Hilbert Envelope Analysis Research Articles

Intelligent Diagnosis of Bearing Failures Based on Recurrence Quantification and Energy Difference

Bearing health is key for maintaining good performance and safety in rotating machinery. As the diagnosis of mechanical faults develops toward intelligence and automation, accurate and systematic fault diagnosis algorithms are imperative. Focusing on the diagnosis of rolling bearing failures, this study utilizes a sliding time window to extract essential data segments. A series of signal processing techniques, including filtering, amplitude–frequency analysis, Hilbert envelope analysis, and energy analysis, is applied to establish a comprehensive dataset. For extraction of the hidden properties of the data, the recurrence quantity spectrum is defined for the input of the neural network. The goal is to obtain a cleaner dataset with enhanced features. A convolution neural network is constructed. Different activation functions in the activation layer are compared for better fault diagnosis algorithms. The established feature matrices are specifically defined to accurately identify the subtlest defects of bearings, thereby facilitating early detection. The proposed procedure distinguishes various fault modes. As for the multidimensional complexities of fault signals, this study carries out a comprehensive comparison of energies, recurrence quantification, and amplitude–frequency characteristics of bearing fault detection to assess the accuracy, computational efficiency, and robustness of bearing fault diagnosis. The proposed method and bearing fault detection procedures have potential in practical applications.

Early rolling bearing fault diagnosis in induction motors based on on-rotor sensing vibrations

The traditional on-house sensing (OHS) accelerometer for vibration measurements causes poor signal-to-noise ratio (SNR) and complicated fault modulations, which increases the difficulty and complexity for early bearing fault diagnosis. To overcome these challenges, this paper develops a wireless triaxial on-rotor sensing (ORS) system to largely improve the SNR and deduces fast Fourier transform (FFT) and Hilbert envelope analysis for accurate early rolling bearing fault diagnosis, which largely improves accuracy and efficiency for early fault diagnosis. First, the development of the ORS system for wireless vibration measurements is given. Second, the theoretical diagnostic relationships between dynamic ORS signals and rolling bearing faults are derived for FFT and Hilbert envelope analysis for the first time. Finally, the induction motor tests with outer and inner race faults successfully validate that both simple FFT and Hilbert envelope analysis can achieve more robust early rolling bearing fault diagnosis compared to OHS measurements.

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.

FEM simulation determined band-pass filter with Kurtosis optimized bandwidth to detect faults

Currently, a new method using finite element method (FEM) simulation definite band pass filter was developed to detect defects in axial piston pump bearings with agreeable performance. However, the bandwidth of the band-pass filter is not well addressed. As a signal processing technique, Kurtosis has achieved great success to extract fault features in mechanical systems. In this paper, Kurtosis is employed in optimizing the bandwidth of the constructed band pass filter. Firstly, FEM is utilized to obtain the first bending frequency of bearings with faults. Secondly, the band-pass filter is designed by using the first bending frequency to determine the center frequency and further search for optimal bandwidth using kurtosis. Finally, Hilbert envelope analysis is performed in order to filtered signal to extract faults. Experiment and comparison results of a faulty bearing in an axial piston pump show that the present improvement version of the FEM improved band-pass filter can be applied to extract fault features for the reciprocating motion systems with heavy impact-induced natural periodic impulses.

Diagnosis of multiple faults of an induction motor based on Hilbert envelope analysis

Diagnosis of multiple faults of an induction motor based on Hilbert envelope analysis

Compound fault diagnosis of rolling bearings based on improved tunable Q-factor wavelet transform

