Variational Mode Decomposition Method Research Articles

Enhancing GNSS Deformation Monitoring Forecasting with a Combined VMD-CNN-LSTM Deep Learning Model

Hydraulic infrastructures are susceptible to deformation over time, necessitating reliable monitoring and prediction methods. In this study, we address this challenge by proposing a novel approach based on the combination of Variational Mode Decomposition (VMD), Convolutional Neural Network (CNN), and Long Short-Term Memory (LSTM) methods for Global Navigation Satellite Systems (GNSS) deformation monitoring and prediction modeling. The VMD method is utilized to decompose the complex deformation signals into intrinsic mode functions, which are then fed into a CNN method for feature extraction. The extracted features are input into an LSTM method to capture temporal dependencies and make predictions. The experimental results demonstrate that the proposed VMD-CNN-LSTM method exhibits an improvement by about 75%. This research contributes to the advancement of deformation monitoring technologies in water conservancy engineering, offering a promising solution for proactive maintenance and risk mitigation strategies.

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

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.

Speech emotion recognition using a combination of variational mode decomposition and Hilbert transform

The objective of automated speech emotion recognition (SER) is to recognize each emotion of the speech signal uniquely and efficiently using machines like computers, mobile devices, etc. The popularity of SER has been widely acknowledged among researchers due to its extensive applicability in practical contexts. The use of SER has shown to be advantageous in several domains, including medical treatment, enhancement of security systems, surveillance operations, online marketing strategies, online educational platforms, online search engines, personal communication, customer relationship management, reinforcement of machine and human connection, and numerous other areas. Numerous authors have used various techniques, including the combination of multiple features (acoustic, non-acoustic, or both) and classifiers (machine learning, deep learning, or both), in order to enhance the efficacy of emotion categorization. In the present work, our objective is to enhance the performance of emotion classification (PECL) by using a combined approach of the variational mode decomposition (VMD) and Hilbert transform (HT) techniques. Using the VMD method, we decomposed the speech signal frame into many sub-signals, or intrinsic mode functions (IMFs). Then HT is applied to each VMD-based IMF signal to find the mode instantaneous amplitude (MIA) and mode instantaneous frequency (MIF) signal vectors. We extracted proposed features such as HT-based approximate entropy (HTAE), HT-based permutation entropy (HTPE), HT-based increment entropy (HTIE), and HT-based sample entropy (HTSE) using each MIA and MIF signal vector. The combination of the proposed HT-based features is called HT-based entropy (HTE) features. Then, we accessed the PECL using the HTE and MFCC features alone and in conjunction with a deep neural network (DNN) classifier. The experiment's results showed that the combinations of the proposed feature (MFCC + HTE) using a DNN classifier outperformed the individual features and obtained a SER accuracy of 86.92% for the EMOVO dataset and 91.63% for the EMO-DB dataset.

Application of 2D Variational Mode Decomposition Method in Seismic Signal Denoising

Seismic data are typical nonlinear and nonstationary data. In the acquisition and processing of seismic data, many factors interfere with it. Seismic data contain both effective waves and random noises, seriously affecting the quality of seismic data and not conducive to the goal of fine interpretation of subsequent seismic data. Therefore, studying new seismic data denoising methods is beneficial for improving the quality of seismic data and plays a very important role in subsequent seismic data interpretation. In this paper, the principle of variational mode decomposition (VMD) and 2D-VMD is introduced in detail, and the seismic profile with a simple signal and fault model is denoised. Compared to traditional empirical mode decomposition (EMD), the 2D-VMD method has the best seismic data denoising effect. The test results of the synthesised signal show that the 2D-VMD method has a signal-to-noise ratio of 47.14 dB after denoising, which is higher than the signal-to-noise ratio after EMD and VMD denoising, indicating that it has a better denoising effect. The VMD and 2D-VMD methods are applied to the denoising of actual seismic data. The application results show that the 2D-VMD method can effectively improve the quality of the seismic data, enhance the continuity and reliability of the seismic data, and is conducive to the fine interpretation of subsequent seismic data.

