Parameters Of Variational Mode Decomposition Research Articles

Rotating machinery fault diagnosis based on parameter-optimized variational mode decomposition

Variational Mode Decomposition (VMD) has been widely applied in rotating machinery fault diagnosis. However, VMD needs to solve two key problems in its application: parameter optimization and the selection of high-quality Intrinsic Mode Functions (IMFs). To address these issues, firstly, the Sparrow Search Algorithm (SSA) is employed to optimize VMD parameters, incorporating fitness functions based on the Hoyer measure and the square envelope spectrum negative entropy. Subsequently, by minimizing the fitness function, optimal parameters for VMD are obtained. Secondly, a novel IMF selection method is proposed, evaluating IMF quality through sample entropy, energy ratio, and Spearman rank correlation coefficient to identify IMFs sensitive to fault features. Finally, the proposed method is validated using gear and bearing datasets containing noise of varying intensities, demonstrating its outstanding capability for extracting sensitive information in different noise environments.

A hybrid machine learning forecasting model for photovoltaic power

The increasing use of photovoltaic (PV) power generation presents a significant opportunity for global energy transformation. However, accurately forecasting PV power remains a challenge. This study proposes a hybrid approach that combines variational mode decomposition (VMD), whale optimization algorithm (WOA), and long short-term memory neural network (LSTM) to forecast photovoltaic (PV) power accurately. The model decomposes the time series of PV power using VMD to address the non-stationary nature of the time series. The VMD parameters are optimized using WOA. Subsequently, and the PV power time series data is then decomposed using the optimized VMD parameters to obtain multiple intrinsic mode functions (IMFs) components and a residual component. These components are then reconstructed with meteorological parameters to obtain the reconstructed IMF components and residuals. Finally, multiple LSTM sub-models are built, with each of them taking the IMF components and residual from the previous reconstruction as inputs. The sub-models are optimized using the WOA method to determine their hyperparameters and then constructed with these optimized hyperparameters. The predicted values of each IMF and residual are output and added for sequence reconstruction to derive the final predicted value of PV power. The model's effectiveness was verified for one-hour-ahead forecasting at the 1.8 MW solar system in Yulara, central Australia. The test results show that the proposed model outperforms other benchmark models, with mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and R-squared value (R2) of 15.247 kW, 19.753 kW, 4.405 % and 0.997, respectively. Compared to the LSTM, MAE, RMSE, and MAPE decreased by 84.942 %, 86.746 %, and 82.611 %, respectively, while R2 increased by 23.438 %. The proposed model has better predictive performance for both stable power changes and large fluctuations, essential for effectively integrating renewable energy sources into the power grid.

Short-term wind power prediction using a novel model based on butterfly optimization algorithm-variational mode decomposition-long short-term memory

The precise forecasting of wind power output is crucial for the integration of large-scale renewable energy generation into the power grid. It plays a vital role in ensuring safe and stable operation of power grid, diminishing fuel consumption, and minimizing environmental impacts. This research presents a machine learning prediction model that integrates intelligent optimization algorithms and data decomposition techniques for short-term wind power output forecasting. The initial phase of this research develops a prediction model utilizing variational mode decomposition and long short-term memory networks. To mitigate the randomness and uncertainty of wind energy, and improve prediction accuracy, the butterfly optimization algorithm is introduced to optimize the parameters of variational mode decomposition and long short-term memory networks. Several in-depth case studies are carried out on the actual wind power generation dataset in mainland China to confirm the feasibility and effectiveness of the proposed hybrid model. Experimental results demonstrate that the proposed model outperforms the compared model in terms of prediction accuracy across different seasons, showing good practicality and generalizability.

