基于过完备字典的缺失振动数据压缩感知重构算法

针对振动数据采集过程中由于设备短路或环境变化等诸多因素导致的数据丢失问题,提出了一种基于过完备字典的缺失振动数据压缩感知重构算法。首先利用K 奇异值分解算法对大量振动数据进行字典学习得到过完备字典,然后构建缺失振动数据的采样矩阵作为压缩感知框架下的测量矩阵。最后利用正则化正交匹配追踪算法完成缺失数据的重构。通过振动数据库数据和实测航空发动机振动数据实验表明，所提算法优于传统基于离散余弦变换和离散傅里叶变换的数据修复算法,同时具有一定的鲁棒性。

Missing vibration data reconstruction using compressed sensing based on over complete dictionary

To deal with the problem that the data collector fails to obtain complete vibration data due to short circuit or environment changing or other reasons, a method combining compressed sensing and over complete dictionary is proposed. Firstly, lots of related vibration data are learned so as to obtain an over complete dictionary for the data remained to be recovered by K-singular value decomposition. Then a measurement matrix is constructed under the frame of compressed sensing. Finally, data recovery is implemented by regular orthogonal matching pursuit. Experiments of vibration database and practical aero engine vibration demonstrate the proposed method is superior to traditional methods based on discrete cosine transform or discrete Fourier transform and has certain robustness.