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Keywords = improved complementary ensemble empirical mode decomposition with adaptive noise

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20 pages, 4231 KB  
Article
Prediction Model for Deformation of Concrete Dam Based on Interpretable Component Decomposition and Integration
by Feng Han and Chongshi Gu
Sensors 2026, 26(8), 2495; https://doi.org/10.3390/s26082495 - 17 Apr 2026
Viewed by 528
Abstract
A dam deformation prediction method based on interpretable component decomposition and integration is proposed to address the problems of weak interpretability, difficult identification of key factors, and insufficient accuracy in the prediction model of deformation monitoring values of concrete dams due to multiple [...] Read more.
A dam deformation prediction method based on interpretable component decomposition and integration is proposed to address the problems of weak interpretability, difficult identification of key factors, and insufficient accuracy in the prediction model of deformation monitoring values of concrete dams due to multiple factors such as environmental loads and time factors. This method first strips the temporal component from the original sequence to obtain the castration sequence. Furthermore, complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is used to decompose and reconstruct it into environmental load components and residual terms. In the process of deformation prediction, based on the characteristics of each deformation component, logarithmic functions, bidirectional long short-term memory (BiLSTM) networks optimized by The Black-Winged Kite Algorithm (BKA), and cloud models are used to fit and predict the temporal components, environmental load components, and residual terms, and the final prediction results are obtained through integration. At the same time, the SHAP (SHapley Additive exPlanations) method is introduced to quantify the contribution of input factors to enhance the interpretability of the model. Case study shows that the model outperforms the comparison model in both prediction accuracy and trend tracking ability, effectively improving the reliability of prediction results and significantly increasing the interpretability of deformation prediction, providing a more reliable analysis technique for dam deformation safety monitoring. Full article
(This article belongs to the Special Issue Advanced Sensing Technologies in Hydraulic Engineering)
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19 pages, 6417 KB  
Article
Improved Football Team Training Algorithm Based on Modal Decomposition and BiLSTM Method for Short-Term Wind Power Forecasting
by Lingling Xie, Yanjing Luo, Chunhui Li, Long Li and Fengyuan Liu
Processes 2026, 14(6), 951; https://doi.org/10.3390/pr14060951 - 17 Mar 2026
Viewed by 533
Abstract
Reliable wind power forecasting is essential for maintaining the safe and stable operation of power systems with high renewable energy penetration. This study proposes a short-term wind power forecasting model based on decomposition–optimization–prediction, integrating complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN), [...] Read more.
Reliable wind power forecasting is essential for maintaining the safe and stable operation of power systems with high renewable energy penetration. This study proposes a short-term wind power forecasting model based on decomposition–optimization–prediction, integrating complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN), the improved football team training algorithm (IFTTA), and the bidirectional long short-term memory network model (BiLSTM). CEEMDAN is employed to decompose the non-stationary wind power sequence into relatively stable intrinsic mode functions (IMFs), thereby separating multi-scale fluctuation features. The IFTTA incorporates a dynamic probability allocation strategy and an adaptive parameter adjustment mechanism, which contributes to a better balance between global exploration and local exploitation. After optimizing the hyperparameters of BiLSTM using IFTTA, the prediction performance significantly improved. Validations were conducted on three datasets from Xinjiang, Ningxia, and Inner Mongolia, China, each containing 1440 samples (1152 for training and 288 for testing). Comparisons with the benchmark forecasting model demonstrate that the pro-posed model reduces the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) by at least 25.29%, 29.62%, and 20.66%, respectively. Correspondingly, the coefficient of determination (R2) was improved by at least 0.0069. This model provides an effective solution for short-term wind power prediction in practical engineering. Full article
(This article belongs to the Special Issue Adaptive Control and Optimization in Power Grids)
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25 pages, 10025 KB  
Article
Short-Term Photovoltaic Power Forecasting Based on ICEEMDAN-TCN-BiLSTM-MHA
by Yuan Li, Shiming Zhai, Guoyang Yi, Shaoyun Pang and Xu Luo
Symmetry 2025, 17(10), 1599; https://doi.org/10.3390/sym17101599 - 25 Sep 2025
Cited by 8 | Viewed by 1356
Abstract
In this paper, an efficient hybrid photovoltaic (PV) power forecasting model is proposed to enhance the stability and accuracy of PV power prediction under typical weather conditions. First, the Improved Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) is employed to decompose [...] Read more.