Improved DBO-VMD and optimized DBN-ELM based fault diagnosis for control valve

Control valves play a vital role in process production. In practical applications, control valves are prone to blockage and leakage faults. At the small control valve openings, the vibration signals exhibit the drawbacks of significant interference and weak fault characteristics, which causes subpar fault diagnosis performance. To address the issue, a diagnostic model based on optimized variational mode decomposition (VMD) and improved deep belief network-extreme learning machine (DBN-ELM) is proposed. Firstly, good point set population initialization, nonlinear convergence factor, and adaptive Gaussian–Cauchy mutation strategies are applied in the dung beetle optimization algorithm (DBO) to escape local optima. Then, the improved DBO (IDBO) is used to optimize VMD parameters to obtain a series of modal components. Next, the generalized dispersion entropy (GDE) is formed by the combination of generalized Gaussian distribution and refined composite multiscale fluctuation-based dispersion entropy. The maximum correlation coefficient modal components are applied to extract GDE. Finally, the IDBO is applied to optimize the parameters of the DBN-ELM network to improve the classification performance of control valve faults. The comparative experiment results demonstrate that the proposed model can extract effective features and the diagnostic accuracy reaches 99.87%.

Tool Wear State Identification Based on the IWOA-VMD Feature Selection Method

Complex, thin-walled components are the most important load-bearing structures in aircraft equipment. Monitoring the wear status of milling cutters is critical for enhancing the precision and efficiency of thin-walled item machining. The cutting force signals of milling cutters are non-stationary and non-linear, making it difficult to detect wear stages. In response to this issue, a system for monitoring milling cutter wear has been presented, which is based on parameterized Variational Mode Decomposition (VMD) Multiscale Permutation Entropy. Initially, an updated whale optimization technique is used, with the joint correlation coefficient serving as the fitness value for determining the VMD parameters. The improved VMD technique is then used to break down the original signal into a series of intrinsic mode functions, and the Multiscale Permutation Entropy of each effective mode is determined to generate a feature vector. Finally, a 1D Convolutional Neural Network (1D CNN) is employed as the input model for state monitoring using the feature vector. The experimental findings show that the suggested technique can efficiently extract characteristics indicating the wear condition of milling cutters, allowing for the precise monitoring of milling cutter wear states. The recognition rate is as high as 98.4375%, which is superior to those of comparable approaches.

Weak Fault Feature Extraction and Enhancement of Autonomous Underwater Vehicle Thrusters Based on Artificial Rabbits Optimization and Variational Mode Decomposition

Variational Mode Decomposition (VMD) has typically been used in weak fault feature extraction in recent years. The problem analyzed in this study is weak fault feature extraction and the enhancement of AUV thrusters based on Artificial Rabbits Optimization (ARO) and VMD. First, we introduce ARO to solve the problem of long-running times when using VMD for weak fault feature extraction. Then, we propose a VMD denoising method based on an improved ARO algorithm to address the issue of deteriorations in the fault feature extraction effect after introducing ARO. In this method, chaotic mapping and Gaussian mutation are used to improve ARO to optimize the parameters of VMD. This leads to a reduced running time and improved fault feature extraction performance. We then perform fault feature enhancement. Due to the unsatisfactory enhancement effect of traditional modified Bayes (MB) methods for weak fault features, we introduce energy operators to transform the fault signals into the energy domain for fault feature enhancement. Finally, we add differential processing to the signal to address the issue of certain fault feature values decreasing after introducing energy operators. In the end, the effectiveness of the proposed methods is verified via pool experiments on a “Beaver II” AUV prototype.

