【作者】 李胜朋； 王洪礼； 冯剑丰；

【Author】 LI Sheng-peng, WANG Hong-li, FENG Jian-feng (College of Mechanical Engineering, Tianjin University, Tianjin 300072, China)

【机构】 天津大学机械工程学院,天津大学；

【摘要】 非线性动力学的混沌理论在许多领域变得越来越重要,如信号处理。最大李雅谱诺夫指数是判断动力系统稳定性和检验混沌的主要依据。本文提出一种从时间序列计算最大李雅谱诺夫指数的新方法。它运用回归树的随机梯度Boosting拟合非线性函数。由于回归树不连续,其雅可比矩阵不存在,传统的雅可比方法不能运用。本文直接从回归树计算最大李雅谱诺夫指数,不考虑拟合函数的雅可比函数。随机模拟结果表明该方法能很好逼近真值,且对噪音和嵌入维数稳健。运用本文方法和人工神经网络都证实两个实际日观测数据不存在混沌。更多还原

【Abstract】 Chaos theory in dynamics system is becoming more and more important in many fields, like signal processing. Largest Lyapunov exponent is a useful measure of the stability of a dynamics system and successful method to test for chaos. A new method to estimate largest Lyapunov exponent from observed time series is proposed. It fits the nonlinear function by Stochastic Gradient Boosting of regression tree. Since regression trees are discontinuous, its Jacobin matrix doesn’t exist and regular methods based on function estimator fails. we directly calculate Lyapunov exponent from them without using Jacobin matrix of the fitted function. A simulation study to evaluate our method’s performance shows that the new method approximates the true value excellently and has great robustness to noise and embedding dimension. Two observed daily series are deduced not chaotic both by this method and artificial neural network.更多还原