小波神经网络在时间序列中的应用

发布时间：2018-09-14 06:43

【摘要】：在医学中,非平稳时间序列的拟合问题很常见,对时间序列进行拟合的常用方法有数据拟合、回归分析、指数平滑法、ARIMA等,但这些主要是针对线性、或较为规则的时序进行的拟合。对于非平稳序列,或者一些比较复杂并且难以确定类型的数据,传统的方法具有了一定的局限性。小波神经网络是一种对非平稳的数据具有很好应用前景的一类方法。它是小波分析理论与人工神经网络完美结合的产物,并且兼容了两者的优点。一方面,它充分利用了小波变换的时频局部化性质；另一方面,它充分发挥了神经网络的自学习能力。它相当于神经网络引入了两个新的参数：伸缩因子和平移因子,不仅避免了神经网络固有的缺陷,也综合了小波分析局部逼近的性质,从而具有了更强的逼近与容错能力。小波神经网络适用于大量的、非平稳的、不能用公式描述或者机理不太了解的数据。传统的方法解决不了或者效果不佳的时候,也可以用小波神经网络来解决。在医学领域,很少见将小波神经网络应用于非平稳的时间序列数据。本文将小波神经网络应用于医学非平稳时间序列分析中。首先用小波神经网络和神经网络分别对人口死亡率数据进行逼近,并对逼近效果进行比较,文章还对非平稳数据进行拟合,并编制程序在软件中得以实现。以此证明小波神经网络对波动较大的非平稳数据有较好的函数逼近能力以及拟合能力,为时间序列分析提供新的思路和方法。论文第一章阐述了小波分析,神经网络的基本概念,并对其原理以及优缺点进行了简要的说明。论文第二章简述了小波神经网络的原理、类型、优缺点以及在时间序列中的应用前景进行了分析。第三章进行实例分析,来说明小波神经网络在医学时间序列中的应用。本文用软件Matlab7.0编程实现对数据的处理和拟合。
[Abstract]:In medicine, the problem of non-stationary time series fitting is very common. The common methods of time series fitting are data fitting, regression analysis, exponential smoothing method, Arima, etc. Or more regular timing for fitting. The traditional method has some limitations for nonstationary sequences, or some more complex and difficult to determine the type of data. Wavelet neural network is a kind of method with good application prospect for non-stationary data. It is the result of the perfect combination of wavelet analysis theory and artificial neural network, and it is compatible with the advantages of both. On the one hand, it makes full use of the time-frequency localization property of wavelet transform; on the other hand, it gives full play to the self-learning ability of neural network. It is equivalent to the neural network to introduce two new parameters: the scaling factor and the translation factor, which not only avoid the inherent defects of the neural network, but also synthesize the properties of local approximation in wavelet analysis, so it has stronger approximation and fault tolerance ability. Wavelet neural network is suitable for a large number of non-stationary data which can not be described by formula or whose mechanism is not well understood. When the traditional method can not be solved or the effect is poor, wavelet neural network can also be used to solve the problem. In medical field, wavelet neural network is rarely applied to non-stationary time series data. In this paper, wavelet neural network is applied to medical non-stationary time series analysis. Firstly, wavelet neural network and neural network are used to approximate the population mortality data, and the approximation results are compared. The non-stationary data are fitted and the program is implemented in the software. It is proved that wavelet neural network has better function approximation ability and fitting ability for non-stationary data with large fluctuation, and provides a new way of thinking and method for time series analysis. In the first chapter, the basic concepts of wavelet analysis and neural network are introduced, and its principle, advantages and disadvantages are briefly explained. In the second chapter, the principle, types, advantages and disadvantages of wavelet neural network and its application prospect in time series are analyzed. In chapter 3, an example is given to illustrate the application of wavelet neural network in medical time series. In this paper, data processing and fitting are realized by software Matlab7.0 programming.
【学位授予单位】：山西医科大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：R318.0

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