基于分形维和局部切空间均值重构的非线性降噪方法  

Nonlinear noise reduction method based on fractal dimension and the local tangent space mean reconstruction

作　　者：王广斌[1,2] 黄良沛[1] 赵先琼[2] 

机构地区：[1]湖南科技大学先进矿山装备教育部工程研究中心,湘潭411201 [2]中南大学机电工程学院,长沙410083

出　　处：《电子测量与仪器学报》2010年第8期699-704,共6页Journal of Electronic Measurement and Instrumentation

基　　金：国家自然科学基金(编号:50875082)资助项目;湖南省科技计划(编号:2010CK3031)资助项目

摘　　要：基于主流形识别的非线性降噪方法中,约简目标维数选择随意和相空间数据在降维、全局排列和反求过程中可能畸变,使得降噪效率和效果降低。针对此问题,提出一种新的基于分形维和局部切空间重构的降噪算法。将主流形识别降噪通过仿射变换求解全局低维主流形的过程,变为对局部切空间低维坐标进行全局均值重构直接获取降噪后的全局相空间信号,并用分形几何方法估计信号的本征维数,以此作为主流形提取时的约简目标维数,在此维数空间之外的向量数据作为噪声进行消除。对混沌含噪信号和风机振动信号的降噪实验表明本文方法具有更好的降噪效果。In nonlinear noise reduction method based on principle manifold learning,reduction targets are chosen at random,and phase space data may be distorted in the process of dimension reduction,global array and signal reverse solution.It makes efficiency and effect of noise reduction lower.To solve this problem,a new noise reducation method based on fractal dimension and the local tangent space mean reconstruction is proposed.The process of solving global low-dimensional principle manifold by affine transformation will be replaced with mean reconstruction,and the intrinsic dimension is estimate as dimension of reduction targets by using fractal geometry method,the data in addition to intrinsic dimension space will be eliminated.Noise reduction experiments to chaotic signal with noise and fan’s vibration signal show this method has better noise reduction effect.

关 键 词：分形维 流形学习 局部切空间排列 降噪 

分 类 号：TN911[电子电信—通信与信息系统] TH133[电子电信—信息与通信工程]