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Purpose: The purpose of this paper is building the regression model related to tool wear, and the regression model is used to identify the state of tool wear. Design/methodology/approach: In this paper, genetic programming (GP), which is originally used to solve the symbolic regression problem, is used to build the regression model related to tool wear with the strong regression ability. GP is improved in genetic operation and weighted matrix. The performance of GP is verified in the tool vibration, force and acoustic emission data provided by 2010 prognostics health management. Findings: In result, the regression model discovered by GP can identify the state of tool wear. Compared to other regression algorithms, e.g. support vector regression and polynomial regression, the identification of GP is more precise. Research limitations/implications: The regression models built in this paper can only make an assessment of the current wear state with current signals of tool. It cannot predict or estimate the tool wear after the current state. In addition, the generalization of model has some limitations. The performance of models is just proved in the signals from the same type of tools and under the same work condition, and different tools and different work conditions may have influences on the performance of models. Originality/value: In this study, the discovered regression model can identify the state of tool wear precisely, and the identification performances of model applied in other tools are also excellent. It can provide a significant information about the health of tool, so the tools can be replaced or repaired in time, and the loss caused by tool damage can be avoided. [ABSTRACT FROM AUTHOR]

Bolted joints are widely used in industrial applications and joint failure can cause a disastrous accident if loosening happens. Bolt loosening detection can be made by regular manual inspection or by using sensors based on different physical principles, such as acoustoelastic effect, piezoelectric active sensing, and electromechanical impedance. Compared with the above methods, vibration based bolt looseness monitoring using accelerometers is appealing for its economy and convenience for measurement. In this paper, cargo bolts looseness monitoring under random excitation is studied based on vibration transmissibility, which overcomes the drawback of commonly used vibration methods in finding local bolt looseness. Vibration transmissibility analysis only uses two vibration transducers to monitor bolt group looseness, where the vibration signal below the cargo bolts is used as the "input" and the other one above the cargo bolts is used as the "output." There are 12 bolts in the cargo bolts studied in this paper, providing an essential clamping force to fix cargo during transportation. Six kinds of bolt group looseness with an increasing degree are simulated in the experiment. The experimental analysis shows that variation of the spectral moment can be used to monitor the global variation of the torque wrench exerted on the cargo bolts. The early stage of the bolt group looseness is that some one or two bolts begin to loose; however, the spectrum moment factor is insensitive to the local bolt looseness in the bolt group. To address this issue, the eigensystem realization algorithm (ERA) based on random input and output is utilized to find the subtle eigenvalue variation of the system matrix, which is neglected by the frequency transmissibility function. The experimental results show the effectiveness of the proposed method for detecting local bolt looseness. [ABSTRACT FROM AUTHOR]

[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]

Although various methods have been presented in the literature for rotating machine fault detection, it still remains a huge challenge to accurately extract features from non-stationary vibration signals with a high noise level, typically in the case of rolling element bearings faults diagnosis. Due to its random and non-stationary nature, fault related features are difficult to extract by common techniques and are usually overwhelmed by noise and macro-structural vibrations. In this paper, a new time series decomposition method based on a dynamic linear model is proposed, which provides time domain decomposition of a non-stationary signal into collections of latent components. The signal of a damaged bearing consists of exponentially decaying ringing that occurs periodically at the bearing characteristic defect frequency. Dynamic linear models with time-varying cyclical components provide a more generalized and adaptive description on rolling element bearings’ vibration signal with time-varying cyclical behavior. This allows the precise isolation of latent, quasi-cyclical bearing fault components via inferences on the time-varying parameters which characterize these components. An accelerated whole lifetime test of bearing has been performed to collect vibration data, which is utilized to validate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

