Envelope Spectrum Analysis Research Articles

Development of a diagnostic and prognostic tool for predictive maintenance in the railcar industry

Abstract The use of a diagnostic and prognostic tool for predictive maintenance serves as a continuous inspection, detective and predictive tool for making important decisions on maintenance activities before failure occurs. The prediction of failure is important in the railway industry in reducing the maintenance and operating cost, minimizing interruptions, risk, unscheduled maintenance and accidents while enhancing higher productivity and component lifespan. In this study, a diagnostic and prognostic tool was developed to constantly monitor and predict the rate of degradation and Remaining Useful Life (RUL) of a railcar wheel bearing. The tool uses the envelope spectrum and kurtosis analysis, which employs the wheel acceleration data obtained from a primary source and the data was interpreted with the aid of statistical and computational methods. The input data was first pre-processed and important features are extracted in a MATLAB 2018b environment. The extracted features were thereafter integrated into the diagnostic and prognostic tool with a pre-set threshold value or feature for the wheel acceleration for predictive purpose. The results obtained indicate the suitability of the diagnosis and prognostic tool for the determination of the railcar wheel condition, prediction of the Mean Time to Failure (MTTF), as well as the remaining useful life of the railcar bearing.

A Fault Detection Approach Using Variational Mode Decomposition, L-kurtosis and Random Decrement Technique for Rotating Machinery

Fault detection of rotating machinery under heavy noise background, is a significant but difficult issue, and traditional fault detection approaches are difficult to apply. To address this problem, a novel approach that combines variational mode decomposition (VMD), L-Kurtosis and random decrement technique (RDT) is proposed, which procedures are summarized as follows. First, the raw vibration signal collected from the rotating component is decomposed using VMD into a set of intrinsic mode functions (IMFs), and the noise components can be separated from the raw signal. Second, the L-Kurtosis indicator is introduced to solve the problem that the fault information is difficult to track, and the optimal intrinsic mode function (IMF) can be determined according to the maximum L-Kurtosis value. Then, RDT is further employed to purify the optimal IMF to eliminate the other unknown interference sources. Finally, a Hilbert envelope spectrum analysis is used for detecting the fault type. In order to validate the proposed approach, the numerical simulations and real experimental investigations about rolling element bearing and gear are conducted. The results illustrate that the proposed approach can effectively detect faults of rotating components.

An Improved Empirical Mode Decomposition Based on Adaptive Weighted Rational Quartic Spline for Rolling Bearing Fault Diagnosis

As a powerful time-frequency signal analysis technique, empirical mode decomposition (EMD) has been commonly applied in fault diagnosis. However, the cubic spline-curve often causes outstanding over and undershoot problem, which significantly limits the performance of conventional EMD. To address this problem, an improved EMD (I-EMD) based on adaptive weighted rational quartic spline is proposed. Firstly, the original cubic spline interpolation in conventional EMD is replaced with the weighted rational quartic spline interpolation (WRQSI) which has two adjustable shape control parameters. Secondly, a novel parameter selection criterion termed envelope characteristic frequency ratio (ECFR) is designed to guide the construction of the optimal local envelope. And simulation analysis proved that ECFR is not only sensitive to the characteristic information but also robust to the weak noise and sudden impulses. Subsequently, the optimal shape control parameter can be searched by grasshopper optimization algorithm (GOA) using the maximum ECFR as the objective function. Then the sensitive modes selected via weighted Kurtosis index are employed for further Hilbert envelope spectrum analysis. Finally, two case studies on rolling bearing fault diagnosis are constructed to verify the rationality and effectiveness of the I-EMD method. The results show that I-EMD method can evidently solve the over and undershoot problem and restrain the mode mixing phenomenon. Moreover, I-EMD also performs better fault feature extraction ability under the same conditions compared with EMD, VMD and CEEMDAN. So it is expected that I-EMD will serve as a potential improvement for signal processing, fault feature extraction and fault diagnosis.