In order to solve the difficulty of compound fault diagnosis of rolling bearings, a novel rolling bearings fault diagnosis method based on improved tunable Q-factor wavelet transform (TQWT) is proposed in this paper. Firstly, a new evaluation index of signal decomposition called KR is defined by summing kurtosis and root mean square (RMS) with weight. KR is the compromise between impulse factor and energy factor, which can better represent the fault characteristics of sub-bands obtained by TQWT. Secondly, the KR is used to improve the TQWT. The improved TQWT can adaptively determine the parameters Q-factor and decomposition level. Thirdly, the bearing vibration signal is decomposed by the improved TQWT and the sub-bands are sorted descending according to the KR. Finally, the Hilbert envelope analysis is carried out and the fault types are determined by comparing the fault characteristic frequencies obtained from the Hilbert envelopes to the fault characteristic frequencies calculated by formula. The proposed fault diagnosis method is fully evaluated by simulation and experiments. The results demonstrate that the KR takes advantage of kurtosis and RMS and can be better used to optimize the parameter of TQWT. And the compound fault features of rolling bearings can be accurately separated into different sub-bands by the improved TQWT, which is helpful to improve the accuracy of compound fault diagnosis of rolling bearings.

A Novel Parameter-Adaptive VMD Method Based on Grey Wolf Optimization with Minimum Average Mutual Information for Incipient Fault Detection

Recently, variational mode decomposition (VMD) has attracted wide attention on mechanical vibration signal analysis. However, there are still some dilemmas in the application of VMD, such as the determination of the number of mode decomposition K and quadratic penalty term α. In order to acquire appropriate parameters of VMD, an improved parameter-adaptive VMD method based on grey wolf optimizer (GWO) is developed by taking the minimum average mutual information into consideration (GWOMI). Firstly, the parameters (K, α) are adaptively determined through GWOMI. Then, the vibration signal is decomposed by the developed method and effective modes are extracted according to the maximum kurtosis. Finally, the extracted modes are processed by Hilbert envelope analysis to acquire the incipient fault features. With the simulation and experimental analysis, it is clearly found that the developed method is effective and performs better than some existing ones.

Detection of broken rotor bars of induction motors based on the combination of Hilbert envelope analysis and Shannon entropy

Abstract Broken rotor bar (BRB) is one of the most common fault types of induction motors. One of the common methods to detect the broken rotor bars is the observation of the characteristic sideband frequencies in the stator current. If the motor is lightly loaded, the sideband harmonics are attached to the fundamental frequency of the main supply and the amplitudes of these harmonics are quite low. Therefore, it is difficult to detect the broken rotor bars under light loading conditions by using conventional motor current signature analysis (MCSA) methods. Moreover, in some cases, the sideband harmonics of fundamental frequency may exist although there is no rotor fault in induction motors due to load oscillations. Therefore, there is a risk for false broken rotor bars alarm with the existence of lower amplitude of harmonics. This paper provides an alternative approach for the detection of broken rotor bars by applying Hilbert envelope analysis along with Shannon entropy to stator current signals. The proposed method includes two-stage evaluation system to eliminate false BRB alarms such as detecting sidebands from envelope spectrum and calculating entropy rates from envelope signals. The results are verified experimentally under 25 %, 50 %, 75 % and 100 % loading conditions.

Casing vibration signal characteristic extractions and applications in rolling bearing

A method of combining autocorrelation function with cyclostationary theory and Hilbert envelope analysis is proposed and applied to extract characteristic frequency of rolling bearing. Meanwhile, mean power ratio is calculated and used to identify the fault types of aero-engine rolling bearing based on single-channel casing vibration signal. To verify the effectiveness of proposed method, a comparing analysis is carried out between traditional studies and proposed new method. Furthermore, the influences on the extraction of characteristics and calculation of mean power ratio are taken into account, including the ones of sensor installation position, fault types, type of experiment rigs, failure mode and rotational speed of rolling bearing. The result shows that the proposed method can diagnose running conditions and identify fault types of rolling bearing accurately and effectively just by single-channel casing vibration signal.