A Data-Driven Method and Hybrid Deep Learning Model for Flood Risk Prediction

Flood disasters occur worldwide, and flood risk prediction is conducive to protecting human life and property safety. Influenced by topographic changes and rainfall, the water level fluctuates randomly and violently during the flood, introducing many noises and directly increasing the difficulty of flood prediction. A data-driven flood forecasting method is proposed based on data preprocessing and a two-layer BiLSTM-Attention network to improve forecast accuracy. First, the Variational Mode Decomposition (VMD) is used to decompose the data for reducing noise and produce suitable Intrinsic Mode Functions (IMFs); Then, an optimized two-layer attention-based Bidirectional Long Sshort-Term memory (BiLSTM-Attention) network is constructed to predict each IMF. Finally, two optimization algorithms are used to obtain the optimized parameters of VMD and BiLSTM intelligently, increasing the self-adaptability. The inertia factor of particle swarm optimization is improved and then used to optimize the five hyperparameters of BiLSTM. The proposed model reduces storage errors for smaller training sets and can achieve good performance. Three water level data sets from the Yangtze River in China are used for comparative experiments. Numerical results show that the peak height absolute error is within 2 cm, and the relative error of peak time arrival is within 30%. Compared with LSTM, BiLSTM, CNN-BiLSTM-attention, etc., the proposed model reduces the root mean square error by at least 50% and has advantages for high-risk forecasting when the water level exceeds the defense line and fluctuates prominently.

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.

Multi-Step Prediction of Wind Power Based on Hybrid Model with Improved Variational Mode Decomposition and Sequence-to-Sequence Network

Due to the complexity of wind power, traditional prediction models are incapable of fully extracting the hidden features of multidimensional strong fluctuation data, which results in poor multi-step prediction performance. To predict continuous power effectively in the future, an improved wind power multi-step prediction model combining variational mode decomposition (VMD) with sequence-to-sequence (Seq2Seq) is proposed. Firstly, the wind power sequence is smoothed using VMD and the decomposition parameters of VMD are optimized by using the squirrel search algorithm (SSA) to effectively optimize the decomposition effect. Then, the subsequence obtained from decomposition, together with the original wind power data, is reconstructed into multivariate time series features. Finally, a Seq2Seq model is constructed, and convolutional neural networks (CNNs) with bidirectional gate recurrent units (BiGRUs) are used to learn the coupling and timing relationships of the input data and encode them. The gate recurrent unit (GRU) is decoded to achieve continuous power prediction. Based on the actual operating data of a wind farm, a case analysis is conducted. Experimental results show that SSA-VMD can effectively optimize the decomposition effect, and the subsequences obtained with its decomposition are highly accurate when applied to predictions. The Seq2Seq model has better multi-step prediction results than traditional prediction methods, and as the prediction step size increases, the advantages are more obvious.

Fault Location of Grid-connected Microgrid Lines Based on AVMD and Double-ended Traveling Wave Ranging

To enhance the accuracy of fault location in microgrid lines, a fault location method based on adaptive variational mode decomposition (AVMD) and double-ended traveling wave ranging is proposed. Firstly, a microgrid radial structure model, incorporating wind, light, and water systems, is established. The parameters of variational mode decomposition are optimized by using the Aquila optimizer (AO) algorithm, allowing the original fault signal to be decomposed into multiple modal components using AVMD. Only a limited number of modal components retain the fault signal information. The effective weighted peak relevance index (EWPR) is employed to select the sensitive modal components, identified as the four modes that best preserve the fault information, for signal reconstruction. Finally, the reconstructed signal is applied for fault localization. Simulation results indicate that the proposed method is scarcely influenced by the fault type, exhibiting superior accuracy compared to the single-ended traveling wave method.

Mine Surface Settlement Prediction Based on Optimized VMD and Multi-Model Combination

The accurate prediction of mining area surface deformation is essential to preventing large-scale coal mining-related surface collapse and ensure safety and daily life continuity. Monitoring subsidence in mining areas is challenged by environmental interference, causing data noise. This paper employs the Sparrow Search Algorithm, which integrates Sine Cosine and Cauchy mutation (SCSSA), to optimize variational mode decomposition (VMD) and combine multi-models for prediction. Firstly, SCSSA is employed to adaptively determine the parameters of VMD using envelope entropy as the fitness value. Subsequently, the VMD method optimized using SCSSA adaptively decomposes the original mining area subsidence data sequence into various sub-sequences. Then, SCSSA-VMD is applied to adaptively decompose the original mining subsidence data sequence into multiple sub-sequences. Meanwhile, using sample entropy, the sub-sequences are categorized into trend sequences and fluctuation sequences, and different models are employed to predict sub-sequences at different frequencies. Finally, the prediction results from different sub-sequences are integrated to obtain the final prediction of mining area subsidence. To validate the predictive performance of the established model, experiments are conducted using GNSS monitoring data from the 110801 working face of Banji Coal Mine in Bozhou. The results demonstrate the following: (1) The hybrid model enhanced the prediction accuracy and trends by decomposing the data and optimizing the parameters with VMD. It outperformed single models, reducing errors and improving predictive trends. (2) The hybrid model significantly improved the prediction accuracy for subsidence data at work surface monitoring stations. It is particularly effective at critical subsidence points, making it a valuable reference for safety in mining operations.

