scholarly journals Distributed Control of a Manufacturing System with One-Dimensional Cellular Automata

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Irving Barragan-Vite ◽  
Juan C. Seck-Tuoh-Mora ◽  
Norberto Hernandez-Romero ◽  
Joselito Medina-Marin ◽  
Eva S. Hernandez-Gress
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Distributed Control ◽  
Manufacturing Process ◽  
Manufacturing Systems ◽  
Manufacturing System ◽  
Complex Dynamics ◽  
Initial Conditions ◽  
Global Dynamics ◽  
One Dimensional

We present a distributed control modeling approach for an automated manufacturing system based on the dynamics of one-dimensional cellular automata. This is inspired by the fact that both cellular automata and manufacturing systems are discrete dynamical systems where local interactions given among their elements (resources) can lead to complex dynamics, despite the simple rules governing such interactions. The cellular automaton model developed in this study focuses on two states of the resources of a manufacturing system, namely, busy or idle. However, the interaction among the resources such as whether they are shared at different stages of the manufacturing process determines the global dynamics of the system. A procedure is shown to obtain the local evolution rule of the automaton based on the relationships among the resources and the material flow through the manufacturing process. The resulting distributed control of the manufacturing system appears to be heterarchical, and the evolution of the cellular automaton exhibits a Class II behavior for some given disordered initial conditions.

Classifying elementary cellular automata using compressibility, diversity and sensitivity measures

2014 ◽  
Vol 25 (03) ◽  
pp. 1350098 ◽  
Author(s):  
Shigeru Ninagawa ◽  
Andrew Adamatzky
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Initial Conditions ◽  
Morphological Diversity ◽  
Compression Algorithm ◽  
One Dimensional ◽  
Elementary Cellular Automata ◽  
Eca Rules ◽  
Substantial Correlation ◽  
Elementary Cellular Automaton

An elementary cellular automaton (ECA) is a one-dimensional, synchronous, binary automaton, where each cell update depends on its own state and states of its two closest neighbors. We attempt to uncover correlations between the following measures of ECA behavior: compressibility, sensitivity and diversity. The compressibility of ECA configurations is calculated using the Lempel–Ziv (LZ) compression algorithm LZ78. The sensitivity of ECA rules to initial conditions and perturbations is evaluated using Derrida coefficients. The generative morphological diversity shows how many different neighborhood states are produced from a single nonquiescent cell. We found no significant correlation between sensitivity and compressibility. There is a substantial correlation between generative diversity and compressibility. Using sensitivity, compressibility and diversity, we uncover and characterize novel groupings of rules.

scholarly journals TRANSITIVE BEHAVIOR IN REVERSIBLE ONE-DIMENSIONAL CELLULAR AUTOMATA WITH A WELCH INDEX 1

2002 ◽  
Vol 13 (06) ◽  
pp. 837-855 ◽  
Author(s):  
JUAN CARLOS SECK TUOH MORA
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Symbolic Dynamics ◽  
Transitive Closure ◽  
Matrix Representation ◽  
Global Dynamics ◽  
One Dimensional ◽  
Interesting Topic

The problem of knowing and characterizing the transitive behavior of a given cellular automaton is a very interesting topic. This paper provides a matrix representation of the global dynamics in reversible one-dimensional cellular automata with a Welch index 1, i.e., those where the ancestors differ just at one end. We prove that the transitive closure of this matrix shows diverse types of transitive behaviors in these systems. Part of the theorems in this paper are reductions of well-known results in symbolic dynamics. This matrix and its transitive closure were computationally implemented, and some examples are presented.

scholarly journals Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Pabitra Pal Choudhury ◽  
Sudhakar Sahoo ◽  
Mithun Chakraborty
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Boolean Functions ◽  
State Transition ◽  
The State ◽  
Transition Diagram ◽  
One Dimensional ◽  
State Transition Diagram ◽  
Linear Rule

Dynamics of a nonlinear cellular automaton (CA) is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s) of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.

