Periodic Impulses Research Articles

Cycle kurtosis entropy guided symplectic geometry mode decomposition for detecting faults in rotating machinery

Strong noise interference or compound fault coupling phenomenon may lead to the failure of fault diagnosis technology. This paper focuses on weak feature extraction and compound faults detection for rotating machinery fault diagnosis and proposes adaptive symplectic geometric mode decomposition (SGMD) using cycle kurtosis entropy. Firstly, an index named cycle kurtosis entropy (CKE) is presented to measure the strength of periodic impulses in a signal. The CKE uses the entropy value of calculating all delay cycle kurtosis (CK) to overcome the shortcomings of the CK in adaptive ability and obtain more stable values. Thirdly, CKE is applied to construct an adaptive slip window with optimal length. This process is called the adaptive window segmentation method, which is mainly used to dig out weak fault features in signals. Finally, CKE is used as the component selection criterion to select the components decomposed by SGMD. The selected components are reconstructed to obtain a de-noised signal. Hilbert envelope analysis is applied to the denoised signal to demodulate the fault characteristic frequency. Numerical simulations and experimental investigations using bearings and gears are performed to testify the property of the presented method. The results indicate that the adaptive slip window can enhance the decomposing ability of SGMD under strong noise condition. Moreover, for the strong periodic impulse identification ability, the cycle kurtosis entropy is suitable to determine the optimal components of SGMD. It is expected that the presented method will be effectively used for fault feature extractions in rotating machinery under stationary running conditions.

Enhanced weight symplectic geometry decomposition based on maximum periodic kurtosis deconvolution

To enhance the periodic impact component and improve the accuracy of planetary gear fault detection, an enhanced weighted symplectic geometry decomposition based on maximum periodic kurtosis deconvolution (MPKD-EWSGD) is proposed in the paper. On the one hand, MPKD-EWSGD adopts the MPKD method for noise reduction preprocessing to highlight the periodic impulse component. On the other hand, MPKD-EWSGD introduces the periodic impulse intensity (PII) to choose components with fault information, avoiding the disadvantages of denoising methods that use the component energy as the measurement standard. Emulation and experimental signals show that MPKD-EWSGD can effectively reduce noise and is an effective method for planetary gearbox fault detection.

Periodicity measure of cyclo-stationary impulses based on low sparsity of Gini index and its application to bearing diagnosis

A key problem in the fault diagnosis of rolling element bearings is the extraction of features of repetitive transients from vibration signals. The accurate evaluation of maximizing spectral sparsity under complex interference conditions for measuring the periodicity of transients is typically difficult to implement. Accordingly, a novel periodicity measurement approach was designed for time waveforms. According to the Robin Hood criteria, the Gini index of a sinusoidal signal has a stable low sparsity. The periodic modulation of cyclo-stationary impulses can be represented by several sinusoidal harmonics based on envelope autocorrelation and bandpass filtering. Thus, this low sparsity of Gini index can be used to evaluate the periodic strength of modulation components. Finally, a sequential feature evaluation method is developed to extract periodic impulses accurately. The proposed method is tested on simulation and bearing fault datasets and compared with the state-of-art methods so to assess its effectiveness.

Fault diagnosis of sensor pulse signals based on improved energy fluctuation index and VMD

Variational mode decomposition (VMD) has been widely applied in sensors. However, the mode number and balance parameter seriously limit VMD application. To solve this problem, this study proposes a novel method, which combines an improved energy fluctuation index (IEFI) and modified VMD (MVMD). In the proposed method, IEFI provided better performance to resist interference from random impulses by considering the periodicity of fault feature components. Consequently, it is applied to determine the initial center frequency for MVMD, which fixed the problem of the mode number. Moreover, a novel balance parameter search strategy, which can adaptively determine the optimal balance parameter, is combined with MVMD whose stop condition is replaced by kurtosis to extract the fault feature. Simulation results indicated that the proposed method does well in detecting the feature of a periodic impulse signal from the signal polluted by some interference impulses. Moreover, the bearing fault diagnosis results demonstrate that the proposed method can accurately detect bearing fault features. Furthermore, the method was validated with bearing fault data. The results showed that the method can accurately extract the fault characteristics of the impulse signal and achieve fault diagnosis.

