Variational Mode Decomposition Algorithm Research Articles

A novel lidar signal denoising method based on variational mode decomposition optimized using whale algorithm

Original lidar return signals are covered by high levels of noise that seriously affect the accuracy of subsequent data processing and inversion. Therefore, it is important to separate the effective signal from the returned signal with noise interference. In this paper, an efficient denoising method based on the variational mode decomposition (VMD) algorithm optimized using the global search strategy-based whale algorithm and the total variational stationary wavelet transform (GSWOA-VMD-SWTTV) is proposed, and this method is applied to denoising of lidar return signals. First, the global search strategy-based whale optimization algorithm (GSWOA) is used to acquire the optimal parameters of the VMD algorithm adaptively, and the lidar return signal is then decomposed by global search strategy-based whale optimization algorithm (GSWOA)-VMD. The effective modal components are then determined using the cross-correlation coefficient method from the decomposed modal components, and total variation stationary wavelet denoising is performed on each effective mode. Finally, the effective modes are reconstructed to obtain a clean lidar return signal. Moreover, to provide further verification of the effectiveness of the proposed method, it is compared with the ensemble empirical mode decomposition (EEMD) method, the complete EEMD with adaptive noise (CEEMDAN) method, the singular value decomposition (SVD) method, and the wavelet threshold method under sunny, cloudy, and dusty weather conditions. The experimental results demonstrate the superior noise reduction performance of the proposed algorithm, which can filter out strong noise from the signal while retaining the complete signal details without distortion; additionally, the proposed method has the highest signal-to-noise ratio and lowest mean square error.

A Method for Identifying the Wear State of Grinding Wheels Based on VMD Denoising and AO-CNN-LSTM

Monitoring the condition of the grinding wheel in real-time during the grinding process is crucial as it directly impacts the precision and quality of the workpiece. Deep learning technology plays a vital role in analyzing the changes in sensor signals and identifying grinding wheel wear during the grinding process. Therefore, this paper innovatively proposes a grinding wheel wear recognition method based on Variational Mode Decomposition (VMD) denoising and Aquila Optimizer—Convolutional Neural Network—Long Short-Term Memory (AO-CNN-LSTM). The paper utilizes Acoustic Emission (AE) signals generated during grinding to identify the condition of the grinding wheel. To address noise interference, the study introduces the VMD algorithm for denoising the sample dataset, enhancing the effectiveness of neural network training. Subsequently, the dataset is fed into the designed Convolutional Neural Network—Long Short-Term Memory (CNN-LSTM) structure with AO-optimized parameters. Experimental results demonstrate that this method achieves high accuracy and performance.

Non-stationary signal analysis utilizing VMD and EMD algorithm for multiple fault classification for industrial applications

The Hilbert spectrum images of intrinsic mode functions (IMF) of empirical mode decomposition (EMD) analysis and variational mode decomposition (VMD) analysis of faulty machine vibration signals are used in deep convolutional neural network (DCNN) for machine fault classification in which the DCNN automatically learns the features from spectral images using convolution layer. Though both EMD and VMD analysis suit well for non-stationary signal analysis, VMD has the merit of aliasing free IMFs. In this paper, the performance improvement of DCNN classification for a non-stationary vibration signal dataset using VMD is brought out. The numerical experiment uses the Hilbert spectrum images of 4 EMD-IMFs and 4 VMD-IMFs in DCNN to classify 10 different faults of the Case Western Reserve University (CWRU) bearing dataset. The confusion matrices are obtained and the plot of model accuracies in terms of epochs for the DCNN is analysed. It is shown that the spectrum images of one of the four EMD-IMFs, IMF0, give a validation accuracy of 100% and in the case of VMD the spectrum images of two of the four VMD-IMFs, IMF0, and IMF1 give a validation accuracy of 100%. This reveals that non-aliasing IMFs of VMD are better at classifying bearing faults. Further to bring out the merits of VMD analysis for non-stationary signals the numerical experiment is conducted using VMD analysis for binary fault classification of the milling dataset which is more non-stationary than the bearing dataset which is proved by plotting the statistical parameters of both datasets against time. It is found that the DCNN classification is 100% accurate for IMF3 of VMD analysis which is much better than the 81% accuracy provided by EMD analysis as per existing literature. The performance comparison highlights the merits of VMD analysis over EMD analysis and other state-of-the-art methods and ensemble learning methods.

