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As the sound signal of ships obtained by sensors contains other many significant characteristics of ships and called ship-radiated noise (SN), research into a denoising algorithm and its application has obtained great significance. Using the advantage of variational mode decomposition (VMD) combined with the correlation coefficient for denoising, a hybrid secondary denoising algorithm is proposed using secondary VMD combined with a correlation coefficient (CC). First, different kinds of simulation signals are decomposed into several bandwidth-limited intrinsic mode functions (IMFs) using VMD, where the decomposition number by VMD is equal to the number by empirical mode decomposition (EMD); then, the CCs between the IMFs and the simulation signal are calculated respectively. The noise IMFs are identified by the CC threshold and the rest of the IMFs are reconstructed in order to realize the first denoising process. Finally, secondary denoising of the simulation signal can be accomplished by repeating the above steps of decomposition, screening and reconstruction. The final denoising result is determined according to the CC threshold. The denoising effect is compared under the different signal-to-noise ratio and the time of decomposition by VMD. Experimental results show the validity of the proposed denoising algorithm using secondary VMD (2VMD) combined with CC compared to EMD denoising, ensemble EMD (EEMD) denoising, VMD denoising and cubic VMD (3VMD) denoising, as well as two denoising algorithms presented recently. The proposed denoising algorithm is applied to feature extraction and classification for SN signals, which can effectively improve the recognition rate of different kinds of ships.

To improve the reliability of Global Positioning System (GPS) signal extraction, the traditional variational mode decomposition (VMD) method cannot determine the number of intrinsic modal functions or the value of the penalty factor in the process of noise reduction, which leads to inadequate or over-decomposition in time series analysis and will cause problems. Therefore, in this paper, a new approach using improved variational mode decomposition and wavelet packet transform (IVMD-WPT) was proposed, which takes the energy entropy mutual information as the objective function and uses the grasshopper optimisation algorithm to optimise the objective function to adaptively determine the number of modal decompositions and the value of the penalty factor to verify the validity of the IVMD-WPT algorithm. We performed a test experiment with two groups of simulation time series and three indicators: root mean square error (RMSE), correlation coefficient (CC) and signal-to-noise ratio (SNR). These indicators were used to evaluate the noise reduction effect. The simulation results showed that IVMD-WPT was better than the traditional empirical mode decomposition and improved variational mode decomposition (IVMD) methods and that the RMSE decreased by 0.084 and 0.0715 mm; CC and SNR increased by 0.0005 and 0.0004 dB, and 862.28 and 6.17 dB, respectively. The simulation experiments verify the effectiveness of the proposed algorithm. Finally, we performed an analysis with 100 real GPS height time series from the Crustal Movement Observation Network of China (CMONOC). The results showed that the RMSE decreased by 11.4648 and 6.7322 mm, and CC and SNR increased by 0.1458 and 0.0588 dB, and 32.6773 and 26.3918 dB, respectively. In summary, the IVMD-WPT algorithm can adaptively determine the number of decomposition modal functions of VMD and the optimal combination of penalty factors; it helps to further extract effective information for noise and can perfectly retain useful information in the original time series.

【Background and Objective】Accurate prediction of dam deformation is crucial for ensuring the safety of dam structures in engineering monitoring. Dam deformation is influenced by multiple factors, including water pressure, temperature, and material aging, which often exhibit nonlinear and dynamic relationships. During monitoring, system noise and observation errors frequently interfere with data quality, posing additional challenges for analysis. To address the challenges posed by system noise and strong nonlinear effects in dam deformation, this paper proposes a dam deformation monitoring model based on multi-layer integrated signal processing technology.【Method】The model uses sample entropy reconstruction and the K-means clustering algorithm to optimize the adaptive noise complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) process, generating multiple intrinsic mode functions (IMF). High-frequency modal components undergo secondary decomposition using variational mode decomposition (VMD) to extract the optimal intrinsic mode function. Finally, an improved symbiotic biological search algorithm combined with a Bidirectional Gated Recurrent Unit (BiGRU) is used to accurately predict dam deformation.【Result】Case analysis demonstrates that, compared to traditional prediction models, the proposed model achieves a root mean square error (RMSE) of 0.031 9 mm, mean absolute error (MAE) of 0.015 3 mm, mean absolute percentage error (MAPE) of 2.51%, and determination coefficient (R2) of 0.971 2.【Conclusion】 The results verify that the proposed model captures and simulates the dam deformation process more accurately, exhibiting higher prediction accuracy and stronger generalization ability.

