Sparse Signal Decomposition Research Articles

An extraction method for early fault features of rolling bearings based on resonance sparse signal decomposition and non-convex second-order total variation denoising

A primary challenge in the field of fault diagnosis is extracting weak fault characteristics of bearings under large background noise and non-stationary conditions. Due to significant noise interference in the signals of rolling bearings, resonance sparse signal decomposition (RSSD) cannot efficiently extract the transient impact components in the early failure stage and the total variation denoising (TVD) method distorts signal waveforms. In this study, a combined extraction method for early fault features of rolling bearings based on RSSD and non-convex second-order total variation denoising (NCSOTVD) is proposed. Firstly, a non-convex function is introduced to define the regularisation term in the second-order TVD method, and the regularisation parameter and the convexity parameter in the NCSOTVD method are respectively screened using the noise standard deviation and the permutation entropy value to enhance the impact characteristics of signals and induce signal sparsity. The NCSOTVD model is solved using the optimisation-minimisation algorithm, so as to achieve noise reduction and feature enhancement of the vibration signals. Then, the low-resonance components of RSSD are denoised using the NCSOTVD method to highlight periodic pulse signals and extract the fault features of the rolling bearings. The simulation results and experimental data show that the method largely suppresses the noise interference, highlights the fault characteristics and reduces the problems of waveform distortion and poor sparsity of the TVD method in the denoising process.

Research on a Fault Feature Extraction Method for an Electric Multiple Unit Axle-Box Bearing Based on a Resonance-Based Sparse Signal Decomposition and Variational Mode Decomposition Method Based on the Sparrow Search Algorithm.

In light of the issue that the vibration signal from an axle-box bearing collected during the operation of an electric multiple unit (EMU) is seriously polluted by background noise, which leads to difficulty in identifying fault characteristic frequency, this paper proposes a resonance-based sparse signal decomposition (RSSD) and variational mode decomposition (VMD) method based on sparrow search algorithm (SSA) optimization to extract the fault characteristic frequency of the bearing. Firstly, the RSSD method is utilized to decompose the signal based on the obtained optimal combination of quality factors, resulting in the optimal low-resonance component with periodic fault information. Then, the VMD method is performed on this low-resonance component. The parameter combinations for both methods are optimized utilizing the SSA method. Subsequently, envelope demodulation is applied to the intrinsic mode function (IMF) with maximum kurtosis, and fault diagnosis is achieved by comparing it with the theoretical fault characteristic frequency. Finally, experimental validation and comparison are conducted by utilizing simulated signals and example signals. The results demonstrate that the proposed method extracts more obvious periodic fault impact components. It effectively filters out the interference of complex noise and reduces the blindness of setting weights on parameters due to human experience, indicating excellent adaptability and robustness.

Detection of seeded fault and growing fault in rotating machinery under different speed scenarios using adaptive resonance-based signal sparse decomposition

Detection of seeded faults (SFs) in machinery elements such as gears and bearing has been widely explored, whereas there is limited research considering the growing fault (GF). The literature indexes separate techniques for diagnosing SFs and GFs, because of their nature. No technique yet reported is capable to detect both types of faults. This work proposes a novel adaptive approach and an uncertainty index (UI) to detect both SF and GF. In the proposed approach, the signal is pre-processed by adaptive resonance-based signal sparse decomposition to get low-resonance components (LRCs) and high-resonance components across different decomposition levels. Using the UI, the fault prone LRC is identified based on impulsiveness and complexity content. Afterwards the empirical mode decomposition (EMD) is applied to extract the intrinsic mode functions. The Fast Fourier Transform (FFT)s of the modes extracted from EMD reflected the characteristic frequencies and increased amplitude of sidebands. Lastly, the statistical analysis of the FFTs was performed using the sideband energy ratio to validate the state of faults. The proposed approach when examined for both SFs in gears and GFs in bearings at different conditions, yielded satisfactory results. The proposed approach performance was found to be at least 15% better for incipient fault detection and more than 50% for severe fault conditions.