Research on the detection of axle abnormal noise based on maximum autocorrelation kurtosis deconvolution

The axle off-line detection is an important link to ensure the sound quality of the axle. The traditional methods mainly rely on condition indicators, psychoacoustic parameters and artificial intelligence, in which the generation mechanism of the abnormal signal is ignored, thus leading to low accuracy and poor interpretability. To solve these problems, a vehicle axle abnormal sound detection method based on abnormal sound mechanism is proposed in this paper. Firstly, the sound quality of 30 newly produced axles is determined by subjective evaluation, and it is clear that the tooth frequency impulse is the main reason for the abnormal sound of axles. Then, a new objective function, autocorrelation kurtosis, is used to deconvolute the axle vibration signal for the periodic impulse feature. Simulation and experimental results show that the proposed maximum autocorrelation kurtosis deconvolution (MACKD) is more effective than maximum correlation kurtosis deconvolution (MCKD) and minimum entropy deconvolution (MED). On this basis, the impulse autocorrelation kurtosis index (IACK) is constructed and used to quantify the abnormal sound of the axle. The results show that the correlation between the proposed index and the subjective evaluation results is more than 0.9, which can better identify the sound quality of the axle.

An innovative hybrid approach for better detection of bearing faults in highly noisy environments

Rolling element bearings (REBs) are critical components in rotating machinery, and timely detection of faults in these bearings can prevent catastrophic failure and costly downtime. Vibration signals collected from REBs contain important information regarding the bearing health states. A localized defect in a REB produces periodic impulses in the vibration signals at relevant bearing characteristic frequencies (BCFs) that are commonly used for bearing condition monitoring. Envelope analysis that has been a powerful technique in detecting BCFs in signals, however, poses a significant challenge as it requires the selection of an effective band-pass filtering region due to the variable nature of resonant frequencies in bearing systems. A novel hybrid method for bearing fault diagnosis based on Cepstrum Pre-Whitening (CPW) and high-pass filtering has been developed to overcome this shortcoming in envelope analysis and has shown to be a powerful technique in accurately detecting early bearing faults on a range of machines under different operating conditions. In contrast to the existing signal processing methods, the new hybrid method eliminates the need for manual parameter selection or optimization algorithms, such as filtering bands selection in enveloping analysis. Instead, it requires inputs including bearing geometries and its operating conditions such as shaft rotating speed for bearing fault diagnosis. This enhances the practicality and accuracy of bearing fault diagnosis in real-world scenarios, especially when data is limited. This study evaluates the effectiveness of this hybrid method for bearing fault diagnosis in the highly noisy environments under which machine is often operated in real applications. To achieve this purpose, firstly, numerical simulations of bearing vibration signals have been conducted, wherein Gaussian white noise with varying levels of signal-to-noise ratio (SNR) is DOI: 10.1784/cm2023.3f4 added to the simulated signals. Secondly, the effectiveness of the method is tested on vibration data collected from an experimental run-to-failure bearing dataset, which contains significant amount of background noise in the early stage of the fault progression. The results from this work have shown that the new hybrid method achieves high accuracy in diagnosing fault features in the simulated signals with a SNR of down to ‐ 13 dB for outer ring fault and ‐ 15 dB for inner ring and ball faults, much more effective than other methods in the literature. It has also shown to detect bearing faults at very early stages from a run-to-failure test.

Adaptive Swarm Decomposition Algorithm for Compound Fault Diagnosis of Rolling Bearings

The feature extraction of compound faults is still considered the bottle neck task of machinery fault diagnosis. In this article, a novel adaptive swarm decomposition (ASWD) algorithm based on fine to coarse (FTC) segmentation is proposed for compound fault detection of rolling bearings. Firstly, the number of oscillating components that affects the results of ASWD is automatically determined by the order statistics filter and energy spectrum segmentation method without any prior knowledge. Secondly, the Teager energy kurtosis (TEK) of successively extracted components is employed as the indicator to evaluate the effectiveness of iterations. This not only setups the swarm decomposition (SWD) threshold, but also improves the performance of periodic impulses separation. Finally, ASWD is applied to intelligently separate the different oscillating components and suppress the redundant decomposition. The testing results of ASWD on the simulation and real cases indicate that ASWD can effectively extract compound fault impulses from multicomponent vibration signals. The comparison between SWD and other decomposition methods further verifies the superiority of ASWD. The characteristic frequency intensity coefficient (CFIC) of ASWD is increased by 34.2%, 49.2%, and 56.5% in the three cases, respectively, than SWD, variational mode decomposition (VMD), and ensemble empirical mode decomposition (EEMD).

