Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (5,121)

Search Parameters:
Keywords = nonlinear features

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
18 pages, 2971 KB  
Article
AI-Driven Prediction of Surface Roughness and Cutting Force in Milling Aluminum Alloy Under Data-Scarce Conditions
by Mohammad Hossein Ebrahimi and Seyed Ali Niknam
Machines 2026, 14(7), 756; https://doi.org/10.3390/machines14070756 (registering DOI) - 5 Jul 2026
Abstract
Accurate prediction of surface roughness and cutting forces in milling aluminum alloys remains challenging under data-scarce conditions, where limited experimental data restricts the application of conventional machine learning models. This study addresses this gap by developing a systematic machine learning framework using 108 [...] Read more.
Accurate prediction of surface roughness and cutting forces in milling aluminum alloys remains challenging under data-scarce conditions, where limited experimental data restricts the application of conventional machine learning models. This study addresses this gap by developing a systematic machine learning framework using 108 milling experiments (repeated to 216 tests) on aluminum alloys AA2024-T351 and AA6061-T6. Five primary machining inputs—material type, spindle speed, feed rate, depth of cut, and tool coating—were used. Through feature engineering, 35 interaction features were generated to capture non-linear relationships. A two-step preprocessing strategy was applied: Winsorization at the 5th and 95th percentiles to handle outliers, followed by hybrid scaling combining RobustScaler and MinMaxScaler. Eight machine learning algorithms, including XGBoost, NGBoost, LightGBM, CatBoost, Random Forest, MLP, SVR, and Least Squares Boosting, were developed and hyperparameter-optimized using the Optuna framework with Tree-structured Parzen Estimator. Models were evaluated using R2, MAE, and RMSE on a 70/15/15 train–validation–test split. Results demonstrate that XGBoost achieved the highest predictive accuracy for surface roughness (Ra) (R2 = 0.99829) and for resultant cutting force (FN) (R2 = 0.997). Feed rate was identified as the dominant machining parameter, accounting for 87.7% of the total importance in predicting surface roughness. SHAP analysis confirmed that engineered interaction features—particularly Feed_Coating and Material_Feed—carry strong physical relevance. Additionally, NGBoost enabled probabilistic regression, providing uncertainty estimates. The proposed framework proves highly effective for multi-output prediction in machining under limited data, offering a robust, interpretable, and industry-ready solution for quality control in aluminum alloy milling operations. Full article
Show Figures

Figure 1

21 pages, 3273 KB  
Article
Few-Shot Cross-Domain Fault Diagnosis via Wavelet Convolution Embedding and BDC-Based Metric Meta-Learning
by Zaiyou Xu, Jiale Kai and Jun Wang
Sensors 2026, 26(13), 4276; https://doi.org/10.3390/s26134276 (registering DOI) - 5 Jul 2026
Abstract
Few-shot cross-domain bearing fault diagnosis is challenging because labeled fault samples are limited and signals collected by vibration sensors under different operating conditions often show significant distribution shifts. To improve bearing fault identification under limited-sample and cross-condition scenarios, this paper proposes a wavelet [...] Read more.
Few-shot cross-domain bearing fault diagnosis is challenging because labeled fault samples are limited and signals collected by vibration sensors under different operating conditions often show significant distribution shifts. To improve bearing fault identification under limited-sample and cross-condition scenarios, this paper proposes a wavelet convolution (WC) and Brownian distance covariance (BDC)-based metric meta-learning framework, termed WCBDC. In this framework, the WC is inserted into the feature extraction process to capture multiscale time–frequency information from vibration signals. The BDC is then applied to model nonlinear inter-channel statistical dependencies and improve the discriminability of fault embeddings. The obtained feature embeddings are further organized within a prototypical-network-based classifier, in which category prototypes are estimated from support samples and query instances are assigned by prototype-distance comparison. The proposed method is evaluated on the Paderborn University (PU) and Beijing Jiaotong University (BJTU) bearing datasets under both 5-way 5-shot and 5-way 1-shot scenarios. On the PU dataset, WCBDC reaches average accuracies of 92.19% and 84.13%, while the corresponding results on the BJTU dataset are 77.24% and 62.57%. These results exceed those of representative meta-learning baselines, demonstrating that WCBDC provides improved diagnostic performance for sensor-based bearing fault recognition when labeled samples are scarce and operating conditions vary. Full article
(This article belongs to the Special Issue Deep Learning Based Intelligent Fault Diagnosis)
Show Figures

