Quadratic Surface Research Articles

Tri-Dexel Based Cutter-Workpiece Engagement Determination For Robotic Machining Simulator

In the spirit of digital twins, computer simulations is a crucial aspect for a technology. Within the frame of virtual manufacturing, and more precisely robotic machining simulation, this article aims to present a simulator developed in C++ for test purposes. It computes the machining forces and the update of the workpiece for 5-axis operations. The proposed method is based on the modelling of workpiece using multi-dexels with scalable resolution and a disk modelled tool with triangle-mesh surfaces. Chip thickness computation approaches are based on the interference between the dexel network with the surface swept by cutting edges either modelled as quadratic surfaces or planar swept surfaces coupled with a quadratic interpolation in the tool space, in the view of reducing computation time. Simulation results of both methods are compared with benchmark operations from the literature in terms of machining forces and with each other in terms of computation performances.

Feature Curves and Surfaces of 3D Asymmetric Tensor Fields.

3D asymmetric tensor fields have found many applications in science and engineering domains, such as fluid dynamics and solid mechanics. 3D asymmetric tensors can have complex eigenvalues, which makes their analysis and visualization more challenging than 3D symmetric tensors. Existing research in tensor field visualization focuses on 2D asymmetric tensor fields and 3D symmetric tensor fields. In this paper, we address the analysis and visualization of 3D asymmetric tensor fields. We introduce six topological surfaces and one topological curve, which lead to an eigenvalue space based on the tensor mode that we define. In addition, we identify several non-topological feature surfaces that are nonetheless physically important. Included in our analysis are the realizations that triple degenerate tensors are structurally stable and form curves, unlike the case for 3D symmetric tensors fields. Furthermore, there are two different ways of measuring the relative strengths of rotation and angular deformation in the tensor fields, unlike the case for 2D asymmetric tensor fields. We extract these feature surfaces using the A-patches algorithm. However, since three of our feature surfaces are quadratic, we develop a method to extract quadratic surfaces at any given accuracy. To facilitate the analysis of eigenvector fields, we visualize a hyperstreamline as a tree stem with the other two eigenvectors represented as thorns in the real domain or the dual-eigenvectors as leaves in the complex domain. To demonstrate the effectiveness of our analysis and visualization, we apply our approach to datasets from solid mechanics and fluid dynamics.

Process optimization for hot forging of difficult parts by computer experiments and response surface analysis

Closed die hot forging of 304L stainless steel is difficult compared to carbon and micro-alloyed steels in terms of higher forming force and defects. An appropriate combination of design and process factors including cross-section diameter, initial billet temperature, and flash land thickness is crucial to minimize the forming force without causing any under-filling or folding defects. This paper aims to develop an optimized closed-die hot forging process for long, thin, and tubular rail body components used in gasoline direct injection systems. The effects on the forging load are investigated using computer experiments containing the finite element method under a full factorial array of three factors at three levels to obtain the main and interaction effects. Linear and quadratic surface response analyses are performed to define the relation between forging load and input factors, and finally, the simulations are validated with some limited experiments. The simulation results that fit the nonlinear regression model were in close agreement with the experiments, and an optimal set of parameters is conveniently proposed for industrial production.

Strain-based reliability analysis of dented pipelines using a response surface method

Dent defects can decrease the life span of oil and gas pipelines. Therefore, they need constant monitoring and maintenance to ensure the pipeline’s safety and integrity. Subsequently, this paper performs a strain-based reliability analysis on pipe dent defects using a response surface method (RSM) with a quadratic response surface (RS), including the interaction terms between the RS variables. The analyses are performed to determine the factors controlling the dent defects’ probability of failure (POF). Different pipe configurations, pipe lengths, indenter sizes, and dent depths are considered in this study. A suitable finite element (FE) model for the reliability analysis was developed for this study using the FE analysis software ABAQUS. The uncertainties in the pipe wall thickness, the dent depth, the yield strength of the pipe material, and the strain capacity are considered for the reliability analysis. The first-order reliability method (FORM) is used in the RSM as the reliability method to calculate the POF and the most probable point (MPP). The POFs of several dent defects were calculated. It has been found that the POF, which is highly related to the nominal value of the maximum equivalent plastic strains generated in the dent defect, is not only related to the indentation depth or the size of the indenter. Thus, the dent depth criterion used in the engineering practice can lead to inconsistent reliability levels in dented pipes.

