Application Of Variational Mode Decomposition Research Articles

A dynamic prediction model of landslide displacement based on VMD–SSO–LSTM approach

Addressing the limitations of existing landslide displacement prediction models in capturing the dynamic characteristics of data changes, this study introduces a novel dynamic displacement prediction model for landslides. The proposed method combines Variational Mode Decomposition (VMD) with Sparrow Search Optimization (SSO) and Long Short-Term Memory (LSTM) techniques to formulate a comprehensive VMD–SSO–LSTM model. Through the application of VMD, the method dissects cumulative displacement and rainfall data, thereby extracting distinct components such as trend, periodicity, and fluctuation components for displacement, as well as low-frequency and high-frequency components for rainfall. Furthermore, leveraging Gray Correlational Analysis, the interrelationships between the periodic component of displacement and the low-frequency component of rainfall, as well as the fluctuation component of displacement and the high-frequency component of rainfall, are established. Building upon this foundation, the SSO–LSTM model dynamically predicts the interrelated displacement components, synthesizing the predicted values of each component to generate real-time dynamic forecasts. Simulation results underscore the effectiveness of the proposed VMD–SSO–LSTM model, indicating root-mean-square error (RMSE) and mean absolute percentage error (MAPE) values of 1.2329 mm and 0.1624%, respectively, along with a goodness of fit (R2) of 0.9969. In comparison to both back propagation (BP) prediction model and LSTM prediction model, the VMD–SSO–LSTM model exhibits heightened predictive accuracy.

Application of variational mode decomposition in vibration-based bridge damage detection

Bridges are critical infrastructure that require continuous structural health monitoring to ensure safety. Vibration-based methods utilize changes in dynamic response for damage detection. This study applies variational mode decomposition (VMD), a signal analysis technique, to detect damage in a three-span beam bridge model subjected to moving loads. A finite element model is developed to represent the bridge-vehicle interaction, and damage is simulated by reducing flexural stiffness. Sensors placed on each span record vibrations during vehicle passage. VMD decomposes the signals to analyze for damage indications. Different damage levels (30-50% stiffness reduction) and locations (each span) are evaluated. Vehicle speed is also varied to assess its effect. Damage is identified as peaks in the instantaneous energy diagrams of decomposed signals, correctly indicating the axle locations. Detection improves with sensors nearer the damage and lower speed. The results demonstrate VMD's ability to detect and locate damage without a baseline, indicating its potential as a non-baseline vibration-based damage detection method for bridges.

Research on the Application of Variational Mode Decomposition Optimized by Snake Optimization Algorithm in Rolling Bearing Fault Diagnosis

The rolling bearing is one of the commonly used mechanical components in rotating machinery, and its health directly affects the normal operation of equipment. However, the fault signal of rolling bearing is susceptible to noise interference, which makes it difficult to extract the fault characteristics of the rolling bearing and thus affects the accuracy of the diagnosis results. To address this problem, this paper proposes a method by using a snake optimization algorithm to optimize variational mode decomposition (SOA-VMD) and applies it to the extraction of the fault feature of rolling bearing. First, the minimum Shannon entropy to kurtosis ratio (EKR) is used as the fitness function of SOA to search for the best parameter combination of VMD. Second, the optimized VMD is used to decompose the vibration signal of rolling bearing to obtain K intrinsic mode functions (IMFs). Then, the IMF with the most fault information is selected for reconstruction through EKR. The Teager–Kaiser energy operator (TKEO) spectrum analysis is performed on the reconstructed signal. Finally, this method is used to analyze the simulation signal and rolling bearing vibration signal and compared with empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) algorithms to verify the feasibility and effectiveness of the SOA-VMD method.

