Variational Mode Decomposition Research Articles

Spectrum feature extraction method combining Allan variance, VMD, and PSD

Spectrum feature extraction plays a crucial role in identifying seismic events and calculating structural response parameters. However, the criteria for identifying effective modal components in Variational Mode Decomposition (VMD) are not well-defined, resulting in inaccurate spectrum feature extraction. To address this issue, we propose a novel spectrum feature extraction method that combines Allan variance, VMD, and power spectral density (PSD). Firstly, VMD is applied to filter noise components from triaxial accelerometer observations and add effective signals. Secondly, PSD is utilized to extract three groups of seismic frequencies (tri-axial accelerometers). Finally, the Allan method is introduced to identify the group of accelerometer observations with the highest reliability as the vibration frequency caused by the seismic excitation. We validate the effectiveness of our method by analyzing a Mw 2.6 micro-seismic event that occurred in Huairou, Beijing in 2022. The result shows that our proposed method accurately extracts spectrum features of the Great Wall. Specifically, the seismic excitation vibration frequencies at four monitoring stations were found to be 26.95 Hz, 12.89 Hz, 12.89 Hz, and 12.5 Hz. These findings underscore our method's utility in evaluating the Great Wall's structural response to seismic loading, which has significant implications for the conservation and protection of heritage structures.

A combined model using secondary decomposition for crude oil futures price and volatility forecasting: Analysis based on comparison and ablation experiments

To accurately forecast crude oil futures price and volatility, this article presents a novel deep learning combined model using secondary decomposition with West Texas Intermediate crude oil futures (WTI) and North Sea Brent crude oil futures (Brent) as examples. Firstly, a trend subsequence and several noise subsequences are obtained by decomposing the crude oil futures price or volatility using the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and the secondary decomposition is performed on the highest frequency noise subsequence using the variational mode decomposition (VMD). Secondly, the remaining subsequences obtained from CEEMDAN and the subsequences obtained from VMD are predicted separately using the BiGRU-Attention-CNN model. Finally, the predicted crude oil futures price or volatility is calculated by linearly integrating the predicted values of each subsequence. The empirical analysis shows that the novel combined model using secondary decomposition proposed in this paper has the best forecasting performance among many models, both in the comparison experiments and in the ablation experiments. The model is also shown to have good robustness by predicting the volatility at different maturities, varying the ratio of the training set and the test set for crude oil futures price prediction, and predicting the price of crude oil futures after extreme events. Overall, the novel combined forecasting model using secondary decomposition proposed in this paper can help countries grasp the direction of the crude oil market and improve national economic and political security.

An enhanced hybrid scheme for ship roll prediction using support vector regression and TVF-EMD

In order to represent the complex characteristics of ship roll motion such as nonlinearity, uncertainty, and time-varying dynamics thus improving the ship roll prediction accuracy, an enhanced hybrid prediction scheme is proposed by using improved swarm intelligent optimization, time series decomposition, and machine learning. Firstly, the novel time-varying filtering-based empirical mode decomposition (TVF-EMD) is employed to decompose the ship roll motion data into multiple mode components with dynamic time-varying characteristics, which immunes of the mode mixing and intermittency problems of traditional empirical mode decomposition (EMD). Then, the support vector regression is utilized to train and predict mode components. Finally, the predicted results of individual components are reconstructed to achieve the final ship roll prediction angles. To avoid the unfavorable influence of manual parameter selection for TVF-EMD, an improved black widow optimization algorithm is employed to optimize the parameter configuration. The feasibility and effectiveness of the enhanced hybrid model are validated by ship roll prediction simulation based on the measured data of M.V. YuKun at sea. The experimental results show that the enhanced hybrid scheme can improve the prediction accuracy of ship roll motion and outrank those by using methods of EMD, ensemble empirical mode decomposition, and variational mode decomposition.

