A Novel Compound Fault Diagnosis Method for Rotating Machinery Based on Dynamic Adaptive MWPE and Dual-Graph Regularization Strategy

In the field of fault diagnosis, machine learning is highly valued for its broad applicability and efficiency. Feature extraction and feature selection are key steps in the application of machine learning, and the performance of fault diagnosis methods relies heavily on the effective execution of these two steps. For this reason, this paper aims to enhance the performance of fault diagnosis methods by improving these two aspects. Firstly, to address the non-linearity and non-stationarity of rotating machinery vibration signals under variable operation conditions, this paper proposes an improved rapid refined composite multiscale sample entropy (IR2CMSE) feature extraction method. In addition, this paper decomposes the vibration signals with improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) and extracts the sensitive intrinsic modal functions’ (IMFs') IR2CMSE values (SI-IR2CMSE) as the initial feature vector, which more accurately reveals the intrinsic time-scale characteristics of the vibration signals. Secondly, to address the problem of over-reliance on sample labels in most feature selection methods, this paper proposes a semi-supervised Gaussian mixing model with sparse regularization (SSGMM-SR) feature selection model. The model does not require complete fault labels and can automatically identify important features. Finally, validation with two rotating machinery fault datasets shows that the method proposed in this study exhibits high diagnostic accuracy and stability across multiple classifiers.

Rotating machinery fault diagnostics has received a lot of attention in recent years. As a result, there has been an increase in research interest in rotating machine intelligent fault detection, especially when using measurement from multi-sensors. However, an accurate fault diagnosis is still challenged based on nonlinear and non-stationary vibration signals. On the other hand, not enough research has been done on structural information fusion from multi-sensor measurement due to the complexity of spatial–temporal correlation. This paper explores the use of vibration signals in multi-sensor measurement fusion for rotating machinery fault diagnostics, and a method using a cross-attention-based dual-branch graph neural network (CA-GNN) is proposed. First, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is used to decompose vibration signals. Variational mode decomposition is then used to further deconstruct the highest-frequency subsequence after its parameters have been optimized using the whale optimization algorithm. Next, we build the CA-GNN, which contains two space branches for high- and low-frequency signals after initially creating the graph using multiple sensor data sets. Information across both branches for high- and low-frequency components can then be efficiently fused. Lastly, two experimental scenarios are used to illustrate the suggested technique and assess its viability and accuracy for rotating machinery fault diagnosis. Results indicate that the proposed method can diagnose rotating machinery health issues with an average accuracy of up to 99%, indicating that the method’s performance can fulfill real-world requirements.

Ferromagnetic materials are extensively utilized in industrial settings where the early detection and repair of defects is paramount for ensuring industrial safety. During the enhanced magnetic memory detection of micro-defects, many interference signals appear in the detection signal, which makes it difficult to accurately extract the characteristics of the micro-defect signals, significantly affecting detection effectiveness. When improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is employed independently for signal denoising, the noise and feature signals of the transition components are retained or removed. When variational mode decomposition (VMD) is employed independently for signal denoising, the denoising effect is restricted because of the difficulty in determining the penalty factor α and the number of decomposition layers m. To solve these problems, a denoising method for enhanced magnetic memory detection signals based on ICEEMDAN and VMD, called ICEEMDAN–VMD, is proposed in this paper. First, a comprehensive index (CI) combining information entropy (IE) and the correlation coefficient R is proposed, then the signal components obtained by performing decomposition with the ICEEMDAN method are divided into noise-dominant components, transition components, and useful signal components based on the CI. Subsequently, VMD is employed to perform secondary decomposition on the transition components obtained from the ICEEMDAN method and calculate the correlation coefficients. Ultimately, the optimal VMD components and useful signal components obtained by the ICEEMDAN method are selected for signal reconstruction to obtain a denoised signal. To validate the effectiveness of the proposed method, the denoising effects of the ICEEMDAN–VMD, ICEEMDAN, and VMD methods were compared based on the signal-to-noise ratio (SNR) and fuzzy entropy (FE). The comparison indicated that the ICEEMDAN–VMD denoising method significantly enhanced the denoising effect, and the SNRs of the components of the magnetic field signal could be increased by up to 69.426%. The SNR of each gradient component of the magnetic field signal could be improved by up to ten times, and the FEs of the signal components and their corresponding gradient components could be reduced by 24.198%–81.011%, respectively.