Microwave-Assisted Extraction of Phenolic Compounds from Spent Coffee Grounds. Process Optimization Applying Design of Experiments.

In this study, sustainable technology microwave-assisted extraction (MAE) in association with green solvents was applied to recover phenolic compounds from spent coffee grounds (SCGs). A design of experiments (DOE) was used for process optimization. Initially, a 24−1 two level Fractional Factorial Design was used and ratios “solvent to solute” and “ethanol to water” were identified as the significant experimental factors. Consequently, Central Composite Design (CCD) was applied to analyze the effects of the significant variables on the response yield, total polyphenols content (TPC), and antioxidant activity (AA) by the DPPH assay method, and quadratic surfaces to optimize those responses were generated. The values of the significant factors of 16.7 (solvent/solute) and 68.9% (ethanol/water) were optimized simultaneously the yield (%) at 6.98 ± 0.27, TPC (mg GAE/g) at 117.7 ± 6.1, and AA (µmol TE/g) at 143.8 ± 8.6 and were in excellent agreement with those predicted from the CCD model. The variations of the compositions of the lipids, caffeine, pentacyclic diterpenes, and FAME as a function of the dominant factor % ethanol in the solvent mixture were analyzed by applying NMR and GC-FID, and the results obtained confirmed their determinative significance.

The Polar Coordinate Transformation Numerical Steepest Descent Path Method for Calculating Physical Optical Scattering Field of Quadric Concave or Convex Surfaces

In this letter, the polar coordinate transformation numerical steepest descent path (PCT-NSDP) method is proposed to calculate the physical optics (PO) scattered field from concave or convex quadratic surfaces. In the proposed method, only three triangles integral domains are calculated, which avoids the complicated decomposition in the former NSDP methods. The PCT-NSDP method has a closed-form formula of the contribution of PO stationary phase point. Therefore, the calculation time can be much smaller. Moreover, the workload is frequency-independent. The numerical examples of the radar cross section of a quadratic convex surface demonstrate the high accuracy and efficiency of the PCT-NSDP method.

Sampling from Quadric‐Based CSG Surfaces

AbstractWe present an efficient method to create samples directly on surfaces defined by constructive solid geometry (CSG) trees or graphs. The generated samples can be used for visualization or as an approximation to the actual surface with strong guarantees. We chose to use quadric surfaces as CSG primitives as they can model classical primitives such as planes, cubes, spheres, cylinders, and ellipsoids, but also certain saddle surfaces. More importantly, they are closed under affine transformations, a desirable property for a modeling system. We also propose a rendering method that performs local quadric ray‐tracing and clipping to achieve pixel‐perfect accuracy and hole‐free rendering.

Development of a Learning Model of Quadric Surfaces With Augmented Reality and Didactic Engineering

<p class="0abstract">Augmented reality (AR) is an emerging technology that has permeated different spheres of life, one of them is education, and specifically the teaching-learning process at different educational levels and objects of study. For this reason, this paper presents the development of a learning model of quadric surfaces mediated by a mobile AR application and based on didactic engineering. The model was applied to a group of environmental engineering students of the Catholic University of Manizales. To obtain information on the use of the application and the learning results obtained, some intervention instruments were developed. The students stated that the use of AR allowed them to better understand the concepts of quadric surfaces, even more so in a time of pandemic by COVID-19, where education was highly measured by ICTs.</p>

PREDICTION OF PROCESS VARIABLES IN INDOMETHACIN TERNARY SYSTEM USING EXPERIMENTAL DESIGN SOLID STATE CHARACTERIZATION AND IN-VIVO STUDIES

