electrochemical noise studies of anodic dissolution and electrodeposition processes. During this time the practical aspects of electrochemical noise were also revisited in some work carried out at UMIST on cavitation and pitting attack. This latter work led to the original electrochemical noise patent application by Hladky(2) which dates back to January 1981, and it is stated in this document that "..the purpose of the invention is for the monitoring of corrosion using potential measurements between the metallic article of interest and a second reference electrode." The principle of non-perturbation of the system (for example it is not necessary to disturb the system by applying a current or voltage signal) is intrinsic to the methodology described. The voltage measurement was then used to provide an indication of the corrosion of the material under test. In the case of electrochemical noise measurements the voltage measured is, or is a function of, the corrosion potential of the test specimen and is a result of naturally occurring reactions, for example metal dissolution and hydrogen evolution and/or erosion of the electrode under the effects (such as cavitation) in the electrolyte such as occurs in high velocity fluid systems. The potential difference between the two electrodes is a voltage noise signal, which fluctuates at rather low frequency. Hladky states in this document that "..the highest component frequency worth observing appears not to exceed 10 Hz, and an appropriate range can have about 1 Hz as the upper frequency limit, though for practical purposes observation of the range of component frequencies between about 1 mHz and 100 mHz appears satisfactory. The voltages observed are low and require measurement to a resolution of microvolts, and accordingly the voltmeter must be very sensitive". Methodologies for analysis of the potential signals are detailed including, statistical analysis and frequency domain transforms. In the patent document it is stated that; "except for very small electrodes, it appears that the voltage is independent of the surface area of the electrode exposd to the electrolyte, and that the voltage measured corresponds to the maximum rate of corrosion occurring at any instant at any part of the surface of the first electrode in a general area close to the second electrode".

In parallel with the studies of potential noise, work was being undertaken to understand the phenomenon of coupling current and associated current noise signals arising from the galvanic coupling of nominally identical materials. Conventional electrochemical theory would appear to discount the existence of such coupling currents, although practically these currents are finite. Ultimately this led to a further patent application in 1986 (Eden et al(3)), which described a method and apparatus for the detection of localised corrosion using current noise measurements. Also outlined in this patent is the concept of electrochemical noise resistance or impedance which may be derived by comparing the potential and current noise signals. The concept of noise impedance was further developed leading to a patent(4) filed in 1991 which described a method and apparatus for producing electrochemical impedance spectra using the spontaneous electrochemical potential and current noise signals.

Patents aside, the technology has been practically applied over the last 15 years to a wide variety of corrosion related problems in major industrial sectors such as, oil and gas, fossil fuel power generation, petrochemicals, nuclear power, and aerospace industries. Specific problems studied have included general corrosion, pitting corrosion, transgranular stress corrosion cracking (TGSCC), intergranular stress corrosion cracking (IGSCC), coatings degradation, chemical cleaning, corrosion under fouling, microbiologically induced corrosion (MIC), preferential weld corrosion, crevice corrosion, cavitation and erosion corrosion. In recent years the focus for the application of the technology has been towards mitigation of corrosion damage in plant by continuous monitoring and feedback of corrosion related information to plant operators to enable remedial or corrective action to be taken to reduce the impact of corrosion related incidents.

I. PRACTICAL NOISE MEASUREMENTS

The following section is concerned with the more practical aspects of electrochemical noise measurements and is included in order that the reader will appreciate the methodology adopted for electrochemical noise measurements. It is recognised that measurements can be made with a wide variety of instrumentation, and therefore, the approach adopted is one of a modular nature, which will be applicable to a wide variety of instrumentation. The systems described will assume that digital signals processing techniques will be used, in conjunction with data acquisition, analysis and control software packages.

Several issues are of importance from the instrumentation aspects. In particular a knowledge of the intrinsic noise of the instrumentation itself is required, as is immunity to adventitious noise arising from external sources. Test methods are suggested which may be used to ascertain both the baseline noise levels and, the correct operation of the system.

In order to make effective measurements in the laboratory, attention must be paid to experimental design, in particular to; electrode size (dependent on the corrosion processes being monitored), orientation, environment, stress & etc. Reference will be made to particular examples of typical corrosion systems.