Research on Annual Runoff Prediction Model Based on Adaptive Particle Swarm Optimization–Long Short-Term Memory with Coupled Variational Mode Decomposition and Spectral Clustering Reconstruction

Accurate medium- and long-term runoff prediction models play crucial guiding roles in regional water resources planning and management. However, due to the significant variation in and limited amount of annual runoff sequence samples, it is difficult for the conventional machine learning models to capture its features, resulting in inadequate prediction accuracy. In response to the difficulties in leveraging the advantages of machine learning models and limited prediction accuracy in annual runoff forecasting, firstly, the variational mode decomposition (VMD) method is adopted to decompose the annual runoff series into multiple intrinsic mode function (IMF) components and residual sequences, and the spectral clustering (SC) algorithm is applied to classify and reconstruct each IMF. Secondly, an annual runoff prediction model based on the adaptive particle swarm optimization–long short-term memory network (APSO-LSTM) model is constructed. Finally, with the basis of the APSO-LSTM model, the decomposed and clustered IMFs are predicted separately, and the predicted results are integrated to obtain the ultimate annual runoff forecast results. By decomposing and clustering the annual runoff series, the non-stationarity and complexity of the series have been reduced effectively, and the endpoint effect of modal decomposition has been effectively suppressed. Ultimately, the expected improvement in the prediction accuracy of the annual runoff series based on machine learning models is achieved. Four hydrological stations along the upper reaches of the Fen River in Shanxi Province, China, are studied utilizing the method proposed in this paper, and the results are compared with those obtained from other methods. The results show that the method proposed in this article is significantly superior to other methods. Compared with the APSO-LSTM model and the APSO-LSTM model based on processed annual runoff sequences by single VMD or Wavelet Packet Decomposition (WPD), the method proposed in this paper reduces the RMSE by 40.95–80.28%, 25.26–57.04%, and 15.49–40.14%, and the MAE by 24.46–80.53%, 16.50–59.30%, and 16.58–41.80%, in annual runoff prediction, respectively. The research has important reference significance for annual runoff prediction and hydrological prediction in areas with data scarcity.

Load forecasting for regional integrated energy system based on two-phase decomposition and mixture prediction model

Current load forecasting methods struggle with the randomness and complexity of multiple loads in regional integrated energy systems, resulting in less accurate predictions. To address this problem, this paper proposes a novel two-phase decomposition hybrid forecasting model that combines complementary ensemble empirical mode decomposition, sample entropy, variational mode decomposition, and genetic algorithm-bidirectional long short term memory. The proposed approach begins by decomposing the load sequence into multiple intrinsic mode function components at different frequencies using complementary ensemble empirical mode decomposition. Afterward, the sample entropy values are calculated for each intrinsic mode function. The intrinsic mode function with the highest sample entropy value is subjected to a two-stage decomposition using the variational mode decomposition method. Through this technique, a series of stationary components is acquired. Subsequently, the bidirectional long short term memory model is optimized using the genetic algorithm, and the genetic algorithm-bidirectional long short term memory approach is employed to predict all the decomposed components. Finally, the prediction results are combined and reconstructed to obtain the final prediction value. Experimental results demonstrate the effective handling of non-stationary load sequences by the forecasting model, showcasing the highest level of accuracy in regional integrated energy system multiple loads forecasting.

Measurement of aero-engine feature-hierarchy fusion degradation trend based on parameter-adaptive VMD method and improved transformer model

