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Signal Processing is, arguably, the fundamental enabling technology for vibration-based Structural Health Monitoring (SHM), which includes damage detection and more advanced tasks. However, the investigation of real-life vibration measurements is quite compelling. For a better understanding of its dynamic behaviour, a multi-degree-of-freedom system should be efficiently decomposed into its independent components. However, the target structure may be affected by (damage-related or not) nonlinearities, which appear as noise-like distortions in its vibrational response. This response can be nonstationary as well and thus requires a time-frequency analysis. Adaptive mode decomposition methods are the most apt strategy under these circumstances. Here, a shortlist of three well-established algorithms has been selected for an in-depth analysis. These signal decomposition approaches—namely, the Empirical Mode Decomposition (EMD), the Hilbert Vibration Decomposition (HVD), and the Variational Mode Decomposition (VMD)—are deemed to be the most representative ones because of their extensive use and favourable reception from the research community. The main aspects and properties of these data-adaptive methods, as well as their advantages, limitations, and drawbacks, are discussed and compared. Then, the potentialities of the three algorithms are assessed firstly on a numerical case study and then on a well-known experimental benchmark, including nonlinear cases and nonstationary signals.

Precipitation forecasting is vital for managing disasters, urban traffic, and agriculture. This study develops an improved model for short-term precipitation forecasting by combining Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Gated Recurrent Unit (GRU). Using precipitation data from January 1, 2019, to December 31, 2022, as a sample, the model capitalizes on CEEMDAN’s superior signal decomposition capabilities and GRU’s ability to capture nonlinear dynamic patterns in time series. To assess the model’s effectiveness, comparisons were conducted with 12 benchmark models, including CEEMDAN-LSTM, EMD-GRU, EMD-LSTM, BI-LSTM, GRU, LSTM, and TCN. The results demonstrate that the CEEMDAN-GRU model achieves higher accuracy and stability in short-term precipitation forecasting. Leveraging an Adam optimizer with adaptive learning rate reduction enhances convergence and ensures reliable predictions, achieving an R²of 0.7915, MAE of 0.05382, and MSE of 0.09081.

Accurate electric load forecasting can provide critical support to makers of energy policy and managers of power systems. The support vector regression (SVR) model can be hybridized with novel meta-heuristic algorithms not only to identify fluctuations and the nonlinear tendencies of electric loads, but also to generate satisfactory forecasts. However, many such algorithms have numerous drawbacks, such as a low population diversity and trapping at local optima, which are problems of premature convergence. Accordingly, approaches to increase the accuracy of forecasting must be developed. In this investigation, quantum computing mechanism is used to quantamize dragonfly behaviors to enhance the searching effectiveness of the dragonfly algorithm, namely QDA. In addition, conducting the data preprocessing by the complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) is useful to improve the forecasting accuracy. Thus, a new electric load forecasting model, the CEEMDAN-SVRQDA model, that combines the CEEMDAN and hybridizes the QDA with an SVR model, is proposed to provide more accurate forecasts. Two numerical examples from the Tokyo Electric Power Company (Japan) and the National Grid (UK) demonstrate that the proposed model outperforms other models.

Identification of multiple mechanical faults from vibration signals has always been one of the most challenging tasks in the field of condition monitoring and fault diagnosis. This study proposes a new fault-oriented vibration signal decomposition method, called adaptive feature mode decomposition (AFMD), to identify multiple localized faults in rotating machines interfered by strong periodic harmonics in a robust and effective manner. The autoregressive model is first introduced as a preprocessing technique for initially reducing deterministic components of the raw signal. Then, for signal decomposition, an adaptive finite impulse response (FIR) filter bank is designed utilizing the blind deconvolution theory. The filter coefficients of the FIR filter bank are iteratively updated to make each filtered sub-signal infinitely approach their deconvolution objective functions based on the correlated kurtosis. Meanwhile, the filter length is adaptively determined using the developed evaluation indicator termed as the weighted squared envelope harmonic-to-noise ratio. Finally, several decomposed modes focusing on fault signatures can be acquired automatically, using the newly proposed mode selection strategy that considers signal similarity across multiple domains. The proposed AFMD method can significantly reduce the likelihood of incorrect diagnoses, as demonstrated by two simulated and two experimental datasets with multiple localized bearing and gear faults. The analysis results show that the proposed method outperforms over the state-of-the-art feature mode decomposition and the most popular variational mode decomposition in multi-fault feature extraction and weak fault detection, when interfered by strong periodic harmonics as well as other background noise.

The precise forecasting of daily solar radiation (DSR) is receiving prominent attention among thriving solar energy studies. In this study, three standalone models, including gene expression programing (GEP), multivariate adaptive regression splines (MARS), and self-adaptive MARS (SaMARS), were evaluated to forecast DSR. A SaMARS model was classified as MARS model when using the crow search algorithm (CSA). In addition, to overcome the limitations of the standalone models, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) was employed to enhance the accuracy of DSR forecasting. Therefore, three hybrid models including CEEMDAN-GEP, CEEMDAN-MARS, and CEEMDAN-SaMARS were proposed to forecast DSR in Busan and Incheon stations in South Korea. The performance of proposed models were evaluated and affirmed that the accuracy of the CEEMDAN-SaMARS model (NSE = 0.878–0.883) outperformed CEEMDAN-MARS (NSE = 0.819–0.818), CEEMDAN-GEP (NSE = 0.873–0.789), SaMARS (NSE = 0.846–0.769), MARS (NSE = 0.819–0.758), and GEP (NSE = 0.814–0.755) models at both stations. Therefore, it can be concluded that the optimized CEEMDAN-SaMARS model significantly enhanced the accuracy of DSR forecasting compared to that of standalone models.