LoRa Radio Frequency Fingerprinting with Residual of Variational Mode Decomposition and Hybrid Machine-Learning/Deep-Learning Optimization

LoRa Radio Frequency Fingerprinting with Residual of Variational Mode Decomposition and Hybrid Machine-Learning/Deep-Learning Optimization

A novel coupled rainfall prediction model based on stepwise decomposition technique

The traditional decomposed ensemble prediction model decomposes the entire rainfall sequence into several sub-sequences, dividing them into training and testing periods for modeling. During sample construction, future information is erroneously mixed into the training data, making it challenging to apply in practical rainfall forecasting. This paper proposes a novel stepwise decomposed ensemble coupling model, realized through variational mode decomposition (VMD) and bidirectional long short-term memory neural network (BiLSTM) models. Model parameters are optimized using an improved particle swarm optimization (IPSO). The performance of the model was evaluated using rainfall data from the Southern Four Lakes basin. The results indicate that: (1) Compared to the PSO algorithm, the IPSO algorithm-coupled model shows a minimum decrease of 2.70% in MAE and at least 2.62% in RMSE across the four cities in the Southern Four Lakes basin; the IPSO algorithm results in a minimum decrease of 25.58% in MAE and at least 28.19% in RMSE for the VMD-BiLSTM model. (2) When compared to IPSO-BiLSTM, the VMD-IPSO-BiLSTM based on the stepwise decomposition technique exhibits a minimum decrease of 26.54% in MAE and at least 34.16% in RMSE. (3) The NSE for the testing period of the VMD-IPSO-BiLSTM model in each city surpasses 0.88, indicating higher prediction accuracy and providing new insights for optimizing rainfall forecasting.

A hybrid machine learning forecasting model for photovoltaic power

The increasing use of photovoltaic (PV) power generation presents a significant opportunity for global energy transformation. However, accurately forecasting PV power remains a challenge. This study proposes a hybrid approach that combines variational mode decomposition (VMD), whale optimization algorithm (WOA), and long short-term memory neural network (LSTM) to forecast photovoltaic (PV) power accurately. The model decomposes the time series of PV power using VMD to address the non-stationary nature of the time series. The VMD parameters are optimized using WOA. Subsequently, and the PV power time series data is then decomposed using the optimized VMD parameters to obtain multiple intrinsic mode functions (IMFs) components and a residual component. These components are then reconstructed with meteorological parameters to obtain the reconstructed IMF components and residuals. Finally, multiple LSTM sub-models are built, with each of them taking the IMF components and residual from the previous reconstruction as inputs. The sub-models are optimized using the WOA method to determine their hyperparameters and then constructed with these optimized hyperparameters. The predicted values of each IMF and residual are output and added for sequence reconstruction to derive the final predicted value of PV power. The model's effectiveness was verified for one-hour-ahead forecasting at the 1.8 MW solar system in Yulara, central Australia. The test results show that the proposed model outperforms other benchmark models, with mean absolute error (MAE), root mean square error (RMSE), mean absolute percentage error (MAPE), and R-squared value (R2) of 15.247 kW, 19.753 kW, 4.405 % and 0.997, respectively. Compared to the LSTM, MAE, RMSE, and MAPE decreased by 84.942 %, 86.746 %, and 82.611 %, respectively, while R2 increased by 23.438 %. The proposed model has better predictive performance for both stable power changes and large fluctuations, essential for effectively integrating renewable energy sources into the power grid.

The application of artificial intelligence in Unmanned Underwater Vehicle communication systems

Artificial Intelligence (AI) has the potential to significantly enhance decision-making techniques in Unmanned Underwater Vehicle (UUV) communication systems by utilizing real-time sensor feedback and environmental data. To address the challenges posed by high data volume and error rates, we propose an advanced methodology known as the Variational Deep Network (VDN). This method integrates Variational Modal Decomposition (VMD) algorithms with the Deep Convolutional Neural Network (DCNN) to create a realizable AI decision-making system. In conjunction with the DCNN and VMD algorithms, our research focuses on accurately identifying received signals under data constraints. Considering the spectral efficiency and robustness, the Filter-Bank Multicarrier (FBMC) technology have been employed in this paper. Our results demonstrate that the VDN significantly reduces the volume of data needed for neural network training and effectively recognizes FBMC signals. These insights confirm the potential of VDN decision-making systems to drive advancements in UUV communication technologies.

