(中南工業(yè)大學(xué)資源環(huán)境與建筑工程學(xué)院， 長(zhǎng)沙 410083)
摘 要: 系統(tǒng)闡述了分形插值的原理, 介紹了分形布朗運(yùn)動(dòng)(FBM)的概念及其構(gòu)造方法，針對(duì)自然界實(shí)際系統(tǒng)分形特性，提出了實(shí)際FBM系統(tǒng)分形特性的判別準(zhǔn)則。在此基礎(chǔ)之上提出了基于FBM的分形插值方法，闡述了分形插值的基本條件；對(duì)于實(shí)際的裂隙結(jié)構(gòu)，利用分形插值方法建立的模型進(jìn)行了滲流計(jì)算，并與常規(guī)插值所得結(jié)果進(jìn)行了比較。結(jié)果表明，對(duì)于具有分形特性的實(shí)際的復(fù)雜、非線性系統(tǒng)，利用基于FBM的分形插值方法從大尺度來(lái)構(gòu)造微觀細(xì)節(jié)，能保持微觀與宏觀之間的相似性， 更能取得有效的結(jié)果。
關(guān)鍵字: 分形 插值 布朗運(yùn)動(dòng)
（College of Resources, Environment and Civil Engineering,Central South University of Technology, Changsha 410083, P. R. China）
Abstract:The principle of the fractal interpolation was systematically discussed, the concept and constructing arithmetic of FBM were introduced, and the authors advanced the ruler to identify fractal property and the arithmetic of the fractal interpolation of real FBM system. Based on the fractal FBM interpolation, the authors advanced a fractal model of seepage of real fracture, and gave the comparison between the fractal model and other model. The result proved that the method, that used FBM method to build the small scale date with the big scale date, could keep the similarity between the macrostructure and microstructure and got more useful result.
Key words: fractal interpolation Brownian Motion