Languages, equicontinuity and attractors in cellular automata

1997 ◽  
Vol 17 (2) ◽  
pp. 417-433 ◽  
Author(s):  
PETR KŮRKA
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
State Space ◽  
Finite Type ◽  
Measure Zero ◽  
Initial Conditions ◽  
The State ◽  
Subshift Of Finite Type ◽  
Topologically Transitive ◽  
The Third

We consider three related classifications of cellular automata: the first is based on the complexity of languages generated by clopen partitions of the state space, i.e. on the complexity of the factor subshifts; the second is based on the concept of equicontinuity and it is a modification of the classification introduced by Gilman [9]. The third one is based on the concept of attractors and it refines the classification introduced by Hurley [16]. We show relations between these classifications and give examples of cellular automata in the intersection classes. In particular, we show that every positively expansive cellular automaton is conjugate to a one-sided subshift of finite type and that every topologically transitive cellular automaton is sensitive to initial conditions. We also construct a cellular automaton with minimal quasi-attractor, whose basin has measure zero, answering a question raised in Hurley [16].

ON THE STRUCTURE OF REAL-VALUED ONE-DIMENSIONAL CELLULAR AUTOMATA

2011 ◽  
Vol 21 (05) ◽  
pp. 1265-1279 ◽  
Author(s):  
XU XU ◽  
STEPHEN P. BANKS ◽  
MAHDI MAHFOUF
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Fixed Points ◽  
Periodic Solutions ◽  
Cellular Systems ◽  
One Dimensional ◽  
Dynamical Behaviors ◽  
New Type ◽  
Complex Patterns

It is well-known that binary-valued cellular automata, which are defined by simple local rules, have the amazing feature of generating very complex patterns and having complicated dynamical behaviors. In this paper, we present a new type of cellular automaton based on real-valued states which produce an even greater amount of interesting structures such as fractal, chaotic and hypercyclic. We also give proofs to real-valued cellular systems which have fixed points and periodic solutions.

scholarly journals CELLULAR AUTOMATON SUPERCOLLIDERS

2011 ◽  
Vol 22 (04) ◽  
pp. 419-439 ◽  
Author(s):  
GENARO J. MARTÍNEZ ◽  
ANDREW ADAMATZKY ◽  
CHRISTOPHER R. STEPHENS ◽  
ALEJANDRO F. HOEFLICH
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Elastic Collision ◽  
Collective Excitations ◽  
Compact Groups ◽  
Dimensional Torus ◽  
Nonlinear Media ◽  
One Dimensional ◽  
Spatially Extended ◽  
Binary Strings

Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular automaton analogous of localizations or quasi-local collective excitations traveling in a spatially extended nonlinear medium. They can be considered as binary strings or symbols traveling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyze what types of interaction occur between gliders traveling on a cellular automaton "cyclotron" and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in nonlinear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analyzed via implementation of cyclic tag systems.

scholarly journals A Multi-State Model for Reliability Analysis of Metal Sheet Manufacturing Process Using Artificial Neural Network Technique

2020 ◽  
Vol 28 (4) ◽  
Author(s):  
Anil Chandra ◽  
Surbhi Gupta ◽  
Chandra Kant Jaggi
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Reliability Analysis ◽  
Manufacturing Process ◽  
Manufacturing Systems ◽  
Manufacturing System ◽  
Metal Sheet ◽  
Time Period ◽  
Artificial Neural ◽  
Over Time

A manufacturing system is governed by its various processes upon which its efficiency is dependent. Since failure results in considerable losses, many manufacturing systems have certain redundancies for some processes. These redundancies cause the system to work under different efficiency states called multi-state elements. In this paper, various processes of metal sheet manufacturing unit have been categorized as subsystems to determine the multi-state probabilities of its different efficiency states. Artificial Neural Network Technique (ANN) has been used to estimate the change in these multi-state probabilities over time. The ANN has also been used to estimate variation in upstate and downstate probabilities of the system for a particular-time period. The results have been used to determine variation in profit over time for the system.

