Surface Fitting Method Research Articles

Research on on-machine measurement of machining error based on T-spline surface reconstruction

The machining quality of the parts can be directly inspected and analyzed through contact on-machine measurement. However, during the measurement of free-form surfaces, aiming at the problem that the spline surface fitting method requires too many measuring points and the original design information is not borrowed during reconstruction, a T-spline surface reconstruction method based on the centroidal Voronoi tessellation (CVT) sampling strategy is proposed. In the uv parameter region of the original designed NUBRS surface, the Gaussian curvature of the surface is taken as the regional density function, and the CVT is generated by the Lloyd algorithm. Based on the T-grid constructed by an adaptive quadtree method, three kinds of surface feature points are defined as measuring points. By using constrained optimization theory and hierarchical T-mesh knowledge, the generation and local optimization of T-spline surface based on the reconstruction of the original NUBRS surface control points is realized. At last, the example of the surface machined by Makino V77 machine tool and measured with BLUM TC60 probe shows that, the method in this paper can effectively fit a surface which is more suitable for actual processing by adjusting a relatively small number of control vertices with a limited number of measurement points.

Rational polynomial image magnification based on edge and distance constraints

Surface fitting is one of the most effective methods in image magnification. The key is to construct the surface fitting the image.Image details and edges play a key role in the visual effect of the image. Therefore, one of the keys to constructing the fitting surface is to preserve the image details and edges.The surface fitting methods based on spline and polynomial cannot effectively preserve the edge information of the image, so that the magnified image has obvious jagged edges. In this paper, a new image magnification algorithm based on edge and distance constraints is proposed. The algorithm constructs a quadratic polynomial surface patch on the adjacent region of each pixel, which fits the pixels in the neighborhood, and a quadratic polynomial median surface patch is constructed on each quadrilateral mesh. The rational polynomial patch is generated from the weighted average of five patches on each quadrilateral mesh. The patch has the accuracy of the quadratic polynomial approximation, and the resulting image has a better visual effect. The accuracy and visual effects of the magnified image are improved by constructing error patches. The new algorithm calculates the constant term, the first term and the second term of the quadratic polynomial by different methods, which provides a new technique for constructing the polynomial function with constraints. The experimental results show that compared with other algorithms, the proposed algorithm not only has higher approximation accuracy but also has better visual effect of the magnified image.

The method of comprehensive performance optimization design for trimaran unmanned vehicle

The comprehensive performance optimization design of the trimaran unmanned vehicle can be summarized as a complex optimization design problem with multiple objective functions under multiple constraints. First, this paper uses the towing resistance test data of a certain ship model to establish a ship type and resistance database using the response surface fitting method. Then, a single total objective function is used in the form of power exponential product to normalize the objective functions of the trimaran unmanned craft’s speed, maneuverability and seakeeping. Secondly, the constraint conditions are the upper and lower limits of the design variables, the penalty function is composed of multiple equality and inequality constraints involved, the fitness function is established, and a more complete comprehensive optimization mathematical model is constructed. Finally, the overall performance of the trimaran unmanned vehicle is optimized by genetic algorithm, particle swarm algorithm and two improved optimization algorithms. Discussed the pros and cons of each optimization algorithm and the sensitivity of the influence factor under the parallel strategy, compared and analyzed the calculation results of each optimization algorithm, selected the best optimization calculation plan, and obtained the best optimization calculation result, which is trimaran how to ensure the comprehensive and optimal navigation performance during the design of unmanned boats provides a practical way and method.