In this paper, an efficient hybrid photovoltaic (PV) power forecasting model is proposed to enhance the stability and accuracy of PV power prediction under typical weather conditions. First, the Improved Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) is employed to decompose both meteorological features affecting PV power and the power output itself into intrinsic mode functions. This process enhances the stationarity and noise robustness of input data while reducing the computational complexity of subsequent model processing. To enhance the detail-capturing capability of the Bidirectional Long Short-Term Memory (BiLSTM) model and improve its dynamic response speed and prediction accuracy under abrupt irradiance fluctuations, we integrate a Temporal Convolutional Network (TCN) into the BiLSTM architecture. Finally, a Multi-head Self-Attention (MHA) mechanism is employed to dynamically weight multivariate meteorological features, enhancing the model’s adaptive focus on key meteorological factors while suppressing noise interference. The results show that the ICEEMDAN-TCN-BiLSTM-MHA combined model reduces the Mean Absolute Percentage Error (MAPE) by 78.46% and 78.59% compared to the BiLSTM model in sunny and cloudy scenarios, respectively, and by 58.44% in rainy scenarios. This validates the accuracy and stability of the ICEEMDAN-TCN-BiLSTM-MHA combined model, demonstrating its application potential and promotional value in the field of PV power forecasting. Full article
(This article belongs to the Section A: Computer Science)
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18 pages, 1611 KB  
Article
Hybrid Decomposition Strategies and Model Combinatorial Optimization for Runoff Prediction
by Wenbin Hu and Xiaohui Yuan
Water 2025, 17(17), 2560; https://doi.org/10.3390/w17172560 - 29 Aug 2025
Cited by 1 | Viewed by 2052
Abstract
Runoff prediction plays a critical role in water resource management and flood mitigation. Traditional runoff prediction methods often rely on single-layer optimization frameworks that process the data without decomposition and employ relatively simple prediction models, leading to suboptimal performance. In this study, a [...] Read more.
Runoff prediction plays a critical role in water resource management and flood mitigation. Traditional runoff prediction methods often rely on single-layer optimization frameworks that process the data without decomposition and employ relatively simple prediction models, leading to suboptimal performance. In this study, a novel two-layer optimization framework is proposed that integrates data decomposition techniques with multi-model combination strategies, establishing a closed-loop feedback mechanism between decomposition and prediction processes. The framework employs the Snow Ablation Optimizer (SAO) to optimize combination weights across both layers. Its adaptive fitness function incorporates three evaluation metrics—Mean Absolute Percentage Error (MAPE), Relative Root Mean Square Error (RRMSE), and Nash–Sutcliffe Efficiency (NSE)—to enable adaptive data processing and intelligent model selection. We validated the framework using observational data from Huangzhuang Hydrological Station in the Hanjiang River Basin. The results demonstrate that, at the decomposition layer, optimal performance was achieved by combining non-decomposition, Singular Spectrum Analysis (SSA), and Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) (with coefficients 0.4061, 0.6115, and −0.0063), paired with the long short-term memory (LSTM) model. At the prediction layer, the proposed algorithm achieved a 32.84% improvement over the best single decomposition method and a 30.21% improvement over the best single combination optimization approach. These findings confirm the framework’s effectiveness in enhancing runoff data decomposition and optimizing multi-model selection. Full article
(This article belongs to the Special Issue Hydrodynamics Science Experiments and Simulations, 2nd Edition)
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24 pages, 6464 KB  
Article
A Hybrid Model for Carbon Price Forecasting Based on Secondary Decomposition and Weight Optimization
by Yongfa Chen, Yingjie Zhu, Jie Wang and Meng Li
Mathematics 2025, 13(14), 2323; https://doi.org/10.3390/math13142323 - 21 Jul 2025
Cited by 4 | Viewed by 2491
Abstract
Accurate carbon price forecasting is essential for market stability, risk management, and policy-making. To address the nonlinear, non-stationary, and multiscale nature of carbon prices, this paper proposes a forecasting framework integrating secondary decomposition, two-stage feature selection, and dynamic ensemble learning. Firstly, the original [...] Read more.
