【摘要】：在醫(yī)學(xué)中,非平穩(wěn)時(shí)間序列的擬合問題很常見,對(duì)時(shí)間序列進(jìn)行擬合的常用方法有數(shù)據(jù)擬合、回歸分析、指數(shù)平滑法、ARIMA等,但這些主要是針對(duì)線性、或較為規(guī)則的時(shí)序進(jìn)行的擬合。對(duì)于非平穩(wěn)序列,或者一些比較復(fù)雜并且難以確定類型的數(shù)據(jù),傳統(tǒng)的方法具有了一定的局限性。 小波神經(jīng)網(wǎng)絡(luò)是一種對(duì)非平穩(wěn)的數(shù)據(jù)具有很好應(yīng)用前景的一類方法。它是小波分析理論與人工神經(jīng)網(wǎng)絡(luò)完美結(jié)合的產(chǎn)物,并且兼容了兩者的優(yōu)點(diǎn)。一方面,它充分利用了小波變換的時(shí)頻局部化性質(zhì)；另一方面,它充分發(fā)揮了神經(jīng)網(wǎng)絡(luò)的自學(xué)習(xí)能力。它相當(dāng)于神經(jīng)網(wǎng)絡(luò)引入了兩個(gè)新的參數(shù)：伸縮因子和平移因子,不僅避免了神經(jīng)網(wǎng)絡(luò)固有的缺陷,也綜合了小波分析局部逼近的性質(zhì),從而具有了更強(qiáng)的逼近與容錯(cuò)能力。小波神經(jīng)網(wǎng)絡(luò)適用于大量的、非平穩(wěn)的、不能用公式描述或者機(jī)理不太了解的數(shù)據(jù)。傳統(tǒng)的方法解決不了或者效果不佳的時(shí)候,也可以用小波神經(jīng)網(wǎng)絡(luò)來(lái)解決。 在醫(yī)學(xué)領(lǐng)域,很少見將小波神經(jīng)網(wǎng)絡(luò)應(yīng)用于非平穩(wěn)的時(shí)間序列數(shù)據(jù)。本文將小波神經(jīng)網(wǎng)絡(luò)應(yīng)用于醫(yī)學(xué)非平穩(wěn)時(shí)間序列分析中。首先用小波神經(jīng)網(wǎng)絡(luò)和神經(jīng)網(wǎng)絡(luò)分別對(duì)人口死亡率數(shù)據(jù)進(jìn)行逼近,并對(duì)逼近效果進(jìn)行比較,文章還對(duì)非平穩(wěn)數(shù)據(jù)進(jìn)行擬合,并編制程序在軟件中得以實(shí)現(xiàn)。以此證明小波神經(jīng)網(wǎng)絡(luò)對(duì)波動(dòng)較大的非平穩(wěn)數(shù)據(jù)有較好的函數(shù)逼近能力以及擬合能力,為時(shí)間序列分析提供新的思路和方法。 論文第一章闡述了小波分析,神經(jīng)網(wǎng)絡(luò)的基本概念,并對(duì)其原理以及優(yōu)缺點(diǎn)進(jìn)行了簡(jiǎn)要的說(shuō)明。論文第二章簡(jiǎn)述了小波神經(jīng)網(wǎng)絡(luò)的原理、類型、優(yōu)缺點(diǎn)以及在時(shí)間序列中的應(yīng)用前景進(jìn)行了分析。第三章進(jìn)行實(shí)例分析,來(lái)說(shuō)明小波神經(jīng)網(wǎng)絡(luò)在醫(yī)學(xué)時(shí)間序列中的應(yīng)用。 本文用軟件Matlab7.0編程實(shí)現(xiàn)對(duì)數(shù)據(jù)的處理和擬合。
[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.
【學(xué)位授予單位】：山西醫(yī)科大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：R318.0

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