To enhance the accuracy of short-term photovoltaic (PV) power forecasting, this study proposes a novel hybrid model that integrates Random Forest (RF), Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), Sample Entropy (SE), the Random Walk with Compulsory Evolution (RWCE) algorithm, and the Gated Recurrent Unit (GRU) network. Initially, RF is applied to select relevant meteorological features, minimizing redundancy and improving both training efficiency and predictive robustness under complex operating conditions. ICEEMDAN is then employed to decompose the PV power series into multiple quasi-stationary components, mitigating the adverse effects of non-stationarity on forecasting accuracy. Following this, SE is applied to quantify the complexity of each component and reconstruct the decomposed signals into high-, mid-, and low-frequency bands, simplifying the inputs to the forecasting model. To further improve performance, the RWCE algorithm optimizes GRU network hyperparameters through global exploration, individual evolution, and enforced evolution strategies. The optimized GRU network then predicts each reconstructed component, and the component-wise forecasts are aggregated to yield the final PV power output. Simulation results from several representative months indicate that the proposed approach reduces RMSE by an average of 9.02% compared to comparison model and by 43.41% relative to the baseline model, demonstrating its superior forecasting capability. Additionally, the model demonstrated scalability across varying climate conditions, confirming its applicability in real-world scenarios.

Aiming to address the nonlinear and non-stationary characteristics of rolling bearing fault vibration signals, traditional diagnostic methods face challenges such as mode mixing, insufficient feature discrimination, and sensitivity to classifier parameters, which limit further improvements in diagnostic accuracy. This paper proposes a comprehensive optimization framework for fault diagnosis, covering signal decomposition and fault feature classification. First, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is applied to decompose the signal into intrinsic mode functions (IMF), effectively suppressing mode mixing. Next, the correlation coefficient and multiscale permutation entropy (MPE) are employed to quantify the dynamic complexity of each IMF across multiple scales, enabling the extraction of highly discriminative multidimensional feature vectors. Finally, the black-winged kite algorithm (BKA) is used to optimize the penalty factor and kernel parameters of the least squares support vector machine (LSSVM). BKA achieves a dynamic balance between local exploitation and global exploration, and its integration with Cauchy mutation improves robustness to noise, thereby enhancing convergence speed and stability. Experimental results from publicly available datasets and a custom experimental platform show that the proposed approach effectively distinguishes among various fault types, offering superior performance, improved interpretability, and enhanced robustness.

The underwater electrostatic hydraulic actuator (EHA) has high precision, fast response time, and low noise level, etc. It is widely used for ocean exploration and deep-sea operations. However, the tough underwater conditions could cause considerable problems, particularly with the hydraulic system of EHA, which is prone to leakage failures. To address this issue, this paper presents a methodology for diagnosing hydraulic cylinder leakage faults based on Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) combined with CNN, which has been optimized by using the improved Dung Beetle Optimization (IDBO). By studying the various properties of leakage signals from underwater EHA hydraulic cylinders, the denoised output from the ICEEMDAN approach serves as the input vector for the CNN model. The hyperparameters of the Convolutional Neural Network (CNN) model are fine-tuned and optimized by using the enhanced IDBO algorithm. The testing results reveal that the hydraulic cylinder fault diagnosis model combined with the ICEEMDAN-CNN optimized by the IDBO has an accurate rate of 97.73%; and it has a much superior diagnostic impact than other models. This strategy can significantly increase the accuracy of the underwater EHA defect diagnosis model.

