Sensitive Intrinsic Mode Functions Research Articles

A novel robust intelligent fault diagnosis method for rolling bearings based on SPAVMD and WOA-LSSVM under noisy conditions

Aiming at the problem that the fault information of rolling bearings under harsh operation environment is easily submerged by strong noise interference, which causes the traditional method to be difficult to identify bearing faults effectively, this paper proposes a novel robust intelligent fault diagnosis method for rolling bearings based on sparsity-assisted parameter adjustable variational mode decomposition (VMD) and whale optimization algorithm-based optimized least-squares support vector machine (WOA-LSSVM). Firstly, a sparsity measurement named the improved Gini index is introduced as the fitness function of grid search algorithm to adaptively adjust and search for the optimal decomposed mode number K and penalty factor α of VMD. Additionally, VMD containing the optimal parameters is adopted to decompose the original bearing vibration signal into several intrinsic mode function (IMF), and the effective signal reconstruction is performed by screening the sensitive IMF components according to the effective weighted kurtosis Gini index criterion. Subsequently, the refine composite multi-scale dispersion entropy of the reconstructed signal is further calculated to establish a multi-dimensional feature vector set. Finally, the constructed feature vector set is fed into the WOA-LSSVM to achieve automatic fault identification of rolling bearings. The effectiveness of the proposed method is verified by two experimental examples. Experimental results show that the proposed method has higher fault recognition accuracy and better robustness against noise than other homologous methods in noisy conditions. This study provides a new perspective for the developing of robust diagnosis methods.

Feature Extraction of Flow Sediment Content of Hydropower Unit Based on Voiceprint Signal

The hydropower turbine parts running in the sand-bearing flow will experience surface wear, leading to a decline in the hydropower unit’s stability, mechanical performance, and efficiency. A voiceprint signal-based method is proposed for extracting the flow sediment content feature of the hydropower unit. Firstly, the operating voiceprint information of the hydropower unit is obtained, and the signal is decomposed by the Ensemble Empirical Mode Decomposition (EEMD) algorithm, and a series of intrinsic mode functions (IMFs) are obtained. Combined with correlation analysis, more sensitive IMF components are extracted and input into a convolutional neural network (CNN) for training, and the multi-dimensional output of the fully connected layer of CNN is used as the feature vector. The k-means clustering algorithm is used to calculate the eigenvector clustering center of the hydropower unit with a clean flow state and a high sediment content state, and the characteristic index of the hydropower unit sediment content is constructed based on the Euclidean distance method. We define this characteristic index as SI, and the change in the SI value can reflect the degree of sediment content in the flow of the unit. A higher SI value indicates a lower sediment content, while a lower SI value suggests a higher sediment content. Combined with the sediment voiceprint data of the test bench, when the water flow changed from clear water to high sediment flow (1.492 × 105 mg/L), the SI value decreased from 1 to 0.06, and when the water flow with high sediment content returned to clear water, the SI value returned to 1. The experiment proves the effectiveness of the method. The extracted feature index can be used to detect the flow sediment content of the hydropower unit and give early warning in time, so as to improve the maintenance level of the hydropower unit.

An Improved Denoising Method for Fault Vibration Signals of Wind Turbine Gearbox Bearings

Vibration monitoring (VM) is an important tool for fault diagnosis in key components of wind turbine gearboxes (WTGs). However, due to the influence of white noise and random interference, it is difficult to realize high-quality denoising of WTG-VM signals. To overcome this limitation, a novel joint denoising method for fault WTG-VM signals is proposed in this article, which we have named EWTKC-SVD. First, the empirical wavelet transform (EWT) boundary exploration method is used to optimize frequency band allocation and obtain the multiple intrinsic mode functions (IMFs). Second, the sensitive IMFs are selected according to the calculated correlation coefficient and kurtosis index, avoiding IMF redundancy. Finally, the fault WTG-VM signals are obtained using SVD denoising. Using this approach, the proposed method realizes high-quality denoising of WTG-VM signals. Furthermore, it also effectively solves the existing problems of conventional methods, namely, inefficient IMF selection, high noise, false frequencies, mode mixing, and end effect. Finally, the effectiveness, superiority, and reliability of the proposed method are proved using simulation and practical case results.

