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[Display omitted] • Dictionary has a deep architecture, where each deeper dictionary layer is learned from a few atoms of previous dictionary layer. • Shared sub-dictionary is added into dictionary learning for learning and removing the common features from different classes. • Dictionary is extended by the shift-invariant strategy with circulant matrix to overcome the time-shift problem of vibration signals. • DSDL is more accurate than deep learning methods in the time-varying fault diagnosis with small training sample. As the core of the Sparseland, dictionary learning has represented excellent performances in many fields, such as pattern recognition, fault diagnosis, noise reduction, image recognition and so on. Its key idea is that the data can have a good sparse representation on a specific dictionary consisting of a few basis atoms, so it demands that this specific dictionary is accurate and suitable enough to make the data sparse. Learning a good dictionary requires sufficient and comprehensive training data, while an efficient algorithm of dictionary learning is also essential. However, in many application fields, especially for the fault diagnosis, the training data is often scarce due to the cost of experimentation and time or other reasons. Thus, it's not guaranteed that the data can have a good sparse representation on the single learned dictionary. To solve this problem, we proposed a novel dictionary learning named deep and shared dictionary learning (DSDL), which has the deep structure from deep learning and shared structure. In DSDL, the data is decomposed into several dictionary layers, where the deeper dictionary layer is learned from a few atoms of the previous layer. On the other hand, the shared structure aims to learn the common features from different classes and remove them for highlighting the class-specific features. We apply DSDL in two experimental cases of fault diagnosis under time-varying condition, and the results show that our proposed method always has better performances than other six state-of-the-art sparse representation methods. Compared to two popular deep learning methods, namely convolutional neural network (CNN) and deep belief network (DBN), DSDL is more accurate with small training sample. [ABSTRACT FROM AUTHOR]

Abstract: Rolling element bearings are frequently used in rotary machinery, but they are also fragile mechanical parts. Hence, exact condition monitoring and fault diagnosis for them plays an important role in ensuring machinery''s reliable running. Timely diagnosis of early bearing faults is desirable, but the early fault signatures are easily submerged in noise. In this paper, Wigner–Ville spectrum based on cyclic spectral density (CSWVS for a brief notation) is studied, which is able to represent the cyclostationary signals while reducing the masking effect of additive stationary noise. Both simulations and experiments show that CSWVS is a noise resistant time frequency analysis technique for extracting bearing fault patterns, when bearing signals are under influences of random noise and gear vibrations. The 3-D feature of the CSWVS is proved useful in extracting bearing fault pattern from gearbox vibration signals, where bearing signals are affected by gear meshing vibration and noise. Besides, CSWVS utilizes the second order cyclostationary property of the vibration signals produced by bearing distributed fault, and clearly extracts its fault features, which cannot be extracted by envelope analysis. To quantitatively describe the extent of bearing fault, Renyi information encoded in the time frequency diagram of CSWVS is studied. It is shown to be a more sensitive index to reflect bearing performance degradation, compared with the spectral entropy (SE), squared envelope spectrum entropy (SESE) and Renyi informations for WVD, PWVD, especially when SNR is low. [Copyright &y& Elsevier]

Fault feature extraction is crucial to condition monitoring and fault prognostics. However, when fault is in the initial stage, it is often very weak and submerged in the strong noise. This makes the fault feature very difficult to be extracted. In this paper, we propose a novel method based on sparse representation theory. It is inspired by the traditional K-SVD based de-noising method and can penetrate into the underlying structure of the signal. It learns sparse coefficients and dictionary from the noisy signal itself. The coefficients are globally optimized based on an l 1 -regularized least square problem solving method, which can locate the impulse coordinates more accurately compared with orthonormal matching pursuit (OMP) applied in the traditional K-SVD. The dictionary learning is based on an approximation of singular value decomposition (SVD). With the learned dictionary, we can capture the higher-level structure of the signal. Combining the sparse coefficients and the learned dictionary, we can de-noise the signal effectively and extract the incipient weak fault features of rolling bearings. The results of processing both simulated and experimental signals are illustrated and both validate the proposed method. All the experimental data are also processed by SpaEIAD, wavelet shrinkage, and fast kurtogram for comparison. [ABSTRACT FROM AUTHOR]

