Since fractional order chaotic time series prediction has low precision and slow speed, a prediction model of new orthogonal basis neural network based on Quantum Particle Swarm Optimization (QPSO) algorithm was proposed. Firstly, on the basis of Laguerre orthogonal basis function, a new orthogonal basis function was put forward combined with the neural network topology to form a new orthogonal basis neural network. Secondly, QPSO algorithm was used for parameter optimization of the new orthogonal basis neural network, thus the parameter optimization problem was transformed into a function optimization problem on multidimensional space. Finally, the prediction model was established based on the optimized parameters. Fractional order Birkhoff-shaw and Jerk chaotic systems were taken as models respectively, then chaotic time series produced according to Adams-Bashforth-Moulton estimation-correction algorithm were used as the simulation objects. In the comparison experiments on single-step prediction with Back Propagation (BP) neural network, Radical Basis Function (RBF) neural network and general new orthogonal basis neural network, Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) of the new orthogonal basis neural network based on QPSO algorithm were significantly reduced, and Coefficients of Decision (CD) of it was closer to 1; meanwhile, Mean Modeling Time (MMT) of it was greatly shortened. The theoretical analysis and simulation results show that the new orthogonal basis neural network based on QPSO algorithm can improve the precision and speed of fractional order chaotic time series prediction, so the prediction model can be easily expanded and applied.

Concerning low precision and slow speed of traditional intelligent optimization algorithm for parameter identification in chaotic system, a new method of parameter identification in chaotic system based on feedback teaching-learning-based optimization algorithm was proposed. This method was based on the teaching-learning-based optimization algorithm, where the feedback stage was introduced at the end of the teaching and learning stage. At the same time the parameter identification problem was converted into a function optimization problem in parameter space. Three-dimensional quadratic autonomous generalized Lorenz system, Jerk system and Sprott-J system were taken as models respectively, intercomparison experiments among particle swarm optimization algorithm, quantum particle swarm optimization algorithm, teaching-learning-based optimization algorithm and feedback teaching-learning-based optimization algorithm were conducted. The identification error of the feedback teaching-learning-based optimization algorithm was zero, meanwhile, the search times was decreased significantly. The simulation results show that the feedback teaching-learning-based optimization algorithm improves the precision and speed of the parameter identification in chaotic system markedly, so the feasibility and effectiveness of the algorithm are well demonstrated.