Figure 1

67 pages, 3288 KB  
Article
An Optimization-Driven Fuzzy Transformer–Deep Belief Network for PM2.5 Air Pollution Prediction: A Spatio-Temporal Framework Based on Aerosol Optical Depth
by Mohammad Mehdi Sharifi Nevisi, Pardis Sadatian Moghaddam, Mehrdad Kaveh, Diego Martín, Nuria Serrano and José Vicente Álvarez-Bravo
Mathematics 2026, 14(13), 2402; https://doi.org/10.3390/math14132402 (registering DOI) - 5 Jul 2026
Abstract
Forecasting fine particulate matter with a diameter of 2.5 μm (PM2.5) is critically important due to its adverse effects on human health and environmental sustainability. Although ground-based monitoring stations provide accurate measurements, their limited spatial coverage restricts large-scale PM2.5 assessment, [...] Read more.
Forecasting fine particulate matter with a diameter of 2.5 μm (PM2.5) is critically important due to its adverse effects on human health and environmental sustainability. Although ground-based monitoring stations provide accurate measurements, their limited spatial coverage restricts large-scale PM2.5 assessment, especially in complex urban regions. Consequently, aerosol optical depth (AOD) derived from satellite imagery, combined with advanced deep learning (DL) techniques, has emerged as an effective alternative by offering wide spatial coverage and rich spatio-temporal information. This paper proposed an optimization-driven fuzzy transformer–deep belief network (ODFT-DBN) for accurate PM2.5 air pollution prediction. The proposed framework integrates a fuzzy inference module to model uncertainty and nonlinear environmental relationships, a transformer encoder to capture long-range spatio-temporal dependencies, and a DBN to extract hierarchical features and improve prediction robustness. In addition, a novel multi-objective gray wolf optimizer (NMOGWO) is employed to jointly optimize the model hyper-parameters and fuzzy membership functions. The proposed approach is implemented for the city of Tehran, Iran, using meteorological variables, topographical features, ground-based PM2.5 measurements, and satellite-derived AOD data. The ODFT-DBN model is compared with several benchmark methods, including bidirectional encoder representations from transformers (BERT), transformer, long short-term memory (LSTM), gated recurrent unit (GRU), convolutional neural network (CNN), DBN, and extreme gradient boosting (XGBoost). Experimental results demonstrate that the proposed framework achieves superior predictive performance, attaining an R2 value of 0.94 and root mean square error (RMSE) of 0.8 μg/m3. Scatter plot analyses indicate a strong agreement between predicted and observed PM2.5 values, while the proposed model exhibits low variance, stable convergence behavior, and acceptable computational time. Overall, the results confirm the effectiveness, robustness, and practical applicability of the proposed ODFT-DBN framework for spatio-temporal PM2.5 forecasting. Full article
(This article belongs to the Special Issue Applications of Optimization Algorithms and Evolutionary Computation)
15 pages, 423 KB  
Article
A Wavelet-Embedded Residual Attention Convolutional Neural Network for Fault Location in Distribution Networks
by Zhengkai Sun and Qian Zhang
Electronics 2026, 15(13), 2935; https://doi.org/10.3390/electronics15132935 (registering DOI) - 4 Jul 2026
Abstract
Accurate fault location is essential for improving the reliability and service restoration capability of distribution networks. With the increasing penetration of distributed generation, power electronic devices, and flexible loads, fault transient signals become increasingly nonlinear and nonstationary, posing challenges to conventional impedance-based, traveling-wave-based, [...] Read more.
Accurate fault location is essential for improving the reliability and service restoration capability of distribution networks. With the increasing penetration of distributed generation, power electronic devices, and flexible loads, fault transient signals become increasingly nonlinear and nonstationary, posing challenges to conventional impedance-based, traveling-wave-based, and feature-engineering-based methods. To improve transient fault feature representation, this paper proposes a wavelet-embedded residual attention convolutional neural network (CNN) for distribution network fault location. The task is formulated as a multi-class classification problem, in which each predefined line section is treated as a candidate fault location class. The proposed method embeds discrete wavelet decomposition into the convolutional feature extraction process, enabling low-frequency trend components and high-frequency transient components to be jointly represented and fused by subsequent trainable network modules. Residual connections improve deep feature propagation, and an attention mechanism enhances fault-sensitive representations. Simulation studies on the IEEE 33-bus distribution system show that the proposed method outperforms multi-layer perceptron (MLP), support vector machine (SVM), standard CNN, ResNet, and Attention-CNN, achieving 98.27% accuracy and a 98.33% F1-score. The class-wise results and robustness tests under different transition resistances, noise levels, and fault types further verify the effectiveness and adaptability of the proposed method. Full article
(This article belongs to the Special Issue Wireless Power Transfer: Modeling, Optimization and Applications)
Show Figures