This paper presents a fault diagnosis method for rolling bearings working in non-stationary running conditions. The proposed approach is based on an improved version of the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), the multivariate denoising using wavelet analysis and principal component analysis (PCA), the spectral kurtosis, and the order tracking analysis (OTA). The results show that the improved CEEMDAN has completely decomposed the raw signal into different intrinsic mode functions (IMFs) representing the natural oscillatory modes embedded into the signal. The most relevant IMF from which the defect was extracted is selected by the kurtogram plot which allows locating the optimal frequency band having the highest kurtosis value. Multivariate denoising based on wavelet analysis and PCA is used to increase the signal-to-noise ratio (SNR) of the selected IMF. The results show the great contribution of the denoising approach when comparing the selected denoised IMF with the original one. Finally, order tracking analysis is applied on the denoised IMF’s envelope to remove the effect of speed variation, and an envelope order spectrum is obtained. The proposed approach is first applied on theoretical signal simulating rolling bearing defect in variable regime including three different phases. The final order spectrum shows exactly the simulated defect order and several of its harmonics. For the experimental validation, several signals of defective rolling bearings have been measured on the Machine Fault Simulator test rig in variable regime. Despite the combined variable regime including acceleration-constant regime-deceleration, at the same time, the obtained results indicate the efficiency of the proposed method to extract the fault order with high accuracy. The maximum error between the theoretical order and the experimentally obtained one was 1.3% for outer race defect and 1% for inner race defect. Finally, the performances of the proposed method are compared to those of another diagnosis method designed for variable regime conditions. Both outer race and inner race defects are considered in acceleration regime. The results show the superiority of the proposed method to highlight the defect order with highest clarity.

Accurate prediction of Global Navigation Satellite System-derived precipitable water vapor (GNSS-PWV), which is a crucial indicator for climate change monitoring, holds significant scientific value for climate disaster prevention and mitigation. In the study of GNSS-PWV prediction, the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm within a decomposition–integration framework effectively addresses the non-stationarity and complexity of PWV sequences, enhancing prediction accuracy. However, residual noise and pseudo-modes from decomposition can distort signals, reducing the predictor system’s reliability. Additionally, independent modeling of all decomposed components decreases computational efficiency. To address these challenges, this paper proposes a hybrid model combining the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), autoregressive integrated moving average (ARIMA), and long short-term memory (LSTM) networks. Enhanced by local mean optimization and adaptive noise regulation, the ICEEMDAN algorithm effectively suppresses pseudo-modes and minimizes residual noise, enabling its decomposed intrinsic mode functions (IMFs) to more accurately capture the multi-scale features of GNSS-PWV. Sample entropy (SE) is used to quantify the complexity of IMFs, and components with similar entropy values are reconstructed into the following three sub-sequences: high-frequency, low-frequency, and trend. This process significantly reduces modeling complexity and improves computational efficiency. We propose different modeling strategies tailored to the dynamics of various subsequences. For the nonlinear and non-stationary high-frequency components, the LSTM network is used to effectively capture their complex patterns. The LSTM’s gating mechanism and memory cell design proficiently address the long-term dependency issue. For the stationary and weakly nonlinear low-frequency and trend components, linear patterns are extracted using ARIMA. Differencing eliminates trends and moving average operations capture random fluctuations, effectively addressing periodicity and trends in the time series. Finally, the prediction results of the three components are linearly combined to obtain the final prediction value. To validate the model performance, experiments were conducted using measured GNSS-PWV data from several stations in Hong Kong. The results demonstrate that the proposed model reduces the root mean square error by 56.81%, 37.91%, and 13.58% at the 1 h scale compared to the LSTM, EMD-LSTM, and ICEEMDAN-SE-LSTM benchmark models, respectively. Furthermore, it exhibits strong robustness in cross-month forecasts (accounting for seasonal influences) and multi-step predictions over the 1–6 h period. By improving the accuracy and efficiency of PWV predictions, this model provides reliable technical support for the real-time monitoring and early warning of extreme weather events in Hong Kong while offering a universal methodological reference for multi-scale modeling of geophysical parameters.

