Fractal-Based Reliability Measure for Heterogeneous Manufacturing Networks

Nowadays, production-oriented manufacturing is transforming to service-oriented one, which leads to an increasing demand for high reliability of manufacturing systems. However, a popular approach to measuring terminal reliability of complex networked systems is based on graph theory, which has been shown to be an NP-hard problem. Though the NP-hard problem can be avoided by employing a statistical measure method for terminal reliability of random networks based on percolation theory, there is still lack of a general assessment approach to calculating terminal reliability of heterogeneous complex networks in intelligent manufacturing. In this paper, we propose a novel fractal-based approach to measuring the terminal reliability of heterogeneous networks. With help of the renormalization procedure that coarse grains a network into boxes containing nodes within given lateral size and inverse renormalization, which gives a fractal network growth model, a fractal network approximation of an arbitrary complex network is obtained. This fractal network topology can be described by a superposition of fractal elements based on fractal theory. Following this description, terminal reliability is the function of reliability of fractal elements. Then, a reliability assessment algorithm with computational complexity $O(N^2)$ based on fractal elements is developed. Numerical simulation is performed on a real network and a fractal network to validate the effectiveness of our method.

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