基于Chebyshev神经网络的非线性动态系统预测

The prediction of nonlinear dynamic system based on Chebyshev neural networks

针对非线性动态系统的预测常受到噪声或其他过程的耦合影响,使得规律变得难以发现的问题,提出了以一组Chebyshev正交基函数作为神经网络中各隐神经元的激励函数的新型的Chebyshev基函数神经网络预测模型.将该模型作为非线性动态系统预测模型,并采用基于粒子群和模拟退火组成的文化基因算法优化神经网络的权值,可以达到很高的预测精度和很好的预测结果.Chebyshev神经网络与传统的BP(back propagation)神经网络相比,工作量大大减少,加快了收敛性.文化基因算法用于确定权值的Chebyshev神经网络分别与粒子群和模拟退火优化的Chebyshev神经网络相比具有更好的拟合效果.

For prediction of nonlinear dynamic systems is often affected by noise or coupling of other process, so the regularity is difficult to find. This paper put forward a set of Chebyshev orthogonal basis functions, as the excitation function of hidden neurons in neural networks, and constructed a new type of Chebyshev basis function neural network prediction model. This model was used as the nonlinear dynamic system prediction models, and optimized the weights of neural network by the memetie algorithm based on particle swarm optimization and simulated annealing algorithm. This method could achieve high prediction precision and good prediction results. Chebyshev neural network greatly reduced the workload, sped up the convergence than the traditional BP neural network. When compared with simulated annealing optimization or particle swarm optimization Chebyshev neural network, Chebyshev of memetic algorithm, when it was used to determine the weights of the neural network, had better fitting effect.