Newton-Raphson Method Research Articles

Impact study of flexible alternating current transmission system on power flow and power loss in power systems using MATLAB and PSAT

The work presented in this paper is to study the impact of FACTS (flexible alternating current transmission system) on the power flow and power losses of a multi-machine electrical system. In this work, we have calculated the power flow and the active and reactive power losses for a 6-bus 3-machine network system, in the first case where there are no FACTS, and in the second case where there are FACTS (SVC). So, and in the second case we used an SVC ((Static Var Compensator) because it is one of the elements of FACTS, to see their influence on power flow and power losses in electrical systems using MATLAB software (we used the Newton-Raphson method) and using PSAT software (Power System Analysis Toolbox), we calculated the power flow and the active and reactive power losses in the lines, respectively. Finally, we compare the results obtained by the simulation programs MATLAB and PSAT, and see what effect FACTS (SVC) has on the power flow and power loss in our electrical system that we are studying.

Optimization of the Voltage Total Harmonic Distortion in Multilevel Inverters by Using the Taguchi Method

A critical reduction in the total harmonic distortion in the output voltage of multilevel inverters can be obtained with an appropriate selection of the angles to switch the power semiconductors at low frequency. Among the methods used to obtain the required sequence of angles, it is possible to recognize both standard and optimized methods, like the Newton–Raphson method or the genetic algorithm, to mention a few. However, implementing the genetic algorithm implies using several configuration parameters, so it is difficult to know if the best option was chosen. This paper implements the Taguchi design of experiments, the Taguchi method, to obtain the appropriate switching angles for an multilevel inverter producing an output voltage of five and seven levels. Experimental results obtained from a laboratory prototype using the computed angles in the MATLAB GA solver demonstrate the superiority of the proposed method.

Sustainable Development of a Direct Methanol Fuel Cell Using the Enhanced LSHADE Algorithm and Newton Raphson Method

This paper presents a mathematical model for stacks of direct methanol fuel cells (DMFCs) using an optimised method. In order to reduce the sum of squared errors (SSE) in calculating the polarisation profile, the suggested technique makes use of simulated experimental data. Given that DMFC is one of the viable fuel cell choices, developing an appropriate model is essential for cost reduction. However, resolving this issue has proven difficult due to its complex and highly nonlinear character, particularly when adjusting the DMFC model to various operating temperatures. By combining the algorithm and the objective function, the current work introduces a novel method called LSHADE (ELSHADE) for determining the parameters of the DMFC model. This technique seeks to accurately identify DMFCs’ characteristics. The ELSHADE method consists of two stages, the first of which is controlled by a reliable mutation process and the latter by a chaotic approach. The study also recommends an improved Newton–Raphson (INR) approach to deal with the chaotic nature of the I-V curve equation. The findings show that, when used on actual experimental data, the ELSHADE-INR technique outperforms existing algorithms in a variety of statistical metrics for accurately identifying global solutions.

Influence of Heat Source on Thin Film Flow of Ferrofluid Past an Unsteady Stretching Sheet

In this work, the impact of a heat source on the thin-film ferrofluid flow over an unstable stretching sheet in the presence of an external magnetic field has been examined. The governing partial differential equations are transformed into a system of ordinary differential equations by similarity transformation. The resultant system of ordinary differential equations is solved numerically through shooting technique involving Runge-Kutta-Fehlberg (RKF45) method. To improve the initial guess values, the Newton-Raphson method is used. The significance of magnetization parameter, Prandtl number and heat source parameter on the flow and heat transmission process have been graphically analysed. The decrease in film thickness is observed for growing values of heat source parameter.

