Quadratic Interpolation Technique Research Articles

An efficient Approximate Solution for Non-Linear Solar Cell Equation using Inverse Quadratic Interpolation Method

The main purpose of this research is to discuss the numerical solutions of a single-diode nonlinear equation for a solar cell in a more efficient way. The inverse quadratic interpolation technique for finding the root(s) of a function is applied to our study problem. Numerical results show that the proposed three points iterative method is compatible to Newton's method, accurate and effective.

Novel embedding secrecy within images utilizing an improved interpolation-based reversible data hiding scheme

This paper proposed an innovative approach for reversible data hiding (RDH) within images in such a way that the image can be accurately recovered after extracting the data. The work presented a challenging task due to the need to compromise between the quality of the stego-image and the capacity of the hidden data. It is used in applications that need to reconstruct the original images without any distortion, such as medical diagnosis, remote sensing images and military maps. The aim of this paper is to study improving RDH methods using interpolation-based scheme. The proposed interpolation-based RDH (IRDH) scheme improves the embedding capacity and security over state-of-the-art schemes. We investigated the interpolation techniques improving the parabolic interpolation (PI) method to scale-up the original image, then embedding within it the secret data using newly proposed embedding technique. The experimental results demonstrate that the proposed quadratic Bezier interpolation (QBI) technique reduced the computational complexity of PI with same quality of the produced image. Additionally, the proposed cubic interpolation techniques improved the image quality of PI but with more computational complexity. On the other hand, the proposed circle interpolation (CIRI) achieved less PSNR value than PI showing interesting remarks. The general steps of this scheme are generation of the interpolated image, data embedding, data extraction and image recovery showing attractive promising research contribution.

A Discrete-Time Approach to Evaluate Path-Dependent Derivatives in a Regime-Switching Risk Model

This paper provides a discrete-time approach for evaluating financial and actuarial products characterized by path-dependent features in a regime-switching risk model. In each regime, a binomial discretization of the asset value is obtained by modifying the parameters used to generate the lattice in the highest-volatility regime, thus allowing a simultaneous asset description in all the regimes. The path-dependent feature is treated by computing representative values of the path-dependent function on a fixed number of effective trajectories reaching each lattice node. The prices of the analyzed products are calculated as the expected values of their payoffs registered over the lattice branches, invoking a quadratic interpolation technique if the regime changes, and capturing the switches among regimes by using a transition probability matrix. Some numerical applications are provided to support the model, which is also useful to accurately capture the market risk concerning path-dependent financial and actuarial instruments.

Eliminating starting hesitation for reliable operation of switched reluctance motor without machine parameters for light electric vehicle applications

In this study, an initial rotor position estimation at standstill condition is presented for reliable operation of switched reluctance motor (SRM) without initialising machine parameters for light electric vehicle (LEV) applications. The prime objective of this method is to startup an SRM without using the mechanical position sensor, and eliminate the starting hesitation and starting jerk issues from standstill condition. In the proposed method, the initial rotor position at standstill is determined by injecting a single pulse dc voltage simultaneously into all stator phase windings for a very short period (microsecond). The obtained current envelope data is then used to calculate the initial rotor position with the quadratic polynomial interpolation technique without any prior knowledge of other motor parameters. The experimental results for a 3.5 kW, 6/4 SRM are provided to substantiate the overall good performance. The developed system can be considered as a strong candidate for high precision LEV applications.

Image Enhancement Based on Improved Antlion Optimization Algorithm

Swarm intelligence based image enhancement method is an important method to improve the image visual effect. In order to improve the image enhancement algorithm based on the antlion optimization, a quadratic interpolation technique is introduced to improve the image enhancement algorithm of the antlion optimization method which has the disadvantages of slow convergence speed and low computational accuracy. The new algorithm uses quadratic interpolation to accelerate the convergence speed of ant population and antlion population, to balance the global and local searching ability of the antlion algorithm, so as to improve the estimation precision of the optimal parameters in the incomplete Beta function and improve the image quality. The two evaluation indexes verify that the new algorithm is better than the contrast algorithm in statistical meaning, and extend the research of the antlion optimization algorithm.

Numerical Simulation of a One-Dimensional Water-Quality Model in a Stream Using a Saulyev Technique with Quadratic Interpolated Initial-Boundary Conditions

The one-dimensional advection-diffusion-reaction equation is a mathematical model describing transport and diffusion problems such as pollutants and suspended matter in a stream or canal. If the pollutant concentration at the discharge point is not uniform, then numerical methods and data analysis techniques were introduced. In this research, a numerical simulation of the one-dimensional water-quality model in a stream is proposed. The governing equation is advection-diffusion-reaction equation with nonuniform boundary condition functions. The approximated pollutant concentrations are obtained by a Saulyev finite difference technique. The boundary condition functions due to nonuniform pollutant concentrations at the discharge point are defined by the quadratic interpolation technique. The approximated solutions to the model are verified by a comparison with the analytical solution. The proposed numerical technique worked very well to give dependable and accurate solutions to these kinds of several real-world applications.