A milling tool wear predicting method with processing generalization capability

Tool Wear Prediction (TWP) is crucial to ensure machining quality. Compared to traditional prediction methods based on full-life or failure data, labelled data are limited or nonexistent when a new tool or similar tools have emerged. This makes it extremely challenging to predict wear using limited tracking data. This work aims to provide an innovative method for accurate long-term wear prediction of milling processes using limited monitoring data of individual tools. First, the Variational Modal Decomposition (VMD) and Pearson Correlation Threshold (PCT) are combined to adaptively filter the corresponding machining signals. Second, fitness analysis is performed by selecting features strongly related to tool degradation using feature monotonicity metrics, and sensitive information is fused based on Kernel Principal Components Analysis (KPCA). Third, a Stacked Bi-directional Long Short-Term Memory with attention mechanism (AT-SBiLSTM) model is constructed to ascertain the connection between sensitive feature and the future wear state of the tool by multi-step advance rolling prediction. The results of the various milling experiment show that the proposed approach can provide accurate forecasts of tool wear using limited monitoring data.

A novel technology based on Raman spectroscopy for effective differentiation of alanine chiral isomers

In this study, Raman time-domain spectroscopy (R-TDS) was used to record the spectra of β-alanine, D-alanine, L-alanine, and DL-alanine molecules in the Raman shift range of 250–2000 cm−1. Baseline correction and smoothing of the original spectra yielded considerably different scattering peaks for β-alanine than the other three alanine isomers. The positions and intensities of the peaks in the spectra of D-alanine, L-alanine and DL-alanine were very similar, enabling β-alanine to be easily distinguished from the aforementioned isomers based on the Raman spectra. The Raman spectral data of D-alanine, L-alanine and DL-alanine were subjected to variational mode decomposition (VMD), whereby each spectral line was decomposed into four intrinsic mode functions (IMFs). Finally, a grid search-support vector machine (GS-SVM) classification recognition model was established for Raman spectral analysis and classification analysis using the first four IMFs as datasets. VMD-GS-SVM classification had a 96.67 % discriminative accuracy for predicted samples of the three isomers of D-alanine, L-alanine and DL-alanine. The classification recognition accuracy gradually trended downward as the number of mode components increased. The results show that the fast identification model of alanine isomers based on R-TDS and VMD-GS-SVM is effective and feasible, providing an accurate and fast optical measurement solution for the development of novel drugs and quality monitoring of fine chemicals.

A Novel Improved Variational Mode Decomposition-Temporal Convolutional Network-Gated Recurrent Unit with Multi-Head Attention Mechanism for Enhanced Photovoltaic Power Forecasting

Photovoltaic (PV) power forecasting plays a crucial role in optimizing renewable energy integration into the grid, necessitating accurate predictions to mitigate the inherent variability of solar energy generation. We propose a novel forecasting model that combines improved variational mode decomposition (IVMD) with the temporal convolutional network-gated recurrent unit (TCN-GRU) architecture, enriched with a multi-head attention mechanism. By focusing on four key environmental factors influencing PV output, the proposed IVMD-TCN-GRU framework targets a significant research gap in renewable energy forecasting methodologies. Initially, leveraging the sparrow search algorithm (SSA), we optimize the parameters of VMD, including the mode component K-value and penalty factor, based on the minimum envelope entropy principle. The optimized VMD then decomposes PV power, while the TCN-GRU model harnesses TCN’s proficiency in learning local temporal features and GRU’s capability in rapidly modeling sequence data, while leveraging multi-head attention to better utilize the global correlation information within sequence data. Through this design, the model adeptly captures the correlations within time series data, demonstrating superior performance in prediction tasks. Subsequently, the SSA is employed to optimize GRU parameters, and the decomposed PV power mode components and environmental feature attributes are inputted into the TCN-GRU neural network. This facilitates dynamic temporal modeling of multivariate feature sequences. Finally, the predicted values of each component are summed to realize PV power forecasting. Validation using real data from a PV station corroborates that the novel model demonstrates a substantial reduction in RMSE and MAE of up to 55.1% and 54.5%, respectively, particularly evident in instances of pronounced photovoltaic power fluctuations during inclement weather conditions. The proposed method exhibits marked improvements in accuracy compared to traditional PV power prediction methods, underscoring its significance in enhancing forecasting precision and ensuring the secure scheduling and stable operation of power systems.