ZILLMER RESERVE ON ENDOWMENT LAST SURVIVOR LIFE INSURANCE USING LOMAX DISTRIBUTION

This article discusses Zillmer's reserves for endowment last survivor of life insurance. Zillmer reserves are a type of modification of premium reserves which are calculated using prospective reserves and the Zillmer rate. In Zillmer reserves, loading which is the difference between gross premium and net premium in the first policy year is greater than standard loading. In this article, the life insurance used is endowment last survivor of life insurance, where the reserve calculation for last survivor status is calculated for 3 cases, namely, both participants survive until the end of the policy, participant x survive but participant y died, and participant y survive but participant x died. So the purpose of this research is to find a way to make the loading value in 3 cases on the dwiguna last survivor of life insurance Zillmer reserves smaller. To achieve this goal, this article uses the Lomax distribution with the parameters estimated using maximum likelihood estimation and then determined by a Newton-Raphson iteration method. Based on the illustration, even though in the first policy year in cases where both participants survive until the end of the policy there was still a negative loading, overall Zillmer's reserves in each case continues to increase over time

Klasik Test Kuramı’na ve Madde Tepki Kuramı’na Dayalı Test Eşitleme Yöntemlerinin Karşılaştırılması

This study aims to choose the equating method with the least equating error by using the equating methods in Classical Test Theory and Item Response Theory. In this study, booklet 1 and booklet 3 data were used for PISA (Programme for International Student Assessment) 2012 Mathematics test. Data from Turkey, Indonesia, Shanghai/China and Finland, countries participating in PISA 2012, were selected for this study. Non-equivalent groups design was used in the test equating process. Linear equating methods [Tucker (w1=1, w1=0.5), Levine observed score (w1=1, w1=0.5), Levine true score, Classical Congeneric and Braun-Holland), equipercentile equating methods (pre smoothing according to C6 polynomial degree, beta4, post smoothing according to S 0.05 cubic function, frequency estimation (w1=1, w1=0.5) ] were used in the study. In Classical Test Theory, the least error is obtained from the frequency estimation method with a synthetic universe weight of w1 = 0.5. For the Item Response Theory, the calibration method was first decided, which is the Stocking-Lord method. After the scale transformation was achieved with the Stocking-Lord calibration method, the equating scores were calculated from the IRT's true and observed equating methods. The least error in IRT was obtained from the true score equating method. For error values, error coefficients were calculated according to Newton-Raphson's delta method and bootstrap methods. When the error coefficients (delta and bootstrap) of the equating methods in both theories were compared, it was found that the equating methods based on IRT had fewer errors than the equating methods in CTT, and the method with the least equating error was the IRT true score equating. The least equating error frequency estimation in CTT (w1=0.5) and the most error Levine true score equating method.

Implementation of a modified Graham-Walles viscosity function within a Chaboche viscoplastic constitutive model

This work provides a numerical framework for the accurate prediction of operational life of metallic components exhibiting a non-classical creep behavior under constant loadings and very high temperature. A modified Graham-Walles type analytical viscoplastic function is implemented into a Chaboche unified viscoplastic constitutive model. The numerical model is integrated into the finite element software Lagamine following a fully-implicit two-step radial return mapping algorithm. The non-linear system of equations is solved using a robust Newton-Raphson method. The computational efficiency of the model is enhanced by implementing a sub-step routine, thereby decreasing the average number of iterations of the finite element software. The validation of the model is performed using experimental data available in the literature on the non-classical creep behavior of Incoloy 800H, a Ni-superalloy exhibiting a two-step creep strain rate minima attributed to multiple complex dislocation-precipitate interactions.

Modifikasi Garis Singgung Untuk Mempercepat Iterasi Pada Metode Newton Raphson

The Newton-Raphson method is one of the methods to find solutions or roots of nonlinear equations. This method converges faster than other methods and is more effective in finding doubles. In this study, it will be shown that the Newton-Raphson modification uses modifications to the tangent equation. The results show that for every nth iteration, the speed difference of Newton Raphson modification is __. Furthermore, the convergence of Newton Raphson is __, and for Newton Raphson modification is __.