Variational mode decomposition based self-adaptive denoising imaging method for ultrasonic array testing of coarse-grained titanium alloys processed by additive manufacturing

The coarse columnar grain structure in titanium alloys processed by additive manufacturing leads to strong grain noise in ultrasonic testing, which affects the accurate detection and quantification of its defects. In this paper, a self-adaptive denoising imaging method for ultrasonic array testing is proposed based on variational mode decomposition (VMD). The proposed method uses VMD to decompose complex ultrasonic signals in full matrix capture (FMC) data collected by a linear ultrasonic array transducer. According to the particle swarm optimization (PSO) method, VMD parameters for FMC methods of the total focusing method (TFM), the plane wave imaging (PWI), and the Hadamard spatial encoding are self-adaptively determined. The evaluation parameters are set to select the intrinsic mode function components by VMD to complete the denoising reconstruction and imaging of FMC data. An additive-manufactured titanium alloy specimen was used to verify the improvement of defect detection capability by PSO-VMD denoising method. For a defect at large thickness in the specimen, compared with the conventional TFM and PWI methods, VMD denoising method based on the Hadamard spatial encoding can improve the signal-to-noise ratio by 7.7 dB and 9.0 dB, and reduce the quantitative error by 74 % and 68 %.

Demand-Side Electricity Load Forecasting Based on Time-Series Decomposition Combined with Kernel Extreme Learning Machine Improved by Sparrow Algorithm

With the rapid development of new power systems, power usage stations are becoming more diverse and complex. Fine-grained management of demand-side power load has become increasingly crucial. To address the accurate load forecasting needs for various demand-side power consumption types and provide data support for load management in diverse stations, this study proposes a load sequence noise reduction method. Initially, wavelet noise reduction is performed on the multiple types of load sequences collected by the power system. Subsequently, the northern goshawk optimization is employed to optimize the parameters of variational mode decomposition, ensuring the selection of the most suitable modal decomposition parameters for different load sequences. Next, the SSA–KELM model is employed to independently predict each sub-modal component. The predicted values for each sub-modal component are then aggregated to yield short-term load prediction results. The proposed load forecasting method has been verified using actual data collected from various types of power terminals. A comparison with popular load forecasting methods demonstrates the proposed method’s higher prediction accuracy and versatility. The average prediction results of load data in industrial stations can reach RMSE = 0.0098, MAE = 0.0078, MAPE = 1.3897%, and R2 = 0.9949. This method can be effectively applied to short-term load forecasting in multiple types of power stations, providing a reliable basis for accurate demand-side power load management and decision-making.

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.

Fault diagnosis method of weak vibration signal based on improved VMD and MCKD

During the manufacturing process of electronic equipment, objects such as tin beads and glue blocks may be left in the electronic equipment, causing failure of the electronic equipment. This paper uses experimental equipment to collect weak vibration signals on the surface of electronic equipment. In view of the nonlinear and non-stationary characteristics of the vibration signal and its easy to be masked by strong background noise, a fault diagnosis method of weak vibration signal based on improved variational mode decomposition (VMD) and maximum correlation kurtosis deconvolution (MCKD) is proposed. Cosine factors and adaptive weights are introduced to improve the convergence accuracy of the Whale Optimization Algorithm (WOA). The envelope spectrum peak factor is used as the adaptability function of the improved whale algorithm (IWOA) to optimize the parameters of VMD and MCKD. Firstly, based on the decomposition results of weak fault signals by IWOA-VMD, the optimal modal components are selected. Secondly, the fault impact component in the optimal modal component is enhanced based on the IWOA-MCKD algorithm. Finally, the fault characteristic frequency is extracted through the envelope spectrum. The feasibility and superiority of the proposed optimization method are verified through simulation signal analysis and actual case study.

