Page 197 - 2024-Vol20-Issue2

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E cell denotes the electrical cell potential(E cathode+E anode).
When ?G < 0, corrosion becomes spontaneous, while ?G >
0 results in nonspontaneous corrosion[33].
III. IMPLEMENTATION OF CORROSION
DIFFUSION OPTIMIZATION ALGORITHM
(CDOA)
The proposed algorithm in this study is mainly based on the
pitting corrosion diffusion. As mentioned earlier, this type of
corrosion goes through three stages. Firstly, it passes though
the initiation stage, where the onset of this type of corrosion
is random on the surface of the metal. Therefore, suppose that
there are a number of pits on the surface of the metal which
represents the number of pitting (W ). Each of these pits has a
number of electrons and ions that move from the positive side
which is represented by the surface of the metal to negative
side which is represented by the surrounding environment.
The number of transferred electrons or ions is symbolized
by (N). Actually, N is the dimension of each variable x that
represents each pit. Therefore, it is possible to describe the
case of the x at the iteration (iter) as in the below matrix:
? x1,1iter · · · x1,Niter ?
xiter = ? ... ... ... ? (4)
? ?
xW,1iter · · · xW,Niter
where N = (1, 2,. . . , D), the D represents the dimension of each In this case, the sum of energy level is less than zero, and the
variable, W = (1,2,. . . ,number of pitting), and the iteration
number iter = (1,2,. . . , itermax).
Initially, the pitting distributes randomly on the surface of the
metal as described in the following formula:
xni.iter = xmin + RAND * (xmax - xmin) (5)
where RAND is random number uniformly distributed be-
tween 0 and 1, and xmax , xmin represent the boundary reign
on the metal where xmax is the maximum limited of transfer
electrons or ions, and xminis the minimum limited of transfer
electron or ions. It has already been clarified that the envi-
ronmental conditions surrounding the corroded metal have a
very significant impact on the corrosion rate. It is possible to
increase or decrease the corrosion rate by changing the envi-
ronmental conditions. For this reason, equation (6) combines
the effect of the conditions mentioned in Section II.A in the
following form:
E NVE F F ECT = 1+ ENVFACTOR - LOENCON (6)
HIENCON - LOENCON
where ENVEFFECT represents the environmental effects on
Al-mtory, Alnahwi & Ali
corrosion rate, HIENCON is the high environmental condition,
LOENCON is the low environmental condition, and ENVFactordenotes
the random disruption between the high environmental condi-
tion and low environmental condition given by:
ENVf actor = LOENCON + RAND(HIENCON - LOENCON ) (7)
The previous subsection also reveals that the stability and
growth of the pit mainly depend on the amount of electrical
potential difference between the electrodes of the corrosion
cell as well as Gibbs free energy equation. For the purpose of
determining the stability of the pit, it is necessary to have a
decision equation which depends on the potential difference
of cell and the number of transferred electrons as given in (8):
energylevel = -N * uni f orm rand[lowvoltage, highvoltage]
* (xoldbest - xprivous)
(8)
where (energylevel) represents Gibb’s free energy, (uniform
rand) represents a uniform disruption between low and high
stander level voltages, xoldbest is the global best value, and
xprivous is the previous iteration value of x.
At each iteration, the sum of the row, which represents the
sum of the energy of each pit, is named (sum of energy level).
The sum of energy that represents Gibb’s free energy is used
to determine the stability of the pit as given below two condi-
tions:
CASE ONE : THE UNSTABLE STATE
potential difference exists. Therefore, it is considered as an
unstable situation, and by sure it is not the optimum solution.
The updating equation is as follows:
xdi iter = xdi iter-1 + ENVEFFECT * (xdi iter best - xdi iter-1 best )
(9)
CASE TWO : THE STABLE STATE
This case happens when the sum of energy level is greater
than or equal to zero, or when the potential difference is equal
to zero. Therefore, it is considered a stable state in which the
value of x remains as it is in the previous iteration.
xdi iter = xdi iter-1 (10)
Fig. 2. and Alg. 1. show the flow chart and the pseudo-code
of the proposed algorithm, respectively.
IV. PERFORMANCE COMPARISON BASED ON
BENCHMARK FUNCTIONS
To verify the performance and efficiency of the proposed al-
gorithm, different types of benchmark functions were used.