Cubic Interpolation: A Line Search Technique for Fuzzy Optimization Problems

This article continues the research on line search techniques for fuzzy optimization problems. Previously, in Ghosh and Chakraborty (Int J Appl Comput Math 3(2):527–547, 2017), a quadratic interpolation technique for fuzzy optimization problem was studied. In this article, we propose a cubic interpolation technique. For the optimality concept, a partial ordering of fuzzy numbers is used. In order to derive the cubic interpolation method, the generalized Hukuhara difference between a pair of fuzzy numbers and the generalized Hukuhara differentiability for fuzzy functions are applied. The convergence analysis of the proposed technique is also exhibited. It is found that the developed method has quadratic rate of convergence. A detailed numerical example is included to explore the developed technique. The iteration points in the example are also pictorially shown in detail.

Quadratic Interpolation Technique to Minimize Univariable Fuzzy Functions

In this paper, a quadratic interpolation technique is proposed to minimize a univariable fuzzy-number-valued function. The fuzzy max-ordering relation of fuzzy numbers is used for optimal solution concept. The Hausdorff distance and Hukuhara difference between two fuzzy numbers, and the Hukuhara differentiability of fuzzy functions, are employed in order to derive the quadratic interpolation method. Convergence rates of the proposed two points and three points quadratic interpolation techniques are also analyzed. A numerical example is included to illustrate the proposed techniques.

Spectral Galerkin Method for Optimal Control Problems Governed by Integral and Integro- Differential Equations

In this paper a Legendre integral method is proposed to solve integral and integro- differential problems and optimal control problems governed by integral and integro- differential equations. Galerkin method is used to reformulate the problem as constrained optimization problem. The resulting constrained optimization problem is solved by Hybrid penalty partial quadratic interpolation technique. Numerical results are included to confirm the efficiency and accuracy of the method.

A Project-Based Laboratory for Learning Embedded System Design With Industry Support

A project-based laboratory for learning embedded system design with support from industry is presented in this paper. The aim of this laboratory is to motivate students to learn the building blocks of embedded systems and practical control algorithms by constructing a line-following robot using the quadratic interpolation technique to predict the line position. For those students who have acquired basic microcontroller hardware and software programming skills from previous courses, the hands-on exercises in the laboratory include several specific hardware circuits and software algorithms for the final project of constructing the line-following robot. The students are allowed to discuss the hardware and software problems with each other while solving each exercise, although they have to answer the teacher's questions individually to earn the score. To enhance the learning outcomes, a racing contest for the students' line-following robots is also organized to see how well the techniques learned in the laboratory are applied in the final project. The support from the local branch of Microchip Inc. allows students to obtain C-compilers and microcontrollers at no cost. The feedback from students shows that the final project of constructing line-following robots and the racing contest motivates the students to learn actively all the skills included in the laboratory for embedded system design.

High-Performance Special Function Unit for Programmable 3-D Graphics Processors

An high-speed special function unit (SFU) is presented in this paper. The system supports the single-precision IEEE-754 floating-point standard and implements faithfully rounded reciprocal, square root, reciprocal square root, logarithm, and exponential functions. The functions are approximated by using a novel constrained piecewise quadratic interpolation technique. In this way, the lookup table size is reduced by 40% with respect to previously proposed techniques, without any loss in accuracy. Error analysis and sizing methodology are presented in the paper. The SFU has been implemented in a 0.18-mum CMOS technology. The circuit is able to operate up to 420-MHz clock frequency, with a power dissipation of 160 mW at 420 MHz. The system can be employed in programmable graphics accelerators and in other applications where high-performance function evaluation is needed.

Broadband VHF sources locating system using arrival-time differences for mapping of lightning discharge process

This paper presents a three-dimensional lightning discharge mapping system using arrival-time difference of broadband VHF electromagnetic pulses (20–200 MHz) methodology. The system consists of four circular plate antennas; three of which are placed to form two perpendicularly crossed-short base lines, with the fourth located at some distance. The directions of the electromagnetic radiation sources are determined using perpendicularly aligned antennas whereas the 3-D positions are obtained using all the four antennas. Broadband pulses arrival time differences are estimated incorporating time-domain signal analysis and the least-squares error method is applied to the detected broadband pulses to estimate the time delay with the quadratic interpolation technique utilized to achieve the resolution less than 1 ns. In this paper, the implementation of the system along with the successful reconstruction of the lightning discharge progression in 2-D and 3-D space is described. Additionally, instances of observation results of the cloud-to-ground and ground-to-cloud lightning discharge have been presented.