This paper is in the field of vibration based fault diagnosis for rolling element bearings, where one major issue is the ability to detect faults as early as possible. Bispectrum analysis has been applied in bearing diagnosis. In this paper, a frequency-shifted bispectrum is studied for bearing diagnosis. It is found that the frequency-shifted bispectrum is more suitable for analyzing amplitude modulated and frequency modulated signals than the bispectrum, when choosing the carrier frequency as the specific frequency shift value. For bearing vibration signals with amplitude modulation characteristics, in which the carrier frequencies are structural resonant frequencies, one of the structural resonances can be chosen as the specific frequency shift value for the frequency-shifted bispectrum analysis. To increase diagnostic ability of the frequency-shifted bispectrum for bearing faults, firstly, the frequency resolution is increased in the frequency-shifted bispectrum analysis through band pass filtering and frequency zooming; secondly, integration of the frequency-shifted bispectrum along one frequency variable is used to produce a one-dimensional spectral representation. Numerical simulation and experimental results show the feasibility of the proposed method for qualitatively and quantitatively diagnosing bearing faults. [ABSTRACT FROM AUTHOR]

The randomness of road–tyre excitations can excite the low frequency ride vibrations of bounce, pitch and roll modes of an on-road vehicle. In this paper, modal parameters and mass moments of inertia of an on-road vehicle are estimated with an acceptable accuracy only by measuring accelerations of vehicle sprung mass and unsprung masses, which is based on subspace identification methods. The vehicle bounce, pitch and roll modes are characterized by their large damping (damping ratio 0.2–0.3). Two kinds of subspace identification methods, one that uses input/output data and the other that uses output data only, are compared for the highly damped modes. It is shown that, when the same data length is given, larger error of modal identification results can be clearly observed for the method using output data only; while additional use of input data will significantly reduce estimation variance. Instead of using tyre forces as inputs, which are difficult to be measured or estimated, vertical accelerations of unsprung masses are used as inputs. Theoretical analysis and Monte Carlo experiments show that, when the vehicle speed is not very high, subspace identification method using accelerations of unsprung masses as inputs can give more accurate results compared with the method using road–tyre forces as inputs. After the modal parameters are identified, and if vehicle mass and its center of gravity are pre-determined, roll and pitch moments of inertia of an on-road vehicle can be directly computed using the identified frequencies only, without requiring accurate estimation of mode shape vectors and multi-variable optimization algorithms. [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]

A novel bearing fault diagnosis method combining feature extraction based on wavelet packets quantifiers and pattern recognition method based on improved initialization method of Discriminative K-SVD (D-KSVD) algorithm is proposed. In D-KSVD algorithm, the representational power of dictionary and discriminative ability of classifier are seriously affected by their initialization values. Therefore, the improved initialization method of D-KSVD is presented and employed for bearing fault diagnosis. The improvement is that during the initialization of training stage, subdictionaries corresponding to each category are trained by K-SVD separately and then the initial dictionary is constructed by cascading the subdictionaries, which can completely represent the characteristics of all categories, and as for the initialization of linear classifier, naive Bayesian classifier is utilized. The experimental results show that under the same parameters the improved D-KSVD has better classification ability compared with traditional D-KSVD and some other classification methods. [ABSTRACT FROM AUTHOR]

A novel bearing fault diagnosis method based on improved locality-constrained linear coding (LLC) and adaptive PSO-optimized support vector machine (SVM) is proposed. In traditional LLC, each feature is encoded by using a fixed number of bases without considering the distribution of the features and the weight of the bases. To address these problems, an improved LLC algorithm based on adaptive and weighted bases is proposed. Firstly, preliminary features are obtained by wavelet packet node energy. Then, dictionary learning with class-wise K-SVD algorithm is implemented. Subsequently, based on the learned dictionary the LLC codes can be solved using the improved LLC algorithm. Finally, SVM optimized by adaptive particle swarm optimization (PSO) is utilized to classify the discriminative LLC codes and thus bearing fault diagnosis is realized. In the dictionary leaning stage, other methods such as selecting the samples themselves as dictionary and K-means are also conducted for comparison. The experiment results show that the LLC codes can effectively extract the bearing fault characteristics and the improved LLC outperforms traditional LLC. The dictionary learned by class-wise K-SVD achieves the best performance. Additionally, adaptive PSO-optimized SVM can greatly enhance the classification accuracy comparing with SVM using default parameters and linear SVM. [ABSTRACT FROM AUTHOR]

