Mode Functions Research Articles

Detecting damage on engine mounts using hilbert-huang transform vibration analysis

Engine mounts, which are usually composed of elastomeric materials like rubber that can absorb excessive vibrations, are built to withstand vibration sources from engines. Engine mounts may eventually degrade from extended use. When rubber products age or sustain damage, they may grow harder and crack. Engine mounts need to be maintained regularly to ensure optimal performance. Visual examinations and the detection of excessive vibrations can be used to accomplish this. Vibration sensors are mounted on the engine mount in axial, vertical, and horizontal orientations using a vibration detection technique utilizing the Hilbert-Huang Transform (HHT) methodology. Matlab is used to examine the data that is gathered at three distinct rotational speeds: 750 rpm, 2000 rpm, and 3000 rpm. The HHT approach combines two key components: the Hilbert Transform, which analyzes the time-frequency signal of the first decomposition until only residuals remain, and Empirical Mode Decomposition (EMD), which breaks down the signal into Intrinsic Mode Functions (IMFs). According to test data, a damaged mount had an amplitude of 0.00005212 m/s² and a frequency of 8 Hz. On the other hand, in typical circumstances, the highest frequency was 7 Hz with the same amplitude. Five frequency increases were made in the damaged mount throughout this operation. In the damaged mount, the Hilbert Transform showed a frequency of 2124 Hz with an amplitude of 0.007594 m/s², indicating a significant resonance. This illustrates how the Hilbert-Huang Transform's capacity to handle non-stationary and nonlinear signal forms allows it to detect damage in components efficiently

Financial Time Series Forecasting Based on Long-Short Term Memory, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Batch Normalization

Long-short term memory (LSTM) is a state-of-art and widely used model to forecast financial time series. However, primitive LSTM networks do not perform well due to over-fitting problems of the deep learning model and nonlinear and non-stationary characteristics of financial time series data. In addition, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is an outstanding data frequency decomposition technique that can decompose original time series into several intrinsic mode functions and a residue. Thus, this paper proposed a novel hybrid network CEEMDAN-LSTM-BN based on LSTM. Specifically, to avoid over-fitting, the modified LSTM-BN network consists of two LSTM layers, two Batch Normalization (BN) layers following each LSTM layer, and a dropout layer. Each of the intrinsic mode functions and the residue would be processed by CEEMDAN-LSTM-BN and the final prediction results are obtained by reconstructing each predictive series. The advantages of the proposed CEEMDANLSTM-BN networks are verified by comparing them to primitive LSTM, other hybrid models, and some famous machine learning models. Moreover, the robustness of the networks is assessed by numerical experiments on different stock indices datasets.

Magnetic Properties of a Nickel–Zinc Ferrite Powder with Different Degrees of Dispersion

The influence of the degree of dispersion of a nickel–zinc ferrite powder of a Ni0.7Zn0.3Fe2O4 composition on its magnetic properties has been considered. The material has been synthesized using the ceramic technology with preliminary mechanical activation of precursors. The degree of dispersion has been varied using different modes of its dry grinding in a ball mill. The patterns of the changes in saturation magnetization and the coercive force as a function of grinding modes and a specific surface area of the ferrite powder have been established. The changes in the pattern of the magnetic phase transition in the region of the Curie temperature of materials with different degrees of dispersion have been determined.

Integral predictive sliding mode control for high-speed trains: A dynamic linearization and input constraint-based data-driven scheme

A control scheme with high reliability and excellent tracking performance is essential for the automatic operation of high-speed trains (HSTs). In this study, a novel discrete-time data-driven predictive sliding mode control (DDPSMC) scheme is proposed for multi-power unit HSTs. Initially, a nonlinear integral terminal sliding mode surface was designed to replace the traditional linear sliding mode function, thereby achieving a rapid system error convergence and alleviating chattering. Then, receding horizon optimization was integrated into predictive control, which allowed the predicted sliding mode state to follow the expected trajectory of a predefined continuous convergence law. This scheme enabled the system to obtain higher output error accuracy and explicitly handle input constraints. Moreover, to enhance robustness, a parameter update law and disturbance delay estimation algorithm were introduced to calculate the control gain and total uncertainty, respectively. Finally, a comparative test of the proposed control scheme was conducted using a CRH380A HST simulation experimental platform in a laboratory setting. Simulation results demonstrate that the velocity error range of each power unit of the HST under the proposed control scheme is within [−0.176 km/h, 0.152 km/h], while the control force and acceleration are within [−55.7 kN, 44.8 kN] and [−0.564 m/s2, 0.496 m/s2], respectively, with stable variation, and other performance indicators are also better than other comparison methods. These results satisfy the safety, stability, and punctuality requirements of the train.