Accurate carbon price forecasting is essential for market stability, risk management, and policy-making. To address the nonlinear, non-stationary, and multiscale nature of carbon prices, this paper proposes a forecasting framework integrating secondary decomposition, two-stage feature selection, and dynamic ensemble learning. Firstly, the original price series is decomposed into intrinsic mode functions (IMFs), using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). The IMFs are then grouped into low- and high-frequency components based on multiscale entropy (MSE) and K-Means clustering. To further alleviate mode mixing in the high-frequency components, an improved variational mode decomposition (VMD) optimized by particle swarm optimization (PSO) is applied for secondary decomposition. Secondly, a two-stage feature-selection method is employed, in which the partial autocorrelation function (PACF) is used to select relevant lagged features, while the maximal information coefficient (MIC) is applied to identify key variables from both historical and external data. Finally, this paper introduces a dynamic integration module based on sliding windows and sequential least squares programming (SLSQP), which can not only adaptively adjust the weights of four base learners but can also effectively leverage the complementary advantages of each model and track the dynamic trends of carbon prices. The empirical results of the carbon markets in Hubei and Guangdong indicate that the proposed method outperforms the benchmark model in terms of prediction accuracy and robustness, and the method has been tested by Diebold Mariano (DM). The main contributions are the improved feature-extraction process and the innovative use of a sliding window-based SLSQP method for dynamic ensemble weight optimization. Full article
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15 pages, 3636 KB  
Article
Prediction of Ultra-Short-Term Photovoltaic Power Using BiLSTM–Informer Based on Secondary Decomposition
by Ruoqi Zhang, Zishuo Xu, Shuangquan Liu, Kaixiang Fu and Jie Zhang
Energies 2025, 18(6), 1485; https://doi.org/10.3390/en18061485 - 18 Mar 2025
Cited by 10 | Viewed by 1172
Abstract
Photovoltaic power generation as a green energy source is often used in power systems, but the volatility of PV output and randomness of the problem affect the stability of the power-grid power supply; so, for the problem of low prediction accuracy of photovoltaic [...] Read more.
Photovoltaic power generation as a green energy source is often used in power systems, but the volatility of PV output and randomness of the problem affect the stability of the power-grid power supply; so, for the problem of low prediction accuracy of photovoltaic power generation under different weather conditions, this paper proposes a Variational Mode Decomposition (VMD), combined with a Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) secondary decomposition method for the original signal decomposition, to reduce the signal volatility and reduce the complexity of feature mapping the PV data, followed by the use of a BiLSTM model to model the timing information of the decomposed IMF. Simultaneously, the Informer model predicts the components obtained from the secondary decomposition, and finally, the subsequence is reconstructed and superimposed to obtain the PV power prediction value. The results show that the RMSE and MAE of the proposed model are improved by up to 10.91% and 17.33% on the annual PV dataset, with high prediction accuracy and stability, which can effectively predict the ultra-short-term power of PV power plants. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
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22 pages, 4438 KB  
Article
Combined Prediction of PM10 Concentration at Smart Construction Sites Based on Quadratic Mode Decomposition and Deep Learning
by Ming Li, Xin Li, Kaikai Kang and Qiang Li
Sustainability 2025, 17(2), 616; https://doi.org/10.3390/su17020616 - 15 Jan 2025
Cited by 3 | Viewed by 2237
Abstract
The accurate prediction of PM10 concentrations at smart construction sites is crucial for improving urban air quality, protecting public health, and advancing sustainable development in the construction industry. PM10 concentrations at construction sites are influenced by the interaction of construction intensity and environmental [...] Read more.