For use in plant monitoring situations, a similar approach is required to that for laboratory studies, where suitable sensors are required to simulate the performance of critical parts of the plant, and sensor design is therefore discussed in some detail.

System description

The system used for measuring the electrochemical noise signals will have several key components. These components will depend upon the type of noise measurements being undertaken, however, a typical schematic arrangement for the system is shown in Figure 1 below:

Figure 1. Electrochemical Noise Measurement Schematic.

The Sensors may be designed for laboratory or plant monitoring, and their design will depend on the type of noise measurement being undertaken. It is common practice to use a three electrode cell/sensor arrangement, although the actual electrode configurations used may vary from application to application. The noise signals being measured may require some form of signal conditioning, and this is included in the Interface. For the purposes of logging data from a series of sensors a Multiplexer is often incorporated. This may be configured in two particular ways, either before or after the signal conditioning units, the latter is shown in the diagram. The Data Acquisition Unit and the Computer/Controller may be either an integrated sub-system, or separate devices.

Sensors

The sensors may be configured so as to measure either potential or current noise in isolation, or, as is more usual for simultaneous measurements.

Two typical three electrode cell configurations are shown below (Figure 2). The first illustrates a system which could be used for potentiostatic or galvanostatic control (monitoring current or potential fluctuations respectively). This type of arrangement is often used for laboratory studies, particularly for accelerated testing of material susceptibility to a variety of failure mechanisms, (e.g. SCC, pitting attack), within defined potential regimes.

Figure 2. Three electrode arrangement for potentiostatic or galvanostatic control. Comprising;

• WE - Working electrode
• RE - Reference electrode
• AE - Auxiliary electrode
• This configuration of electrodes is extensively used for electrochemical studies of systems under polarised conditions

By comparison, Figure 3 illustrates a typical configuration of electrodes which would be used for noise measurements at the free corrosion potential, such that the naturally occurring current and potential fluctuations may be monitored simultaneously. This type of arrangement is useful for the study of the evolution of naturally occurring corrosion processes and is widely used in plant monitoring/surveillance situations.

Under certain circumstances it is possible to engineer a differential working electrode arrangement such that effects of, for example, stress, differential aeration, sensitisation & etc. can be simulated. One such case would be the study of susceptibility of materials to stress corrosion cracking, in this instance the sensor arrangement would be a sample of unstressed material as one working electrode, and a sample of stressed material as the second working electrode.

Figure 3. Electrode arrangement for studies at the free corrosion potential without polarisation control.

Under certain conditions a third working electrode may be substituted for the reference electrode, particularly in plant monitoring situations where reference electrodes are impractical or are difficult to use satisfactorily. This enables simultaneous monitoring of current and potential at the free corrosion potential.

Electrode sensor / transducer arrangement examples;

Sensor design considerations.

The sensor array design depends upon the specific application and type of corrosion process being monitored. A prime consideration for the sensor array is that the elements need to be electrically isolated from each other. There are a wide variety of means by which insulation can be accomplished including; polymeric materials (for low temperature, aqueous applications), glasses (chemical inertness), and ceramics (high temperature, low pressure applications). The following factors require consideration before a particular sensor design is employed.

1. Corrosion type and rate.

The sensor array needs to be designed to take into account the type of corrosion process being monitored, and should incorporate sufficient corrosion allowance to allow long term operation. This is of particular importance if high general rates of corrosion or when localised corrosion phenomena such as pitting and SCC are operative.

2. Conductivity of environment

The current measured by the system will be directly affected by the conductivity of the environment. In many cases the corrosion rate, and hence the current measured, will be related to the solution conductivity. In certain cases, for example in organic phases, thin film condensate and high purity water systems, the corrosion rates may be high, even though the solution conductivity is low. In these cases, the effects of the solution conductivity may be minimised (although not entirely eliminated) by suitable sensor design. In particular this is often achieved by minimising the separation between the sensor elements and increasing their numbers.

3. Special requirements - application specific (location, pressure, temperature etc).

The location of the sensor and its continued operation with respect to operating temperature and pressure need to be considered. The operating environment may preclude certain types of sensor design, and therefore all materials used in their manufacture should be adequately rated for a particular end-use.

