Quadratic Surface Research Articles

Imaging theories of rotating quadric surface

Imaging theories of rotating quadric surface

Multi-line laser 3D reconstruction method based on spatial quadric surface and geometric estimation

The traditional multi-line laser 3D reconstruction is based on binocular epipolar constraints and the equation of the laser optical plane. Firstly, matching points are identified based on the epipolar constraints. Then, the correct matching points are selected based on the optical plane equation of the multi-line laser. Finally, 3D reconstruction is performed using the selected matching points. In actual production processes involving multi-line lasers, noticeable distortion occurs due to the projection of Diffractive Optical Elements (DOE) at a large angle. This results in curved laser light planes and curved reflections on the measured objects. Under such circumstances, efficiently screening matching points using the traditional method based on the laser plane equation becomes challenging. Additionally, inherent noise in multi-line laser systems introduces errors in extracted laser center coordinates, making it impossible to directly obtain high-precision 3D data. To address these issues, this paper proposes a method that utilizes spatial quadric surfaces and geometric estimation for completing multi-line laser 3D reconstructions. By analyzing the distortion principle of DOE and the positional relationship after optical diffraction, the multi-line laser manifests as a quadric surface on the optical output plane. Consequently, by calibrating the equations of the quadric surface and applying binocular polar constraints, suitable matching points for the multi-line laser can be chosen. Once an accurate matching point is identified, a minimum geometric distance estimation can be established based on the distance constraint between the point and its corresponding epipolar line. This distance represents the separation between the left and right camera’s laser center points and their respective epipolar lines. Utilizing this estimate of the minimum geometric distance, a refined calculation can be performed to better satisfy epipolar constraints and obtain new matching points. Ultimately, utilizing these new matching points enables the completion of 3D reconstruction for multi-line lasers. In comparison with methods relying on spatial plane and epipolar constraints, our algorithm exhibits a superior degree of matchability and accuracy.According to multiple groups of test data, the average error before optimization is 0.3126 mm, and can be increased to 0.0336 mm after optimization.

Optimising nanoparticles: harnessing quality by design through 3-level factorial design and box-behnken methodology

Nanoparticles (NPs) have become essential elements in a number of scientific and industrial domains, such as materials research, drug delivery, and diagnostics, because of their special qualities and potential for focused uses. An ideal formulation procedure is essential to maximising the effectiveness and efficiency of nanoparticles. In order to optimise the formulation and production processes for nanoparticles, this research investigates the application of Quality by Design (QbD) principles in conjunction with sophisticated statistical approaches, namely the 3-level factorial design and the Box-Behnken methodology. The Quality by Design methodology is a methodical approach that prioritises predetermined goals, in-depth process comprehension, and careful control grounded in reliable science and quality risk management. When QbD is incorporated into nanoparticle optimisation, reliable and repeatable formulations that adhere to specifications with little variation are guaranteed. To look into how different factors interact and affect the properties of nanoparticles, the 3-level factorial design is used. With this design approach, a thorough understanding of the process variables can be obtained by exploring a broad variety of component values. Critical quality attributes (CQAs) include important parameters such drug encapsulation efficiency, zeta potential, polydispersity index (PDI), and particle size. These parameters are methodically examined to determine the ideal amounts of each. To further refine the 3-level factorial design, the Box-Behnken methodology is applied. Without the requirement for extensive combination testing, this response surface methodology (RSM) is especially useful for building second-order polynomial models and investigating quadratic response surfaces. By enabling a more accurate comprehension of the interactions between inputs and responses, the Box-Behnken design improves the optimisation process and makes it easier to identify the ideal circumstances for nanoparticle synthesis. By utilising both approaches in tandem, this work methodically determines ideal formulation parameters that minimise nanoparticle size and polydispersity while optimising stability and drug loading efficiency. The outcomes highlight how important a QbD framework is for directing the creation of reliable nanoparticle systems that function consistently and predictably.