[Display omitted] • RSTFR gets the TFR by decomposing each envelope of signal segment into the Fourier basis. • A reweighted scheme is applied in the process of solving sparse coefficient to solve the underestimation problem of fault characteristic frequency. • Compared to other TFR methods, RSTFR can present more precise TFRs with higher time–frequency resolution. In the field of fault diagnosis, time–frequency representation (TFR) is a very popular tool due to its good performance under time-varying condition. TFR provides both time and frequency information of fault signal, and the component related to fault characteristic frequency (FCF) can be found in the time–frequency image. To improve the time–frequency resolution of TFR, a special kind of TFR method named sparse time frequency representation (STFR) combines TFR and sparse theory, where the TFR is processed in a sparse way and the energy is more concentrated on FCF. However, the underestimation problem from the optimization process limits the efficiency of STFR. Concretely, the coefficients of the components of FCF are easy to be underestimated in the iterative process of solving coefficient, which will enhance other interference components. Especially for the weak faults from the early stage or the serious noise pollution, STFR is easy to be contaminated and is hard to reveal the components of FCF because of the underestimation problem. To solve the underestimation problem, we propose a novel STFR with reweighted regularization (RSTFR) for fault diagnosis. In the proposed method, the envelope of signal is divided into small segments, and each segment is decomposed into the Fourier basis. Naturally, the sparse coefficient represents the envelope spectrum of each segment. Meanwhile, the reweighted scheme is used to solve the underestimation problem. The components related to FCF are encouraged with low thresholds while other interference components are punished with high thresholds. At last, the envelope spectrums of all segments at different time form the TFR. The proposed method can provide a higher time–frequency resolution and diagnose the fault precisely. RSTFR is applied in the both simulation cases and experimental cases of bearing fault diagnosis, and it shows the overwhelming superiority compared to other four state-of-art TFR methods. [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]

Rolling element bearings are vital components in rotating machines, and it is important to diagnose bearing faults to avoid serious accidents in equipment. In this paper, singular spectrum analysis (SSA) is utilized to extract the bearing fault features. SSA is a non-parametric technique of time series analysis which decomposes the acquired vibration signals into an additive set of time series. Based on the selected singular features from SSA, a continuous hidden Markov model (CHMM) is introduced to diagnose the bearing fault. The detailed description and identification results of applying the proposed method to rolling element bearing fault diagnosis are shown in experiment 1. In experiment 2, a rolling element bearing accelerated life test is performed to simulate the performance variation of the bearing. The result demonstrates that the singular features and CHMM can reflect the performance degradation of the bearing from health to failure. A conclusion can be made that SSA and CHMM are feasible and effective in bearing fault diagnosis and performance assessment. [ABSTRACT FROM PUBLISHER]

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]

This paper studies a novel time-frequency representation method--adaptive non-parametric short-time Fourier transform (ANSTFT), together with its application to the echolocation signal analysis. By rotating the signal in the analysis window, the local instantaneous frequency has been reset to parallel to the time axis. Then the high frequency and time resolution have been achieved with the mono-frequency signal simultaneously. To find the optimal rotating angle of the local signal, an iterative approximation algorithm has been utilized, which makes the ANSTFT a non-parametric data driving method and have the better generalization ability than the conventional adaptive STFT. Moreover, several numerical examples are presented to illustrate the aforementioned characteristics and the application of ANSTFT to echolocation signal analysis demonstrates its validity. [ABSTRACT FROM AUTHOR]