The accurate prediction of PM10 concentrations at smart construction sites is crucial for improving urban air quality, protecting public health, and advancing sustainable development in the construction industry. PM10 concentrations at construction sites are influenced by the interaction of construction intensity and environmental meteorological factors, resulting in nonlinear and volatile data. To improve prediction accuracy, this paper presents a two-stage mode decomposition method that integrates Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Variational Mode Decomposition (VMD). This method is combined with a Bidirectional Long Short-Term Memory (BiLSTM) neural network, optimized using the Sparrow Search Algorithm (SSA), to establish a hybrid model for forecasting PM10 concentrations at construction sites. Initially, CEEMDAN decomposes the original sequence into several Intrinsic Mode Functions (IMFs). The sample entropy of each component is then calculated, and K-means clustering is used to group them. VMD is applied to further decompose the high-frequency components obtained after clustering. SSA is then employed to optimize the parameters of the BiLSTM network, which models all the components with the optimized predictive model. The predicted values of all components are aggregated to generate the final forecast. Real-time monitoring data from Construction Site A in Nanjing are used for case study validation. The empirical results demonstrate that the proposed hybrid prediction model outperforms comparison models on all evaluation metrics, offering a scientific foundation for sustainable and automated dust reduction decision-making at smart construction sites, thereby facilitating the shift toward greener, smarter, and more digitized construction practices. Full article
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21 pages, 3614 KB  
Article
Power Quality Disturbance Identification Method Based on Improved CEEMDAN-HT-ELM Model
by Ke Liu, Jun Han, Song Chen, Liang Ruan, Yutong Liu and Yang Wang
Processes 2025, 13(1), 137; https://doi.org/10.3390/pr13010137 - 7 Jan 2025
Cited by 8 | Viewed by 2370
Abstract
The issue of power quality disturbances in modern power systems has become increasingly complex and severe, with multiple disturbances occurring simultaneously, leading to a decrease in the recognition accuracy of traditional algorithms. This paper proposes a composite power quality disturbance identification method based [...] Read more.
The issue of power quality disturbances in modern power systems has become increasingly complex and severe, with multiple disturbances occurring simultaneously, leading to a decrease in the recognition accuracy of traditional algorithms. This paper proposes a composite power quality disturbance identification method based on the integration of improved Complementary Ensemble Empirical Mode Decomposition (CEEMDAN), Hilbert Transform (HT), and Extreme Learning Machine (ELM). Addressing the limitations of traditional signal processing techniques in handling nonlinear and non-stationary signals, this study first preprocesses the collected initial power quality signals using the improved CEEMDAN method to reduce modal aliasing and spurious components, thereby enabling a more precise decomposition of noisy signals into multiple Intrinsic Mode Functions (IMFs). Subsequently, the HT is utilized to conduct a thorough analysis of the reconstructed signals, extracting their time-amplitude information and instantaneous frequency characteristics. This feature information provides a rich data foundation for subsequent classification and identification. On this basis, an improved ELM is introduced as the classifier, leveraging its powerful nonlinear mapping capabilities and fast learning speed to perform pattern recognition on the extracted features, achieving accurate identification of composite power quality disturbances. To validate the effectiveness and practicality of the proposed method, a simulation experiment is designed. Upon examination, the approach introduced in this study retains a fault diagnosis accuracy exceeding 95%, even amidst significant noise disturbances. In contrast to conventional techniques, such as Convolutional Neural Network (CNN) and Support Vector Machine (SVM), this method achieves an accuracy enhancement of up to 5%. Following optimization via the Particle Swarm Optimization (PSO) algorithm, the model’s accuracy is boosted by 3.6%, showcasing its favorable adaptability. Full article
(This article belongs to the Special Issue Modeling, Simulation and Control in Energy Systems)
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14 pages, 5327 KB  
Article
Ensemble All Time-Scale Decomposition Method and Its Application in Bevel Gear Fault Diagnosis
by Zhengyang Cheng, Yu Yang, Chengcheng Duan, Xin Kang and Jianxin Cui
Sensors 2025, 25(1), 23; https://doi.org/10.3390/s25010023 - 24 Dec 2024
Cited by 1 | Viewed by 1746
Abstract
All time-scale decomposition (ATD) is a non-parametric adaptive signal decomposition method, which relies on zero-crossing points and extreme points to jointly construct the baseline, achieving the suppression of modal mixing caused by the proximity of component frequencies. However, ATD is unable to solve [...] Read more.