Based on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) algorithm and kernel online sequential extreme learning machine (KOSELM) algorithm, a new hybrid short-term traffic flow prediction model (ICEEMDAN-KOSELM-ARIMA) for signalized intersections is proposed according to the current and historical traffic flow data. First, traffic flow historical time series are decomposed by ICEEMDAN algorithm for the purpose of improving the prediction accuracy. Several intrinsic mode functions could be obtained by the decomposition process. Then, permutation entropy algorithm is employed to analyze the random properties of intrinsic mode function components. According to the different random properties of intrinsic mode functions, different prediction models can be built. On this basis, KOSELM prediction models are established for the intrinsic mode function components with big randomness. And auto-regressive integrated moving average (ARIMA) prediction models are built for the intrinsic mode function components with small randomness. Finally, an actual signalized intersection is selected to verify the effect and performance of the hybrid prediction model proposed in this article. Results show that compared with other models, the new proposed hybrid prediction model can effectively improve prediction accuracy, of which prediction errors are the lowest and fitting effect with actual values is the best.

The rising sea level caused by global climate change might impact the human living environment. Global navigation satellite systems (GNSS)-multipath reflection (MR) technology holds significant potential for monitoring tide level changes. GNSS-MR technology typically employs low-order polynomials to extract the signal-to-noise ratio (SNR) residuals containing GNSS interference signals. It utilizes Lomb-Scargle (LSP) spectral analysis or empirical mode decomposition (EMD) to obtain the dominant frequency of the SNR residuals, which is then converted into tidal heights. However, as the satellite elevation angle increases, the GNSS interference signals decrease and the traditional method does not adapt well to the extraction of SNR residuals under such conditions. A series of improved EMD-kind algorithms, namely ensemble empirical mode decomposition (EEMD), complementary ensemble empirical mode decomposition (CEEMD), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), and improved complete ensemble empirical mode decomposition with adaptive noise (ICEEDMAN), have been proposed to address the shortcomings of EMD algorithms such as end effect and mode aliasing. However, these improved EMD-kind algorithms have yet to be reported in sea level inversion. This study investigates the mitigation effects of EMD-kind algorithms on GNSS-MR direct signal and noise to improve the stability and accuracy of an SNR residual sequence with high satellite elevation angles. Experimental data from the HKQT station for one week and the SC02 station for one year are utilized to validate the effectiveness and accuracy of these algorithms in extracting SNR residuals. Compared to the traditional polynomial method, the experimental results demonstrate that all EMD-kind algorithms effectively address the distortion issue in traditional inversion methods under long periods, higher satellite elevation angles, and low GNSS receiver sampling rates. Among these algorithms, the results from the experiments show that ICEEMDAN consistently provides the best inversion accuracy. The results of the comparative analysis show that ICEEMDAN effectively reduces non-interference signals in SNR residuals at higher satellite elevation angles, expanding the useable range of satellite elevation angles and improving the utilization and temporal resolution of GNSS data inversion. Hence, it is an effective and appropriate approach to improving the accuracy of GNSS-MR tide level monitoring.

Hybrid wind speed forecasting using ICEEMDAN and transformer model with novel loss function

To improve the accuracy of rock failure monitoring, this article addresses the optimization of denoising acoustic emission (AE) signals. Combining laboratory experiments on rock AE and theoretical research on signal denoising, a denoising method based on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is proposed for rock fracture AE signals. The ICEEMDAN algorithm is used to decompose the original noisy signal into multiple intrinsic mode functions (IMFs) and employs cluster analysis to determine data thresholds based on their characteristics. Subsequently, using multiple criteria such as permutation entropy, correlation coefficient, and variance contribution rate, the IMFs are categorized into two groups. The low-correlation IMFs are partially removed based on the combination of indicators, while the high-correlation portion is denoised using wavelet thresholding (WT). Finally, a wavelet analysis is performed to reconstruct the signal, effectively achieving an optimized denoising of the original signal. Quantitative analysis of denoising effects on typical rock uniaxial compression fracture AE signals reveals that the optimized method has a positive impact on high-frequency noise reduction. The peak frequency range is unaffected before and after optimization, while the main amplitude reduction is concentrated in the high-frequency range. Compared to traditional wavelet denoising methods, the proposed method exhibits higher signal-to-noise ratio (SNR) improvement, as well as varying degrees of reduction in mean squared error (MSE) and total harmonic distortion (THD). This research introduces a novel approach for optimizing the application of rock AE signals.