Prediction of IGBT junction temperature using improved cuckoo search-based extreme learning machine

The insulated-gate bipolar transistor (IGBT) is one of the most widely used power transistors in switching and industrial control systems. Its actual junction temperature plays a critical factor in determining the dynamic performance, reliability and life-time of the device. Although some noninvasive measurement methods such as optical and physical contact methods may be used to estimate the junction temperature, the measurement accuracy is very sensitive to the measured position. Therefore, the prediction using cuckoo search-based extreme learning machine for junction temperature is developed to reach a high-accuracy solution without measured-location sensitivity. Firstly, the accelerated aging and single pulse tests in IGBT are implemented to collect the IGBT failure related parameters, e.g. collector-emitter saturation voltage (VCE(sat)), junction temperature, collector current (Ic) and the aging cycles number. With the curved surface fitting for the collected data, the relationship between the junction temperature and the other parameters can be formed. Based on the extreme learning machine optimized by the improved Cuckoo Search method, called ICS-ELM, VCE(sat), Ic and the aging cycles number are taken as input, and the output is the predicted junction temperature. The performance results reveal that the determination coefficient (R2) by ICS-ELM model achieves the optimal value, i.e. 0.9975, which is superior to the curved surface fitting method, Cuckoo search optimizing extreme learning machine, support vector machine and extreme learning machine.

Study on the performance of pervious concrete mixed with waste glass powder

In this study, pervious concrete (PC) was prepared by partially replacing the cement with waste glass powder (WGP). The effects of varying the WGP content (0%, 10%, 15%, 20%, and 25%) and water-cement ratio (w/c) (0.22, 0.24, 0.26, and 0.28) on the mechanical properties, water permeability, and frost resistance of PC were analyzed. The results showed that the compressive strength of the PC initially increased and then decreased with the increasing w/c. With an increase in the WGP content, the compressive strength decreased in the early stage (28 d), and slowly increased in the middle stage (56 d); however, at the age of 112 d, this value first increased and then decreased. Similar trends were observed for the splitting tensile and flexural strengths of the PC. The water permeability of the PC first increased and then decreased with increasing w/c. With the increasing WGP content, the water permeability presented a downward trend. In addition, it was observed that the increase in WGP content can improve the freeze–thaw resistance of the PC. Based on the experimental data, a series of models was established to predict the effect of the w/c and WGP content on compressive strength and water permeability of PC using a non-linear surface fitting method. The proposed models showed good agreement with the experimental results.

Selective methods of TOC content estimation for organic-rich interbedded mudstone source rocks

The total organic carbon content (TOC) is one of the key parameters for evaluating the hydrocarbon generation potential of source rocks. Petroleum geochemists and geologists usually use conventional logging curves to predict TOC content in order to reduce the errors caused by limited TOC content data. The ΔlogR method is the most widely used TOC prediction method. However, it is not applicable to organic-rich mudstone interlayers, due to the rapidly changing lithology and the difficulty in determining a baseline. Some improved ΔlogR methods and artificial neural network techniques have also been proposed by previous authors. In this paper, a 3D surface fitting technique based on biharmonic interpolation is proposed to optimize an improved ΔlogR method. A total of 76 samples were divided into pure mudstone and mudstone interlayers. The correlation coefficient (R) and the root mean square error (RMSE) between the measured TOC and the predicted TOC obtained using the improved ΔlogR method, the artificial neural network method, and the 3D surface fitting method were calculated. These methods were applied to assess the source rocks of the Eocene Liushagang Formation in the Fushan Depression, South China Sea. The results show that the 3D surface fitting method can effectively distinguish source rocks from non-source rocks and has a higher accuracy, which makes it the most suitable method for assessing the TOC content of organic-rich source rocks with alternating mudstone layers.

Elevation and Volume Changes in Greenland Ice Sheet From 2010 to 2019 Derived From Altimetry Data