The bearing is the key component in a rotating machine. It is important to assess the performance degradation of bearings for realizing proactive maintenance and near-zero downtime. In this paper, a methodology based on the zero crossing characteristic features and a coupled hidden Markov model is introduced for estimating bearing performance degradation. Zero crossing features are time domain representations of the vibration signature in the spectrum domain. They discover the change of bearing performance. When zero crossing features are extracted, a coupled hidden Markov model is employed to assess the performance degradation quantitatively. Results from a bearing accelerated life experiment validate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

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]

The rolling bearing fault signal under strong background noise is very weak because of environmental noise impaction and the attenuation of signal. The feature extraction of rolling bearings’ weak fault is very important in avoiding serious disaster, but it is also very difficult. Sparse decomposition has been used in the fault feature extraction of rolling bearings. But its performance is very poor when the background noise is very strong. This text combines the minimum entropy de-convolution (MED) and sparse decomposition to extract the feature of a rolling bearing’s weak fault. Firstly, the rolling bearing weak fault signal with strong background noise is de-noised using the MED method, and subsequently the de-noised signal is handled by sparse decomposition. Finally, the fault feature extraction method-envelope demodulation is carried on the last given signal and better results are obtained. In conclusion, through simulation and experiment the effectiveness and the feasibility of the proposed method are verified. [ABSTRACT FROM PUBLISHER]

In condition monitoring of mechanical equipment, the collected signals are mostly mixtures of several different sources. It is very important to recover the individual effects of each source for exact feature extraction and further fault diagnosis. A blind separation method based on second-order cyclic statistics is presented for convolved cyclostationary processes such as those observed in rotating machinery. The convolutive mixtures in time domain are transformed into instantaneous mixtures in frequency domain by discrete Fourier transform (DFT). Then the aim is to find a separating matrix that simultaneously and jointly diagonalizes the set of cyclic spectral density (CSD) matrices of the observed signals. Examples of successful separation are provided on both synthetic convolutive mixed bearing signals and real data tested from a gearbox. [ABSTRACT FROM PUBLISHER]

Fast Fourier transform-based near-field acoustic holography requires that the acoustic field should be sampled with a uniform spacing which is less than a half wave length of the highest frequency of interest to avoid spatial aliasing. Therefore, a large number of microphones are demanded for high frequencies. To overcome this difficulty and enhance the reconstruction accuracy, a data interpolation method based on the wave superposition algorithm (WSA) is proposed. At first, WSA is employed to regenerate the acoustic pressures between the measurement points. Then, the accuracy of the regenerated data is improved through an iterative process. In the end, taking the interpolated pressures as input data, the acoustic field can be reconstructed precisely with relatively few measurements. To solve the inherent ill-posed problem, Tikhonov regularization method together with generalized cross validation parameter choice method is utilized in the data interpolation method. Numerical simulation and experimental results demonstrate that this method can enhance the reconstruction accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Fan noise, comprising both tonal and broadband components, is a predominant source of noise in aero-engines. Calculating duct acoustic modes for random broadband noise is more complex than that for tonal noise. This paper proposes a probabilistic method for identifying duct acoustic modes based on non-synchronous measurements from microphone arrays. The method overcomes the challenge of acoustic mode aliasing and accurately identifies duct modes in the presence of broadband fan noise. By rotating a circular duct with a microphone array, the proposed method equivalently increases the number of non-synchronous microphone measurement points. The completion of the cross-spectral matrix is realized by the Fast Iterative Shrinkage Thresholding Algorithm (FISTA) to obtain the sound pressure signals from more measurement points. The mode coefficients are estimated using a hierarchical a priori probability method. The inverse problem of mode identification is represented by a Bayesian framework based on a Gaussian-scale mixture prior model. Simulations and experiments validate the method's effectiveness in suppressing mode aliasing, providing accurate results for duct mode identification with broadband noise, eliminating the influence of interfering modes on identification results, and offering improved observation of mode characteristics across a wide frequency and rotational speed range. • The non-synchronous measurements technique is employed to increase the number of measurement points. • A probabilistic model with a hierarchical prior is utilized to characterize the sound field. • The iterative parameter adjustment process is adaptive. • Experiments were performed on an axial compressor test rig to validate the proposed method. [ABSTRACT FROM AUTHOR]

