A cellular automaton model for predicting intergranular corrosion

Modeling pitting corrosion by means of a 3D discrete stochastic model

“…Similar research questions in literature have been tackled by iterative optimization using the Nelder and Mead method and genetic algorithms [42]. However, when parametrizing models that give rise to multiple local optima and where one model evaluation is highly time consuming, which is often the case for CA-based models, unnecessary model evaluations should be avoided and more protection against local optima is desired [47,70].…”

“…For that reason, some kind of discretization has to be used to be able to solve the problem numerically, which unavoidably gives rise to approximation errors and stability problems [51,52]. Finally, the macroscopic modeling of electrochemical reactions is unable to capture the stochasticity of the corrosion processes causing that some of the information, important to engineers, is not readily available [42]. The mesoscopic approach is seen as a way to combine the macroscopic phenomenology with the stochastic character of the processes originating from the microscopic scale processes [53].…”

“…However, it is not the goal to describe a specific system but rather to analyze how a combination of a small number of basic processes, very well accepted by electrochemists, might determine general features. Another advantage of employing CA-based models is that they are so-called gray-box models that stand between white-box models, which are based on a detailed understanding of the underlying physical laws and processes, and black-box models, which simply reproduce the input-output behavior of the system but make no use of physics or chemistry [42]. Like the black-box models, the gray-box models are parametric models where the parameters are learned from data, but the difference with black-box models is that here the parametric model is motivated by basic physical ideas instead of simply being selected from a class of universal approximators.…”

“…Although many different aspects that influence corrosion, such as film formation, pH, potential differences and heterogeneous composition of alloys, are being explored and are incorporated in CAbased models, most of them only establish a qualitative resemblance between the simulated model output and the real-world phenomenon, ignoring the importance of a sound model validation that is a prerequisite to have a model with predictive value [2,17,19,[38][39][40][41]. Only very recently, a few authors validated their CA-based model using time series of data, but with modest success [42]. Furthermore, CA-based models in literature are usually two-dimensional, making them unsuited to model the growth of corrosion pits in the direction of the pit depth and surface simultaneously [19].…”

Impact of grain size and rock composition on simulated rock weathering

“…This probability increased linearly with the number of fluid elements by which it was surrounded, so that a solid element in contact with a single fluid element was assigned a P value of 12.5 %, determined from a random Gaussian distribution, while an element surrounded by eight fluid elements was given a P value of 100 %. The number of surrounding elements was defined using the Moore neighborhood method (range = 1; Lishchuk et al, 2011). Any element that underwent dissolution became a fluid and was assigned a characteristic value of M F .…”