Research on fault feature extraction method of rolling bearing based on improved wavelet threshold and CEEMD

Because bearing fault feature information is not easy to extract in noisy background, this paper proposes an improved rolling bearing fault feature extraction method based on combination of wavelet threshold and complementary ensemble empirical mode decomposition (CEEMD). Firstly, the improved wavelet threshold denoising method is used to reduce the noise of the vibration signal, and the impact characteristics in the signal are enhanced. Then, the CEEMD decomposition is used to obtain a set of Intrinsic Modal Functions (IMFs), and IMFs with larger kurtosis and correlation coefficients are selected for signal reconstruction. At last, the envelope spectrum analysis of reconstructed signal is carried out to extract fault characteristic information. Through the experimental analysis of the vibration signals of the outer ring and inner ring of the rolling bearing, it is proved that this method can effectively extract the fault characteristics of the bearing.

A novel weak fault signal detection approach for a rolling bearing using variational mode decomposition and phase space parallel factor analysis

Considering the difficulty of fault feature extraction from a rolling bearing under strong background noise, we present a novel approach based on variational mode decomposition (VMD) and phase space parallel factor analysis, for detecting the weak fault signal of a rolling bearing. In this scheme, the VMD method is first adopted to decompose the raw vibration signal into several intrinsic mode components. The selected intrinsic mode function component with maximal kurtosis is subsequently embedded into the high dimensional phase space by phase space reconstruction. Then, the independent components are estimated in the high dimensional phase space by parallel factor analysis. In addition, a new criterion combining kurtosis and feature energy factor (FEF) is proposed for the selection of the time delay and embedding dimension. Finally, the optimal independent component with the largest FEF is selected for envelope spectrum analysis, and the faint fault characteristic frequencies of the vibration signal can be extracted. The feasibility of the proposed scheme is demonstrated through simulation and experimental vibration signals. Results indicate that the proposed method has better capability in detecting a weak fault signal of a rolling bearing, compared with VMD-fast spectral kurtogram and phase space independent component analysis.

A weak fault feature extraction of rolling element bearing based on attenuated cosine dictionaries and sparse feature sign search

The time domain signal of bearing pitting/spalling fault always presents shock and modulation, and it is often submerged by strong noises, especially in the early stage. the conventional fault feature extraction method may have insufficient feature extraction accuracy, and even in some extreme cases, the fault feature frequency cannot be extracted because of the strong noise interference. Aiming at overcoming the noise interference problem encountered in this kind of weak fault feature extraction, a novel weak fault feature extraction algorithm termed as ACFSS of rolling bearing is proposed. The ACFSS is based on an overcomplete dictionary (or overcomplete atomic library) of Attenuated Cosines(AC) basis, which is highly matched to the bearing fault waveforms, and an improved Basis Pursuit algorithm with Feature Sign Search(FSS) is introduced into the ACFSS to improve the calculating speed. In order to select the suitable parameters of the attenuated cosine dictionary, some methods such as peak resonance frequency (PRF), power variation peak (PVK), time shift parameter (TSP), etc. are introduced. These parameters span the sparse overcomplete dictionary. Finally, the bearing fault data of Case-Western University and full life accelerated IMS bearing data are utilized to verify the validation of ACFSS. Compared with the ordinary envelope spectrum analysis(ESA) method /the ordinary Basis Pursuit Denoising(BPDN) method/ Wavelet package transform(WPT) Kurtogram method and Empirical Mode Decomposition(EMD) combining Singular Value Decomposition(SVD) method, The experiment show that the proposed method are more redundant and robust when facing strong noise interference, and it can be used to extract the weak fault feature frequency efficiently and accurately.