Research on Deformation Prediction of VMD-GRU Deep Foundation Pit Based on PSO Optimization Parameters

As a key guarantee and cornerstone of building quality, the importance of deformation prediction for deep foundation pits cannot be ignored. However, the deformation data of deep foundation pits have the characteristics of nonlinearity and instability, which will increase the difficulty of deformation prediction. In response to this characteristic and the difficulty of traditional deformation prediction methods to excavate the correlation between data of different time spans, the advantages of variational mode decomposition (VMD) in processing non-stationary series and a gated cycle unit (GRU) in processing complex time series data are considered. A predictive model combining particle swarm optimization (PSO), variational mode decomposition, and a gated cyclic unit is proposed. Firstly, the VMD optimized by the PSO algorithm was used to decompose the original data and obtain the Internet Message Format (IMF). Secondly, the GRU model optimized by PSO was used to predict each IMF. Finally, the predicted value of each component was summed with equal weight to obtain the final predicted value. The case study results show that the average absolute errors of the PSO-GRU prediction model on the original sequence, EMD decomposition, and VMD decomposition data are 0.502 mm, 0.462 mm, and 0.127 mm, respectively. Compared with the prediction mean square errors of the LSTM, GRU, and PSO-LSTM prediction models, the PSO-GRU on the PTB0 data of VMD decomposition decreased by 62.76%, 75.99%, and 53.14%, respectively. The PTB04 data decreased by 70%, 85.17%, and 69.36%, respectively. In addition, compared to the PSO-LSTM model, it decreased by 8.57% in terms of the model time. When the prediction step size increased from three stages to five stages, the mean errors of the four prediction models on the original data, EMD decomposed data, and VMD decomposed data increased by 28.17%, 3.44%, and 14.24%, respectively. The data decomposed by VMD are more conducive to model prediction and can effectively improve the accuracy of model prediction. An increase in the prediction step size will reduce the accuracy of the deformation prediction. The PSO-VMD-GRU model constructed has the advantages of reliable accuracy and a wide application range, and can effectively guide the construction of foundation pit engineering.

Performance degradation assessment of rolling bearings based on the comprehensive characteristic index and improved SVDD

Abstract Rolling bearing is one of the most critical parts of mechanical equipment, so the performance degradation assessment of rolling bearing is vital to ensure the normal operation of the whole mechanical equipment. Aiming at the problems that a single degradation characteristic can only contain limited performance degradation information of rolling bearings, a large number of redundant characteristics exist in the high-dimension characteristic set resulting in the inability to effectively mine the characteristic information of rolling bearings, and that traditional degradation assessment models are not suitable for the shortage of fault data during the actual operation of rolling bearings, a performance degradation assessment method of rolling bearings based on the comprehensive characteristic index and improved support vector data description (SVDD) is proposed in this paper. Firstly, to solve the parameter selection problem of variational mode decomposition (VMD), a parameter-adaptive VMD method based on salp swarm algorithm based on mixed strategy (MSSSA) is proposed. Secondly, to extract the performance degradation information of rolling bearings more comprehensively and fully, the comprehensive characteristic index is proposed. Then, a kernel locality preserving projection orthogonal kernel principal component analysis (KLPPOKPCA) method is proposed to reduce the dimensionality of the extracted multi-domain characteristic set of the rolling bearing. Finally, a support vector data description with negative samples (NSSVDD) is proposed and optimized by MSSSA to solve the problem that traditional degradation assessment models are not suitable for the shortage of fault data during the actual operation of rolling bearings and improve the detection performance of abnormal data. The experimental results show that the proposed method can accurately divide the performance degradation process of the rolling bearing. Moreover, the comparison with other methods further highlights the superiority of the proposed method in determining the point in time of early fault of the rolling bearing. 