Figure 1

18 pages, 4045 KB  
Article
Prediction of the Young’s Modulus of Polylactic Acid Specimens Manufactured by Fused Deposition Modeling Using Machine Learning-Based Stacking Ensemble Methods
by Alexandru Constantin Stanciu, Anton Hadăr, Nicolae Goga, Mihai-Constantin Butolo, Florin Baciu, Stefan-Dan Pastrama and Daniel Vlăsceanu
Polymers 2026, 18(13), 1661; https://doi.org/10.3390/polym18131661 (registering DOI) - 4 Jul 2026
Abstract
In this paper, a machine learning model to predict the Young’s modulus of polylactic acid specimens manufactured by Fused Deposition Modeling is proposed, based on a stacked ensemble architecture. The model uses as input parameters the fill degree, printing speed, filling pattern, yield [...] Read more.
In this paper, a machine learning model to predict the Young’s modulus of polylactic acid specimens manufactured by Fused Deposition Modeling is proposed, based on a stacked ensemble architecture. The model uses as input parameters the fill degree, printing speed, filling pattern, yield strength, and tensile strength, along with additional features obtained through feature engineering. The proposed approach integrates nine base models with a linear meta-model, allowing it to capture both linear and nonlinear relationships between the variables. The results obtained on the test dataset show strong predictive performance, with a Mean Squared Error with a value of 7.31 together with a Coefficient of Determination R2 with a value of 0.99, which is noticeably better than the performance of the individual models. To validate the model, a separate group of specimens was tested, and the difference between the measured and predicted Young’s modulus was about 1% on average. The model was also implemented in a desktop application with a graphical interface, in which the calculation can be run directly, thus allowing a rapid estimation of Young’s modulus. In this way, the need for laborious experimental testing is reduced with the help of AI-based approaches in additive manufacturing. Full article
(This article belongs to the Section Artificial Intelligence in Polymer Science)
Show Figures

Graphical abstract

13 pages, 2294 KB  
Article
Reactive Hyperemia Reveals Fractal Scaling and Multiscale Complexity in Photoplethysmography Waveforms
by Henrique Silva
Biology 2026, 15(13), 1073; https://doi.org/10.3390/biology15131073 (registering DOI) - 4 Jul 2026
Abstract
Post-occlusive reactive hyperemia (PORH) is a classical probe of microvascular function, yet its assessment remains largely based on amplitude-derived indices that do not capture the temporal organization of vascular regulation. Photoplethysmography (PPG), widely used in clinical and wearable technologies, offers a practical platform [...] Read more.
Post-occlusive reactive hyperemia (PORH) is a classical probe of microvascular function, yet its assessment remains largely based on amplitude-derived indices that do not capture the temporal organization of vascular regulation. Photoplethysmography (PPG), widely used in clinical and wearable technologies, offers a practical platform for nonlinear characterization of PORH. Twelve healthy adults underwent a standardized PORH protocol (10 min baseline, 5 min suprasystolic occlusion, 10 min reperfusion) with bilateral reflective green-light PPG. Pulse amplitude, detrended fluctuation analysis (global DFA α exponent), and multiscale entropy (Complexity Index, CI) were computed in 5 min epochs. Occlusion nearly abolished pulsatility in the test limb but produced only modest changes in fractal structure, as α decreased minimally despite near-zero flow. In contrast, CI showed a marked collapse, indicating loss of multiscale organization. During reperfusion, α exhibited a trend toward increased fractal persistence, whereas CI recovered only partially. Contralateral responses were small and detectable mainly through subtle reductions in α during occlusion and consistently higher CI compared with the test limb. These findings indicate that occlusion disrupts multiscale complexity without eliminating fractal persistence, whereas reperfusion restores correlation structure and only partially re-establishes dynamical richness. Overall, DFA and MSE reveal nonlinear features of PORH that are not captured by conventional amplitude-based metrics, extending the physiological interpretation of microvascular responses using widely available PPG technology. Full article
(This article belongs to the Section Physiology)
Show Figures