General corrosion

For studies of general corrosion, for example in low pressure, low temperature aqueous systems, relatively simple sensors may be used. For immersed conditions, standard "finger-electrode" assemblies (Figure 4) are often satisfactory, provided that the solution conductivity is relatively high. In flowing conditions, pipe "spool-pieces" may fabricated, particularly for the study of corrosion in highly turbulent regimes. This latter type of arrangement can be manufactured for operation at high temperatures and pressures.

For use in oil and gas flow-lines, sea water injection systems & etc., commercially available high pressure access fittings may be used with three or more sensing elements.

Figure 4. Typical sensor arrangement for general corrosion in laboratory studies.

Figure 5. Schematic of spool piece arrangement

Stress corrosion cracking in slow strain rate tests.

Slow strain rate tests are frequently used to compare materials for their susceptibility to SCC phenomena. The electrochemical signals associated with crack initiation/propagation (in conductive media) can be readily monitored either at the free corrosion potential or in controlled potential regimes of known susceptibility to SCC. For studies at the free corrosion potential, a standard tensile specimen may be used as one of the working electrodes (Figure 6). In order to measure the current transients which arise as a consequence of the cracking process, a secondary, unstressed working electrode is incorporated and coupled to the stressed specimen through the ZRA. The potential of the couple is usually measured with respect to a reference electrode, for example, a silver/silver chloride half cell.

Figure 6. Schematic arrangement for slow strain rate specimens.

In cases of polarisation into a known cracking regime, the current response may be monitored using a conventional three electrode arrangement (working, auxiliary and reference electrodes) with the stressed specimen as the working electrode.

Stress corrosion cracking of bulk loaded specimens

For bulk loaded specimens e.g. C-rings, reverse U-bends, three or four point bend specimens, compact tensile specimens & etc., an arrangement, such as that outlined above for slow strain rate testing, may be used in the laboratory. In plant situations, studies are usually undertaken at the free corrosion potential with a three electrode configuration, with the stressed element as the working electrode, and two unstressed elements, one for use as the secondary working electrode for current measurement and one for use as a pseudo reference electrode.

Pitting corrosion

Sensor arrays used for the detection of pit initiation and propagation have particular requirements. In the first instance, the area of the electrodes should be of sufficient size such that the probability of localised attack under the test conditions is high, this may mean that electrode areas of greater than 10cm2 may be required. The fundamental problem with systems which are prone to pitting attack, is that crevice corrosion may initiate first, and care must be taken to minimise any areas where crevice attack may initiate.

Crevice corrosion

Crevice corrosion attack in real situations is usually associated with component design and usage. For studies of material susceptibility to crevice corrosion in laboratory studies, standard crevice electrode assemblies may be used as electrodes. A typical arrangement would be to have; one working electrode with a crevice former, a second, plain, working electrode, and a reference electrode. In real plant situations, crevice attack is often associated with flanges and gasket materials. It is possible, in these circumstances, to utilise an existing flange for studies of susceptibility to crevice corrosion, by inserting blank flanges for use as electrodes. The key to this approach is to ensure electrical isolation between the blank flanges, and to build up a "sandwich" of gaskets and blank flanges. It is probably unnecessary to monitor potential fluctuations in this particular instance, since crevice corrosion is usually associated with differential cells, with the anodic corrosion process occurring within the crevice, and the cathodic process taking place externally. The current observed can often be directly related to the severity of crevice corrosion in these cases.

Coating degradation studies

The degradation of coatings and linings can be readily studied in laboratory situations. Due to the high impedance of the coatings, and for the purposes of using a representative sample, the electrode area used is typically in excess of 30cm2. For thicker coatings much larger surface areas may be required. A conventional three electrode system is employed, with two nominally identical coated specimens as the working electrodes, along with a standard reference electrode. An alternative arrangement is to have a sensor array beneath the coating, such that it is sensitive to permeation of corrosive species through the coating. In plant situations, it is usually inappropriate to have separate isolated specimens of coated material, and it is suggested that underfilm sensors be employed in these situations.