Motor Speed Signature Analysis for Local Bearing Fault Detection With Noise Cancellation Based on Improved Drive Algorithm

Motor speed signature analysis provides a noninvasive method for bearing fault detection. However, for the vector-controlled ac motors, periodic speed ripples related to fundamental frequency fe and its twice harmonic 2fe, which are caused by current measurement errors, are difficult to be attenuated by motor inertia or bandwidth of speed loop under low-speed conditions. The unwanted components would reduce the signal-to-noise ratio of motor speed and increase the difficulty of bearing fault detection. To solve the problem, this paper proposes a new noise cancellation strategy, which applies the improved drive algorithm instead of conventional signal processing schemes to cancel out the noise component before the data acquisition. Specifically, resonance controllers are introduced and set in parallel with the existed proportional-integral controller to suppress the speed ripples. Moreover, the envelope spectrum analysis is carried out to detect fault characteristic. The effectiveness of the proposed method is validated through simulation and experimental tests. Besides, its superiority under low-speed conditions is also demonstrated, compared with the spectral kurtosis of speed signal and three current-based methods.

A mechanical fault detection strategy based on the doubly iterative empirical mode decomposition

Empirical mode decomposition (EMD) has been widely used in the fault detection of rotating machineries. However, the deviation of the local extrema can decline the decomposition performance of the conventional EMD. This paper proposes a fault detection strategy based on the doubly iterative empirical mode decomposition (DIEMD), where the local extrema are fixed during the sifting process. This strategy combines the DIEMD to obtain decomposed intrinsic mode functions (IMFs), correlation analysis to select the representative IMF and envelope spectrum analysis to extract the fault feature frequency. The decomposition performance of the DIEMD was validated through the dual signal analysis. A numerical simulation and experimental investigations on four fault cases (the bearing with the inner race and outer race fault, the gear with broken teeth and the piston pump with cylinder block fault) of rotating machineries were carried out. The amplitude enhancement index (AEI) was defined as an indicator of the performance improvement. Results showed that the proposed strategy is applicable and effective for the fault detection of rotating machineries with AEI being 17.8%, 8.6%, 23.0%, 19.0% and 4.1%, respectively.

Separating Multiple Moving Sources by Microphone Array Signals for Wayside Acoustic Fault Diagnosis

Abstract Wayside acoustic defective bearing detector (ADBD) system is a potential technique in ensuring the safety of traveling vehicles. However, Doppler distortion and multiple moving sources aliasing in the acquired acoustic signals decrease the accuracy of defective bearing fault diagnosis. Currently, the method of constructing time-frequency (TF) masks for source separation was limited by an empirical threshold setting. To overcome this limitation, this study proposed a dynamic Doppler multisource separation model and constructed a time domain-separating matrix (TDSM) to realize multiple moving sources separation in the time domain. The TDSM was designed with two steps of (1) constructing separating curves and time domain remapping matrix (TDRM) and (2) remapping each element of separating curves to its corresponding time according to the TDRM. Both TDSM and TDRM were driven by geometrical and motion parameters, which would be estimated by Doppler feature matching pursuit (DFMP) algorithm. After gaining the source components from the observed signals, correlation operation was carried out to estimate source signals. Moreover, fault diagnosis could be carried out by envelope spectrum analysis. Compared with the method of constructing TF masks, the proposed strategy could avoid setting thresholds empirically. Finally, the effectiveness of the proposed technique was validated by simulation and experimental cases. Results indicated the potential of this method for improving the performance of the ADBD system.

Improving the Accuracy of Fault Frequency by Means of Local Mean Decomposition and Ratio Correction Method for Rolling Bearing Failure

The fault frequencies are as they are and cannot be improved. One can only improve its estimation quality. This paper proposes a fault diagnosis method by combining local mean decomposition (LMD) and the ratio correction method to process the short-time signals. Firstly, the vibration signal of rolling bearing is decomposed into a series of product functions (PFs) by LMD. The PF, which contains the richest fault information, is selected to perform envelope spectrum analysis by the Hilbert transform (HT). Secondly, the Hilbert envelope spectrum of the selected PF is corrected with the ratio correction method. Finally, higher precision fault frequencies are extracted from the corrected Hilbert envelope spectrum, and then the fault location is accurately determined. The proposed method of this paper can be used in online real-time monitoring technology of rolling bearing failure.