Figure 1

21 pages, 2966 KB  
Article
Morphological Features of the Pygidial Glands and Chemical Composition of Their Secretions in Three Ground Beetle Taxa of the Tribe Chlaeniini (Coleoptera: Carabidae)
by Marija Vasović, Sofija Vranić, Marina Todosijević, Danica Pavlović, Nikola Vesović, Stefan Ivanović, Nina Ćurčić, Milan Radovanović, Ljubodrag Vujisić and Srećko Ćurčić
Insects 2026, 17(7), 695; https://doi.org/10.3390/insects17070695 - 3 Jul 2026
Abstract
The relationship between the morphology of pygidial glands and the chemical nature of their secretions in the tribe Chlaeniini (family Carabidae) has long been recognised. We analysed the morphological features of the pygidial glands and the chemical composition of their secretions in three [...] Read more.
The relationship between the morphology of pygidial glands and the chemical nature of their secretions in the tribe Chlaeniini (family Carabidae) has long been recognised. We analysed the morphological features of the pygidial glands and the chemical composition of their secretions in three taxa: Chlaenius (Chlaeniellus) tristis (Schaller, 1783), C. (Chlaenites) spoliatus spoliatus (Rossi, 1792), and C. (Chlaenius) festivus festivus (Panzer, 1796). We examined the morphology of the pygidial glands in all three taxa using bright-field microscopy (BFM) and nonlinear microscopy (NLM). We used gas chromatography–mass spectrometry (GC–MS) and nuclear magnetic resonance (NMR) to analyse the chemical composition of the secretions. We measured and photographed the glands and conducted comparative morphological analyses. We detected a total of 21 chemicals in the pygidial gland secretions of the studied Chlaeniini. We found the highest number of compounds in C. tristis (17), slightly fewer in C. festivus festivus (13), and the lowest number in C. spoliatus spoliatus (seven). Thirteen compounds were new to the tribe Chlaeniini, eight of which were also new to the entire family Carabidae. The most dominant compound in the secretions of all three taxa was 3-methylphenol. We also discussed the taxonomic value of the chemical composition of the pygidial gland secretions. Full article
(This article belongs to the Section Insect Physiology, Reproduction and Development)
38 pages, 3758 KB  
Article
A Vertically Structured Machine Learning Approach for Cloud Liquid and Ice Water Content Profiling
by Zhengyu Pan, Yansong Bao, Hong Wei, Haoran Li, Fang Pang and Wei Tao
Remote Sens. 2026, 18(13), 2177; https://doi.org/10.3390/rs18132177 - 3 Jul 2026
Abstract
Accurate retrieval of cloud liquid water content (LWC) and ice water content (IWC) vertical profiles remains limited by strong vertical variability and nonlinear dependencies among observed variables. Ground-based cloud radar reflectivity and microwave radiometer-derived thermodynamic profiles provide complementary constraints, but their joint use [...] Read more.
Accurate retrieval of cloud liquid water content (LWC) and ice water content (IWC) vertical profiles remains limited by strong vertical variability and nonlinear dependencies among observed variables. Ground-based cloud radar reflectivity and microwave radiometer-derived thermodynamic profiles provide complementary constraints, but their joint use requires consistent time–height matching and bias-controlled predictors. This study develops a vertically structured machine-learning framework that explicitly represents profile-level dependencies by constructing vertical-structure-enhanced features to encode local gradients and contextual information, integrating multiple tree-based learners with heterogeneous configurations through a profile-aware stacking strategy, and introducing a profile-level refinement step to suppress layer-to-layer inconsistencies. The framework is evaluated using year-round Cloudnet observations from the Lindenberg site, where IWC RMSE decreases from 0.0152 g m−3 to 0.0092 g m−3 with R2 increasing from 0.412 to 0.784, and LWC RMSE decreases from 0.0786 g m−3 to 0.0591 g m−3 with R2 increasing from 0.303 to 0.606. Additional boundary-region evaluation shows that the improvement is particularly evident near radar-derived cloud boundaries, where cloud structure and hydrometeor content may vary rapidly with height. These results indicate that treating cloud retrieval as a vertically structured learning problem reduces inconsistencies inherent in pointwise models and establishes a data-driven baseline for incorporating vertical constraints into atmospheric profile retrieval. Full article
