Dynamically Tuned Variational Mode Decomposition and Convolutional Bidirectional Gated Recurrent Unit Algorithm for Coastal Sea Level Prediction

The research about online monitoring and leakage automatic location of water distribution networks (WDN) has a wide range of applications that include water resource protection, monitoring, and allocation. Variational mode decomposition (VMD) and cross-correlation (CC) based leakage location is a popular and effective method in WDN. However, the value of K intrinsic mode functions (IMFs) based on VMD decomposition needs to be determined artificially, which affects the separation effect of signal frequency band characteristics directly. Hence, this work proposes an adaptive method to determine the parameter K of leakage vibration signal’s IMFs, which will be applied to automatic leakage location in WDN. Firstly, the number of saddle points in the frequency domain envelope of the sampled signal in different step sizes is calculated. The parameter K is determined according to the curvature change of the number of saddle points and the sampled signal. Finally, the selective IMFs are reconstituted into a new signal, which can determine a leak position using CC based time-delay estimation (TDE). To verify the effectiveness of the proposed algorithm, the different methods based on EMD and Fast ICA are compared. The experimental results demonstrate that the proposed parameter K value adaptive VMD (KVA-VMD) decomposition method is more suitable for leakage location in WDN.

Variational Mode Decomposition (VMD) is widely used for inspection purposes. The initial parameters are usually set manually, which is a limitation of this technique. In this paper, a method to automatically select these parameters through a combination of Singular Value Decomposition (SVD) and Improved-VMD (IVMD) is proposed. VMD is applied multiple times with a varying K-value parameter. The original signal and its sub-signals arising from VMD decomposition are all subjected to SVD. An index representing the relevance between sub-signals and the original signal is obtained by comparing eigenvalues, which are calculated by SVD. The result shows the effectiveness of VMD with different initial K-value parameters. SVD is then further applied to the VMD result for the selected K-value parameter to obtain Shannon entropy, which can be used in the detection and classification of corrosion on the underside of the rail. Comparing with current energy-based methods, the Shannon entropy obtained by IVMD–SVD has the advantage of reducing environmental interference to obtain more uniform energy results. The proposed method can improve the effectiveness of VMD for the impact response signal. The classification of underside corrosion of rails can be realised according to the results obtained from the proposed method.

In order to solve the problem that it is difficult to extract slight fault features in the process of fault diagnosis of rolling bearing, this paper proposes a fault diagnosis method based on variational mode decomposition (VMD) and modified convolution neural network (CNN). Firstly, in the process of eigenvalue extraction, VMD decomposition is used to extract more fault feature details of rolling bearing vibration signals; then, dense block and other methods are applied in the network with fewer layers; finally, global average pooling is used instead of full connection layer for the complex calculation of full connection layer. Through the diagnosis experiments of different fault conditions of rolling bearing, it is proved that the proposed method can improve the fault recognition rate and has good feasibility.

To enhance the precision of rolling bearing fault diagnosis, an intelligent hybrid approach is proposed in this paper for signal processing and fault diagnosis in small samples. This approach is based on advanced techniques, combining parameter optimization variational mode decomposition weighted by multiscale permutation entropy (MPE) with maximal information coefficient and multi-target attention convolutional neural networks (MTACNN). First, an improved variational mode decomposition (VMD) is developed to denoise the raw signal. The whale optimization algorithm was used to optimize the penalty factor and mode component number in the VMD algorithm to obtain several intrinsic mode functions (IMFs). Second, separate MPE calculations are performed for both the raw signal and each of the IMF components obtained from the VMD decomposition; the results are used to calculate the maximum information coefficient (MIC). Subsequently, each MIC is normalized and converted to a weight coefficient for signal reconstruction. Ultimately, the reconstructed signals serve as input to the MTACNN for diagnosing rolling bearing faults. Results demonstrate that the signal processing approach exhibits superior noise reduction capability through simple processing. Furthermore, compared to several similar approaches, The method proposed for fault diagnosis achieves superior performance levels in the fault pattern recognition target and the fault severity recognition target.

The volatility and randomness of wind power generation pose significant challenges to grid integration and dispatching. Accurate wind power forecasting is crucial for ensuring grid security and optimizing dispatching strategies. This study proposes an ultra‐short‐term wind power forecasting model based on Variational Mode Decomposition (VMD) and an adaptive weighting integration mechanism. The model first employs VMD to decompose wind power time series into multiple Intrinsic Mode Functions (IMFs) to extract latent multiscale features. Subsequently, Convolutional Neural Networks (CNN) and Long Short‐Term Memory networks (LSTM) are utilized to independently model the IMFs, capturing spatial features and temporal dependencies. The outputs of CNN and LSTM are then dynamically weighted using an attention mechanism to adaptively enhance the representation of critical features. Finally, the predictions of CNN and LSTM are integrated using a Gradient Boosting Decision Tree (GBDT) meta‐learner to produce the final output. Experimental results on wind farm data from Xinjiang, China, demonstrate that the proposed model significantly outperforms traditional and state‐of‐the‐art forecasting methods in terms of accuracy and robustness, especially in handling the nonlinear and nonstationary characteristics of wind power.

In order to solve the difficulties that the uncertain characteristics of PV output, such as volatility and intermittency, will bring to the development of microgrid scheduling plans, this paper proposes a Transformer–Bidirectional Long Short-Term Memory (BiLSTM) neural network PV power generation forecasting fusion model based on the Newton–Raphson optimization algorithm (NRBO) and Variational Modal Decomposition (VMD). Firstly, the principle of the VMD technique and the Gray Wolf Optimization (GWO) algorithm’s key parameter optimization method for VMD are introduced. Then, the Transformer decoder partially fuses the BiLSTM network and retains the encoder to obtain the body of the prediction model, followed by explaining the principle of the NRBO algorithm. And finally, the VMD-NRBO-Transformer-BiLSTM prediction model and hyperparameter selection are evaluated by the NRBO algorithm. The algorithm sets up a multi-model comparison experiment, and the results show that the prediction model proposed in this paper has the best prediction accuracy and the optimal evaluation index.