Long-term altimetry data are one of the major sources to analyze the change in global ice reserves. This study focuses on the elevation and volume changes in the Greenland ice sheet (GrIS) from 2010 to 2019 derived from altimetry observations. In this study, the methods for determining surface elevation change rates are discussed, and specific strategies are designed. A new elevation difference method is proposed for CryoSat-2 synthetic aperture interferometric (SARin) mode observations. Through validation with Airborne Topographic Mapper (ATM) data, this new method is proved to be effective for slope terrains at the margins of the ice sheet. Meanwhile, a surface fit method is applied for the flat interior of the ice sheet where low resolution mode (LRM) observations are provided. The results of elevation change rates in the GrIS from 2010 to 2019 are eventually calculated by combining CryoSat-2 and ATM observations. An elevation change rate of −11.83 ± 1.14 cm·a−1 is revealed, corresponding to a volume change rate of −200.22 ± 18.26 km3·a−1. The results are compared with the elevation changes determined by Ice, Cloud, and Land Elevation Satellite (ICESat) from 2003 to 2009. Our results show that the overall volume change rate in the GrIS slowed down by approximately 10% during the past decade, and that the main contributor of GrIS ice loss has shifted from the southeast coast to the west margin of the ice sheet.

Atomic-Level Features for Kinetic Monte Carlo Models of Complex Chemistry from Molecular Dynamics Simulations.

The high computational cost of evaluating atomic interactions recently motivated the development of computationally inexpensive kinetic models, which can be parameterized from molecular dynamics (MD) simulations of the complex chemistry of thousands of species or other processes and accelerate the prediction of the chemical evolution by up to four orders of magnitude. Such models go beyond the commonly employed potential energy surface fitting methods in that they are aimed purely at describing kinetic effects. So far, such kinetic models utilize molecular descriptions of reactions and have been constrained to only reproduce molecules previously observed in MD simulations. Therefore, these descriptions fail to predict the reactivity of unobserved molecules, for example, in the case of large molecules or solids. Here, we propose a new approach for the extraction of reaction mechanisms and reaction rates from MD simulations, namely, the use of atomic-level features. Using the complex chemical network of hydrocarbon pyrolysis as an example, it is demonstrated that kinetic models built using atomic features are able to explore chemical reaction pathways never observed in the MD simulations used to parameterize them, a critical feature to describe rare events. Atomic-level features are shown to construct reaction mechanisms and estimate reaction rates of unknown molecular species from elementary atomic events. Through comparisons of the model ability to extrapolate to longer simulation time scales and different chemical compositions than the ones used for parameterization, it is demonstrated that kinetic models employing atomic features retain the same level of accuracy and transferability as the use of features based on molecular species, while being more compact and parameterized with less data. We also find that atomic features can better describe the formation of large molecules enabling the simultaneous description of small molecules and condensed phases.

A shape reconstruction and visualization method for a flexible hinged plate using binocular vision

A binocular vision-based shape deformation reconstruction and visualization method for a flexible hinged plate is proposed. The deformation of the flexible hinged plate in bending mode and torsional mode is investigated. In order to measure the deformation, a binocular vision system is used as the detector. Image processing functions are called to obtain offsets of the mark points pasted on the plate surface. Several types of surface fitting methods are implemented to fit the mark point array into a curved surface. The shape reconstruction graphics of the flexible hinged plate can be obtained. Moreover, the influence of deformation amplitude and stiffness of two flexible hinges on visualization results is studied. The simulation work for curve fitting is conducted by using the measured signals by the binocular stereo vision. The experiments on visual measurement, shape reconstruction and visualization are conducted, using the constructed experimental system and investigated methods. The experimental results show that the quadratic fitting method can be a better curved surface fit for the flexible hinged plate both in bending mode and in torsional mode, and visualization can be realized in real time.

Characterizing water vapour concentration dependence of commercial cavity ring-down spectrometers for continuous on-site atmospheric water vapour isotope measurements in the tropics