Vibration monitoring and analysis play a crucial role in the fault diagnosis of hydroelectric units. However, accurate extraction and identification of fault features from vibration signals are challenging because of noise interference. To address this issue, this study proposes a novel denoising method for vibration signals based on improved complementary ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), permutation entropy (PE), and singular value decomposition (SVD). The proposed method is applied for the analysis of hydroelectric unit sway monitoring. Firstly, the ICEEMDAN method is employed to process the signal and obtain several intrinsic mode functions (IMFs), and then the PE values of each IMF are calculated. Subsequently, based on a predefined threshold of PE, appropriate IMFs are selected for reconstruction, achieving the first denoising effect. Then, the SVD is applied to the signal after the first denoising effect, resulting in the SVD spectrum. Finally, according to the principle of the SVD spectrum and the variation in the singular value and its energy value, the signal is reconstructed by choosing the appropriate reconstruction order to achieve the secondary noise reduction effect. In the simulation and case analysis, the method is better than the commonly used wavelet threshold, SVD, CEEMDAN–PE, and ICEEMDAN–PE, with a signal-to-noise ratio (SNR) improvement of 6.9870 dB, 4.6789 dB, 8.9871 dB, and 4.3762 dB, respectively, and where the root-mean-square error (RMSE) is reduced by 0.1426, 0.0824, 0.2093 and 0.0756, respectively, meaning that our method has a better denoising effect and provides a new way for denoising the vibration signal of hydropower units.

The variational mode decomposition (VMD) and its variants aim to decompose a given signal into a set of narrow band modes. The analysis of these modes is usually based on the Fourier analysis. That is, the center frequencies of these modes are found without exploiting the local time varying information of the signal during the iteration in the existing algorithms for performing the VMD. To address this issue, this paper proposes a recursive windowed VMD (RWVMD) approach for performing the signal decomposition. First, the window is sliding across the signal. Then, the variational mode extraction is performed on each frame to obtain the first mode. Then, the difference between the first mode and the signal is computed to obtain the residual signal. The above process is repeated on the residual signal until the algorithm converges. The effectiveness of the RWVMD algorithm is demonstrated through the computer numerical simulations. It is found that the center frequency in the time frequency plane is more accurately matched with the characteristics of the original signal.

The compound fault acoustic signal of a rolling bearing has the characteristics of a varying noise mixture, a low signal-to-noise ratio (SNR), and nonlinearity, which makes it difficult to separate and extract exactly the fault features of compound fault signals. A fault feature extraction approach combining adaptive variational modal decomposition (AVMD) and improved multiverse optimization (IMVO) algorithm parameterized maximum correlated kurtosis deconvolution (MCKD)—named AVMD-IMVO-MCKD—is proposed. In order to adaptively select the parameters of VMD and MCKD, an adaptive optimization method of VMD is proposed, and an improved multiverse optimization (IMVO) algorithm is proposed to determine the parameters of MCKD. Firstly, the acoustic signal of bearing compound faults is decomposed by AVMD to generate several modal components, and the optimal modal component is selected as the reconstruction signal depending on the minimum information entropy of the modal components. Secondly, IMVO is utilized to select the parameters of MCKD, and then MCKD processing is performed on the reconstructed signal. Finally, the compound fault features of the bearing are extracted by the envelope spectrum. Both simulation analysis and acoustic signal experimental data analysis show that the proposed approach can efficiently extract the acoustic signal fault features of bearing compound faults.

To address the issue of excessive grid-connected power fluctuations in wind farms, this paper proposes a capacity optimization method for a hybrid energy storage system (HESS) based on wind power two-stage decomposition. First, considering the susceptibility of traditional k-means results to initial cluster center positions, the k-means++ algorithm was used to cluster the annual wind power, with the optimal number of clusters determined by silhouette coefficient and Davies–Bouldin Index. The overall characteristics of each cluster and the cumulative fluctuations were considered to determine typical daily data. Subsequently, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) was used to decompose the original wind power data for typical days, yielding both the grid-connected power and the HESS power. To leverage the advantages of power-type and energy-type storage while avoiding mode aliasing, the improved pelican optimization algorithm—variational mode decomposition (IPOA-VMD) was applied to decompose the HESS power, enabling accurate distribution of power for different storage types. Finally, a capacity optimization model for a HESS composed of lithium batteries and supercapacitors was developed. Case studies showed that the two-stage decomposition strategy proposed in this paper could effectively reduce grid-connected power fluctuations, better utilize the advantages of different energy storage types, and reduce HESS costs.

Crude oil is one of the strategic energies and plays an increasingly critical role effecting on the world economic development. The fluctuations of crude oil prices are caused by various extrinsic and intrinsic factors and usually demonstrate complex characteristics. Therefore, it is a great challenge for accurately forecasting crude oil prices. In this study, a self-optimizing ensemble learning model incorporating the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), sine cosine algorithm (SCA), and random vector functional link (RVFL) neural network, namely ICEEMDAN-SCA-RVFL, is proposed to forecast crude oil prices. Firstly, we employ ICEEMDAN to decompose the raw series of crude oil prices into a group of relatively simple subseries. Secondly, RVFL is used to forecast the target values for each decomposed subseries individually. Due to the complex parameter settings of ICEEMDAN and RVFL, SCA is introduced to optimize the parameters for ICEEMDAN and RVFL in the above decomposition and prediction stages simultaneously. Finally, we assemble the predicted values of all individual subseries as the final predicted values of crude oil prices. Our proposed ICEEMDAN-SCA-RVFL significantly outperforms the single and ensemble benchmark models, as demonstrated by a case study conducted using the time series of West Texas Intermediate (WTI) daily crude oil spot prices.