Path length and sediment transport estimation from DEMs of difference: a signal processing approach

Abstract. The difficulties of measuring bedload transport in gravel-bed rivers have given rise to the morphological method wherein sediment transport can be inferred from changes in riverbed elevation and estimates of the distance traveled by sediment: its path length. Because current methods for estimating path length are time- and labor-intensive, we present a method to estimate a characteristic path length from repeat digital elevation models (DEMs of difference, i.e., DoDs). We propose an automated method to extract the spacing between erosional and depositional sites on the DoD by the application of variational mode decomposition (VMD), a signal processing method, to quantify the spacing as a proxy for path length. We developed this method using flume experiments where bed topography and sediment flux were measured and then applied it to published field data with physical path length measured from tracer measurements. Our sediment transport estimates were not significantly different than the measured sediment flux at lower discharges in the lab. However, we observed an underestimation of sediment flux at the higher discharges in the flume study. We interpret this as a limit of the method in confined settings, where sediment transport becomes decoupled from morphological changes. We also explore how the time between survey acquisitions, the morphological active width relative to the channel width, and DoD thresholding techniques affect the proposed method and the potential issues they pose for the morphological method in general.

Fluid-Solid Interaction Analysis of a Flow Passing Cylinder Based on Variational Mode Decomposition

The fluid-structure interaction problem of cylindrical flow around the cylinder is a classic problem, especially in many fields such as energy engineering, fluid dynamics, engineering structure, energy utilization and development, and environmental protection. In this article, we have heard about the simplified model and analyzed it with the help of the classical cylindrical flow model. In this paper, the flow field was pre-processed on the Workbench software platform, and the pressure distribution and eddy current phenomenon were observed by post-processing given the velocity of the flow field of 1m/s. There is a large number of thunder (2.799552×106) and the Carmen Vortex appears around the cylinder. The vortex falls off periodically, and the wake structure is relatively irregular. The maximum pressure appears at the bottom of the cylinder and the maximum deformation at the top. Then, the pressure term of the simulation results was transferred to the Ansys solver for finite element structural analysis to observe the stresses and strains of the structure under the action of fluids. Finally, the response signal is based on Variational Mode Decomposition (VMD). Its periodic signal corresponded to the flow field, and its components were analyzed in detail. The application of VMD in this area provides innovative inspiration for related fields.

Application of Variational Mode decomposition in GPR Detection of Oil Contaminated Soil

In this article, Ground penetrating radar (GPR) is used to investigate the contaminated soil by oil pollutants in oilfield operation area. Time frequency analysis method is applied to GPR data to reveal the changes of GPR signal frequency components with time variation, which is very important for data interpretation. We use variational mode decomposition (VMD) for time frequency analysis. It can decompose radar signal into several quasi-orthogonal intrinsic mode functions (IMFs) with limited bandwidth, and has strong robustness and local decomposition ability. We apply the VMD on field data acquired in the area with waste liquid contaminated soil in oilfield. The decomposed IMFs from GPR data shows that the signals from the contaminated soil is characterized by the strong energy and low frequency. Then the instantaneous attribute analysis of the IMF is carried out to delineate the scope and thickness of contaminated soil. The experimental results show that the limited bandwidth IMF with specific sparsity obtained by VMD method is more conducive to the processing and interpretation of GPR data.

High voltage shunt reactor acoustic signal denoising based on the combination of VMD parameters optimized by coati optimization algorithm and wavelet threshold

The goal of this research is the application of variational mode decomposition (VMD) in the denoising process of acoustic signals from high-voltage shunt reactors. This paper propose a unique joint denoising method that combines improved VMD and wavelet threshold. The coati optimization algorithm (COA) was introduced to optimally find the optimal combination of VMD decomposition parameters. The optimized and improved VMD was then used to decompose the original noisy reactor acoustic signal. The correlation coefficient method was introduced to remove uncorrelated intrinsic mode functions (IMFs). The wavelet threshold denoising algorithm was applied for secondary noise reduction on the extracted IMFs. The denoised IMFs were subsequently superimposed and reconstructed to obtain the denoised acoustic signal. Comprehensive comparison and analysis of these methods were conducted through simulation experiments and practical tests. The results indicate that COA-VMD-Wavelet Threshold—significantly reduces the reconstructed signal errors with high practicality and effectiveness.

