# Complex Battery Storage Fire Propagation Translational Forensic Study Using Cellular Automata
## 2 Materials and Methods
### Cellular Automata and Monte Carlo Approach  
Cellular automata, initially conceptualized by [PERSON] [32], represent extensive discrete dynamical systems characterized by their simple structure, yet capable of exhibiting complex and varied behaviors. These models consist of cells organized in a grid that evolves according to rules based on the states of neighboring cells. They reveal how intricate patterns can emerge from simple local rules and have found applications in various fields such as physics, biology, and computer science, particularly for simulating patterns and processing information [33]. The complete structure of state transition diagrams is formulated using algebraic and theoretical principles. In its simplest form, a cellular automaton consists of a linear arrangement of sites, each assigned a binary value of 0 or 1. These values progress through synchronous evolution across discrete time intervals, influenced by the states of neighboring sites. For example, a common rule of evolution dictates that a site's value at a given timestep is computed as the sum of its nearest neighbors' values from the previous timestep, with the rule applied simultaneously at each site [34]. Figure 6 depicts a series of nodes aligned in a row, with each node assigned a binary value of either 0 or 1. The resulting pattern of nonzero sites generated by this rule emerges from an initial condition that features a single nonzero site. Such illustrations elucidate the dynamics and emergent properties inherent in CA systems, offering valuable insights into their behavior and potential applications [35]. The fire propagation risk assessment is conducted through a constrained Monte Carlo-driven dynamic model. This model, derived from CA principles, simulates the distinct state, space, and temporal characteristics of fire propagation. Within this simulation, each unit cell is presumed to possess identical properties and fire behaviors. The fire initiation is modeled as commencing from a single battery cell, with the spread occurring randomly, based on a designated probability, to adjacent cells. The progression of fire at each time interval depends on the condition of the cell and its neighboring cell. The fire spread probabilities in the CA model are specifically designed to reflect the stochastic nature of thermal runaway propagation in densely packed battery modules. When a battery undergoes thermal runaway, the heat or flames emitted from one cell may or may not trigger similar events in adjacent cells, influenced by factors such as thermal resistance and the unique characteristics of each cell. This randomness, unlike traditional fire spread, arises from the variability in cell interactions and the likelihood of ignition. The model is further enhanced by employing the Monte Carlo approach, which simulates a range of random scenarios to assess fire spread probabilities under various conditions, thereby capturing real-world uncertainties. It is noteworthy that this study involved 100,000 randomly generated simulations. This extensive number of simulations not only refines prior research but also significantly improves the accuracy in determining the probability of fire spread. Figure 7 illustrates the correlation between individual cells and their neighboring counterparts as follows:  
* Cell Identification: Each cell is identified by its (i, j) index and possesses a specific state influenced by neighboring cells. * Fire Propagation: The spread of fire is contingent upon assessing neighboring cell states at each timestep. * Diagonal Cells: Diagonally positioned cells do not affect the state of the focal cell. * Boundary Assumption: The module periphery is assumed to contain empty cells. * Matrix Configuration: The computational matrix size is (n + 2, n + 2). Figure 6: A primary demonstration of cellular automata basic configuration and site’s time evolution [36].