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We investigate main theoretical aspects of two-dimensional linear-hybrid cellular automata with periodic boundary condition over the Galois field GF(2). We focus on the characterization of two-dimensional hybrid linear cellular automata by way of a special algorithm. Here we set up a relation between reversibility of cellular automata and characterization of two-dimensional hybrid linear cellular automata with a special boundary conditions, i.e. periodic case. The determination of the characterization problem of special type of cellular automaton is studied by means of the matrix algebra theory. It is believed that this type of cellular automata could find many different applications in special case situations, e.g. image processing area, textile design, video processing, DNA research, etc., in the near future. [ABSTRACT FROM AUTHOR]

In the present paper, there are studied main theoretical views of two-dimensional (2D) linear uniform cellular automata with reflective boundary condition over the ternary field, i.e. three states spin case or Z3. We set up a relation between reversibility of cellular automata and characterization of 2D uniform linear cellular automata with this special boundary conditions by using of the matrix theory. In near future, these cellular automata can be found in many different real life applications, e.g. computability theory, theoretical biology, image processing area, textile design, video processing, etc. [ABSTRACT FROM AUTHOR]

Design and analysis of modern engineering systems are complicated, mostly relying on computational analyses codes and hence often computationally expensive. Meanwhile, improved computer-aided design and numerical simulation methods are used extensively in the design process. Even continuing growth of computing power and speed, computationally cheap and reliable models or simulation techniques are not available, at least as ready-to-use computer analysis codes. The necessity of tolerance analysis takes important place at the same time with improved CAD and computer based process planning, because of high quality production requirements, and reduces manufacturing costs. Simulation based design and optimization becomes the only option to meet the specifications, and improves the system reliability. In the last few decades, the use of surrogate models has achieved significant advantages, because they provide fast computation and design investigation as they replace computationally expensive to run computer analyses with cheap to run approximations. Surrogate models also simplify the integration of analyses codes to optimization and reliability assessment studies. In this paper, response surface and Kriging surrogate models are used within a Monte Carlo simulation framework for tolerance analysis. As an illustrative example problem, tolerance analyses of a clutch assembly with nonlinear objection function are used. The effects of the surrogate model parameters (e.g., the use of different regression polynomials) and the number of training points on tolerance analysis are explored. [ABSTRACT FROM AUTHOR]