Hidden Markov model (HMM) has been widely applied in bearing performance degradation assessment. As a machine learning-based model, its accuracy, subsequently, is dependent on the sensitivity of the features used to estimate the degradation performance of bearings. It׳s a big challenge to extract effective features which are not influenced by other qualities or attributes uncorrelated with the bearing degradation condition. In this paper, a bearing performance degradation assessment method based on HMM and nuisance attribute projection (NAP) is proposed. NAP can filter out the effect of nuisance attributes in feature space through projection. The new feature space projected by NAP is more sensitive to bearing health changes and barely influenced by other interferences occurring in operation condition. To verify the effectiveness of the proposed method, two different experimental databases are utilized. The results show that the combination of HMM and NAP can effectively improve the accuracy and robustness of the bearing performance degradation assessment system. [ABSTRACT FROM AUTHOR]

Many existing signal processing methods usually select a predefined basis function in advance. This basis functions selection relies on a priori knowledge about the target signal, which is always infeasible in engineering applications. Dictionary learning method provides an ambitious direction to learn basis atoms from data itself with the objective of finding the underlying structure embedded in signal. As a special case of dictionary learning methods, shift-invariant dictionary learning (SIDL) reconstructs an input signal using basis atoms in all possible time shifts. The property of shift-invariance is very suitable to extract periodic impulses, which are typical symptom of mechanical fault signal. After learning basis atoms, a signal can be decomposed into a collection of latent components, each is reconstructed by one basis atom and its corresponding time-shifts. In this paper, SIDL method is introduced as an adaptive feature extraction technique. Then an effective approach based on SIDL and hidden Markov model (HMM) is addressed for machinery fault diagnosis. The SIDL-based feature extraction is applied to analyze both simulated and experiment signal with specific notch size. This experiment shows that SIDL can successfully extract double impulses in bearing signal. The second experiment presents an artificial fault experiment with different bearing fault type. Feature extraction based on SIDL method is performed on each signal, and then HMM is used to identify its fault type. This experiment results show that the proposed SIDL-HMM has a good performance in bearing fault diagnosis. [ABSTRACT FROM AUTHOR]

Due to the important role rolling element bearings play in rotating machines, condition monitoring and fault diagnosis system should be established to avoid abrupt breakage during operation. Various features from time, frequency and time–frequency domain are usually used for bearing or machinery condition monitoring. In this study, NCA-based feature extraction (FE) approach is proposed to reduce the dimensionality of original feature set and avoid the “curse of dimensionality”. Furthermore, coupled hidden Markov model (CHMM) based on multichannel data acquisition is applied to diagnose bearing or machinery fault. Two case studies are presented to validate the proposed approach both in bearing fault diagnosis and fault severity classification. The experiment results show that the proposed NCA-CHMM can remove redundant information, fuse data from different channels and improve the diagnosis results. [ABSTRACT FROM AUTHOR]

Fan noise is a predominant noise component of the aero-engine, which consists of tonal noise and broadband noise. Duct mode calculation of random broadband noise is more complex than that of tonal noise. A probabilistic approach for duct acoustic mode identification is proposed to identify duct modes of broadband fan noise with high efficiency and accuracy. The inverse problem of mode identification is represented by a Bayesian framework based on a Gaussian-scale mixture prior model. Computational complexity and consuming time are remarkably decreased by approximating the Gaussian likelihood through a surrogate function. The block coordinate descent algorithm in the majorization–minimization framework is adopted for the indirect and iterative calculation of the mode coefficients. Simulations and experiments have verified the high computational efficiency afforded by the method, which provides more accurate results for duct mode identification of broadband noise, removes the influence of interfering modes on the recognition results, and allows better observation of the characteristics of the mode in a wide range of frequencies and rotating speeds. [ABSTRACT FROM AUTHOR]