The aim of the present investigation is (i) to apply and analyze response surface methodology to optimize the preparation method of indomethacin solid dispersion which involves three significant independent variables: amounts of each carrier β-Cyclodextrin (βCD), Polyvinyl pyrrolidone (PVP K30), and solvent mixture (ethanol-water), (ii) to characterize by solid state analysis, and evaluate by in vivo study. A 3-factor, 3- level ‘Central Composite Face Centered design’ was used to explore the quadratic and linear response surfaces and to construct a second order polynomial models which can predict responses ‘aqueous solubility’, and ‘% release’ with minimum % error. In addition, the desirability function approach was applied to obtain the best compromise among the multiple responses. It was found that both the independent variables played a significant role on the solubility and percentage drug release. The solid state studies enable the phase (crystalline) transform of drug which influences its solubility and drug release. The enhancement of Cmax and AUC0-24 of indomethacin (in solid dispersion)with that of pure drug imply the increase in bioavailability of drug.

Reservoir Inflow Prediction by Employing Response Surface-Based Models Conjunction with Wavelet and Bootstrap Techniques

Reservoir inflow prediction is a vital subject in the field of hydrology because it determines the flood event. The negative impact of the floods could be minimized greatly if the flood frequency is predicted accurately in advance. In the present study, a novel hybrid model, bootstrap quadratic response surface is developed to test daily streamflow prediction. The developed bootstrap quadratic response surface model is compared with multiple linear regression model, first-order response surface model, quadratic response surface model, wavelet first-order response surface model, wavelet quadratic response surface model, and bootstrap first-order response surface model. Time series data of monsoon season (1 July to 30 September) for the year 2010 of the Chenab river basin are analyzed. The studied models are tested by using performance indices: Nash–Sutcliffe coefficient of efficiency, mean absolute error, persistence index, and root mean square error. Results reveal that the proposed model, i.e., bootstrap quadratic response surface shows good performance and produces optimum results for daily reservoir inflow prediction than other models used in the study.

Determination of the three-dimensional diffusion optimal path

The diffusion of passing over the saddle point of a three-dimensional quadric potential energy surface was studied by analytically solving a set of coupled generalized Langevin equations. An accurate expression of the passing probability was obtained. The effect of the coupling between different degrees of freedom which is represented by the off-diagonal elements of the inertia, friction and potential-curvature tensors was analyzed in detail. It is found that some of the coupling have great influence on the diffusion process, while others not. The combination of them results in an optimal injecting direction of the diffusing particles, revealing an optimal three-dimensional diffusion path.

Research on the Operational Modal Prediction of Dry Gas Seal System Based on Response Surface Method

The cross power spectrum function is used to realize the operational modal analysis and identification of the dry gas seal device system through the multi-reference point least squares complex frequency domain method. The steady state diagram and mathematical indicators MAC, MPD, MPC, MOV and MIF are used to verify the modal results. At the same time, based on the response surface method, with two different operating conditions of medium pressure and rotating speed, modal direction and modal order as the response surface variables, a time-varying modal recognition model is established. Through the Full Factorial experiment design, Box-Behnken experiment design and Central Composite experiment design, the suitable variable sample points are formed. A complete quadratic polynomial response surface model of the system operational modal parameters is established. The complex correlation coefficient, the modified complex correlation coefficient and the root mean square error are used to verify the effectiveness of the response surface model. It provides new method and technical support for realizing time-varying modal identification in this paper.

Probabilistic Seismic Displacement Hazard Assessment of Earth Slopes Incorporating Spatially Random Soil Parameters

