Search Results (10,558)

We investigate the Lagrange formulation for the one-dimensional Saint Venant–Exner system. The system describes shallow-water equations with a bed evolution, for which the bedload sediment flux depends on the velocity, $Q\left(t,x\right)=A_g{u}^m,m\ge 1$. In terms of the Lagrange variables, the nonlinear hyperbolic system is reduced to one master third-order nonlinear partial differential equation. We employ Lie’s theory and find the Lie symmetry algebra of this equation. It was found that for an arbitrary parameter m, the master equation possesses four Lie symmetries. However, for $m=3$, there exists an additional symmetry vector. We calculate a one-dimensional optimal system for the Lie algebra of the equation. We apply the latter for the derivation of invariant functions. The invariants are used to reduce the number of the independent variables and write the master equation into an ordinary differential equation. The latter provides similarity solutions. Finally, we show that the traveling-wave reductions lead to nonlinear maximally symmetric equations which can be linearized. The analytic solution in this case is expressed in closed-form algebraic form. Full article

With the increasing frequency extreme weather events associated with climate change, real-time monitoring of rainfall intensity is critical for water resource management, disaster warning, and other applications. Traditional methods, such as ground-based rain gauges, radar, and satellites, face challenges like high costs, low resolution, and monitoring gaps. This study proposes a novel real-time rainfall intensity monitoring method based on deep learning and audio signal processing, using acoustic features from rainfall to predict intensity. Conducted in the semi-arid region of Northwest China, the study employed a custom-designed sound collection device to capture acoustic signals from raindrop-surface interactions. The method, combining multi-feature extraction and regression modeling, accurately predicted rainfall intensity. Experimental results revealed a strong linear relationship between sound pressure and rainfall intensity (r = 0.916, R² = 0.838), with clear nonlinear enhancement of acoustic energy during heavy rainfall. Compared to traditional methods like CML and radio link techniques, the acoustic approach offers advantages in cost, high-density deployment, and adaptability to complex terrain. Despite some limitations, including regional and seasonal biases, the study lays the foundation for future improvements, such as expanding sample coverage, optimizing sensor design, and incorporating multi-source data. This method holds significant potential for applications in urban drainage, agricultural irrigation, and disaster early warning. Full article

Validation of ICON model configurations optimized over a limited domain is essential before accepting new semi-empirical parameters that influence the behavior of subgrid-scale schemes. Because such parameters can modify the dynamics of a numerical weather prediction (NWP) model in highly nonlinear ways, we analyze one season of forecasts (December 2022, January and February 2023) generated with the NWP ICON-LAM through the lens of machine learning–based diagnostics as a complement to traditional evaluation metrics. The goal is to extract physically interpretable information on the model behavior induced by the optimized parameters. This work represents the first part of a wider study exploring machine learning tools for model validation, focusing on two specific approaches: Empirical Orthogonal Functions (EOFs), which are widely used in meteorology and climate science, and autoencoders, which are increasingly adopted for their nonlinear feature extraction capability. In this first part, EOF analysis is used as the primary tool to decompose weather fields from observed reanalysis and forecast datasets. Hourly 2-m temperature forecasts for winter 2022–2023 from multiple regional ICON configurations are compared against downscaled ERA5 data and in situ observations from ground station. EOF analyses revealed that the optimized configurations demonstrate a high skill in predicting surface temperature. From the signal error decomposition, the fourth EOF mode is effective particularly during night-time hours, and contributes to enhancing the performance of ICON. Analyses based on autoencoders will be presented in a companion paper (Part II). Full article

The residential energy sector contributes substantially to global energy-related emissions. Effective energy management requires an understanding occupant behavior through activity detection and habit identification. Recent advances in artificial intelligence (AI) and machine learning (ML) enable the automatic detection of user activities and prediction of energy needs based on historical consumption data. Non-intrusive load monitoring (NILM) facilitates device-level disaggregation without additional sensors, supporting demand forecasting and behavior-aware control in Home Energy Management Systems (HEMSs). This review synthesizes various AI and ML approaches for detecting user activities and energy habits in HEMSs from 2020 to 2025. The analyses revealed that deep learning (DL) models, with their ability to capture complex temporal and nonlinear patterns in multisensor data, achieve superior accuracy in activity detection and load forecasting, with occupancy detection reaching 95–99% accuracy. Hybrid systems combining neural networks and optimization algorithms demonstrate enhanced robustness, but challenges remain in limited cross-building generalization, insufficient interpretability of deep models, and the absence of dataset standardized. Future work should prioritize lightweight, explainable edge-ready models, federated learning, and integration with digital twins and control systems. It should also extend energy optimization toward occupant wellbeing and grid flexibility, using standardized protocols and open datasets for ensuring trustworthy and sustainability. Full article