Strategy of Flywheel–Battery Hybrid Energy Storage Based on Optimized Variational Mode Decomposition for Wind Power Suppression

The fluctuation and intermittency of wind power generation seriously affect the stability and security of power grids. Aiming at smoothing wind power fluctuations, this paper proposes a flywheel–battery hybrid energy storage system (HESS) based on optimal variational mode decomposition (VMD). Firstly, the grid-connected power and charging–discharging power of the HESS are determined based on the sliding average algorithm. Secondly, the VMD algorithm, optimized using long short-term memory (LSTM), is used to decompose the hybrid energy storage power (HESP) into a series of sub-modes with frequencies from low to high. Then, the state of charge of the battery energy storage system and the speed of the flywheel energy storage system are monitored in real time, and the primary power of the HESS is modified according to the rules formulated by fuzzy control. Finally, through a simulation example, it is concluded that the method meets the requirements of smoothing wind power fluctuations and gives full play to the characteristics of energy storage battery and flywheel energy storage to ensure the stable operation of the energy storage system. The method presented in this paper can provide a reference for HESP configuration and control operation strategy formulation.

Evaluation method for electromagnetic interference complexity of high voltage switch based on feature extraction and GCC‐GRU network

AbstractWhen some new‐type sensors are subjected electromagnetic interference (EMI), the traditional standard can no longer serve as the guidance for their EMI protection. Therefore, it is necessary to evaluate the complexity of the new sensing equipment's suffering from electromagnetic interference. A hybrid method of feature extraction and complexity evaluation of Electromagnetic Interference signals based on generalised correntropy criterion (GCC) is proposed. First, a variational mode decomposition algorithm for adaptive extraction of decomposed signals is constructed using GCC, and Generalised S‐transform is used for processing and reorganisation. Then, according to the time‐frequency space model, a new quantitative evaluation criterion interference factor is proposed, which overcomes the shortcomings of the traditional qualitative classification and the inability to solve the cross classification of indicators. Then, the Gated Recurrent Unit is introduced, and the GCC‐GRU evaluation model with GCC as the loss function is derived. The authors conduct EMI tests and measured signal evaluation with Medium Voltage and High Voltage switches, and the results show that the method proposed is correct and effective.

Novel hybrid intelligence predictive model based on successive variational mode decomposition algorithm for monthly runoff series

A high-accuracy estimation of the runoff has always been an extremely relevant and challenging subject in hydrology science.Therefore, in the current research, a novel hybrid decomposition-integration-optimization based model is developed to enhance the estimation precision of the runoff. The suggested predictive model is a combination of successive variational mode decomposition (SVMD) technique and Multi-Layer Perceptron neural network (MLP) model integrated with particle swarm optimization (PSO) meta-heuristic algorithm (i.e., hybrid SVMD-MLP-PSO model). To test its performance, the mean monthly runoff data recorded from Sep 1986-Aug 2017 in Dez River basin (MRDRm), southwest of Iran, are used. The performance of the recommended model is also matched with other different hybrid and single models including MLP-PSO, SVMD-MLP, and MLP as the benchmark model. In all models, the sequence-to-one regression module of forecasting (i.e., without using meteorological parameters recorded in the study region) is utilized. In the SVMD based hybrid models, the optimal value of compactness of mode (α) for the original MRDRm time series is achieved at 100. Then, the PACF(partial autocorrelation function) diagram related to the lag length from each decomposed intrinsic mode function (IMF) sub-signals sequence generated is operated to select the ideal input variables. Performance evaluation metrics prove that the hybrid SVMD-MLP-PSO model under the best predictor and meta-parameters, outperformed with an R2 of 0.89, modified 2012 version of Kling-Gupta efficiency (KGEʹ) of 0.83, volumetric efficiency (VE) of 0.91, Nash–Sutcliffe efficiency (NSE) of 0.88, and RMSE of 13.91 m3/s. Comparatively, the standalone MLP as the benchmark model results in an R2 of 0.24, VE of 0.33, KGEʹ of 0.2, NSE of 0.29, and RMSE of 153.39 m3/s.

Estimating Rotational Acceleration in Shoulder and Elbow Joints Using a Transformer Algorithm and a Fusion of Biosignals.