Enhanced Rolling Bearing Fault Diagnosis Combining Novel Fluctuation Entropy Guided-VMD with Neighborhood Statistical Model

Variational Mode Decomposition (VMD) provides a robust and feasible scheme for the analysis of mechanical non-stationary signals based on the variational principle, but this method still has no adaptability, which greatly limits the application of this method in bearing fault diagnosis. To solve this problem effectively, this paper proposes a novel fluctuation entropy (FE) guided-VMD method based on the essential characteristics of fault impulse signals. The FE reported in this paper not only considers the order of amplitude values but also considers the variation of amplitude, and hence it can comprehensively characterize the transient and fluctuation characteristics of rolling bearing fault impulse signal. On the basis of establishing FE, the FE-based fitness functions are then conducted, after which the mode number and balance parameter can be adaptively determined. Meanwhile, an adaptive neighborhood statistical model is developed to further reduce the noise of the mode component containing fault information so as to highlight the periodic impulse component more significantly and improve the diagnostic accuracy. Simulation and case analysis show that this research is effective and quite accurate in fault mode separation and fault feature enhancement. Compared with the traditional VMD method and the current common diagnosis methods, the proposed method has obvious advantages in the comprehensive utilization of fault impulse information and enhanced diagnosis.

An adaptive variational mode extraction method based on multi-domain and multi-objective optimization for bearing fault diagnosis

When a local fault in the rolling element bearing appears during operational running, the induced bearing vibration signal is essentially equivalent to a mixed multi-component signal, which usually includes multiple frequency components (e.g., periodic impulses, random impulses, discrete harmonics, and heavy environmental noise). This indicates that it is difficult to detect the weak periodic impulses related to bearing faults by traditional signal processing methods. Variational mode extraction (VME) as a new signal processing method with band-pass filtering properties can separate the desired periodic impulse component from the mixed multi-component signal due to its similar basis as the popular variational mode decomposition (VMD). However, the filtering performance of VME is significantly influenced by two parameters (i.e., penalty factor and center-frequency). To address this issue, all the previous work focused on single-domain and single-objective parameter optimization from the filtering signal or its envelope, whereas the objective function with a single-criterion cannot depict bearing fault signatures from the impulsiveness and cyclostationarity simultaneously in general cases. Therefore, to improve the bearing fault feature extraction ability and avoid the problem of artificial parameter selection of VME, this paper proposes an adaptive variational mode extraction method based on multi-domain and multi-objective optimization (AVME-MDMO), in which two key parameters of VME are automatically determined by multi-objective gray wolf optimizer (MOGWO) with a novel multi-objective function named integrated measure of sparsity-impact (IMSI) of square envelope (SE) and square envelope spectrum (SES). As a result, the optimal VME is employed to obtain the specific mode component and its corresponding SES for achieving bearing fault diagnosis. The effectiveness of the proposed method has been validated on simulation signal and experiment data of rolling element bearing. Besides, the comparison results demonstrate its superiority and robustness in excavating fault signatures over the VME or VMD with single-objective function, and the fast kurtogram.

Fault Characteristics Analysis of High-Speed Train Transmission Systems

The high-speed train speed has a higher requirement for stability and operating safety with its operating speed increasing. The main focus of this paper is on the fault characteristics analysis of a high-speed train transmission system. The governing equation and boundary conditions of the transmission system are derived using the finite element method, in which a Timoshenko beam element is introduced to represent the wheelset shaft, and a rigid mass element is utilized to represent the gears, bearings, and wheels. To investigate the vibration response mechanism of a high-speed train transmission system, the critical speed of the system and its modal response are given. According to the types of high-speed train component fault features, the local fault features of gear, bearing, and wheelset are given. Healthy and faulty systems with localized faults in gear, bearing, and wheelset are studied. The characteristics of amplitude and frequency are verified numerically and the transmission characteristics of signal and relation are explained when there is local fault defect in the system. The results show that under different fault types, the time domain response of the system has obvious periodic impulse response faults, and the fault frequency band characteristic distribution is different in the frequency domain response. The simulation results are consistent with the experimental results.

