The guided ultrasonic wave (GUW) is extensively employed in non-destructive testing (NDT) for the purpose of detecting defects in aerospace vehicles, oil pipelines and mechanical equipment. The filtration of GUW signals, which often contain substantial environmental noise, is a crucial procedure in signal processing. This paper presents a novel denoising approach that combines Variational Mode Decomposition (VMD) with an enhanced Singular Value Decomposition (SVD). The VMD method is employed to preprocess the initial signal, thereby segregating the signal component from the noise component. Subsequently, the SampEn-SVD (Sample Entropy-SVD) method is utilized to extract the effective component from the VMD-preprocessed noise component. Finally, the VMD-preprocessed signal component and the SampEn-SVD-processed effective component are combined to yield the resultant signal, which effectively filters out the noise. The efficacy of this integrated denoising approach is substantiated through the examination of experimental signals. Furthermore, a comparative analysis is conducted to evaluate the efficacy of this method in relation to other denoising techniques. The results indicate that the SampEn-SVD method yields a superior signal-to-noise ratio (SNR) when processing the GUW signal transmitted through the steel strand. Moreover, the denoising procedure significantly reduces the discretization of characteristic parameters in the signal waveform, thereby addressing the issue of inadequate reproducibility in testing outcomes. Consequently, the denoised signal exhibits high fidelity and demonstrates a strong correlation between its combined eigenvector and strand stress.

GNSS time series prediction plays a significant role in monitoring crustal plate motion, landslide detection, and maintenance of the global coordinate framework. Long Short-Term Memory (LSTM), a deep learning model has been widely applied in the field of high-precision time series prediction especially when combined with Variational Mode Decomposition (VMD) to form the VMD-LSTM hybrid model. To further improve the prediction accuracy of the VMD-LSTM model, this paper proposes a dual variational modal decomposition long short-term memory (DVMD-LSTM) model to effectively handle the noise in GNSS time series prediction. This model extracts fluctuation features from the residual terms obtained after VMD decomposition to reduce the prediction errors associated with residual terms in the VMD-LSTM model. Daily E, N, and U coordinate data recorded at multiple GNSS stations between 2000 and 2022 are used to validate the performance of the proposed DVMD-LSTM model. The experimental results demonstrate that compared to the VMD-LSTM model, the DVMD-LSTM model achieves significant improvements in prediction performance across all measurement stations. The average RMSE is reduced by 9.86%, and the average MAE is reduced by 9.44%. Furthermore, the average accuracy of the optimal noise model for the predicted results is improved by 36.50%, and the average speed accuracy of the predicted results is enhanced by 33.02%. These findings collectively attest to the superior predictive capabilities of the DVMD-LSTM model, thereby enhancing the reliability of the predicted results.

Changes in sea level exhibit nonlinearity, nonstationarity, and multivariable characteristics, making traditional time series forecasting methods less effective in producing satisfactory results. To enhance the accuracy of the predictions of changes in sea level, this study introduced an improved VMD–EEMD–LSTM hybrid model. This model decomposes satellite altimetry data from near the Dutch coast using VMD, resulting in components of the Intrinsic Mode Function (IMF) with various frequencies and a residual sequence. EEMD further dissects the residual sequence obtained from VMD into second-order components. These IMFs decomposed by VMD and EEMD are utilized as features in the LSTM model for making predictions, culminating in the final forecasted results. The experimental results demonstrated significant improvements in the predictive performance compared with the VMD–LSTM model. The RMSE (root mean square error) decreased by an average of 58.68%, the MAE (mean absolute error) reduced by an average of 59.96%, and the R2 (coefficient of determination) increased by an average of 49.85% compared with the VMD–LSTM model. In comparison with the EEMD–LSTM model, the RMSE decreased by an average of 26.95%, the MAE decreased by an average of 28.00%, and the R2 increased by an average of 6.53%. The VMD–EEMD–LSTM model exhibited significantly improved predictive performance.

