Search Results (22)

This paper extends Woźny and Chudy’s linear-complexity Bézier evaluation algorithm (2020) to all parametric curves/surfaces with normalized basis functions via a novel basis function matrix decomposition. The unified framework covers the following: (i) B-spline/NURBS models; (ii) Bézier-type surfaces (tensor-product, rational, and triangular); (iii) enhanced models with shape parameters or non-polynomial basis spaces. For curves, we propose sequential and reverse corner-cutting modes. Surface evaluation adapts to type: non-tensor-product surfaces are processed through index-linearization to match the curve format, while tensor-product surfaces utilize nested curve evaluation. This approach reduces computational complexity, resolves cross-model compatibility issues, and establishes an efficient evaluation framework for diverse parametric geometries. Full article

Accurate and efficient white-spot defects detection for the surface of galvanized strip steel is one of the most important guarantees for the quality of steel production. It is a fundamental but “hard” small target detection problem due to its small pixel occupation in low-contrast images. By fully exploiting the low-rank and sparse prior information of a surface defect image, a Schatten-p norm-based low-rank tensor decomposition (SLRTD) method is proposed to decompose the defect image into low-rank background, sparse defect, and random noise. Firstly, the original defect images are transformed into a new patch-based tensor mode through data reconstruction for mining valuable information of the defect image. Then, considering the over-shrinkage problem in the low-rank component estimation caused by a vanilla nuclear norm and a weighted nuclear norm, a nonlinear reweighting strategy based on a Schatten $p$-norm is incorporated to improve the decomposition performance. Finally, a solution framework is proposed via a well-designed alternating direction method of multipliers to obtain the white-spot defect target image by a simple segmenting algorithm. The white-spot defect dataset from a real-world galvanized strip steel production line is constructed, and the experimental results demonstrate that the proposed SLRTD method outperforms existing state-of-the-art methods qualitatively and quantitatively. Full article

Additive manufacturing technologies have allowed the production of complex geometries that are typically obtained by applying topology optimization techniques. The outcome of the optimization process is a tessellated geometry, which has reduced aesthetic quality and unwanted spikes and cusps. Filters can be applied to improve the surface quality, but volume shrinking and geometry modification can be noticed. The design practice suggests manually re-designing the object in Computer-Aided Design (CAD) software, imitating the shape suggested by topology optimization. However, this operation is tedious and a lot of time is wasted. This paper proposes a methodology to automate the conversion from topology optimization output to a CAD-compatible design for industrial components. Topology optimization usually produces a dense triangle mesh with a high topological genus for those objects. We present a method to automatically generate a collection of spline (tensor-product) patches joined watertight and test the approach on real-wise industrial components. The methodology is based on the use of quadrilateral patches which are built on the external surface of the components. Based on the tests carried out, promising results have been obtained. It constitutes a first step towards the automatic generation of shapes that can readily be imported and edited in a CAD system. Full article

In plasticulture production systems, the conventional practice involves broadcasting pre-emergent herbicides over the entire surface of raised beds before laying plastic mulch. However, weed emergence predominantly occurs through the transplant punch-holes in the mulch, leaving most of the applied herbicide beneath the plastic, where weeds cannot grow. To address this issue, we developed and evaluated a precision spraying system designed to target herbicide application to the transplant punch-holes. A dataset of 3378 images was manually collected and annotated during a tomato experimental trial at the University of Florida. A YOLOv8x model with a p2 output layer was trained, converted to TensorRT^® to improve the inference time, and deployed on a custom-built computer. A Python-based graphical user interface (GUI) was developed to facilitate user interaction and the control of the smart sprayer system. The sprayer utilized a global shutter camera to capture real-time video input for the YOLOv8x model, which activates or disactivates a TeeJet solenoid for precise herbicide application upon detecting a punch-hole. The model demonstrated excellent performance, achieving precision, recall, mean average precision (mAP), and F1score exceeding 0.90. Field tests showed that the smart sprayer reduced herbicide use by up to 69% compared to conventional broadcast methods. The system achieved an 86% punch-hole recognition rate, with a 14% miss rate due to challenges such as plant occlusion and variable lighting conditions, indicating that the dataset needs to be improved. Despite these limitations, the smart sprayer effectively minimized off-target herbicide application without causing crop damage. This precision approach reduces chemical inputs and minimizes the potential environmental impact, representing a significant advancement in sustainable plasticulture weed management. Full article

Implied volatility is known to have a string structure (smile curve) for a given time to maturity and can be captured by the B-spline. The parameters characterizing the curves can change over time, which complicates the modeling of the implied volatility surface. Although machine learning models could improve the in-sample fitting, they ignore the structure in common over time and might have poor prediction power. In response to these challenges, we propose a two-step procedure to model the dynamic implied volatility surface (IVS). In the first step, we construct the bivariate tensor-product B-spline (BTPB) basis to approximate cross-sectional structures, under which the surface can be represented by a vector of coefficients. In the second step, we allow for the time-dependent coefficients and model the dynamic coefficients with the tree-based method to provide more flexibility. We show that our approach has better performance than the traditional linear models (parametric models) and the tree-based machine learning methods (nonparametric models). The simulation study confirms that the tensor-product B-spline is able to capture the classical parametric model for IVS given different sample sizes and signal-to-noise ratios. The empirical study shows that our two-step approach outperforms the traditional parametric benchmark, nonparametric benchmark, and parametric benchmark with time-varying coefficients in predicting IVS for the S&P 500 index options in the US market. Full article

