Aiming at the problem that the actual engineering vibration noise signal has strong noise with strong nonlinear characteristic, a phase space reconstruction method based on adaptive intrinsic dimension estimation manifold learning was proposed. Firstly, one-dimensional time series with noise were reconstructed into a high dimensional phase space by phase space reconstruction. Secondly, the intrinsic dimension of each sample point in the phase space was estimated based on the maximum likelihood estimate (MLE) and adaptive weighted average method was used to obtain the global intrinsic dimension. At last, the manifold learning algorithm local tangent space alignment ( LTSA) was employed project the signal with noise from the high-dimensional phase space to the intrinsic dimensional space of useful signal and eliminate the noise distributed in high-dimensional space. The Lorenz simulation and wind noise reduction of vibration signal instance proved that the proposed method has good performance in nonlinear noise reduction.
马婧华，汤宝平，宋涛. 基于自适应本征维数估计流形学习的相空间重构降噪方法[J]. 振动与冲击, 2015, 34(11): 29-34.
MA Jing-hua, TANG Bao-ping, SONG Tao. Phase space reconstruction method based on adaptive intrinsic dimension estimation manifold learning. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(11): 29-34.
[1] Jiang Y H, Tang B P, Qin Y, et al. Feature extraction method of wind turbine based on adaptive Morlet wavelet and SVD[J]. Renewable energy, 2011, 36(8): 2146-2153.
[2] Zhong M C, Zhang C L, Cheng L, et al. Vibration signal of recoil mechanism de-noising processing based on wavelet analysis[J]. Applied Mechanics and Materials, 2013(401): 1424-1427. 说
[3] Takens F, Detecting sange attractors in turbulence [R]． Lecture Notes in Math．New York： SpringeL 1981．
[4] Yin J, Hu D, Zhou Z. Noisy manifold learning using neighborhood smoothing embedding[J]. Pattern Recognition Letters, 2008, 29(11): 1613-1620.
[5] Zhang Z, Zha H. Local linear smoothing for nonlinear manifold learning[J]. Technical Report, CSE, Penn State Univ, 2003.
[6] Chang H, Yeung D Y. Robust locally linear embedding[J]. Pattern recognition, 2006, 39(6): 1053-1065.
[7] 阳建宏,徐金梧,杨德斌,等. 基于主流形识别的非线性时间序列降噪方法及其在故障诊断中的应用, 机械工程学报,2006,42(8):154-158.
YANG Jian-hong, XU Jin-wu, YANG De-bin, et al. Noise reduction method for nonlinear time series based on principal manifold learning and its application to fault diagnosis[J]. Jixie Gongcheng Xuebao(Chinese Journal of Mechanical Engineering), 2006, 42(8): 154-158.
[8] 王广斌, 黄良沛, 赵先琼.基于分形维和局部切空间均值重构的非线性降噪方法[J]. 电子测量与仪器学报, 2010, (08): 699-704.
WANG Guang-bin, HUANG Liang-pei, ZHAO Xian-qiong. Nonlinear noise reduction method based on fractal dimension and the local tangent space mean reconstruction[J]. Journal of Electronic Mesaurement and Instrument. 010, (08): 699-704.
[9] 余成义.流形学习在混沌时间序列降噪中的应用[D]. 武汉： 武汉科技大学, 2012.
[10] Xiao H B, Xie X P, Zhou S Q, et al. Feature extraction of diesel engine wear fault based on local tangent space alignment[J]. Applied Mechanics and Materials, 2014(482): 179-182.
[11] Fu B, Wang X, Yang B, et al. A novel approach for intrinsic dimension estimation based on maximum likelihood estimation[C]//Proceedings of the 2012 International Conference on Cybernetics and Informatics. Springer New York: 2013. 91-97.
[12] Cao Lianyue. Practical method for determining the minimum embedding dimension of a scalar time series[J]. Physica D : Nonlinear Phenomena, 1997(110)：43-50.