Microbioligically Induced Corrosion (MIC)

In the case of MIC, the microbiological agents are usually responsible for the production of corrosive species. In addition to the local changes in solution chemistry, there may also be some aspect of fouling of surfaces, which may lead to differential cell formation (as in crevice attack). The corrosion processes occurring in these situations are still electrochemical in nature. Sensors for this type of application are usually designed in a similar manner to those used for the study of general or pitting corrosion. Where fouling of the surface is a requirement, this may be simulated or induced by correct orientation of the sensor array.

Thin film condensate/low conductivity environments

For thin film condensate and other low conductivity bulk environments it is important to minimise the effects of the solution conductivity. In order to achieve this end a compound array of sensors is usually produced, such that the separation between the sensor elements is minimised, whilst the length of the individual sensors is maximised. Care should be used in choosing the insulating material in these cases, in particular with regard to their "wetting", since it is essential to maintain a thin, contiguous film of condensate. Materials such as fluoropolymers may not be suitable in thin film condensate applications.

Figure 7. Schematic sensor assembly for low conductivity environments.

High temperature

For high temperature applications (>300 C), organo-polymeric materials reach the limit of their usefulness and are prone to thermal degradation. In these cases, glass and ceramic materials may be used as insulators. Ionic conductivity is still required for correct operation, and the notes above for thin film conditions are often equally applicable in these cases. Other conducting phases such as molten salts or deposits may be present, and in these cases the insulating material itself may be prone to degradation, although the most aggressive situation with respect to the insulation material is likely to be conditions of very high pH.

Corrosion under fouling of heat transfer surfaces

In cooling water systems fouling of heat exchanger surfaces may occur due to a combination of high heat flux and poor water chemistry. In the absence of fouling, general corrosion is usually observed, and this may be controlled by chemical additions. When fouling is present, the heat transfer characteristics of the heat exchanger are reduced, resulting in increased tube wall temperatures. Under these conditions, local concentrations of aggressive species may accumulate and lead to pitting attack of the tube. The conditions of heat transfer can be simulated, and the effects of fouling on the corrosion processes studied, using a suitably designed sensor array. This is typically in the form of a spool piece, such as may be used for general corrosion studies, with the addition of heaters and control system to maintain a constant heat flux condition.

Interfaces.

There are basically three different types of interfaces which can be used to follow the evolution of the electrochemical processes. Standard potentiostatic / galvanostatic interface arrangements are illustrated in Figures 8 and 9 respectively, and the third is a zero resistance ammeter / potential buffer combination, Figure 10.

Figure 8. Potentiostatic arrangement for measurement of current noise at controlled potentials. In this arrangement the current is simply measured as the voltage drop across the sensing resistor R. Some potentiostats may incorporate current followers (not shown).

In the potentiostatic mode the potential of the working electrode with respect to the reference electrode is controlled to the set potential. The current required to maintain the controlled potential flows through the sensing resistor R. It is advisable in these circumstances to monitor both the potential and current in the cell, in order that the intrinsic noise arising from the potentiostat can be assessed. Evaluation of intrinsic instrumentation noise is easily achieved by substituting a resistor network for the electrode array.

In the galvanostatic mode (Figure 9), the system acts to maintain the voltage across R at the set potential, thus the current through the cell is kept at a constant value. The variation in potential of the working electrode is measured directly with respect to a reference electrode. The instrumentation component of the potential and current fluctuations can be assessed in a similar manner to that for the potentiostatic configuration by substituting a resistor network for the electrodes.

Figure 9. Galvanostatic arrangement for measurement of potential noise under constant current. In this arrangement the potential is simply measured between the reference and working electrodes.

For measurements at the free corrosion potential, it is possible to measure potential and current fluctuations together, or independently, using an interface arrangement as illustrated in Figure 10.

Figure 10. Interface for simultaneous monitoring of potential and current noise. Comprising a Zero Resistance Ammeter (ZRA) and a potential buffer/follower. If the input impedance of the data acquisition unit is sufficiently high, the potential follower may be omitted.

