Search results for: Bezier curve.
396 The Distance between a Point and a Bezier Curveon a Bezier Surface
Authors: Wen-Haw Chen, Sheng-Gwo Chen
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The distance between two objects is an important problem in CAGD, CAD and CG etc. It will be presented in this paper that a simple and quick method to estimate the distance between a point and a Bezier curve on a Bezier surface.Keywords: Geodesic-like curve, distance, projection, Bezier.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2550395 Approximating Maximum Speed on Road from Curvature Information of Bezier Curve
Authors: M. Y. Misro, A. Ramli, J. M. Ali
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Bezier curves have useful properties for path generation problem, for instance, it can generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segment smoothly to generate the path. Some of the useful properties of Bezier are curvature. In mathematics, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line. Another extrinsic example of curvature is a circle, where the curvature is equal to the reciprocal of its radius at any point on the circle. The smaller the radius, the higher the curvature thus the vehicle needs to bend sharply. In this study, we use Bezier curve to fit highway-like curve. We use different approach to find the best approximation for the curve so that it will resembles highway-like curve. We compute curvature value by analytical differentiation of the Bezier Curve. We will then compute the maximum speed for driving using the curvature information obtained. Our research works on some assumptions; first, the Bezier curve estimates the real shape of the curve which can be verified visually. Even though, fitting process of Bezier curve does not interpolate exactly on the curve of interest, we believe that the estimation of speed are acceptable. We verified our result with the manual calculation of the curvature from the map.Keywords: Speed estimation, path constraints, reference trajectory, Bezier curve.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4043394 The Control Vector Scheme for Design of Planar Primitive PH curves
Authors: Ching-Shoei Chiang, Sheng-Hsin Tsai, James Chen
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The PH curve can be constructed by given parameters, but the shape of the curve is not so easy to image from the value of the parameters. On the contract, Bézier curve can be constructed by the control polygon, and from the control polygon, we can image the figure of the curve. In this paper, we want to use the hodograph of Bézier curve to construct PH curve by selecting part of the control vectors, and produce other control vectors, so the property of PH curve exists.Keywords: PH curve, hodograph, Bézier curve.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1484393 Mobile Robot Path Planning Utilizing Probability Recursive Function
Authors: Ethar H. Khalil, Bahaa I. Kazem
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In this work a software simulation model has been proposed for two driven wheels mobile robot path planning; that can navigate in dynamic environment with static distributed obstacles. The work involves utilizing Bezier curve method in a proposed N order matrix form; for engineering the mobile robot path. The Bezier curve drawbacks in this field have been diagnosed. Two directions: Up and Right function has been proposed; Probability Recursive Function (PRF) to overcome those drawbacks. PRF functionality has been developed through a proposed; obstacle detection function, optimization function which has the capability of prediction the optimum path without comparison between all feasible paths, and N order Bezier curve function that ensures the drawing of the obtained path. The simulation results that have been taken showed; the mobile robot travels successfully from starting point and reaching its goal point. All obstacles that are located in its way have been avoided. This navigation is being done successfully using the proposed PRF techniques.Keywords: Mobile robot, path planning, Bezier curve.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1449392 Parametric Transition as a Spiral Curve and Its Application in Spur Gear Tooth with FEA
Authors: S. H. Yahaya, J. M. Ali, T.A. Abdullah
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The exploration of this paper will focus on the Cshaped transition curve. This curve is designed by using the concept of circle to circle where one circle lies inside other. The degree of smoothness employed is curvature continuity. The function used in designing the C-curve is Bézier-like cubic function. This function has a low degree, flexible for the interactive design of curves and surfaces and has a shape parameter. The shape parameter is used to control the C-shape curve. Once the C-shaped curve design is completed, this curve will be applied to design spur gear tooth. After the tooth design procedure is finished, the design will be analyzed by using Finite Element Analysis (FEA). This analysis is used to find out the applicability of the tooth design and the gear material that chosen. In this research, Cast Iron 4.5 % Carbon, ASTM A-48 is selected as a gear material.Keywords: Bézier-like cubic function, Curvature continuity, Cshapedtransition curve, Spur gear tooth.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2329391 Computations of Bezier Geodesic-like Curves on Spheres
Authors: Sheng-Gwo Chen, Wen-Haw Chen
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It is an important problem to compute the geodesics on a surface in many fields. To find the geodesics in practice, however, the traditional discrete algorithms or numerical approaches can only find a list of discrete points. The first author proposed in 2010 a new, elegant and accurate method, the geodesic-like method, for approximating geodesics on a regular surface. This paper will present by use of this method a computation of the Bezier geodesic-like curves on spheres.Keywords: Geodesics, Geodesic-like curve, Spheres, Bezier.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1612390 Circular Approximation by Trigonometric Bézier Curves
Authors: Maria Hussin, Malik Zawwar Hussain, Mubashrah Saddiqa
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We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach to reproduce a circular arc. The radius error is calculated and found less than the existing techniques.