A Two-Terminal Directional Protection Method for HVDC Transmission Lines of Current Fault Component Based on Improved VMD-Hilbert Transform

The traveling wave protection of high voltage direct current (HVDC) transmission lines is susceptible to the influence of transition resistance. As a backup protection, current differential protection has absolute selectivity, but usually requires an increase in delay to avoid misoperation caused by distributed capacitance on the line, resulting in a longer action time. Based on this, a two-terminal directional protection method for HVDC transmission lines is proposed based on Sparrow Search Algorithm (SSA)-Variational Mode Decomposition (VMD) and Hilbert phase difference. On the basis of analyzing the directional characteristics of the current fault component at both ends of the rectifier and inverter sides under different faults, SSA is first used to optimize the parameters of VMD. The residual components representing the direction of the current fault component at both ends are extracted through VMD, and then the Hilbert phase difference of the residual components at both ends is calculated to identify faults inside and outside the line area. In addition, fault pole selection can be achieved based on the ratio of the sum of multi-band Hilbert energy of single-terminal voltage fault components at the positive and negative poles. Simulation experiments have shown that the proposed protection scheme can quickly and effectively identify fault and has good tolerance to transition resistance and noise interference.

A novel non-ferrous metal price hybrid forecasting model based on data preprocessing and error correction

Accurately forecasting the price of non-ferrous metals is of great significance for traders to avoid risks, enterprises to arrange production plans, and countries to formulate economic policies. In order to improve the forecasting accuracy of non-ferrous metal prices, this paper proposes a novel non-ferrous metal price hybrid forecasting model named IVWAIEE (IVMD-WPD-ARIMA-IELM-ECD). Firstly, the original price series is decomposed into several smoother IMFs using variational mode decomposition (VMD). Simultaneously, the improved sparrow search algorithm (IFASSA) is used to optimize the parameters of VMD to improve the adaptability of VMD. Secondly, wavelet packet decomposition (WPD) is used to decompose the residual sequence generated by VMD to further extract the information in the residual sequence. Then, the components generated by VMD and WPD are defined as high frequency components and low frequency components according to the zero-crossing rate. ARIMA is used to forecast the low frequency components with gentle fluctuations, and extreme learning machine optimized by IFASSA (IELM) is used to forecast the high frequency components with strong fluctuations. The forecasting results of each component are accumulated to obtain the initial forecasting results and error sequence of the non-ferrous metal price. Next, WPD is used to further decompose the error sequence, and the error subsequence is predicted by ARIMA and IELM to obtain the error prediction results. Finally, the error prediction results are used to correct the initial forecasting results, and the final forecasting results of non-ferrous metal prices are obtained. In order to verify the superiority of the proposed model, the copper, aluminum, and zinc futures prices of the London Metal Exchange (LME) are selected as empirical data to verify the model. The results show that the proposed IVWAIEE model has better prediction accuracy and robustness than other benchmark models. Its RMSE values in predicting copper, aluminum, and zinc futures prices are 0.2238, 0.1863, and 0.2137, respectively, and MAE values are 0.1696, 0.1171, and 0.1644, respectively, which are lower than those of other benchmark models; The proposed model not only enriches the application of secondary decomposition and error correction in the field of non-ferrous metal price forecasting, but also solves the problems of insufficient adaptability and underutilization of residual sequence in the traditional variational mode decomposition method; The research results of this paper can provide scientific and effective guidance for the investment, production, and decision-making of non-ferrous metal stakeholders.