Permanent sliding displacement is a parameter that is used widely to evaluate the seismic performance of earthen slopes, and the inherent variability of soil strength parameters is considered simply using a logic tree in current practice. This study thus proposes a fully probabilistic framework to assess the seismic displacement hazard of earthen slopes by quantifying the inherent spatial variability of soil strength parameters. The framework incorporates the random field theory and a multiple quadratic response surface (MQRS) model into the fully probabilistic seismic sliding displacement hazard analysis. Random field theory was employed to characterize the spatial variability of soil parameters, and the MQRS model is proposed to estimate the yield acceleration (ky) of slopes in an efficient way. The performance of the proposed framework was demonstrated by slope examples. The results indicated that (1) the predicted ky values of the MQRS model are comparable with those computed by the traditional pseudostatic procedure, validating its accuracy in applications; (2) slope strength parameters exhibiting a weaker spatial variability (larger scale of fluctuation) yield a larger dispersion of ky and a larger displacement hazard; and (3) a larger displacement hazard is produced for soil parameters exhibiting weaker correlation between cohesion and friction angle. The proposed framework enables assessment of the probabilistic seismic displacement hazard of earthen slopes with proper consideration of the spatial variability of soil parameters.

Fabrication of micro-structured surface with controllable randomness by using FTS-based diamond turning

Random micro-structured surfaces (RSS) have great application potentials as various functional surface elements, such as optical diffusers, with homogeneous surface properties. Conventional fabrication methods for RSS, such as chemical etching, can no longer meet modern requirements of high precision and controllability. In this study, a novel method was proposed for fabricating micro dimple arrays with controllable randomness in dimple size and depth by using fast tool servo (FTS)-based single-point diamond turning. Firstly, for tool path generation, a computer program was developed to periodically arrange small patches of quadratic surfaces over a large surface area. Then the position, height, and size of each quadratic surface were adjusted by applying random values, whose dynamic range was preset, to control the spatial difference among the dimples. Finally, the designed RSS was machined by continuous and segment cutting methods, respectively, to evaluate their effects on dimple edge formation. Results showed that the segmented cutting method improved the edge accuracy, thus was effective for RSS machining. The machined surface matched precisely with the designed surface with a form error of 10 nm level. The machining method proposed in this study enables high-precision patterning of mold inserts for molding/imprinting RSS on polymer materials.

3D point cloud lossy compression using quadric surfaces.

The presence of 3D sensors in hand-held or head-mounted smart devices has motivated many researchers around the globe to devise algorithms to manage 3D point cloud data efficiently and economically. This paper presents a novel lossy compression technique to compress and decompress 3D point cloud data that will save storage space on smart devices as well as minimize the use of bandwidth when transferred over the network. The idea presented in this research exploits geometric information of the scene by using quadric surface representation of the point cloud. A region of a point cloud can be represented by the coefficients of quadric surface when the boundary conditions are known. Thus, a set of quadric surface coefficients and their associated boundary conditions are stored as a compressed point cloud and used to decompress. An added advantage of proposed technique is its flexibility to decompress the cloud as a dense or a course cloud. We compared our technique with state-of-the-art 3D lossless and lossy compression techniques on a number of standard publicly available datasets with varying the structure complexities.

Identification of best discrimination surface by mixed-integer semi-definite programming for support vector machine

This paper proposes two improvements to the support vector machine (SVM): (i) extension to a semi-positive definite quadratic surface, which improves the discrimination accuracy; (ii) addition of a variable selection constraint. However, this model is formulated as a mixed-integer semi-definite programming (MISDP) problem, and it cannot be solved easily. Therefore, we propose a heuristic algorithm for solving the MISDP problem efficiently and show its effectiveness by using corporate credit rating data.

Optimization on Thermomechanical Behavior for Improving the Reliability of Press Pack IGBT Using Response Surface Method

A press pack insulated gate bipolar transistor (PP IGBT) device consists of multiple materials. Under the influence of alternating current and clamping force, the device suffers from complex thermomechanical stress. However, the experience-based packaging design does not consider the coupling effect of junction temperature fluctuation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta T_{\mathrm{ j}}$ </tex-math></inline-formula> ) and mechanical stress, which may not ensure the optimal thermomechanical behavior and cause the advance failure of the PP IGBT device. Thus, it is significant to provide a theoretical basis and select appropriate parameters for device packaging design. In this article, a finite-element model of a 3300-V/50-A PP IGBT device is first built and verified via experiments. The influence of principal parameters on the thermomechanical behavior is then illustrated. Next, the response surface method is proposed to reveal the significance level of each parameter. According to simulation results under different combinations of parameters, quadratic response surfaces are obtained. The combined effects of packaging parameters on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta T_{\mathrm{ j}}$ </tex-math></inline-formula> and stress are clarified. Finally, optimal results are derived and verified. An approximate 4 °C decrease in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta T_{\mathrm{ j}}$ </tex-math></inline-formula> and a 19.8% decrease in stress are achieved simultaneously in the long-time power cycling test. A 2.6 °C reduction in junction temperature is achieved under the practical high-voltage direct current (HVDC) condition.