Sparse reconstruction of ultrasonic guided wave signals of fluid-filled pipes by multistrategy hybrid DBO-OMP using dispersive Hanning-windowed chirplet model

Ultrasonic guided waves (UGWs) in fluid-filled pipes are subject to more severe dispersion and coherent noise than those of vacant pipes, posing significant challenges for defect identification and localization. To this end, a novel sparse signal decomposition method called multistrategy hybrid dung beetle optimization based orthogonal matching pursuit (MHDBO-OMP) using dispersive Hanning-windowed chirplet model was proposed, of which the model not only represents the nonlinear frequency and asymmetric envelope of the dispersive UGW, but also contains the mode and propagation distance information, and this model exhibits better matching and interpretability than the other UGW models. For dispersive perturbed UGW signals with multiple modes and features, MHDBO-OMP achieves high reconstruction accuracy in both signal reconstruction (RES < 0.3) and propagation distance estimation (RES < 3 cm). When applied to experimental UGW signals obtained from water/oil-filled pipes containing cracks and corrosion pits, MHDBO-OMP successfully reconstructs dispersion-compensated signals that solely contain feature signals, and the minimum location error is 0.72 cm while the average location error is 2.65 cm. © 2001 Elsevier Science. All rights reserved.

Point Rail of High-Speed Railway Turnout Induced Feature Extraction Using Oscillatory Behavior-Based Signal Sparse Decomposition

Point Rail of High-Speed Railway Turnout Induced Feature Extraction Using Oscillatory Behavior-Based Signal Sparse Decomposition

Reconstruction of Water-Filled Pipe Ultrasonic Guided Wave Signals in the Distance Domain by Orthogonal Matching Pursuit Based on Dispersion and Multi-Mode.

Ultrasonic guided waves (UGWs) in water-filled pipes are subject to more severe dispersion and attenuation than vacant pipes, posing significant challenges for defect identification and localization. To this end, a novel sparse signal decomposition method called orthogonal matching pursuit based on dispersion and multi-mode (DMOMP) was proposed, which utilizes the second-order asymptotic solution of dispersion curves and the conversion characteristics of asymmetric UGWs in the defect contact stage to reconstruct the dispersive signals and converts the time-domain dispersive signals to distance-domain non-dispersive signals by dispersion compensated time-distance mapping. The synthesized simulation results indicate that DMOMP not only exhibits higher reconstruction accuracy compared to OMP, but also reveals more accurate and stable mode recognition and localization compared to DOMP, which only considers the dispersion under perturbation and noise. In addition, the UGW testing experimental results of water-filled pipes verify the effectiveness of DMOMP, the localization accuracies of three feature signals (defct 1, defct 2 and end echo) with DMOMP are 99.10%, 98.72% and 98.36%, respectively, and the average localization accuracy of DMOMP is as high as 98.73%.

Research on gearbox compound fault diagnosis method and system development based on entire gearbox health maintenance

In general, gearbox is prone to occur compound fault due to its harsh working environment and its fault vibration signal contains multi-components which correspond to each gearbox parts. As the multi-components are often coupled with each other and accompanied by strong noise which brings great difficulties to diagnose fault, however, the existing diagnosis methods are mainly applied on single fault rather than the entire gearbox health maintenance, therefore, this paper presents a gearbox compound fault diagnosis method and develops a diagnosis system which has potential value for gearbox health maintenance. In specific, on account of the morphological difference between multi-components, this paper uses resonance sparse signal decomposition (RSSD) to decompose the fault vibration signal into high and low resonance components respectively for achieving gearbox compound fault separation. Furthermore, as for low resonance component containing rolling bearing fault information, a weak fault feature extraction algorithm based on singular value decomposition (SVD) and cepstrum pre-whitening stochastic resonance is proposed, besides, aiming at the high resonance component containing gear fault information, an early gear fault warning algorithm based on local mean decomposition and two-dimensional approximate entropy of chaotic oscillator is also given. Finally, a gearbox fault diagnosis system, which has the ability such as the gearbox vibration signal acquisition, fault indicator warning, health status evaluation, fault signal storage is developed. Simulation validation and comparison prove the effectiveness of proposed method in this paper.

