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Blind deconvolution (BD) has proven to be an effective approach to detecting repetitive transients caused by bearing faults. However, BD suffers from instability issues including excessive sensitivity of kurtosis-guided BD methods to the single impulse and high computational time cost of the eigenvector algorithm-aided BD methods. To address these critical issues, this paper proposed a novel BD method maximizing negative entropy (NE), shortened as maximum negative entropy deconvolution (MNED). MNED utilizes NE instead of kurtosis as the optimization metric and optimizes the filter coefficients through the objective function method. The effectiveness of MNED in enhancing repetitive transients is illustrated through a simulation case and two experimental cases. A quantitative comparison with three existing BD methods demonstrates the advantages of MNED in fault detection and computational efficiency. In addition, the performance of the four methods under different filter lengths and external shocks is compared. MNED exhibits lower sensitivity to random impulse noise than the kurtosis-guided BD methods and higher computational efficiency than the BD methods based on the eigenvalue algorithm. The simulation and experimental results demonstrate that MNED is a robust and cost-effective method for bearing fault diagnosis and condition monitoring. [ABSTRACT FROM AUTHOR]

Maintaining exceptional product quality and boosting processing efficiency requires precise evaluation of various aspects of the turning process, including the cutting depth, feed rate, and size of the workpiece. This article presents a novel approach for observing the turning process state using modulation signal bispectrum (MSB) and motor current signals. A nonlinear model was established that clarifies the load torque oscillations during turning, which in turn affects the amplitude and phase modulation of the motor stator current. Random noise can be efficiently minimized using the MSB algorithm, allowing the extraction of the current-modulation characteristic sideband phase and amplitude from the collected current signal. This technique enables clear representation and enhanced monitoring of load torque changes throughout the turning process. The proposed method was validated via mathematical simulations and universal lathe tests, with the results indicating that the MSB phase and amplitude values effectively capture both dynamic and static torque alterations during the turning operation, making this approach a valuable tool for overseeing the turning process. [ABSTRACT FROM AUTHOR]

A sparse squared envelope is crucial for efficient and accurate diagnosis of bearing faults. Blind deconvolution (BD) is a well-established sparse feature enhancement method for the diagnostics of rolling bearings. Traditional BD methods, such as minimum entropy deconvolution (MED), are susceptible to random transients, making it difficult to enhance fault features of rolling bearings subject to strong random shocks. Deconvolution methods that take the fault characteristic frequency (or fault impulse period) of interest as an algorithm input parameter, such as maximum second-order cyclostationarity blind deconvolution (CYCBD), can alleviate this deficiency. However, bearing fault features are difficult to be enhanced by these methods when the specified characteristic frequency deviates from the actual value greatly. To overcome these problems, the modified smoothness index (MSI) of the squared envelope is proposed as the objective function of the deconvolution method, and a new BD method is developed to achieve a sparse squared envelope for fault diagnosis of rolling bearings. Furthermore, the methodology is extended to the frequency domain, and another new BD method that utilizes the MSI of the squared envelope spectrum as the objective function is established to achieve a sparse squared envelope spectrum for bearing diagnostics. These two proposed BD methods are robust to random transients and do not require characteristic frequency or impulse period as an input parameter for feature enhancement. The performance of the two proposed BD methods is verified on experimental datasets from two different railway axle bearing test rigs and compared with the state-of-the-art deconvolution methods. The results show that the two proposed methods can effectively enhance repetitive transient features in noisy vibration signals and accurately diagnose different faults of railway axle bearings. [ABSTRACT FROM AUTHOR]

