## 2 Method Proposed
### Simulation of the Initial Damage by Using Cellular Automata (CA)  
The cellular automaton (CA) method was first proposed by [PERSON] in the 1940s. At present, CA has been used in many different fields to simulate the behavior of various systems, such as traffic statistics [20], bioinformatics [21] and material science [22]. For the metal corrosion problem, CA is also a powerful tool [23; 24; 25]. Compared with other the uncertainty methods, such as the neural network model [26], probabilistic analysis process model [27; 28] and stochastic process model [29], the CA method has strong universality and stability in simulating the corrosion damage evolution process because it can integrate a lot of random parameters and present pit morphology comprehensively [30]. This article therefore adopts CA technology and the practical nature of the electrochemical reaction to simulate random pitting morphology and study the fatigue damage evolution process of corroded steel wire. In the CA model, the metal/passive film/corrosive medium system is discretized into ordered cells in the three-dimensional cylindrical CA space. The cell space, the static component in the CA model, includes, based on the geometry of steel wire, the cylindrical coordinate system; according to the requirement of corrosion simulation accuracy, the steel wire and the external corrosion environment are divided into an array consisting of cells where the cell size is shown in Figure 2 and each cell is represented by its position coordinate (i, j, k); the constant boundary condition is selected, that is, the outer cells of the boundary is endowed with a constant to describe a finite CA space; a three-dimensional cell space is established, as shown in Figure 2.  
Figure 2: Schematic diagram of cellular automata (CA) model for the corrosion process of high-strength steel wire. The state of each cell (i, j, k) in the cell space is determined by the cell characteristics at this position. In the CA model of metal corrosion, three cell types are mainly involved:  
1. Metal cell (M): the metal cell can be etched away by the corrosive cell, and its position remains unchanged throughout the simulation;
2. Passive film cell (P): in the CA model, the passive film cell will cover the outermost metal cell initially. The position of the passive film cell is basically fixed, but the initial defect will randomly appear during the simulation, when the passive film cell at the position is converted into a metal cell;
3. Corrosive cell (C): The corrosive cell is randomly distributed in solution and the concentration of the corrosive solution is set to 0.1. It can corrode the metal cell and move freely. In the cell space, the corrosive cell can randomly select to move along one direction of coordinate axis in each time step. That is to say, a 6-neighbor type is chosen. The evolution rules of cells in the CA space are based on the basic metal corrosion process. Firstly, it is assumed that the corrosion system is a diffusion-controlled system, and the corrosion process only occurs at the interface of metal and electrolytes [31; 32; 33]. Thus, the general metal corrosion process can be described as: the passive film on the metal surface breaks; the exposed metal surface reacts electrochemically in a humid environment; the positive electrode gradually dissolves [30]. If the re-oxidation is not considered during the corrosion process, the basic reaction formula of the metal solution in an aqueous solution or a humid environment can be expressed as [32]:  
\[\mathrm{Me}+\mathrm{H}_{2}0\rightarrow\mathrm{MeOH}_{\mathrm{aq}}+(1/2) \mathrm{H}_{2} \tag{4}\]  
where \(\mathrm{MeOH}_{\mathrm{aq}}\) is the substance in the solution after the reaction, which has no influence on the subsequent corrosion process. Therefore, in the CA model, the metal corrosion process can be divided into the following variation rules:  
1. Random diffusion of corrosive media in solution.