Adaptive parameter selection variational mode decomposition based on a novel hybrid entropy and its applications in locomotive bearing diagnosis

The emission signal of locomotive bearings is non-stationary, nonlinear and mixed with complex noise when operating online. The adaptive decomposition method is widely employed for denoising and feature extraction. Variational mode decomposition (VMD) is a powerful adaptive decomposition method, but the number of modes K and the penalty factor α are difficult to set in advance and the unreasonable parameter selection may probably bring faulty feature loss. To address this problem, a novel hybrid entropy, which includes the envelope fuzzy and dispersion characteristics of entropy, is proposed to describe the complexity and detect dynamic change of intrinsic mode functions component of VMD. Furthermore, an adaptive parameter selection variational mode decomposition (APSVMD) based on the novel hybrid entropy is presented to obtain the optimal parameter combination (K and α). Then the sensitive intrinsic mode function (IMF) can be chosen by novel hybrid entropy based on its new features. In order to verify the performance of the proposed diagnostic approach, the locomotive online running test was performed. The experimental results demonstrated that the APSVMD represents the signal modes explicitly and can process different types of signals. As a result, different kinds of bearings faults were diagnosed successfully.

An operating condition information-guided iterative variational mode decomposition method based on Mahalanobis distance criterion for surge characteristic frequency extraction of the centrifugal compressor

As a significant high-speed rotating machinery being widely used in modern industry, the centrifugal compressor is subject to a potentially damaging phenomenon called surge, which may lead to property damage, casualties and even catastrophic accidents. Therefore, it is necessary to identify the early surge state of centrifugal compressors to prevent such accidents. In this paper, an operating condition information-guided iterative variational mode decomposition (OCIGIVMD) analysis method is proposed to extract the surge characteristic frequencies (SCFs) from the vibratory signals of centrifugal compressors under early surge state. The variational mode decomposition (VMD) is an effective methodology to decompose a multi-component signal into a series of amplitude-modulated-frequency-modulated (AM-FM) sub-signals with limited bandwidth, from which the characteristic frequencies can be extracted. However, when implementing VMD, the optimal determination of the decomposition mode number is still a challenging task, especially in face of complex signals containing a lot of noise and unknown interference components. Coping with the complex vibration signals of the centrifugal compressor, the VMD in an iterative form based on operating condition information is developed to extract the SCFs, while the decomposition process is controlled by Mahalanobis distance criterion to avoid under-decomposition or over-decomposition and it is needless to select the sensitive intrinsic mode function (IMF) from the multiple IMFs generated by OCIGIVMD. Finally, comparisons with the conventional VMD, empirical mode decomposition (EMD), spectral kurtosis (SK), local mean decomposition (LMD) and two improved VMD methods are conducted using both simulation and experimental data, which demonstrates that the proposed OCIGIVMD is a superior approach in extracting SCFs of the centrifugal compressor under different operating conditions.

Rotor-Stator Rub-Impact Fault and Position Identification of Aero-Engine Based on VMD-MF-Cepstrum-KNN

In order to precisely estimate rub-impact fault between rotor and stator in aero-engine and identify a rub-impact location, the method combining variation modal decomposition (VMD), margin factor (MF) and cepstrum has been proposed (VMD-MF-Cepstrum). Firstly, to effectively separate rub-impact fault information, VMD algorithm has been recruited to decompose original vibration acceleration signals due to its excellent time-frequency locality and the result provides intrinsic mode function (IMF) from different frequency bands. Furthermore, in view of the sensitivity of margin factor to the wear extent of equipment, it has been used to select the sensitive IMF which can best embody the characteristic information of rub-impact faults and is labelled as optimal IMF. Moreover, considering about the consistency and difference of transfer path of rub-impact fault characteristic information shown by the signals obtained by the sensors which are installed in the different or same position when rubbing position is the same (or different), cepstrum has been taken advantage to depict the feature of transfer path and the transfer path from optimal IMF is extracted. Finally, according to the characteristics which correspond to the transfer-path and the k-nearest neighbor (KNN) algorithm, the fault and locations of rub-impact were judged and identified. Check analysis from 2 independent experiments conducted in 2 days and comparison with classical cepstrum method both indicate that the proposed method will be more ideal for unknown samples. Compared with classical cepstrum method, the correctly identified percentage which corresponds to 2 independent experiments has been raised 52.00% and 43.25%.