Corneal Curvature Change After Strabismus Surgery: An Experience from a Single-academic Center

Objective: This study aimed to explore corneal curvature changes following strabismus surgery using a quadric surface fitting model to address ocular misalignment. Material and Methods: In this prospective cross-sectional study, 54 completed cases (84 eyes) of patients aged 6–60 years old (mean 10 years old) undergoing horizontal rectus muscle surgery were examined using placido-based keratometry with the Oculus Keratograph 5M system. Data on corneal curvature were collected one week pre-operation, and again one week, one month, and three months post-operation. Asphericity in the vertical meridian (Qy) and horizontal meridian (Qx), and surgical-induced astigmatism (SIA) were calculated. Results: The 84 eyes included were categorized into three groups: horizontal muscle surgeries, oblique muscle surgery, and combined horizontal and oblique muscle surgeries. Significant corneal prolation (steep central, flat peripheral) was revealed in the vertical meridian (Qy) at 3 months postoperatively for lateral rectus (LR) recession in the first group (p < 0.001), and the mean SIA was 0.45 D (95% CI: 0.35–0.56 D). A similar effect was seen in the vertical meridian of the third group (p < 0.01), with a mean SIA at 3 months of 0.27 D (95% CI: 0.23–0.32 D). Conclusion: Lateral rectus muscle recession induces corneal vertical prolation for up to 3 months post-operation. Surgeons are thus advised to re-evaluate refraction and defer contact lens refitting, refractive surgery, and intraocular lens calculations for at least 3 months after the procedure.

The Application of Converter Sludge and Slag to Produce Ecological Cement Mortars.

The paper presents an analysis of the effective use of a mixture of steel sludge (S1) and slag (S2) from the converter process of steel production for the production of cement mortars. Metallurgical waste used in the research, which is currently deposited in waste landfills and heaps near plants, posing a threat to groundwater (possibility of leaching metal ions present in the waste), was used as a substitute for natural sand in the range of 0-20% by weight of cement (each). The obtained test results and their numerical analysis made it possible to determine the conditions for replacing part of the sand in cement mortars with a mixture of sludge and slag from a basic oxygen furnace (BOF) and to determine the effects of such modification. For the numerical analysis, a full quadratic Response Surface Model (RSM) was utilized for two controlled factors. This model was subsequently optimized through backward stepwise regression, ensuring the inclusion of only statistically significant components and verifying the consistency of residual distribution with the normal distribution (tested via Ryan-Joiner's test, p > 0.1). The designated material models are helpful in designing ecological cement mortars using difficult-to-recycle waste (i.e., sludge and converter slag), which is important for a circular economy. Mortars modified with a mixture of metallurgical waste (up to 20% each) are characterized by a slightly lower consistency, compressive and flexural strength, and water absorption. However, they show a lower decrease in mechanical strength after the freezing-thawing process (frost resistance) compared to control mortars. Mortars modified with metallurgical waste do not have a negative impact on the environment in terms of leaching heavy metal ions. The use of a mixture of sludge and steel slag in the amount of 40% (slag/sludge in a 20/20 ratio) allows you to save 200 kg of sand when producing 1 m3 of cement mortar (cost reduction by approx. EUR 5.1/Mg) and will also reduce the costs of the environmental fee for depositing waste.

Kernel-free Reduced Quadratic Surface Support Vector Machine with 0-1 Loss Function and L$$_p$$-norm Regularization

Kernel-free Reduced Quadratic Surface Support Vector Machine with 0-1 Loss Function and L$$_p$$-norm Regularization

Validation of the fully rationalized Tsai-Wu failure criterion for unidirectional laminates under multiaxial stress states through a ring-on-ring test

Validating a failure criterion under complex stress states is important because composites often encounter multiaxial stress in practical applications, but it also helps to expose any deficiencies of the criterion in failure prediction in the presence of stress interactions. This study examines the recently formulated fully rationalized Tsai-Wu criterion for unidirectional laminates under multiaxial stress states created by ring-on-ring loading. Distinct stress distributions under this loading condition are exhibited and quantified by numerical modeling, featuring critical biaxial tension on the bottom surface and triaxial compression on the top surface. The fully rationalized Tsai-Wu criterion and the original Tsai-Wu criterion are used to predict failure, with the results indicating good agreement between the former and experimental data. In comparison with the latter, quadric failure surfaces of the two criteria are constructed to analyze differences in prediction. The findings demonstrate the validity of the rationalization work for the Tsai-Wu criterion and its potential in predicting failure under multiaxial stress states.