Fault feature extraction for planetary bearing of CRF pump in nuclear power plant based on TFDC-QPSO-optimised MOMEDA

To address the issue of weak fault features and difficulty in feature extraction for planetary gearbox bearings of the circulation water pump (CRF pump) unit in the conventional island of a nuclear power plant, a deconvolution method, named the multipoint optimal minimum entropy deconvolution adjusted (MOMEDA), is optimised by a mixing operator improved quantum behaviour particle swarm optimisation (QPSO) algorithm, to extract the periodic fault impulse of planetary gearbox bearings. In the mixing operator, a differential evolution operator is introduced to improve particle swarms’ diversity and enhance the algorithm’s global optimisation capability. Meanwhile, a proposed adaptive CrossOver operator is incorporated into the algorithm to increase its convergence speed. Then, combining these two types of operators can construct a parameter optimisation algorithm displaying both global optimisation capability and high algorithm execution efficiency. Consider capturing the periodic impulsive features relating to bearing faults. A fitness function based on the characteristic information of the deconvolution signal in the time and frequency domain is proposed. This function serves as the objective function to facilitate the parameter optimisation on MOMEDA. Thereby, it enhances the optimisation capability of our feature extraction method. Experiments were conducted by adopting the proposed method on the signals collected from the inner- and outer-race faulty planetary bearing in a test bed, in which favourable feature extraction results are obtained. After the comparative analysis, we observed that both significances of features extracted by this method and the execution efficiency of the algorithm are superior compared to other methods. The on-site feature extraction results of the input shaft bearing in the planetary gearbox of a CRF pump unit in a nuclear power plant also demonstrated the engineering practicability of the method proposed in this work.

Acoustic feature enhancement in rolling bearing fault diagnosis using sparsity-oriented multipoint optimal minimum entropy deconvolution adjusted method

Rolling element bearings are of great importance and widely used in rotating machineries, whose fault detection and diagnosis (FDD) are essential for insuring reliability of the entire mechanical system. Therefore, extracting fault-related transient features from noisy signals to reveal bearing weak fault is a crucial prerequisite for long term condition monitoring. However, in complex working conditions, the measured acoustic signals are typically multi-component, submerged by strong interference noise and affected by unknown transmission path, resulting in the indistinctive fault-induced features and unsatisfactory diagnosis accuracy. To tackle this problem, a sparsity-oriented Multipoint Optimal Minimum Entropy Deconvolution Adjusted (MOMEDA) method is proposed for bearing fault feature enhancement and diagnosis based on acoustic signals. As a non-iterative blind deconvolution approach, MOMEDA has been proven to be an effective tool to extract fault-related impulses from the noisy signal and compensate the complex unknown transmission path, enabling target propositioning and fault indication of bearings at an earlier termination condition. Furthermore, a sparsity operation which is originally designed for acoustic signal analysis, based upon the Laplace distribution characteristics of the fault-induced outliers, can further suppress the noise component and enhance the periodic fault impulses. The feasibility and effectiveness of the proposed sparsity-oriented MOMEDA method is validated by both simulated and experimental data. It is worth mentioning that bearing cage fault diagnosis and bearing mixed fault diagnosis, usually receiving limited attention before, are also investigated by the proposed method. The results demonstrate that the presented method gets preferable performance than existing methods, and it can achieve robust FDD of rolling bearings based on acoustic signals.