Abstract. The recent development and improvement of commercial laser-based spectrometers have expanded in situ continuous observations of water vapour (H2O) stable isotope compositions (e.g. δ18O and δ2H) in a variety of sites worldwide. However, we still lack continuous observations in the Amazon, a region that significantly influences atmospheric and hydrological cycles on local to global scales. In order to achieve accurate on-site observations, commercial water isotope analysers require regular in situ calibration, which includes the correction of H2O concentration dependence ([H2O] dependence) of isotopic measurements. Past studies have assessed the [H2O] dependence for air with H2O concentrations of up to 35 000 ppm, a value that is frequently surpassed in tropical rainforest settings like the central Amazon where we plan continuous observations. Here we investigated the performance of two commercial analysers (L1102i and L2130i models, Picarro, Inc., USA) for measuring δ18O and δ2H in atmospheric moisture at four different H2O levels from 21 500 to 41 000 ppm. These H2O levels were created by a custom-built calibration unit designed for regular in situ calibration. Measurements on the newer analyser model (L2130i) had better precision for δ18O and δ2H and demonstrated less influence of H2O concentration on the measurement accuracy at each concentration level compared to the older L1102i. Based on our findings, we identified the most appropriate calibration strategy for [H2O] dependence, adapted to our calibration system. The best strategy required conducting a two-point calibration with four different H2O concentration levels, carried out at the beginning and end of the calibration interval. The smallest uncertainties in calibrating [H2O] dependence of isotopic accuracy of the two analysers were achieved using a linear surface fitting method and a 28 h calibration interval, except for the δ18O accuracy of the L1102i analyser for which the cubic fitting method gave the best results. The uncertainties in [H2O] dependence calibration did not show any significant difference using calibration intervals from 28 up to 196 h; this suggested that one [H2O] dependence calibration per week for the L2130i and L1102i analysers is sufficient. This study shows that the cavity ring-down spectroscopy (CRDS) analysers, appropriately calibrated for [H2O] dependence, allow the detection of natural signals of stable water vapour isotopes at very high humidity levels, which has promising implications for water cycle studies in areas like the central Amazon rainforest and other tropical regions.

Dynamic analysis of autonomous risk avoidance of amphibious floating bridge based on discrete element method and physical engine

In this paper, based on an intelligent floating bridge, by using discrete element methods and physical engines, under the action of certain missile repulsion fields, the force process and motion path in the process of autonomous evasion of missiles are studied. Firstly, the static simulation of missile repulsion fields is carried out by using the polynomial least square surface fitting method. According to the strength of repulsion field at different times and the extrusion force between the pontoons, the kinematic equation of the pontoon is established. The equation is discretised by using a discrete element method, and the kinematic equation is obtained according to the time iteration. Then, motion analysis is carried out by using a physical engine on the basis of equation Analysis. Finally, the position parameters before and after the self-evasion missile of the floating bridge are calculated, and the simulation program is written in MATLAB. The dynamic simulation experiment of the whole evasion missile process is carried out, and the results are satisfactory.

Lung Lobe Segmentation Based on Lung Fissure Surface Classification Using a Point Cloud Region Growing Approach

In anatomy, the lung can be divided by lung fissures into several pulmonary lobe units with specific functions. Identifying the lung lobes and the distribution of various diseases among different lung lobes from CT images is important for disease diagnosis and tracking after recovery. In order to solve the problems of low tubular structure segmentation accuracy and long algorithm time in segmenting lung lobes based on lung anatomical structure information, we propose a segmentation algorithm based on lung fissure surface classification using a point cloud region growing approach. We cluster the pulmonary fissures, transformed into point cloud data, according to the differences in the pulmonary fissure surface normal vector and curvature estimated by principal component analysis. Then, a multistage spline surface fitting method is used to fill and expand the lung fissure surface to realize the lung lobe segmentation. The proposed approach was qualitatively and quantitatively evaluated on a public dataset from Lobe and Lung Analysis 2011 (LOLA11), and obtained an overall score of 0.84. Although our approach achieved a slightly lower overall score compared to the deep learning based methods (LobeNet_V2 and V-net), the inter-lobe boundaries from our approach were more accurate for the CT images with visible lung fissures.