(This article belongs to the Special Issue Advanced AI Technology for Remote Sensing Analysis (Second Edition))
19 pages, 750 KB  
Article
The Solution Structure of the Elenbaas–Heller Equation for Inductively Coupled Plasmas and Wall Stabilized Arcs
by Rizos N. Krikkis
J 2026, 9(3), 20; https://doi.org/10.3390/j9030020 - 3 Jul 2026
Abstract
A numerical bifurcation analysis is presented for inductively coupled plasmas and wall-stabilized arcs for argon and hydrogen. Because of the non-linear transport and radiative properties, both problems admit multiple solutions, up to three for argon and up to four for hydrogen. The multiplicity [...] Read more.
A numerical bifurcation analysis is presented for inductively coupled plasmas and wall-stabilized arcs for argon and hydrogen. Because of the non-linear transport and radiative properties, both problems admit multiple solutions, up to three for argon and up to four for hydrogen. The multiplicity structure primarily dependents on the non-linear, and, especially, the non-monotonic relationship between thermal conductivity and temperature. As a result of the non-monotonicity, a multipoint energy equilibrium between joule heating (heat generation) and heat dissipation by conduction and radiation exists, giving rise to the multiplicity that is a characteristic feature of both radiating and non-radiating arcs. Despite the relatively simple one-dimensional model employed, the agreement with the experimental data is good. Full article
36 pages, 6069 KB  
Article
Rate of Penetration Prediction Using an ExtraTrees Model Optimized by an Improved Harris Hawks Algorithm
by Xi Cui, Dachuan Liang, Daoxiong Li and Chen Yang
Appl. Sci. 2026, 16(13), 6680; https://doi.org/10.3390/app16136680 - 3 Jul 2026
Abstract
Rate of penetration (ROP) is a key indicator of drilling efficiency, governed by nonlinear coupling among mechanical, hydraulic, drilling fluid, and formation factors. This study develops an ExtraTrees model optimized by an improved Harris hawks optimization algorithm (IHHO-ET) using field while drilling data [...] Read more.
Rate of penetration (ROP) is a key indicator of drilling efficiency, governed by nonlinear coupling among mechanical, hydraulic, drilling fluid, and formation factors. This study develops an ExtraTrees model optimized by an improved Harris hawks optimization algorithm (IHHO-ET) using field while drilling data from Well Z in the Tarim Oilfield. A preprocessing workflow involving drilling section identification, abnormal condition filtering, 3 × IQR outlier removal, Savitzky–Golay smoothing, and standardization is combined with correlation and gray relational analysis under engineering mechanism constraints to select 14 input features. Logistic chaotic initialization, adaptive Gaussian mutation, and dynamic weighting are introduced into HHO, with validation set RMSE as the fitness function. To reduce the influence of random splitting and initialization, all comparison models are evaluated with repeated seeds and validation set tuning. Using R2 and RMSE as primary criteria, IHHO-ET achieves R2 = 0.910 ± 0.004 and RMSE = 0.871 ± 0.019 on the same-well test set. Its improvement over HHO-ET is small and not significant (p = 0.109), indicating that the IHHO strategies mainly refine search stability. Same-region leave-one-well-out validation gives an average R2 = 0.696, suggesting that the model suits same-region trend prediction rather than direct closed-loop control. The proposed workflow provides a practical reference for ROP prediction. Full article
Show Figures