The Gini index (GI), GI II, and GI III are proven to be effective sparsity measures in the fields of machine condition monitoring and fault diagnosis, and they can be reformulated as the ratio of different quasi-arithmetic means (RQAM). Under this framework, generalized Gini indices (GGIs) have been developed for sparse quantification by applying nonlinear weights to GI, and another generalized form of GI, referred to here as power function-based Gini indices I (PFGI1s), has been introduced by using power function as the generator of quasi-arithmetic means. The GGIs with different weight parameters exhibit reliable sparse quantization capability for repetitive transient features, while their repetitive transient discriminability is lower than kurtosis and negentropy under noise contamination. PFGI1 achieves enhanced repetitive transient discriminability with increasing power exponent, showing the advantage of the generalization approach. In this paper, based on RQAM, a single-parameter generalization method for generating PFGI1s is introduced into GI II and GI III from the perspective of the quasi-arithmetic mean generator, which leads to the power function-based Gini indices II and III (PFGI2s and PFGI3s) constructed from GI II and GI III, respectively. Mathematical derivation proves that PFGI2s and PFGI3s satisfy at least five of six typical attributes of sparsity measures and are two new families of sparsity measures. Simulation analysis shows that, similar to PFGI1s, PFGI2s and PFGI3s can monotonically estimate the sparsity of the data sequence and can simultaneously achieve strong random transient resistibility and high repetitive transient discriminability compared with traditional sparsity measures. The experimental results of bearing run-to-failure demonstrate that PFGI1s, PFGI2s, and PFGI3s with appropriate power exponents can effectively quantify the repetitive transient features caused by bearing faults and can accurately characterize the bearing degradation status compared with the state-of-the-art sparsity measures. [ABSTRACT FROM AUTHOR]

This paper proposes a novel multiple amplitude modulation and frequency modulation (AM–FM) demodulation method based on local modulation signal bispectrum (LMSB), which can demodulate the fault features of different components from the gearbox signal with multi-mesh frequency bands and multi-modulation components. Firstly, the collected measurement signal is decomposed into a series of sub-band signals, and the generated sub-band signals are demodulated by modulation signal bispectrum (MSB), which realizes the simultaneous demodulation of multi-mesh frequency bands and multi-modulation components. Subsequently, each sub-band signal resulting from MSB demodulation is synchronously averaged to generate the LMSB, which removes random noise and interference frequencies from the sub-band signals. Finally, the periodic modulation intensity (PMI) is utilized to evaluate the ability of the LMSB to demodulate multi-component signals with AM–FM components. The effectiveness of LMSB in processing multi-component signals with AM–FM components is demonstrated by numerical simulation signals and experimental analysis. Analysis results demonstrate the superiority of LMSB in multiple AM–FM demodulation compared with MSB, envelope analysis (EA) and Teager energy operator (TEO). This research provides a novel perspective for gearbox fault detection. [ABSTRACT FROM AUTHOR]

Epicyclic gearboxes are prevalent in a variety of important engineering systems such as automotive, aerospace, wind turbines, civil equipment and industrial robots owing to the merits of compact structure and high power density. To ensure the productivities of such important systems, condition monitoring techniques are being actively studied to resolve the challenge of varying transmission paths and multiple modulations in vibration signals acquired from ring gear housing. This paper proposes a new Modulation Signal Bispectrum (MSB) Enhanced Squared Envelope method to analyse the vibration signals acquired by a special On-Rotor Sensing (ORS) transducer that is mounted on the shaft of an epicyclic gearbox. A vibration signal model of ORS measurements from epicyclic gearboxes is presented to show the multiple modulation influences. Moreover, inevitable noise influences are also investigated on the conventional squared envelope and the state-of-the-art spectral correlation analysis. On this base, MSB is introduced to suppress these influences for accurately extracting equally spaced harmonics in the squared envelope and is then integrated to isolate fault signatures, allowing effective fault detection and diagnosis of epicyclic gearboxes, which lead to novel contributions of an MSB Enhanced Squared Envelope (MSB-ESE) approach. An experimental study of compound epicyclic gear faults was conducted to demonstrate the superior performance of MSB-ESE along with the special ORS technique in detecting and diagnosing the compound faults on sun and planet gears. [ABSTRACT FROM AUTHOR]

Weak fault feature extraction is of great significance to the fault diagnosis of rolling bearing. At the early stage of defects, fault features are usually weak and easily submerged in strong background noise, which makes feature information extremely difficult to be excavated. This paper proposes an iterative morphological difference product wavelet (MDPW) to address this issue. In this scheme, firstly, the morphological difference product filter (MDPF) is developed using the combination morphological filter-hat transform operator and difference operator. The MDPF is then incorporated into a morphological undecimated wavelet to construct the MDPW, which can achieve noise suppression and fault feature enhancement. Subsequently, the optimal iteration numbers that influence the performance of MDPW is determined using the fault severity indicator, which effectively extracts periodic impulse related to the failure of rolling bearing. Finally, the fault identification is inferred by the occurrence of fault defect frequencies in the MDPW spectrum with the optimal iteration numbers. The validity of the iterative MDPW is evaluated through numerical simulations and experiment cases. The analysis results demonstrate that the iterative MDPW has higher diagnosis accuracy than existing algorithms (e.g., adaptive single-scale morphological wavelet and weighted multi-scale morphological wavelet). This research provides a new perspective for improving the weak fault feature extraction of rolling bearing. [ABSTRACT FROM AUTHOR]

