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Data measurement of roller bearings condition monitoring is carried out based on the Shannon sampling theorem, resulting in massive amounts of redundant information, which will lead to a big-data problem increasing the difficulty of roller bearing fault diagnosis. To overcome the aforementioned shortcoming, a two-stage compressed fault detection strategy is proposed in this study. First, a sliding window is utilized to divide the original signals into several segments and a selected symptom parameter is employed to represent each segment, through which a symptom parameter wave can be obtained and the raw vibration signals are compressed to a certain level with the faulty information remaining. Second, a fault detection scheme based on the compressed sensing is applied to extract the fault features, which can compress the symptom parameter wave thoroughly with a random matrix called the measurement matrix. The experimental results validate the effectiveness of the proposed method and the comparison of the three selected symptom parameters is also presented in this paper.

Compound faults often occur in rotating machinery, which increases the difficulty of fault diagnosis. In this case, blind source separation, which usually includes independent component analysis (ICA) and sparse component analysis (SCA), was proposed to separate mixed signals. SCA, which is based on the sparsity of target signals, was developed to sever the compound faults and effectively diagnose the fault due to its advantage over ICA in underdetermined conditions. However, there is an issue regarding the vibration signals, which are inadequately sparse, and it is difficult to represent them in a sparse way. Accordingly, to overcome the above-mentioned problem, a sparsity-promoted approach named wavelet modulus maxima is applied to obtain the sparse observation signal. Then, the potential function is utilized to estimate the number of source signals and the mixed matrix based on the sparse signal. Finally, the separation of the source signals can be achieved according to the shortest path method. To validate the effectiveness of the proposed method, the simulated signals and vibration signals measured from faulty roller bearings are used. The faults that occur in a roller bearing are the outer-race flaw, the inner-race flaw and the rolling element flaw. The results show that the fault features acquired using the proposed approach are evidently close to the theoretical values. For instance, the inner-race feature frequency 101.3 Hz is very similar to the theoretical calculation 101 Hz. Therefore, it is effective to achieve the separation of compound faults utilizing the suggest method, even in underdetermined cases. In addition, a comparison is applied to prove that the proposed method outperforms the traditional SCA method when the vibration signals are inadequate.

The traditional approaches for condition monitoring of roller bearings are almost always achieved under Shannon sampling theorem conditions, leading to a big-data problem. The compressed sensing (CS) theory provides a new solution to the big-data problem. However, the vibration signals are insufficiently sparse and it is difficult to achieve sparsity using the conventional techniques, which impedes the application of CS theory. Therefore, it is of great significance to promote the sparsity when applying the CS theory to fault diagnosis of roller bearings. To increase the sparsity of vibration signals, a sparsity-promoted method called the tunable Q-factor wavelet transform based on decomposing the analyzed signals into transient impact components and high oscillation components is utilized in this work. The former become sparser than the raw signals with noise eliminated, whereas the latter include noise. Thus, the decomposed transient impact components replace the original signals for analysis. The CS theory is applied to extract the fault features without complete reconstruction, which means that the reconstruction can be completed when the components with interested frequencies are detected and the fault diagnosis can be achieved during the reconstruction procedure. The application cases prove that the CS theory assisted by the tunable Q-factor wavelet transform can successfully extract the fault features from the compressed samples.