Search Results (366)

The design of smart skin with lightweight requirements utilizes high-performance composite materials, resulting in thin structural characteristics. When subjected to complex aerodynamic loads, the smart skin structure experiences warping deformation, which significantly impacts both flight efficiency and structural integrity. However, this deformation behavior has been largely overlooked in current shape sensing methods embedded within the structural health monitoring (SHM) systems of smart skin, leading to insufficient monitoring capabilities. To address this issue, this paper proposes a novel shape sensing methodology for the real-time monitoring of warping deformation in smart skin. Initially, the structural displacement field of the smart skin and the warping function are mathematically defined, incorporating constitutive relations and considering the influence of material parameters on sectional strains. Subsequently, the inverse finite element method (iFEM) is employed to establish a shape sensing model. The interpolation function and the actual sectional strains, derived from discrete strain measurements, are calculated based on the current constitutive equations. Finally, to validate the accuracy of the proposed iFEM for monitoring warping deformation, numerical tests are conducted on curved skin structures. The results indicate that the proposed methodology enhances reconstruction capability, with a 10% improvement in accuracy compared to traditional iFEM methods. Consequently, the shape sensing algorithm can be seamlessly integrated into the SHM system of smart skin to ensure the predicted performance. Full article

The combination of both Passive Thermography and machine learning in materials science and engineering allows rapid progress in advanced fatigue analysis. Focusing on mechanical aspects, the combination of these approaches is capable of interpolating the fatigue resistance in diverse conditions with minimal data, when compared to the classical solution, in which analyses are conducted using statistical processes such as the Staircase Method. Even though the thermal increment and thermal area are crucial parameters for the fatigue limit analysis, the implementation of machine-learning interpolation improves data consistency and reduces variability in the fatigue limit estimation through Type-A repeatability uncertainty reduction. This way, the two-layer artificial neural network does not have any predefined form of functions; second, it maintains the inherent non-linear features of the data. The validation of the proposed approach was conducted for a C45 steel, and two different experimental campaigns were conducted using a resonant machine. At the end, the analysis of the fatigue limit was conducted by means of an interpolation-assisted Two-Curve Method, starting from the classical thermal data evolution properly optimized with a machine-learning approach, achieving a more precise result in estimating the fatigue limit. Full article

This expository paper provides a unified and pedagogical introduction to optimal quantization for probability measures supported on spherical curves and discrete subsets of the sphere, emphasizing both continuous and discrete settings. We first present a detailed geometric and analytical foundation for intrinsic quantization on the unit sphere, including definitions of great and small circles, spherical triangles, geodesic distance, Slerp interpolation, the Fréchet mean, spherical Voronoi regions, centroid conditions, and quantization dimensions. Building upon this framework, we develop explicit continuous and discrete quantization models on spherical curves, namely great circles, small circles, and great circular arcs—supported by rigorous derivations and pedagogical exposition. For uniform continuous distributions, we compute optimal sets of n-means and the associated quantization errors on these curves; for discrete distributions, we analyze antipodal, equatorial, tetrahedral, and finite uniform configurations, illustrating convergence to the continuous model. The central conclusion is that for a uniform probability distribution supported on a one-dimensional geodesic subset of total length L, the optimal n-means form a uniform partition and the quantization error satisfies $V_n=L^2/\left(12n^2\right)$.The exposition emphasizes geometric intuition, detailed derivations, and clear step-by-step reasoning, making it accessible to beginning graduate students and researchers entering the study of quantization on manifolds. This article is intended as an expository and tutorial contribution, with the main emphasis on geometric reformulation and pedagogical clarity of intrinsic quantization on spherical curves, rather than on the development of new asymptotic quantization theory. Full article