Application of VMD–SSA–BiLSTM algorithm to smart grid financial market time series forecasting and sustainable innovation management

Introduction: This paper proposes a deep learning algorithm based on the VMD-SSA-BiLSTM model for time series forecasting in the smart grid financial market. The algorithm aims to extract useful information from power grid signals to improve the timing prediction accuracy and meet the needs of sustainable innovation management.Methods: The proposed algorithm employs the variational mode decomposition (VMD) method to decompose and reduce the dimensionality of historical data, followed by singular spectrum analysis (SSA) to perform singular spectrum analysis on each intrinsic mode function component. The resulting singular value spectrum matrices serve as input to a bidirectional long short-term memory (BiLSTM) neural network, which learns the feature representation and prediction model of the smart grid financial market through forward propagation and backpropagation.Results: The experimental results demonstrate that the proposed algorithm effectively predicts the smart grid financial market's time series, achieving high prediction accuracy and stability. The approach can contribute to sustainable innovation management and the development of the smart grid.Discussion: The VMD-SSA-BiLSTM algorithm's efficiency in extracting useful information from power grid signals and avoiding overfitting can improve the accuracy of timing predictions in the smart grid financial market. The algorithm's broad application prospects can promote sustainable innovation management and contribute to the development of the smart grid.

Detection and evaluation of load oscillations in induction motors based on MCSA

Load oscillations of induction motors can be the consequence of electrical or mechanical faults. One of the most important techniques to diagnose load oscillations is the so-called motor current signature analysis (MCSA). It has won widespread popularity owing to its non-intrusive and cost-effective performance. The common practice of MCSA is to detect the characteristic harmonic components of stator current caused by load fluctuations. However, in certain scenarios, the characteristic components can be hardly tracked from the current spectrum. Power frequency interference, nonstationary randomness of the sampled signals, and other factors could all limit the use of classical current spectrum analysis. The presented solution is the joint application of variational mode decomposition (VMD), delay addition method, multiple signal classification (MUSIC), and neural network. Specifically, VMD, delay addition and MUSIC are combined to decompose the raw signals, eliminate the power frequency leakage interference and extract the weak oscillation features with enhanced visualization. Meanwhile, a neural network is generated to describe the statistical features of the processed signals, and further realize the automatic evaluation of the load oscillation severity level. Theoretical analysis and experimental verification have been conducted to support this article. The results suggest that the proposed algorithm contributes to a more sensitive detection of the presence of load oscillations, and a more reliable evaluation of their severity with respect to traditional MCSA techniques.

Application of Variational Mode Decomposition and Whale Optimization Algorithm to Laser Ultrasonic Signal Denoising

Laser ultrasound signal echoes are easily drowned out by the surrounding environmental noise in industrial field applications, and it is worthwhile to study methods of retaining the weak ultrasound signal during signal processing. To address this problem, this paper proposes to adopt the parameters optimized by the whale optimization algorithm to the variational mode decomposition (VMD) of laser ultrasound signals. The optimized parameters can avoid the frequency mixing and incomplete noise separation caused by the choice of artificial VMD parameters. The Hausdorff distance is applied in the process of reconstructing the signal to help accurately select the relevant modes and improve the signal-to-noise ratio. Simulation and experimental results show that the proposed method is feasible and effective compared with the other three available denoising methods.

An enhanced variational mode decomposition based on correntropy and a periodicity-assisted log-cycligram for bearing fault diagnosis

Variational mode decomposition (VMD) outperforms other decomposition methods in extracting fault-related modes. However, the major issue in the practical application of VMD is how to determine some key parameters appropriately, especially the mode number. To overcome this problem, an enhanced VMD is presented in this paper. A powerful tool, the rate of change of correntropy, is applied to estimate the mode number precisely. Then, the target mode is selected by a periodicity-assisted log-cycligram rather than conventional kurtosis. The advantages of the enhanced VMD are exposed by applying it to the experimental data collected from two different bearing test benches. Compared with the conventional fast kurtogram and empirical mode decomposition method, the enhanced VMD can extract the target fault mode from the collected vibration signal with strong background noise.