Figure 1

27 pages, 3682 KB  
Article
Dynamic Soft Sensing of Stack NOx Concentration in Cement Kiln SNCR–SCR Denitrification Using a DAC-IVY-Optimized TCN-SE-LSTM Model
by Zheng Zhao, Si-Yuan Liu, Yu-Xin Zhang, Jia-Le Quan and Xin-Yu Tang
Processes 2026, 14(13), 2176; https://doi.org/10.3390/pr14132176 - 3 Jul 2026
Abstract
Accurate single-step prediction of stack NOx concentration is essential for emission monitoring and ammonia-injection control in cement kiln SNCR–SCR hybrid denitrification systems. However, this task is challenging because industrial kiln data are affected by nonstationary emission fluctuations, nonlinear multivariable coupling, process-dependent time [...] Read more.
Accurate single-step prediction of stack NOx concentration is essential for emission monitoring and ammonia-injection control in cement kiln SNCR–SCR hybrid denitrification systems. However, this task is challenging because industrial kiln data are affected by nonstationary emission fluctuations, nonlinear multivariable coupling, process-dependent time delays, and online deployment constraints. To address these process-specific challenges, this study develops a leakage-free dynamic soft-sensing framework for stack NOx concentration prediction. In the proposed framework, variational mode decomposition (VMD) is used to characterize the multi-scale nonstationarity of the stack NOx sequence under a sliding-window protocol. Trend-guided maximal information coefficient (MIC) analysis is then applied for nonlinear feature selection and delay compensation using only the training data, and the identified feature subset and delay parameters are fixed for validation and testing. A TCN-SE-LSTM model is constructed to extract temporal dependencies, recalibrate informative feature channels, and capture long-lag dynamic behavior. In addition, the Dual Adaptive Constrained Ivy Algorithm (DAC-IVY) is used only for offline hyperparameter optimization, so that the online stage requires only the trained prediction model. Experiments using 21,600 raw samples collected from an actual cement kiln Distributed Control System (DCS) show that the proposed framework achieves an RMSE of 0.2084 mg/Nm3 and an R2 of 0.9844 on the test set, outperforming conventional baseline models. These results indicate that the proposed framework can provide an effective soft-sensing basis for subsequent denitrification control and operational optimization. Full article
(This article belongs to the Section Process Control, Modeling and Optimization)
Show Figures