A novel hybrid model based on Empirical Mode Decomposition and Echo State Network for wind power forecasting

Accurate wind power forecasting is essential for (i) the management of wind energy, (ii) increasing the integration of generated power into the electrical grid, and (iii) enhancing maintenance efficiency. This paper proposes a novel hybrid model for short-term (1-hour ahead) wind power forecasting. The model integrates the echo-state network (ESN) architecture with empirical mode decomposition (EMD) to improve forecast accuracy. Unlike existing approaches that use separate models for each decomposed signal after EMD method, proposed model uses a single ESN structure to predict wind power by incorporating all decomposed signals and their past values. The main advantage of this architecture is that it eliminates the need to train multiple models, thereby streamlining the forecasting process. To evaluate the performance of the proposed model, one year of data from the West of Duddon Sands, Barrow, and Horns Power offshore wind farms is utilized. Firstly, the classical ESN model and the EMD-ESN hybrid model are compared for the three datasets. Then, a comprehensive evaluation is performed by comparing the results of the proposed model with commonly used standalone and hybrid forecasting models such as Multi-Layer Perceptron (MLP), Adaptive-Neuro Fuzzy Inference System (ANFIS), Long Short-Term Memory (LSTM), Bidirectional LSTM (BiLSTM), EMD-LSTM, EMD-BiLSTM, Variational Mode Decomposition based ESN (VMD-ESN), and Wavelet Decomposition based ESN (WD-ESN). The results show that the EMD-ESN hybrid model outperforms implemented models in predicting wind power in all three datasets. Furthermore, the proposed EMD-ESN model for an onshore wind turbine power data in Germany is compared with the SOTA models, such as Transformer, Informer, Autoformer, and Graph Patch Informer (GPI), in the literature. This study highlights the superior predictive capabilities of proposed model, making it a valuable tool for enhancing the accuracy of wind power forecasts, thereby contributing to the reliable integration of wind energy into the power grid.

Ensemble learning using multivariate variational mode decomposition based on the Transformer for multi-step-ahead streamflow forecasting

Accurate streamflow forecasting is critical in the domain of water resources management. However, the inherently non-stationary and stochastic nature of streamflow poses a significant challenge to achieving accuracy in streamflow forecasting. In this study, we introduce an MVMD-ensembled Transformer model (MVMD-Transformer), which incorporates the MVMD for concurrent time–frequency analysis of streamflow and related potential influencing variables. The model aligns common modes in the decomposition results, ensuring that the different variables corresponding to each mode have the same center frequency. This alignment overcomes frequency mismatches and helps uncover the intrinsic patterns and essential features between streamflow and associated variables. During the forecasting phase, the Transformer component of the MVMD-Transformer model establishes connections among streamflow and other influencing variables across pairs of nodes in each mode. We tested the performance of the MVMD-Transformer model in forecasting streamflow across 1-, 3-, 5-, and 7-day horizons within the Shiyang River, Heihe River, and Shule River basins situated in the Hexi Corridor of Northwest China. The MVMD-Transformer model harnesses MVMD to concurrently decompose both predictor variables (precipitation, air temperature, air pressure, soil moisture) and the response variable (streamflow). Subsequently, the modes drived from the MVMD were fed into the Transformer, serving as the predictive analytics engine, to forecast streamflow. Furthermore, we conducted a comprehensive performance evaluation by comparing the MVMD-Transformer model against four alternatives: the VMD-ensembled Transformer model (VMD-Transformer), CEEMDAN-ensembled Transformer model (CEEMDAN-Transformer), stand-alone Transformer model, and LSTM model. The results indicate that MVMD-Transformer outperformed all other models, achieving Nash-Sutcliffe coefficient (NSE) values exceeding 0.85 in the majority of the forecasting scenarios. This superior performance highlights the proficiency of the MVMD approach in more accurately unraveling the intricate interdependencies between streamflow and its various potential influencing variables, thus significantly improving the precision of streamflow forecasting.

