基于M-K检验和最小二乘法的SSA算法研究  

Research on SSA Algorithm Based on M-K Trend Test and Least Square Method

作　　者：贾国庆[1] 程明龙 易辉跃[2,3] 房卫东 许晖[2,3] JIA Guoqing;CHENG Minglong;YI Huiyue;FANG Weidong;XU Hui(College of Physics and Electronic Information Engineering,Qinghai Minzu University 810007,China;Shanghai Institute of Microsystem and Information Technology,Chinese Academy of Sciences,Shanghai 201800,China;Shanghai Wireless Communication Research Center,Shanghai 201800,China)

机构地区：[1]青海民族大学物理与电子信息工程学院,青海西宁810007 [2]中国科学院上海微系统与信息技术研究所,上海201899 [3]上海无线通信研究中心,上海201210

出　　处：《佳木斯大学学报（自然科学版）》2022年第5期29-33,61,共6页Journal of Jiamusi University：Natural Science Edition

基　　金：青海省应用基础研究计划(2020-ZJ-724)。

摘　　要：在对振动信号处理过程中,由于环境噪声等因素的影响,会使得信号产生畸变,影响分析结果。传统奇异谱分析(Singular Spectrum Analysis,SSA)在进行振动信号处理时,可以分离出振动信号的趋势项和周期项,但是仍然存在信号相位移动和奇异值突变的现象。针对该问题,提出了一种基于M-K检验和最小二乘法的SSA改进算法。首先,通过对原始数据两端添加一定长度的伪数据,修正和消除了SSA重构后的信号相位移动现象。对奇异值进行最小二乘法拟合,降低奇异值突变的程度。然后,经M-K趋势项检验,根据统计值自适应选择最优分组重构阶次,获取能量占比高的奇异值,提高信号降噪能力。实验结果表明,相比于传统SSA和其他一些改进SSA算法,基于M-K检验和最小二乘法的SSA改进算法在振动信号降噪处理能力上有明显的优势,信号质量得到了改善,有利于准确获取振动体的振动频率等参数。In the process of vibration signal processing,due to the influence of environmental noise and other factors,the signal will be distorted and the analysis result will be affected.The traditional Singular Spectrum Analysis(SSA)can separate the trend term and period term of the vibration signal,but there are still phenomena of signal phase shift and singular value mutation.In order to solve these problems,an improved SSA algorithm based on M-K test and least square method is proposed.Firstly,by adding dummy data of a certain length to the both ends of the original data,the signal phase shift phenomenon after SSA sub-reconstruction is corrected.Moreover,the singular values are fitted with least squares method to reduce the degree of sudden change of singular values.After the M-K trend item test and according to the statistical value,the optimal group reconstruction order is adaptively selected to obtain the singular value with a high energy content,and thus the noise in the signal is significantly reduced.Finally,the experimental results show that compared with the traditional SSA algorithm,the improved SSA algorithm has obvious advantages in noise reduction ability for the vibration signal,and in turn it is conducive to accurately obtain the vibration frequency and other parameters of the vibration body.

关 键 词：奇异谱分析 M-K检验 最小二乘法 奇异值突变 振动信号 

分 类 号：TP535[自动化与计算机技术]