The accumulation of operational time in aero-engines leads to irreversible mechanical wear and tear, necessitating accurate measurement of the health evolution trend for effective predictive maintenance, thus reducing the risk of accidents and ensuring personnel safety. In this paper, a parameter-adaptive variational mode decomposition (VMD) method and improved transformer model are proposed to forecast the degradation trend of aero-engine feature hierarchy fusion. Firstly, in order to quantitatively evaluate the engine health evolution process, the health state aggregate indicator (HSAI) is innovatively constructed by employing the deep blend auto-encoder and self-organizing map network, which facilitate the feature-hierarchy fusion of multi-source sensory data. Secondly, for the significant characteristics with nonlinearity and stochastic fluctuation of the HSAI sequence, the multiscale frequency features are extracted by the parameter-adaptive VMD method with the improved gray wolf optimizer, which analyzes the inherent degradation law. Finally, considering the problem of parameter sharing in the transformer model, a simplified mixture of experts routing algorithm is introduced to implement the switch transformer model to further measure the future aero-engine health trends. Extensive experiments on the multi-source dataset of aero-engine confirm that the proposed method accomplishes the more superior performance for health evolution measurement compared with other available methods.

Drive-by bridge mode shape identification using novel reference-based component scaling method

This article proposes a novel method, entitled Reference-based Component Scaling (RCS) method, for estimation of bridge mode shapes using vehicle scanning methods. The proposed method uses two instrumented vehicles to measure the accelerations on the bridge. While one vehicle remains stationary on a pre-determined location, the other one travels over the bridge with a constant speed both exciting the bridge and recording its response. The accelerations recorded on both vehicles are then processed using variational mode decomposition method and Hilbert transform to obtain their modal components. Leveraging its comprehensive framework that incorporates modal components derived from both vehicles, the RCS method effectively tackles the primary challenges encountered by vehicle scanning methods. These challenges include: i) shifting and shrinking effects of bridge damping on mode shapes, ii) distortions in modal components due to incomplete elimination of the roughness effect and iii) distortions in modal components caused by acceleration peaks during the vehicle´s transition from a rigid platform to the bridge. To this end, the RCS method addresses adverse effects of bridge damping without a priori knowledge of the modal damping ratios. To assess the accuracy of the proposed method, numerical analyses were carried out on three different bridges with different number of spans and boundary conditions. The effect of crucial parameters such as road roughness, bridge damping, uncertainties in measurements, and existing traffic on the accuracy of the proposed method was investigated. The results of the numerical study show that the RCS method stands alone in providing accurate estimates of mode shapes of bridges that are seated on elastic bearings, that have realistic damping ratios and relatively high road roughness profiles.

Short-term Wind Power Forecasts based on VMD-KPCA and CFSBOA-BiLSTM

Accurate prediction of wind power is of great significance to reduce the impact of large-scale wind power connection and improve the security and stability of power grid. A short-term wind power forecasting method based on VMD-KPCA and CFSBOA-BiLSTM is proposed. Firstly, the key environmental factors restricting the volatility of wind power are fully considered, and the variational mode decomposition method is used to decompose the wind power and meteorological factors. Secondly, the kernel principal component analysis method is used to reduce the dimension and construct the sub-sequence characteristic data set. Finally, the multi-strategy improved butterfly algorithm is used to optimize the BiLSTM network hyperparameters and establish the CFSBOA-BiLSTM prediction model. The simulation analysis uses the measured data of a wind farm in northwest China. The experimental results show that the combined forecasting model can fully mine the hidden information of the data and improve the accuracy of short-term wind power forecasting. Compared with the BiLSTM model, RMSE, MAE and MAPE decreased by 60.37%, 66.6% and 67.59%, respectively.

Grouped Multivariate Variational Mode Decomposition With Application to EEG Analysis.

In this paper, a novel extended form of multivariate variational mode decomposition (MVMD) method to multigroup data named as grouped MVMD (GMVMD) is proposed. GMVMD is distinct from MVMD as it extracts common frequencies with strong correlations among regional channels. Firstly, GMVMD utilizes a new clustering algorithm named as frequencies grouping algorithm to classify the nearest common frequencies among all channels to specified groups. Secondly, a generic variational optimization model which is extended from MVMD is formulated. Thirdly, alternating direction method of multipliers (ADMM) is utilized to obtain optimal solution of GMVMD model. The proposed method introduces an extra parameter to decide the number of clusterings which need to be specified by the user. The effectiveness and superiority of the algorithm are demonstrated on a series of experiments. The utility of GMVMD is verified by grouping real-world electroencephalogram (EEG) data having similar center frequencies successfully. GMVMD outperforms MVMD in mode-alignment, signal reduction error and et al. Significance: GMVMD can obtain more accurate center frequencies and less signal reduction error than MVMD.