In the present study, we used a transformer model and a fusion of biosignals to estimate rotational acceleration in elbow and shoulder joints. To achieve our study objectives, we proposed a mechanomyography (MMG) signal isolation technique based on a variational mode decomposition (VMD) algorithm. Our results show that the VMD algorithm delivered excellent performance in MMG signal extraction compared to the commonly used technique of empirical mode decomposition (EMD). In addition, we found that transformer models delivered estimates of joint acceleration that were more precise than those produced by mainstream time series forecasting models. The average R2 values of transformer are 0.967, 0.968, and 0.935, respectively. Finally, we found that using a fusion of signals resulted in more precise estimation performance compared to using MMG signals alone. The differences between the average R2 values are 0.041, 0.053, and 0.043, respectively. Taken together, the VMD isolation method, the transformer algorithm and the signal fusion technique described in this paper can be seen as supplying a robust framework for estimating rotational acceleration in upper-limb joints. Further study is warranted to examine the effectiveness of this framework in other musculoskeletal contexts.

Research on Ocular Artifacts Removal from Single-Channel Electroencephalogram Signals in Obstructive Sleep Apnea Patients Based on Support Vector Machine, Improved Variational Mode Decomposition, and Second-Order Blind Identification.

The electroencephalogram (EEG) has recently emerged as a pivotal tool in brain imaging analysis, playing a crucial role in accurately interpreting brain functions and states. To address the problem that the presence of ocular artifacts in the EEG signals of patients with obstructive sleep apnea syndrome (OSAS) severely affects the accuracy of sleep staging recognition, we propose a method that integrates a support vector machine (SVM) with genetic algorithm (GA)-optimized variational mode decomposition (VMD) and second-order blind identification (SOBI) for the removal of ocular artifacts from single-channel EEG signals. The SVM is utilized to identify artifact-contaminated segments within preprocessed single-channel EEG signals. Subsequently, these signals are decomposed into variational modal components across different frequency bands using the GA-optimized VMD algorithm. These components undergo further decomposition via the SOBI algorithm, followed by the computation of their approximate entropy. An approximate entropy threshold is set to identify and remove components laden with ocular artifacts. Finally, the signal is reconstructed using the inverse SOBI and VMD algorithms. To validate the efficacy of our proposed method, we conducted experiments utilizing both simulated data and real OSAS sleep EEG data. The experimental results demonstrate that our algorithm not only effectively mitigates the presence of ocular artifacts but also minimizes EEG signal distortion, thereby enhancing the precision of sleep staging recognition based on the EEG signals of OSAS patients.

Ultra-short term wind power forecasting method based on improved VMD

A CNN-GRU ultra-short term wind power prediction method based on improved VMD is proposed. Firstly, in the data processing part, according to the irregularity and non-stationary peculiarities of wind power, the variational mode decomposition algorithm is adopted to decompose the original sequence of wind power to reduce the non-stationarity. At the same time, considering that the parameter setting and selection in the variational modal decomposition algorithm are of great significance to the decomposition effect, the improved whale improvement method is adopted to find the best parameters in VMD to avoid the problem of poor decomposition effect caused by artificial setting. Finally, the CNN-GRU and GRU models are simulated and compared on the Matlab platform through the field wind farm data.

Fault Diagnosis Method for Rolling Bearings Based on Grey Relation Degree.

Aiming at the difficult problem of extracting fault characteristics and the low accuracy of fault diagnosis throughout the full life cycle of rolling bearings, a fault diagnosis method for rolling bearings based on grey relation degree is proposed in this paper. Firstly, the subtraction-average-based optimizer is used to optimize the parameters of the variational mode decomposition algorithm. Secondly, the vibration signals of bearings are decomposed by using the optimized results, and the feature vector of the intrinsic mode function component corresponding to the minimum envelope entropy is extracted. Finally, the grey proximity and similarity relation degree based on standard distance entropy are weighted to calculate the grey comprehensive relation degree between the feature vector of vibration signals and each standard state. By comparing the results, the diagnosis of different fault states and degrees of rolling bearings is realized. The XJTU-SY dataset was used for experimentation, and the results show that the proposed method achieves a diagnostic accuracy of 95.24% and has better diagnosis performance compared to various algorithms. It provides a reference for the fault diagnosis of rolling bearings throughout the full life cycle.