Suppose K_Y and K_X are the image and the preimage of a nonlinear operator K_Y → K_X.
It is supposed that the cardinality of each K_Y and K_X is N and N is large. We provide an
approximation to the map F that requires prior information only on a few elements p from
K_Y, where p ≪ N, but still effectively represents F(K_Y). It is achieved under Lipschitz
continuity assumptions. The device behind the proposed method is based on a special
extension of the piecewise linear interpolation technique to the case of sets of stochastic
elements. The proposed technique provides a single operator that transforms any element
from the arbitrarily large set K_Y. The operator is determined in terms of pseudo-inverse
matrices so that it always exists. Full article

Urban vitality is a crucial indicator of a city’s sustainable development and the quality of life of its residents. Investigating the spatiotemporal patterns and influencing mechanisms of urban vitality is essential for optimizing the built-environment and improving governance. Using the central urban area of Guiyang, China, as a case study, this research integrates multi-source urban sensing data to investigate the spatiotemporal patterns of urban vitality and their driving factors. Geographically weighted regression (GWR) and machine learning combined with SHapley Additive exPlanations (SHAP) are applied to capture spatial heterogeneity, nonlinear relationships, and threshold effects among influencing variables. Results show that urban vitality exhibits a Y-shaped, single-core, multi-center, and clustered spatial configuration, with slightly higher intensity on weekdays and similar diurnal rhythms across weekdays and weekends. The effects of influencing factors display strong spatial non-stationarity, characterized by a concentric gradient radiating outward from the historic Laocheng core. Building density (BD), residential point density (RED), normalized difference vegetation index (NDVI), and road density (RD) emerge as the dominant contributors to urban vitality, while topographic conditions play a relatively minor role. The relationships between key landscape and built-environment variables and urban vitality are highly nonlinear, with distinct threshold effects. By integrating spatial econometric modeling and explainable machine learning, this study advances methodological approaches for urban vitality research and provides practical insights for landscape-oriented urban planning and human-centered spatial design. Full article

With accelerating urbanization and climate change, outdoor thermal comfort (OTC) in high-intensity urban blocks presents a critical challenge. While existing studies have established the general correlation between morphology and microclimate, most remain descriptive and lack a systematic framework to quantitatively integrate the non-linear coupled effects between multi-dimensional morphological variables and green infrastructure. To address this, this study proposes an automated performance-based design (PBD) framework for urban morphology optimization in Shenzhen. Unlike traditional simulation-based analysis, this framework serves as a generative tool for urban renewal planning. It integrates a multi-dimensional design element system with a genetic algorithm (GA) workflow. Analysis across four urban typologies demonstrated that the Full Enclosure layout is the most effective strategy for mitigating thermal stress, achieving a final optimized UTCI of 37.15 °C. Crucially, this study reveals a non-linear synergistic mechanism: the high street aspect ratios (H/W) of enclosed forms act as a “radiation shelter”, which amplifies the cooling efficiency of green infrastructure (contributing an additional 1.79 °C reduction). This research establishes a significant, strong negative correlation between UTCI and the combined factors of building density and green shading coverage. The results provide quantifiable guidelines for retrofitting existing high-density districts, suggesting that maximizing structural shading is prioritized over ventilation in ultra-high-density, low-wind climates. Full article

Addressing the challenge of optimizing the fatigue life of cylindrical roller bearings under high-speed and heavy-duty conditions, a collaborative multi-parameter optimization design method is proposed. First, a novel five-parameter profiling equation is introduced to overcome the limitations of traditional profiling methods based on the elastohydrodynamic lubrication property of the roller–raceway contact pair. Second, a nonlinear constrained optimization model that comprehensively considers key bearing structural parameters and the new profiling characteristics is constructed. In this model, the fatigue life is taken as the direct optimization objective, and geometric constraints, strength conditions, and lubrication performance are contained. Finally, using a NU2218E cylindrical roller bearing as the study case, the synchronous optimization achieved about a 196% enhancement in fatigue life over that of optimizing structural or profiling parameters alone. The proposed multi-parameter collaborative optimization framework and the innovative profiling approach provide new technical approaches and theoretical foundations for the design of high-performance rolling bearings. Full article