Research on Transmission Efficiency Prediction of Heavy-Duty Tractors HMCVT Based on VMD and PSO–BP

Transmission efficiency is a key characteristic of Hydro-mechanical Continuously Variable Transmission (HMCVT), which is related to the performance of heavy-duty tractors. Predicting the HMCVT transmission efficiency is beneficial for the real-time adjustment of transmission ratio during heavy-duty tractor operations, so as to obtain better performance. Aiming at the problems of accurate method, low accuracy, and high noise in the prediction of HMCVT transmission efficiency, this paper proposes a method based on Variational Mode Decomposition (VMD), Particle Swarm Optimization (PSO), and Back Propagation (BP) neural networks to improve the quality of transmission efficiency prediction. Firstly, a simple theoretical model was established to obtain the influencing factors of transmission efficiency. Then, based on these factors, the transmission efficiency was tested on the bench under multiple conditions and the influence degree of each factor on transmission efficiency was divided using Partial Least Squares (PLS) method. Finally, the VMD method was used to denoise the test data, and a BP model, which was improved using the PSO method, was established to predict the processed data. The results showed that transmission efficiency of HMCVT is most affected by output speed, followed by power, and least by input speed. The VMD method can accurately extract effective signals and noise signals from the original data, and reconstruct signals, reducing the noise proportion. Using three conditions, the prediction regression accuracy of the PSO–BP model is 7.02%, 7.88%, and 9.26% higher than that of the BP model, respectively. In the three prediction experiments, the maximum differences in the MAE, the MAPE, and the RMSE of the PSO–BP model are 0.002, 0.463%, and 0.004, respectively, which are 0.006, 0.796%, and 0.003 lower than those of the BP model.

A concurrent fault diagnosis method for electric isolation valves in nuclear power plants based on rule-based reasoning and data-driven methods

In order to improve the fault diagnosis ability of electric isolation valves in nuclear power plants, especially for the diagnosis of concurrent faults, a novel concurrent fault diagnosis method based on rule reasoning and data-driven methods is proposed in this study. The concurrent fault diagnosis method is divided into two layers: the rule-based reasoning layer and data-driven layer. In order to realize the diagnosis of most concurrent faults, the rule-based reasoning layer is established by a rule inference model according to the failure mode and effects analysis (FMEA) of the electric isolation valve. In order to diagnose concurrent faults with mutual interference of fault features that cannot be diagnosed by rule-based reasoning layer, the data-driven layer is established by variational mode decomposition (VMD) and fast independent component analysis (Fast-ICA) method to separate concurrent fault signals and gate recurrent unit (GRU) method to identify fault patterns. After testing on the electric valve test bench and simulation data, multiple concurrent faults of the electric isolation valve are diagnosed accurately by the proposed concurrent fault diagnosis framework, including complex concurrent faults such as internal leakage and external leakage, and the framework can also work in a single fault diagnosis scenario without changing models. Compared with the concurrent fault diagnosis based on multi-label support vector machine, the accuracy of concurrent fault diagnosis is improved by about 25.3%. The research can provide a new idea for the concurrent fault diagnosis of electric isolation valves and other equipment.