A rolling bearing fault signal denoising algorithm that combines a new adaptive information entropy with a new wavelet threshold function

Abstract Mechanical fault diagnosis is of great significance to industrial automation, and extracting vibration fault signals is one of the important tasks in mechanical health monitoring and fault diagnosis. However, due to the complex working environment of rolling bearings, a large amount of noise makes it difficult to extract vibration fault signals. Denoising the vibration signal of bearings can remove interference noise, simplify the early identification of signal features, and thus improve diagnostic accuracy and mechanical maintenance efficiency. This paper proposes a rolling bearing fault signal denoising algorithm, which constructs a new feature extraction and denoising function. This method first decomposes the noisy signal into Intrinsic Mode Functions (IMFs) by Intrinsic Computing Expressive Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN). Secondly, a new adaptive information entropy threshold function is constructed to extract the noisy IMFs from it. Then, the noisy IMF signal is denoised by a new wavelet threshold function. Finally, the noise-free IMFs are reconstructed to reconstruct the denoised signal. To verify the actual performance of the algorithm, comparative experiments were conducted on a self-collected dataset and a public dataset, the results show that this method improves the continuity of signal reconstruction and can remove various types of vibration fault noise signals more effectively and accurately, \hl{thereby improving the fault detection accuracy by 2%-9%.

Adaptive Feature Extraction Using Sparrow Search Algorithm-Variational Mode Decomposition for Low-Speed Bearing Fault Diagnosis

To address the challenge of extracting effective fault features at low speeds, where fault information is weak and heavily influenced by environmental noise, a parameter-adaptive variational mode decomposition (VMD) method is proposed. This method aims to overcome the limitations of traditional VMD, which relies on manually set parameters. The sparrow search algorithm is used to calculate the fitness function based on mean envelope entropy, enabling the adaptive determination of the number of mode decompositions and the penalty factor in VMD. Afterward, the optimised parameters are used to enhance traditional VMD, enabling the decomposition of the raw signal to obtain intrinsic mode function components. The kurtosis criterion is then used to select relevant intrinsic mode functions for signal reconstruction. Finally, envelope analysis is applied to the reconstructed signal, and the results reveal the relationship between fault characteristic frequencies and their harmonics. The experimental results demonstrate that compared with other advanced methods, the proposed approach effectively reduces noise interference and extracts fault features for diagnosing low-speed bearing faults.

Heart Rate Estimation Considering Reconstructed Signal Features Based on Variational Mode Decomposition via Multiple-Input Multiple-Output Frequency Modulated Continuous Wave Radar

Accurate heart rate estimation using Doppler radar and Frequency Modulated Continuous Wave (FMCW) radar is highly valued for privacy protection and the ability to measure through clothing. Conventional methods struggle to isolate the heartbeat from respiration and body motion. This paper introduces a novel heart rate estimation method using Variational Mode Decomposition (VMD) via Multiple-Input Multiple-Output (MIMO) FMCW radar. The proposed method first estimates human positions within the radar’s coverage, reducing noise by focusing on signals from these positions. The signal is then decomposed into multiple Intrinsic Mode Function (IMF) signals using VMD, and the heartbeat-specific IMF is extracted based on its center frequency. The heart rate signal is reconstructed using weighted addition of IMF signals for each radar cell, with cells defined by specific angles and distances within the coverage area. Peak detection is used to estimate heart rate from these reconstructed signals. To ensure accuracy, the method selects the heart rate estimate with the highest energy and periodicity for the first four time windows. From the fifth time window onward, it selects the estimate closest to the average of the previous four, minimizing extraneous variations. Experiments conducted with one and two subjects showed promising results. In case 1, with one subject, the method achieved a Mean Absolute Error (MAE) of 2.54 BPM and an exclusion rate of 0.94% using MIMO FMCW radar, compared to 4.72% with Doppler radar. In case 2, with two subjects, the method achieved an MAE of 2.28 BPM, confirming accurate simultaneous heart rate estimation.