Improved Particle Swarm Optimization Approach for Vibration Vision Measurement

Traditional template matching-based motion estimation is a popular but time-consuming method for vibration vision measurement. In this study, the particle swarm optimization (PSO) algorithm is improved to solve this time-consumption problem. The convergence speed of the algorithm is increased using the adjacent frames search method in the particle swarm initialization process. A flag array is created to avoid repeated calculation in the termination strategy. The subpixel positioning accuracy is ensured by applying the surface fitting method. The robustness of the algorithm is ensured by applying the zero-mean normalized cross correlation. Simulation results demonstrate that the average extraction error of the improved PSO algorithm is less than 1%. Compared with the commonly used three-step search algorithm, diamond search algorithm, and local search algorithm, the improved PSO algorithm consumes the least number of search points. Moreover, tests on real-world image sequences show good estimation accuracy at very low computational cost. The improved PSO algorithm proposed in this study is fast, accurate, and robust, and is suitable for plane motion estimation in vision measurement.

Effect of surface normal variability on local surface strain measurements in StereoDIC

Surface shape and surface displacement measurements for non-planar specimens are obtainable using a stereo vision system with digital image correlation (StereoDIC). The surface measurements can be employed with appropriate local surface fitting methods to extract full-field estimates for surface strains on the specimen surface. Since StereoDIC provides a dense set of 3D surface position measurements, Xi, for the entire field of view in the stereo vision system, it has been shown that these measurements will have inherent variability. This variability will propagate into any optimally defined local surface representation, including the surface's local unit vectors, such as the surface normal, n; a surface tangent, t, and the cross product, b = n x t. Once the unit vectors are estimated at surface position, Y, the surface representation at this point can be used with the orthogonal unit vectors n, b and t to obtain a set of local surface strains at Y, with variability in the initial surface shape measurements propagating into variations in the strain estimates.In the enclosed work, the authors develop a set of equations for local strain variability due to inaccuracies in the local unit vectors n, b, and t. Results are reported for the case where the unit vectors are obtained assuming a local planar fit to an N x N set of measurements Xi, and strains are determined along the two estimated in-plane directions b and t. Simulations show that the resulting strains have variability that is a strong function of the estimated normal, n. Specifically, simulations show that the estimated local strains have errors that are a strong function of both the direction of nand variability in the estimated normal, n, relative to the stereo system bisector, even if the surface strains in the original directions are exact. Experimental studies for cylindrical specimens are shown to be in agreement with the trends predicted by the simulations, demonstrating the potential importance of surface normal estimation in experimental studies.

Research on UAV Large Scale Mapping and its elevation fitting

Due to the influence of the external environment and the limitation of data processing methods, the accuracy of the unmanned aerial vehicle (UAV) aerial photogrammetry needs further studies in the aspect of mapping large-scale topographic maps. In order to verify whether the measurement accuracy of the UAV aerial photography system meets the requirements of large-scale topographic maps, this paper conducts an accuracy test on a topographic map, using the surface fitting model, the plane fitting model, quadratic surface fitting and polyhedral function method fitting based on field measured data. The fitting of four models to the elevation points by the combined polyhedral function method. The elevation difference between the flat area and the mountain area was corrected, and the elevation accuracy of the four methods was compared. This paper shows that in flat areas the elevation accuracy of the surface fitting model is better than the plane fitting model, quadratic surface fitting, and polyhedral function method fitting. In the mountainous region, the elevation accuracy of the quadratic surface fitting model is better than that of the plane fitting model, surface fitting model, and polyhedral function method.

Noise Analysis and Compensation Strategy of Photoelectric Detection Circuit

A photoelectric detection circuit was designed for improving the accuracy of photoelectric detection and reducing the system error. On the basis of analyzing the noise of the photoelectric detection circuit, the error compensation was proceeded on photoelectric detection circuit using lookup method, linear interpolation method, surface fitting method and adaptive neuro-fuzzy inference method, and the effects of the major error compensation method were compared. The measured data of photoelectric diode experimental platform was used as the sample data. The simulation results in the MATLAB environment demonstrate that under the same condition, the adaptive neuro-fuzzy inference method (ANFIS) can improve the detecting accuracy, and is more effective than lookup method, linear interpolation method, and surface fitting method.

