本文關(guān)鍵詞： 非線性動力系統(tǒng) 數(shù)值解 圖像分割 模糊粗糙集 小波神經(jīng)網(wǎng)絡(luò)　出處：《寧夏大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：近二十年來,關(guān)于非線性科學(xué)的研究發(fā)展速度非�？�.非線性動力系統(tǒng)具有多樣性,而且依賴于之前的狀態(tài),發(fā)生變化的方式更復(fù)雜,在一般情況下很難得到解析解.因此,構(gòu)造具有精確度高,簡單易行的方法來求解非線性動力系統(tǒng),以數(shù)值解近似代替解析解,是實際應(yīng)用過程中需要解決的難題.賀蘭山巖畫圖像時間跨度大,年代久遠(yuǎn)且均為露天石刻,由于遭受自然現(xiàn)象的腐蝕和人為因素的影響,普遍存在信息缺失以及模糊不確定的情況.如果僅僅采用傳統(tǒng)的圖像分割方法,會造成結(jié)構(gòu)復(fù)雜,訓(xùn)練速度慢,分類精度低等問題.本文著重探討了粗糙集、模糊集及小波神經(jīng)網(wǎng)絡(luò),在傳統(tǒng)模糊C-均值算法的基礎(chǔ)上,提出基于模糊集的粗集小波神經(jīng)網(wǎng)絡(luò)分割方法,并將其應(yīng)用于賀蘭山巖畫的圖像分割中.本文主要研究工作如下:1.研究了基于三次樣條函數(shù)求解非線性動力系統(tǒng)的數(shù)值解.與現(xiàn)有方法相比,文中所構(gòu)造的方法不僅具有較高的逼近精度,而且還能避免Runge現(xiàn)象.然后通過兩個數(shù)值算例給出了幾種方法的誤差分析,結(jié)果表明本文所提方法具有更高的逼近精度及較低的計算復(fù)雜性.2.針對粗糙集在處理連續(xù)屬性方面的不足,在此主要介紹了結(jié)合空間信息的模糊C-均值聚類算法,對初始決策表的每一個連續(xù)屬性采用模糊變量進(jìn)行表示,通過隸屬函數(shù)對論域空間實現(xiàn)最優(yōu)劃分.然后再將該方法應(yīng)用到賀蘭山巖畫圖像及噪聲圖像中,利用聚類有效性函數(shù)對分割結(jié)果進(jìn)行綜合評價.3.在利用基于空間信息的模糊C-均值聚類算法得到論域空間的最優(yōu)劃分后,將小波神經(jīng)網(wǎng)絡(luò)和粗糙集相結(jié)合.設(shè)計了賀蘭山巖畫分割實驗,·將實驗結(jié)果與小波神經(jīng)網(wǎng)絡(luò)和傳統(tǒng)的粗集小波神經(jīng)網(wǎng)絡(luò)算法進(jìn)行比較,通過UM、GC、UMA及算法運行時間這四個評價指標(biāo)對分割效果進(jìn)行綜合分析,驗證了本文設(shè)計的算法具有泛化能力強、訓(xùn)練精度高及運行速度快的優(yōu)勢.最后總結(jié)了全文的主要研究內(nèi)容和成果,對當(dāng)前還未深入探討、今后需要進(jìn)一步研究的工作進(jìn)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.
【學(xué)位授予單位】：寧夏大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O19;TP391.41;TP183

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