Fault Diagnosis of Train Wheelset Bearing Roadside Acoustics Considering Sparse Operation with GA-RBF

Trackside acoustic signals are useful for non-contact measurements as well as early warnings in the diagnosis of train wheelset bearing faults. However, there are two important problems when using roadside acoustic signals to diagnose wheel-to-wheel bearing faults; one is the presence of strong interference from strong noise and high harmonics in the signal, and the other is the low efficiency of bearing fault identification caused by it. Therefore, from the viewpoint of solving the two problems, a sparse operation method is proposed for denoising and detuning the modulation of the roadside acoustic signal, and a machine learning classifier with a Genetic Algorithm (GA)-optimized Radial Basis Neural Network (RBFNN) is proposed to improve the rate at which the features of roadside acoustic signal faults are recognized. Firstly, the background noise is filtered out from the Doppler-corrected acoustic signal using the Sparse Representation method, and the inverse wavelet transform is reconstructed into a noiseless signal. Secondly, the interference high-harmonic signal in the signal is filtered out using the Resonant Sparse Signal Decomposition (RSSD) method. Then, the GA is selected to optimize the parameters of the RBF neural network and build a fault diagnosis model. Finally, the extracted acoustic signal feature set is trained on the network model, and the trained model is used for testing. In summary, the sparse operation on the roadside acoustic signal processing and the GA-RBFNN diagnosis model were verified as being very effective in the diagnosis of roadside acoustic train wheel pair faults through the simulation experiment.

Fast and accurate T2 mapping using Bloch simulations and low-rank plus sparse matrix decomposition

PurposeMRI's T2 relaxation time is one of the key contrast mechanisms for clinical diagnosis and prognosis of pathologies. Mapping this relaxation time, however, involves extensive scan times, which are needed to collect quantitative data, thereby impeding its integration into clinical routine. This study employs a low-rank plus sparse (L + S) signal decomposition approach in order to reconstruct accurate T2-maps from highly undersampled multi-echo spin-echo (MESE) MRI data. MethodsTwo new algorithms are presented: the first uses standard L + S approach, where both L and S are iteratively updated. The second technique, dubbed SPArse and fixed RanK (SPARK), uses a fixed-rank L, under the assumption that most MESE information is found in the L component and that this rank can be pre-calculated. The utility of these new techniques is demonstrated on in vivo brain and calf data at x2 to x6 acceleration factors. ResultsAccelerated T2 maps showed improved accuracy compared to fully sampled ground truth maps, when using L + S and SPARK techniques vis-à-vis standard GRAPPA acceleration. ConclusionSPARK provides accurate T2 maps with increased robustness to the selection of reconstruction parameters making it suitable to a wide range of applications and facilitating the use of quantitative T2 information in clinical settings.

Harmonic Elimination and Magnetic Resonance Sounding Signal Extraction Based on Matching Pursuit Algorithm

Magnetic resonance sounding (MRS) is a non-invasive, direct, and quantitative geophysical method for detecting groundwater, and has been widely used in groundwater survey, water resource assessment, and disaster water source forecasting. However, the MRS signal is weak (nV level) and highly susceptible to environmental noise, such as random noise and power-line harmonics, resulting in reduced quality of received data. Achieving reliable extraction of MRS signals under strong noise is difficult. To solve this problem, we propose a matching pursuit algorithm based on sparse decomposition theory for data noise suppression and MRS signal extraction. In accordance with the characteristics of the signal and noise, an oscillating atomic library is constructed as a sparse dictionary to realize signal sparse decomposition. A two-step denoising strategy is proposed to reconstruct the power-line harmonics and then extract the MRS signal. We simulated synthetic data with different signal-to-noise ratios (SNRs), relaxation times, and Larmor frequencies. Our results show that the proposed algorithm can effectively remove power-line harmonics and reduce random noise. SNR is significantly improved by up to 35.6 dB after denoising. The effectiveness and superiority of the proposed algorithm are further verified by the measured data and through comparison with the singular spectrum analysis algorithm and harmonic modeling cancellation algorithm.