Keywords: Control points, rational trigonometric Bézier curves, radius error, shape measure, weight functions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4682389 Arc Length of Rational Bezier Curves and Use for CAD Reparametrization
Authors: Maharavo Randrianarivony
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The length of a given rational B'ezier curve is efficiently estimated. Since a rational B'ezier function is nonlinear, it is usually impossible to evaluate its length exactly. The length is approximated by using subdivision and the accuracy of the approximation n is investigated. In order to improve the efficiency, adaptivity is used with some length estimator. A rigorous theoretical analysis of the rate of convergence of n to is given. The required number of subdivisions to attain a prescribed accuracy is also analyzed. An application to CAD parametrization is briefly described. Numerical results are reported to supplement the theory.Keywords: Adaptivity, Length, Parametrization, Rational Bezier
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1787388 Application of Generalized NAUT B-Spline Curveon Circular Domain to Generate Circle Involute
Authors: Ashok Ganguly, Pranjali Arondekar
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In the present paper, we use generalized B-Spline curve in trigonometric form on circular domain, to capture the transcendental nature of circle involute curve and uncertainty characteristic of design. The required involute curve get generated within the given tolerance limit and is useful in gear design.
Keywords: Bézier, Circle Involute, NAUT B-Spline, Spur Gear.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1782387 Dynamic Optimization of Industrial Servomechanisms using Motion Laws Based On Bezier Curves
Authors: Giovanni Incerti
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The motion planning procedure described in this paper has been developed in order to eliminate or reduce the residual vibrations of electromechanical positioning systems, without augmenting the motion time (usually imposed by production requirements), nor introducing overtime for vibration damping. The proposed technique is based on a suitable choice of the motion law assigned to the servomotor that drives the mechanism. The reference profile is defined by a Bezier curve, whose shape can be easily changed by modifying some numerical parameters. By means of an optimization technique these parameters can be modified without altering the continuity conditions imposed on the displacement and on its time derivatives at the initial and final time instants.
Keywords: Servomechanism, residual vibrations, motion optimization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1401386 Geometric Modeling of Illumination on the TFT-LCD Panel using Bezier Surface
Authors: Kyong-min Lee, Moon Soo Chang, PooGyeon Park
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In this paper, we propose a geometric modeling of illumination on the patterned image containing etching transistor. This image is captured by a commercial camera during the inspection of a TFT-LCD panel. Inspection of defect is an important process in the production of LCD panel, but the regional difference in brightness, which has a negative effect on the inspection, is due to the uneven illumination environment. In order to solve this problem, we present a geometric modeling of illumination consisting of an interpolation using the least squares method and 3D modeling using bezier surface. Our computational time, by using the sampling method, is shorter than the previous methods. Moreover, it can be further used to correct brightness in every patterned image.Keywords: Bezier, defect, geometric modeling, illumination, inspection, LCD, panel.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1839385 An Approach to Polynomial Curve Comparison in Geometric Object Database
Authors: Chanon Aphirukmatakun, Natasha Dejdumrong
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In image processing and visualization, comparing two bitmapped images needs to be compared from their pixels by matching pixel-by-pixel. Consequently, it takes a lot of computational time while the comparison of two vector-based images is significantly faster. Sometimes these raster graphics images can be approximately converted into the vector-based images by various techniques. After conversion, the problem of comparing two raster graphics images can be reduced to the problem of comparing vector graphics images. Hence, the problem of comparing pixel-by-pixel can be reduced to the problem of polynomial comparisons. In computer aided geometric design (CAGD), the vector graphics images are the composition of curves and surfaces. Curves are defined by a sequence of control points and their polynomials. In this paper, the control points will be considerably used to compare curves. The same curves after relocated or rotated are treated to be equivalent while two curves after different scaled are considered to be similar curves. This paper proposed an algorithm for comparing the polynomial curves by using the control points for equivalence and similarity. In addition, the geometric object-oriented database used to keep the curve information has also been defined in XML format for further used in curve comparisons.Keywords: Bezier curve, Said-Ball curve, Wang-Ball curve, DP curve, CAGD, comparison, geometric object database.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2204384 Shape Error Concealment for Shape Independent Transform Coding
Authors: Sandra Ondrušová, Jaroslav Polec
