基于量子粒子群优化算法的新型正交基神经网络分数阶混沌时间序列单步预测

针对分数阶混沌时间序列预测精度低、速度慢的问题,提出了基于量子粒子群优化(QPSO)算法的新型正交基神经网络预测模型。首先,在Laguerre正交基函数的基础上提出一种新型正交基函数,并结合神经网络拓扑构成新型正交基神经网络;其次,利用QPSO算法优化新型正交基神经网络参数,将参数优化问题转化为多维空间上的函数优化问题;最后,根据已优化参数建立预测模型并进行预测分析。分别以分数阶Birkhoff-shaw和Jerk混沌系统为模型,利用Adams-Bashforth-Moulton预估-校正法产生混沌时间序列作为仿真对象,进行单步预测对比实验。仿真表明,与反向传播(BP)神经网络、径向基函数(RBF)神经网络及普通的新型正交基神经网络相比,基于QPSO算法的新型正交基神经网络的平均绝对值误差(MAE)、均方根误差(RMSE)明显减小,决定度系数(CD)更接近于1,平均建模时间(MMT)明显缩短。实验结果表明,基于QPSO算法的新型正交基神经网络提高了分数阶混沌时间序列预测的精度和速度,便于该预测模型的应用和推广。

New orthogonal basis neural network based on quantum particle swarm optimization algorithm for fractional order chaotic time series single-step prediction

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.