Acoustic Feature Extraction Method of Rotating Machinery Based on the WPE-LCMV

Fault diagnosis plays an important role in the safe and stable operation of rotating machinery, which is conducive to industrial development and economic improvement. However, effective feature extraction of rotating machinery fault diagnosis is difficult in the complex sound field with characteristics of reverberation and multi-dimensional signals. Therefore, this paper proposes a novel acoustic feature extraction method of the rotating machinery based on the Weighted Prediction Error (WPE) integrating the Linear Constrained Minimum Variance (LCMV). The de-reverberation signal is obtained by inputting multi-channel signals into the WPE algorithm using an adaptive optimal parameters selection function with the sound field changes. Then, the incident angle going from the fault source to the center of the microphone array is calculated from the full-band sound field distribution, and the signal is de-noised and fused using the LCMV. Finally, the fault feature frequency is extracted from the fused signal envelope spectrum. The results of fault data analysis of the centrifugal pump test bench show that the Envelope Harmonic Noise Ratio (EHNR) is more than twice that of the original signal after the WPE-LCMV processing. Compared to the Recursive Least Squares and the Resonance Sparse Signal Decomposition (RLS-RSSD) and the parameter optimized Variational Mode Decomposition (VMD), the EHNR has a higher value for all types of faults after applying the WPE-LCMV processing. Furthermore, the proposed method can effectively extract the frequency of bearing faults.

Fault detection of rotating machinery based on marine predator algorithm optimized resonance-based sparse signal decomposition and refined composite multiscale fluctuation dispersion entropy.

Feature extraction is the key to the fault detection of rotating machinery based on vibration signals, and the quality of the features influences the reliability of the detection. This paper develops a fault feature extraction method of rotating machinery based on optimized resonance-based sparse signal decomposition and refined composite multiscale fluctuation dispersion entropy. First, resonance-based sparse signal decomposition is used to decompose the vibration signals adaptively. In order to obtain the resonance-based sparse signal decomposition algorithm with optimal performance, the marine predator algorithm is used for the parameters optimization with correlation kurtosis as the fitness function. Subsequently, based on the refined composite coarse-grained process and fluctuation dispersion entropy, a refined composite multiscale fluctuation dispersion entropy is developed, enabling a more accurate and comprehensive measure of the complexity of time series. Then, all feature matrices are input to the support matrix machine for fault identification. Experiments are conducted using two typical rotating machinery datasets for the validity of the proposed method, and comparisons are made with other methods. The results show that the proposed scheme outperforms other comparative methods regarding classification accuracy and stability. In addition, the proposed scheme can obtain relatively reliable classification results even when the data volume is small and the background noise is significant, demonstrating the scheme's potential for application in practical engineering.

New approach for multidimensional prognostic of stochastic time series based on sparse-based fractional Levy quaternion extended Kalman filter

Multidimensional data are frequently encountered in numerous industrial systems, standard techniques regarding statistical multichannel prognostic methods naturally cannot fully exploit and capture the coupled nature and spatiotemporal relationship of the available information among channels. To alleviate a bottleneck problem, in this paper, a new approach named sparse-based fractional Levy quaternion extended Kalman filter (SFLQEKF) is formulated for the prognostic of stochastic time series. Initially, the stochastic time series is decomposed into the static component and the dynamic component resorting to the piecewise representation through a new improved sparse low-rank matrix (SLRM) approximation algorithm namely singular value penalty resonance sparse signal decomposition (SVP-RSSD). Afterward, both static component and dynamic component are predicted individually through the proposed fractional Levy quaternion extended Kalman filter (FLQEKF) method, the final time series of interest can be obtained by integrating the predicted static- and dynamic components correspondingly, in which a new predictive derivation of the proposed FLQEKF model is formulated for the first time by considering fractional-order characteristic and Levy flight process damping term, hence the issue of oscillating indeterminacy induced from classical extended Kalman filter (EFK) can be addressed. Eventually, the prognostic behavior of the proposed approach is investigated via the stochastic time series conducted from two experimental cases, the predicted results illustrate the availability and applicability of the proposed approach compared with three state-of-the-art benchmarks.