Application of the Variational Mode Decomposition (VMD) method to river tides

Tides in fluvial estuaries are distorted by non-stationary river discharge, which makes the analysis of estuarine water levels less accurate when using the conventional tidal analysis method. As a powerful and widely-used method for non-stationary and nonlinear time series, the application of Variational Mode Decomposition (VMD) method to non-stationary tides is nonexistent. This paper aims to illustrate and verify the suitability of the VMD method as a new tidal analysis tool for river tides. The efficiency of VMD is validated by the measurements from the Columbia River Estuary. VMD strictly divides different tidal species into different modes, and thus avoids mode mixing. Compared to VMD, Ensemble Empirical Mode Decomposition (EEMD), which is another commonly-used method, fails to completely solve the problem of mode mixing. The observed water levels at Longview station are decomposed into 12 modes via VMD. Based on the mean periods and amplitudes of each VMD mode, the 12 VMD modes sequentially correspond to the tidal species from the sub-tides (D0), diurnal tides (D1), semi-diurnal tides (D2), and up to D11 tides. The non-stationary characteristics of tides influenced by river discharge are accurately captured by VMD without mode mixing. The results also show that the EEMD and VMD modes can capture the subtidal signals better than the nonstationary tidal harmonic analysis tool (NS_TIDE). As a general method, the VMD model can also be used for other research purposes related to non-stationary tides, such as detiding.

Application of VMD in Pipeline Leak Detection Based on Negative Pressure Wave

Leakage problems are common in the water supply pipeline system, which will threaten the health of residents and cause economic losses. Negative pressure wave (NPW) technology calculates the time difference through the inflection point to locate the leak. However, due to the nonlinear and nonstationary characteristics of the pressure signal, it is difficult to obtain an accurate inflection point of the NPW by the traditional method. Therefore, the advantages of applying variational mode decomposition (VMD) in NPW technology are explored. Firstly, the correlation coefficient and permutation entropy (PE) are used for effective intrinsic mode function (IMF) component selection and parameter optimization. Thus, an adaptive denoising method based on VMD (AD-VMD) is presented. Then, to effectively separate the detail features of the NPW, a novel inflection point extraction method based on VMD (IPE-VMD) is proposed. Simulation and experimental results show that AD-VMD can effectively suppress noise interference and conserve the mutation characteristic of the leakage. IPE-VMD can obtain a distinct maximum peak at the inflection point and has good robustness to noise interference. This method can calculate the time difference precisely and stably. In addition, the accuracy of the leak location is verified. The average relative positioning error is 5.13%.

Application of variational mode decomposition and chaotic grey wolf optimizer with support vector regression for forecasting electric loads

Accurate electric load forecasting is critical in guaranteeing the efficiency of the load dispatch and supply by a power system, which prevents the wasting of electricity and facilitates energy sustainability. Applications of hybrid intelligent computing methods and swarm-based algorithms with the support vector regression (SVR) model are very promising for solving the problem of premature convergence. This paper presents a novel SVR-based electric load forecasting model by hybridizing variational mode decomposition (VMD), the chaotic mapping mechanism, and the grey wolf optimizer (GWO) in the VMD-SVR-CGWO model to improve the solution searching experiences and to determine the appropriate combination of SVR’s parameters that improve forecasting accuracy. Numerical examples that involve two widely known electric load data sets reveal that the proposed VMD-SVR-CGWO model outperforms other models with respect to forecasting accuracy.

Double ensemble system for wind energy forecasting based on generalized autoregressive conditional heteroskedasticity and neural network models with variational mode decomposition

ABSTRACT With the steady integration of wind energy into electricity networks, precise wind speed forecasting is an essential element in the administration and management of power systems. However, wind energy forecasting research has focused increasingly on short-term forecasting, leaving aside the challenging horizons of medium- and long-term predictions. Therefore, this study proposes a wind speed forecasting methodology based on two types of ensembles, which addresses the nonlinearity and chaotic behavior of wind speed using decomposition-based models. With the results of the first ensemble of 90 ARMA-generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) models, the second ensemble is established based on three types of neural networks and learning functions. Finally, we propose the application of variational mode decomposition (VMD) before or after the first ensemble. The experimental outcomes lead us to divide the prediction horizons into two broad groups, those where VMD inclusion did and did not improve the ensemble results. These horizons are classified as short-term (3, 4, and 5 steps) and mid- and long-term forecast horizons (6, 12, 24, and 48 steps), where the best performance arises with the VMD application after the first ensemble. The research contributes to the existing literature studying a wide variety of innovation distribution and optimization methods that can be implemented with GARCH-type models. Simultaneously, the VMD application is proposed in a novel way not seen in the literature by applying it to the predictions already made by other models, in this case, in ensembles of GARCH-type models.