Numerical treatment of multiobjective optimal control problems

We present a numerical procedure for solving optimal control problems with both linear terminal constraints and multiple criteria. Using a Chebyshev spectral procedure, the problem reduces to a constrained optimization problem which can be solved using hybrid penalty partial quadratic interpolation (HPPQI) technique. The proposed procedure compares quite favorably with other methods on a sample of well-known examples.

Analytical and numerical solutions of a quasilinear parabolic optimal control problem

This paper presents analytical and numerical solutions of an optimal control problem for a quasilinear parabolic equation. The existence and uniqueness theorems of the solution are investigated. The derivation of formulae for the gradient of the modified cost function by solving the conjugated boundary value problem is explained. The numerical algorithm for solving the optimal control problem using partial quadratic interpolation technique is given. The computed optimal controls is helped to identify the unknown coefficients of the quasilinear parabolic equation. Numerical results are reported.

Interpolation techniques applied to the Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates

A weighted second-order (quadratic) interpolation technique is proposed to eliminate the oscillation phenomena manifested in the numerical Eulerian-Lagrangian solution of the convection-dispersion equation in natural coordinates when sharp fronts of concentration occur. Weighting is based on the interpolation of local moving points by using the known points in the fixed Eulerian grid. To increase numerical accuracy, the use of a third order (cubic) polynomial is discussed. Numerical experiments show that, in comparison with the quadratic formula, the application of this cubic interpolation technique has a number of advantages: (1) numerical oscillation is much less important or disappears; (2) the upstream spatial shift brought about by the quadratic formula disappears; and (3) stability is greater, even when the grid current number is larger than 1. The proposed numerical model is tested against two classical problems for which analytical solutions exist. The additional comparison of the numerical results obtained by the Eulerian-Lagrangian method using cubic interpolation, and those obtained by a purely Eulerian method (UWMCB), is carried out to illustrate the possibility of a real gain in precision.

Optimum heat pipe design: A nonlinear programming approach

In this paper, the optimum design of a heat pipe is formulated as a nonlinear programming problem. The objective is to minimize the weight of the heat pipe, subject to nonlinear inequality constraints and side constraints. These constraints correspond to desirable performance criteria and limitations of heat transport. An Interior Penalty Function Method incorporating Modified Powell's Method with Quadratic Interpolation Technique is used to solve the problem. The optimum values of the various design parameters are arrived at and presented. The effects of orientation and adiabatic section length of the heat pipe on the optimum design parameters are studied.

Electromagnetic optimization of 3-D structures

This paper discusses novel techniques and methodologies suitable for automated electromagnetic (EM) design of arbitrary three-dimensional (3-D) structures. In the context of parameterization of arbitrary 3-D structures, the authors outline the concept of the geometry capture technique. The authors present efficient response interpolation with respect to optimizable parameters-the key to effective automation. The authors' formulation is based on the maximally flat quadratic interpolation (MFQI) technique and provides gradient estimation essential to efficient optimization. The authors address the issue of storing the results of expensive EM simulations in a dynamically updated database, integrated with the interpolation technique. The automated EM optimization process is illustrated by the design of waveguide mitered bends. The authors also apply the aggressive space mapping (SM) technique to the optimization of multistep waveguide transformers.

Generalized stability analysis of reinforced embankments on soft clay

By modifying Janbu's generalized procedure of slices (GPS), the stability of a reinforced embankment constructed on a non-homogeneous clay deposit of finite depth is analysed to compute the factor of safety. The non-circular critical surface corresponding to the minimum factor of safety is obtained by a sequential unconstrained minimization technique in conjunction with a conjugate direction method for a multidimensional search and a quadratic interpolation technique for a unidimensional search. The effect of the thickness of the desiccated zone and the variation of undrained shear strength of clay with depth on the factor of safety is considered in the analysis. The influence of the tensile reinforcement force on the location of the critical surface is presented. The effects of the tensile reinforcement force and its orientation as well as the number of reinforcing layers on the stability of embankment have also been studied. The results obtained from the present analysis are compared with solutions reported in the literature.

Boundary element method with high order time element for transient eddy current problems

A boundary-element method with a quadratic time interpolation technique is developed for transient eddy-current problems. A time-domain discretization element and its integral formulations are presented. Two examples are given and compared with previous solutions to demonstrate that the proposed technique has the important advantage that a larger time step can be used. >

Determining optical flow from sequential images

AbstractAn exact method determining the optical flow is presented by means of pixel‐based mutual‐correlation analysis of dynamic images. The mutual‐correlation function is calculated between the temporal brightness change of the target pixel and that of its neighboring 16 (or 8) pixels. The local velocity of the target pixel is determined exactly through logical considerations using a reliable lag time estimated by the quadratic interpolation technique. The validity of the proposed method is confirmed by computer simulation of various dynamic images.