An Optimized VMD Method for Predicting Milling Cutter Wear Using Vibration Signal

Tool wear has a negative impact on machining quality and efficiency. As for the nonlinear and non-stationary characteristics of vibration signals and strong background noises during the milling process, an identification method of the milling cutter wear state based on the optimized Variational Mode Decomposition (VMD) was proposed, in which the objective function is to minimize the Envelope Entropy (Ep); the various modes of the vibration signal are decomposed using the self-adaptive optimization parameters with Differential Evolution (DE). According to the cross-correlation coefficient in the frequency domain between Intrinsic Mode Function (IMF) and the original signals, the informative IMF components were selected as the sensitive IMF components to superimpose the reconstruction signal and extract the eigenvalues. The mapping relationship between the eigenvalues and the milling cutter wear degree is established by the Naive Bayes classifier method. The experimental results under the various operation conditions indicate that the proposed optimized VMD method possesses an excellent generalization performance. Compared with Empirical Mode Decomposition (EMD) and Ensemble Empirical Mode Decomposition (EEMD), it has better denoising capacity, and so can improve the identification accuracy of the milling cutter wear. Therefore, the processing quality and production efficiency are ensured effectively.

A method to identify wet ball mill’s load based on CEEMDAN, RCMDE and SRNN classification

Ball mill plays a key role in mineral processing plant, and its load identification for optimal control has great significance for the energy consumption reduction and production efficiency improvement. The vibration signal of ball mill shell contains abundant load information, which can be used to identify ball mill load. However, due to the non-linear and non-stationary characteristics of vibration signals, as well as the heavy background noises, the load identification becomes a challenging task in practice. In this paper, a novel method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), refined composite multi-scale dispersion entropy (RCMDE), and stacked recurrent neural network (SRNN) is proposed. First, CEEMDAN algorithm is used to decompose the ball mill’s vibration signals and obtain the intrinsic mode function (IMF) components. Then, the sensitive IMF components are selected through the correlation coefficient method, and the signal is reconstructed with the sensitive IMF components. Secondly, the RCMDE of the reconstructed signal is calculated to obtain the load feature vector, and the dimension of the feature vector is reduced by principle component analysis (PCA). Thirdly, the SRNN is applied to establish a load recognition model, taking the feature vector as its input and the load state as its output. The experimental results show encouraging accuracy to apply this approach to recognize the wet ball mill’s load, with a recognition rate of 98.67%.

Remaining Useful Life Estimation Combining Two-Step Maximal Information Coefficient and Temporal Convolutional Network With Attention Mechanism

Remaining useful life (RUL) estimation has received extensive attention in many fields, which provides improved decision-making for condition-based maintenance (CBM) and enhances the stability of engineered systems. However, the effective construction of the feature set and design of the high-accuracy prediction model are the main challenges in RUL estimation. Consequently, a novel RUL estimation method is proposed in this paper. Initially, to extract the deep characteristics of the raw sensor data, the modified ensemble empirical mode decomposition (MEEMD), combined with the correlation coefficient threshold to select the sensitive intrinsic mode function (IMF) components, is proposed to reconstruct more representative features. Additionally, maximal information coefficient-based two-step feature selection (TSMIC) method is used to select the optimal feature subset. Ultimately, temporal convolutional network with attention mechanism (TCNA) is proposed to capture long-term time-series information and achieves more precise prediction results. The proposed framework is verified through a case study on aircraft turbofan engines, and comparisons with other state-of-the-art methods are presented. The experimental results of the case study show the effectiveness and superiority of the proposed approach.

Fault diagnosis based on the quantification of the fault features in a rotary machine