Accurate identification of in-duct acoustic modes is crucial for comprehending fan noise generation mechanisms, propagation characteristics, and control strategies. The number of fan noise modes increases with frequency, and using a sufficient number of microphones for higher-order mode identification becomes challenging due to cost considerations. A Bayesian compressive sensing method for mode identification is proposed in this paper to address the issue of insufficient microphones. The sensing matrix is constructed by randomizing the arrangement of a small number of microphones. The acoustic field is characterized using a Bayesian probabilistic model, and the inverse problem is formulated as the estimation of mode coefficients within the Bayesian compressed sensing framework. The proposed method accurately identifies acoustic modes in the presence of adaptive parameters and achieves more precise magnitude recovery than previous methods. The effectiveness and robustness of the proposed method under various parameters is demonstrated by comparing the simulation results of different mode identification methods. The effectiveness of proposed method is further substantiated by experimental validation using a 1.5-stage axial flow compressor, demonstrating accurate identification of target modes with fewer microphones. • A Bayesian compressive sensing method for identifying tonal modes is proposed to solve the problem of insufficient microphones. • Simulation and experiments proved the effectiveness and modes can be accurately identified with a small number of microphones. [ABSTRACT FROM AUTHOR]

Abstract: Rolling element bearing faults are among the main causes of breakdown in rotating machines. In this paper, a rolling bearing fault model is proposed based on the dynamic load analysis of a rotor-bearing system. The rotor impact factor is taken into consideration in the rolling bearing fault signal model. The defect load on the surface of the bearing is divided into two parts, the alternate load and the determinate load. The vibration response of the proposed fault signal model is investigated and the fault signal calculating equation is derived through dynamic and kinematic analysis. Outer race and inner race fault simulations are realized in the paper. The simulation process includes consideration of several parameters, such as the gravity of the rotor-bearing system, the imbalance of the rotor, and the location of the defect on the surface. The simulation results show that different amplitude contributions of the alternate load and determinate load will cause different envelope spectrum expressions. The rotating frequency sidebands will occur in the envelope spectrum in addition to the fault characteristic frequency. This appearance of sidebands will increase the difficulty of fault recognition in intelligent fault diagnosis. The experiments given in the paper have successfully verified the proposed signal model simulation results. The test rig design of the rotor bearing system simulated several operating conditions: (1) rotor bearing only; (2) rotor bearing with loader added; (3) rotor bearing with loader and rotor disk; and (4) bearing fault simulation without rotor influence. The results of the experiments have verified that the proposed rolling bearing signal model is important to the rolling bearing fault diagnosis of rotor-bearing systems. [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]

An energy analyzing method called the Impact Energy Model (IEM) is introduced to assess and diagnose the rub–impact fault of a rotor system. The main purpose of the model is to indicate the probability of rub–impact or the severity level of the fault. Utilizing the nonlinear predictive energy, an effective quantitative evaluation index IEM is obtained from the model. Some work has been done elsewhere to partly demonstrate the IEM through experiments. In this paper we mainly discuss the variation of the IEM index with the speed ratio Ω at different levels of damping ratio ξ. The stagnation point is discussed in detail which is important to the assessment for the probability or severity of a rub–impact fault. The influence of dynamic stiffness is discussed which may affect the assessment result of the IEM. Furthermore, a sensitive area of the rotor operating system is presented. The result shows that this sensitive area provides a reference for the operation and design of a rotor system. [ABSTRACT FROM PUBLISHER]