Based on the traditional theory of singular value decomposition (SVD), singular values (SVs) and ratios of neighboring singular values (NSVRs) are introduced to the feature extraction of vibration signals. The proposed feature extraction method is called SV–NSVR. Combined with selected SV–NSVR features, continuous hidden Markov model (CHMM) is used to realize the automatic classification. Then the SV–NSVR and CHMM based method is applied in fault diagnosis and performance assessment of rolling element bearings. The simulation and experimental results show that this method has a higher accuracy for the bearing fault diagnosis compared with those using other SVD features, and it is effective for the performance assessment of rolling element bearings. [ABSTRACT FROM AUTHOR]

Abstract: When early weak fault emerges in rolling bearing the fault feature is too weak to extract using the traditional fault diagnosis methods such as Fast Fourier Transform (FFT) and envelope demodulation. The tunable Q-factor wavelet transform (TQWT) is the improvement of traditional one single Q-factor wavelet transform, and it is very fit for separating the low Q-factor transient impact component from the high Q-factor sustained oscillation components when fault emerges in rolling bearing. However, it is hard to extract the rolling bearing’ early weak fault feature perfectly using the TQWT directly. Ensemble empirical mode decomposition (EEMD) is the improvement of empirical mode decomposition (EMD) which not only has the virtue of self-adaptability of EMD but also overcomes the mode mixing problem of EMD. The original signal of rolling bearing’ early weak fault is decomposed by EEMD and several intrinsic mode functions (IMFs) are obtained. Then the IMF with biggest kurtosis index value is selected and handled by the TQWT subsequently. At last, the envelope demodulation method is applied on the low Q-factor transient impact component and satisfactory extraction result is obtained. [Copyright &y& Elsevier]

Abstract: Weak machinery fault detection is a difficult task because of two main reasons (1) At the early stage of fault development, signature of fault related component performs incompletely and is quite different from that at the apparent failure stage. In most instances, it seems almost identical with the normal operating state. (2) The fault feature is always submerged and distorted by relatively strong background noise and macro-structural vibrations even if the fault component already performs completely, especially when the structure of fault components and interference are close. To solve these problems, we should penetrate into the underlying structure of the signal. Sparse representation provides a class of algorithms for finding succinct representations of signal that capture higher-level features in the data. With the purpose of extracting incomplete or seriously overwhelmed fault components, a sparse representation based latent components decomposition method is proposed in this paper. As a special case of sparse representation, shift-invariant sparse coding algorithm provides an effective basis functions learning scheme for capturing the underlying structure of machinery fault signal by iteratively solving two convex optimization problems: an L1-regularized least squares problem and an L2-constrained least squares problem. Among these basis functions, fault feature can be probably contained and extracted if optimal latent component is filtered. The proposed scheme is applied to analyze vibration signals of both rolling bearings and gears. Experiment of accelerated lifetime test of bearings validates the proposed method׳s ability of detecting early fault. Besides, experiments of fault bearings and gears with heavy noise and interference show the approach can effectively distinguish subtle differences between defect and interference. All the experimental data are analyzed by wavelet shrinkage and basis pursuit de-noising (BPDN) method for comparison. [Copyright &y& Elsevier]

Abstract: Rolling element bearing faults are among the main causes of rotating machines breakdown. It is important to distinguish the incipient fault before the bearings step into serious failure. Based on the traditional singular value decomposition (SVD) theory, short-time matrix series (STMS) and singular value ratio (SVR) are introduced to the vibration signal processing. The proposed signal processing method is called S-SVDR (STMS based SVD method using SVR) and it has been proved to have a good local identification capability in the rolling bearing fault diagnosis. The detailed description of applying S-SVDR methods to rolling bearing fault diagnosis is given through the artificial fault signal processing in experiment 1. In experiment 2, rolling element bearing accelerated life test is performed in Hangzhou Bearing Test & Research Center (HBRC). The experimental result shows that the incipient fault can be well detected through S-SVDR processing method. However, the envelope analysis of original signal cannot detect the fault due to the existence of signal interference. A conclusion can be made that the proposed S-SVDR method has a good effect on de-noising and eliminating the signal interference of rolling bearing for the fault diagnosis. [Copyright &y& Elsevier]