Fault diagnosis of rotary machinery is essential to fixing defective rotary machines and preventing rotary systems from breaking. Recently, fault diagnosis techniques have moved from traditional methods to artificial intelligence techniques. Many research groups have reported on the development of various artificial intelligence-based classifiers to improve diagnostic performance. In classifier design, selecting the datasets that include standard or fault features is essential to obtaining a high-performance classifier. However, there are few studies on the techniques to evaluate the quality of datasets numerically. In this study, we have developed a fault severity criterion to quantify the faultless and fault features of measured data. Using the proposed criterion, we have determined the dominant direction of representative faults in a rotary machine. The standard and fault data have been obtained, considering the dominant direction of each fault. The intrinsic mode function (IMF) that presents the fault features has been obtained by an empirical mode decomposition and a sensitive IMF selection criterion. Finally, we have designed an accurate and memory-efficient classifier using the extracted data and verified its performance by diagnosing a 7.5 kW servo motor. A conventional support vector machine has been used to verify the effects of the proposed algorithm on the classifier’s performance improvement. The developed classifier demonstrated an increase of performance up to an average of 51.9%, compared with the classifiers using training datasets measured in an arbitrary direction, with the detection rate of 99.9%. The study results suggest that the proposed classifier design technique based on the quantification of the fault features is useful for creating high-quality training datasets, machine learning, and deep learning-based classifiers.

An optimized VMD method and its applications in bearing fault diagnosis

Variational mode decomposition (VMD) is a newly proposed signal processing method which is diffusely used in fault diagnosis of rotating equipment. It has two issues that need to be addressed: (1) its impact parameters need to be determined in advance; (2) its sensitive intrinsic mode function (IMF) needs to be chosen from the multiple IMFs generated by VMD. The purpose of this paper is to introduce effective solutions to the above two issues respectively, to get an optimized VMD method. The method can be characterized as follows: the envelope kurtosis maximum is first used as an indicator to optimize and determine the mode number of VMD in this paper. Then, a novel method to realize the selection of the optimal IMF(s) of VMD which containing abundant fault information based on frequency band entropy (FBE) is introduced. Finally, the envelope power spectrum analysis is performed on the selected IMF(s) to pick up the fault feature frequency to identify the bearing fault type. The feasibility and ascendancy of the presented optimized VMD method are confirmed by the simulation signal analysis and the actual case analysis.

Fault Diagnosis for Rolling Bearings Using Optimized Variational Mode Decomposition and Resonance Demodulation.

It is difficult to extract the fault signal features of locomotive rolling bearings and the accuracy of fault diagnosis is low. In this paper, a novel fault diagnosis method based on the optimized variational mode decomposition (VMD) and resonance demodulation technology, namely GNVRFD, is proposed to realize the fault diagnosis of locomotive rolling bearings. In the proposed GNVRFD method, the genetic algorithm and nonlinear programming are combined to design a novel parameter optimization algorithm to adaptively optimize the two parameters of the VMD. Then the optimized VMD is employed to decompose the collected vibration signal into a series of intrinsic mode functions (IMFs), and the kurtosis value of each IMF is calculated, respectively. According to the principle of maximum value, two most sensitive IMF components are selected to reconstruct the vibration signal. The resonance demodulation technology is used to decompose the reconstructed vibration signal in order to obtain the envelope spectrum, and the fault frequency of locomotive rolling bearings is effectively obtained. Finally, the actual data of rolling bearings is selected to testify the effectiveness of the proposed GNVRFD method. The experiment results demonstrate that the proposed GNVRFD method can more accurately and effectively diagnose the fault of locomotive rolling bearings by comparing with other fault diagnosis methods.

Research on the Fault Diagnosis Method for Rolling Bearings Based on Improved VMD and Automatic IMF Acquisition

This paper proposes a novel method to improve the variational mode decomposition (VMD) method and to automatically acquire the sensitive intrinsic mode function (IMF). First, since fault signals are impulsive and periodic, a weighted autocorrelative function maximum (AFM) indicator is constructed based on the Gini index and autocorrelation function to serve as the optimization objective function. The mode number K and the penalty parameter α of VMD are automatically obtained through an optimal parameter searching process underpinned by the improved particle swarm optimization (PSO) algorithm with a variety of inertia weights. This improvement solves one of the major drawbacks of the conventional VMD method, that is, the need to manually set parameters. Then, an optimal IMF automatic selecting process is performed for single-failure faults and compound faults, according to the principles of the maximum weighted AFM indicator and maximum spectrum peak ratio (SPR), respectively. The sensitive IMFs are then subjected to an envelope demodulation analysis to obtain the fault characteristic frequency. The results of simulations and experiments show that the proposed method can effectively identify fault characteristics early, especially compound faults, demonstrating great potential for real-world applications.