Establishing a mathematical model of a Francis turbine is the foundation for the simulation of hydropower station operation and is of great significance for the analysis of the hydropower station’s transient process. Currently, in engineering practice, the model is often established based on the comprehensive characteristic curves of the Francis turbine provided by the manufacturer, using the external characteristic method. Traditional modeling methods mostly adopt manual reading of points or the use of dedicated numerical software for curve tracing to discretely sample the comprehensive characteristic curves of the turbine. This method is labor-intensive, inefficient, and relies on manual experience, with a small sample size, which, to some extent, affects the accuracy and reliability of the numerical processing results and cannot meet the needs of transient process simulation analysis. To address these shortcomings, this paper proposes a refined modeling method based on image numerical processing and an RBF neural network. Taking the HLA685 Francis turbine as an example, the method first uses image processing to achieve large-scale automated discrete sampling of the turbine’s high-efficiency zone characteristic data, then reasonably extends the small-opening and low-speed regions, and finally uses the RBF neural network method for interpolation and extrapolation to obtain the full characteristic data. This method can effectively improve the efficiency and accuracy of comprehensive characteristic modeling of the turbine and has good reference significance for the comprehensive characteristic modeling of blade-type machinery. Full article

Drug delivery from cylindrical tablets of arbitrary dimensions is discussed here, using the analytical solution of diffusion equation. Utilizing dimensionless quantities, we show that the release profiles are determined by a unique parameter, represented by the aspect ratio of the cylindrical formulation. Fractional release curves are presented for different values of the aspect ratio, covering a range of many orders of magnitude. The corresponding release profiles lie in between the two opposite limits of release from thin slabs and two-dimensional radial release, pertinent to the cases of thin and long cylinders, respectively. In a quest for a part of the delivery process closer to a zero-order release, the release rate is calculated, which is found to exhibit the typical behavior of purely diffusional release systems. Two simple fitting formulae, containing two parameters each, are considered to approximate the infinite series of the exact solution: The stretched exponential (Weibull) function and a recently suggested expression interpolating between the correct time dependencies at the initial and final stages of the process. The latter provides a better fitting in all cases. The variation of the fitting parameters with the aspect ratio of the device is presented for both fitting functions. We also calculate the characteristic release time, which is found to correspond to an amount of fractional release between 64% and around 68% depending on the cylindrical aspect ratio. We discuss how the last quantities can be used to estimate the drug diffusion coefficient from experimental release profiles and apply these ideas to published drug delivery data. Full article

This paper introduces a novel Lithium-Ion Battery (LIB) State-of-Charge (SOC) estimation approach that integrates Akima–Savitzky–Golay curve reconstruction with a Bayesian-optimized, adaptive Extended Kalman Filter (EKF). The method addresses crucial SOC estimation challenges by means of three foundational advancements: (i) a refined open-circuit voltage (OCV)-SOC curve reconstruction grounded in Akima interpolation coupled with Savitzky–Golay filtering, (ii) an adaptive EKF weighting strategy, and (iii) systematic hyperparameter value optimization executed through Bayesian optimization. Comprehensive performance validation utilizes an extensive dataset collected from LG HG2 18650 cells across temperatures of −20 °C to 40 °C, incorporating multiple standard driving cycles—namely HPPC, UDDS, HWFET, LA92, and US06 cycles. The proposed method achieves an improved estimation accuracy with an average Root Mean Square Error (RMSE) of 2.65% over the different operating conditions and temperature variations. Notably, the method markedly enhances SOC estimation reliability in the critical mid-SOC range (20–80%), while preserving the computational overhead necessary for real-time integration into Battery Management Systems (BMSs). The adaptive weighting successfully compensates for the present physical limitations, thereby delivering a resilient SOC estimation tailored for Electric Vehicle (EV) battery applications. Full article

This study focuses on high-cycle fatigue (HCF) of aircraft landing gear (LG) components, covering material testing, full-scale component experiments, finite element (FE) modeling, life-prediction comparison, and probabilistic assessment. Fully reversed axial fatigue tests on forty 300M steel specimens were conducted to establish a reliable S-N curve. Full-scale fatigue experiment conducted on the upper torque link components showed that the one cracking at approximately 184,000 cycles (at the filet), while another remained undamaged after 166,000 cycles, providing a benchmark for model validation. FE simulations using ANSYS accurately captured the stress field within the component, with a maximum error of less than 10% compared to experimental strain measurements. Based on the FKM guideline, this work developed an improved FKM local-stress approach (LSA) for HCF life prediction, which integrates load-dependent stress gradients, FKM mean stress correction, and interpolated surface-condition factors for S-N curve adjustment specific to the component’s surface treatment. It predicts the fatigue life as 174,000 cycles (−5.4% error relative to test), outperforming standard FKM-LSA calculations and nCode software simulations. Furthermore, by augmenting the experimental data and constructing p-S-N curves, the improved LSA was extended to predict fatigue life under different survival probabilities and confidence levels, providing a practical tool for reliability-based design. Full article