Figure 1

21 pages, 354 KB  
Article
Explicit Runge–Kutta–Nyström-Type Schemes for Third-Order Systems y‴ = f(x, y, y′)
by Rubayyi T. Alqahtani, Theodore E. Simos and Charalampos Tsitouras
Axioms 2026, 15(7), 502; https://doi.org/10.3390/axioms15070502 - 3 Jul 2026
Abstract
Initial value problems of the third order featuring explicit dependence on velocity, denoted as y=f(x,y,y), emerge regularly across applications such as electromechanical networks, structural mechanics, and robotic trajectory control. Despite their [...] Read more.
Initial value problems of the third order featuring explicit dependence on velocity, denoted as y=f(x,y,y), emerge regularly across applications such as electromechanical networks, structural mechanics, and robotic trajectory control. Despite their practical prevalence, these differential equations remain insufficiently addressed by standard numerical integration techniques. Orthodox Runge–Kutta–Nyström (RKN) schemes are fundamentally formulated for differential equations lacking the first derivative, specifically y=f(x,y). Due to this algorithmic constraint, researchers frequently resort to computationally demanding first-order system reductions or rely upon standard Runge–Kutta methods. The present study resolves this methodological gap by defining an explicit s-stage integration architecture that natively incorporates the first derivative within the internal stage evaluations. Such structural modifications require the deployment of a supplementary coefficient matrix, denoted as D, to formulate the corresponding order theory. The complete set of algebraic order conditions is systematically established up to the seventh order, accompanied by a generic mathematical framework for generating schemes of arbitrary order. Based on this analytical foundation, an embedded 6(4) method is constructed. This specific pair achieves strict error tolerances utilizing merely six function evaluations per integration step, representing a substantial operational reduction compared to the eight computations strictly required by equivalent Runge–Kutta pairs. Direct numerical integration of the native third-order system prevents the dimensionality increase from reducing to first-order systems. Performance validation of the numerical solver involves two representative physical benchmarks: a coupled robotic appendage subjected to platform excitation and an electromechanical actuator array regulated by transient control inputs. Both dynamical systems exhibit severe velocity-dependent dissipation mechanisms and nonlinear external forcing. Quantitative numerical evaluations confirm that the constructed 6(4) pair yields higher precision and demands less computational expenditure than prevailing RK and RKN integrators. The analytical and empirical findings establish that derivative-capable Nyström integration algorithms furnish mathematically rigorous and computationally efficient numerical solutions for velocity-coupled third-order dynamics. Full article
21 pages, 4192 KB  
Article
Dust Concentration Forecasting Method for Intermittent Processing of Powder and Granular Materials
by Mingming Wang, Zhiyuan Li, Chaobo Li, Xiaoyun Sun, Yi Wang and Zhaofeng He
Sensors 2026, 26(13), 4207; https://doi.org/10.3390/s26134207 - 3 Jul 2026
Viewed by 43
Abstract
Dust concentration during intermittent processing of powder and granular materials is characterized by high-frequency abrupt changes, local accumulation, and complex coupling among multiple sensors. Existing forecasting models still exhibit limitations in modeling global dependencies and characterizing local trends. To address these issues, this [...] Read more.
Dust concentration during intermittent processing of powder and granular materials is characterized by high-frequency abrupt changes, local accumulation, and complex coupling among multiple sensors. Existing forecasting models still exhibit limitations in modeling global dependencies and characterizing local trends. To address these issues, this paper proposes an iTransformer-based dust concentration forecasting model that integrates a dual-stage feed-forward network and a DLinear branch. With iTransformer as the backbone network, the proposed model captures the coupling relationships among multi-source sensing signals through variate-wise modeling. A progressive dual-stage feed-forward feature refinement mechanism is constructed to enhance the model’s representation capability for transient variations and peak fluctuations in dust concentration. In addition, a collaborative modeling framework consisting of an iTransformer main branch and a DLinear auxiliary branch is designed to jointly learn global nonlinear features and local linear trends. An adaptive gated fusion mechanism is further introduced to dynamically allocate the contribution weights of different branches according to sequential characteristics. Experiments were conducted on a public 1 Hz smoke-sensing dataset, which was used as a proxy benchmark for high-frequency multivariate PM2.5 forecasting rather than direct industrial dust data. Under the setting of a 300-step input length and a 60-step forecasting horizon, the proposed model achieves an MSE of 1.8292 × 10−3, an MAE of 0.0334, an RMSE of 0.0428, an MAPE of 0.0177, and an R2 of 0.9744, outperforming the compared baseline models in overall performance. The results indicate that the proposed method improves overall forecasting accuracy and provides a methodological reference for sensor-driven particulate concentration forecasting and early warning, while further validation using field data from actual powder and granular material processing workshops is still required before practical deployment. Full article
(This article belongs to the Section Industrial Sensors)
Show Figures