Emergent Structures

2010 ◽  
pp. 83-113
Author(s):  
Eleonora Bilotta ◽  
Pietro Pantano
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Initial Conditions ◽  
Natural Sciences ◽  
Forward Problem ◽  
Second Step ◽  
Large Collection ◽  
Parameter Values

There are two classes of problem in the study of Cellular Automata. The forward. problem is the problem of determining the properties of the system. Solutions often consist of finding quantities that are computable on a rules table and characterizing the behavior of the rule upon repeated iterations, starting from different initial conditions. Solutions to the backwards problem begin with the properties of a system and find a rule or a set of rules which have these properties. This is especially useful in the application of Cellular Automata to the natural sciences, when researchers deal with a large collection of phenomena (Gutowitz, 1989). Another approach is to identify the basic structures of a Cellular Automaton (Adamatzky, 1995). Once these are known it becomes possible to develop specific models for particular systems and to detect general principles applicable to a wide variety of systems (Wolfram, 1984; Lam, 1998). According to Adamatzky, the identification of a system consists of two related steps, namely specification and estimation. In specification we choose a useful and efficient description of the system: perhaps an equation and a set of parameters. The second step involves the estimation of parameter values for the equation: exploiting measures of similarity.

Designing a Modular Rapid Manufacturing Process

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Jacquelyn K. S. Nagel ◽  
Frank W. Liou
Keyword(s):  
Manufacturing Process ◽  
Design Methodology ◽  
Manufacturing Systems ◽  
Manufacturing System ◽  
Modular Design ◽  
Process Integration ◽  
Process Analysis ◽  
Integrated System ◽  
Rapid Manufacturing ◽  
Potential Cost

Freeform fabrication and additive fabrication technologies have been combined with subtractive processes to achieve a variety of fully integrated rapid manufacturing systems. The combination of separate fabrication techniques into one rapid manufacturing system results in unit manufacturing process integration, sometimes known as a hybrid system. However, the design methods or approaches required to construct these integrated systems are vaguely described or not mentioned at all. The final product from any integrated system is affected not only by the unit manufacturing processes themselves, but also by the extent the individual units are assimilated into an integrated process. A wide variety of integrated and hybrid manufacturing systems and current manufacturing design methodologies are described in this paper, along with their similarities and differences. Through our extensive review, it was discovered that there are five key elements to a reliable integrated rapid manufacturing system: process planning software, motion system, control system, unit manufacturing process, and a finishing process. By studying the manner in which all other systems have been integrated, a table of successful integrated manufacturing system element combinations has been complied, documenting each of the key element choices, resulting in a variety of modular designs. This paper further discusses the importance of the five elements in manufacturing system integration, and how an integrated system is the way to move forward in the manufacturing domain. To that end, a rapid manufacturing system design methodology was developed that explores designs via process analysis to discover integration potential. Cost-benefit analysis is then used to assess the performance of the new system. This analysis determines if all needs have been met, while staying within the constraints of time and resources. Additionally, a table of common issues and obstacles encountered during manufacturing system development has been compiled to assist in the design and development of future rapid manufacturing systems. To illustrate the design methodology, our modular design experience with a laser aided manufacturing process is presented. Unit manufacturing process integration has increased the productivity and capabilities of our system, which reduced resource volume and increased productivity.

GLOBALLY SYNCHRONIZED OSCILLATIONS IN AN ONE-DIMENSIONAL CELLULAR AUTOMATON

2004 ◽  
Vol 15 (03) ◽  
pp. 409-425
Author(s):  
FRANCISCO JIMÉNEZ-MORALES ◽  
MARCO TOMASSINI
Keyword(s):  
Genetic Algorithm ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Random Noise ◽  
Regular Pattern ◽  
Final State ◽  
One Dimensional ◽  
Lattice Size ◽  
Spatial Periodicity ◽  
Temporal Periodicity

Using a genetic algorithm a population of one-dimensional binary cellular automata is evolved to perform a computational task for which the best evolved rules cause the concentration to display a period-three oscillation. One run is studied in which the final state reached by the best evolved rule consists of a regular pattern or domain Λ, plus some propagating particles. It is shown that globally synchronized period-three oscillations can be obtained if the lattice size L is a multiple of the spatial periodicity S(Λ) of the domain. When L=m.S(Λ)-1 there is a cyclic particle reaction that keeps the system in two different phases and the concentration has a temporal periodicity that depends on the lattice size. The effects of random noise on the evolved cellular automata has also been investigated.

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