Analysis method of impact echo based on variational mode decomposition

Signal analysis is a fundamental field in engineering and data science, focused on the study of signal representation, transformation, and manipulation. The accurate estimation of harmonic vibration components and their associated parameters in vibrating mechanical systems presents significant challenges in the presence of very similar frequencies and mode mixing. In this context, a hybrid strategy to estimate harmonic vibration modes in weakly damped, multi-degree-of-freedom vibrating mechanical systems by combining Empirical Mode Decomposition and Variational Mode Decomposition is described. In this way, this hybrid approach leverages the detection of mode mixing based on the analysis of intrinsic mode functions through Empirical Mode Decomposition to determine the number of components to be estimated and thus provide greater information for Variational Mode Decomposition. The computational time and dependency on a predefined number of modes are significantly reduced by providing crucial information about the approximate number of vibratory components, enabling a more precise estimation with Variational Mode Decomposition. This hybrid strategy is employed to compute unknown natural frequencies of vibrating systems using output measurement signals. The algorithm for this hybrid strategy is presented, along with a comparison to conventional techniques such as Empirical Mode Decomposition, Variational Mode Decomposition, and the Fast Fourier Transform. Through several case studies involving multi-degree-of-freedom vibrating systems, the superior and satisfactory performance of the hybrid method is demonstrated. Additionally, the advantages of the hybrid approach in terms of computational efficiency and accuracy in signal decomposition are highlighted.

Variational mode decomposition is a new signal decomposition method, which can process non-linear and non-stationary signals. It can overcome the problems of mode mixing and compensate for the shortcomings in empirical mode decomposition. Permutation entropy is a method which can detect the randomness and kinetic mutation behavior of a time series. It can be considered for use in fault diagnosis. The complexity of wind power generation systems means that the randomness and kinetic mutation behavior of their vibration signals are displayed at different scales. Multi-scale permutation entropy analysis is therefore needed for such vibration signals. This research investigated a method based on variational mode decomposition and permutation entropy for the fault diagnosis of a wind turbine roller bearing. Variational mode decomposition was adopted to decompose the bearing vibration signal into its constituent components. The components containing key fault information were selected for the extraction of their permutation entropy. This entropy was used as a bearing fault characteristic value. The nearest neighbor algorithm was employed as a classifier to identify faults in a roller bearing. The experimental data showed that the proposed method can be applied to wind turbine roller bearing fault diagnosis.

Hilbert marginal spectrum is an adaptive signal processing method, which is suitable for processing nonlinear and non-stationary signal and has less energy leakage. Using the Hilbert marginal spectrum of sea level anomaly (SLA) and seawater temperature, this paper successfully detects the mesoscale eddy. Variational mode decomposition (VMD) based on reverse weighted-permutation entropy (RWPE) is used to obtain the marginal spectrum of the non-stationary time series. Simulations verify that the performance of the Hilbert marginal spectrum is better than that of the Fourier spectrum when dealing with non-stationary signals. The marginal spectrum of the SLA and that of the seawater temperature at different depths reveal the periodic and vertical characteristics of the mesoscale eddy, which exhibits a good consistency with the actual phenomenon.

Cable is an important role in Curtain wall cable structures. In order to detect cable damage in a timely and accurate manner, this paper focuses on the problem of non-stationary nonlinear vibration information and mode mixing in Empirical Mode Decomposition (EMD) itself. Based on the damage detection method combining Variational Mode Decomposition (VMD) and Hilbert Transform (HT), further parameter optimization is carried out. This method determines the penalty factor and decomposition level K by searching for the minimum envelope entropy. VMD is used to decompose the vibration information into different BIMF components, and then Hilbert transform is applied to the extracted components to obtain the corresponding marginal spectrum. cable damage identification is performed based on the modal anomaly index. This article confirms through local damage analysis of a single cable that this method can effectively identify the damage location and degree of the cable.

