基于小波的神经网络研究及其在信息处理中的应用

发布时间：2018-07-08 10:27

本文选题：小波神经网络 + 参数初始化　；参考：《中北大学》2015年博士论文

【摘要】：小波分析与神经网络都是新一代计算智能信息处理技术的主要组成部分。小波变换是一个时间域和频率域的局部变换,利用对小波函数的伸缩平移运算对信号进行不同尺度下的分析,可以有效地从信号中提取有用信息。它克服了传统傅里叶变换不能同时进行时频分析的缺陷,因而成为了非线性科学的前沿技术之一。人工神经网络是通过对人脑神经网络的合理抽象而形成的理论化模型,它可以依靠自身对环境的自学习能力获取知识,并利用神经元之间的连接权值存储获取的知识。小波神经网络(简称小波网络)是小波分析与神经网络相结合的产物,它可以一方面保持神经网络的多输入并行处理能力、自学习能力、非线性映射和容错能力等,另一方面将具有强数学基础的小波分析方便地应用于高维问题,有效地发挥二者的优势。本文在研究了已有经典小波神经网络模型的基础上,以前馈式小波网络为主要研究对象,对具有张量积型小波函数的自适应小波网络的初始化、与模糊机制结合的模糊小波网络构造与算法、径向小波网络的算法等方面做了较为深入的研究与分析,并将其应用于信号预测,系统辨识,模式分类等方面,使得这几类小波网络在应用方面具有更高的实用价值与意义。具体工作主要有:首先,具有张量积型小波激活函数的多维输入自适应小波网络(WNN_M)是最早也是最经典的小波网络模型,其尺度参数、平移参数及线性权值均为网络可调参数,应用中增加了网络的灵活性,使得用更小规模的小波网络逼近非线性系统成为可能,在其应用中,初始参数的设置仍多采取Q.H.Zhang提出的启发式方法(HIA)。为了得到针对该模型的更理想的参数初始值,使得网络训练能够快速收敛,提出了一种利用隐层小波函数时频局部化特点的改进参数初始化方法(CIA)。该方法首先根据多维输入数据的统计特征设定阈值向量,利用最邻近聚类的思想确定网络隐层神经元个数,并由聚类后的类中心与半径,通过隐层小波函数的时间窗宽确定相应的小波平移参向量与尺度参向量的初始值。在对三类不同的时间序列预测的实验中看出,相比于WNN_M-HIA,WNN_M-CIA的初始误差明显较低,在经过梯度下降法的数次迭代后,其预测精度仍优于基于HIA初始化的网络预测精度,说明了该初始化算法的有效性和合理性。其次,考虑到将模糊理论与小波分析、神经网络结合研究的趋势,提出了一种将TSK模糊系统与小波网络结合的模糊小波网络模型。该模型将具有连续参数和张量积型多维小波激活函数的小波网络作为TSK模糊系统的结论部分,分析了与已有模糊小波网络模型的区别,并将其应用于非线性系统辨识。在训练算法方面,选择使用基于粒子群算法和在线梯度下降法结合的混合优化算法。通过对两个非线性系统进行辨识实验,可以看出,即使采用了较少的模糊规则和参数规模,相比于已有的模型,本文提出的模型与算法仍能得到更加满意的辨识结果。再次,基于含有竞争算法的Kohonen自组织映射(SOM)神经网络,提出了一种对车牌图像进行倾斜校正与字符分割的方法,将车牌中字符部分的像素点根据坐标间的欧氏距离聚为七类,根据神经元权值向量得到车牌的倾斜角度估计值,从而达到倾斜校正的目的。另外经过预处理后,SOM算法得到的权值向量还可以进一步利用最短距离法对车牌字符进行分割,实例说明了本算法的有效性。最后,在SOM竞争算法的基础上,结合径向小波网络,提出了一种自生成圆盘细胞分裂算法,并作为前一工作的后续,将其应用于车牌字符的识别应用中。该算法利用竞争机制将输入模式映射到二维单位圆盘上而不是矩形域中的神经元上,作为径向小波神经网络的隐层神经元,且不需事先给定规模,所需神经元的个数与分布情况均可由网络分类结果确定并由初始神经元模仿细胞分裂的方式得到。其中用于赋值分裂后神经元权值的“圆周近邻策略”不仅可以使得输入样本的圆盘映射保持拓扑序,还可以有效利用已经通过竞争算法训练过的神经元权值,使得算法更具高效性。通过对车牌中的英文字母样本、英文字母或数字样本进行分类识别实验,相比于经典径向基函数(RBF)网络,本文提出的算法可以在得到较小规模的网络前提下达到更高的识别正确率,具有较高的实用价值。
[Abstract]:Wavelet analysis and neural network are the main components of the new generation of computing intelligent information processing technology. The wavelet transform is a local transformation of a time domain and frequency domain. Using the expansion and translation operation of the wavelet function to analyze the signal in different scales, the useful information can be extracted from the signal effectively. It overcomes the tradition. Fu Liye transform can not simultaneously carry on the defect of time frequency analysis, so it becomes one of the frontier technologies of nonlinear science. The artificial neural network is a theoretical model formed by the rational abstraction of the neural network of the human brain. It can rely on self learning ability of the environment to obtain knowledge, and use the connection weights between the neurons. The wavelet neural network (WNN) is a product of the combination of wavelet analysis and neural network. It can maintain the ability of multi input parallel processing, self learning, nonlinear mapping and fault tolerance on one hand. On the other hand, the wavelet analysis with strong mathematical basis is easily applied to the high level. On the basis of the existing classical wavelet neural network model, this paper has studied the existing classical wavelet neural network model. The former is the main research object, the initialization of the adaptive wavelet network with tensor product type wavelet function, the structure and algorithm of the fuzzy wavelet network combining with the fuzzy mechanism, the radial wavelet network. The algorithm of the collaterals has been studied and analyzed in detail, and it is applied to signal prediction, system identification, pattern classification and so on, which make the wavelet networks have higher practical value and significance in application. The main work is: first, multidimensional input adaptive wavelet with the tensor product type wavelet activation function Network (WNN_M) is the earliest and most classic wavelet network model. Its scale parameters, translation parameters and linear weights are all adjustable parameters of the network. In application, the flexibility of the network is added, making it possible to approximate the nonlinear system with a smaller scale wavelet network. In its application, the initial parameters