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Vibration signals induced by faulty roller bearing usually contain much interference, which increases the difficulty of fault diagnosis. Thus, it is significant to enhance the fault features and carry out noise reduction. To achieve fault feature enhancement for roller bearing, a novel method based on Majorization-Minimization (MM) algorithm is developed in this study. First, a sparsity optimization objective function is designed, which integrates impulsive feature preserving factor and penalty function factor. In this function, the regularization parameter is taken into consideration for corresponding different working situations. Second, a nonquadratic majorization iterative method based on MM is used to address the convex optimization problem of the designed function. A series of sparse coefficients can be got through iterating, which just contain the transient components. Finally, envelope analysis is used to extract the bearing fault features. Simulated signal and experimental data are applied to verify the effectiveness and applicability of the researched method. The results show that the bearing signals can be represented sparsely and the bearing fault features can be enhanced and extracted easily using the proposed approach.

The fault features of roller bearing vibration signal are usually immerged in heavy background noise and difficult to be extracted. Especially for the diagnosis of weak fault, it is even harder. To extract the weak fault features of bearings effectively, a new method which used complementary ensemble empirical mode decomposition (CEEMD) and Dempster-Shafer (DS) evidence theory is proposed. Firstly, the noise reduction of original signal based on CEEMD is carried out. The vibration signal of roller bearing is decomposed into a series of intrinsic mode functions (IMFs) by CEEMD. The cross correlation coefficients between the original signal and each IMF are calculated to select effective IMF. Secondly, the data-based fusion of effective IMFs is carried on by DS fusion rules. The fault feature components and interference components in the vibration signal can be considered as two incompatible propositions of DS “recognition framework”. The effective IMFs represent the evidences supporting the fault features. Fusing the effective IMFs to integrate the local incomplete information of single IMF and enhance the weak fault features of bearings. Finally, the fault features can be extracted after Hilbert envelope demodulation. The effectiveness of the presented method is validated by simulation and experimental signal. And the results indicate that the proposed method is available for detecting the bearing faults and able to diagnose the weak fault at an early stage.

Multi-faults which usually exists in roller bearing makes fault diagnosis difficult. Thus, it is of great significance to carry out fault diagnosis of rotating machinery to ensure the complete machinery system to perform in a normal statement. To effectively separate the multi-faults and achieve the fault diagnosis, sparse component analysis based on the sparsity of objective signals was proposed. However, the vibration signals are scantily sparse and it usually cannot be represented in a sparse way. Therefore, a novel approach is suggested to overcome the above problem. First, tunable Q-factor wavelet transform is used to obtain the sparse signal. Then, the quantity of source signal and the mixed matrix are approximated grounded on the potential function which is calculated according to the sparse signal. Ultimately, the shortest path method is taken advantage of gaining separation of the source signal. The simulate signals and vibration signals are used to verify the effectiveness of the proposed method. The results show that it is telling to accomplish the separation of multi-faults.

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.

With the development of rotary machinery condition monitoring, challenges have often been encountered due to the cumbersome nature of data monitoring. Common methods in signal processing are primarily based on the Shannon sampling principle, which requires substantial amounts of data to achieve the desired accuracy from on-line monitoring signals. This limits their applications in cases for which only small samples can be collected, or cases for which too much data are generating which needs to be largely reduced with under-sampling. Using the Shannon sampling principle, it seems impossible to significantly reduce the quantity of data while preserving adequate useful information for condition monitoring. A newly developed theory termed compressive sensing provides a new insight to condition monitoring and fault diagnosis. It states that a signal can be perfectly recovered from under-sampled data, which means that useful condition information can still be represented by small samples. This study presents novel methods for rotary machinery fault detection from compressed vibration signals inspired by compressive sensing, which can largely reduce the data collection and detect faults of rotary machinery from only a few signal samples. This will greatly help reduce the amount of monitoring data while still guaranteeing a high accuracy of fault detection. Case studies related to roller bearing fault signals are also presented in this study to illustrate the effectiveness of the present strategy.

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.

Vibration signals generated by faulty bearings often constitute “big data”, and it is therefore difficult to sparsely decompose them for dimensional reduction. In addition, vibration signals are generally buried in noise, especially at the initial fault stages. This increases the difficulty of determining roller bearing status. Therefore, it is essential to reduce the data dimension and noise influence as much as possible. To overcome these problems, this paper proposes a compressed-signal-based fault detection method using a tunable Q-factor wavelet transform. With this technique, the sparsity of the decomposed vibration signals in the modified wavelet bases is increased, which helps to increase the compressibility and suppress noise of the vibration signals. Also, based on the decomposition of the vibration signals realized using the tunable Q-factor wavelet transform, a compressive sensing approach to roller bearing fault detection is developed. This technique can detect fault features from data that are under-sampled far below the Nyquist sampling rate. Compared with traditional fault detection methods, the proposed method increases the sparsity of vibration signal decompositions and relaxes the requirements on signal samples for roller bearing fault diagnosis. Successful applications in detecting roller bearing faults validate the effectiveness of the proposed method.

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.

Roller bearings are essential components of rotating machinery and are often exposed to complex operating conditions, which can easily lead to their failures. Thus, to ensure normal production and the safety of machine operators, it is essential to detect the failures as soon as possible. However, it is a major challenge to maintain a balance between detection efficiency and big data acquisition given the limitations of sampling theory. To overcome these limitations, we try to preserve the information pertaining to roller bearing failures using a sampling rate far below the Nyquist sampling rate, which can ease the pressure generated by the large-scale data. The big data of a faulty roller bearing's vibration signals is firstly reduced by a down-sample strategy while preserving the fault features by selecting peaks to represent the data segments in time domain. However, a problem arises in that the fault features may be weaker than before, since the noise may be mistaken for the peaks when the noise is stronger than the vibration signals, which makes the fault features unable to be extracted by commonly-used envelope analysis. Here we employ compressive sensing theory to overcome this problem, which can make a signal enhancement and reduce the sample sizes further. Moreover, it is capable of detecting fault features from a small number of samples based on orthogonal matching pursuit approach, which can overcome the shortcomings of the multiple down-sample algorithm. Experimental results validate the effectiveness of the proposed technique in detecting roller bearing faults.