Soldiers rely heavily on their vision, which is crucial not only for daily activities but also for the effective operation of defense systems, weaponry, and other military applications. However, various eye disorders, such as those related to increased intra-ocular pressure, can lead to irreversible vision loss, severely impacting a soldier’s operational capabilities. While extensive research has been conducted on detecting such ocular conditions, there remains a critical need for more accurate diagnostic methods to ensure early detection and treatment. In this study, we propose a novel approach combining Empirical Mode Decomposition (EMD) and Variational Mode Decomposition (VMD) for enhanced detection of eye disorders from retinal fundus images. The proposed method includes a comprehensive preprocessing phase, followed by decomposition using EMD and VMD techniques. The decomposed images undergo feature extraction through feature combination, with subsequent normalization and selection using z-score and the Relief method, respectively. Classification is performed using Support Vector Machines (SVM) with various kernels, including cubic, Gaussian, linear, and quadratic. The results demonstrate that the proposed method achieves high accuracy, with SVM kernel functions yielding accuracies of 98.30 %, 96.59 %, 96.59 %, and 97.87 % for 10-fold cross-validation, respectively. Additionally, the evaluation metrics, including sensitivity and specificity, indicate superior performance compared to state-of-the-art methods for similar datasets. This advanced diagnostic approach offers significant improvements in detecting eye disorders, which could be crucial in defense applications. Early and accurate diagnosis by military ophthalmologists can lead to better decision-making and timely interventions, ultimately preserving the vision and effectiveness of soldiers in the war.

The bearing fault diagnosis is of vital significance in maintaining the safety of rotation machine. Among various fault detection techniques, the diagnosis based on vibration signal is widely applied in monitoring the condition of rotation machine. Variational mode decomposition (VMD) is a novel signal analysis method, which can decompose a multi-component signal into a certain number of band-limited intrinsic mode functions (BLIMFs) nonrecursively. VMD could overcome some problems such as mode mixing, the inference of noise, the determination of wavelet base, which exist in empirical mode decomposition, ensemble empirical mode decomposition, wavelet transform, respectively. However, the empirical selection of the parameters for VMD would affect the result of the decomposition. This paper presents an adaptive VMD method with parameter optimization for detecting the localized faults of rolling bearing. Kurtosis, sensitive to transient impulsive components, is employed as optimization index to evaluate the performance of the VMD. Two parameters in the VMD, namely the number of decomposition modes and data-fidelity constraint, are optimized synchronously based on the kurtosis index through artificial fish swarm algorithm. Executing VMD with the acquired parameters, the optimal BLIMF is obtained. The spectrum analysis of the optimal BLIMF could identify the characteristic frequency caused by the localized crack effectually. The validity of the proposed method is proved by means of a cyclic transient impulse response signal and two experiments with practical vibration signals of rolling bearings. Compared to several existing methods, the proposed method demonstrates reinforced results.

Variational mode decomposition (VMD), which is an alternative to empirical mode decomposition (EMD), has been widely used to extract the feature components of nonstationary signals. However, as a parameterized method, the performance of VMD is heavily influenced by its parameters. Meanwhile, it cannot efficiently extract weak feature components submerged in powerful ones. To address these problems, a novel method based on an optimized VMD is developed for precisely extracting the weak feature of viscoelastic sandwich cylindrical structures (VSCSs). In this method, a parameter optimization algorithm first is proposed to simultaneously select the crucial parameters in the VMD, and to reveal the characteristics of the influence of these parameters on the decomposition performance. Then, the weak feature components submerged in low-frequency strong ones are extracted twice by using the VMD with the optimized parameters. The effectiveness of the proposed method is verified by simulation signals and the experiment vibration signal collected from the VSCS. Its robustness to noise is also discussed. The results indicate that the parameter optimization algorithm can adaptively obtain optimal parameters, and compared with the optimized complementary ensemble EMD (CEEMD) and the original VMD, the proposed method can precisely extract the weak feature components submerged in strong ones.

Machine-learning-enabled adaptive signal decomposition for a brain-computer interface using EEG

X-ray pulsar navigation as a new type of autonomous navigation has very important application prospects and research value. The pulsar signal is a non-stationary signal with low signal-to-noise ratio, so it needs to be denoised. In this paper, a denoising method for X-ray pulsars based on variational mode decomposition is proposed. Simulation results show that the proposed method can improve the signal-to-noise ratio better than existing methods based on wavelet transform and empirical mode decomposition.

