基于多变量最大Lyapunov指数高边坡 稳定分区研究

 最大Lyapunov指数(MLE)能够揭示边坡变形系统演化的非线性混沌特征，且理论与实践证明多变量较单变量时序计算得到的MLE更为真实。探讨多变量相空间重构理论，基于相点演化的时间轨道不可逆与可逆特性提出三维变形时序MLE双向搜索修正方法。采用小湾水电站左岸2#山梁高边坡三维变形监测数据进行MLE计算，以MLE为稳定判据并结合边坡变形失稳率与失稳度进行分区研究，得出2#山梁高边坡由下至上牵引式变形特征。研究表明，新方法有效可靠，且能够为高边坡稳定性分区评价与治理提供依据。

ANALYSIS OF STABILITY ZONING OF HIGH SLOPES USING MAXIMAL LYAPUNOV EXPONENT BASED ON MULTIVARIATE TIME SERIES

The maximal Lyapunov exponent(MLE) can reveal the nonlinear chaos feature of the dynamical evolution of steep slopes，and the MLE derived from multivariate time series is more practical than univariate time series. The 3D multivariate phase space reconstruction is investigated. Then，the modified method of bi-direction search is developed for calculating the MLE from 3D deformation time series based on the reversible and irreversible properties of time trajectories. Finally，the proposed method is applied to the high slope No.2 at Xiaowan Hydropower Station. Bottom-up towing deformation mechanic of this slope is obtained by the MLE used as the judging criterion of slope stability zoning，which agree well with practical situation. Thus，the proposed method is proven to be effective and reliable，and the research results have useful references to the evaluation and prevention of stability zoning of high slopes.