Diffraction-based velocity analysis is a key data interpretation technique in geophysical exploration, typically relying on the geometric characteristics, energy distribution, or propagation paths of diffraction waves. The hyperbola-based method is a classical strategy in this category, which extracts depth-dependent velocity (or dielectric properties) by correlating the hyperbolic shape of diffraction events with subsurface parameters for characterizing subsurface structures and material compositions. In this study, we propose a layer-stripping velocity analysis method applicable to ground-penetrating radar (GPR) and lunar-penetrating radar (LPR) data, with two main innovations: (1) replacing traditional local optimization algorithms with an intuitive parallelism check scheme, eliminating the need for complex nonlinear iterations; (2) performing depth-progressive velocity scanning of radargram diffraction signals, where shallow-layer velocity analysis constrains deeper-layer calculations. This strategy avoids misinterpretations of deep geological objects’ burial depth, morphology, and physical properties caused by a single average velocity or independent deep-layer velocity assumptions. The workflow of the proposed method is first demonstrated using a synthetic rock-fragment layered model, then applied to derive the near-surface dielectric constant distribution (down to 27 m) at the Chang’e-4 landing site. The estimated values range from 2.55 to 6, with the depth-dependent profile revealing lunar regolith stratification and interlayer material property variations. Consistent with previously reported results for the Chang’e-4 region, our findings confirm the method’s applicability to LPR data, providing a new technical framework for high-resolution subsurface structure reconstruction. Full article

Modern power distribution networks are increasingly challenged with nonlinear operating conditions, the high penetration of distributed energy resources, and conflicting operational objectives such as loss minimization and voltage regulation. Existing load-flow optimization approaches often suffer from slow convergence, premature stagnation in non-convex search spaces, and limited robustness when handling conflicting multi-objective performance criteria under fixed network constraints. To address these challenges, this paper proposes a Fractional Multi-Objective Load Flow Optimizer (FMOLFO), which integrates a fractional-order numerical regularization mechanism with an adaptive Pareto-based Differential Evolution framework. The fractional-order formulation employed in FMOLFO operates over an auxiliary iteration domain and serves as a numerical regularization strategy to improve the sensitivity conditioning and convergence stability of the load-flow solution, rather than modeling the physical time dynamics or memory effects of the power system. The optimization framework simultaneously minimizes physically consistent active power loss and voltage deviation within existing network operating constraints. Extensive simulations on IEEE 33-bus and 69-bus benchmark distribution systems demonstrate that FMOLFO achieves an up to 27% reduction in active power loss, improved voltage profile uniformity, and faster convergence compared with classical Newton–Raphson and metaheuristic baselines evaluated under identical conditions. The proposed framework is intended as a numerically enhanced, optimization-driven load-flow analysis tool, rather than a control- or dispatch-oriented optimal power flow formulation. Full article

Forecasting stock market crashes is difficult because such events are rare, highly nonlinear, and shaped by latent structural and behavioral forces. This study introduces a calibrated and interpretable Random Forest framework for detecting pre-crash conditions through structural feature engineering, early-warning calibration, and model explainability. Using daily data on global equity indices and major large-cap stocks from the U.S., Europe, and Asia, we construct a feature set that captures volatility expansion, moving-average deterioration, Bollinger Band width, and short-horizon return dynamics. Probability-threshold optimization significantly improves sensitivity to rare events and yields an operating point at a crash-probability threshold of 0.33. Compared with econometric and machine learning benchmarks, the calibrated model attains higher precision while maintaining competitive F1 and MCC scores, and it delivers meaningful early-warning signals with an average lead-time of around 60 days. SHAP analysis indicates that predictions are anchored in theoretically consistent indicators, particularly volatility clustering and weakening trends, while robustness checks show resilience to noise, structural perturbations, and simulated flash crashes. Taken together, these results provide a transparent and reproducible blueprint for building operational early-warning systems in financial markets. Full article

Industrial gateways serve as critical data aggregation points within the Industrial Internet of Things (IIoT), enabling seamless data interoperability that empowers enterprises to extract value from equipment data more efficiently. However, their role exposes a fundamental trade-off between computational efficiency and prediction accuracy—a contradiction yet to be fully resolved by existing approaches. The rapid proliferation of IoT devices has led to a corresponding surge in network traffic, posing significant challenges for traffic forecasting methods, while deep learning models like Transformers and GNNs demonstrate high accuracy in traffic prediction, their substantial computational and memory demands hinder effective deployment on resource-constrained industrial gateways, while simple linear models offer relative simplicity, they struggle to effectively capture the complex characteristics of IIoT traffic—which often exhibits high nonlinearity, significant burstiness, and a wide distribution of time scales. The inherent time-varying nature of traffic data further complicates achieving high prediction accuracy. To address these interrelated challenges, we propose the lightweight and theoretically grounded DOA-MSDI-CrossLinear framework, redefining traffic forecasting as a hierarchical decomposition–interaction problem. Unlike existing approaches that simply combine components, we recognize that industrial traffic inherently exhibits scale-dependent temporal correlations requiring explicit decomposition prior to interaction modeling. The Multi-Scale Decomposable Mixing (MDM) module implements this concept through adaptive sequence decomposition, while the Dual Dependency Interaction (DDI) module simultaneously captures dependencies across time and channels. Ultimately, decomposed patterns are fed into an enhanced CrossLinear model to predict flow values for specific future time periods. The Dream Optimization Algorithm (DOA) provides bio-inspired hyperparameter tuning that balances exploration and exploitation—particularly suited for the non-convex optimization scenarios typical in industrial forecasting tasks. Extensive experiments on real industrial IoT datasets thoroughly validate the effectiveness of this approach. Full article