This paper introduces a novel hybrid framework, ICEEMDAN-PatchTST+FDPO, which integrates advanced signal decomposition, Transformer-based time series forecasting, and forecast-driven portfolio optimization (FDPO). Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) enhances signal stationarity by decomposing noisy financial series into intrinsic mode functions, while PatchTST employs patch-wise self-attention to capture complex temporal dependencies. These components enable precise multi-step return forecasting, which is subsequently operationalized through FDPO to generate dynamically optimized allocations aligned with predicted market movements. Extensive out-of-sample evaluations from January 2022 to December 2024 on a rule-based selection of ten representative NIFTY 50 constituents demonstrate that the proposed framework delivers substantial gains over conventional baselines (EqualWeight, Mean–Variance Optimization, Risk Parity) and alternative deep learning models (LSTM, TimesNet, NBEATSx, Informer) in both forecasting accuracy and portfolio performance. The model achieves the lowest MAE (38.25), RMSE (55.92), and MAPE (2.06%), with an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of 0.9776. It also attains a CAGR of 1.8453, a Sharpe ratio of 3.615, a Sortino ratio of 3.985, and the lowest maximum drawdown of –0.0971. Alignment metrics such as Cosine Similarity and Jensen–Shannon Divergence further indicate that its weight vectors closely approximate ideal allocations based on actual future returns. A supplementary validation on a rule-based S&P 500 subset corroborates these trends, suggesting that the framework maintains its performance advantages across distinct market environments. Overall, the findings highlight the practical viability of the ICEEMDAN-PatchTST+FDPO framework for robust and adaptive asset management under real-world market dynamics.

Doppler radar for monitoring vital signals is an emerging tool, and how to remove the noise during the detection process and reconstruct the accurate respiration and heartbeat signals are hot issues in current research. In this paper, a novel radar vital signal separation and de-noising technique based on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), sample entropy (SampEn), and wavelet threshold is proposed. First, the noisy radar signal was decomposed into a series of intrinsic mode functions (IMFs) using ICEEMDAN. Then, each IMF was analyzed using SampEn to find out the first few IMFs containing noise, and these IMFs were de-noised using the wavelet threshold. Finally, in order to extract accurate vital signals, spectrum analysis and Kullback–Leible (KL) divergence calculations were performed on all IMFs, and appropriate IMFs were selected to reconstruct respiration and heartbeat signals. Moreover, as far as we know, there is almost no previous research on radar vital signal de-noising based on the proposed technique. The effectiveness of the algorithm was verified using simulated and measured experiments. The results show that the proposed algorithm could effectively reduce the noise and was superior to the existing de-noising technologies, which is beneficial for extracting more accurate vital signals.

Climate change is of great significance to vegetation coverage. However, the long time series of climatic factors and vegetation index is non-stationary and non-linear, containing different information in frequency and time scales. The study innovatively integrated Support Vector Machine (SVM) and Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), and analyzed the relationship between climatic factors and the Normalized Difference Vegetation Index (NDVI) at three-time scales in Loess Plateau (LP). The results indicate that: (1) The mode mixing phenomenon of EMD can be better solved by using ICEEMDAN, and the end effect can be mitigated by using SVM to expand both ends of the data before decomposition. (2) The residual NDVI stripped out using ICEEMDAN-SVM can represent the long-term trend of the original data. The results show that the NDVI and climate factors performed noticeable spatial and temporal differences under different climate zones. (3) The relationship between vegetation and climatic factors revealed obvious spatial heterogeneity at different time scales, and the climate change in the overall trend explained the vegetation change to the greatest extent, about 95&#x0025;. The study has shown that temperature is a limiting factor affecting the growth of vegetation on the Loess Plateau. We propose ICEEMDAN-SVM to study the relationship between climate factors and vegetation indices at multiple timescales., revealing some hidden information in long time series and providing a new method to quantify the impact of climate change on vegetation dynamics.