Figure 1

30 pages, 1987 KB  
Article
XGBoost-Guided Spectrogram Pruning with SE-Augmented Residual CNN for Wind Turbine Gearbox Fault Diagnosis Under Unsteady Conditions
by Chiheng Huang, Attia Bibi, Wenxian Yang, Fang Duan, Haiyan Miao and Rakesh Mishra
Energies 2026, 19(13), 3153; https://doi.org/10.3390/en19133153 - 2 Jul 2026
Viewed by 75
Abstract
Reliable condition monitoring of wind turbine gearboxes is critical to reducing unplanned downtime and maintenance costs in wind farms. However, this task presents significant challenges due to the non-stationary nature of vibration signals, in which fault-relevant features are sparsely and unevenly distributed across [...] Read more.
Reliable condition monitoring of wind turbine gearboxes is critical to reducing unplanned downtime and maintenance costs in wind farms. However, this task presents significant challenges due to the non-stationary nature of vibration signals, in which fault-relevant features are sparsely and unevenly distributed across the time–frequency map. Although time–frequency analysis has been widely adopted to represent nonlinear and non-stationary vibration signals, existing deep learning methods typically process the full spectrogram directly, without distinguishing redundant or uninformative regions. This leads to high input dimensionality and exposes the model to substantial spectral noise. Consequently, it increases computational burden and potentially reduces the diagnostic reliability. To address this issue, this paper proposes a two-stage hybrid framework based on complementary selection mechanisms operating on two distinct feature spaces. In the first stage, eXtreme Gradient Boosting (XGBoost) importance scores are used to identify and permanently prune uninformative time–frequency features from the input spectrogram, reducing the input map size by 25%. In the second stage, a Squeeze-and-Excitation (SE) block, inserted after the deepest residual layer, performs soft channel-wise recalibration of the abstract feature maps produced by the residual convolutional neural network (ResCNN), thereby amplifying discriminative representations prior to classification. The proposed method was evaluated in an eight-class variable-speed fault classification task using the MCC5-THU benchmark, where data were collected from a 2.2 kW motor-driven gearbox test rig. The proposed method achieves a mean accuracy of 97.81% ± 0.33% under 5-fold stratified cross-validation (CV), while reducing classifier training time by approximately 23% compared to a baseline model trained on the full spectrogram. These results demonstrate that explicit input-level spectrogram pruning, combined with model-level channel attention, yields a robust and computationally efficient diagnostic framework for wind turbine gearbox condition monitoring. Full article
(This article belongs to the Section A3: Wind, Wave and Tidal Energy)
34 pages, 4462 KB  
Article
Physics-Guided Machine Learning for Predicting the Internal Temperature of Mushroom Bags
by Mingwen Shi, Xianpeng Sun, Xiaoying Ma, Xuelong Li, Jun Cao, Wei Qi and Hong Wang
Agriculture 2026, 16(13), 1454; https://doi.org/10.3390/agriculture16131454 - 2 Jul 2026
Viewed by 85
Abstract
Accurate prediction of the internal temperature of mushroom bags is essential but remains challenging owing to the complex nonlinear coupling between ambient conditions and the bag’s thermal state. This study proposes a physics-guided machine learning framework that translates thermodynamic prior knowledge into a [...] Read more.
Accurate prediction of the internal temperature of mushroom bags is essential but remains challenging owing to the complex nonlinear coupling between ambient conditions and the bag’s thermal state. This study proposes a physics-guided machine learning framework that translates thermodynamic prior knowledge into a set of interpretable engineered features. Specifically, we construct features that capture temporal thermal lags via cross-correlation optimal lag analysis, represent integrative thermal memory through cumulative moving averages and exponentially weighted moving averages (EWMAs) with a physically calibrated half-life, and quantify the interaction between evaporative cooling and ventilation using a vapor pressure deficit-gated temperature gradient. The engineered features are combined with standard environmental variables and supplied to several machine learning algorithms. Four paradigms—a physics model, a one-step physics model, a purely data-driven model, and the proposed physics-guided model—are systematically compared across four representative cultivation scenarios. The physics-guided XGBoost achieves the highest predictive accuracy, with R2 values of 0.996, 0.993, 0.997, and 0.973 for the four datasets, significantly outperforming all baselines. SHAP and Accumulated Local Effects analyses reveal that EWMA dominates predictions and that the learned feature–response relationships align with established thermodynamic principles, confirming physical consistency. The framework provides a practical, interpretable solution for feedforward environmental control in edible mushroom cultivation. Full article
(This article belongs to the Section Artificial Intelligence and Digital Agriculture)
Back to TopTop