基于稀疏分解的振动信号数据压缩算法

Data compression algorithm of vibration signal based on sparse decomposition

针对齿轮传动装置在状态监测与故障诊断过程中面临的大量振动信号传输困难问题,提出利用K-SVD算法进行信号的稀疏分解,进而完成对大量振动数据的压缩。传统K-SVD算法在字典更新过程中对时间的消耗量较大,特别是在大量振动数据压缩过程中,对数据压缩效率较低,为此提出一种K-SVD字典更新的改进算法。改进算法从单次迭代过程中参与更新的字典原子列数出发,每次奇异值分解后对多列字典原子同时进行赋值,从而减少单次迭代计算量。根据不同原子列数在稀疏分解过程中的迭代收敛次数、时间消耗与重构峰值信噪比,以此确定最佳的字典更新列数。实验结果表明:传统K-SVD算法对振动信号的数据压缩效率较低,改进算法能够在保证信号压缩比与重构效果的前提下,有效缩短训练字典的时间消耗。

Aiming at the difficulty that gear transmission devices confront large amount of vibration signal transmission in the condition monitoring and fault diagnosis process,the K-SVD algorithm is proposed to conduct the sparse decomposition of the signals,and then complete the massive vibration data compression. The traditional K-SVD algorithm requires high time consumption in the dictionary update process,and the data compression efficiency is low,particularly in the massive vibration data compression,so an improved algorithm is proposed for K-SVD dictionary update. Starting from the number of columns in the dictionary participating the update in single iteration process,the improved algorithm assigns values to the atoms in several columns of the dictionary after each singular value decomposition,so that the computation burdens of single iteration are reduced. At the same time,the optimal number of columns of dictionary update is determined according to the iteration convergence number,time consumption and peak signal to noise ratio of reconstruction of different number of columns in sparse decomposition process. Experiment results show that traditional K-SVD algorithm has a low efficiency for the vibration signal data compression,and the improved algorithm can effectively shorten the dictionary training time consumption under the premise of ensuring the signal compression ratio and reconstruction effects.