Polyethylene terephthalate (PET) recycling is one of the most important environmental issues, assuring a cleaner environment and reducing the carbon footprint of technological products, taking into account the quantities used year by year. The recycling possibilities depend on the quality of the collected material and on the targeted product. Current research aims to increase recycling quantities by putting together recycled PET in an innovative way as a filler for the additive manufactured metallic lattice structure. Starting from the structures mentioned above, a new range of composite materials was created: IPC (interpenetrating phase composites), materials with a complex architecture in which a solid phase, the reinforcement, is uniquely combined with the other phase, heated to the temperature of melting. The lattice structure was modeled by the intersection of two rings using Solid Works, which generates the lattice structure, which was further produced by an additive manufacturing technique from 316L stainless steel. The compressive strength shows low values for recycled PET, of about 26 MPa, while the stainless-steel lattice structure has about 47 MPa. Recycled PET molding into the lattice structure increases its compressive strength at 53 MPa. The Young’s moduli are influenced by the recycled PET reinforcement by an increase from about 1400 MPa for the bare lattice structure to about 1750 MPa for the reinforced structure. This sustains the idea that recycled PET improves the composite elastic behavior due to its superior Young’s modulus of about 1570 MPa, acting synergically with the stainless-steel lattice structure. The morphology was investigated with SEM microscopy, revealing the binding ability of recycled PET to the 316L surface, assuring a coherent composite. The failure was also investigated using SEM microscopy, revealing that the microstructural unevenness may act as a local tensor, which promotes the interfacial failure within local de-laminations that weakens the composite, which finally breaks. Full article

Said-Ball curves and surfaces are extensively applied in the realm of geometric modeling. Their appearance is only decided by the control points, which produces a great deal of inconvenience for the shape design of sophisticated products. To overcome this defect, we construct a novel kind of quartic generalized Said-Ball (QGS-Ball, for short) curves and surfaces, which contain multiple shape parameters, and the global and local shape can be easily modified via shape parameters. The specific research contents are as follows: Firstly, the QGS-Ball basis functions carrying multiple shape parameters are defined, and the correlative properties are proved. Secondly, the QGS-Ball curve is proposed according to the QGS-Ball basis functions, and the effect of shape parameters on the curve is discussed. Thirdly, in view of the constructed QGS-Ball curve, we further propose the combined quartic generalized Said-Ball (CQGS-Ball, for short) curves, and deduce the conditions of first-order and second-order geometric continuity (namely, G¹ and G² continuity). Finally, the QGS-Ball surface is defined by tensor product method, and the influence of shape parameters on the surface is analyzed. The main contribution of this article is to construct the QGS-Ball curve model, and deduce the G¹ and G² geometric joining conditions of QGS-Ball curves. Combined with some modeling examples, it further illustrates that the QGS-Ball curve as a new geometric model provides a powerful supplement for the geometric design of sophisticated form in computer-aided design (CAD) and computer-aided manufacturing (CAM) systems. Full article

Strong mining tremors (SMTs) frequently occur in super-thick strata near the goaf when mining. Since 2021, there have been three consecutive SMTs with magnitude greater than 2.0 in longwall 1208 of the Shilawusu Coal Mine. These SMTs caused mine production to be suspended for more than 290 days and affected over 100 households located on the shaking ground, and seriously threatened the safety of underground workers and restricted production capacity. Therefore, it is essential to investigate the occurrence mechanism of SMTs in super-thick strata goaf mining in order to understand the phenomenon, how the disaster of mining tremors occurs, and the prevention and control of mining tremor disasters. In this study, field observation, numerical analysis, and theoretical calculation were used to study the occurrence mechanism of three SMTs in the Shilawusu Coal Mine. The results show that the super-thick strata fracture induced by the SMTs is generally higher by one to three orders of magnitude in some of the source mechanical parameters compared to other mining tremors, and so is more likely to cause ground shaking. Field observations revealed that before and after the occurrence of SMTs, the maximum surface subsidence suddenly increased by about 0.1 m and showed a “stepped” increase, and the super-thick strata began to experience fractures. The following theoretical mechanics model of super-thick strata was established: at the goaf stage of mining, with the increase in the area of the hanging roof, the super-thick strata will experience initial and periodic fractures, which can easily induce SMTs. The relative moment tensor inversion method was used to calculate the source mechanism of SMTs, which was found to be caused by the tensile rupture resulting from the initial and periodic ruptures of super-thick strata, in addition to the shear rupture generated by the adjustment of unstable strata structures. As the mining continues on the longwall face, there is still a possibility of SMT occurrence. This paper provides some insights into the mechanism and prevention of SMT in underground coal mines. Full article