Fault diagnosis method of rolling bearing based on EMD-Hilbert envelope spectrum and BPNN

Rolling bearings are an important component of rotating machinery, and accurate diagnosis of their faults is also very important. This paper proposes a rolling bearing fault diagnosis method combining empirical mode decomposition (EMD)-Hilbert envelope spectrum analysis and BP neural network (BPNN). First, EMD is used to decompose the intrinsic modal function (IMF) component containing the bearing fault feature information from the original vibration signal data of the rolling bearing, and then the IMF component is processed in combination with the Hilbert envelope analysis method to obtain a clear fault feature frequency. The processed fault characteristic frequency is subjected to dimensionality reduction by principal component analysis (PCA) to propose redundant data. Finally, the dimensionality-reduced feature data is input into B PNN to establish a fault diagnosis model. The results show that the rolling bearing fault diagnosis method based on EMD-Hilbert envelope spectrum analysis and BPNN can effectively identify different fault states of rolling bearings.

Autoregressive model‐enhanced variational mode decomposition for mechanical fault detection

Mechanical fault detection is an important research direction attracted a great attention. Variational mode decomposition (VMD) has been widely used due to the ability to generate in highly localised time-frequency (TF) representation. However, the method usually fails to analyse the non-stationary signal with the unknown low-frequency interferences. Combined with autoregressive (AR) model technique, an enhancement version of VMD method is proposed. First, VMD is employed to decompose the raw non-stationary vibration signal into a set of intrinsic mode functions (IMFs), which contain the faulty information, and the interference of high-frequency noises can be almost eliminated. Second, AR model is introduced to further purify each IMF through decreasing the interferences of unknown low-frequency components. Finally, Hilbert envelope analysis is applied to demodulate the purified signal and the fault can be determined by comparing the demodulation frequency with the theoretical faulty feature frequency. Numerical simulations and experimental investigations are conducted to validate the performance of the proposed method. The comparisons with two combinations, AR model and empirical mode decomposition (EMD), AR model and local mean decomposition (LMD) are given, and the comparative results verify the proposed method is superior to other methods for mechanical fault detection.

A novel method of weakness imbalance fault identification and application in aero-hydraulic pump

A method of combining auto-correlation and Hilbert envelope analysis is proposed and used to identify weakness imbalance fault of aero-hydraulic pump, the central part of hydraulic system of aircraft. Firstly, the integral and polynomial least square fitting is applied to convert acceleration signal to velocity one; secondly, the Hilbert envelope spectrum of auto-correlation function of velocity signal is obtained and used to identify the weakness imbalance fault of aero-hydraulic pump; finally, the energy ratio of velocity signal is calculated according to Hilbert envelope spectrum for identifying imbalance fault of aero-hydraulic pump by means of easier and more visual method. Meanwhile, the comparing analysis is carried out between traditional research method and proposed new one. The result shows that the weakness imbalance fault of aero-hydraulic pump can be identified and diagnosed effectively and correctly according to the velocity signal whether Hilbert envelope spectrum or calculation energy ratio while direct acceleration signal cannot.

Kernel regression residual signal-based improved intrinsic time-scale decomposition for mechanical fault detection

Correct identification of the faults in mechanical components is the key to monitoring health conditions of machines. However, the interference of low-frequency signals and environmental noises greatly restricts the performance of traditional fault detection methods. Considering that the signals of interest (SOI) are usually carried by high-frequency signals and the interference of low-frequency signals, a novel preprocessing technique called one-level kernel regression residual decomposition (KRRD) is presented. Combined with the improved intrinsic time-scale decomposition (IITD) and Hilbert envelope analysis technique, a novel mechanical fault detection method is proposed. The method combines KRRD to extract the high-frequency signals from the raw vibration signals to track the faulty information, IITD to further extract the SOI from the high-frequency signals by removing the noises, and Hilbert envelope analysis to demodulate the denoised signals to detect faults in the rolling element bearings and gears. In order to verify the performance of the proposed method, the simulated data and real experimental data collected from faulty bearings and gears are analyzed. Three commonly used methods, namely empirical mode decomposition (EMD), local mean decomposition (LMD) and variational mode decomposition (VMD) are introduced and comparisons with the three combinations (KRRD and EMD, KRRD and LMD, KRRD and VMD) are given. The analysis results indicate that the proposed method is superior to other methods for detecting faults in mechanical components.