This paper focuses on optimisation of material parameters to describe the elastoplastic stress–strain relationship in finite element solvers. Two new methods are introduced to minimise the numerical error that occurs in the interspace between the experimental cyclic stress–strain curve and its representation using multilinear interpolation. Specifically, both methods are integrated into a Prandtl operator approach, which can be used to simulate the elastoplastic response of mechanical components subjected to variable thermomechanical loadings. The improvement as compared to standard interpolation is most substantial when the number of yield planes is limited, especially in the case of bilinear stress–strain curves. The innovation of this study is an algorithm that optimises positions of the stress–strain points across the temperature range of interest considering several input temperatures. It is shown that these methods are especially applicable for optimisation of material parameters when the stress–strain curves are available for a range of test temperatures that are needed for simulating thermomechanical fatigue. The improvement in the interpolation using these methods is exhibited for two materials with available experimental results: stainless steel EN 1.4512 and polyamide PA12. Full article

Background/Objectives: In computer graphics, virtual worlds are constructed and visualized through algorithmic processes. These environments are typically populated with objects defined by mathematical models, traditionally based on Euclidean geometry. However, there is increasing interest in exploring non-Euclidean geometries, which require adaptations of the modeling techniques used in Euclidean spaces. Methods: This paper focuses on defining parametric curves and surfaces within elliptic and hyperbolic geometries. We explore free-form splines interpreted as hierarchical motions along geodesics. Translation, rotation, and ruling are managed through supplementary curves to generate surfaces. We also discuss how to compute normal vectors, which are essential for animation and lighting. The rendering approach we adopt aligns with physical principles, assuming that light follows geodesic paths. Results: We extend the Kochanek–Bartels spline to both elliptic and hyperbolic geometries using a sequence of geodesic-based interpolations. Simple recursive formulas are introduced for derivative calculations. With well-defined translation and rotation in these curved spaces, we demonstrate the creation of ruled, extruded, and rotational surfaces. These results are showcased through a virtual reality application designed to navigate and visualize non-Euclidean spaces. Full article

Enhancing solar cell performance is effectively attainable through optimization of the front electrode layout. This research tackles the electrode design problem via a geometry-driven optimization framework to discover high-efficiency front electrode patterns. The introduced methodology employs wide quadratic curves for representing the electrode geometry, wherein both the interpolation points and the widths of these curves function as design variables. Two solar cell configurations are utilized to test the optimization technology. In contrast to traditional shape optimization, the current strategy provides enhanced design flexibility, promoting novel and high-performance electrode configurations. Key parameters analyzed encompass the initial geometry, the count of wide quadratic curves, mesh resolution, and the size of the solar cell. Results demonstrate that the presented approach constitutes a viable and efficient design pathway for elevating solar cell operation. The performance of solar cells optimized using this technology outperforms those processed with a modified Solid Isotropic Material with Penalization (SIMP) approach. Furthermore, relative to typical H-pattern electrode grids, the optimized layouts not only achieve superior efficiency but also considerably minimize the consumption of electrode materials. Full article

The evolution of space technology in recent years, fueled by advancements in computing such as Artificial Intelligence (AI) and machine learning (ML), has profoundly transformed our capacity to explore the cosmos. Missions like the James Webb Space Telescope (JWST) have made information about distant objects more easily accessible, resulting in extensive amounts of valuable data. As part of this work-in-progress study, we are working to create an atmospheric absorption spectrum prediction model for exoplanets. The eventual model will be based on both collected observational spectra and synthetic spectral data generated by the ROCKE-3D general circulation model (GCM) developed by the climate modeling program at NASA’s Goddard Institute for Space Studies (GISS). In this initial study, spline curves are used to describe the bin heights of simulated atmospheric absorption spectra as a function of one of the values of the planetary parameters. Bayesian Adaptive Exploration is then employed to identify areas of the planetary parameter space for which more data are needed to improve the model. The resulting system will be used as a forward model so that planetary parameters can be inferred given a planet’s atmospheric absorption spectrum. This work is expected to contribute to a better understanding of exoplanetary properties and general exoplanet climates and habitability. Full article