Geometric iterative methods, including progressive iterative approximation and geometric interpolation methods, are efficient for fitting a given data set. With the development of big data technology, the number of fitting data points has become massive, and the progressive iterative approximation for least-squares fitting (LSPIA) is generally applied to fit mass data. Combining the Schulz iterative method for calculating the Moore–Penrose generalized inverse matrix with the traditional LSPIA method, this paper presents an accelerated LSPIA method for tensor product surfaces and shows that the corresponding iterative surface sequence converged to the least-squares fitting surface of the given data set. The iterative format is that of a non-stationary iterative method, and the convergence rate increased rapidly as the iteration number increased. Some numerical examples are provided to illustrate that the proposed method has a faster convergence rate. Full article

For non-uniform control polygons, a parameterized four-point interpolation curve ternary subdivision scheme is proposed, and its convergence and continuity are demonstrated. Following curve subdivision, a non-uniform interpolation surface ternary subdivision on regular quadrilateral meshes is proposed by applying the tensor product method. Analyses were conducted on the updating rules of parameters, proving that the limit surface is continuous. In this paper, we present a novel interpolation subdivision method to generate new virtual edge points and new face points of the extraordinary points of quadrilateral mesh. We also provide numerical examples to assess the validity of various interpolation methods. Full article

Laser-based plastic–metal joints have high potential to enable cost-efficient lightweight structures in multi-material design. By an appropriate load-optimized positioning of the microstructure on the joining zone, cost- and strength-optimized joints can be realized. However, there are no design methods and models to efficiently develop these tailored microstructures. Currently, time-consuming experiments are necessary to find the optimum microstructure concepts. These experiments must be repeated when requirements change, e.g., dimensions of the components. To provide a simple and efficient design tool, this paper presents an automated numerical method for the development of cost- and strength-optimized microstructure concepts for laser-based joining zones. The basis for the approach is a new numerical model which generates concepts for microstructures automatically based only on the stress tensor in the joining zone. A new finite element cohesive zone model (CZM) was developed to estimate the joint strength. The CZM parameters were efficiently derived from a finite element model of a single cavity. To determine the costs, a new model is presented that calculates the production time and the cost for any given microstructure. The models were interconnected in a combined optimization procedure and a genetic algorithm was used to determine cost- and strength-optimized microstructure concepts. The approach was applied to a demonstration example where the laser costs were reduced by up to 67% compared with benchmarks with surface-covering parallel linear cavities. The approach shows high potential for the efficient design of cost- and strength-optimal laser-based hybrid joints since it is fully based on simulation models and iterative experiments in the design stage are eliminated. Full article

Advances in additive manufacturing enable the fabrication of complex structures with intricate geometric details, which bring opportunities for high-resolution structure design and transform the potential of functional product development. However, the increasingly delicate designs bring computational challenges for structural optimization paradigms, such as topology optimization (TO), since the design dimensionality increases with the resolutions. Two-scale TO paves an avenue for high-resolution structural design to alleviate this challenge. This paper investigates the efficacy of introducing function-based microstructures into the two-scale TO. Both isotropic and orthotropic microstructure are considered to develop this TO framework. Implicit functions are exploited to model the two classes of cellular materials, including triply periodic minimal surfaces (TPMS) and Fourier series-based functions (FSF). The elasticity tensor of microstructures is computed with numerical homogenization. Then, a two-scale TO paradigm is formulated, and a gradient-based algorithm is proposed to simultaneously optimize the micro-scale structures and macro-scale material properties. Several engineering benchmark cases are tested with the proposed method, and experimental results reveal that using proposed microstructures leads to, at most, a $36\%$ decrease in the compliance of optimal structures. The proposed framework provides achievable directionality and broader design flexibility for high-resolution product development. Full article

In this paper, we propose a method for constructing spline surfaces interpolating a B-spline curve network, allowing the presence of free parameters, in order to model the interpolating surface. We provide a constructive algorithm for its generation in the case of biquadratic tensor product B-spline surfaces and bivariate B-spline surfaces on criss-cross triangulations. Finally, we present graphical results. Full article

Electricity production from ocean waves with different solutions is a topic of major research interest. Many of such designs are based on linear generators that inherently introduce end forces. In this paper, detent force using Maxwell Stress Tensor and induced voltage is initially investigated for two different winding patterns for a generator topology with buried magnets in a finite element software. Two ways of overcoming the end forces are further examined: the first method reduces the magnetic flux variations of the translator between stator and air. The second method aims at countering the end forces at both ends for full active stator area. A comparison is then made between buried and surface-mounted topologies for the second end effect compensation method. Both no-load and load conditions are investigated in the comparison. The end effect compensation shows promising results for both topologies. Some clear similarities of the extended stator used to counter the end forces are also apparent, where the stator extensions completely cover the outer poles of both topologies. The results also indicate a longer full active stator area for the buried topology for the same pole-pitch and stroke length, resulting in a higher average voltage for partial stator overlap. Full article

In computer-aided geometric design, a polynomial surface is usually represented in Bézier form. The usual form of evaluating such a surface is by using an extension of the de Casteljau algorithm. Using error-free transformations, a compensated version of this algorithm is presented, which improves the usual algorithm in terms of accuracy. A forward error analysis illustrating this fact is developed. Full article