Ferromagnetic materials are extensively utilized in industrial settings where the early detection and repair of defects is paramount for ensuring industrial safety. During the enhanced magnetic memory detection of micro-defects, many interference signals appear in the detection signal, which makes it difficult to accurately extract the characteristics of the micro-defect signals, significantly affecting detection effectiveness. When improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is employed independently for signal denoising, the noise and feature signals of the transition components are retained or removed. When variational mode decomposition (VMD) is employed independently for signal denoising, the denoising effect is restricted because of the difficulty in determining the penalty factor α and the number of decomposition layers m. To solve these problems, a denoising method for enhanced magnetic memory detection signals based on ICEEMDAN and VMD, called ICEEMDAN–VMD, is proposed in this paper. First, a comprehensive index (CI) combining information entropy (IE) and the correlation coefficient R is proposed, then the signal components obtained by performing decomposition with the ICEEMDAN method are divided into noise-dominant components, transition components, and useful signal components based on the CI. Subsequently, VMD is employed to perform secondary decomposition on the transition components obtained from the ICEEMDAN method and calculate the correlation coefficients. Ultimately, the optimal VMD components and useful signal components obtained by the ICEEMDAN method are selected for signal reconstruction to obtain a denoised signal. To validate the effectiveness of the proposed method, the denoising effects of the ICEEMDAN–VMD, ICEEMDAN, and VMD methods were compared based on the signal-to-noise ratio (SNR) and fuzzy entropy (FE). The comparison indicated that the ICEEMDAN–VMD denoising method significantly enhanced the denoising effect, and the SNRs of the components of the magnetic field signal could be increased by up to 69.426%. The SNR of each gradient component of the magnetic field signal could be improved by up to ten times, and the FEs of the signal components and their corresponding gradient components could be reduced by 24.198%–81.011%, respectively.

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

The decomposition number $K$ and penalty factor $\alpha $ in the variational mode decomposition (VMD) algorithm have a great influence on the decomposition effect and the accuracy of subsequent fault diagnosis. Therefore, a gear fault diagnosis method based on genetic mutation particle swarm optimization VMD and probabilistic neural network (GMPSO-VMD-PNN) algorithm is proposed in this paper. Firstly, the GMPSO algorithm is used to optimize the $[K,\alpha]$ parameter combination in the VMD algorithm, and the optimal $[K,\alpha]$ parameter combination of each gear fault vibration signal to be decomposed is selected. Then, the gear fault vibration signal is decomposed into several intrinsic mode functions (IMFs) by VMD, and the sample entropy value of each IMFs is extracted to form the feature vector of subsequent fault diagnosis. Finally, the characteristic vector of gear fault vibration signal is input into PNN model, and gear fault is accurately classified. By comparing with fixed parameter VMD algorithm, empirical mode decomposition (EMD) and complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) algorithm, the superiority of this method in gear fault diagnosis is verified. Therefore, the GMPSO-VMD-PNN algorithm proposed in this paper has certain application value for gear fault diagnosis.

Random noise suppression is of great importance in seismic processing and interpretation, and time–frequency peak filtering (TFPF) is a classic denoising approach. In TFPF, pseudo Wigner–Ville distribution (PWVD) is used to linearise the given signal for an unbiased estimation of the instantaneous frequency. However, window length is a trade-off parameter for preserving valid signals and attenuating random noise. A long window length may cause loss of the desired signal, whereas a short window length may be inadequate to suppress noise. To ensure a good trade-off between signal preservation and noise reduction, empirical mode decomposition (EMD) has been introduced into the TFPF method. Although the EMD-TFPF method can achieve good results, the mode mixing problem in EMD is non-negligible. In this article, we introduce variational mode decomposition (VMD) to overcome the mode mixing problem. VMD decomposes a signal into an ensemble of modes that own their respective centre frequencies. Thus, the modes obtained by VMD contain less noise, which simplifies selection of the window width of TFPF. Therefore, we propose the VMD-based TFPF (VMD-TFPF) method to suppress random noise. Synthetic and field seismic data examples are employed to illustrate the superior performance of the proposed method in attenuating random noise and preserving the desired signal.

Application of tentative variational mode decomposition in fault feature detection of rolling element bearing

Due to the complicated structure, vibration signal of rotating machinery is multicomponent with nonstationary and nonlinear features, so it is difficult to diagnose faults effectively. Therefore, effective extraction of vibration signal characteristics is the key to diagnose the faults of rotating machinery. Mode mixing and illusive components existed in some conventional methods, such as EMD and EEMD, which leads to misdiagnosis in extracting signals. Given these reasons, a new fault diagnosis method, namely, variation mode decomposition (VMD), was proposed in this paper. VMD is a newly developed technique for adaptive signal decomposition, which can decompose a multicomponent signal into a series of quasi-orthogonal intrinsic mode functions (IMFs) simultaneously, corresponding to the components of signal clearly. To further research on VMD method, the advantages and characteristics of VMD are investigated via numerical simulations. VMD is then applied to detect oil whirl and oil whip for rotor systems fault diagnosis via practical vibration signal. The experimental results demonstrate the effectiveness of VMD method.