To address the noise issue in the measured vibration signals of spillway radial gate discharge, this paper utilizes the Multiverse Optimization Algorithm (MVO) to optimize the number of decomposition modes (K) and the penalty factor (α) in Variational Mode Decomposition (VMD). This approach ensures improved efficiency of VMD decomposition while maintaining accuracy. Subsequently, the obtained Intrinsic Mode Functions (IMFs) from VMD decomposition are classified based on Multi-scale Permutation Entropy (MPE). IMFs are divided into pure components and noisy components; the noisy components are processed with Wavelet Threshold Denoising (WTD), while the pure components are overlaid and reconstructed to obtain the denoised vibration signal of the gate. Comprehensive comparisons involving artificial signal simulations, gate flow-induced vibration model tests, and numerical simulations lead to the following conclusions: compared to other algorithms, the proposed combined denoising method (MVO-VMD-MPE-WTD) achieves the highest signal-to-noise ratio (SNR) in both the frequency and time domains for artificial signals, while yielding the lowest mean square error (MSE). In the gate flow-induced vibration model tests, the method significantly reduces noise in the vibration signals and effectively preserves characteristic information. The error in preserving characteristic information across model tests and numerical simulations is kept below 1%. Furthermore, compared to other optimization algorithms, the MVO demonstrates higher computational efficiency. The parameter-optimized combined denoising method proposed in this study provides insights into denoising measured vibration signals of hydraulic spillway radial gates and other drainage structures, and it opens possibilities for exploring more efficient optimization algorithms for achieving online monitoring in the future.

This paper outlines time series data analysis from Varna tidal station (Black sea, Bulgaria), with the objective being to determine the influences of long-period and short-period tides. Observations series from monthly mean sea level values cover the period 1928-2023. The sea level measurements until 2013 were done with a mechanical float tide gauge. Since 2013 a radar tide gauge was installed in place of the mechanical one. A least squares linear regression model was applied for the analysis of monthly sea level data. As a result of the analysis, mean sea level, trend, seasonal and long-term tidal influences were established. In order to determine the influence of short-term tides, the method of least squares harmonic analysis was applied. In this method, observed sea level values are considered to be represented as a sum of tidal harmonics operating at previously known frequencies. The observation data include hourly values for the period 06.2013-12.2023. Some of the advantages of the applied method are that it allows to analyze series with interruptions in the observations, as well as assist to easily determine tides with close frequencies. From the analysis was determined the influence of: the annual and semi-annual tides, as well as about 68 short-period tides.

A novel hybrid algorithm based on Empirical Fourier decomposition and deep learning for wind speed forecasting

In this application medical images of different modalities are used for image analysis and fusion. For final fusion MRI (Magnetic Resonance Imaging) and CT (Computed Tomography) images are taken as input and which gives fused image as output. This fused image has more information than individual images. Proposed method uses VMD (Variational Mode Decomposition) decomposition method and IMF method for fusion. Final fused image is compared with individual MRI and CT image using different metrics such as entropy, mutual information, edge intensity, PSNR, SSIM, MSE etc. Proposed method used CNN (Convolutional Neural Network) for analysis of fused image and to predict the final results as a normal scan or scan with tumor. Proposed CNN model finds results very perfectly than state of art machine learning models.

A novel integrated method based on a machine learning model for estimating evapotranspiration in dryland

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

Sea level prediction is essential information for citizens who live in the coastal area and plan to build structures, especially in the construction stage around the inshore and offshore locations. The statistical method and tidal harmonic analysis have been used to predict the sea level but require long terms historical sea level data to achieve reasonable accuracy. This paper uses Transformer deep learning approaches to predict sea data levels. This paper uses only four months of data in Pangandaran, Indonesia. We use the sea level dataset obtained from the Inexpensive Device for Sea Level measurement (IDSL). The model is trained to predict 1, 7, and 14 days. We also study the sensitivity of the model in terms of lookbacks. The performance of the Transformer was compared with two other popular deep-learning methods; RNN and LSTM. To forecast 14 days, the Transformer model results in a higher coefficient correlation (CC) of 0.993 and a lower root mean squared error (RMSE) value of 0.055 compared to the other two models. Moreover, the Transformer has a faster computing performance than the other two models.

For existing offline real-time fault diagnosis systems for vehicle control motors, efficient and accurate fault detection remains challenging due to weak vibration fault signals under varying working conditions, significant noise interference, and high model complexity. This paper proposes a fault diagnosis method based on the acoustic-vibration signal fusion. The diagnostic framework comprises four modules: raw signal acquisition, data preprocessing, multi-sensor signal fusion, and network-based diagnosis. First, sound and vibration signals are collected using an NVH test rig. The signals are then decomposed and reconstructed using Pearson correlation coefficient filtering, with parameters of the variational mode decomposition optimized by the gray wolf optimization algorithm. Next, the reconstructed signals undergo continuous wavelet transform to produce time–frequency representations, and a multimodal feature fusion network is employed to integrate the sound and vibration signals. Finally, fault detection and classification are achieved by training an enhanced MobileNetV2 network. Experimental results show that this method outperforms single-sensor approaches and other comparative techniques in diagnostic accuracy under variable operating conditions. Furthermore, the total processing time for offline inspection is less than 30 s, meeting the real-time diagnostic requirements for automotive control motors.

Medium-term prediction of atmospheric PM2.5 concentration based on the VG-TCABI hybrid architecture.