A genetic programming approach based on Lévy flight applied to nonlinear identification of a poppet valve

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Abstract

Genetic programming (GP) is an evolutionary algorithm-based paradigm inspired by natural evolution to find a generalized hierarchy computer program description. GP adopts a tree-structured code to describe an identification problem. This paper proposed a GP method based on Lévy flight to estimate discrete polynomial NARX (Nonlinear AutoRegressive with eXogenous inputs) models. The Lévy flight random walks on increments distributed according to a heavy-tailed probability distribution formed by the α-stable distribution family. Besides, Lévy flight is a Markov processes. The distance from the origin of the random walk tends to a stable distribution after a large number of steps. These sorts of movements describe not only the fluctuations in share prices, but also natural behaviors as the way in which albatrosses search for food or the flight of many insects. In this paper, the contribution of Lévy flight is related to the tune of crossover and mutation probabilities in GP. The proposed GP method based on Lévy flight is utilized in an experimental application, a poppet valve. Poppet-type of valve is normally used in combustion engines to open and close intake and exhaust ports in the cylinder head. The very well machined adjust between seat and poppet face gives the sealing feature that is improved every time that the pressure inside the cylinder rises up pushing the valve head against its seat. This type of device is also used in the automotive industry to control the emission levels on combustion engines by recirculating burned gases into the combustion chamber. Results are presented to demonstrate the utility of the proposed GP method based on Lévy flight as promising technique in NARX (Nonlinear AutoRegressive with eXogenous inputs) model identification of a poppet valve.

Keywords

Nonlinear identification
Genetic programming
Lévy flight
Poppet valves
NARX modeling

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