All time-scale decomposition (ATD) is a non-parametric adaptive signal decomposition method, which relies on zero-crossing points and extreme points to jointly construct the baseline, achieving the suppression of modal mixing caused by the proximity of component frequencies. However, ATD is unable to solve mode mixing induced by noise. To improve this defect, a new noise-assisted signal decomposition method named ensemble all time-scale decomposition (EATD) is proposed in this paper. EATD introduces the noise-assisted technique of complementary ensemble empirical mode decomposition based on ATD, adding complementary noises to mask the noise interference in the signal. EATD not only overcomes mode mixing caused by noise but also preserves the capability of ATD to suppress mode mixing caused by the proximity of component frequencies. Simulation signals and bevel gear fault signals are utilized to validate EATD, and the results indicate that EATD can successfully overcome mode mixing induced by noise and can be effectively applied for gear fault diagnosis. Full article
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23 pages, 4788 KB  
Article
Forecasting of Standardized Precipitation Index Using Hybrid Models: A Case Study of Cape Town, South Africa
by Siphamandla Sibiya, Nkanyiso Mbatha, Shaun Ramroop, Sileshi Melesse and Felix Silwimba
Water 2024, 16(17), 2469; https://doi.org/10.3390/w16172469 - 30 Aug 2024
Cited by 5 | Viewed by 3478
Abstract
Droughts have negative impacts on agricultural productivity and economic growth. Effective monitoring and accurate forecasting of drought occurrences and trends are crucial for minimizing drought losses and mitigating their spatial and temporal effects. In this study, trend dynamics in monthly total rainfall time [...] Read more.
Droughts have negative impacts on agricultural productivity and economic growth. Effective monitoring and accurate forecasting of drought occurrences and trends are crucial for minimizing drought losses and mitigating their spatial and temporal effects. In this study, trend dynamics in monthly total rainfall time series measured at Cape Town International Airport were analyzed using the Mann–Kendall (MK) test, Modified Mann–Kendall (MMK) test and innovative trend analysis (ITA). Additionally, we utilized a hybrid prediction method that combined the model with the complementary ensemble empirical mode decomposition with adaptive noise (CEEMDAN) technique, the autoregressive integrated moving average (ARIMA) model, and the long short-term memory (LSTM) network (i.e., CEEMDAN-ARIMA-LSTM) to forecast SPI values of 6-, 9-, and 12-months using rainfall data between 1995 and 2020 from Cape Town International Airport meteorological rainfall stations. In terms of trend analysis of the monthly total rainfall, the MK and MMK tests detected a significant decreasing trend with negative z-scores of −3.7541 and −4.0773, respectively. The ITA also indicated a significant downward trend of total monthly rainfall, especially for values between 10 and 110 mm/month. The SPI forecasting results show that the hybrid model (CEEMDAN-ARIMA-LSTM) had the highest prediction accuracy of the models at all SPI timescales. The Root Mean Square Error (RMSE) values of the CEEMDAN-ARIMA-LSTM hybrid model are 0.121, 0.044, and 0.042 for SPI-6, SPI-9, and SPI-12, respectively. The directional symmetry for this hybrid model is 0.950, 0.917, and 0.950, for SPI-6, SPI-9, and SPI-12, respectively. This indicates that this is the most suitable model for forecasting long-term drought conditions in Cape Town. Additionally, models that use a decomposition step and those that are built by combining independent models seem to produce improved SPI prediction accuracy. Full article
(This article belongs to the Section Water and Climate Change)
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15 pages, 7719 KB  
Article
An Improved Empirical Wavelet Transform Filtering Method for Rail-Head Surface-Defect Magnetic-Flux Leakage Signal
by Yinliang Jia, Jing Lin, Ping Wang and Yue Zhu
Appl. Sci. 2024, 14(2), 526; https://doi.org/10.3390/app14020526 - 7 Jan 2024
Cited by 2 | Viewed by 2268
Abstract
The rail is an important factor in railway traffic safety. Surface defects in the rail head comprise a common type of rail damage, and magnetic flux leakage (MFL) technology is applied for its detection. MFL detection is influenced by various factors, resulting in [...] Read more.