A Hybrid Method for Detection and Diagnosis of Faulty Roller Bearings

There are few research on bearing fault detection and diagnosis which combine constant speed with variable speed. In this paper, a hybrid method is proposed to realize the nondestructive testing and fault diagnosis of roller bearing faults. First, adopts computed order tracking (COT) and variational mode decomposition (VMD) based order spectrum method to detect bearing faults under variable speed condition. Then, by using the method of VMD-based envelope spectrum analysis, we analyze a certain speed signal which is consistent with the velocity in the condition of variable speed, and verify the analysis under the condition of variable speed. The experimental results show that the method can realize the effective diagnosis of the fault bearing.

Application of improved MCKD method based on QGA in planetary gear compound fault diagnosis

An improved maximum correlated kurtosis deconvolution (MCKD) method based on quantum genetic algorithm (QGA) named QGA-MCKD is proposed, which can be used for gear and bearing compound fault diagnosis. Two key parameters, filter length (L) and deconvolution period (T) of MCKD, corresponding to each single fault are adaptively selected by QGA. MCKD is set by the obtained key parameters to process the compound fault signal, and each single fault feature related to the single failed part can be extracted. QGA-MCKD was applied to process the simulated and experimental compound fault signals of planetary gear tooth breakage and bearing rolling element damage, and the gear and bearing fault signals were extracted, respectively. Then power spectrum analysis of gear fault signal and envelop spectrum analysis of bearing fault signal were carried out to diagnose the compound faults. The superiority of QGA-MCKD was verified in comparison with direct spectrum analysis and ensemble empirical mode decomposition (EEMD). The stability of QGA-MCKD was verified in the compound fault diagnosis of gear tooth wear and bearing outer race fault. Results show that QGA-MCKD has a good effectiveness in improving the accuracy of gearbox gear and bearing compound fault diagnosis.

Fault Diagnosis Accuracy Improvement Using Wayside Rectangular Microphone Array for Health Monitoring of Railway-Vehicle Wheel Bearing

Wayside acoustic detection is a promising technology for railway-vehicle bearing health monitoring due to its merits of non-conduct measurement, low cost, and early warning capacity. However, the diagnostic accuracy will be reduced by the problems of strong background noise and Doppler distortion. Considering the super spatial directivity ability of the microphone array, in this paper, a uniform rectangular array (URA) and an optimal spatial filter (OSF) based on the principle of minimum variance distortion-less response (MVDR) are designed to improve the diagnostic accuracy. Compared with the traditional single microphone and linear array, spatial directivity can be improved significantly so that the better anti-noise performance and higher diagnostic accuracy can be achieved. First, a URA consisting of 15 microphone elements arranged into five columns and three rows is designed to capture the wayside acoustic signal. Second, the direction angle of the target moving sound source with high accuracy is calculated at different times. Third, an OSF based on the principle of the MVDR is designed to extract the target sound source signal. Fourth, Doppler effect embedded in the filtered signal is eliminated using the MVDR spectrum estimation and resampling method. Finally, the diagnosis decision is made through an envelope spectrum analysis. The comparative simulation and experimental case studies are carried out to verify the effectiveness and improvement of the proposed method.

Early Fault Diagnosis for Planetary Gearbox Based on Adaptive Parameter Optimized VMD and Singular Kurtosis Difference Spectrum

Variational mode decomposition (VMD) is widely used in the condition monitoring and fault diagnosis of rotary machinery for its unique advantages. An adaptive parameter optimized VMD (APOVMD) is proposed in order to adaptively determine the suitable decomposed parameters and further enhance its performance. The traditional singular value decomposition (SVD) method cannot effectively select the reconstructed order, which often leads to unsatisfactory results for signal reconstruction. Thus, a singular kurtosis difference spectrum method is proposed to accurately determine the effective reconstructed order for signal noise reduction. In addition, because the fault signal of the planetary gearbox at the early fault stage is weak and susceptible to ambient noise and other signal interference, the fault feature information is difficult to extract. To address this issue, a novel method for early fault feature extraction of planetary gearbox based on APOVMD and singular kurtosis difference spectrum is proposed in this paper. First, the APOVMD is applied to decompose the planetary gearbox vibration signal into a series of band-limited intrinsic mode functions adaptively and non-recursively. Second, the sensitive component is selected from the IMFS according to the cosine similarity index. Third, the Hankel matrix is constructed for the sensitive component in the phase space and decomposed by SVD. Here, the effective reconstructed order is automatically selected by the singular kurtosis difference spectrum method for noise reduction. Finally, the Hilbert envelope spectrum analysis is carried out on the reconstructed signal, and the fault characteristic frequency information of planetary gearbox can be accurately extracted from the envelope spectrum to realize the fault identification and location. The results of simulation studies and actual experimental data analysis demonstrate that the proposed method has superior ability to extract the early weak fault characteristics of the planetary gearbox compared with the VMD-SVD and EEMD-SVD methods, and the validity and feasibility of the presented method are proved.