Transient impulses caused by local faults are critical informative indicators for rolling element bearing fault diagnosis. The methods for accurately extracting transient impulses while suppressing strong background noise and interference components have received extensive studies. In this article, a novel fault diagnosis scheme based on optimized wavelet packet denoising and modulation signal bispectrum is proposed, which takes advantage of the transient impulse enhancement of wavelet packet denoising and the demodulation ability of modulation signal bispectrum to diagnose bearing faults more accurately. First, the measured signals are decomposed into a series of time–frequency subspaces using wavelet packet transform. An optimal threshold value is selected based on the proposed threshold criterion by considering unbiased autocorrelation of envelope and Gini index of the transient impulses. Subsequently, the subspaces are denoised by the wavelet packet denoising with the optimized threshold value, and the master subspaces that containing the fault-related transient impulses are selected based on the Gini index indicator. Finally, the modulation signal bispectrum is utilized to further purify the signal and extract the modulation components contained in the transient impulses, and the suboptimal modulation signal bispectrum slices are selected based on the characteristic frequency intensity coefficient. The modulation signal bispectrum detector is then obtained by averaging the suboptimal modulation signal bispectrum slices to determine the type of the bearing faults. The proposed wavelet packet denoising-modulation signal bispectrum is validated based on the simulation and experimental studies. Compared with the variational mode decomposition and Teager energy operator, fast kurtogram as well as conventional modulation signal bispectrum, the proposed wavelet packet denoising-modulation signal bispectrum method has superior performance in extracting the fault feature of the incipient defects on different bearing components. [ABSTRACT FROM AUTHOR]

Global orbits connect the saddle points in an infinite period through the homoclinic and heteroclinic types of manifolds. Different from the periodic movement analysis, it requires special strategies to obtain expression of the orbit and detect the associated profound dynamic behaviors, such as chaos. In this paper, a global dynamic frequency method is applied to detect the homoclinic and heteroclinic bifurcation of the complicated nonlinear systems. The so-called dynamic frequency refers to the newly introduced frequency that varies with time t, unlike the usual static variable. This new method obtains the critical bifurcation value as well as the analytic expression of the orbit by using a standard five-step hyperbolic function-balancing procedure, which represents the influence of the higher harmonic terms on the global orbit and leads to a significant reduction of calculation workload. Moreover, a new homoclinic manifold analysis maps the periodic excitation onto the target global manifold that transfers the chaos discussion of non-autonomous systems into the orbit computation of the general autonomous system. That strategy unifies the global bifurcation analysis into a standard orbit approximation procedure. The numerical simulation results are shown to compare with the predictions. [ABSTRACT FROM AUTHOR]

Bearings are used as the most important load-carrying transmission components in various machines, thus subjecting to a number of faults including wear, fatigue pitting, cracks and so on. Fault detection and diagnosis of bearings can effectively prevent the machine from such typical failures and subsequent consequences. The faults in bearings can lead to the vibration signals that exhibit cyclostationary characteristics due to the inevitably random phase noise (or slippage between bearing components). In this article, a phase linearisation–based modulation signal bispectrum is proposed to tune up the cyclostationary bearing signal into a periodic waveform by linearizing the instantaneous phase of the narrow frequency band signals. In this way, the signal becomes more deterministic and modulation signal bispectrum can be effectively applied to suppression noise and obtain accurate and robust diagnosis results. As a result, this fault detector can achieve high performance in characterising the nonstationary bearing vibration signals and hence diagnose the bearing faults even in the case of extremely low signal-to-noise ratio (<−20 dB), which is benchmarked by the method of conventional modulation signal bispectrum in both simulation and experiment studies. [ABSTRACT FROM AUTHOR]