This paper presents an effective method for generating blending meshes by leveraging geodesic curves on triangular meshes. Depending on whether the input meshes intersect, the blending regions are automatically initialized using either minimum-distance points or intersection curves, while allowing users to intuitively adjust boundary curves directly on the mesh. Each blending region is parameterized via geodesic linear interpolation, and a reparameterization strategy is employed to establish optimal correspondences between boundary curves, ensuring smooth, twist-free connections. The resulting blending mesh is merged with the input meshes through subdivision, trimming, and co-refinement along the boundaries. The proposed method is applicable to both intersecting and non-intersecting meshes and offers flexible control over the shape and curvature of the blending region through various user-defined parameters, such as boundary radius, scaling factor, and blending function parameters. Experimental results demonstrate that the method produces stable and smooth transitions even for complex geometries, highlighting its robustness and practical applicability in diverse domains including digital fabrication, mechanical design, and 3D object modeling. Full article

To address the building settlement issues induced by an urban geological hazard in a northern city, this study utilizes settlement monitoring data from 16 high-rise buildings. The non-uniform temporal data were processed using the Akima interpolation method to construct a settlement prediction model based on a backpropagation (BP) neural network. The model’s predictive performance was validated against traditional approaches, including the hyperbolic and exponential curve methods, and was further employed to estimate the stabilization time of building settlements. Additionally, spatiotemporal characteristics of settlement behavior under the influence of geological hazards were investigated through a comparative analysis of deformation data across the building group. The results demonstrate that the BP neural network model achieves a 58.3% improvement in predictive accuracy compared to traditional empirical methods, effectively capturing the settlement evolution of buildings. The model also provides reliable predictions for the time required for buildings to reach a stable state. The temporal evolution of building settlement exhibits a distinct three-stage pattern: (1) an initial abrupt phase dominated by rapid water and soil loss; (2) a rapid settlement phase primarily driven by the consolidation of sandy and clayey soils; and (3) a slow consolidation phase governed by the prolonged consolidation of cohesive soils. Spatially, building deformations show significant regional heterogeneity, and the existence of potential finger-like preferential pathways for water and soil loss appears to exert a substantial influence on differential settlements. Full article

Spatial-temporal optimal interpolation (STOI) is a data assimilation method based on minimizing the error in an estimate. Error correlations can be modeled with analytical functions. We investigated the effect of the form of the error correlation functions on the uncertainty in an estimate. We applied STOI to the estimation of aerosol distribution over Europe using the results of GEOS-Chem chemical transport model simulations and observations from a ground-based radiometric Aerosol Robotic Network. We used exponential functions to model correlation curves. The results show that a ±15–25% change in the argument of the constructed exponential functions has little effect on the mean square error in the estimate in regions where observations are dense. STOI estimates are sensitive to the form of the correlation curves in regions where observations are sparse. Full article

Accurate identification of mechanical excitation forces is of great significance for the control of ship radiated noise and structural design. Currently, the identification of excitation forces mostly relies on indirect calculations, which suffer from ill-conditioned problems. Regularization correction is one of the main means to solve this problem. Although regularization methods have been widely developed, their application in the field of ships is relatively rare. Currently, the commonly used methods are truncation singular values and Givonov regularization methods. This paper starts from the practical application of ships and addresses the problem of poor correction effect of traditional regularization methods. Two optimized regularization methods, quasi-optimal discriminant criterion and B-spline interpolation function method, are proposed. These methods are verified through simulations and experiments. The results of the scaled model experiments show that compared with using the L-curve alone, the Q-O method reduces the regularization error by 29%, while the BL curve improves the robustness by 38% under a 15 dB noise condition. Full article