Fault Feature Extraction of Automobile Wheel Hub Bearing Based on RSK and RSSD

Abstract Wheel hub bearing not only bears axial load but also radial load, and then its running status directly affects the performance and safety of the automobile. In particular, complicated and variable driving conditions of the automobile are not only liable to aggravate the occurrence of mechanical fault such as localized wear, but also often cause powerful intermittent interference noise. It is difficult to extract the vibration characteristics of the transient impact and harmonic components of the wheel bearings in the event of a local fault. An extraction method of fault feature based on ration of smooth and kurtosis (RSK) index and resonance-based signal sparse de-composition (RSSD) is proposed for automobile wheel hub bearings, which aims at the minimum value of RSK index, sequentially optimizes the Q-factor of the resonance sparse decomposition, and obtains its optimal value adaptively to achieve the decomposition of low resonance components with transient impact components and high resonance components with harmonic components. The effect of the method has been verified by powerful intermittent interference simulation signals and experiment signals from local fault of wheel hub bearing with periodic dynamic radial loading.

An Integrated Model of Atom Search Optimization-Based Resonance Sparse Signal Decomposition and Cross-Validation SVM for Gearbox Fault Diagnosis

In the aspect of gearbox fault diagnosis, the periodic pulse signal containing fault characteristics is often overwhelmed with other strong interference components, which brings a great challenge for gearbox fault detection and status identification. To address these issues, this paper develops a novel resonance-based sparse signal decomposition (RSSD) fault diagnosis method combined with support vector machine (SVM). Based on the key of the decomposition parameters in the resonant sparse decomposition method, the influence of atom search optimization (ASO) on the quality factor in the resonance-based sparse signal decomposition method is primarily studied. The vibration signal of the gearbox was decomposed by resonance sparse decomposition with the optimal quality factor, from which the high and low-resonance components were obtained. Then, the power spectrum entropy, singular spectrum entropy, and time-domain energy entropy of the low-resonance signal were calculated. Finally, the pattern recognition of gearbox fault was completed with a designed cross-validation SVM pattern recognition model. The numerical simulation and gearbox fault experiments demonstrate that the presented method can achieve great recognition accuracies and effect capacities against interference components involved in the gearbox vibration signal.

Feature enhancement method of rolling bearing acoustic signal based on RLS-RSSD

The bearing acoustic signal is interfered by reflected sounds and background noises, resulting in a low signal-to-noise ratio (SNR). To address this problem, this paper proposes a feature enhancement method that combines recursive least squares (RLS) with resonance-based sparse signal decomposition (RSSD) into the RLS-RSSD method. First, the RLS method is used as the inverse filter to remove the reverberation as well as reduce the interference of the late reflected sound on the direct signal, then RSSD and wavelet denoising are used to eliminate aperiodic component in the low and high frequency bands. The signals are synthesized based on the amplitudes of different frequency signals, and finally, the bearing fault is determined by envelope spectrum analysis. The results of the simulation data, experimental data, and field application data analysis indicate that the frequency of bearing defects can be accurately extracted by the proposed method.