Application of variational mode decomposition optimized with improved whale optimization algorithm in bearing failure diagnosis

The vibration signals of rolling bearings are unstable and nonlinear, with weak information on failure features and extremely low signal-to-noise ratio (SNR). To solve these problems, this paper presents a failure diagnosis method based on variational mode decomposition (VMD) optimized by the improved whale optimization algorithm (IWOA) is proposed, and verifies the effectiveness of the method through a failure experiment on a test stand. Specifically, the whale optimization algorithm (WOA) was improved by replacing the linear parameter a1 with a nonlinear rule. The replacement effectively improves the solution accuracy, and convergence speed. Next, the VMD parameters were optimized with IWOA. Experimental results show that the VMD optimized with IWOA can effectively and easily extract the early failure features of rolling bearings by enhancing the weak information on failure features.

Application of Variational Mode Decomposition and Deep Learning in Short-Term Power Load Forecasting

Accurate load forecasting of power system operation and development is of great significance. Because of the power load time series has strong nonlinear, the traditional forecasting model does not apply. Therefore, a short-term load forecasting model based on variational model (VMD) and length (LSTM) is proposed. Firstly, the VMD decomposes the original load sequence to get the modal of different size frequency component. Then, phase space reconstruction (PSR) organizes the modal components into deep learning inputs. Then, the LSTM network is employed to predict each group of modal components. Finally, all the modal component predictive value addition to the power load to predict the future. The experimental results show that compared with the BP, LSTM and EEMD - LSTM model, the model completely weakens the non-stationary load sequence, minimize the prediction error, reached the highest prediction accuracy.

A Novel Parameter-Adaptive VMD Method Based on Grey Wolf Optimization with Minimum Average Mutual Information for Incipient Fault Detection

Recently, variational mode decomposition (VMD) has attracted wide attention on mechanical vibration signal analysis. However, there are still some dilemmas in the application of VMD, such as the determination of the number of mode decomposition K and quadratic penalty term α. In order to acquire appropriate parameters of VMD, an improved parameter-adaptive VMD method based on grey wolf optimizer (GWO) is developed by taking the minimum average mutual information into consideration (GWOMI). Firstly, the parameters (K, α) are adaptively determined through GWOMI. Then, the vibration signal is decomposed by the developed method and effective modes are extracted according to the maximum kurtosis. Finally, the extracted modes are processed by Hilbert envelope analysis to acquire the incipient fault features. With the simulation and experimental analysis, it is clearly found that the developed method is effective and performs better than some existing ones.

Application of variational mode decomposition based on particle swarm optimization in pipeline leak detection

Denoising of pipeline leak signals is of great significance to improve the accuracy of pipeline leak detection. Variational mode decomposition (VMD) has the function of signal denoising. However, the inaccurate setting of VMD parameters will affect the result of signal decomposition. This paper proposes a method for optimizing VMD parameters using particle swarm optimization (PSO-VMD). The ratio of the mean and variance of permutation entropy is used as the fitness function of the particle swarm optimization algorithm to search for the optimal number of signal decomposition layers K and penalty factors α. The signal is decomposed using the VMD with the best parameters. Finally, permutation entropy (PE) is used to select the intrinsic modal functions (IMFs) which contains signal characteristics, and these IMFs are used for reconstruction, so as to complete the pipeline signal denoising and leak detection. Experiments show that, compared with the other three denoising methods, the SNR of pipeline signal denoised by the proposed method is increased by 2.1127 on average, MSE and MAE are reduced by 0.000 35 and 0.0043 respectively, and the recognition accuracy of SVM is improved. 5.5%. Therefore, the proposed method has better denoising performance and higher leak detection rate.

Retraction notice: Application of variational mode decomposition to seismic random noise reduction

Retraction notice: Application of variational mode decomposition to seismic random noise reduction