Research on heart and lung sound separation method based on DAE–NMF–VMD

Auscultation is the most effective method for diagnosing cardiovascular and respiratory diseases. However, stethoscopes typically capture mixed signals of heart and lung sounds, which can affect the auscultation effect of doctors. Therefore, the efficient separation of mixed heart and lung sound signals plays a crucial role in improving the diagnosis of cardiovascular and respiratory diseases. In this paper, we propose a blind source separation method for heart and lung sounds based on deep autoencoder (DAE), nonnegative matrix factorization (NMF) and variational mode decomposition (VMD). Firstly, DAE is employed to extract highly informative features from the heart and lung sound signals. Subsequently, NMF clustering is applied to group the heart and lung sounds based on their distinct periodicities, achieving the separation of the mixed heart and lung sounds. Finally, variational mode decomposition is used for denoising the separated signals. Experimental results demonstrate that the proposed method effectively separates heart and lung sound signals and exhibits significant advantages in terms of standardized evaluation metrics when compared to contrast methods.

Bearing fault diagnosis of induction machines using VMD-DWT and composite multiscale weighted permutation entropy

Purpose Bearings play a critical role in the reliable operation of induction machines, and their failure can lead to significant operational challenges and downtime. Detecting and diagnosing these defects is imperative to ensure the longevity of induction machines and preventing costly downtime. The purpose of this paper is to develop a novel approach for diagnosis of bearing faults in induction machine. Design/methodology/approach To identify the different fault states of the bearing with accurately and efficiently in this paper, the original bearing vibration signal is first decomposed into several intrinsic mode functions (IMFs) using variational mode decomposition (VMD). The IMFs that contain more noise information are selected using the Pearson correlation coefficient. Subsequently, discrete wavelet transform (DWT) is used to filter the noisy IMFs. Second, the composite multiscale weighted permutation entropy (CMWPE) of each component is calculated to form the features vector. Finally, the features vector is reduced using the locality-sensitive discriminant analysis algorithm, to be fed into the support vector machine model for training and classification. Findings The obtained results showed the ability of the VMD_DWT algorithm to reduce the noise of raw vibration signals. It also demonstrated that the proposed method can effectively extract different fault features from vibration signals. Originality/value This study suggested a new VMD_DWT method to reduce the noise of the bearing vibration signal. The proposed approach for bearing fault diagnosis of induction machine based on VMD-DWT and CMWPE is highly effective. Its effectiveness has been verified using experimental data.

Surface roughness estimation using vibration characteristics extracted by variational mode decomposition in turning

Abstract This study presents an approach that combines variational mode decomposition (VMD) and relevance vector machine (RVM) as a prediction technique for surface roughness during turning. The method helps machinists detect irregularities during machining, such as looseness in machine parts or tool wear. The study uses work hardened EN8 steel and extracts vibration signal features into five modes. PSO optimized RVM prediction models are developed using these modes with and without combining cutting parameters. The most sensitive mode is selected for accurate surface roughness prediction. The results show that the first mode of decomposition when combined with cutting parameters provides the least mean square error of 0.1095. Surface roughness was found to be primarily influenced inversly by cutting speed and directly by feed rate respectively. The signal with high surface roughness value has high amplitude noise scattered over the large frequency range. The first decomposed mode of vibration signal increases noise with a large amplitude as surface roughness increases. The approach can be integrated into a microcontroller to regulate machine settings based on vibration data.

