基于最大Lyapunov指数预测的BP神经网络权值学习规则的研究.pdf

武汉科技大学 硕士学位论文 第 I 页

摘 要
BP 神经网络（Back Propagation Neural Networks）是人工神经网络中最为重要的网络
之一，在智能控制、模式识别、计算机视觉、自适应滤波和信号处理、非线性系统辨识
及非线性组合优化等领域应用广泛。BP 神经网络具有很强的映射能力，可以解决许多实
际问题，但同时还存在着收敛速度慢，易陷于局部极小的缺点。
混沌是二十世纪科学史上的重大发现之一，它揭示了非线性科学的共同属性——有
序性与无序性的统一、确定性和随机性的统一。这一发现正在冲击和改变着几乎所有的
科学和技术领域。
最大 Lyapunov 指数预测是混沌时间序列预测中一种常用方法。它是根据数据序列本
身所计算出来的客观规律进行预测，具有良好的预测效果。
本文将最大 Lyapunov 指数预测方法与神经网络权值优化相结合，论证了该算法的具
体实现过程。仿真和实验结果充分表明了该算法的有效性和稳定性，克服了 BP 神经网络
收敛速度慢和易陷入局部极小的问题，为混沌时间序列预测运用开辟了新的应用领域。





关键词：混沌，BP 神经网络，Lyapunov 指数，时间序列
第 II 页 武汉科技大学 硕士学位论文
Abstract
The BP neural network is one of most important artificial neural networks. It is widely
used in some field, including the intelligent control, the pattern recognition, the computer
vision, the adaptive filtering and the signal processing, the non-linear system recognizes and
domain utilization and so on non-linear combination optimization. The BP neural network has
the ability to solve many practical problems because of its strong mapping. However, it has
slow convergence rate and is prone to fall into local extremum.
The chaos is one of the significant discoveries in the natural science. It gives the common
characteristics of the non-linear science, which is the unification of order and disorder，
unification of certain and stochastic. This discovery makes an impressive influence on all the
fields of science and technology.
The maximum Lyapunov index is a common used method in the chaos time series
forecast. It can make the forecasts according to the objective law obtained from date sequence
and has the good forecast effect.
In this paper, the learning algorithm arithmetic of the neural network is incorporated