The ZRA acts to maintain the potentials of the two working electrodes at the same potential (with modern devices the potential difference can be maintained within a microvolt). The current required to maintain the two working electrodes at the same potential flows through the feedback resistor R, and the voltage output of the ZRA is related to the current flowing through the system by V=IR. The potential buffer is often used to ensure that there is no current drain on the reference electrode. Ideally, with no cells connected, the ZRA will give a signal of zero volts, however, intrinsic noise sources and offsets will inevitably be present. It is important to understand the limitations of such interfaces, and the baseline offset and intrinsic noise parameters should be measured as a matter of course.

Whereas it is possible to configure most potentiostats in a ZRA mode, this may not be desirable, particularly if low current values are being measured. It is advisable to use potentiostats with low noise and offset specification in all noise monitoring applications.

Instrumentation

There are many commercially available data acquisition systems (DAS), of which a few are suited to electrochemical noise measurements. Ideally the DAS unit should be able to resolve signals in the microvolt range, and have sufficient resolution to accommodate dc offset voltages which will arise if reference electrodes are used for potential measurements. A basic minimum of a 16 bit analogue to digital converter is recommended, although 20 bit converters (or better) may be required in certain circumstances. Ideally the potential and current noise signals should be measured at the same time, but slight differences in timing are not considered to be problematical. In terms of the data acquisition rate, there does not appear to be any advantage in taking measurements at high rates, and a minimum logging period of one second has been found to be satisfactory for most circumstances. At higher rates of data acquisition, the amplitude of instrumentation noise approaches the electrochemical noise levels. In addition electromagnetic interference at power supply frequencies becomes problematical. By measuring at low frequencies, it is possible to reject most spurious noise sources. The advantage of using 16 bit converter technology is that the conversion itself is sufficiently fast to allow multiplexing of inputs from a number of sensors. The major disadvantage of this type of system is the amount of data which can be generated in a short period of time. Fortunately, data storage and manipulation are facilitated by the computing power available, and it is possible to process the data either on or off-line using, for example, digital filtering techniques, statistical analysis, and frequency domain transform techniques.

The analysis of electrochemical noise signals obtained as potential and current time record series may be undertaken by a variety of means, for example;

1. Examination of the time record trace may give an indication of the types of processes occurring (general corrosion, pitting, SCC),
2. Statistical analysis may be used to derive values of the low frequency rms values of the signals and indication of localisation & etc,
3. Frequency domain transforms can provide insight into the fundamental mechanisms operative and give information about low frequency impedance of the interface & etc.
4. Fractal analysis, chaos theory etc.

Whereas the above techniques may provide an insight into the fundamental processes occurring within a single time record, this type of batch analysis is not particularly useful in plant monitoring situations, and usually involves retrospective examination of data. In addition this type of data acquisition and analysis scheme is dependent on large data storage capacity.

For corrosion control purposes, a continuous update of corrosion related information is required in order to provide operator feedback about corrosion rates and mechanisms. In order to achieve this, there must be continuous, on-line, evaluation of data, which will provide the operator with information as opposed to data. By conversion of the raw time record data into information, it should be possible to significantly reduce the amount of data stored, provided that the data can be processed at a sufficiently fast rate. This, in essence, is a requirement for an on-line expert system, where the algorithms used to detect and extract the information should be derived from a working knowledge of a variety of corrosion processes.

This section examines the different types of on-line filtering techniques which may be applied, their advantages and disadvantages, and techniques which may be applied to reduce the data storage requirements for data. In particular, digital filtering techniques are described which are particularly applicable to a variety of commercially available data acquisition systems.

1. Information extraction requirements.

The information most likely to be of use to a plant operator, is that which is related to the rates and mechanisms of the corrosion processes occurring, and if the corrosion processes are correlated with plant variables.

In essence, there are fundamentally two mechanisms which are of particular importance, these are: general corrosion, and processes involving stochastic events such as pitting and SCC. These two types of process will be examined in order to identify methods by which information, pertaining to corrosion rates and mechanisms, may be extracted.

1.1 General corrosion.

General corrosion processes may be identified by several techniques, some of which will be described here. In the first instance, the time record data for these types of processes exhibit few signs of individual uncorrelated events, i.e. there are few, if any, rapid transients. A statistical treatment of the data provides some indication of the rate and stability of the corrosion process in the short term. These types of processes have a typically Gaussian distribution of data, and examination for the types of distribution of both the current and potential data can be used to estimate if the process is indeed Gaussian. This can be a time consuming exercise, and can usually be achieved simply by examining the statistical data, particularly of the current time record. General corrosion processes can often be estimated from the moments, skewness, kurtosis, and coefficient of variance and its derivatives. Alternatively, the data may be transformed into the frequency domain. In this case the amplitudes of the signals at specific frequencies, and the slope of the frequency spectrum, can be used to distinguish between general and localised phenomena.