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Arbitrarily shaped video objects are an important concept in modern video coding methods. The techniques presently used are not based on image elements but rather video objects having an arbitrary shape. In this paper, spatial shape error concealment techniques to be used for object-based image in error-prone environments are proposed. We consider a geometric shape representation consisting of the object boundary, which can be extracted from the α-plane. Three different approaches are used to replace a missing boundary segment: Bézier interpolation, Bézier approximation and NURBS approximation. Experimental results on object shape with different concealment difficulty demonstrate the performance of the proposed methods. Comparisons with proposed methods are also presented.Keywords: error concealment, shape coding, object-based image, NURBS, Bézier curves.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1277383 Comparison of the Distillation Curve Obtained Experimentally with the Curve Extrapolated by a Commercial Simulator
Authors: Lívia B. Meirelles, Erika C. A. N. Chrisman, Flávia B. de Andrade, Lilian C. M. de Oliveira
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True Boiling Point distillation (TBP) is one of the most common experimental techniques for the determination of petroleum properties. This curve provides information about the performance of petroleum in terms of its cuts. The experiment is performed in a few days. Techniques are used to determine the properties faster with a software that calculates the distillation curve when a little information about crude oil is known. In order to evaluate the accuracy of distillation curve prediction, eight points of the TBP curve and specific gravity curve (348 K and 523 K) were inserted into the HYSYS Oil Manager, and the extended curve was evaluated up to 748 K. The methods were able to predict the curve with the accuracy of 0.6%-9.2% error (Software X ASTM), 0.2%-5.1% error (Software X Spaltrohr).Keywords: Distillation curve, petroleum distillation, simulation, true boiling point curve.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1608382 Determination the Curve Number Catchment by Using GIS and Remote Sensing
Authors: Abouzar Nasiri, Hamid Alipur
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In recent years, geographic information systems (GIS) and remote sensing using has increased to estimate runoff catchment. In this research, runoff curve number maps for captive catchment of Tehran by helping GIS and also remote sensing which based on factors such as vegetation, lands using, group of soil hydrology and hydrological conditions were obtained. Runoff curve numbers map was obtained by combining these maps in ARC GIS and SCS table. To evaluate the accuracy of the results, the maximum flow rate of flood which was obtained from curve numbers, was compared with the measured maximum flood rate at the watershed outlet and correctness of curve numbers were approved.
Keywords: Curve number, GIS, Remote sensing, Runoff.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4965381 Accurate Dimensional Measurement of 3D Round Holes Based on Stereo Vision
Authors: Zhiguo Ren, Lilong Cai
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This paper present an effective method to accurately reconstruct and measure the 3D curve edges of small industrial parts based on stereo vision. To effectively fit the curve of the measured parts using a series of line segments in the images, a strategy from coarse to fine is employed based on multi-scale curve fitting. After reconstructing the 3D curve of a hole through a curved surface, its axis is adjusted so that it is parallel to the Z axis with least squares error and the dimensions of the hole can be calculated on the XY plane easily. Experimental results show that the presented method can accurately measure the dimensions of round holes through a curved surface.
Keywords: Stereo Vision, 3D Round Hole Measurement, Curve Fitting, 3D Curve Reconstruction, Least Squares Error.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1617380 Solving 94-bit ECDLP with 70 Computers in Parallel
Authors: Shunsuke Miyoshi, Yasuyuki Nogami, Takuya Kusaka, Nariyoshi Yamai
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Elliptic curve discrete logarithm problem(ECDLP) is one of problems on which the security of pairing-based cryptography is based. This paper considers Pollard’s rho method to evaluate the security of ECDLP on Barreto-Naehrig(BN) curve that is an efficient pairing-friendly curve. Some techniques are proposed to make the rho method efficient. Especially, the group structure on BN curve, distinguished point method, and Montgomery trick are well-known techniques. This paper applies these techniques and shows its optimization. According to the experimental results for which a large-scale parallel system with MySQL is applied, 94-bit ECDLP was solved about 28 hours by parallelizing 71 computers.Keywords: Pollard’s rho method, BN curve, Montgomery multiplication.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1855379 Generating Arabic Fonts Using Rational Cubic Ball Functions
Authors: Fakharuddin Ibrahim, Jamaludin Md. Ali, Ahmad Ramli
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In this paper, we will discuss about the data interpolation by using the rational cubic Ball curve. To generate a curve with a better and satisfactory smoothness, the curve segments must be connected with a certain amount of continuity. The continuity that we will consider is of type G1 continuity. The conditions considered are known as the G1 Hermite condition. A simple application of the proposed method is to generate an Arabic font satisfying the required continuity.Keywords: Continuity, data interpolation, Hermite condition, rational Ball curve.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1455378 Proposed Developments of Elliptic Curve Digital Signature Algorithm