Tool Wear Monitoring Based on the Gray Wolf Optimized Variational Mode Decomposition Algorithm and Hilbert–Huang Transformation in Machining Stainless Steel

The online monitoring and prediction of tool wear are important to maintain the stability of machining processes. In most cases, the tool wear condition can be evaluated by signals such as force, sound, vibration, and temperature, which are often processed via Fourier-transform based methods, typically, the short-time Fourier transform (STFT). However, the fixed-width window function in STFT has many limitations. In this paper, a novel tool wear monitoring method based on variational mode decomposition (VMD) and Hilbert–Huang transformation (HHT) were developed to monitor the wear of carbide tools in machining stainless steel. In this method, the intrinsic mode function (IMF) was used as the fitness function, and the (K alpha) parameter sets for VMD were optimized by the gray wolf optimization (GWO). The results show that the characteristic frequency in the GWO-VMD-HHT method is more significant with no aliasing compared with the EMD-HHT method, and an obvious characteristic frequency shift phenomenon is present. By utilizing the energy value of IMF3 as the feature to classify the wear state of the cutting tool, the increase of energy reached 85.48% when 260–315 milling passes were in severe wear state. GWO, which can accurately find the best parameters for VMD, not only solves the problem that the Entropy Function is not suitable for force signals, but also provides reference for the selection of parameters of VMD.

Coal-rock drilling states recognition of drilling robot for rockburst prevention based on multi-sensor information fusion

Accurate recognition of coal-rock drilling sates is a prerequisite for achieving intelligent drilling pressure relief. In this paper, a novel coal-rock drilling states recognition method of drilling robot for rockburst prevention is proposed. Firstly, different coal-rock drilling signals are collected and processed by using improved antlion optimization (ALO) algorithm and variational mode decomposition (VMD). Meanwhile, the elite opposition-based learning (EOL) strategy is used to improve the global search ability and optimization performance of ALO, and the EOL-ALO is developed and employed to automatically search the optimal key parameters of VMD. Subsequently, the root mean square of frequency and kurtosis are used to extract the feature information from the decomposed signals and the singular value decomposition method is employed to reduce the dimensionality of high-dimensional feature vectors. Furthermore, an improved D-S evidence theory is developed to fuse the recognition results of support vector machine through a single sensor information and the fusion recognition framework of coal-rock drilling states is designed. Finally, a coal-rock drilling experimental platform is established and some experimental analysis is carried out. The experimental results indicate the feasibility and superiority of proposed coal-rock drilling states recognition method.

Application of Auto-Regulative Sparse Variational Mode Decomposition in Mechanical Fault Diagnosis

The variational mode decomposition (VMD) method has been widely applied in the field of mechanical fault diagnosis as an excellent non-recursive signal processing tool. The performance of VMD depends on its inherent prior parameters. Searching for the key parameters of VMD using intelligent optimization algorithms poses challenges for the internal essence and fitness function selection of intelligent optimization algorithm. Moreover, the computational complexity of optimization is high. Meanwhile, such methods are not competitive in evaluating orthogonality between intrinsic mode functions and the reconstruction error of the signal as a joint indictor for the termination of decomposition. Therefore, this paper proposes a new auto-regulative sparse variational mode decomposition method (ASparse–VMD) to achieve accurate feature extraction. The regularization term of the VMD handles sparsification by constructing an L2-norm with a damping coefficient ε, and mode number K is set adaptively in a recursive manner to ensure appropriateness. The penalty parameter α is dynamically selected according to the number of modes and sampling frequency. The update step τ of the VMD algorithm is set using the signal-to-noise ratio to ensure the singleness and orthogonality of the modal components and suppress mode aliasing. The experimental results of the simulation signal and measured signal demonstrate the effectiveness of the proposed strategies for improving the inherent defects of VMD. Extensive comparisons with state-of-the-art methods show that the proposed algorithm is more effective and practical for hybrid feature extraction in mechanical faults.α