Predictive modeling of extrusion processes through machine learning (ML) offers significant improvements over classical response surface methodology (RSM) when addressing nonlinear and multivariable systems. This study evaluated hemp residues (Cannabis sativa) as a non-conventional ingredient in ruminant diets and compared the performance of polynomial regression models against several ML algorithms, including artificial neural networks (ANNs), random forest (RF), K-Nearest neighbors (KNN), and XGBoost. Three experimental datasets from previous extrusion studies were concatenated with new laboratory experiments, creating a unified database in excel. Input variables included extrusion parameters (temperature, screw speed, and moisture) and formulation components, while output variables comprised expansion index, BD, penetration force, water absorption index and water solubility index. Data preprocessing involved robust z-score detection of outliers (MAD criterion) with intra-group winsorization, followed by normalization to a [−1, +1] range. Hyperparameter optimization of ANN models was performed with Optuna, and all algorithms were evaluated through 5-fold cross-validation and independent external validation sets. Results demonstrated that ML models consistently outperformed quadratic regression, with ANNs achieving R² > 0.80 for BD and water solubility index, and RF excelling in predicting solubility. These findings establish machine learning as a robust predictive framework for extrusion processes and highlight hemp residues as a sustainable feed ingredient with potential to improve ruminant nutrition and reduce environmental impacts. Full article

Public health impacts of non-optimal temperatures and air pollution have received insufficient attention in Southeast Europe, one of the most air-polluted regions in Europe, simultaneously pressured by climate change. This study employed a multimodal approach to characterize the microclimate and air quality and conduct a health impact assessment in the three biggest cities in Bulgaria. Simulation of atmospheric thermo-hydrodynamics and assessment of urban microclimate relied on the Weather Research and Forecasting model. Concentrations of fine particulate matter (PM_2.5) and nitrogen dioxide (NO₂) were calculated with a land-use regression model. Ischemic heart disease (IHD) hospital admissions were linked to daily measurements at background air quality stations. The results showed declining trends in PM_2.5 but persistent levels of NO₂, especially in Sofia and Plovdiv. Distributed lag nonlinear models revealed that, in Sofia and Plovdiv, PM_2.5 was associated with IHD hospitalizations, with a fifth of cases in Sofia attributable to PM_2.5. For NO₂, an increased risk was observed only in Sofia. In Sofia, the risk of IHD was increased at cold temperatures, while both high and low temperatures were associated with IHD in Plovdiv and Varna. Short-term effects were observed in response to heat, while the effects of cold weather took up to several weeks to become apparent. These findings highlight the complexity of exposure–health interactions and emphasize the need for integrated policies addressing traffic emissions, urban design, and disease burden. Full article

Computer-based engineering design tools can quicken the cadence for machine design, which enables companies to compete better in the global marketplace. The application of nonlinear optimization and tradespace analysis methods allows the exploration of design variables within dynamic mechanisms. In this paper, the design of a classical machine, the Seth Thomas pendulum street clock, which offered precision timekeeping and time display at the turn of the 20th century, will be investigated from a modern perspective. A mathematical model serves as the basis for the genetic algorithm optimization method to assess the system design in terms of accuracy, mass, quality factor, and bending stress. To validate the model, experimental data was collected on a 1906 Seth Thomas Model 04 movement. The engineering study findings indicate that the target accuracy, quality factor, and bending stress can be achieved with pendulum mass and gear thickness reductions of 1.4% and 50.3%, respectively. The tradespace exploration offers a visualization of the machine’s performance per design variable adjustments for greater insight into the original solution and subsequent recommended changes. Overall, this mechanical machine review enables an assessment of original design choices made over a century ago and provides an awareness of engineering’s progress during this period. Full article