1.2 Localised phenomena

Localised corrosion processes, pitting and SCC in particular, are characterised by transients which may be observed in the time record data. Pit initiation, SCC phenomena etc. have characteristics which can help to distinguish between them. The basic process however is stochastic, i.e. random in nature, and therefore is essentially a Poisson process. The characteristics of Poisson processes are such that they can easily be distinguished from Gaussian processes by a variety of means, both from an appreciation of the statistics of the data, and from frequency domain information. In addition, it should be possible to differentiate between the different operative mechanisms, and to provide an indication of the severity of the corrosion problem. This can be achieved by an appreciation of how different processes contribute to the noise signals.

It should be possible therefore to provide an on-line data evaluation process, which is either;

(a) tailored for a specific application or

(b) be application non-specific.

The latter goal is desirable, but relies heavily on sufficient experience being available in order to be achieved.

2. Statistical analysis

Statistical analysis is typically undertaken on batch data, although modifications can be made to make this semi-continuous by data blocking, or by discounting of the past. For batch processing of data, the following sample statistics may be derived:

Mean

............(1)

Variance

............(2)

Third moment

............(3)

Skewness

............(4)

Fourth moment

............(5)

Kurtosis

............(6)

Standard deviation

............(7)

Coefficient of variance (C of V)

............(8)

Root mean square (rms)

............(9)

In addition to the above, another statistic has been routinely used in the analysis of current noise signals, this is the ratio of the standard deviation to the rms value of the current, referred to as Localisation Index (LI);

............(10)

This statistic has been used, since the current may exhibit a mean of zero having both positive and negative values.

The mean value of current or potential values does not provide a great deal of information in typical plant monitoring situations. The mean current value may give a very broad appreciation of the rate of the process, but generally may only be applied to provide a rough estimate of rate. The mean potential may have significance if it is measured with respect to a reference electrode, but if a pseudo reference is used this is relatively useless.

The variance of the signal relates to the power in the data, and it is more usual to use the standard deviation of the signal. The standard deviation of the signal is a measure of the spread of the data around the mean value. In essence it relates to the broadband ac component of the signal. The third central moment is a measure of the asymmetry of the data around the mean value, and the fourth moment is used to derive a value for kurtosis.

The coefficient of variance, or more usually the Localisation Index(LI), is a measure of the distribution of the data around the mean or rms value respectively. As a general rule, if the LI has a value approaching 1, the corrosion process is unstable, and therefore more likely to be stochastic. More uniform corrosion processes on the other hand have LI values which are typically of the order of 1e-3. This relates to the basic statistics of a Poisson process, where the standard deviation is equal to the mean, i.e. an LI value of 1. This is usually applied to the current data. However, slow drift in the current through zero may give an artificially high value of LI, and therefore indicate localised corrosion even though the corrosion process has a Gaussian distribution which is symptomatic of general corrosion. The LI must therefore be used with care.

Another method for the identification of changes in the distribution of the noise signals (such as occurs during localised corrosion such as pit initiation/propagation, stress corrosion cracking) is to use the calculated Kurtosis values. The value of Kurtosis reflects the distribution of the signals, and for data which exhibits spontaneous changes in amplitude distribution, the Kurtosis value will typically be >5. The value of Kurtosis will also reflect sudden changes in corrosion rate which may occur due to changes in flow rate, pH, & etc. This is probably a better approach than the use of the localisation index.

The statistics can always be calculated for existing blocks of data, but this can be inefficient in terms of use of computer memory, since all the data must be available all the time. Running mean versions of these statistics, for calculating their next or (n+1)th values, can be performed by using the following calculations successively in the given order:

............(11)

............(12)

............(13)

............(14)

............(15)

............(16)

If n = t: gives full weight to past values

min(t, n0):weights past as equivalent to n0 observations at most

n0 if t > n1 otherwise t: with n0 < n1 equivalent to overlapping runs of length n1 by amounts n0.