Variational Mode Decomposition-Based Processing for Detection of Short-Circuited Turns in Transformers Using Vibration Signals and Machine Learning

Transformers are key elements in electrical systems. Although they are robust machines, different faults can appear due to their inherent operating conditions, e.g., the presence of different electrical and mechanical stresses. Among the different elements that compound a transformer, the winding is one of the most vulnerable parts, where the damage of turn-to-turn short circuits is one of the most studied faults since low-level damage (i.e., a low number of short-circuited turns—SCTs) can lead to the overall fault of the transformer; therefore, early fault detection has become a fundamental task. In this regard, this paper presents a machine learning-based method to diagnose SCTs in the transformer windings by using their vibrational response. In general, the vibration signals are firstly decomposed by means of the variational mode decomposition method, where a comparison with the empirical mode decomposition (EMD) method and the ensemble empirical mode decomposition (EEMD) method is also carried out. Then, entropy, energy, and kurtosis indices are obtained from each decomposition as fault indicators, where both the combination of features and the dimensionality reduction by using the principal component analysis (PCA) method are analyzed for the global effectiveness improvement and the computational burden reduction. Finally, a pattern recognition algorithm based on artificial neural networks (ANNs) is used for automatic fault detection. The obtained results show 100% effectiveness in detecting seven fault conditions, i.e., 0 (healthy), 5, 10, 15, 20, 25, and 30 SCTs.

Short-Term Load Forecasting Method for Industrial Buildings Based on Signal Decomposition and Composite Prediction Model

Accurately predicting the cold load of industrial buildings is a crucial step in establishing an energy consumption management system for industrial constructions, which plays a significant role in advancing sustainable development. However, due to diverse influencing factors and the complex nonlinear patterns exhibited by cold load data in industrial buildings, predicting these loads poses significant challenges. This study proposes a hybrid prediction approach combining the Improved Snake Optimization Algorithm (ISOA), Variational Mode Decomposition (VMD), random forest (RF), and BiLSTM-attention. Initially, the ISOA optimizes the parameters of the VMD method, obtaining the best decomposition results for cold load data. Subsequently, RF is employed to predict components with higher frequencies, while BiLSTM-attention is utilized for components with lower frequencies. The final cold load prediction results are obtained by combining these predictions. The proposed method is validated using actual cold load data from an industrial building, and experimental results demonstrate its excellent predictive performance, making it more suitable for cold load prediction in industrial constructions compared to traditional methods. By enhancing the accuracy of cold load predictions. This approach not only improves the energy efficiency of industrial buildings but also promotes the reduction in energy consumption and carbon emissions, thus contributing to the sustainable development of the industrial sector.

Structural rotor rub-impact diagnosis under intricate noise interferences based on targeted component extraction and stochastic resonance enhancement

Rub-impact is a common nonlinear fault of the rotor system, occurring in rotating machines with radial clearance between the rotor and the stator, which may lead to serious consequences. Since the vibration response of rotor rub-impact is shown as multicomponent with time-varying characteristics of undulatory instantaneous frequency, it is desired to exploit advanced signal processing methods for rub-related feature excavation and failure diagnosis under complex noise interferences, which is of crucial significance to ensure the stable and efficient operation of the whole unit. This paper concerns the processing of acceleration signals and proposes a novel intrawave frequency modulation detection approach for structural rotor rubbing diagnosis based upon targeted component extraction and stochastic resonance enhancement. First, the acquired vibratory acceleration signal is converted into displacement signal via a two-stage integration strategy. Next, to extract the rotating frequency component of high information clarity for further time–frequency analysis from the multicomponent signal, an especially designed improved variational mode decomposition method based on the modified target frequency index is put forward, and the instantaneous frequency of the objective component is estimated. Then, the optimum stochastic resonance is leveraged for intrawave frequency modulation enhancement. Finally, the rotor rub-related symptom can be distinctly revealed and the diagnostic procedure can be performed. The effectiveness and superiority of the proposed rotor rub-impact diagnosis approach are demonstrated through both simulations and experiments, indicating that it is suitable to be implemented in practical applications, with high noise-resistance ability, and can efficiently extract the potential characteristics of rotor rub-impact malfunction from multicomponent signals.

Quantifying the Impact of Environment Loads on Displacements in a Suspension Bridge with a Data-Driven Approach.