Vibration signature based stability studies in internal turning with a wavelet denoising preprocessor

Detection of accurate chatter is one of the significant problems in machining science due to the contaminated noise present in the acquired signals, which reduces the efficiency of the signal processing tool. In the present work, an efficient chatter detection approach based on the combined modified wavelet de-noising (WD) and Hilbert-Huang transforms (HHT) is adopted. The proposed methodology is implemented in four stages: (i) de-noising of contaminated signals using novel adaptive threshold-based wavelet de-noising, (ii) analysis of de-noised signals with Hilbert-Huang transform to obtain the time-frequency spectrum, (iii) extraction of features such as mean, standard deviation, root mean square and kurtosis of the sensitive intrinsic mode function (IMF) to identify the chatter onset and (iv) classification of chatter onset states based on statistical measures using an improved probabilistic neural network (PNN). The proposed approach is implemented for identifying the cutting states of experimentally measured vibration signals from internal turning operation.

Application of optimized variational mode decomposition based on kurtosis and resonance frequency in bearing fault feature extraction

Variational mode decomposition (VMD) is an adaptive signal processing method proposed recently. It has gradually been widely used due to its good performance. According to the problem that the parameters of VMD need to be determined in advance, a simple and feasible method of determining the influence parameters based on the principle of kurtosis maximum is put forward. A novel intrinsic mode function (IMF) selection method based on resonance frequency is proposed in order to select the IMF that contains the abundant fault feature information. Firstly, the parameters of VMD are optimized by the principle of kurtosis maximum, the optimal penalty parameter and mode number of VMD are set, and the original fault signal is processed by the optimized VMD to obtain the established IMF components. Then, the sensitive IMF(s) with the fault information is selected by resonance frequency. Finally, the selected IMF(s) is analyzed by the envelope demodulation analysis to extract the fault characteristic frequency to judge the fault type of the rolling bearing. It is shown that the method can extract the weak characteristics of the early fault signal of the rolling bearing, and it can realize the judgment of the bearing fault accurately through the analysis of simulated signal and the actual data of bearing.

Pulsation Signals Analysis of Turbocharger Turbine Blades based on Optimal EEMD and TEO

Abstract Turbocharger turbine blades suffer from periodic vibration and flow induced excitation. The blade vibration signal is a typical non-stationary and sometimes nonlinear signal that is often encountered in turbomachinery research and development. An example of such signal is the pulsating pressure and strain signals measured during engine ramp to find the maximum resonance strain or during engine transient mode in applications. As the pulsation signals can come from different disturbance sources, detecting the weak useful signals under a noise background can be difficult. For this type of signals, a novel method based on optimal parameters of Ensemble Empirical Mode Decomposition (EEMD) and Teager Energy Operator (TEO) is proposed. First, an optimization method was designed for adaptive determining appropriate EEMD parameters for the measured vibration signal, so that the significant feature components can be extracted from the pulsating signals. Then Correlation Kurtosis (CK) is employed to select the sensitive Intrinsic Mode Functions (IMFs). In the end, TEO algorithm is applied to the selected sensitive IMF to identify the characteristic frequencies. A case of measured sound signal and strain signal from a turbocharger turbine blade was studied to demonstrate the capabilities of the proposed method.

A Feature Extraction Method for the Wear of Milling Tools Based on the Hilbert Marginal Spectrum

The Hilbert–Huang transform (HHT) can adaptively delineate complex non-linear, non-stationary signals when used as the Hilbert–Huang marginal spectrum through empirical mode decomposition (EMD) and the Hilbert transform, to highlight local features of signals. Characterized by high resolution, the Hilbert marginal spectrum has been widely applied in mechanical signal processing and fault diagnosis. In the research, an HHT based on the improved EMD was proposed to analyze the cutting force, vibration acceleration (AC), and acoustic emission (AE) signals during tool wear in the milling process. At first, the collected signals were subjected to range analysis, which revealed that tool wear was closely related to the signals collected during the cutting process. Then, EMD was applied to the signals, followed by variance analysis after calculating the energies of each intrinsic mode function (IMF) component. Afterwards, the IMF components significantly influenced by wear degree, while slightly influenced by the three cutting factors (cutting velocity, feed per tooth, and cutting depth), were selected as IMF sensitive to the degree of wear. The HHT was finally applied to the sensitive IMF components of signals containing major tool wear information, thus obtaining the Hilbert marginal spectra of the signals, which were able to reflect the changes in signal amplitude with frequency. On the basis of the Hilbert marginal spectrum, the method defined the feature energy function which was then used as the eigenvector for predicting tool wear in milling processes. The analysis of signals in four tool wear states indicated that the method can extract salient tool wear features.