By computing in the given order all "n" and "n+1" suffices can be ignored i.e. can set;

............(17)

............(18)

............(19)

Note that the smallest value for n0 is zero, while the smallest value for n1 is one.

In addition to the above methods, recursive techniques, similar to those used for digital filtering, may be used.

Using recursive techniques a running mean of the data may be estimated using the formula:

............(20)

where the value of A determines the weighting for past and present values.

For the calculation of second and higher moments a similar scheme of data discounting may be used, for example the second moment may be estimated by:

............(21)

The third moment by:

............(22)

The fourth moment by:

............(23)

The values for skewness, kurtosis, coefficient of variation etc. may be derived from these moments.

The value for standard deviation can be simply derived as the square root of the second moment, or, alternatively, from the following:

............(24)

and the value of the rms of the signal from:

............(25)

alternatively, and more easily, the rms may be obtained from the absolute value of the running mean:

............(26)

The above are applicable to short term stationary processes, and the data discounting factor A, is as described in the digital filtering section.

For simultaneous current and potential noise signals, certain derivatives are used to estimate the rate and mechanism of the process(es) occurring. In particular, the resistance noise value, which is defined as:

............(27)

and the localisation index (LI) from:

............(28)

The resistance noise may be equated to a corrosion rate from a knowledge of the Stern-Geary constant, and the localisation index may be used to estimate the localised nature of the corrosion process. If a pseudo reference electrode is used (i.e. three identical electrode set-up), then the potential noise value must be corrected for this fact. The potential noise (as measured) will be the geometric mean of the sums of the uncorrelated potential noise signals, i.e.

............(29)

such that the measured potential noise signal needs to be corrected by a factor ofÖ 2:

............(30)

The current measurements need to be normalised for area, and this is usually achieved by dividing, for example the mean current, by the area of one electrode. It should be remembered that the current measured is equivalent to that flowing through one working electrode, and that the current flowing through the second working electrode is equal in amplitude but opposite in sign.

Unfortunately it is difficult to produce a continuous frequency domain transform, since this technique is better suited to batch data processing. However, this should not be totally discounted since the use of a technique such as MEM from which one can derive equivalent filter coefficients, is another method of reducing the data. Provided that the data sets are not too long, the MEM coefficients can be calculated quite rapidly.

It may prove possible to produce a limited spectral estimate on a continual basis using digital filtering techniques, described below, by assessing the bandpass characteristics at a number of discrete frequencies.

Digital filtering techniques, which are related to the statistical methods, may be used to provide data discounting. Again this may be treated on batch data or continuously with data discounting.

For a symmetrical filter response, it can be shown that the frequency response is given by:

............(31)

where ts is the time between samples. Thus the individual hk s are recognisable as the Fourier series components of the desired frequency response curve, for such a symmetrical filter the phase shift at any frequency is either zero or 180°.

Of more interest for continuous analysis with data discounting are recursive filters. The outputs of the filter are generated according to:

............(32)

This gives a low-pass response, equivalent to that of a simple first order RC low-pass filter, according to:

............(33)

where ts is the time between successive samples of the input waveform, and is equivalent to a "running mean" derived from statistics. Increasing values of A provide increased averaging of data points, for example, in order to take into account the last successive 20 input values, then A = 0.95123.

By cascading filters it is possible to provide 2nd or higher order filters. Band pass filters can be achieved by simply subtracting the outputs of two low-pass filters having different time constants, provided that the time constants are not too close together otherwise this may cause some attenuation of the filtered signal. If this technique is used it is advisable to make the filter with the longer time constant a second, third or even fourth order filter.

Band pass filters can be realised using:

............(34)

With equation 34, it can be seen intuitively that the low frequency characteristics are dependant on the low pass estimate of the mean value, and the value of A is important in determining the overall high pass characteristics, such that if A=0 then the high pass function is determined solely by the estimate of the mean, whereas as A increases in value the high pass 3dB point moves to lower frequencies.

