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中文摘要：
在小数据量法的基础上,采用非线性最小二乘法估算含噪声多变量混沌时间序列的最大Lyapunov指数（λ1）.首先介绍了小数据量法求解λ1的原理,然后给出了非线性最小二乘法估算λ1的算法原理和具体实现步骤,最后将该方法分别用于Rossler耦合混沌系统和多组冲击地压监测时间序列的λ1求解.Rossler耦合系统结果表明该方法能明显提高有限长且含有噪声的多变量混沌时间序列的λ1的估算精度.冲击地压数据的结果表明这些数据均具有混沌特性,可进行8～15d的预测,这为冲击地压的短期预测提供了有力的支撑.
英文摘要：
This paper proposed a nonlinear least squares algorithm to solve the Largest Lyaponuv Exponent （λ1） of multivariate chaotic time-series with noise based on a small-data method.Firstly,a small-data method was introduced.Then,the algorithm principle and realization of nonlinear least squares estimation were given.The method was employed to solve λ1 of a Rossler coupled chaotic system and multiple sets of data to monitor Rockburst,respectively.The results of the Rossler coupled system showed that the algorithm could significantly improve λ1 calculation accuracy of multivariate time-series with limited-length and noise.The results of Rockburst data demonstrated that these data had chaotic characteristic,and could be predicted for 8 ～ 15 days,which provided a power support for short-term forecasting of Rockburst.
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