Method and Application of Spillway Radial Gate Vibration Signal Denoising on Multiverse Optimization Algorithm-Optimized Variational Mode Decomposition Combined with Wavelet Threshold Denoising

To address the noise issue in the measured vibration signals of spillway radial gate discharge, this paper utilizes the Multiverse Optimization Algorithm (MVO) to optimize the number of decomposition modes (K) and the penalty factor (α) in Variational Mode Decomposition (VMD). This approach ensures improved efficiency of VMD decomposition while maintaining accuracy. Subsequently, the obtained Intrinsic Mode Functions (IMFs) from VMD decomposition are classified based on Multi-scale Permutation Entropy (MPE). IMFs are divided into pure components and noisy components; the noisy components are processed with Wavelet Threshold Denoising (WTD), while the pure components are overlaid and reconstructed to obtain the denoised vibration signal of the gate. Comprehensive comparisons involving artificial signal simulations, gate flow-induced vibration model tests, and numerical simulations lead to the following conclusions: compared to other algorithms, the proposed combined denoising method (MVO-VMD-MPE-WTD) achieves the highest signal-to-noise ratio (SNR) in both the frequency and time domains for artificial signals, while yielding the lowest mean square error (MSE). In the gate flow-induced vibration model tests, the method significantly reduces noise in the vibration signals and effectively preserves characteristic information. The error in preserving characteristic information across model tests and numerical simulations is kept below 1%. Furthermore, compared to other optimization algorithms, the MVO demonstrates higher computational efficiency. The parameter-optimized combined denoising method proposed in this study provides insights into denoising measured vibration signals of hydraulic spillway radial gates and other drainage structures, and it opens possibilities for exploring more efficient optimization algorithms for achieving online monitoring in the future.

Tornado Occurrence in the United States as Modulated by Multidecadal Oceanic Oscillations Using Empirical Model Decomposition

Studies have analyzed U.S. tornado variability and correlated F1–F5 tornado occurrence with various natural climate oscillations and anthropogenic factors. Using a relatively new empirical mode decommission (EMD) method that extracts time-frequency modes adaptively without priori assumptions like traditional time-series analysis methods, this study decomposes U.S. tornado variability during 1954–2022 into intrinsic modes on specific temporal scales. Correlating the intrinsic mode functions (IMFs) of EMD with climate indices found that 1. the U.S. overall tornado count is negatively (positively) correlated with the Atlantic Multidecadal Oscillation (AMO) index (the Southern Oscillation Index (SOI)); 2. the negative (positive) correlation tends to be more prevalent in the western (eastern) U.S.; 3. the increase in weak (F1–F2) and decrease in strong (F3–F5) tornadoes after around 2000, when both the AMO and the Pacific Decadal Oscillation (PDO) shifted phases, are likely related to their secular trends and low-frequency IMFs; and 4. the emerging Dixie Tornado Alley coincides with an amplifying intrinsic mode of the SOI that correlates positively with the eastern U.S. and Dixie Alley tornadoes. The long-term persistence of these climate indices can offer potential guidance for future planning for tornado hazards.

Carbon price prediction in China based on ensemble empirical mode decomposition and machine learning algorithms.

The carbon emission trading market is crucial for reducing emissions, conserving energy, and enhancing the climate and environment. Studying carbon price forecasting can encourage China's involvement in international carbon financial instruments trading and promote the development of China's pilot carbon markets. This study employs ensemble empirical mode decomposition (EEDM) to convert the initial carbon price, which is a non-stationary signal, into several intrinsic mode functions and residual terms. Subsequently, hybrid machine learning methods are used to estimate the carbon price. For empirical analysis, the three main carbon markets with large trading volumes, Guangdong, Hubei, and Shenzhen, are selected from the eight pilot carbon markets. To achieve short-term carbon price prediction, a hybrid model combining a genetic algorithm (GA) and back propagation (BP) neural network is used. This model effectively addresses the issue of neural networks falling into local optimization. The results indicate that the hybrid algorithm is significantly superior to other algorithms for short-term prediction. Additionally, another hybrid model, combining the least squares support vector machine (LSSVM) and particle swarm optimization (PSO) algorithms, is employed to reduce forecast error while minimizing search parameters, which is not possible with traditional neural network models.