Complex variational mode decomposition (CVMD) has been proposed to extend the original variational mode decomposition (VMD) algorithm to analyze complex-valued data. Conventionally, CVMD divides complex-valued data into positive and negative frequency components using bandpass filters, which leads to difficulties in decomposing signals with the low-frequency trend. Moreover, both decomposition number parameters of positive and negative frequency components are required as prior knowledge in CVMD, which is difficult to satisfy in practice. This paper proposes a modified complex variational mode decomposition (MCVMD) method. First, the complex-valued data are upsampled through zero padding in the frequency domain. Second, the negative frequency component of upsampled data are shifted to be positive. Properties of analytical signals are used to get the real-valued data for standard variational mode decomposition and the complex-valued decomposition results after frequency shifting back. Compared with the conventional method, the MCVMD method gives a better decomposition of the low-frequency signal and requires less prior knowledge about the decomposition number. The equivalent filter bank structure is illustrated to analyze the behavior of MCVMD, and the MCVMD bi-directional Hilbert spectrum is provided to give the time–frequency representation. The effectiveness of the proposed algorithm is verified by both synthetic and real-world complex-valued signals.

The data-driven method is an important tool in the field of underwater acoustic signal processing. In order to realize the feature extraction of ship-radiated noise (S-RN), we proposed a data-driven optimization method called improved variational mode decomposition (IVMD). IVMD, as an improved method of variational mode decomposition (VMD), solved the problem of choosing decomposition layers for VMD by using a frequency-aided method. Furthermore, a novel method of feature extraction for S-RN, which combines IVMD and sample entropy (SE), is put forward in this paper. In this study, four types of S-RN signals are decomposed into a group of intrinsic mode functions (IMFs) by IVMD. Then, SEs of all IMFs are calculated. SEs are different in the maximum energy IMFs (EIMFs), thus, SE of the EIMF is seen as a novel feature for S-RN. To verify the effectiveness of the proposed method, a comparison has been conducted by comparing features of center frequency and SE of the EIMF by IVMD, empirical mode decomposition (EMD) and ensemble EMD (EEMD). The analysis results show that the feature of S-RN can be obtain efficiently and accurately by using the proposed method.

To address the instability of wind power caused by the randomness and intermittency of wind generation, as well as the challenges in power compensation by hybrid energy storage systems (HESSs), this paper proposes a state of charge (SOC) balancing control strategy based on Successive Variational Mode Decomposition and multi-fuzzy control. First, a consensus algorithm is used to enable communication between energy storage units to obtain the global average SOC. Then, the Secretary Bird Optimization Algorithm (SBOA) is applied to optimize the Successive Variational Mode Decomposition (SVMD) and Variational Mode Decomposition (VMD) for the initial allocation of wind power, resulting in the smoothing power for hybrid energy storage and the grid integration power. Finally, considering the deviation between the current SOC of the storage units and the global average SOC, dynamic partitioning is used for multi-fuzzy control to adjust the initial power allocation, achieving SOC balancing control. Simulations of the control strategy were conducted using Matlab/Simulink, and the results indicate that the proposed approach effectively smooths wind power fluctuations, achieving stable grid integration power. It enables the SOC of the HESS to quickly align with the global average SOC, preventing the HESS from entering unhealthy SOC regions.

Rolling bearings are key components of rotary machines. To ensure early effective fault diagnosis for bearings, a new rolling bearing fault diagnosis method based on variational mode decomposition (VMD) and an improved kernel extreme learning machine (KELM) is proposed in this paper. A fault signal is decomposed via VMD to obtain the intrinsic mode function (IMF) components, and the approximate entropy (ApEn) of the IMF component containing the main fault information is calculated. An eigenvector is created from the approximate entropy of each component. A bearing diagnosis model is created via a KELM; the KELM parameters are optimized using the particle swarm optimization (PSO) algorithm to obtain a KELM diagnosis model with optimal parameters. Finally, the effectiveness of the diagnosis method proposed in this paper is verified via a fan bearing fault diagnosis test. Under identical conditions, the result is compared with the results obtained using a back propagation (BP) neural network, a conventional extreme learning machine (ELM), and a support vector machine (SVM). The test result shows that the method proposed in this paper is superior to the other three methods in terms of diagnostic accuracy.