Optimization design of hydro turbine support structure based on GA-FA-BP method

The rational design of the turbine support structure ensures the safe operation of the system, achieves significant economic benefits and improves the efficiency of the turbine. This paper presents a novel turbine support structure capable of vertical movement along the guide column. In addition, the GA-FA-BP method has been developed for the optimization design of the support structure, which combines genetic algorithm (GA), firefly algorithm (FA) and back-propagation neural network (BP). The use of quadratic response surface (RS) method along with NSGA-II for the result validation of the GA-FA-BP model ensures the robustness and reliability of the optimization results. A finite element model is set up to analyse the mechanical behaviour of the support structure under 10 different combined load conditions. The most critical load conditions in the static mechanical models are used to generate training data, and the mass, deformation and equivalent stress of the optimized and unoptimized support structures are analyzed and compared. The results show that the optimized support structure can maintain deformation and equivalent stress within a weight reduction of 21.83% compared to the original design. Compared to a single optimization model, the proposed GA-FA-BP model shows higher accuracy with a correlation coefficient up to 0.9989.

On the construction of saturated split-plot designs for quadratic response surface models

Split-plot designs are commonly employed in experiments where the levels of some factors are difficult or costly to adjust. One of the primary objectives of many such experiments is to accurately predict responses using fitted response surfaces. While many split-plot designs have been proposed in the literature for this purpose, most of them require large run sizes and an excessive number of whole plots, resulting in expensive and time-consuming experiments. To address this issue, we conduct a study to determine the minimum requirements for a split-plot design that can be used to fit a response surface. Based on these requirements, we construct saturated or nearly saturated response surface split-plot (RSSP) designs that are cost-effective, featuring the fewest possible run sizes and the smallest number of whole plots. We use a motivating example and conduct simulations. Our study shows that the proposed RSSP designs not only provide cost savings, but also maintain good predictive efficiency.

Shaping in the Third Direction: Colloidal Photonic Crystals with Quadratic Surfaces Self-Assembled by Hanging-Drop Method.

High-quality, 3D-shaped, SiO2 colloidal photonic crystals (ellipsoids, hyperboloids, and others) were fabricated by self-assembly. They possess a quadratic surface and are wide-angle-independent, direction-dependent, diffractive reflection crystals. Their size varies between 1 and 5 mm and can be achieved as mechanical-resistant, free-standing, thick (hundreds of ordered layers) objects. High-quality, 3D-shaped, polystyrene inverse-opal photonic superstructures (highly similar to diatom frustules) were synthesized by using an inside infiltration method as wide-angle-independent, reflective diffraction objects. They possess multiple reflection bands given by their special architecture (a torus on the top of an ellipsoid) and by their different sized holes (384 nm and 264 nm). Our hanging-drop self-assembly approach uses setups which deform the shape of an ordinary spherical drop; thus, the colloidal self-assembly takes place on a non-axisymmetric liquid/air interface. The deformed drop surface is a kind of topological interface which changes its shape in time, remaining as a quality template for the self-assembly process. Three-dimensional-shaped colloidal photonic crystals might be used as devices for future spectrophotometers, aspheric or freeform diffracting mirrors, or metasurfaces for experiments regarding space-time curvature analogy.

Exploring copper corrosion inhibition in value added neem biodiesel: Evaluation by traditional and machine learning approaches

Neem seed biodiesel is an eco-friendly fuel, however, to minimize its corrosion on copper metal used in engine parts, ethyl acetate extract of Syzygium aromaticum flowers was tested as an inhibitor. Copper corrosion evaluation in biodiesel revealed an inhibition efficiency of 97.96 %. Corrosion at the operating temperature of diesel engine was predicted by machine learning - quadratic regression. Thermodynamics and spectral evaluations bring to light the adsorption of inhibitors on the metal surface for inhibiting the corrosion of copper metal immersed in biodiesel. Surface morphological studies revealed the protective nature of the copper metal corrosion. Quadratic Surface Vector Machine (SVM) algorithm classified the corrosion classes as low, medium, and high with an overall accuracy value of 94.6 %. The percentage of non-corroded area of copper metal specimen in biodiesel medium with the said inhibitor as estimated with quadratic SVM is 97.193 %. The research findings suggest that the ethyl acetate extract of S. aromaticum flowers has the potential to perform as an effective corrosion inhibitor for copper in biodiesel medium and revealed the potential of quadratic SVM machine learning algorithm in corrosion estimation and classification.

On surface of Apollonius of two ellipsoids

Apollonius defined the circle as the set of points that have a given ratio μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu $$\\end{document} of distances from two given points, where the ratio is not equal to one. In a more general sense, consider two 0-symmetric, bounded, convex bodies K and K′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K'$$\\end{document}, which define two norms. Their unit balls are K and K′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K'$$\\end{document}. The surface of Apollonius is defined as the set of points equidistant from the centres of bodies K and K′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K'$$\\end{document} with respect to the aforementioned norms. In this paper we demonstrate that the surface of Apollonius of two ellipsoids is a quadratic surface. We also examine the circumstances under which this surface becomes a sphere.