Interpretable multi-step hybrid deep learning model for karst spring discharge prediction: Integrating temporal fusion transformers with ensemble empirical mode decomposition

Karst groundwater is a critical freshwater resource for numerous regions worldwide. Monitoring and predicting karst spring discharge is essential for effective groundwater management and the preservation of karst ecosystems. However, the high heterogeneity and karstification pose significant challenges to physics-based models in providing robust predictions of karst spring discharge. In this study, an interpretable multi-step hybrid deep learning model called selective EEMD-TFT is proposed, which adaptively integrates temporal fusion transformers (TFT) with ensemble empirical mode decomposition (EEMD) for predicting karst spring discharge. The selective EEMD-TFT hybrid model leverages the strengths of both EEMD and TFT techniques to learn inherent patterns and temporal dynamics from nonlinear and nonstationary signals, eliminate redundant components, and emphasize useful characteristics of input variables, leading to the improvement of prediction performance and efficiency. It consists of two stages: in the first stage, the daily precipitation data is decomposed into multiple intrinsic mode functions using EEMD to extract valuable information from nonlinear and nonstationary signals. All decomposed components, temperature and categorical date features are then fed into the TFT model, which is an attention-based deep learning model that combines high-performance multi-horizon prediction and interpretable insights into temporal dynamics. The importance of input variables will be quantified and ranked. In the second stage, the decomposed precipitation components with high importance are selected to serve as the TFT model’s input features along with temperature and categorical date variables for the final prediction. Results indicate that the selective EEMD-TFT model outperforms other sequence-to-sequence deep learning models, such as LSTM and single TFT models, delivering reliable and robust prediction performance. Notably, it maintains more consistent prediction performance at longer forecast horizons compared to other sequence-to-sequence models, highlighting its capacity to learn complex patterns from the input data and efficiently extract valuable information for karst spring prediction. An interpretable analysis of the selective EEMD-TFT model is conducted to gain insights into relationships among various hydrological processes and analyze temporal patterns.

Mango leaf disease diagnosis using Total Variation Filter Based Variational Mode Decomposition

Mango leaf diseases significantly threaten mango cultivation, impacting both yield and quality. Accurate and early diagnosis is essential for effectively managing and controlling these diseases. This study introduces a novel approach for diagnosing mango leaf diseases, leveraging Total Variation Filter-based Variational Mode Decomposition. The proposed method enhances the extraction of disease-specific features from leaf images by decomposing them into intrinsic mode functions while simultaneously reducing noise and preserving important edge information. Experimental results demonstrate that the proposed method effectively isolates relevant patterns associated with various mango leaf diseases, improving diagnostic accuracy compared to traditional methods. Deep learning models, DenseNet121 and VGG-19, are used for feature extraction from sub-band images, and extracted features are concatenated and fed to Random Forest for classification. Utilizing tenfold cross-validation, our model demonstrated enhanced classification accuracy (98.85 %), specificity (99.37 %), and sensitivity (98.0 %) in detecting diseases from Mango leaf images. Feature maps and Gradient-weighted Class Activation Mapping analysis was conducted to visualize and scrutinize the essential regions crucial for accurate predictions. Statistical analysis indicates that our proposed architecture outperforms pre-trained models and existing mango leaf disease detection methods. This diagnostic approach can be a rapid disease detection tool for imaging specialists utilizing leaf images. The robustness and efficiency of the presented work in handling complex and noisy image data make it a promising tool for automated agricultural disease diagnosis systems, facilitating timely and precise interventions in mango orchards.

