Reliability modeling and optimization using fuzzy logic and chaos theory

Abstract

Fuzzy sets membership functions integrated with logistic map as the chaos generator were used to create reliability bifurcations diagrams of the system with redundancy of the components. This paper shows that increasing in the number of redundant components results in a postponement of the moment of the first bifurcation which is considered as most contributing to the loss of the reliability. The increasing of redundancy also provides the shrinkage of the oscillation orbit of the level of the system's membership to reliable state. The paper includes the problem statement of redundancy optimization under conditions of chaotic behavior of influencing parameters and genetic algorithm of this problem solving. The paper shows the possibility of chaos-tolerant systems design with the required level of reliability. © 2012 Alexander Rotshtein et al.