Maximum correlation Pearson correlation coefficient deconvolution and its application in fault diagnosis of rolling bearings

Blind deconvolution (BD) has been proved to be an effective tool for recovering periodic impulses from strong background noise signals is widely used for fault diagnosis of bearings and gears. However, the existing BD focus more on improving the quantity and amplitude-frequency characteristics of interested periodic impulses without considering their phase-frequency characteristics and impulse waveform characteristics (attenuation coefficient and oscillation frequency), which results in severe distortion of the reconstructed signal. In this scenario, a new BD method, named maximum correlation Pearson correlation coefficient deconvolution (MCPCCD), is presented in this paper. Firstly, a new objective function is constructed which include two terms: correlation Pearson correlation coefficient (CPC) and signal fidelity term (SFT). CPC is a new norm with strong sensitivity to interested impulse signals, while SFT is a dimensionless error measure similar to RMSE. Then, the optimal FIR filter is obtained by maximizing the objective function of the reconstructed signal. Meanwhile, a new preprocessing step is designed to reduce the requirement of MCPCCD for periodic prior. Finally, the application on simulated and two experimental signals indicates that MCPCCD significantly outperforms the traditional BD method in recovering the periodic impulses.

Research on the Sparse Optimization Method of Periodic Weights and its Application in Bearing Fault Diagnosis

The vibration state monitoring signal of rolling bearings usually shows periodic transient impulse characteristics at the time of the fault, but in the fault sprouting stage and actual monitoring, its impulse components are easily disturbed by random pulses, harmonics, background noise, etc., which increases the difficulty of extracting the periodic shock characteristics of the fault. This paper proposed a rolling bearing fault feature extraction method based on sparse coefficient weighting theory and periodic enhancement strategy to effectively extract weak periodic shock features with a low signal-to-noise ratio. In the proposed period weighted sparse wavelet representation (PWSWR) method, firstly, based on the sparse wavelet model, the mean kurtosis (MK) index was introduced as a weight to distinguish the contribution of the wavelet coefficients of each signal component. Secondly, a sparse signal period enhancement strategy was proposed using the improved envelope harmonic product spectrum period estimation method. The strategy is embedded into the sparse representation model to achieve the periodic enhancement of filtered signals. Finally, the envelope detection of the sparse signal was carried out to identify the fault. The results of bearing fault simulation signals and two engineering test signals showed that the proposed method could effectively extract weak fault features of bearings and had certain advantages compared with other sparse methods.

Rotating machine fault diagnosis by a novel fast sparsity-enabled feature-energy-ratio method

To well extract the early fault characteristics of rotating machines, a new fast sparsity-enabled feature-energy-ratio method is investigated in this paper. This method includes two stages. In the first stage, the spectrum is adaptively segmented through a coarse-to-fine strategy based on the ordered local maximums. Thus, the fault characteristic band can be divided automatically. A novel index based on sparsity, energy ratio, and kurtosis, is constructed to evaluate periodic impulses in each sub-signal, and it can evaluate the periodic impulses from the globality and locality. In the second stage, the Fourier spectrum from the first stage are refined by an improved sparse coding shrinkage denoising (SCSD) method whose parameters can be dynamically determined for each point. Within the improved SCSD approach, the differential result of the amplitude spectrum is used as input to improve the sparsity. Moreover, the ratios between the SCSD output and its input are applied to weigh the Fourier spectrum and maintain the phase information. Finally, the inverse fast Fourier transform and squared envelope spectra are applied to detect the fault characteristics. Bearing and gearbox vibration signals are used to validate the proposed methodology. The experimental results show that the proposed method is superior to some typical methods and the proposed index are robust to the interferences from aperiodic impulses. Therefore, the proposed method has great potential in the fault diagnosis of rotating machine.

Impulse feature extraction via combining a novel voting index and a variational model penalized by center frequency constraint

A key step in rotating machinery fault diagnosis is extracting the subcomponent that best characterizes the fault features. To this end, a fault feature extraction methodology based on an adaptive spectrum segmentation method, a new voting index, and a new variational model is constructed in this paper. More specifically, the spectrum is divided into a series of sub-bands through a fast iteration filter by changing the width of the window. Then, by considering the amplitudes and locations of the fault feature spectral lines in squared envelope spectrum, a novel index based on voting mechanism is constructed to evaluate the periodic impulses in each sub-band. Finally, a new variational model penalized by a center frequency penalty item is proposed to extract the fault characteristics from the raw vibration signal by maximining the proposed index iteratively. The proposed methodology is applied to extract the fault characteristics from rolling bearing and planetary gearbox signals. The comparative results indicate the proposed method is superior to fast kurtogram, fast entrogram, and the proposed fault feature extraction methods based on other classical indices.

