基于神经网络的非线性动力系统数值求解与图像分割研究

发布时间：2018-01-28 11:25

本文关键词： 非线性动力系统数值解图像分割模糊粗糙集小波神经网络　出处：《宁夏大学》2017年硕士论文　论文类型：学位论文

【摘要】：近二十年来,关于非线性科学的研究发展速度非常快.非线性动力系统具有多样性,而且依赖于之前的状态,发生变化的方式更复杂,在一般情况下很难得到解析解.因此,构造具有精确度高,简单易行的方法来求解非线性动力系统,以数值解近似代替解析解,是实际应用过程中需要解决的难题.贺兰山岩画图像时间跨度大,年代久远且均为露天石刻,由于遭受自然现象的腐蚀和人为因素的影响,普遍存在信息缺失以及模糊不确定的情况.如果仅仅采用传统的图像分割方法,会造成结构复杂,训练速度慢,分类精度低等问题.本文着重探讨了粗糙集、模糊集及小波神经网络,在传统模糊C-均值算法的基础上,提出基于模糊集的粗集小波神经网络分割方法,并将其应用于贺兰山岩画的图像分割中.本文主要研究工作如下:1.研究了基于三次样条函数求解非线性动力系统的数值解.与现有方法相比,文中所构造的方法不仅具有较高的逼近精度,而且还能避免Runge现象.然后通过两个数值算例给出了几种方法的误差分析,结果表明本文所提方法具有更高的逼近精度及较低的计算复杂性.2.针对粗糙集在处理连续属性方面的不足,在此主要介绍了结合空间信息的模糊C-均值聚类算法,对初始决策表的每一个连续属性采用模糊变量进行表示,通过隶属函数对论域空间实现最优划分.然后再将该方法应用到贺兰山岩画图像及噪声图像中,利用聚类有效性函数对分割结果进行综合评价.3.在利用基于空间信息的模糊C-均值聚类算法得到论域空间的最优划分后,将小波神经网络和粗糙集相结合.设计了贺兰山岩画分割实验,·将实验结果与小波神经网络和传统的粗集小波神经网络算法进行比较,通过UM、GC、UMA及算法运行时间这四个评价指标对分割效果进行综合分析,验证了本文设计的算法具有泛化能力强、训练精度高及运行速度快的优势.最后总结了全文的主要研究内容和成果,对当前还未深入探讨、今后需要进一步研究的工作进行了展望.
[Abstract]:In the past two decades, the research on nonlinear science has developed very rapidly. Nonlinear dynamic systems are diverse, and depend on the previous state, so the way of change is more complex. In general, it is difficult to obtain an analytical solution. Therefore, the method with high accuracy and simplicity is used to solve the nonlinear dynamic system, and the approximate solution is replaced by the numerical solution. It is a difficult problem to be solved in the process of practical application. Because of the corrosion of natural phenomena and the influence of human factors, the rock paintings of Helan Mountain have a long time span, long time span and are all open-air stone carvings. If traditional image segmentation methods are used only, the structure will be complicated, the training speed will be slow, and the classification accuracy will be low. This paper focuses on rough sets. Based on the traditional fuzzy C-means algorithm, a rough set wavelet neural network segmentation method based on fuzzy set and wavelet neural network is proposed. The main work of this paper is as follows: 1. The numerical solution of nonlinear dynamic system based on cubic spline function is studied. Compared with the existing methods. The proposed method not only has high approximation accuracy but also can avoid Runge phenomenon. Then the error analysis of several methods is given through two numerical examples. The results show that the proposed method has higher approximation accuracy and lower computational complexity. 2. Aiming at the shortcomings of rough sets in dealing with continuous attributes. In this paper, the fuzzy C-means clustering algorithm combining spatial information is introduced. Each continuous attribute of the initial decision table is represented by fuzzy variables. The optimal partition of the domain space is realized by membership function, and then the method is applied to the rock painting image and noise image of Helan Mountain. The clustering validity function is used to evaluate the segmentation results synthetically. 3. After the fuzzy C- means clustering algorithm based on spatial information is used to obtain the optimal partition of the domain space. Combining wavelet neural network with rough set, the experiment of rock painting segmentation in Helanshan is designed, and the experimental results are compared with wavelet neural network and traditional rough set wavelet neural network algorithm through UMGC. The UMA and the running time of the algorithm are the four evaluation indicators for the comprehensive analysis of the segmentation effect, and verify that the algorithm designed in this paper has a strong generalization ability. At last, the main research contents and achievements of the paper are summarized, and the work that needs further research in the future is prospected.
【学位授予单位】：宁夏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O19;TP391.41;TP183

【参考文献】