Upper limit assessment of GIS equipment failure based on time series model and deep learning algorithm

If a sudden fault of gas-insulated switchgear is not handled in time, it will delay production and cause certain economic losses to the enterprise. Therefore, this study proposes an upper limit assessment algorithm for equipment faults based on time series model and deep learning. The irregular fluctuation components in the time series model are stabilized by using empirical mode decomposition, and the long short-term memory network in the deep learning algorithm is introduced to combine the two. The equipment fault data is obtained by the joint algorithm. After empirical mode decomposition, the intrinsic mode function component of the data signal is obtained, and the sensitive component is extracted from it. The relationship value and mutual information between it and the original data signal are analyzed to complete the fault data feature extraction. In the process of equipment fault upper limit assessment, the parameter optimization and convergence are controlled, and the fault deep learning model is constructed. After the refraction coefficient and reflection coefficient are determined, the upper limit assessment of equipment faults is realized. The proposed method is experimentally tested. The results show that the proposed algorithm has an ideal upper limit assessment result of faults, and the obtained curve has a high degree of fit with the actual result curve. It can be proved that the proposed algorithm can scientifically evaluate the upper limit of equipment faults and has certain application value.

Phasic and periodic change of drought under greenhouse effect

Purpose Drought is the primary disaster that negatively impacts agricultural and animal husbandry production. It can lead to crop reduction and even pose a threat to human survival in environmentally sensitive areas of China (ESAC). However, the phases and periodicity of drought changes in the ESAC remain largely unknown. Thus, this paper aims to identify the periodic characteristics of meteorological drought changes. Design/methodology/approach The potential evapotranspiration was calculated using the Penman–Monteith formula recommended by the Food and Agriculture Organization of the United Nations, whereas the standardized precipitation evaporation index (SPEI) of drought was simulated by coupling precipitation data. Subsequently, the Bernaola-Galvan segmentation algorithm was proposed to divide the periods of drought change and the newly developed extreme-point symmetric mode decomposition to analyze the periodic drought patterns. Findings The findings reveal a significant increase in SPEI in the ESAC, with the rate of decline in drought events higher in the ESAC than in China, indicating a more pronounced wetting trend in the study area. Spatially, the northeast region showed an evident drying trend, whereas the southwest region showed a wetting trend. Two abrupt changes in the drought pattern were observed during the study period, namely, in 1965 and 1983. The spatial instability of moderate or severe drought frequency and intensity on a seasonal scale was more consistent during 1966–1983 and 1984–2018, compared to 1961–1965. Drought variation was predominantly influenced by interannual oscillations, with the periods of the components of intrinsic mode functions 1 (IMF1) and 2 (IMF2) being 3.1 and 7.3 years, respectively. Their cumulative variance contribution rate reached 70.22%. Research limitations/implications The trend decomposition and periods of droughts in the study area were analyzed, which may provide an important scientific reference for water resource management and agricultural production activities in the ESAC. However, several problems remain unaddressed. First, the SPEI considers only precipitation and evapotranspiration, making it extremely sensitive to temperature increases. It also ignores the nonstationary nature of the hydrometeorological water process; therefore, it is prone to bias in drought detection and may overestimate the intensity and duration of droughts. Therefore, further studies on the application and comparison of various drought indices should be conducted to develop a more effective meteorological drought index. Second, the local water budget is mainly affected by surface evapotranspiration and precipitation. Evapotranspiration is calculated by various methods that provide different results. Therefore, future studies need to explore both the advantages and disadvantages of various evapotranspiration calculation methods (e.g. Hargreaves, Thornthwaite and Penman–Monteith) and their application scenarios. Third, this study focused on the temporal and spatial evolution and periodic characteristics of droughts, without considering the driving mechanisms behind them and their impact on the ecosystem. In future, it will be necessary to focus on a sensitivity analysis of drought indices with regard to climate change. Finally, although this study calculated the SPEI using meteorological data provided by China’s high-density observatory network, deviations and uncertainties were inevitable in the point-to-grid spatialization process. This shortcoming may be avoided by using satellite remote sensing data with high spatiotemporal resolution in the future, which can allow pixel-scale monitoring and simulation of meteorological drought evolution. Practical implications Under the background of continuous global warming, the climate in arid and semiarid areas of China has shown a trend of warming and wetting. It means that the plant environment in this region is getting better. In the future, the project of afforestation and returning farmland to forest and grassland in this region can increase the planting proportion of water-loving tree species to obtain better ecological benefits. Meanwhile, this study found that in the relatively water-scarce regions of China, drought duration was dominated by interannual oscillations (3.1a and 7.3a). This suggests that governments and nongovernmental organizations in the region should pay attention to the short drought period in the ESAC when they carry out ecological restoration and protection projects such as the construction of forest reserves and high-quality farmland. Originality/value The findings enhance the understanding of the phasic and periodic characteristics of drought changes in the ESAC. Future studies on the stress effects of drought on crop yield may consider these effects to better reflect the agricultural response to meteorological drought and thus effectively improve the tolerance of agricultural activities to drought events.

