Application of Compressed Sensing Based on Adaptive Dynamic Mode Decomposition in Signal Transmission and Fault Extraction of Bearing Signal

Bearings are widely used in mechanical equipment; nevertheless, potential dangers are also widespread, making bearing fault detection very important. For large equipment, the amount of collected signals tends to be huge, which challenges both signal transmission and storage. To solve this problem, compressed sensing (CS), based on specific dynamic modes of adaptive truncated rank dynamic mode decomposition (ADMD), is adopted to achieve the purpose of compressing and transmitting the signal, as well as extracting fault features. Firstly, this paper has proposed a new fitness function, which is called the synthetic envelope kurtosis characteristic energy difference ratio, and adopted the improved particle swarm optimization algorithm (IPSO) to select the best truncated rank adaptively. Then, the historical signal attempts to be decomposed into a series of temporal and spatial coherent modes, through ADMD, and those modes are filtered and cascaded into a highly self-adaptive dictionary, the DMD dictionary, which approximates the original signal with some error. Next, CS is employed to compress and reconstruct the signal, in order to reduce storage space and improve transmission efficiency. Finally, signals of high quality can be reconstructed through orthogonal matching pursuit (OMP) algorithm. Compared with traditional dictionaries, the DMD dictionary, based on the mode structure generated by ADMD decomposition, ass proposed in this paper, can better represent the original signal in the simulation signal and have good noise reduction performance. The correlation coefficient (CORR) between the reconstructed signal and noise signal is 0.8109, between the reconstructed signal and non-noise signal is 0.9278, and the root mean square error (RMSE) is 0.0659 and 0.0351, respectively. Compared with the traditional SVD and EMD denoising methods, ADMD-CS has better noise reduction performance. In this paper, the signal-to-noise ratio (SNR) is taken as the quantitative indicator of denoising performance. It is found that the SNR of simulation signal and experimental signal processed by ADMD-CS is higher than that of the traditional denoising methods, which is 0.3017 and 0.8407, respectively. The storage space of the signal is quite smaller than traditional methods, and the compression ratios (CR) of the simulation and experimental signals are 66.16% and 59.08%, respectively. In conclusion, ADMD-CS has a good application prospect in signal transmission, storage, and feature extraction.