Authors: Sattar B. Sadkhan, Najlae Falah Hameed
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The Elliptic Curve Digital Signature Algorithm (ECDSA) is the elliptic curve analogue of DSA, where it is a digital signature scheme designed to provide a digital signature based on a secret number known only to the signer and also on the actual message being signed. These digital signatures are considered the digital counterparts to handwritten signatures, and are the basis for validating the authenticity of a connection. The security of these schemes results from the infeasibility to compute the signature without the private key. In this paper we introduce a proposed to development the original ECDSA with more complexity.Keywords: Elliptic Curve Digital Signature Algorithm, DSA.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1660377 Detection of Keypoint in Press-Fit Curve Based on Convolutional Neural Network
Authors: Shoujia Fang, Guoqing Ding, Xin Chen
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The quality of press-fit assembly is closely related to reliability and safety of product. The paper proposed a keypoint detection method based on convolutional neural network to improve the accuracy of keypoint detection in press-fit curve. It would provide an auxiliary basis for judging quality of press-fit assembly. The press-fit curve is a curve of press-fit force and displacement. Both force data and distance data are time-series data. Therefore, one-dimensional convolutional neural network is used to process the press-fit curve. After the obtained press-fit data is filtered, the multi-layer one-dimensional convolutional neural network is used to perform the automatic learning of press-fit curve features, and then sent to the multi-layer perceptron to finally output keypoint of the curve. We used the data of press-fit assembly equipment in the actual production process to train CNN model, and we used different data from the same equipment to evaluate the performance of detection. Compared with the existing research result, the performance of detection was significantly improved. This method can provide a reliable basis for the judgment of press-fit quality.Keywords: Keypoint detection, curve feature, convolutional neural network, press-fit assembly.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 922376 Choosing between the Regression Correlation, the Rank Correlation, and the Correlation Curve
Authors: Roger L Goodwin
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This paper presents a rank correlation curve. The traditional correlation coefficient is valid for both continuous variables and for integer variables using rank statistics. Since the correlation coefficient has already been established in rank statistics by Spearman, such a calculation can be extended to the correlation curve. This paper presents two survey questions. The survey collected non-continuous variables. We will show weak to moderate correlation. Obviously, one question has a negative effect on the other. A review of the qualitative literature can answer which question and why. The rank correlation curve shows which collection of responses has a positive slope and which collection of responses has a negative slope. Such information is unavailable from the flat, ”first-glance” correlation statistics.Keywords: Bayesian estimation, regression model, rank statistics, correlation, correlation curve.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1603375 Cost and Productivity Experiences of Pakistan with Aggregate Learning Curve
Authors: Jamshaid ur Rehman, Shahida Wizarat
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The principal focus of this study is on the measurement and analysis of labor learnings in Pakistan. The study at the aggregate economy level focus on the labor productivity movements and at large-scale manufacturing level focus on the cost structure, with isolating the contribution of the learning curve. The analysis of S-shaped curve suggests that learnings are only below one half of aggregate learning curve and other half shows the retardation in learning, hence retardation in productivity movements. The study implies the existence of learning economies in term of cost reduction that is input cost per unit produced decreases by 0.51 percent every time the cumulative production output doubles.Keywords: Cost, Inflection Point, Learning Curve, Minima, Maxima, and Productivity
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1772374 Preparing the Curve Number (CN) and Surface Runoff Coefficient (C) Map of the Basin in the Aghche Watershed, Iran
Authors: Ali Gholami, Ebrahim Panahpour, Amir Hossein Davami
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In this research, a part of Aghche basin in Isfahan province with an area about 2000 hectars, was chosen to be obtain curve number coefficient runoff and W indicator in second Cook method By using aerial photos 1968 and 1995, the satellite data of the IRS in 2008. Then the process of land use changes in the period of study and its effect on the changes of curve number (CN), W indicator and surface runoff coefficient (C) of the basin was investigated. These results showed that on the track of these land use changes the weight averages curve number (CN), surface runoff coefficient (C) and W indicator of the basin were increased to 0.92, 0.02 and 0.78 unit in the first period of study and 1.18, 0.03, 0.99 Unit in the second period of study respectively.Keywords: Aghche Watershed, Curve Numbers (CV), Land UseChanges, Surface Runoff Coefficient(C) Map, W indicator