Electrocardiogram (ECG) is mainly utilized for diagnosing heart diseases. However, various noises can influence the diagnostic accuracy. This paper presents a novel algorithm for denoising ECG signals by employing the Controlled Energy Constraint-Variational Mode Decomposition (CEC-VMD). Firstly, the noisy ECG signal is decomposed using CEC-VMD to obtain a set of intrinsic mode functions (IMFs) and a residual r. A modulation factor is utilized to minimize the modal information contained in the decomposed residuals. Furthermore, this paper presents an update formula for the modal and central frequencies based on ADMM. Finally, all the IMFs are integrated to obtain the ECG signal after denoising. By varying the value of the modulation factor, not only is the spectral energy loss of each mode reduced, but the orthogonality between the modes is also improved to better concentrate the energy of each mode. The experiments on simulated signals and MIT-BIH signals show that the average SNR after CEC-VMD denoising is 22.5139, the RMSE is 0.1128, and the CC is 0.9882. In addition, the proposed algorithm effectively improves the classification accuracy values, which are 99.0% and 99.9% for the SVM and KNN classifiers, respectively. These values are improved compared with those of EMD, VMD, SWT, SVD-VMD, and VMD-SWT. The proposed CEC-VMD technique for denoising ECG signals removes noise and better preserves features.

Sea level rise (SLR) attributed to the melting of ice caps and thermal expansion of seawater is of great global significance to vast populations of people residing along the world’s coastlines. The extent of SLR’s impact on physical coastal areas is determined by multiple factors such as geographical location, coastal structure, wetland vegetation and related oceanic changes. For coastal communities at risk of inundation and coastal erosion due to SLR, the modelling and projection of future sea levels can provide the information necessary to prepare and adapt to gradual sea level rise over several years. In the following study, a new model for predicting future sea levels is presented, which focusses on two tide gauge locations (Darwin and Milner Bay) in the Northern Territory (NT), Australia. Historical data from the Australian Bureau of Meteorology (BOM) from 1990 to 2022 are used for data training and prediction using artificial intelligence models and computation of mean sea level (MSL) linear projection. The study employs a new double data decomposition approach using Multivariate Variational Mode Decomposition (MVMD) and Successive Variational Mode Decomposition (SVMD) with dimensionality reduction techniques of Principal Component Analysis (PCA) for data modelling using four artificial intelligence models (Support Vector Regression (SVR), Adaptive Boosting Regressor (AdaBoost), Multilayer Perceptron (MLP), and Convolutional Neural Network–Bidirectional Gated Recurrent Unit (CNN-BiGRU). It proposes a deep learning hybrid CNN-BiGRU model for sea level prediction, which is benchmarked by SVR, AdaBoost, and MLP. MVMD-SVMD-CNN-BiGRU hybrid models achieved the highest performance values of 0.9979 (d), 0.996 (NS), 0.9409 (L); and 0.998 (d), 0.9959 (NS), 0.9413 (L) for Milner Bay and Darwin, respectively. It also attained the lowest error values of 0.1016 (RMSE), 0.0782 (MABE), 2.3699 (RRMSE), and 2.4123 (MAPE) for Darwin and 0.0248 (RMSE), 0.0189 (MABE), 1.9901 (RRMSE), and 1.7486 (MAPE) for Milner Bay. The mean sea level (MSL) trend analysis showed a rise of 6.1 ± 1.1 mm and 5.6 ± 1.5 mm for Darwin and Milner Bay, respectively, from 1990 to 2022.

The spectral decomposition is a valuable tool for improving the resolution of seismic interpretation, and thus can improve the accuracy of the subtle geo-features (thin and narrow channels, thin reservoirs, etc.). Variational mode decomposition (VMD) is an adaptive signal decomposition algorithm that non-recursively decomposes multicomponent signals into several band-limited intrinsic mode functions, which is competitive in enhancing time-frequency resolution. However, discontinuity is normally caused by the trace-by-trace process, making the 3D seismic interpretation difficult. To address this issue, we present a novel seismic geological channel detection method for 3D seismic dataset based on multi-trace variational mode decomposition (MTVMD). The proposed method decomposes the broadband seismic data into several intrinsic mode functions and then computes seismic attributes from each component for geological feature analysis. Further tested by field seismic case, the proposed method demonstrates strength in depicting the detailed edges and sedimentary signatures of paleochannels. Overall, the proposed method provides an alternative approach to identifying seismic channels, especially for the detailed portrayals of subtle geo-features in low-quality seismic data.