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非双曲线型非线性系统同宿切面点和同宿横截点的存在,使得其时间序列的去噪或轨迹重影变得十分困难。在充分挖掘非线性系统本身特性的基础上,结合Gradient Descent算法的稳定性和Newton-Raphson算法的快速收敛性,提出了一种快速稳定的非双曲线型非线性时间序列去噪新算法,在机器精度内实现了非双曲线型非线性时间序列的去噪。该方法首先计算受扰序列的局部稳定流形和不稳定流形方向,进而确定同宿切面点存在的位置,很大程度上降低了同宿切面对算法性能的影响。不同于现有文献忽视同宿横截点对算法性能影响的做法,研究得出了同宿横截点间的最小距离和干扰噪声均方差二者间的关系,首次定量地估计了同宿横截点可能对算法造成的影响,这无疑对其他算法也将是一个有益的启示。
The existence of homoclinic and homoclinic cross-points in non-hyperbolic nonlinear systems makes it very difficult to denoise or track ghost in time series. On the basis of fully exploiting the characteristics of nonlinear system and combining with the stability of Gradient Descent algorithm and the fast convergence of Newton-Raphson algorithm, a fast non-hyperbolic non-hyperbolic nonlinear time series denoising algorithm is proposed. In Non-hyperbolic nonlinear time series denoising is achieved within machine accuracy. The method first calculates the local stable manifolds and unstable manifolds of the perturbed sequences, and then determines the existence of the homoclinic point, which greatly reduces the influence of the same cut plane on the performance of the algorithm. Different from the existing practice of ignoring the influence of homoclinic crosstalk on the performance of the algorithm, the relationship between the minimum distance between homoclinic intersections and the mean square error of the interfering noise is studied. It is estimated for the first time that the same-site intercept The impact on the algorithm, which undoubtedly will also be a helpful revelation for other algorithms.