Laboratory study of energy transformation characteristics in breaking wave groups

The spilling-breaking waves that appear in chirped wave packets are studied in a two-dimensional wave channel. These waves are produced by superposing waves with gradually decreasing frequencies. The analysis focuses on the nonlinear characteristics, energy variation, and energy transformation during the evolution and breaking of wave groups. Ensemble empirical mode decomposition is used to analyze the non-breaking and breaking energy variations of the intrinsic mode functions (IMFs). It is found that the third-order IMF component is a source of non-breaking energy dissipation and the second-order IMF, which represents a short wave group with a relatively higher energy content, is a primary source of the energy loss caused by wave breaking. Additionally, the findings reveal that among the three waves preceding the maximum crest, the wave closest to the maximum crest carried most of the energy. When wave breaking occurs, the energy dissipation caused by the wave breaking primarily originates from that wave. After wave breaking, whether it is the first breaker or subsequent breakers, the main energy dissipation occurs in a frequency range higher than the dominant frequency. This energy loss plays a significant role in increasing the energy of free waves. Moreover, a potential link between the number of carrier waves and wave breaking phenomena has been found. As the number of carrier waves increased, both the nonbreaking and breaking energy dissipation rates exhibited an overall increasing trend. The amount of nonbreaking energy dissipation was generally more than twice the breaking energy dissipation rate. For wave groups with more carrier waves, the modulation instability plays a significant role in generating larger waves. Furthermore, an analysis of the dominant frequency variations of the wave group before wave breaking suggests that wave breaking is not a sufficient condition for a frequency downshift in the wave spectra.

Adaptive anti-unwinding attitude stabilisation with predefined time for rigid spacecraft

In this paper, the problem of attitude stabilisation without unwinding is investigated for rigid spacecraft. To guarantee predefined-time convergence and unwinding-free performance of the closed-loop system, a predefined-time sliding mode function with adjustable parameters is proposed. This sliding mode function contains two equilibrium points. When the states of the closed-loop system are on the sliding mode surface, they converge to the equilibrium point near the initial states. Based on this sliding mode function, an adaptive attitude stabilising control law with tuning parameters is designed to compensate the external disturbances and inertia uncertainty. The presented control law guarantees that the settling time of the closed-loop system and the bounds of the system states can be explicitly determined in advance by adjusting parameters of the sliding mode function and the control law. Finally, numerical simulations are carried out to demonstrate the effectiveness of the presented control law. The simulation results illustrate that the predefined-time convergence and unwinding-free property of the closed-loop system are guaranteed by adopting the presented control law.

Intelligent identification of defective regions of voids in tunnels based on GPR data

Quantitatively detecting voids behind tunnel linings presents significant challenges in identifying the range of width and depth. This paper develops an innovative method for identifying defective regions of voids based on Ground Penetrating Radar (GPR) data. This method involves three steps: Firstly, the void-identifying-feature-set (VIFS) is constructed by extracting the Amplitude peak (AT), Signal energy (ET), and Amplitude peak of the first intrinsic mode function (IMF1) component (AH) of every A-scan signal. Secondly, the Support Vector Machine (SVM) is utilized to identify defect signals and normal signals, contributing to the width identification of void in the horizontal direction. Thirdly, an innovative Three-Stage-Boundary-Extraction (TSBE) algorithm is proposed to identify the depth range of voids in the vertical direction. Experimental results conducted on both field data and simulated data demonstrated that the Intersection over Union (IOU) value and consumption time of three groups of GPR data (Data I, Data II, and Data V) are 0.739 and 0.888 s, respectively. The average IOU and consumption time of the TSBE algorithm are 0.739 and 0.058 s, respectively.