A Strategy Using Variational Mode Decomposition, L-Kurtosis and Minimum Entropy Deconvolution to Detect Mechanical Faults

When faults occur in mechanical components, the faulty information is usually manifested as a series of periodic impulses which correspond to the faulty feature frequencies. However, due to the non-stationary characteristic of the raw vibration signals, the faulty feature frequencies are difficult extracted. In this paper, a novel strategy using variational mode decomposition (VMD), L-Kurtosis and minimum entropy deconvolution (MED) is proposed to detect mechanical faults. First, VMD is employed to decompose the raw vibration signal into a set of intrinsic mode functions (IMFs) to eliminate the interference of the noise. Second, the optimal intrinsic mode function (IMF) which contains the faulty information is determined using L-Kurtosis. Then, the impact characteristic of the periodic impulses in optimal IMF is enhanced through MED. Finally, a Hilbert envelope spectrum analysis is performed to the enhanced signal to extract the faulty feature frequency. In order to illustrate the performance of the proposed strategy, the simulation signal and real experimental signals collected from faulty rolling element bearings and gears are analyzed. The results show that the strategy using the VMD, L-Kurtosis, and MED can detect mechanical component faults effectively.

Minimum entropy deconvolution based on simulation-determined band pass filter to detect faults in axial piston pump bearings

The fault diagnosis of axial piston pumps is of significance for enhancing the reliability and security of hydraulic systems. Most of the faults occurring in the mechanical components of piston pumps are exhibited as fault-excited impulses. However, the strong impact-induced natural periodic impulses under the common working conditions (i.e. reciprocating motion of pistons) inevitably cause interference that considerably affects the fault detection performance. In this study, a simulation-determined band pass filter is employed to improve the performance of minimum entropy deconvolution (MED) for the fault diagnosis of axial piston pump bearings. First, a finite element method (FEM) simulation is performed to determine the possible carrier frequency. Second, the carrier frequency is used as the center frequency in association with a fixed bandwidth to determine the band pass filter parameters. Finally, the MED technique is applied to enhance weak fault-excited impulses by means of kurtosis maximization. Thereafter, envelope spectrum analysis is applied to the enhanced signals to obtain faulty feature frequencies. Two case studies are conducted, using bearings with faults in the outer and inner races of an axial piston pumps under common working conditions. The case studies confirm the necessity and effectiveness of the proposed method for detecting bearings faults in axial piston pumps.

An experimental study on the fault diagnosis of wind turbines through a condition monitoring system

To detect wind turbine faults at an early stage, an investigation into a practical maintenance and repair approach was carried out on Jeju Island, South Korea. A condition monitoring system was installed in each wind turbine nacelle to detect the vibration signals from the gearbox and the generator. The vibration signals were measured by strain gauges on the gearbox and the generator for a period of approximately one to two years. A time domain analysis to detect the components’ faults was performed, and a frequency domain analysis was conducted to find the location of the faults that occurred. Using the criteria of acceptance level for the root mean square suggested in Verein Deutscher Ingenieure standard 3834, it was determined whether or not the gearbox and the generator were operated normally. After a fault was detected by root mean square analysis, the fast fourier transform spectrum was analyzed and then compared with that suggested by the International Organization for Standardization standard 10816–21 and 13373–1. Repair work was then conducted on the defective parts of the components. The root mean square and the acceleration value of the normal, the warning and the abnormal conditions were compared with one another. As a result, cavitation might occur in the gear oil pump attached to the gearbox due to the high acceleration values observed for frequencies ranging from 5000 Hz to 11000 Hz. Additionally, the generator bearing at the non drive end was found to be broken because the defect frequency of the bearing was 88 Hz, which was derived from envelope spectrum analysis. The root mean square and the acceleration values for the gearbox and the generator decreased to values indicating normal operating conditions after the damage repair. The annual energy production increased by 1.8 % after the generator bearing repair.

