【作者】 李胜；

【导师】 涂源钊；

【作者基本信息】 四川大学 ， 控制理论与控制工程， 2003， 硕士

【摘要】 小波分析是一种新兴的数学分析方法。本文将小波分析理论与传统神经网络理论相结合，用小波函数代替传统神经网络中的sigmoid函数，构成小波神经网络。 小波神经网络和前馈型神经网络均具有一致逼近和L~2逼近的能力。本文将小波神经网络用于逼近非线性函数，并从理论上讨论了它逼近函数的能力。小波神经网络是小波分析与传统神经网络结合而成的，这样就可以借助小波分析的有关理论来设计小波神经网络的结构。本文提出了根据逼近函数的时频空间区域来选择小波基函数，使这些小波基函数共同构成的时频空间区域覆盖完逼近函数的时频空间区域。为了使网络实用并且规模最小，提出了一种结构优化的方法。由于网络的输出与权值是线性关系，可以直接利用LS等方法进行权值修正。本文小波神经网络采用带动量因子的BP算法来修正网络的权值和减小逼近的误差。 最后，对于一个实际的非线性函数，用本文介绍的方法来设计小波神经网络来逼近函数，仿真结果表明该方法的有效性，并且表明小波神经网络在函数逼近上，网络的收敛速度快，逼近精度高的特点，并且网络具有很好的泛化能力和容错性。更多还原

【Abstract】 Wavelet analysis is a rising mathematical analysis method. This paper combines theory of wavelet analysis with conventional neural network. Substituting wavelet function for sigmoid function in neural network, to form wavelet neural network.Both wavelet neural network and neural network of feedforward have ability of coherent approximation and L2 approximation. This paper approximates non-linear function with wavelet neural network, whose ability of approximation function is discussed in theory. Wavelet neural network is a combination of wavelet analysis and conventional neural network, so structure of wavelet neural network can be designed with concerned theory of wavelet analysis. To choose wavelet function based on time-frequency region is put forward, time-frequency region composing of all of these wavelet functions can overlay wholly time-frequency region of non-linear function to approximate. In order to make wavelet neural network efficient and minimize structure of network, a novel method optimizing structure of wavelet neural network is advanced. Because it is linear relation between output of network and right of network, method of LS can be directly used to correct right of wavelet neural network. Arithmetic of back propagation withmomentum gene is used to correct right of network and minimize error of approximation.Finally, take example for a non-linear function, method mentioned in this paper is used to design wavelet neural network to approximate this function. The computer simulations confirm the method that is brought out in this paper is useful, and prove that wavelet neural network has not only fast convergence and better precision of approximation, but also good capability of forecasting and escaping error.更多还原