基于非线性薛定谔方程的时间序列去噪  

Time Series Denoising Using Nonlinear Schrödinger Equation

作　　者：雷一凡 宋刚 高成勇[2] 包芳勋[1] 张云峰[3] Lei Yifan;Song Gang;Gao Chengyong;Bao Fangxun;Zhang Yunfeng(School of Mathematics,Shandong University,Jinan 250100;School of Physics,Shandong University,Jinan 250100;School of Computer Science and Technology,Shandong University of Finance and Economics,Jinan 250014)

机构地区：[1]山东大学数学学院,济南250100 [2]山东大学物理学院,济南250100 [3]山东财经大学计算机科学与技术学院,济南250014

出　　处：《计算机辅助设计与图形学学报》2021年第8期1202-1209,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61672018,61972227,61873117,U1609218);山东省自然科学基金(ZR201808160102,ZR2019MF051);山东省重点研发计划(GG201710090122,2017GGX10109,2018GGX101013);山东省高等学校优势科研人才团队培育计划基金.

摘　　要：针对噪声污染严重的时间序列,提出一种基于动态随机共振效应的去噪方法.通过具体分析非线性光学系统中的动态随机共振效应,推导出非线性薛定谔方程中的非线性扰动项,得到用于描述非线性系统中的信号传播模型,并应用于时间序列去噪.首先将归一化的时间序列信号输入模型系统,然后通过自适应粒子群优化算法确定系统传播方程中的各项参数,最后利用分步傅里叶方法求解传播方程的数值解,作为系统的输出.对于一些典型的时间序列信号,与现有的去噪方法相比,文中方法在信噪比上平均提高0.3~3.7 dB,在均方根误差上平均降低0.03~0.11,该方法在时间序列去噪上具有更好的效果.In order to remove noise in time series with quantities of noise,a denoising method based on dy-namical stochastic resonance is presented.By analyzing the dynamical stochastic resonance in nonlinear op-tical systems,the nonlinear disturbance in nonlinear Schrödinger equation is derived,the propagation model is obtained and applied to time series denoising.Firstly,the time series signal is normalized as system input.Then the parameters of the system propagation equation are determined by the adaptive particle swarm op-timization algorithm.The numerical solution of the propagation equation is obtained by the split step Fourier method as system output.Compared with the existing denoising methods,proposed method improves sig-nal-to-noise ratio by 0.3‒3.7 dB,reduces by 0.03‒0.11 on average for typical time series signals.Experi-mental results show the better denoising ability of proposed method.

关 键 词：非线性薛定谔方程 动态随机共振 自适应粒子群优化 时间序列去噪 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]