Feature extraction of gear and bearing compound faults based on vibration signal sparse decomposition

Compound faults of gear and bearing in a gearbox tend to couple features both of distributed and localized defects. The vibration signal shows overlapped modulation phenomena, which cause most traditional wave-filtering-based diagnosis methods invalid. A sparse-decomposition-based method is proposed to decouple overlapped modulation signals and extract features of gear and bearing compound faults. Two kinds of dictionaries respectively consisted of steady harmonic atoms and transient impact atoms are designed to match features of compound faults. Atom parameters are self-adaptively identified from the spectrum information, and identification precisions are improved by the techniques of discrete spectrum correction and correlation filtering. Fault features respectively related to the distributed and localized defects are successively extracted by a novel piecewise matching pursuit algorithm. Lastly, the compound impact features of gear and bearing localized defects are further separated according to the impact period differences in time domain. Both simulation analyses and experimental tests verified the proposed method’s effectiveness on the diagnosis of gear and bearing compound faults.

An Uncertainty Principle for Lowband Graph Signals

In this article, we introduce a novel lower bound on the support size of lowband graph signals. This result allows the deduction of an optimality criterion for the lowband and sparse decomposition of any graph signal, establishing the uniqueness of well behaving solutions. A comparison of the new bound with previously introduced results is performed, showing the improvements brought by the present work. An illustration on a practical denoising usecase on a real graph is also provided.

Application of compressed sensing in the guided wave structural health monitoring of switch rails

Switch rails are weak but essential components of high-speed rail (HSR) systems. In the condition-based maintenance of HSR, ultrasonic guided wave (UGW) on-line monitoring technology is widely used in judging real-time operating conditions; however, it always generates large amounts of data. Too much data bring significant challenges, such as too many unnecessary costs of energy, storage, and network bandwidth in the structural health monitoring of switch rails, making it challenging to realize embedded sensor networks with high durability and low power consumption. Furthermore, the structural damage occurs relatively less over the long-term, indicating that these measurements are inherently sparse. The sparseness of structural damage makes them attractive for the compressed sensing technique. This study proposes a novel data compression and reconstruction method to meet the challenges and reduce the amount of data transmitted by sensor networks and maintain their accuracies simultaneously. First, a lightweight data dictionary is constructed to perform a sparse decomposition of UGW signals according to the characteristics of UGW propagation. Second, an effective sampling method based on a sparse random matrix is designed for sub-Nyquist sampling and compressing UGW signals. Third, a novel block adaptive matching pursuing algorithm is proposed to reconstruct UGW signals from compressed data. Finally, numerical signals, finite element simulation, and several actual monitoring experiments on the foot of a switch rail are conducted to verify the effectiveness and accuracy of the proposed method. The influence of different compression ratios and block sizes on the reconstruction performance of guided wave signals is investigated. The results indicate that the proposed method can sample UGW signals with much lower requirements than the Nyquist sampling theorem and is superior to other novel algorithms.

A new method of health condition detection for hydraulic pump using enhanced whale optimization-resonance-based sparse signal decomposition and modified hierarchical amplitude-aware permutation entropy

The normal operation of the hydraulic pump is the significant premise for the stable and dependable working of hydraulic equipment. Consequently, this research comes up with a health condition detection method of hydraulic pump. First of all, this approach selects resonance-based sparse signal decomposition (RSDD) to adaptively disintegrate vibration signals. The biggest problem of the RSDD algorithm is the requirement to artificially set a large number of key parameters, such as quality factor Q, weight coefficient A, and Lagrange operator u. The improper parameter settings will seriously affect the decomposition performance. To overcome this shortcoming, an enhanced whale optimization algorithm is presented to search the best parameter combination of the RSDD. The algorithm takes the correlation kurtosis as the optimization objective function to adaptively disintegrate the signal into low and high resonance components. Moreover, on the basis of the modified analytic hierarchy process and the amplitude-aware permutation entropy, the modified hierarchical amplitude-aware permutation entropy is raised for measuring the complexity of the measured time series more accurately and comprehensively. After that, a health condition detection method for hydraulic pump based on enhanced whale optimization-resonance-based sparse signal decomposition and modified hierarchical amplitude-aware permutation entropy is raised. Finally, through the usage of the hydraulic pump vibration data, this method is compared with other approaches. According to the experimental results, the raised method can identify the fault type more effectively, which is capable of offering a feasible idea for the health condition detection of hydraulic equipment.