滑坡位移之混沌非線性預測模式

Application of Chaotic Nonlinear Theory to the Prediction of Landslide Movement

李柏翰(Po-Han Lee)

指導教授 ： 楊長義

淡江大學/工學院/土木工程學系碩士班/碩士(2007年)

https://doi.org/10.6846/TKU.2007.00092

摘要

地滑之動態演化過程中是一個開放系統，在該系統內，各因素間相互作用的過程是一個複雜的非線性過程。在混沌理論下，對於任何觀測資料，若經檢驗相關維度d2、Kolmogrov熵K2及Lyapunov指數LE1，確定為混沌現象，便能對系統未來行為做預測。文中主要以分析台灣地滑案例，探討整體地滑的混沌因子，期有效預測坡體動態之位移，並建立一套即時回饋預報系統。
研究結果得致下列主要結論：（1）地滑位移時間序列資料中，若具有混沌現象者，其相關維度d2隨著嵌入維度m的增加而趨於飽和，具有漸近極值。混沌現象的最大Lyapunov特徵指數LE1＞0，係在描述相空間中兩相鄰軌道呈現指數發散的性質。混沌運動的時間序列其Kolmogorov熵K2為有限的正值。（2）檢視任一時間序列是否有混沌現象，都必須同時檢核d2、K2和LE1三種混沌的特徵因子。（3）梨山滑坡之相關維度d2 = 4.40~4.85，顯示在模式化梨山滑坡動態特性時，至少需用5個變數來描述，相對上阿里山滑坡行為（d2 = 4.31~5.40，至少需要6個變數描述）稍較梨山複雜。而新莊捷運工地的開挖位移行為之d2 = 2.70~3.98，則顯示至少需用4個變數就可以完整描述其動態特性，暗示其所受到之外在影響因素較少。（4）非線性之Lyapunov指數法之預測結果與實際值相差不遠，顯示非線性預測模式可以完整反映地滑行為。

關鍵字

地滑 ； 時間序列 ； 混沌 ； 相關維度 ； Kolmogorov熵 ； Lyapunov指數

並列摘要

The evolution of a landslide is controlled by the intrinsic rock properties and the external factors. In the landslide system, the interactive mechanism between the numerous factors is complicated. However, the measured displacement in the field is the final of these complicated interactions. For any measurement in time series, the landslide behavior is chaos if the correlation dimension (d2), Kolmogorov entropy value (K2), and Lyapunov exponents (LE1) have been insured. The measurement information in this time series could be back-calculated to predict the future movement in the same landslide. This research aims to study the chaotic behavior of landslide measurement displacement in Taiwan. A nonlinear model is to be employed to predict the displacement of landslide.
This study got the results as follows, (1) In landslide time series, if the correlation dimension (d2) with Chaos phenomenon reached the saturation while the correlation dimension (m) increases, it has asymptotic extreme value. The system includes the character of Chaos and if the biggest characteristic Lyapunov exponent is greater than zero(LE1＞0), we can explain that the neighborhood track in phase space displays the nature of index dispersion. The system is in Chaos movement which Kolmogorov entropy value (K2) is limitedly positive. (2) In order to examine if there’s any time series having Chaos phenomenon, we have to check three Chaos characteristic factors (d2、K2、LE1) at the same time. (3) The correlation dimension of Li Shan is d2=4.40~4.85, which means we need 5 variables to describe the dynamic characteristics of landslide. Relatively, the landslide in A-li Shan (d2=4.31~5.40) is more complicated. Moreover, the correlation dimension of the digging project of Xin-Zhuang MRT, d2=2.70~3.98, which shows we can use 4 variables to describe the landslide process and also implies the external factors are less. (4) The forecast result of non-linear theory's Lyapunov exponent method is close to the real measure data and it reflects that non-linear forecast model can completely prove landslide movement.

並列關鍵字

landslide ； time series ； Chaos ； correlation dimension ； Kolmogorov entropy ； Lyapunov exponent

參考文獻

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