A short-term wind power prediction approach based on an improved dung beetle optimizer algorithm, variational modal decomposition, and deep learning

Accurate short-term wind power prediction is crucial for the efficient and safe operation of wind power systems. To enhance the accuracy of short-term wind power prediction, this paper proposes a hybrid short-term wind power prediction model, IDBO-VMD-TCN-GRU-Attention, based on the Improved Dung Beetle Optimizer algorithm (IDBO), Variational Modal Decomposition (VMD), Temporal Convolutional Network (TCN), Gated Recurrent Unit (GRU), and Attention Mechanism. The IDBO is used to optimize the parameters of the VMD. Then the optimized IDBO-VMD is used to decompose the original data into modal components with lower volatility to fully extract the data features. These modal components are inputted into the TCN-GRU-Attention to predict the short-term wind power and obtain the final prediction value. The model is tested and validated using real data from four different months and compared against 11 other models. Results demonstrate that our proposed model significantly reduces the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE) by an average of at least 22.86 %, 18.82 %, and 19.99 %, respectively, across the four different months. This indicates that the proposed model provides a superior fit to the data, offers higher prediction accuracy, and holds significant practical value.

A novel lidar signal denoising method based on variational mode decomposition optimized using whale algorithm

Original lidar return signals are covered by high levels of noise that seriously affect the accuracy of subsequent data processing and inversion. Therefore, it is important to separate the effective signal from the returned signal with noise interference. In this paper, an efficient denoising method based on the variational mode decomposition (VMD) algorithm optimized using the global search strategy-based whale algorithm and the total variational stationary wavelet transform (GSWOA-VMD-SWTTV) is proposed, and this method is applied to denoising of lidar return signals. First, the global search strategy-based whale optimization algorithm (GSWOA) is used to acquire the optimal parameters of the VMD algorithm adaptively, and the lidar return signal is then decomposed by global search strategy-based whale optimization algorithm (GSWOA)-VMD. The effective modal components are then determined using the cross-correlation coefficient method from the decomposed modal components, and total variation stationary wavelet denoising is performed on each effective mode. Finally, the effective modes are reconstructed to obtain a clean lidar return signal. Moreover, to provide further verification of the effectiveness of the proposed method, it is compared with the ensemble empirical mode decomposition (EEMD) method, the complete EEMD with adaptive noise (CEEMDAN) method, the singular value decomposition (SVD) method, and the wavelet threshold method under sunny, cloudy, and dusty weather conditions. The experimental results demonstrate the superior noise reduction performance of the proposed algorithm, which can filter out strong noise from the signal while retaining the complete signal details without distortion; additionally, the proposed method has the highest signal-to-noise ratio and lowest mean square error.

HeMTAN: Hybrid task-adapted experts-based multi-task attention network for unseen compound fault decoupling diagnosis of rotating machinery

In a rotating machinery system, a single fault of one component often causes damage to other related components, thus inducing compound faults. Without compound fault data to train intelligent models, the realization of decoupling diagnosis and accurate identification of unseen compound faults is not only of great practical significance for the safety management of equipment operation and maintenance, but also remains a challenging topic. Considering some shortcomings in the current intelligent diagnosis of compound faults, as well as the relatedness and difference between different fault features in compound fault signals, a hybrid task-adapted experts-based multi-task attention network (HeMTAN) model is investigated in this paper, which can be used for identify single faults and unseen compound faults in mechanical transmission systems. Firstly, variational mode decomposition is combined with Hilbert-Huang transform to obtain time–frequency graphs of time series signal as model input, so as to better characterize different fault features. Secondly, a hybrid task-adapted expert module is designed to extract the common and some private feature information of different learning tasks from different multi-perspective, and then the important information related to the specific learning task is further mined by the constructed private feature attention-based densely connected module. Finally, the diagnosis results can be obtained by fusing the outputs of the classifier of the two learning tasks. The performance of the investigated HeMTAN model is analyzed by the gearbox compound fault dataset and rolling bearing compound fault dataset, and the results demonstrate that the investigated HEMTAN method has significantly improved diagnosis accuracy and generalization performance