lyapunov dimension 中文意思是什麼
lyapunov dimension
解釋
李雅普諾夫維數-
We describe the meaning of chaos > future idea of chaotic theory and influence on forecast ; introduce the character of chaotic time series, and point out the problem and shortage of the methods already existed computing character value which are fractal dimension and the largest lyapunov exponent and improve on it ; present the forecast principle of forecast method based on chaotic attractor, and point out the shortage of local field forecast method based on chaotic attractor and bring forward improved on methodo at the same time, we put forward a banausic algorithm and compare two models using practical example
論述了混飩的含義與混淪理論的未來觀及其對預測的影響；介紹了。混飩時間序列的特徵，指出了己有的計算分形維及最大李雅譜諾夫指數這兩個特徵量的方法存在的問題與不足，並對此進行了改進；給出了基於混飩吸引子的預測方法的預測原理，指出了常用的基於混燉吸引子預測的局域法的不足並給出了改進方法，同時，給出了其實用演算法，並用實例進行了比較。 -
Then r / s analysis, phase space reconstruction of the system, chaos analysis and fractals analysis are done through matlab program, based on original data of hushen stock markets compositive index from year 1991 to year 2002. and the author draws a conclusion based on original data that china ' s stock market obeys low - dimension fractals and ebb - chaos in terms of the experimentation result : hurst exponents are between 0 and 1, memory cycles are obvious, lyapunov exponents are more than zero and chaotic attractors correlative dimensions are between 2 and 3 in hushen stock markets in this thesis the concept information noises is put forward. stock market information about policy and company of the last ten years is packed up and classified for regulators make decisions in terms of power the factor influences the stock market index
之後文章以中國股市1991年至2002年上海和深圳綜合指數每日收盤價原始數據為研究對象，在matlab程序實驗條件下，進行了兩地股市系統的r / s分析、系統相空間重構、混沌分析、分形分析；獲取了兩地股市系統的赫斯特指數（滬深股市赫斯特指數均大於0 . 5而小於1 ） 、非周期記憶循環周期（滬深股市都有明顯的記憶循環周期） 、最大李雅普諾夫指數（兩市都大於0 ）和吸引子的關聯維數（兩市都在2到3維之間） ；從而得出中國股市系統是低維分形的、弱混沌的（基於原始數據）結論。 -
The key of calculating fractal dimension and lyapunov exponents is to establish a good phase space. moreover, catastrophe parameter is an important feature of nonlinear time series. methods of calculating fractal dimension, lyapunov exponents and catastrophe parameter from seismic trace are exhausted
4 、 lyapunov指數混沌控制波阻抗反演的優化方法：從地震信號中反演出地下多層介質的波阻抗，以此判斷介質和含流體性質，是地球物理的難點和重點。 -
3. feature extraction of time series based on chaos theory is explored, which include the problem of temporal correlation in correlation dimension method, the robust method to evaluate the maximum lyapunov exponents, the extraction of generalised dimensions and the evaluation of h2 entropy of time series
研究了時間序列的混沌特徵參數提取方法。包括關聯維數演算法中的時間相關、最大lyapunov指數的穩健估計演算法以及廣義維數和時間序列熵h _ 2的估計問題。 -
The chaotic invariants of measured time series of dams such as correlation dimension, the lyapunov exponent and the kolmogorov entropy, are calculated
對大壩觀測時間序列進行了相空間重構，計算其混沌特徵量，即吸引子維數（關聯維數） 、 lyapunov指數和kolmogorov熵。 -
We reconstructed the phase space and calculated the nonlinear parameters such as correlation dimension, the largest lyapunov exponent, approximate entropy, and l - z complexity of the data. it can be conclud from the results that the reconstruction of heart beat rate signal is strange, its correlation dimension is between 5 to 7 and have the character of fractal dimension, its largest lyapunov exponent is larger than zero, its approximate entropy and l - z complexity are obviously differ from noise. we can draw a conclusion from all above : the heart beat rate signal is n ' t simple noise, it is high dimensional chaos obeys certain dynamical law
我們還對信號進行了相空間重構，計算了信號的關聯維數、最大lyapunov指數、近似熵和復雜度這幾個非線性特徵量，我們發現，心率信號的吸引子是奇怪吸引子，關聯維數介於5到7之間，具有分維的特徵，其最大lyapunov指數大於0 ，其近似熵值和復雜度值明顯區別于噪聲，這說明心率信號不是隨機噪聲，它是服從確定性動力學規律的高維混沌信號。 -
