边坡演化的非线性时间序列多元混沌判别

Multivariable Chaotic Discrimination for Slope Evaluation According to Their Nonlinear Displacement-Time Sequence

以实测非线性时间序列为对象,通过估计延迟时间与嵌入维数的相空间重构方法,采取排除时间相关性点对的方法计算边坡系统关联维数D2;采用改进的Kantz法计算最大Lyapunov指数、以K2熵作为Kolmogorov熵的近似,并引入近似熵ApEn及系统复杂度混沌特征指标,研究了边坡演化的多元混沌特征.通过实例分析,发现多数边坡系统关联维数D2为非整数,最大Lyapunov指数、熵值均大于零以及系统复杂度位于(0,1)区间偏小值,通过与确定性系统特征量的比较,揭示了边坡系统的混沌特征,并得出临滑阶段边坡混沌特征最为明显的结论.

According to the displacement-time sequence data of several slopes, the multivariable chaotic features of slope evaluation process are discussed, including reconstruction for their phase-space by the estimation of delayed time and embedded dimension method, calculation for the correlation dimension D2 of the slope system by eliminating the time correlative points. Then, the multivariable chaotic features of the slopes are studied by calculating their maximum Lyapunov index using the improved Kantz method and taking K2 as the similar one of Kolmogorov entropy, and by introducing the approximation entropy--ApEn and the chaotic feature index describing the complexity degree of the system. Example analysis shows that the correlation dimension D2 is a non-integral number for most of slope systems, the maximum Lyapunov index and the entropy value are all bigger than 0, and the complexity degree of the system is located on the interval of （0, 1）. By comparing the calculated data with the actual characteristic value of the slope systems, the chaotic features of the slope system are revealed and the chaotic features are clearer in the time period closed to sliding.