Adaptive feature enhancement of modulation spectrum of ship radiation noise

The Detection of Envelope Modulation on Noise (DEMON) has been widely used in passive sonar target identification for determining the operational status and propeller structure characteristics of ships. However, the traditional DEMON spectrum is susceptible to environmental noise, which increases the difficulty of feature extraction. To address this issue, this paper investigates an adaptive feature enhancement method that combines Variational Mode Decomposition (VMD) and Singular Value Decomposition (SVD). The VMD algorithm utilizes variational equations to achieve adaptive modal decomposition of multiple feature components, while SVD utilizes the uncorrelated nature of signal and noise to achieve background noise reduction. Simulation results demonstrate that the feature strength and output signal-to-noise ratio of the VMD-SVD algorithm are higher than those of the traditional DEMON algorithm under both uniform and non-uniform modulation modes. Furthermore, processing of actual data validates the superiority of the VMD-SVD algorithm over the traditional DEMON algorithm, with the feature strength and output signal-to-noise ratio being maximally increased by 3 dB and 3.8 dB, respectively, compared to the traditional algorithm.

A failure diagnosis method of ball bearing based on optimized multiscale variational modal extraction with synchro squeezing transformation

When a compound failure occurs in a bearing, the failure information included in vibration signals is featured by being weak, complex and combined. This fact makes it difficult to identify a compound failure precisely. Variational mode extraction (VME) solves the problem of variational mode decomposition (VMD) in being difficult to determine the number of decomposition layers and has certain applications in the identification of bearing failures. However, the initial expected central frequency of VME and option of penalty factor is crucial to the extraction of expected mode. To precisely determine the central frequency and penalty factor of VME and fulfill the correct extraction of feature information of compound failures in bearing, the paper has proposed a method based on synchro squeezing transform (SST) and information entropy to adaptively determine the parameters in VME (SST-VME). Firstly, SST is used to make time-frequency analysis of original vibration signals and characteristic frequency bands with larger energy are chosen from time-frequency spectrum to adaptively determine the expected central frequency of VME. Secondly, as information entropy has representation capacity for information included in the signal, penalty factor of VME was adaptively determined according to information entropy. Thirdly, original signals were subjected to VME according to expected central frequency and penalty factor adaptively determined; the expectation mode obtained was denoised by singular value decomposition algorithm. Finally, the type of compound failures of bearing is determined according to the frequency spectrum of denoised signals. To verify the effectiveness of proposed method, a comparison with VMD algorithm is conducted. As indicated by the result, the proposed method is more precise and comprehensive than VMD algorithm to extract the feature information corresponding to compound faults of bearing, and thereby correctly determines the type of compound failures.

An on-line weld inspection method for underwater offshore structure based on an improved deep convolutional network

ABSTRACT The acoustic signal analysing is a crucial evaluation method for welding repair of in-service marine structures. However, the complex underwater environment complicates the quality evaluations. In addition, the weak acoustic signal poses challenges for traditional methods during signal processing, such as low signal-to-noise ratio and difficulty in feature extraction. In this paper, an improved deep convolutional network method for online weld inspection of underwater offshore structures is proposed. First, a Variational Mode Decomposition (VMD) algorithm is used to extract weak signals. The raw acoustic signal is denoised, and the effective pulses are extracted. Next, the recurrence and gradient plot methods are applied to extract the pulse features and to generate corresponding images. Finally, a VGG16 deep convolutional network is used to classify image samples and determine weld quality online. Results indicate that the VMD algorithm can process and reduce noise, the recurrence and gradient plot provide quality related image features for the neural network. The VGG16 neural network outperforms the VGG19, RESNET34, and RESNET50 neural networks and can achieve a 97.5% recognition rate. This paper offers some avenues for online identification of weld quality in underwater welding.

