Immune evolutionary algorithm and neural network for modeling and predicting chaotic time series

Chaos underlies many natural phenomena and recognizing chaotic dynamics is potentially important for understanding and managing real systems. This paper presents an immune evolutionary algorithm (IEA) based on the clonal selection, affinity maturation principles in immune system and the mutating ideas of biology evolutionary to train neural network for modeling and predicting chaotic time series. The method takes the weight and bias of neural network as antibody, the mean square error between actual and desired output values of neural network as the objective function, and the objective function and constraints as antigen. An antibody that most fits the antigen is the solution. Application for henon chaotic time series and complex mechanical vibration chaotic signal modeling and prediction are investigated. Compared the results with those obtained by back-propagation (BP), an improved genetic algorithm (ICA), particle swarm optimization (PSO) and hypid particle swarm optimization (HPSO), the proposed method has better precision for modelling and predicting chaotic time series.