are still more Q.H.Zhang proposed. The heuristic method (HIA). In order to get the more ideal initial parameters for the model and make the network training fast convergence, an improved parameter initialization method (CIA) is proposed using the time-frequency localization feature of the hidden layer wavelet function (CIA). The method first sets the threshold vector according to the statistical characteristics of the multidimensional input data, and uses the most important method. The idea of adjacent clustering determines the number of neurons in the hidden layer of the network, and determines the initial value of the corresponding wavelet translation reference vector and the scale parameter by the time window width of the hidden layer wavelet function. The initial error of the three different time series prediction shows that the initial error of the WNN_M-CIA is compared to the WNN_M-HIA. It is obviously lower. After several iterations of the gradient descent method, the prediction accuracy is still better than the network prediction accuracy based on HIA initialization. It shows the validity and rationality of the initialization algorithm. Secondly, considering the trend of combining the fuzzy theory with the wavelet analysis and the neural network, a kind of TSK fuzzy system and the wavelet network are proposed. This model uses the wavelet network with continuous parameter and tensor product multidimensional wavelet activation function as the conclusion part of the TSK fuzzy system, analyzes the difference between the fuzzy wavelet network model and the existing fuzzy wavelet network model, and applies it to the nonlinear system identification. In the training algorithm, the selection of the particle swarm optimization is based on the particle swarm optimization. The hybrid optimization algorithm combined with the online gradient descent method. Through the identification experiments of two nonlinear systems, it can be seen that even if less fuzzy rules and parameters are used, compared with the existing models, the proposed model and algorithm can still get more satisfactory identification results. Again, based on the competition algorithm. The Kohonen self organizing mapping (SOM) neural network has proposed a method of tilt correction and character segmentation for the license plate images. The pixels of the characters in the license plate are divided into seven classes according to the Euclidean distance between the coordinates, and the estimation of the tilt angle of the license plate is obtained according to the weight vector of the neuron. In addition, the purpose of the tilt correction is achieved. After preprocessing, the weight vector obtained by the SOM algorithm can also further use the shortest distance method to segment the character of the license plate. The example shows the effectiveness of the algorithm. Finally, on the basis of the SOM competition algorithm, a self generated circular disk cell division algorithm is proposed with the radial wavelet network, which will be used as a follow-up of the previous work. It is applied to the recognition of license plate characters. The algorithm uses competition mechanism to map the input mode to the two-dimensional unit disk instead of the neuron in the rectangular domain. As a hidden layer neuron of the radial wavelet neural network, the number and distribution of the required neurons can be classified by the network classification results. The "circumference nearest neighbor strategy", which is used to assign the weights of the neurons after the splitting, can not only make the disk mapping of the input sample keep the topological order, but also effectively use the weights that have been trained by the competition algorithm, making the algorithm more efficient. Compared with the classic radial basis function (RBF) network, the proposed algorithm can achieve higher recognition accuracy and have higher practical value than the classical radial basis function (RBF) network.
【学位授予单位】：中北大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TP183;TP391.4

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