Kernel regression residual decomposition-based synchroextracting transform to detect faults in mechanical systems

The raw vibration signal of a faulty mechanical component carries a large amount of information reflecting its health condition, and the faulty information is typically carried by the high-frequency term in the vibration signal. However, the high-frequency term can easily by overwhelmed by the interference from the low-frequency term and noise. Considering the elimination of interference of the low-frequency term a novel preprocessing technique is presented, one-level kernel regression residual decomposition (KRRD), which can be used to extract the high-frequency term from the raw vibration signal to track the fault information. Combined with the synchroextracting transform (SET) technique, a one-level KRRD-based SET method is proposed. First, the high-frequency term in the raw vibration signal, which contains the faulty information, is extracted using one-level KRRD. Then, the high-frequency term is purified using SET, and the signal-to-noise ratio (SNR) is increased. Finally, a Hilbert envelope analysis is applied to the purified signal to demodulate the faulty feature frequency. To validate the performance and necessity of the proposed method, numerical simulations and experimental investigations are conducted. By introducing two commonly used methods, i.e., empirical mode decomposition (EMD) and variational mode decomposition (VMD), four comparisons (KRRD & EMD, KRRD & VMD, EMD, VMD) are conducted, and the superiority of the proposed method is verified. The analysis results show the effectiveness of the one-level KRRD-based SET method for the detection of mechanical component faults

An Improved VMD With Empirical Mode Decomposition and Its Application in Incipient Fault Detection of Rolling Bearing

Transient impulse analysis is an effective way to detect the bearing fault at its early stage. However, it is hard to precisely extract these so-called transient impulses because these collected vibration signals usually are non-stationary, nonlinear, and drowned by heavy background noise. Variational mode decomposition (VMD) can play the role as an adaptive signal processing tool to reveal the weak transient impulses from complex vibration signals. However, its reasonable mode number is difficult to pre-set and this would make the loss of useful transient impulses. To solve this issue, an improved VMD strategy is presented in this paper. For this method, it can not only utilize the advantages of traditional VMD and empirical mode decomposition (EMD) but also adaptively select sensitive intrinsic mode function (IMF) components for fault component analysis by proposed indexed values. EMD is first used to process the collected vibration signal into a series of IMFs, and the so-called useful IMFs are then evaluated by a sensitive IMF evaluation index which is based on the conjoint analysis of relatedness and kurtosis. Afterward, VMD is further improved to effectively decompose the denoised signal reconstructed from these selected useful IMFs of traditional EMD. Finally, the improved VMD is used for incipient fault diagnosis by a defined transient impulse monitoring index and Hilbert envelope analysis. Experiments are performed to demonstrate the effectiveness of the proposed method. The experimental results confirm that the proposed method can accurately extract the features of an incipient fault of a bearing.

Multiple Feature Vectors Based Fault Classification for WSN Integrated Bearing of Rolling Mill

For rolling mill machines, the operation status of bearing has a close relationship with process safety and production effectiveness. Therefore, reliable fault diagnosis and classification are indispensable. Traditional methods always characterize fault feature using a single fault vector, which may fail to reveal whole fault influences caused by complex process disturbances. Besides, it may also lead to poor fault classification accuracy. To solve the above-mentioned problems, a fault extraction method is put forward to extract multiple feature vectors and then a classification model is developed. First, to collect sufficient data, a data acquisition system based on wireless sensor network is constructed to replace the traditional wired system which may bring dangers during production. Second, the measured signal is filtered by a morphological average filtering algorithm to remove process noise and then the empirical mode decomposition method is applied to extract the intrinsic mode function (IMF) which contains the fault information. On the basis of the IMFs, a time domain index (energy) and a frequency index (singular values) are proposed through Hilbert envelope analysis. From the above analysis, the energy index and the singular value matrix are used for fault classification modeling based on the enhanced extreme learning machine (ELM), which is optimized by the bat algorithm to adjust the input weights and threshold of hidden layer node. In comparison with the fault classification methods based on SVM and ELM, the experimental results show that the proposed method has higher classification accuracy and better generalization ability.