When overhead lines are impacted by lightning, the traveling wave of the fault contains a wealth of fault information. The accurate extraction of feature quantities from transient components and their classification is fundamental to the identification of lightning faults. The extraction process may involve modal aliasing, optimal wavelet base issues, and inconsistencies between the lightning strike distance and the fault point, which have the potential to impact the effectiveness of recognition. This paper presents a method for identifying lightning strike faults by utilizing Kullback-Leibler (KL) divergence enhanced Variational Mode Decomposition (VMD) and Symmetric Geometry Mode Decomposition (SGMD) improved with Permutation Entropy (PE) to address the aforementioned issues. A model of a 220 kV overhead line is constructed using real faults to replicate scenarios of winding strike, counterstrike, and short-circuit. The three-phase voltage is chosen and then sub-jected to Karenbaren decoupling in order to transform it into zero mode, line mode 1, and line mode 2. The zero mode voltage is decomposed using KL-VMD and PE-SGMD methods, and lightning identification criteria are developed based on various transient energy ratios. The research findings demonstrate that the criteria effectively differentiate between winding strike, counterstrike, and short-circuit faults, thus confirming the accuracy and efficacy of the lightning fault identification criteria utilizing KL-VMD and PE-SGMD.

Advancements in technology, policies, and cost reductions have led to rapid growth in wind power production. One of the major challenges in wind energy production is the instability of wind power generation due to weather changes. Efficient power grid management requires accurate power output forecasting. New wind energy forecasting methods based on deep learning are better than traditional methods, like numerical weather prediction, statistical models, and machine learning models. This is more true for short-term prediction. Since there is a relationship between methods, climates, and forecasting complexity, forecasting methods do not always perform the same depending on the climate and terrain of the data source. This paper proposes a novel model that combines the variational mode decomposition method with a long short-term memory model, developed for next-hour wind speed prediction in a hot desert climate, such as the climate in Saudi Arabia. We compared the proposed model performance to two other hybrid models, six deep learning models, and four machine learning models using different feature sets. Also, we tested the proposed model on data from different climates, Caracas and Toronto. The proposed model showed a forecast skill between 61% to 74% based on mean absolute error, 64% to 72% based on root mean square error, and 59% to 68% based on mean absolute percentage error for locations in Saudi Arabia.

As one of the fastest-growing new energy sources, wind power technology has attracted widespread attention from all over the world. In order to improve the quality of wind power generation, wind speed prediction is an indispensable task. In this paper, an error correction based Variational Mode Decomposition and Broad Learning System (VMD-BLS) hybrid model is proposed for wind speed prediction. First, the wind speed is decomposed into multiple components by the VMD algorithm, and then an ARMA model is established for each component to find the optimal number of sequence divisions. Second, the BLS model is used to predict each component, and the prediction results are summed to obtain the wind speed forecast value. However, in some traditional methods, there is always time lag, which will reduce the forecast accuracy. To deal with this, a novel error correction technique is developed by utilizing BLS. Through verification experiment with actual data, it proves that the proposed method can reduce the phenomenon of prediction lag, and can achieve higher prediction accuracy than traditional approaches, which shows our method’s effectiveness in practice.

Directional protective relaying based on amplitude comparison of traveling wave on continuous co-phase auto-transformer(AT) power transmission system was proposed. Phase-model transformation is used for decoupling transient fault signals and get aerial mode component. The forward and backward traveling wave are obtained by calculating aerial mode component, then the intrinsic mode function(IMF) components can be obtained through Variational Mode Decomposition(VMD), the module maxima are obtained through calculating the IMF components. The fault direction is determined by the ratio of fault components. If two faults relays at the ends of electric traction networks detect a fault to be in the forward direction, the fault occurred in the internal area, the protection would operate properly. The simulation tests indicate that the protection scheme is feasible, and the proposed protection method can discriminate internal faults from external faults under various fault types, and its performances are immune to fault initial angle, ground resistance, etc.