It has been shown in the above how data may be manipulated in a variety of different manners. For the purposes of extracting information from the data, we are concerned with (in order);

1. Identification of overall mechanism
2. Estimates of the general corrosion rate if the process is Gaussian
3. If the process is stochastic, then attribution of the process to a particular mechanism
4. Estimation of the severity of the stochastic process.

The first step in the identification of the overall mechanism is to decide if the data has a Poisson distribution, and if possible over what frequency range. One of the simpler techniques (but by no means infallible), is by examination of the ratio of the standard deviation divided by the rms of the signal. If this ratio approaches 1, then the process is likely to have a Poisson distribution. If the ratio approaches 1e-3, then the distribution is probably Gaussian and therefore relatively general corrosion. Another test for stochastic processes is to count the number of events in a time period as a function of different threshold intensities. This means that some arbitrary rate of change be applied as a filter to the data. The values of Kurtosis for the potential and current signals are sensitive indicators to changes in corrosion rate and mechanism. Alternatively a series of bandpass filtered signals at several frequencies can be compared in order to give an appreciation of the slope in the frequency domain. The expected slopes in the frequency domain (of the current signal) are 0 for stochastic (Poisson) processes, -0.5 for diffusion controlled processes, and -1 for processes having a Gaussian distribution. For corrosion processes, the current signals should be used for the above techniques.

If the process is Gaussian then the corrosion rate may be estimated from the resistance noise value, or alternatively, from the current noise value. Calibration may be necessary in the first instance, but it should be possible in the longer term to relate the potential noise signal to a value of B, and the current noise to the corrosion current using the following relationships:

............(35)

and

............(36)

ideally we would like to make estimates of the value of aand K. For the current signal we would expect that there would be three possible values for a.namely 0, 1, and 2. In the frequency domain power spectral density (PSD) estimate, this would equate to slopes of 0, -1, and -2, respectively (or as amplitudes 0, -0.5 and -1 respectively). A slope of 0 equates to a stochastic, Poisson process, a slope of -1 to a diffusion controlled process, and a slope of -2 to a Gaussian process. The value of the current noise may be estimated at a particular frequency, say 50mHz, and compared with that of a lower frequency say 5mHz to estimate the slope and hence the likely value of a. The factor K could be estimated from a knowledge of a general corrosion process, where a=2, and a knowledge of the measured potential noise and the B value. Initial estimates would suggest a value of ca 1e-5 for K. In theory, provided that the relationship in 35 and 36 are good for stochastic processes, then it should be possible to estimate a value for Icorr irrespective of the type of process occurring. In practice this is unlikely to be the case, as inspection of equation 36 indicates that if stochastic processes are operative then the term within the square root sign reduces to a value of 1 irrespective of the frequency, and the corrosion current is directly related to the noise amplitude at any frequency through the factor K. However, for corrosion processes having a stochastic nature, it is difficult to estimate a localised pit penetration or crack propagation rate unless some assumptions are made regarding geometry and distribution of pits or cracks in the specimen.

The attribution of a particular type of signal to a particular type of process is usually relatively simple in practical situations. Pitting type studies involve unstressed specimens, and it is expected that the pits will initiate and propagate with equal probability on both the working electrodes, resulting in bi-directional current transients, associated with negative going (less noble) potential transients. In the case of a stressed specimen it is usual to make the current measurements between a stressed and an unstressed specimen. In this circumstance, the test is designed to give a differential view of the cracking process, where transients associated with crack initiation and propagation tend to dominate the noise signals. The current transients in this case can be related directly to anodic and cathodic processes associated with the cracking process. In favourable circumstances the Skewness of the signals can be used to identify particular corrosion mechanisms.

The severity of a particular stochastic process is directly related to the current associated with a particular event and the frequency of such events. This can be estimated by several methods. In the first instance the number of current excursions in some time period t, and their mean amplitude may be used. Alternatively, the amplitude of the white noise current spectrum associated with the process may be used. In the past, the value of the localisation index has been used to "weight" the apparent general corrosion rate of the system, to take into account the localised nature of the process, particularly in pitting situations. For control purposes in plant surveillance situations, it may be simply necessary to identify the number of transients above some threshold amplitude, in order to make the operator aware of the change in severity or mechanism of the corrosion process.