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2772373 On the Determination of a Time-like Dual Curve in Dual Lorentzian Space
Authors: Emin Özyılmaz
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In this work, position vector of a time-like dual curve according to standard frame of D31 is investigated. First, it is proven that position vector of a time-like dual curve satisfies a dual vector differential equation of fourth order. The general solution of this dual vector differential equation has not yet been found. Due to this, in terms of special solutions, position vectors of some special time-like dual curves with respect to standard frame of D31 are presented.Keywords: Classical Differential Geometry, Dual Numbers, DualFrenet Equations, Time-like Dual Curve, Position Vector, DualLorentzian Space.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1462372 ROC Analysis of PVC Detection Algorithm using ECG and Vector-ECG Charateristics
Authors: J. S. Nah, A. Y. Jeon, J. H. Ro, G. R. Jeon
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ECG analysis method was developed using ROC analysis of PVC detecting algorithm. ECG signal of MIT-BIH arrhythmia database was analyzed by MATLAB. First of all, the baseline was removed by median filter to preprocess the ECG signal. R peaks were detected for ECG analysis method, and normal VCG was extracted for VCG analysis method. Four PVC detecting algorithm was analyzed by ROC curve, which parameters are maximum amplitude of QRS complex, width of QRS complex, r-r interval and geometric mean of VCG. To set cut-off value of parameters, ROC curve was estimated by true-positive rate (sensitivity) and false-positive rate. sensitivity and false negative rate (specificity) of ROC curve calculated, and ECG was analyzed using cut-off value which was estimated from ROC curve. As a result, PVC detecting algorithm of VCG geometric mean have high availability, and PVC could be detected more accurately with amplitude and width of QRS complex.Keywords: Vectorcardiogram (VCG), Premature Ventricular contraction (PVC), ROC (receiver operating characteristic) curve, ECG
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2931371 The Study of Relative Efficiency in Growth Curve Model
Authors: Nan Chen, Baoguang Tian
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In this paper, some relative efficiency have been discussed, including the LSE estimate with respect to BLUE in curve model. Four new kinds of relative efficiency have defined, and their upper bounds have been discussed.
Keywords: Relative efficiency, LSE estimate, BLUE estimate, Upper bound, Curve model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1426370 A Bathtub Curve from Nonparametric Model
Authors: Eduardo C. Guardia, Jose W. M. Lima, Afonso H. M. Santos
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This paper presents a nonparametric method to obtain the hazard rate “Bathtub curve” for power system components. The model is a mixture of the three known phases of a component life, the decreasing failure rate (DFR), the constant failure rate (CFR) and the increasing failure rate (IFR) represented by three parametric Weibull models. The parameters are obtained from a simultaneous fitting process of the model to the Kernel nonparametric hazard rate curve. From the Weibull parameters and failure rate curves the useful lifetime and the characteristic lifetime were defined. To demonstrate the model the historic time-to-failure of distribution transformers were used as an example. The resulted “Bathtub curve” shows the failure rate for the equipment lifetime which can be applied in economic and replacement decision models.
Keywords: Bathtub curve, failure analysis, lifetime estimation, parameter estimation, Weibull distribution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2223369 A Simple Method for Tracing PV Curve of a Radial Transmission Line
Authors: Asfar Ali Khan
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Analytical expression for maximum power transfer through a transmission line limited by voltage stability has been formulated using exact representation of transmission line with ABCD parameters. The expression has been used for plotting PV curve at different power factors of a radial transmission line. Limiting values of reactive power have been obtained.Keywords: Power Transfer, PV Curve, Voltage Stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3296368 Position Vector of a Partially Null Curve Derived from a Vector Differential Equation
Authors: Süha Yılmaz, Emin Özyılmaz, Melih Turgut, Şuur Nizamoğlu
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In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.
Keywords: Frenet Equations, Partially Null Curves, Minkowski Space-time, Vector Differential Equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1154367 Dynamic Voltage Stability Estimation using Particle Filter
Authors: Osea Zebua, Norikazu Ikoma, Hiroshi Maeda
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Estimation of voltage stability based on optimal filtering method is presented. PV curve is used as a tool for voltage stability analysis. Dynamic voltage stability estimation is done by using particle filter method. Optimum value (nose point) of PV curve can be estimated by estimating parameter of PV curve equation optimal value represents critical voltage and condition at specified point of measurement. Voltage stability is then estimated by analyzing loading margin condition c stimating equation. This maximum loading ecified dynamically.Keywords: normalized PV curve, optimal filtering method particle filter, voltage stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1790