Abstract: An experimental setup which can simulate the rotor-to-stator rub in a rotor system is installed. A rub screw is used to simulate the condition of local rub–impact fault. Based on the theory of elastic collision and energy conservation, an Impact Energy Model (IEM) is proposed to evaluate the probability or severity of rub–impact fault. To prove this model, the paper conducts the experiment in two steps i.e. hammer test and rub–impact fault validation. The wave signal, spectrum and axis orbit are used to analyze the severity of the rub–impact fault when it occurs. The analysis result shows that the proposed Impact Energy Model (IEM) is effective in the assessment of rub–impact fault. Furthermore, the proposed IEM can also provide a reference for the design and operation of a rotor system. [Copyright &y& Elsevier]

Abstract: For machine fault diagnosis the signals from working machine are always numerous, even uncountable, but there contains only a little useful information. Hence how to find out the useful signal from numerous signals, including noises, that is, how to only extract the desired fault signal is very attractive. This paper shows that the constrained independent component analysis (cICA) can solely extract desired faulty signal using some prior mechanical information. The methods of creating reference of cICA for machine diagnostics are discussed, and the effectiveness of the method is successfully verified by simulations and experiments. [Copyright &y& Elsevier]

Abstract: In vibration analysis, weak fault feature extraction under strong background noise is of great importance. A method based on cyclic Wiener filter and envelope spectrum analysis is proposed. Cyclic Wiener filter exploits the spectral coherence theory induced by the second-order cyclostationary signal. The original signal is duplicated and shifted in the frequency domain by amounts corresponding to the cyclic frequencies. The noise component is optimally filtered by a filter-bank. The filtered signal is analyzed by performing envelope spectrum. In the envelope spectrum, characteristic frequencies are quite clear. Then the most impactive part is effectively extracted for further fault diagnosis. The effectiveness of the method is demonstrated on both simulated signal and actual data from rolling bearing accelerated life test. [Copyright &y& Elsevier]

• A new compressed sensing method for acoustic mode detection for aero engines is proposed. • The proposed method performs effectively with a small number of sensors. • The proposed method can enhance the mode detection accuracy compared with the conventional methods. • The cost function is convex, and the global optimum solution can be guaranteed. • Both simulations and experiments validate the effectiveness and application potential. Recently, research interests are increasing in mode detection methods based on compressed sensing, as it can reduce the number of sensors required by the classical Shannon-Nyquist sampling theory. This paper proposes a nonconvex sparse regularization method for azimuthal mode detection for aero engine fan noise. The nonconvex sparse regularization is based on the generalized minimax-concave (GMC) penalty, which can maintain the convexity of the sparse-regularized least squares cost function, and thus the global optimal solution can be solved by convex optimization algorithms. The main advantage of the GMC method over conventional compressed sensing method in mode detection is that the GMC method can better recover the mode amplitudes with a small number of sensors. Besides, the GMC method can suppress effectively the irrelated modes induced by the background noise or sensor installation errors. Therefore, the proposed method for duct mode detection can significantly improve the accuracy of the detected modes. Numerical simulations and experimental tests verify the effectiveness of the GMC method in mode detection for aero engine fan noise, and comparison studies show that the GMC method provides more accurate mode detection results than l 1 minimization in the category of compressed sensing, as well as traditional mode detection methods. [ABSTRACT FROM AUTHOR]

Abstract: A new model for vibration analysis of a crankshaft with a slant crack in crankpin is proposed, and the influence of crack depth on the transient response of a cracked crankshaft is investigated. A slant cracked shaft element is developed by deducing the local flexibility due to a slant crack. The frequently occurred slant crack in crankpin is studied, and a new finite element model of crankshaft including the slant crack in crankpin, which combines the slant cracked shaft element and Timoshenko beam elements, is derived. The support of engine block and the switching behaviour of the crack are considered, and the non-linear equation of motion for cracked crankshaft-bearing system is set up in a rotating coordinate system. The motion of a crankshaft of a four in-line cylinder engine with and without an initial crack is simulated. The influence of the crack depth on the transient response is investigated. The numerical simulation demonstrates that the current model is valid for simulating the motion of cracked crankshaft system. The results show that a useful foundation is laid for crack detection of crankshaft. [Copyright &y& Elsevier]