An adaptive enhanced envelope spectrum technique for bearing fault detection in conditions characterized by strong noise

Rolling bearings are widely used in rotating machinery and have a high failure rate. Regrettably, the task of ensuring dependable bearing fault detection presents a formidable challenge, especially when the bearing fault-related characteristics are non-stationary or even affected by strong noise. In response to this challenge, a novel adaptive enhanced envelope spectrum (AEES) technique is proposed in this study. Firstly, it generates representative intrinsic mode functions (IMFs) using the variational mode decomposition algorithm. Then, based on the analysis of the envelope spectrum normalized mutual information and time-domain fuzzy entropy, a new IMF selection and integration strategy combining time- and frequency-domain metrics is suggested to reconstruct the most informative analytical signal. An adaptive filter is employed to post-process the reconfigured signal to reinforce fault-related impulsive characteristics, the optimal length of which is ascertained through the proposed variable step-size search technique based on unbiased autocorrelation analysis. The efficacy of the AEES technique has been validated through a sequence of experiments conducted under diverse bearing conditions. Its robustness and distinct advantages under strong noise conditions are tested using a publicly available dataset. The validation results show that the AEES technique can effectively identify the health conditions of bearings under high noise conditions (signal-to-noise ratios between 1 dB and 3 dB). Compared with two relevant techniques in the existing literature and a classical method, the proposed AEES technique can achieve signal processing results with fewer interference components and more prominent characteristic frequency information and has a unique ability to identify fault features in some challenging situations.

Photovoltaic output power estimation model based on multi-meteorological variable dimension reduction and improved variational mode decomposition algorithm

ABSTRACT The instability and intermittence of photovoltaic (PV) power generation challenge the large-scale integration of PV power generation systems into the power grid and the development of energy storage systems. To accurately predict the output power of PV power generation, a power prediction model based on the optimized variational modal decomposition (OVMD)-adaptive t-distribution sparrow search algorithm (tSSA)-least squares support vector machine (LSSVM) algorithm was built. The performance of the model was then verified by three-year meteorological data and real-time PV output power data of two different climatic regions in China. The mean absolute percentage error (MAPE) and root mean square error (RMSE) of this model were less than 3.1% and 0.40, respectively, and the determination coefficient (R2) of this model was greater than 95%. Moreover, the prediction accuracy was greatly improved compared to models based on the support vector machine (SVM), LSSVM, variational modal decomposition (VMD)-LSSVM, and VMD-SSA-LSSVM algorithms. Finally, by performing dimension reduction of meteorological variables related to PV output power, the performance of the proposed OVMD-tSSA-LSSVM model was further improved.

Optimized variational mode decomposition denoising method based on weighted mean of vectors algorithm

Aiming at the noise interference in oil and gas pipeline leakage detection, a signal denoising method based on improved variational mode decomposition (VMD) algorithm is proposed. First, the weighted mean of vectors algorithm (INFO) is used to select the parameters of the VMD algorithm adaptively to obtain the best decomposition level K value and penalty factor α value, which effectively solves the problem that the parameters are difficult to select in VMD. Then, according to the Hausdorff distance between the original signal and the probability density of each IMF, the effective modal components are selected for reconstruction and denoising signal is obtained. In oil and gas pipeline leakage signal processing, compared with whale optimization algorithm, grey wolf optimization algorithm, and particle swarm optimization algorithm, the reconstructed signal obtained by the proposed INFO algorithm optimized VMD parameters has higher signal-to-noise ratio and lower mean square error and mean absolute error. It shows that the proposed algorithm has better denoising effect.

Micro-short circuit fault diagnosis of lithium-ion battery based on voltage curve similarity ranking volatility

ABSTRACT An electric vehicle battery system often consists of multiple battery cells that are interconnected in series and parallel. If a micro-short circuit failure occurs in one of the battery cells, it may cause a serious internal short circuit or even thermal runaway. Consequently, it is extremely important to detect micro-short circuit faults in batteries. This paper presents a novel approach for diagnosing faults in lithium-ion batteries based on the similarity ranking fluctuation rate of voltage curve, and verify the feasibility of the method through a series of micro-short circuit experiments containing an external parallel variable resistance device. This approach does not require complete charge-discharge curves. Firstly, the charging voltage data is preprocessed using the Variational Mode Decomposition algorithm, after which the Dynamic Time Warping technique is employed to calculate the similarity between the charging voltage of each battery and a reference battery. Then a ranking fluctuation rate of voltage curve similarity is established, and the Grubbs criterion is utilized to identify batteries exhibiting abnormal fluctuation rate within the ranking. Finally, the effectiveness of the proposed method is validated by analyzing actual battery signals collected from faulty vehicles. The results demonstrate that the method accurately identifies batteries with micro-short circuit faults.