Fault detection of a wheelset bearing in a high-speed train using the shock-response convolutional sparse-coding technique

The wheelset bearing is an essential mechanical component of a high-speed train, and its fault detection is of great importance for ensuring the safety of high-speed train service. However, the strong nonlinear and non-stationary modulation characteristics of the impulses induced by bearing faults, noises and interferences make fault detection of the wheelset bearing difficult and complex. The impulses induced by bearing faults have convolutional sparse characteristics, and can be described as the convolution of shock responses and time location coefficients. This paper presents a new fault detection method based on the shock-response convolutional sparse-coding technique (SRCSCT) to resolve the two inverse problems related to convolution characteristics. One of the problems is that shock responses are learned directly from vibration signals via the shift-invariant dictionary learning (SIDL) of SRCSCT; the other is that the time location coefficients are inferred from vibration signals via shift-invariant sparse coding (SISC) of SRCSCT. Shock responses can reflect the high-level structures of impulses embedded in vibration signals. Time location coefficients can be used to determine the time of impulse occurrence. The convolutions of learned shock responses and inferred corresponding time location coefficients are used to extract impulses submerged in vibration signals and are convenient for post-processing methods, such as Hilbert envelope analysis. Both the simulated signals and real vibration signals collected from a wheelset bearing test bench are used to verify the proposed method. The results show that SRCSCT not only effectively detects faults of the wheelset bearing but also accurately characterizes the fault dynamic behaviours of the bearing defects.

Detection of the broken rotor bars of squirrel-cage induction motors based on normalized least mean square filter and Hilbert envelope analysis

This paper presents a combination of normalized least mean square (NLMS) filter and Hilbert envelope analysis method to detect the broken rotor bars of a squirrel-cage induction motor. Broken rotor bars are one of the most common fault types that may be seen in induction motors. Rotor faults are reflected in the stator current of the motor as side-band harmonics. Most of the previous works utilize motor current signature analysis using spectral methods to determine required features for detecting motor faults. It may be difficult to detect the faults from stator current when the motor is lightly loaded under noisy conditions. In this study, Hilbert envelope analysis method is used along with an NLMS filter to process the stator current of an induction motor to detect the broken rotor bars. The proposed method is verified experimentally (under 25, 50, and 100 % loading conditions). The results of the recommended method are compared with the results of Fast Fourier Transform (FFT) analysis performed on the stator current of the same motor under the same conditions. The results show that the recommended method gives a more accurate solution compared with the results of FFT method.

EMD Based on Independent Component Analysis and Its Application in Machinery Fault Diagnosis

Local rub-impact is the common fault in rotating machinery and results in impact and friction between rotor and stator. The vibration signal due to impact and friction is always non-stationary which includes three components, namely, the rub-impact signal, the background signal and the noise signal. EMD (Empirical mode decomposition) is based upon the local characteristic time scale of signal and could decompose the complicated signal into a number of IMFs (intrinsic mode functions). However, because the weak rub-impact signal is always submerged in the background signal and noise signal. The EMD procedure will generate the components redundancy. In order to solve the problem, a novel method combining with independent component analysis (ICA) and EMD is proposed. ICA is introduced into the EMD procedure, so that the components are orthogonal to each other and the components redundancy can be cut down. In the end, a much better decomposition performances can be obtained. Furthermore, integration of EMD with Hilbert envelope analysis is applied to component instantaneous amplitude in order to obtain envelope spectra from which the mechanical fault can be diagnosed. The analysis results from the rub-impact vibration signals show that the proposed method can be applied to the machinery fault diagnosis effectively.