Mother and sibling interactions during the preweaning period influence myelination and impulse propagation of the sensory sural nerve in the adult rat.

To investigate whether mother and sibling interactions during the preweaning period influence the histological and electrophysiological characteristics of the sensory sural nerve (SUn) in the adult rat, litters composed of 1, 3, 6, 9, and 12 male pups (P) were formed and the pups routinely weighed until postnatal day 60 (PND60). At PND9, 3P and 6P litters showed greater body weight than pups without siblings or from 9P or 12P litters, and such differences in weight were maintained until adulthood. Analysis of maternal licking at PND8 and 9 showed that pups from large litters received fewer licks than pups from small size litters. At PND60, SUn of rats from 6P and 9P litters had greater compound action potential (CAP) amplitude and a higher proportion of axons with large myelin thickness than nerves from rats of 1P, 3P, or 12P litters. SUn of heaviest rats from 9P and 12P litters had greater CAP area and myelination than the lightest rats from the same litters. We propose that a complex interplay of sensory, social, and nutritional factors arising from mother and littermate interactions during the preweaning period influence myelination and the propagation of action potentials in the SUn of adult rats.

Fault feature analysis and detection of progressive localized gear tooth pitting and spalling

Fault feature analysis of gear tooth spalling plays a vital role in gear fault diagnosis. Understanding how fault features evolve as a fault progresses is key to fault severity assessment. Due to the complicated nature of gear meshing, fault features and their development as the fault severity progresses remain mostly unknown. The assessment of fault severity is generally based on the hypothesis that ‘the more severe the fault, the stronger the fault symptom’, an assumption that has not been experimentally validated. This paper provides a comprehensive, experimental analysis of the evolution of fault vibration features of a gear transmission with progressive localized gear tooth spalling. The effects of rotational speed on the vibration features of the gear transmission are analysed. Changes in fault features (e.g. periodic impulses and sideband phenomena) under different fault severity levels and speed conditions are compared. Results indicate that the number, amplitude and distribution of sidebands increase nonlinearly as the fault progresses. Based on feature analysis, a new health indicator of the mean of the nth order peaks is proposed to detect progressive localized tooth spalling. Results indicate that the proposed indicator shows very good performance for tracking the severity of progressive tooth spalling under different speed conditions.

Weak fault diagnosis of machinery using Laplacian eigenmaps and parallel sparse filtering

Machinery fault diagnosis is crucial for maintenance cost reduction and accident prevention. Vibration signal monitoring is an effective and feasible method for machinery fault diagnosis. However, extraction of the fault-related periodic impulses from weakly monitoring signals is basic but difficul . In this paper, a new weak feature extraction model using Laplacian eigenmaps and parallel sparse filtering (LE-PSF) is presented for mechanical weak fault diagnosis. Specifically, the weak vibration signal is measured from the machinery pedestal. Then, LE is used to extract principal components of the overlapped signal segments, and PSF is employed for weak feature extraction from the principal components. Finally, the extracted features are inputted to softmax regression for fault classification. A simulation study and two experimental cases are employed to testify the effect of the LE-PSF model. Experimental performances show that the LE-PSF can not only achieve accurate fault classification but also is superior to other traditional methods.

Maximum average impulse energy ratio deconvolution and its application for periodic fault impulses enhancement of rolling bearing

Periodic fault impulses, inevitably occurring along with a localized defect, are crucial for incipient fault diagnosis of rotating machinery. Whereas, they are awfully weak and masked by other interferences in industrial applications. Blind deconvolution methods (BDMs) are diffusely used in enhancing periodic fault impulses submerged in vibration signals. Due to some drawbacks, the applications of traditional BDMs are restricted. Therefore, the maximum average impulse energy ratio deconvolution (MAIERD) method is proposed, where the maximization of a new index called average impulse energy ratio (AIER) is tailored as the objective function. AIER takes the sampling point with the largest amplitude in every fault period as the location of fault impulse. Also, the fault period is detected by the autocorrelation function of the envelope signal. Furthermore, the Morlet wavelet is appointed as the initial filter. The synthesized signals and experimental data collected from two different rolling bearing test rigs are processed for verification. The results show that the proposed MAIERD method is superior in enhancing periodic fault impulses compared with five popular deconvolution methods.