Research on motor rotation anomaly detection based on improved VMD algorithm

PurposeThe electromechanical brake system is leading the latest development trend in railway braking technology. The tolerance stack-up generated during the assembly and production process catalyzes the slight geometric dimensioning and tolerancing between the motor stator and rotor inside the electromechanical cylinder. The tolerance leads to imprecise brake control, so it is necessary to diagnose the fault of the motor in the fully assembled electromechanical brake system. This paper aims to present improved variational mode decomposition (VMD) algorithm, which endeavors to elucidate and push the boundaries of mechanical synchronicity problems within the realm of the electromechanical brake system.Design/methodology/approachThe VMD algorithm plays a pivotal role in the preliminary phase, employing mode decomposition techniques to decompose the motor speed signals. Afterward, the error energy algorithm precision is utilized to extract abnormal features, leveraging the practical intrinsic mode functions, eliminating extraneous noise and enhancing the signal’s fidelity. This refined signal then becomes the basis for fault analysis. In the analytical step, the cepstrum is employed to calculate the formant and envelope of the reconstructed signal. By scrutinizing the formant and envelope, the fault point within the electromechanical brake system is precisely identified, contributing to a sophisticated and accurate fault diagnosis.FindingsThis paper innovatively uses the VMD algorithm for the modal decomposition of electromechanical brake (EMB) motor speed signals and combines it with the error energy algorithm to achieve abnormal feature extraction. The signal is reconstructed according to the effective intrinsic mode functions (IMFS) component of removing noise, and the formant and envelope are calculated by cepstrum to locate the fault point. Experiments show that the empirical mode decomposition (EMD) algorithm can effectively decompose the original speed signal. After feature extraction, signal enhancement and fault identification, the motor mechanical fault point can be accurately located. This fault diagnosis method is an effective fault diagnosis algorithm suitable for EMB systems.Originality/valueBy using this improved VMD algorithm, the electromechanical brake system can precisely identify the rotational anomaly of the motor. This method can offer an online diagnosis analysis function during operation and contribute to an automated factory inspection strategy while parts are assembled. Compared with the conventional motor diagnosis method, this improved VMD algorithm can eliminate the need for additional acceleration sensors and save hardware costs. Moreover, the accumulation of online detection functions helps improve the reliability of train electromechanical braking systems.

A dual-scale hybrid prediction model for UAV demand power: Based on VMD and SSA optimization algorithm

The prediction of power demand for unmanned aerial vehicles (UAV) is an essential basis to ensure the rational distribution of the energy system and stable economic flight. In order to accurately predict the demand power of oil-electric hybrid UAV, a method based on variational mode decomposition (VMD) and Sparrow Search Algorithm (SSA) is proposed to optimize the hybrid prediction model composed of long-short term memory (LSTM) and Least Squares Support Vector Machine (LSSVM). Firstly, perform VMD decomposition on the raw demand power data and use the sample entropy method to classify the feature-distinct mode components into high-frequency and low-frequency categories. Then, each modality component was separately input into the mixed model for rolling prediction. The LSSVM model and LSTM model were used to process low-frequency and high-frequency components, respectively. Finally, the predicted values for each modal component are linearly combined to obtain the final predicted value for power demand. Compared with the current models, the prediction model constructed in this paper stands out for its superior ability to track the changing trends of power demand and achieve the highest level of prediction accuracy.

RUL prediction of rolling bearings based on adaptive variational mode decomposition and double-discriminator conditional CycleGAN

To accurately evaluate the remaining life (RUL) of rolling bearings under small sample conditions and strong noise interference, a RUL prediction scheme using adaptive variational mode decomposition (VMD) and double-discriminator conditional CycleGAN (DD-cCycleGAN) is put forward. Combining chimp optimization algorithm (ChOA) with VMD, an adaptive VMD algorithm based on ChOA is presented, which selects effective mode components for reconstruction and reduces interference from strong background noise. A DD-cCycleGAN is developed to generate new samples which not only retain sample information of source domain, but also resemble samples of target one. A LSTM network after training is utilized to predict the bearing RUL in test samples. The performance of this scheme was validated by using the XJTU-SY bearing test dataset. The comparison analyses demonstrate this scheme has strong noise resistance and high accuracy.