The rail is an important factor in railway traffic safety. Surface defects in the rail head comprise a common type of rail damage, and magnetic flux leakage (MFL) technology is applied for its detection. MFL detection is influenced by various factors, resulting in high noise and a low signal-to-noise ratio (SNR) in the collected MFL signal, which influence defect assessment. This article improves the empirical wavelet transform (EWT) to apply it to rail surface-defect MFL signal filtering. A boundary optimization method based on mutual information (MI) is proposed to reduce the boundary redundancy caused by adaptive spectrum division. A method for component selection based on MI and kurtosis is proposed to select the suitable components from the decomposed components for signal reconstruction. The experimental results show that the method can effectively filter out the interference in the MFL signal, and the effectiveness is superior to the traditional methods, such as complementary ensemble empirical mode decomposition (CEEMD) and wavelet transform (WT). Full article
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23 pages, 10903 KB  
Article
Noise Reduction Based on a CEEMD-WPT Crack Acoustic Emission Dataset
by Yongfeng Zhao, Yunrui Ma, Junli Du, Chaohua Wang, Dawei Xia, Weifeng Xin, Zhenyu Zhan, Runfeng Zhang and Jiangyi Chen
Appl. Sci. 2023, 13(18), 10274; https://doi.org/10.3390/app131810274 - 13 Sep 2023
Cited by 15 | Viewed by 2565
Abstract
In order to solve the noise reduction problem of acoustic emission signals with cracks, a method combining Complementary Ensemble Empirical Mode Decomposition (CEEMD) and wavelet packet (WPT) is proposed and named CEEMD-WPT. Firstly, the single Empirical Mode Decomposition (EMD) used in the traditional [...] Read more.
In order to solve the noise reduction problem of acoustic emission signals with cracks, a method combining Complementary Ensemble Empirical Mode Decomposition (CEEMD) and wavelet packet (WPT) is proposed and named CEEMD-WPT. Firstly, the single Empirical Mode Decomposition (EMD) used in the traditional CEEMD is improved into the WPT-EMD with a more stable noise reduction effect. Secondly, after decomposition, the threshold value of the correlation coefficient is determined for the Intrinsic Mode Function (IMF), and the low correlation component is further processed by WPT. In addition, in order to solve the problem that it is difficult to quantify the real signal noise reduction effect, a new quantization index “principal interval coefficient (PIC)” is designed in this paper, and its reliability is verified through simulation experiments. Finally, noise reduction experiments are carried out on the real crack acoustic emission dataset consisting of tensile, shear, and mixed signals. The results show that CEEMD-WPT has the highest number of signals with a principal interval coefficient of 0–0.2, which has a better noise reduction effect compared with traditional CEEMD and Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). Moreover, the statistical variance of CEEMD-WPT is evidently one order of magnitude smaller than that of CEEMD, so it has stronger stability. Full article
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21 pages, 9193 KB  
Article
Research on Denoising Method for Hydroelectric Unit Vibration Signal Based on ICEEMDAN–PE–SVD
by Fangqing Zhang, Jiang Guo, Fang Yuan, Yongjie Shi and Zhaoyang Li
Sensors 2023, 23(14), 6368; https://doi.org/10.3390/s23146368 - 13 Jul 2023
Cited by 19 | Viewed by 2824
Abstract
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 [...] Read more.