Long-span bridges are susceptible to damage, aging, and deformation in harsh environments for a long time. Therefore, structural health monitoring (SHM) systems need to be used for reasonable monitoring and maintenance. Among various indicators, bridge displacement is a crucial parameter reflecting the bridge's health condition. Due to the simultaneous bearing of multiple environmental loads on suspension bridges, determining the impact of different loads on displacement is beneficial for the better understanding of the health conditions of the bridges. Considering the fact that extreme gradient boosting (XGBoost) has higher prediction performance and robustness, the authors of this paper have developed a data-driven approach based on the XGBoost model to quantify the impact between different environmental loads and the displacement of a suspension bridge. Simultaneously, this study combined wavelet threshold (WT) denoising and the variational mode decomposition (VMD) method to conduct a modal decomposition of three-dimensional (3D) displacement, further investigating the interrelationships between different loads and bridge displacements. This model links wind speed, temperature, air pressure, and humidity with the 3D displacement response of the span using the bridge monitoring data provided by the GNSS and Earth Observation for Structural Health Monitoring (GeoSHM) system of the Forth Road Bridge (FRB) in the United Kingdom (UK), thus eliminating the temperature time-lag effect on displacement data. The effects of the different loads on the displacement are quantified individually with partial dependence plots (PDPs). Employing testing, it was found that the XGBoost model has a high predictive effect on the target variable of displacement. The analysis of quantification and correlation reveals that lateral displacement is primarily affected by same-direction wind, showing a clear positive correlation, and vertical displacement is mainly influenced by temperature and exhibits a negative correlation. Longitudinal displacement is jointly influenced by various environmental loads, showing a positive correlation with atmospheric pressure, temperature, and vertical wind and a negative correlation with longitudinal wind, lateral wind, and humidity. The results can guide bridge structural health monitoring in extreme weather to avoid accidents.

Remaining Useful Life Prediction of Rolling Bearing Based on Multi-Domain Mixed Features and Temporal Convolutional Networks

For the remaining useful life (RUL) prediction of rolling bearing under strong background noise, it is hard to get accurate results based on the non-stationary vibration signals because of complex degradation characteristics and difficult extraction of key features. The framework of RUL prediction for rolling bearing is established by integrating multi-domain mixed features and temporal convolutional network (TCN). The variational mode decomposition method based on the dung beetle optimization algorithm is developed to reduce signal noise by determining the optimal parameters adaptively. To construct a health indicator of rolling bearing effectively, an isometric feature mapping algorithm is introduced to reduce the dimensionality of multi-domain mixed features, integrating time-domain, frequency-domain, and entropy features of vibration signals under non-stationary and nonlinear conditions. By considering the advantages of a multi-head attention mechanism (MA) and bidirectional gated recurrent unit (BiGRU), a TCN-based multi-head attention and bidirectional gate (TCNMABG) is developed to predict the RUL of rolling bearing accurately, whose detailed implementation process of TCNMABG is described based on XJTU-SY dataset. To verify the performance of TCNMABG, the FEMTO-ST dataset is introduced to perform the numerical experiments, and the results show that prediction error is reduced by 65.96% on average.

New formulation for predicting total dissolved gas supersaturation in dam reservoir: application of hybrid artificial intelligence models based on multiple signal decomposition

