Mechanical vibration signal mapped into a high-dimensional space tends to exhibit a special distribution and movement characteristics, which can further reveal the dynamic behavior of the original time series. As the most natural representation of high-dimensional data, tensor can preserve the intrinsic structure of the data to the maximum extent. Thus, the tensor decomposition algorithm has broad application prospects in signal processing. High-dimensional tensor can be obtained from a one-dimensional vibration signal by using phase space reconstruction, which is called the tensorization of data. As a new signal decomposition method, tensor-based singular spectrum algorithm (TSSA) fully combines the advantages of phase space reconstruction and tensor decomposition. However, TSSA has some problems, mainly in estimating the rank of tensor and selecting the optimal reconstruction tensor. In this paper, the improved TSSA algorithm based on convex-optimization and permutation entropy (PE) is proposed. Firstly, aiming to accurately estimate the rank of tensor decomposition, this paper presents a convex optimization algorithm using non-convex penalty functions based on singular value decomposition (SVD). Then, PE is employed to evaluate the desired tensor and improve the denoising performance. In order to verify the effectiveness of proposed algorithm, both numerical simulation and experimental bearing failure data are analyzed.

Abstract:Gears are key components in rotation machinery and its fault vibration signals usually show strong nonlinear and non-stationary characteristics. It is not easy for classical time-frequency domain analysis methods to recognize different gear working conditions. Therefore, this paper presents a joint fault diagnosis scheme for gear fault classification via tensor nuclear norm canonical polyadic decomposition (TNNCPD) and multi-scale permutation entropy (MSPE). Firstly, the one-dimensional vibration data of different gear fault conditions is converted into a three-dimensional tensor data, and a new tensor canonical polyadic decomposition method based on nuclear norm and convex optimization called TNNCPD is proposed to extract the low rank component of the data, which represents the feature information of the measured signal. Then, the MSPE of the extracted feature information about different gear faults can be calculated as the feature vector in order to recognize fault conditions. Finally, this researched scheme is validated by practical gear vibration data of different fault conditions. The result demonstrates that the proposed scheme can effectively recognize different gear fault conditions.

Abstract:To solve the problem of multi-fault blind source separation (BSS) in the case that the observed signals are under-determined, a novel approach for single channel blind source separation (SCBSS) based on the improved tensor-based singular spectrum analysis (TSSA) is proposed. As the most natural representation of high-dimensional data, tensor can preserve the intrinsic structure of the data to the maximum extent. Thus, TSSA method can be employed to extract the multi-fault features from the measured single-channel vibration signal. However, SCBSS based on TSSA still has some limitations, mainly including unsatisfactory convergence of TSSA in many cases and the number of source signals is hard to accurately estimate. Therefore, the improved TSSA algorithm based on canonical decomposition and parallel factors (CANDECOMP/PARAFAC) weighted optimization, namely CP-WOPT, is proposed in this paper. CP-WOPT algorithm is applied to process the factor matrix using a first-order optimization approach instead of the original least square method in TSSA, so as to improve the convergence of this algorithm. In order to accurately estimate the number of the source signals in BSS, EMD-SVD-BIC (empirical mode decomposition-singular value decomposition-Bayesian information criterion) method, instead of the SVD in the conventional TSSA, is introduced. To validate the proposed method, we applied it to the analysis of the numerical simulation signal and the multi-fault rolling bearing signals.

The acquired bearing fault signal usually reveals nonlinear and non-stationary nature. Moreover, in the actual environment, some other interference components and strong background noise are unavoidable, which lead to the fault feature signal being weak. Considering the above issues, an effective bearing fault diagnosis technique via local robust principal component analysis (LRPCA) and multi-scale permutation entropy (MSPE) was introduced in this paper. Robust principal component analysis (RPCA) has proven to be a powerful de-noising method, which can extract a low-dimensional submanifold structure representing signal feature from the signal trajectory matrix. However, RPCA can only handle single-component signal. Therefore, in order to suppress background noise, an improved RPCA method named LRPCA is proposed to decompose the signal into several single-components. Since MSPE can efficiently evaluate the dynamic complexity and randomness of the signals under different scales, the fault-related single-components can be identified according the MPSE characteristic of the signals. Thereafter, these identified components are combined into a one-dimensional signal to represent the fault feature component for further diagnosis. The numerical simulation experimentation and the analysis of bearing outer race fault data both verified the effectiveness of the proposed technique.

Bearing fault diagnosis is of utmost importance in the maintenance of mechanical equipment. The collected fault vibration signal generally presents a modulated nature due to the special structure and dynamic characteristics of the bearings. This paper introduces a novel demodulation analysis technique via energy separation and local low-rank matrix approximation (LLORMA) to address this type of signal. The amplitude envelope and instantaneous frequency of the signal can be calculated via an energy separation algorithm based on the Teager energy operator. We can confirm the bearing faults by comparing the peak frequencies of the Fourier spectrum of the amplitude envelope and instantaneous frequency with the theoretical bearing fault-related frequencies. However, this algorithm is only suitable for handling single-component signals. In addition, the powerful background noise has a serious effect on the demodulation results. To tackle these problems, a new signal decomposition method based on LLORMA is proposed to decompose the signal into several single-components and eliminate the noise simultaneously. After that, the single-component signal representing the fault characteristics can be identified via the high frequency feature of the modulated signal. The analysis of the simulated signal and the bearing outer race fault signal collected from a bearing-gear fault test rig indicate that the proposed technique has an excellent diagnostic performance for bearing fault signals.

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The health condition of the rolling bearing seriously affects the operation of the whole mechanical system. When the rolling bearing parts fail, the time series collected in the field generally shows strong nonlinearity and non-stationarity. To obtain the faulty characteristics of mechanical equipment accurately, a rolling bearing fault detection technique based on k-optimized adaptive local iterative filtering (ALIF), improved multiscale permutation entropy (improved MPE), and BP neural network was proposed. In the ALIF algorithm, a k-optimized ALIF method based on permutation entropy (PE) is presented to select the number of ALIF decomposition layers adaptively. The completely average coarse-graining method was proposed to excavate more hidden information. The performance analysis of the simulation signal shows that the improved MPE can more accurately dig out the depth information of the time series, and the entropy value obtained is more consistent and stable. In the research application, rolling bearing time series are decomposed by k-optimized ALIF to obtain a certain number of intrinsic mode functions (IMFs). Then the improved MPE value of effective IMF is calculated and input into backpropagation (BP) neural network as the feature vector for automatic fault identification. The comparative analysis of simulation signals shows that this method can extract fault information effectively. At the same time, the experimental part shows that this scheme not only effectively extracts the fault features, but also realizes the classification and identification of different fault modes and faults of different degrees, which has a certain application prospect in the research and application direction of rolling bearing fault identification.