Impact fault detection of gearbox based on variational mode decomposition and coupled underdamped stochastic resonance

In the gear fault diagnosis, the emergence of periodic impulse components in vibration signals is an important symptom of gear failure. However, heavy background noise makes it difficult to extract the weak periodic impulse features. Therefore, the paper presents an impact fault detection method of gearbox by combining variational mode decomposition (VMD) with coupled underdamped stochastic resonance (CUSR) to extract the periodic impulse features. First, the adaptive VMD is presented to decompose the vibration signal into several intrinsic mode functions (IMFs), which can automatically determine the appropriate mode number according to the correlation kurtosis (CK) of decomposition results and extract the sensitive IMF component containing the main fault information. Next, the adaptive CUSR method is developed to analyze the selected sensitive IMF component, and the optimal system parameters are obtained by the genetic algorithm using the CK index as optimization objective function. Finally, the periodic impulse features are extracted by the output signal of CUSR system accurately. Experiments and engineering application verify the effectiveness and superiority of the proposed adaptive VMD-CUSR method for extracting the periodic impulse features in gear fault diagnosis compared to other methods.

An Analysis Approach for Multivariate Vibration Signals Integrate HIWO/BBO Optimized Blind Source Separation With NA-MEMD

The feature extraction of multivariate vibration signals requires a good separation of signals from different sources so as to solve the problem of aliasing between different source signals and background noise. In order to avoid the loss of local information, multiple sensors may be used to collect signals at different locations on the equipment. In this paper, an analysis method combines blind source separation (BSS) and noise-assisted multivariate empirical mode decomposition (NA-MEMD) is proposed. The BSS algorithm optimized by hybrid invasive weed/biogeography-based optimization (HIWO/BBO) is used to separate the multi-component mixed signals with chaotic noise and the negative entropy of the separated signal as the objective function of HIWO/BBO. To reduce computational complexity, the separation matrix takes the form of a parametric representation. Afterward, the multiseparation signals without chaotic noise are decomposed with NA-MEMD, then the sensitive intrinsic mode function (IMF) is extracted by the improved correlation coefficient (ICC) analysis method. The advantage of the ICC is that the sensitive IMFs at different orders can be selected simultaneously in all channels. Finally, the characteristic frequency of the vibration signal can be obtained by analyzing the sensitive IMFs. The effectiveness of this proposed method is verified in the application of the synthetic signals and the actual bearing fault signals. It shows that this approach can play a role in filtering out the chaotic noise while solving the aliasing problem of mixed vibration signals. For another, it synchronously decomposes the multidimensional separated signals and extracts the characteristic frequency.

An improved extreme-point symmetric mode decomposition method and its application to rolling bearing fault diagnosis

HHT (Hilbert-Huang Transform) which consist of EMD (Empirical Mode Decomposition) and HT (Hilbert Transform) now is the most widely used time-frequency analysis technique for rolling element bearing fault diagnosis, however, its fault characteristic information extraction accuracy is usually limited due to the problem of mode mixing in EMD. ESMD (Extreme-point symmetric mode decomposition) is a novel development of HHT which is promising to alleviate this limitation and it has been applied to some fields successfully, but its application for rolling bearing fault diagnosis has rarely been seen in the literature. In this paper, ESMD is applied to extract the bearing fault characteristics for rolling bearing fault detection, and the results proved that ESMD can have a better fault diagnose effect than EMD and HT. What’s more, for further improving bearing fault characteristic extraction accuracy of rolling bearing vibration signals, the sifting scheme is proposed for selecting the sensitive fault-related IMFs (intrinsic mode functions) generated by ESMD, in which a weighted kurtosis index is introduced for automatic selection and reconstruction of the fault-related IMFs, and then the original and reconstructed bearing fault vibration signal after performing Hilbert transform as the results to diagnose the incipient rolling bearing fault. ESMD combined with the proposed sifting scheme are applied to diagnose the simulated and experimental signals, and the results confirmed that the sifting scheme based ESMD is superior to the other conventional method in rolling bearings fault diagnosis.