At first, construct ten sets of surrogate data for each emg data, then calculate the correlation dimension ( dcorr ), correlation time, maximum lyapunov exponent ( a, ), l - z complexity and approximate entropy ( apen ) of both the original emg data and surrogate data, and then compare them
構造這四例肌電信號的代替數據（各十組） ，分別計算原數據及其代替數據的關聯維、關聯時間、最大李雅普諾夫指數、 l - z復雜度和近似熵，我們發現，四例原數據的以上所有特徵量都與各自所對應的十組代替數據存在明顯差別。 -
As an example, the time series of china composite stock index is considered firstly, the distribution of five day ' s return on china composite stock index is studied. secondly, based on the r / s analysis hurst exponent is worked out and determination detecting can be done. lastly, the topological characteristics such as correlation dimension and maximum lyapunov exponent are extracted from time series
作為例子，本文對中國股票指數時間序列做了實證分析，首先研究了中國股票指數的五天收益率的分佈規律，然後運用重標極差分析方法計算出赫斯特指數，並以此為基礎進行確定性檢驗，最後在相空間重構的基礎上提取吸引子的拓撲特徵指數。 -
These include two keys problem in phase space reconstruction theory, that is embedding dimension and optimal delay time, and numeric recognition of chaos, that is lyapunov exponent, as well as numeric recognition of fractal, that is correlative dimension of chaotic attractors
其中重點講述了非線性動力學的數值研究實驗方法：相空間重構的兩個關鍵問題，即嵌入維數和最佳延遲時間；混沌的數值識別，即李雅普諾夫指數；分形的數值識別，即吸引子的關聯維數。 -
The one dimension lyapunov exponent mode of boiler tube leak prediction is confirmed
確定了爐管泄漏預報的一維lyapunov指數模式。 -
The parameters used in this paper are : fractal dimension, lyapunov exponent and entropy
本文涉及的參數有：分形維數、 lyapunov指數和熵。 -
To find out characteristic of lithology and liquid under surface, seismic trace inversion is very important in geophysics. based on chaos theory, chaotic feature of inversion dynamical system is analyzed, and targeting chaos, controlling chaos and algorithm of lyapunov exponent in high dimension dynamical system are discussed, then a new method of seismic trace nonlinear inversion controlled by lyapunov exponent is presented. the successful emulation is realized
本文從廣義反演理論得到的動力系統的混沌特性分析入手，綜合各種優化演算法、目標混沌和混沌控制的最新成果、高維lyapunov指數計算方法，創造性地提出了一種解決高維離散動力系統穩定性問題的lyapunov指數混沌控制優化演算法，數據模擬計算顯示，該方法具有較高的精度和運算速度。 -
The strain softening of dam body and foundation is the necessary condition for dam instability. according to observation data of dam cracks, a gray cusp catastrophe model is established to judge the stability of the crack. according to the slope observation data of a certain hydropower plant, a nonlinear dynamic model is developed by means of reversion and the lyapunov exponent spectrum, and the lyapunov information dimension are calculated for judgement of the stability of the slope
（ 5 ）基於變分原理，研究建立了能量形式的失穩準則，並說明壩體、巖基的材料具有應變軟化的性質，是大壩失穩的必要條件；並利用大壩的裂縫實測資料，建立了相應的灰色尖點突變模型，由此判斷裂縫的穩定性；根據某水電站庫區滑坡體的變形實測資料，反演其非線性動力學模型，進而計算lyapunov指數譜、 lyapunov信息維來判定邊坡的穩定性及穩定程度。 -
The qualitative work including : research the phase trajectory of the system 、 poincare map 、 power spectral and auto - correlation. the quantitative work including : calculation of ratio of period 、 calculation of fractional dimension and coefficient of lyapunov, especially ratio of period and the maximum lyapunov exponent. the results show that chaos occurs in the movement of system
定性的研究工作有：研究系統運動的相軌圖、龐加萊映射圖、功率譜圖和自相關函數圖；定量方面的研究工作有：周期比的計算、分維數的計算和lyapunov指數的計算，並著重進行了周期比和最大lyapunov指數的計算。 -
By the characteristic analysis of slope displacementtime series, the largest lyapunov exponent and saturation inseted dimension are obtained, and the longestforecast time is given. on this base, the number of inputing node of neural network isgiven, moreover, the method of forecasting slope displacement is presented based onadaptive neural network
在此基礎上，確定了神經網路的輸入節點數，建立了基於自適應神經網路的邊坡位移預報方法，並把混沌理論與神經網路方法結合起來對邊坡穩定性進行評價。
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