Hilbert-Huang Transform and machine learning based electromechanical analysis of induction machine under power quality disturbances

Monitoring and predicting Power Quality (PQ) is crucial for quickly minimizing risk, protecting induction machines (IMs), and increasing productivity. This paper proposes an electromechanical analytical framework for IM working with various PQ disturbances based on machine learning (ML). This work collects the motor characteristics and PQ data, motor vibration signals, and other sensor data to identify the failures. The complicated electromechanical data is broken down into intrinsic mode functions (IMFs) using the Hilbert-Huang Transform (HHT), which reveals the modes present in the signals. This frequency-domain data is retrieved, paired with time-domain characteristics, and used as input features for ML algorithms. Support Vector Machines (SVMs) trained on labeled datasets in which features extracted from PQ disturbances are used to categorize the disturbances into several groups. The PQ disturbances caused by voltage sags, swells, harmonics, and transients can all be efficiently classified using SVM classifiers, allowing for real-time determination of the kind of disturbance influencing the IM. The accuracy for the SVM in the proposed scheme is 97.2 %. The SVM method is trained with PQ data and classification results using MATLAB classifier and Python software.

Relevance-Based Reconstruction Using an Empirical Mode Decomposition Informer for Lithium-Ion Battery Surface-Temperature Prediction

Accurate monitoring of lithium-ion battery temperature is essential to ensure these batteries’ efficient and safe operation. This paper proposes a relevance-based reconstruction-oriented EMD-Informer machine learning model, which combines empirical mode decomposition (EMD) and the Informer framework to estimate the surface temperature of 18,650 lithium-ion batteries during charging and discharging processes under complex operating conditions. Initially, based on 9000 data points from the U.S. NASA Prognostics Center of Excellence’s random battery-usage dataset, where each data point includes three features: temperature, voltage, and current, EMD is used to decompose the temperature data into intrinsic mode functions (IMFs). Subsequently, the IMFs are reconstructed into low-, medium-, and high-correlation components based on their correlation with the original data. These components, along with voltage and current data, are fed into sub-models. Finally, the model captures the long-term dependencies among temperature, voltage, and current. The experimental results show that, in single-step prediction, the mean squared error, mean absolute error, and maximum absolute error of the model’s predictions are 0.00095, 0.02114, and 0.32164 °C; these metrics indicate the accurate prediction of the surface temperature of lithium-ion batteries. In multi-step predictions, when the prediction horizon is set to 12 steps, the model achieves a hit rate of 93.57% where the maximum absolute error is within 0.5 °C; under these conditions, the model combines high predictive accuracy with a broad predictive range, which is conducive to the effective prevention of thermal runaway in lithium-ion batteries.

Predicting e-commerce product prices through the integration of variational mode decomposition and deep neural networks

Product prices frequently manifest nonlinear and nonstationary time-series attributes, indicating potential variations in their behavioral patterns over time. Conventional linear models may fall short in adequately capturing these intricate properties. In addressing this, the present study leverages the adaptive and non-recursive attributes of the Variational Mode Decomposition (VMD) methodology. It employs VMD to dissect the intricate time series into multiple Intrinsic Mode Functions (IMF). Subsequently, a method rooted in the minimum fuzzy entropy criterion is introduced for determining the optimal modal number (K) in the VMD decomposition process. This method effectively mitigates issues related to modal confusion and endpoint effects, thereby enhancing the decomposition efficacy of VMD. In the subsequent phase, deep neural networks (DNN) are harnessed to forecast the identified modes, with the cumulative modal predictions yielding the ultimate e-commerce product price prognostications. The predictive efficacy of the proposed Variational Mode Decomposition-deep neural network (VMD-DNN) decomposition model is assessed on three public datasets, wherein the mean absolute percentage error (MAPE) on the E-commerce Price Prediction Dataset and Online Retail Dataset is notably low at 0.6578 and 0.5414, respectively. This corresponds to a remarkable error reduction rate of 66.5% and 70.4%. Moreover, the VMD-DNN decomposition model excels in predicting e-commerce product prices through DNN, thereby amplifying the VMD decomposition capability by 4%. The VMD-DNN model attains superior results in terms of directional symmetry, boasting the highest Directional Symmetry (DS) score of 86.25. Notably, the forecasted trends across diverse price ranges closely mirror the actual trends.