Stress invariants and invariants of the failure envelope as a quadric surface: Their significances in the formulation of a rational failure criterion

When stress invariants up to the second order are employed to construct failure criterion for brittle materials, it involves three independent terms and therefore there are three coefficients to be determined. However, there are only two conditions available associated with the strengths under uniaxial tension and compression. Systematic examinations have given to the invariants of the failure envelope as a quadric surface according to analytic geometry. For the failure envelope to meet the basic assumptions, in particular, infinite strength under and only under hydrostatic compression, one of the coefficients can be eliminated based on rigorous mathematical inferences. As a result, it reproduces the Raghava-Caddell-Yeh criterion, which has never been rationally established before but is now in this paper. The failure envelope takes the form of circular paraboloid for brittle materials in general. The criterion degenerates to the von Mises criterion, giving a circular cylindrical failure envelope for ductile materials as a special case. It is as rational as the von Mises criterion in the sense that the assumptions made and the conditions available are logically sufficient for the complete establishment of the failure criterion without any ambiguity.

Optimal configuration of passive flow control devices to reduce the aerodynamics drag of a tractor-trailer model

Aerodynamic drag plays an important role in heavy vehicles, especially when traveling at high speeds. In this context, the application of passive flow control devices emerges as a potential approach to reduce the aerodynamic drag of vehicles, leading to improvements in fuel efficiency and environmental pollution. Consequently, this study focuses on using cab side extenders and rear flaps to reduce the aerodynamic drag of a 1:8 small-scale simplified tractor-trailer model. The main parameters of this device configuration, including the length LR and deflection angle θG of the cab side extenders, the length LR and deflection angle θR of the rear flaps, are optimized to minimize the model aerodynamic drag coefficient. Numerical studies are performed using the Computational Fluid Dynamics method, with the steady k-ω SST and the unsteady DES turbulence model. The optimal solution is implemented based on a 30-level Latin Hypercube design of the experiment and a full quadratic regression response surface method. The obtained results show that a maximum reduction in the aerodynamic drag coefficient of the simplified tractor-trailer model by 20.8 % is achieved with an optimized configuration of control devices. The mechanism of aerodynamic drag reduction is also evaluated based on the analysis of flow fields around the vehicle model.

Stagnation point slip flow of Al2O3/γ-Al2O3 nanofluids subject to Lorentz force and nonlinear thermal radiation over a stretching sheet

The flow analysis of Al 2 O 3 and γ ‐Al 2 O 3 nanofluids near a stagnating point over a stretching sheet having velocity slip at the solid–liquid interface is presented. There is a quadratic surface temperature and a linear deformation acting on the wall boundary. Due to the uniformly applied transverse magnetic flux, the Lorentz force has an impact on the flow. The effect of nonlinear TR is integrated into the heat equation. Further, water H2O and EG C2H6O2 are base fluids. The governing boundary equations are translated into dimensionless ODEs using relevant similarity variables and solved numerically using the Runge-Kutta algorithm scheme (fourth-order) and the shooting algorithm. The impacts of the parameters, that is, velocity ratio ε , velocity slip δ , nonlinear TR Rd, the temperature ratio parameter θ w , and magnetohydrodynamics M are observed for the velocity h 2 ≤ y ≤ 0 and temperature θ ( η ) fields graphically. The results of local skin friction and local Nusselt number are shown in the table. A comparative analysis of the present results and the results of previous studies has also been made in tabular form. The research indicates that water as a base fluid gives better thermal conductivity than ethylene glycol. The consequence of TR enhances the heat transfer rate of both Al 2 O 3 / γ ‐Al 2 O 3 with H2O and C2H6O2.