Total dissolved gas (TDG) concentration plays an important role in the control of the aquatic life. Elevated TDG can cause gas-bubble trauma in fish (GBT). Therefore, controlling TDG fluctuation has become of great importance for different disciplines of surface water environmental engineering.. Nowadays, direct estimation of TDG is expensive and time-consuming. Hence, this work proposes a new modelling framework for predicting TDG based on the integration of machine learning (ML) models and multiresolution signal decomposition. The proposed ML models were trained and validated using hourly data obtained from four stations at the United States Geological Survey. The dataset are composed from: (i) water temperature (Tw), (ii) barometric pressure (BP), and (iii) discharge (Q), which were used as the input variables for TDG prediction. The modelling strategy is conducted based on two different steps. First, six singles ML model namely: (i) multilayer perceptron neural network, (ii) Gaussian process regression, (iii) random forest regression, (iv) random vector functional link, (v) adaptive boosting, and (vi) Bootstrap aggregating (Bagging), were developed for predicting TDG using Tw, BP, and Q, and their performances were compared. Second, a new framework was introduced based on the combination of empirical mode decomposition (EMD), the variational mode decomposition (VMD), and the empirical wavelet transform (EWT) preprocessing signal decomposition algorithms with ML models for building new hybrid ML models. Hence, the Tw, BP, and Q signals were decomposed to extract the intrinsic mode functions (IMFs) by using the EMD and VMD methods and the multiresolution analysis (MRA) components by using the EWT method. Then after, the IMFs and MRA components were selected and regraded as new input variables for the ML models and used as an integral part thereof. The single and hybrid prediction models were compared using several statistical metrics namely, root mean square error, mean absolute error, coefficient of determination (R2), and Nash–Sutcliffe efficiency (NSE). The single and hybrid models were trained several times with high number of repetitions, depending on the kind of modeling process. The obtained results using single models gave good agreement between the predicted TDG and the situ measured dataset. Overall, the Bagging model performed better than the other five models with R2 and NSE values of 0.906 and 0.902, respectively. However, the extracted IMFs and MRA components using the EMD, VMD and the EWT have contributed to an improvement of the hybrid models’ performances, for which the R2 and NSE were significantly increased reaching the values of 0.996 and 0.995. Experimental results showed the superiority of hybrid models and more importantly the importance of signal decomposition in improving the predictive accuracy of TDG.Graphical abstract

A calibration and prediction method of the camera imaging parameters in variable temperature environment

In the on-orbit application of photogrammetry, constraints on thermal control resources or aging of thermal control equipment will trigger increased fluctuations in the camera operating environment temperature. Consequently, the parameters of the camera imaging model vary, such that the measurement accuracy is reduced. Accordingly, the accurate prediction of the camera imaging parameters (e.g., Camera Interior Parameters (CIP) and Lens Distortion Parameters (LDP)) at variable temperatures takes on critical significance.First, a novel method, termed as Virtual Multi-station Camera Calibration (VMCC), is proposed to calibrate the CIP and LDP with each frame at variable temperatures. Second, the Variational Mode Decomposition method combined with the Northern Goshawk Optimizer (NGO-VMD) is employed to decompose the camera imaging parameter signals obtained from VMCC, yielding the n Intrinsic Mode Functions (IMFs) contained in the respective parameter signal. Third, the Generalized Regression Neural Network combined with the Dung Beetle Optimizer (DBO-GRNN) is employed, such that the smoothness parameter q of the GRNN is iteratively optimized based on the camera imaging parameter prediction error. Lastly, the CIP and the LDP are accurately predicted at different temperatures in accordance with the temperature data from multiple parts of the camera.Based on this study, a reliable dataset of camera imaging parameter responses at variable temperatures can be generated for the on-orbit photogrammetry system. Furthermore, the prediction accuracy and immense application potential of neural network modeling methods are demonstrated in camera parameter prediction.

Mode decomposition and spatial propagation regularity analysis of cavitation variation on a twisted hydrofoil

The cavitation phenomenon can induce non-uniformity in the fluid, impacting fluid dynamic performance. This paper focuses on the cavitation shedding of the Delft Twist 11 hydrofoil. First, the reliability of numerical simulations is verified by computational fluid dynamics results. Utilizing the variational mode decomposition method, the cavitation signals on two cavitation paths are decomposed. Finally, the cavitation pulsation tracking network method is proposed to extensively investigate the spatial propagation patterns of cavitation signals at various sections above the twisted hydrofoil. The results reveal that typical frequencies at different monitoring planes are 30, 58, and 88 Hz. The corresponding amplitude analysis at these frequencies provides insight into the spatial propagation and attenuation process of cavitation vortices shedding. This study offers a novel perspective for a deeper understanding of cavitation mechanisms. Simultaneously, this provides references for enhancing the performance of mechanical engineering systems, reducing energy consumption, and improving structural reliability.