The Research On Sparse Decomposition Theory Of Mechanical Vibration Signal

Mechanical vibration signal transmits and carries important information of mechanical equipment in its working process. The signals’on-line monitoring and collection are key technologies in mechanical engineering, especially in fault diagnosis or remote fault diagnosis. This paper will apply compress sensing theory to signal monitoring and signal sparse decomposition is the premise and foundation of the theory contributing to solve the traditional high sampling frequency, large data storage capacity and transmission difficulties. Signal sparse decomposition theory can decompose a signal into a linear combination of a set of bases from a highly redundant transform bases. The signal can be characterized by a small number of feature-distinct components and we can get a simple, flexible and characterized expansion. This adaptive decomposition method is very useful and it will provide great convenience in signal post-processing. Therefore, this study mainly focuses on the problem of mechanical vibration signal’s sparse decomposition. The main work and research results are as follows:(1) Set rolling bearing as the study object, establish a theoretical model of bearing vibration signal and construct an improved atom libraries based on exponentially decaying cosine function according to their characteristics and prior knowledge. Compare the decomposition results of the two atom libraries to the rolling bearing vibration signal with MP algorithm optimized by improved PSO algorithm. Results show the improved atom library holds better similarity and rate of decay, and the residual amount is smaller.(2) Generate some trained samples according to the vibration signal data, then use K-SVD algorithm combined with OMP algorithm design a trained dictionary which can exactly match the signal characteristics. Last make signal sparse decomposition and reconstruction to the ones with similar characteristics of the samples by OMP. Compare the sparse decomposition and reconstruction results under atom library (no training dictionary) and this trained one. Results show the trained dictionary can better meet the vibration signal’s features, can represent the signal with less or more sparse decomposition coefficients, can approximate the signal with higher accuracy, and has better similarity, rate of decay and smaller residual amount.