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. Full article
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17 pages, 2574 KB  
Article
Influence of Sampling Frequency Ratio on Mode Mixing Alleviation Performance: A Comparative Study of Four Noise-Assisted Empirical Mode Decomposition Algorithms
by Yanqing Zhao, Kondo H. Adjallah, Alexandre Sava and Zhouhang Wang
Machines 2021, 9(12), 315; https://doi.org/10.3390/machines9120315 - 26 Nov 2021
Cited by 15 | Viewed by 3128
Abstract
Four noise-assisted empirical mode decomposition (EMD) algorithms, i.e., ensemble EMD (EEMD), complementary ensemble EMD (CEEMD), complete ensemble EMD with adaptive noise (CEEMDAN), and improved complete ensemble EMD with adaptive noise (ICEEMDAN), are noticeable improvements to EMD, aimed at alleviating mode mixing. However, the [...] Read more.
Four noise-assisted empirical mode decomposition (EMD) algorithms, i.e., ensemble EMD (EEMD), complementary ensemble EMD (CEEMD), complete ensemble EMD with adaptive noise (CEEMDAN), and improved complete ensemble EMD with adaptive noise (ICEEMDAN), are noticeable improvements to EMD, aimed at alleviating mode mixing. However, the sampling frequency ratio (SFR), i.e., the ratio between the sampling frequency and the maximum signal frequency, may significantly impact their mode mixing alleviation performance. Aimed at this issue, we investigated and compared the influence of the SFR on the mode mixing alleviation performance of these four noise-assisted EMD algorithms. The results show that for a given signal, (1) SFR has an aperiodic influence on the mode mixing alleviation performance of four noise-assisted EMD algorithms, (2) a careful selection of SFRs can significantly improve the mode mixing alleviation performance and avoid decomposition instability, and (3) ICEEMDAN has the best mode mixing alleviation performance at the optimal SFR among the four noise-assisted EMD algorithms. The applications include, for instance, tool wear monitoring in machining as well as fault diagnosis and prognosis of complex systems that rely on signal decomposition to extract the components corresponding to specific behaviors. Full article
(This article belongs to the Special Issue Advances in Tool Life Prediction in Machining)
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15 pages, 953 KB  
Technical Note
Micro-Motion Parameter Extraction for Ballistic Missile with Wideband Radar Using Improved Ensemble EMD Method
by Nannan Zhu, Jun Hu, Shiyou Xu, Wenzhen Wu, Yunfan Zhang and Zengping Chen
Remote Sens. 2021, 13(17), 3545; https://doi.org/10.3390/rs13173545 - 6 Sep 2021
Cited by 24 | Viewed by 4978
Abstract
Micro-motion parameters extraction is crucial in recognizing ballistic missiles with a wideband radar. It is known that the phase-derived range (PDR) method can provide a sub-wavelength level accuracy. However, it is sensitive and unstable when the signal-to-noise ratio (SNR) is low. In this [...] Read more.
Micro-motion parameters extraction is crucial in recognizing ballistic missiles with a wideband radar. It is known that the phase-derived range (PDR) method can provide a sub-wavelength level accuracy. However, it is sensitive and unstable when the signal-to-noise ratio (SNR) is low. In this paper, an improved PDR method is proposed to reduce the impacts of low SNRs. First, the high range resolution profile (HRRP) is divided into a series of segments so that each segment contains a single scattering point. Then, the peak values of each segment are viewed as non-stationary signals, which are further decomposed into a series of intrinsic mode functions (IMFs) with different energy, using the ensemble empirical mode decomposition with the complementary adaptive noise (EEMDCAN) method. In the EEMDCAN decomposition, positive and negative adaptive noise pairs are added to each IMF layer to effectively eliminate the mode-mixing phenomenon that exists in the original empirical mode decomposition (EMD) method. An energy threshold is designed to select proper IMFs to reconstruct the envelop for high estimation accuracy and low noise effects. Finally, the least-square algorithm is used to do the ambiguous phases unwrapping to obtain the micro-curve, which can be further used to estimate the micro-motion parameters of the warhead. Simulation results show that the proposed method performs well with SNR at −5 dB with an accuracy level of sub-wavelength. Full article
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