Various techniques have been presented to detect rolling element bearing faults, however, it is still a huge challenge to accurately extract features under high noise level. In this paper, a new approach based on matching pursuit for analyzing the signals of rolling element bearings is proposed. Different from most of the matching pursuit related works focusing on the time-frequency plane, complexity spectrum and complexity spectrum entropy are proposed in this research to accurately extract the fault feature of a rolling element bearing signal under a low signal to noise ratio. Both simulation and experiment show that complexity spectrum works better than envelope spectrum in distinguishing characteristic frequencies of fault bearings submerged in noise. An accelerated whole lifetime test of bearing has been performed to collect vibration data, which is analyzed by complexity spectrum entropy and other normal approaches. Results show that complexity spectrum entropy has some unique characteristics. [ABSTRACT FROM PUBLISHER]

Spectral kurtosis (SK) is an algorithm that gives an indication of how kurtosis varies with frequency. A frequency band that contains abundant information, especially the impact signal, can be tracked by calculating SK. In the present article, SK combined with Autoregressive AR model, was applied into the fault diagnosis and condition monitoring of bearings. Accelerated life test of rolling bearings in Hangzhou Bearing Test & Research Center (HBRC) was performed to collect vibration data over their entire lifetime (normal-fault-failure). The result shows that SK can detect early incipient fault by eliminating some other interfering frequency components. In addition, it can detect fault 5 min earlier than root mean value (RMS). This fault detection in advance is significant for condition monitoring. [ABSTRACT FROM AUTHOR]

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]

Abstract: A new method for simulating nonlinear motion of cracked crankshaft is proposed, and the transient vibration response of a cracked crankshaft is evaluated and analyzed. First, the crankshaft without crack is simplified as a finite element model based on spatial Timoshenko beam element, and the vibration modes of the crankshaft are calculated and compared with the results presented in other published literatures. Then, the frequently occurred crack in crankpin-web fillet region is studied. According to the characteristic of this kind of crack, a new spatial crack beam element is developed, and a cracked crankshaft model, which combines crack beam element and Timoshenko beam elements, is established. Subsequently, the breathing behavior of the crack under operating condition is discussed, and the nonlinear equation of motion of cracked crankshaft is set up. Finally, the transient vibration response of the cracked crankshaft under fire condition is evaluated, and the influence of the crack depth on the vibration response of torsion, translation and bending are analyzed. The modeling and analysis procedures are applied to a crankshaft system of a four in-line cylinder engine. This investigation provides a useful tool for the vibration analysis and crack detection of cracked crankshaft system. [Copyright &y& Elsevier]

• The sparse time frequency analysis method is proposed for bearing fault diagnosis. • The sparsity of the time-frequency fault feature is revealed. • The applied basis operator can derive the fault characteristic frequency directly. • The time and frequency resolutions are enhanced effectively. • The proposed method also denoise the signal effectively. In practice, bearings often run at a time-varying speed, which induces non-stationary vibration signals. How to extract the fault characteristic frequency (FCF) effectively under unknown variable speed conditions is a challenging work. This paper proposes a sparse time frequency method for fault diagnosis with no speed information demanded. Firstly, the Hilbert Transform is used to demodulate the vibration signal. Then the iterated soft-thresholding algorithm is applied to solve the l 1 norm regularized linear least squares cost function. The sparsity of the FCF is expounded in detail, and how to choose the basis to map the vibration signal into the sparse space is also detailed. With the appropriate basis, the solution is exactly the optimized sparse TFR, which can enhance both time and frequency resolutions greatly, and meanwhile denoise the signal effectively. This method does not produce the confusing components when the bearing is in the healthy condition, while indicates the FCF when the bearing is defective. To show the robustness of the effectiveness, the proposed method is verified with simulated and experimental signals under various time-varying operating conditions. All the signals are also processed with the STFT, Fourier-based Synchrosqueezing Transform and ridge extraction method for comparison. [ABSTRACT FROM AUTHOR]