發(fā)布時(shí)間：2018-05-01 15:36

  本文選題：演化矩陣 + 切空間　； 參考：《哈爾濱工程大學(xué)學(xué)報(bào)》2017年05期

【摘要】：針對(duì)Lyapunov指數(shù)計(jì)算過程中,鄰近點(diǎn)對(duì)演化難以有效刻畫混沌軌道在相空間不同方向的動(dòng)態(tài)特性問題,本文研究了混沌重構(gòu)相空間中映射矩陣的構(gòu)造方法,推導(dǎo)了混沌振動(dòng)實(shí)測(cè)時(shí)間序列重構(gòu)相空間中Lyapunov特征指數(shù)演化矩陣算法表達(dá)式,分析了軌道演化過程中切空間級(jí)聯(lián)矩陣對(duì)參考點(diǎn)鄰域的拉伸折疊作用,揭示其特征向量方向是鄰域變形的方向、奇異值大小對(duì)應(yīng)特征方向上鄰域拉伸和壓縮的大小。構(gòu)造了包含映射值域和定義域的增廣矩陣,通過微擾法分析了計(jì)算過程的誤差。計(jì)算結(jié)果表明,應(yīng)用重構(gòu)演化矩陣算法能夠有效提取混沌時(shí)間序列最大Lyapunov指數(shù)。設(shè)計(jì)了非線性混沌振動(dòng)實(shí)驗(yàn)裝置,證實(shí)了該方法的有效性。
[Abstract]:In order to solve the problem that it is difficult to describe the dynamic characteristics of chaotic orbits in different directions in phase space during the calculation of Lyapunov exponent, this paper studies the construction method of mapping matrix in chaotic reconstructed phase space. The algorithm expression of Lyapunov characteristic exponential evolution matrix in phase space reconstruction of chaotic vibration measured time series is derived, and the stretching and folding effect of tangent space cascade matrix on the neighborhood of reference point during orbit evolution is analyzed. It is revealed that the direction of eigenvector is the direction of neighborhood deformation, and the value of singular value corresponds to the magnitude of neighborhood stretching and compression in the direction of feature. An augmented matrix including mapping range and domain is constructed, and the error of calculation process is analyzed by perturbation method. The results show that the reconstructed evolutionary matrix algorithm can effectively extract the maximum Lyapunov exponent of chaotic time series. The experimental device of nonlinear chaotic vibration is designed, and the validity of the method is verified.
【作者單位】： 海軍工程大學(xué)動(dòng)力工程學(xué)院;
【基金】：國(guó)家自然科學(xué)基金項(xiàng)目(5157942);國(guó)家自然科學(xué)基金青年基金項(xiàng)目(51509253)
【分類號(hào)】：O415.5

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本文編號(hào)：1830014