Optimization and experimental design by response surface method for reactive extraction of glutaric acid

Abstract Glutaric acid is an attractive chemical compound which can be used for the manufacturing of polyesters, polyamides, and polyols. It can be produced by the synthesis (chemical method) and fermentation (biological method) process. Glutaric acid is presented with the lowest quantity in the fermentation broth and industrial waste streams. The separation methods of glutaric acid are difficult, costly, and non-environment friendly from fermentation broth. Reactive separation is a simple, cheapest, and environment-friendly process for the recovery of carboxylic acid. Which can be employed for the separation of glutaric acid with lower cost and environment-friendly process. In this study, response surface methodology (RSM) was used as a mathematical technique to optimize and experimental design for investigation of the reactive separation of glutaric acid from the aqueous phase. As per RSM study, 20 experiments with different independent variables such as concentration of glutaric acid, % v/v of trioctylamine, and pH for recovery of glutaric acid were performed. The optimum condition with maximum efficiency (η) 92.03% for 20% trioctylamine and pH = 3 at 0.08 mol/L of glutaric acid initial concentration were observed. The lower concentration of trioctylamine provides sufficient extraction efficiency of glutaric acid. This method can also be used for the separation from fermentation broth because a lower concentration of trioctylamine which makes this process environment-friendly. The optimization condition-defined quadratic response surface model is significant with R 2 of 0.9873. The independent variables defined the effect on the extraction efficiency of glutaric acid. This data can be used for the separation of glutaric acid from industries waste and fermentation broth.

The Picard Group of the Moduli Space of Sheaves on a Quadric Surface

Abstract We study the Picard group of the moduli space of semistable sheaves on a smooth quadric surface. We polarize the surface by an ample divisor close to the anticanonical class. We focus especially on moduli spaces of sheaves of small discriminant, where we observe new and interesting behavior. Our method relies on constructing certain resolutions for semistable sheaves and applying techniques of geometric invariant theory to the resulting families of sheaves.

Energy information flow-based ecological risk transmission among communities within the heavy metals contaminated soil system

An energy information flow-based ecological risk assessment framework (EIF-ERA) is developed for identifying ecological risk transmission rules among communities (i.e., vegetation E1, herbivorous animals E2, soil microorganisms E3, and carnivorous animals E4) within the heavy metals contaminated soil system. This framework is integrated with numerous techniques of carcinogenic risk evaluation, ecological risk assessment (ERA), and Monte Carlo simulation. Stepwise quadratic response surface analysis (SQRSA) is employed for reflecting the relation between contaminants' concentration and comprehensive risk. Two scenarios with respect to the environmental quality standards (scenarios 1) and carcinogenic risk reversion (scenarios 2) are merged into the EIF-ERA. A real-world mining area in Xinglong County in Chengde is selected to verify the developed framework's effectiveness. Results reveal that E3 is considered as the most sensitive community when contaminant interference occurs, and its 62.3% and 37.7% of comprehensive risk are contributed by initial and direct risks, respectively. Other communities can receive direct risk through control allocation (CA). Monte Carlo anlysis shows that there are 7.68% and 20.25% increase in the initial risk of Cd and Pb when their quantile statistics increase from 70% to 90%. Determination of an appropriate screening value is vital for contaminated mining soil remediation due to its inefficiency of remediation funds, especially when considering the trict standards of contaminants' concentration within scenarios 1. The surrogates obtained from the SQRSA display the relation of contaminant concentration and comprehensive risks with the adjusted R2 greater than 0.77. These findings can be in support of system design, risk assessment, and site remediation.