An efficient forward propagation of multiple random fields using a stochastic Galerkin scaled boundary finite element method

This paper serves to extend the existing literature on the Stochastic Galerkin Scaled Boundary Finite Element Method (SGSBFEM) in two ways. The first part of this work deals with the formulation of multiple non-correlated Gaussian random fields using the conventional Karhunen–Loéve expansion technique and its forward propagation through the Spectral Stochastic Scaled Boundary Finite Element setting using the polynomial surface fit method in terms of the scaled boundary coordinates. The advantages in adopting such a forward propagation technique in capturing the statistical moments of Quantities of Interest (QoI) across the domain, are highlighted using carefully chosen linear elastic problems having large to least correlated random fields as inputs. The second contribution is the extension of the proposed forward Uncertainty Quantification (UQ) to take into account multiple independent random fields, followed by Polynomial Chaos Expansion (PCE) based sensitivity analysis. Both the computational efficiency and the accuracy of the proposed framework under different input random field correlation settings are elaborated upon by comparing their results against that obtained using the current existing SGSBFEM in the literature. Moreover, the stochastic results are validated for all the numerical examples using the Monte Carlo method.

Using of artificial neural networks (ANNs) to predict the rheological behavior of magnesium oxide‐water nanofluid in a different volume fraction of nanoparticles, temperatures, and shear rates

Laboratory studies are usually time‐consuming and costly; hence, soft computing methodology can be an attractive alternative for predicting results. In this study, the viscosity of MgO‐water nanofluid in a different volume fraction of nanoparticles, temperatures, and shear rates has been predicted by artificial neural networks (ANNs) and surface methods. In the ANN method, an algorithm is proposed to select the best neuron number for the hidden layer. In the fitting method, a surface is proposed for each volume fraction of nanoparticles, and finally, the results of the ANN and surface fitting method have been compared. It can be observed that increasing the volume fraction from 0.07% to 1.25% at temperatures of 25°C, 30°C, 40°C, 50°C, and 60°C resulted in about two‐fold increase in viscosity. Also, the best network has 24 neurons in the hidden layer. It can be seen that for a network with 24 neurons in the hidden layer has the best overall correlation, and this coefficient is 0.999035. The mean absolute value of errors in the ANN and fitting method are 0.0118 and 0.0206, respectively.

GPS elevation fitting study based on ternary polynomial regression

For the traditional GPS elevation fitting method, the accuracy has not been significantly improved in recent years, and the method has become increasingly complicated. This paper proposes to insert the geodetic height ‘H’ into the calculation system and use a ternary polynomial regression function to fit the GPS elevation anomaly. The feasibility of the ternary polynomial regression method in GPS elevation fitting was verified by an example, and compared with the results of the traditional plane fitting and quadric surface fitting method, it was proved that the proposed method is suitable for terrain with large terrain fluctuations. The fitting residual error and the standard deviation are smaller, and through example calculations, it is concluded that the ternary polynomial regression method under the seven parameters has the highest fitting accuracy.

Three dimensional point cloud data reduction algorithm and application in tooth modelling

Reverse engineering is an advanced manufacturing technology, which can design, develop and innovate products. The processing technology of 3D point cloud data is the key of reverse engineering technology, and the simplification technology is an important part of data processing, which plays a decisive role in the quality and efficiency of subsequent surface modelling. The advantages and disadvantages of different point cloud data reduction algorithms are analysed. By combining the efficiency of three-dimensional mesh algorithm with the accuracy of curvature reduction method, a second reduction algorithm is proposed. Firstly, the algorithm uses the non-uniform mesh reduction algorithm of octree to simplify it, to ensure the data of feature points is not damaged, and then uses the curvature reduction method of B-spline surface fitting to simplify it. The experiment of tooth point cloud data reduction shows that this method can retain the details of the original data better on the basis of higher reduction ratio.