Response surface optimization of hydrogen-rich syngas production by methane dry reforming over bimetallic Mn-Ni/La2O3 catalyst in a fixed bed reactor

The present work utilizes a response surface optimization technique to optimize hydrogen-rich syngas production through the process of methane dry reforming (DRM). This optimization is achieved by employing a bimetallic Mn–Ni/La2O3 catalyst. The study aimed to evaluate the impact of three key parameters, namely reaction temperature, time on stream (TOS), and gas hourly space velocity (GHSV), on the hydrogen to carbon monoxide (H2/CO) ratio in syngas during the DRM. The Mn–Ni/La2O3 catalyst, synthesized using the sequential wet impregnation technique, exhibited suitable physicochemical properties necessary for DRM reaction, as evidenced by the obtained characterization data. Among the five models examined, it was found that the quadratic versus 2FI model substantially fit the experimental data, as evidenced by a p-value <0.05. The analysis of variance (ANOVA) conducted on the quadratic response surface model compared to the 2FI model demonstrated that both the reaction temperature and the TOS had a significant impact on the H2/CO ratio in the syngas. The only significant interaction factor was the relationship between the reaction temperature and the TOS. Under the specified optimal circumstances of 15 000 ml/g.h, 850 °C, and 258.15 min, an H2/CO ratio of 0.98 was achieved. The resulting H2/CO ratio of 0.98 is almost 1, indicating its suitability as a feedstock for methanol production in the Fischer-Tropsch synthesis (FTS).

On E–Optimality Design for Quadratic Response Surface Model

On E–Optimality Design for Quadratic Response Surface Model

Orthogonal experimental study of ultrasound-assisted fused deposition molding

To improve the quality of fused deposition molding (FDM), we introduced ultrasonic vibration into the molding process to enhance the strength of the tensile samples. We used the response surface method to optimize the FDM molding process. We carried out orthogonal experiments to investigate the effects of ultrasonic power and process parameters (extrusion temperature, hotbed temperature, and delamination thickness) on the mechanical properties of fused deposition acrylonitrile butadiene styrene products. We obtained the quadratic regression equations and response surfaces of the data through analysis of variance and significance analysis by software. Last, we received the optimum combination of process parameters for tensile strength as extrusion temperature 233.85 °C, hotbed temperature 93.38 °C, delamination thickness 0.1 mm, and ultrasonic power 43.09 W.

Optimizations of structure stiffnesses and sensitivities of Y-type six-axis force/torque sensor

PurposeThe six-axis force/torque sensor based on a Y-type structure has the advantages of simple structure, small space volume, low cost and wide application prospects. To meet the overall structural stiffness requirements and sensor performance requirements in robot engineering applications, this paper aims to propose a Y-type six-axis force/torque sensor.Design/methodology/approachThe performance indicators such as each component sensitivities and stiffnesses of the sensor were selected as optimization objectives. The multiobjective optimization equations were established. A multiple quadratic response surface in ANSYS Workbench was modeled by using the central composite design experimental method. The optimal manufacturing structural parameters were obtained by using multiobjective genetic algorithm.FindingsThe sensor was optimized and the simulation results show that the overload resistance of the sensor is 200%F.S., and the axial stiffness, radial stiffness, bending stiffness and torsional stiffness are 14.981 kN/mm, 16.855 kN/mm, 2.0939 kN m/rad and 6.4432 kN m/rad, respectively, which meet the design requirements, and the sensitivities of each component of the optimized sensor have been well increased to be 2.969, 2.762, 4.010, 2.762, 2.653 and 2.760 times as those of the sensor with initial structural parameters. The sensor prototype with optimized parameters was produced. According to the calibration experiment of the sensor, the maximum Class I and II errors and measurement uncertainty of each force/torque component of the sensor are 1.835%F.S., 1.018%F.S. and 1.606%F.S., respectively. All of them are below the required 2%F.S.Originality/valueHence, the conclusion can be drawn that the sensor has excellent comprehensive performance and meets the expected practical engineering requirements.

A failure criterion for genuinely orthotropic materials and integration of a series of criteria for materials of different degrees of anisotropy.

Existing failure criteria for orthotropic materials are subject to an underlying assumption which cause contradictions when applied to genuinely orthotropic materials that are significantly anisotropic in elasticity as well as in strengths. For such materials, there is lack of consistent failure criteria to support their applications in engineering structures. A general quadratic failure criterion tends to leave undetermined coefficients for interactive terms. A rational approach is adopted in this paper based on mathematical and logical considerations to determine these coefficients as the objective of this paper. Considerations are based on the intrinsic characteristics of the quadric surfaces introduced by the quadratic failure criterion. These coefficients must take the values as obtained, leaving no alternatives if logic prevails. The obtained criterion integrates for the first time a range of criteria separately formulated for materials of different degrees of anisotropy, from genuinely orthotropic, through transversely isotropic, cubically symmetric, to completely isotropic ones with different or identical tensile and compression strengths.