Early fault feature extraction of bearings based on Teager energy operator and optimal VMD

As the fault shock component in vibration signals is extremely sparse and weak, it is difficult to extract the fault features when large-scale, low-speed and heavy-duty mechanical equipment is in the early stage of failure. To solve this problem, an early fault feature extraction method based on the Teager energy operator, combined with optimal variational mode decomposition (VMD) is presented in this study. First, the Teager energy operator was used to strengthen the weak shock component of the original signal. Next, a logistic–sine complex chaotic mapping with variable dimensions was constructed to enhance the global search ability and convergence speed of the pigeon-inspired optimization (PIO) algorithm, which is named the variable dimension chaotic pigeon-inspired optimization (VDCPIO) algorithm. Then, the VDCPIO algorithm is used to search for the optimal combination value of key parameters of VMD. The enhanced vibration signal is decomposed into a set of intrinsic mode functions (IMFs) by the optimized VMD, and then kurtosis for every IMF and mean kurtosis of all IMFs are extracted. According to the average kurtosis, several IMFs, whose kurtosis value is greater than the average kurtosis value, are selected to reconstruct a new signal. Then, envelope spectrum analysis of the reconstructed signal is carried out to extract the early fault features. Finally, experimental verification of the method was performed using the simulated signal and measured signal from a rolling bearing; the experimental results indicate that the method presented in this paper is more effective to extract the early fault features of this kind of mechanical equipment.

Compound fault diagnosis of rotating machinery based on adaptive maximum correlated kurtosis deconvolution and customized multiwavelet transform

Although compound fault diagnosis of rotating machinery based on vibration signals is a prominent method, it is still a challenge due to coupled fault features immersed in strong background noise. An adaptive deconvolution and denoising technology based on adaptive maximum correlated kurtosis deconvolution and multiwavelet transform is studied here. In combination with Hilbert envelope spectrum analysis, a novel compound fault diagnosis method is proposed in this paper. Based on analysis using maximum correlated kurtosis deconvolution (MCKD) theory, a parameter range estimation method is given which is favorable for MCKD parameter optimization. Flexible standard multiwavelets are used in post-processing of MCKD to enhance the denoising effect further. The minimum of a compound faults characteristic index composed of M-shift correlated kurtosis and square envelope spectrum entropy is adopted as the optimization criterion to set reasonable parameters for MCKD and construct customized multiwavelets using particle swarm optimization. The effectiveness of the proposed method is demonstrated by both simulated signal and practical vibration signals of a rotor test rig and an aero engine rotor experimental rig with different compound faults. The superior effectiveness and reliability of the proposed method are confirmed by comparison with other fault detection methods.

A Wavelet-Based Statistical Approach for Monitoring and Diagnosis of Compound Faults With Application to Rolling Bearings

This paper proposes a wavelet-based statistical signal detection approach for monitoring and diagnosis of bearing compound faults at an early stage. The bearing vibration signal is decomposed by an orthonormal discrete wavelet transform to obtain its energy dispersions at multiple levels. We investigate the statistical properties of the decomposed signal energy under both the normal and faulty conditions, based on which a generalized likelihood ratio test is developed. An exponentially weighted moving average control chart is then constructed to detect faults at an early stage. Simulation studies and a real case study are conducted to demonstrate the effectiveness of the proposed method. Furthermore, the comparison studies show that the proposed method outperforms the empirical mode decomposition method and Hilbert envelope spectrum analysis method.