Newton-Raphson-based optimizer: A new population-based metaheuristic algorithm for continuous optimization problems

The Newton-Raphson-Based Optimizer (NRBO), a new metaheuristic algorithm, is suggested and developed in this paper. The NRBO is inspired by Newton-Raphson's approach, and it explores the entire search process using two rules: the Newton-Raphson Search Rule (NRSR) and the Trap Avoidance Operator (TAO) and a few groups of matrices to explore the best results further. The NRSR uses a Newton-Raphson method to improve the exploration ability of NRBO and increase the convergence rate to reach improved search space positions. The TAO helps the NRBO to avoid the local optima trap. The performance of NRBO was assessed using 64 benchmark numerical functions, including 23 standard benchmarks, 29 CEC2017 constrained benchmarks, and 12 CEC2022 benchmarks. In addition, the NRBO was employed to optimize 12 CEC2020 real-world constrained engineering optimization problems. The proposed NRBO was compared to seven state-of-the-art optimization algorithms, and the findings showed that the NRBO produced promising results due to its features, such as high exploration and exploitation balance, high convergence rate, and effective avoidance of local optima capabilities. In addition, the NRBO also validated on challenging wireless communication problem called the internet of vehicle problem, and the NRBO was able to find the optimal path for data transmission. Also, the performance of NRBO in training the deep reinforcement learning agents is also studied by considering the mountain car problem. The obtained results also proved the NRBO's excellent performance in handling challenging real-world engineering problems.

Geometrically exact aeroelastic stability analysis of helicopter composite rotor blades in forward flight

In this paper, a sophisticated method for analyzing the geometrically exact aeroelastic stability of composite rotor blades in forward flight has been proposed. The unique advantage of the proposed method is to use the geometrically exact beam model with the updated Variational Asymptotic Beam Sectional analysis (VABS) for structural modeling to not only calculate the blade cross-sectional properties and blade spanwise deformations more accurately, but also take into account the effect of transverse shear deformation and blade initial twist and curvatures sophisticatedly. The Peters finite state airloads theory and the Peters-He finite state dynamic inflow model are coupled to calculate the three-dimensional unsteady airloads applied on the blade. The auto-pilot trim scheme is adopted to determine the blade pitch controls. The finite element spatial discretization method, the Newmark numerical integration method, the Newton-Raphson method and the moving-block analysis method are combined to solve the established geometrically exact aeroelastic equations and obtain the geometrically exact aeroelastic stability of composite rotor blades. The proposed method is validated by correlation with existing analytical results. The investigations show that the effect of transverse shear deformation on the aeroelastic stability of composite hingeless rotors in forward flight is non-negligible. Blade initial curvatures have significant effect on the aeroelastic stability of composite hingeless rotors in forward flight, which is not only related to the blade elastic couplings, but also to the advance ratio.

Large Deflection and Post-Buckling Analysis of Cantilever Nanorods Including Effects of Couple and Surface Stresses by Intrinsic Coordinate Finite Elements

This paper presents a novel approach to the analysis of large deflection and post-buckling behavior of cantilever nanorods under different load conditions. The proposed approach utilizes a variational method, incorporating the Gurtin–Murdoch surface elasticity theory and the consistent couple stress theory to account for size-dependency effects. By accounting for the strain energy contributions of the bulk material, surface layer, and load conditions, this approach expresses the behavior of the nanorods in terms of their intrinsic coordinates. A finite element method was used to solve this numerical problem, generating a system of non-linear equations that were iteratively solved using the Newton–Raphson method. The results obtained from the finite element method were confirmed by those from the shooting method. Also, it highlights the effectiveness of the variational model in predicting the large deflection and post-buckling behavior of cantilever nanorods while considering both surface stress and couple stress effects. Furthermore, the study investigated the influence of surface stress and couple stress on the response of the nanorods to point and uniform loads. The results showed that incorporating both effects enhanced the stiffness of the nanorods compared to scenarios in which these effects were neglected. In addition, the couple stress effect was found to have a greater influence on the stiffening of nanorods for the same value of unitless parameters compared to surface stress effects. These findings offer valuable insights into the large deflection and post-buckling behavior of cantilever nanorods and highlight the importance of surface stress and couple stress effects. The model proposed in this study has potential applications in advanced technological device designs by providing a comprehensive understanding of the mechanical response of nanorods, allowing for more accurate predictions and enhanced device performance.

Thermoelastic damping and frequency shift of different micro-scale piezoelectro-magneto-thermoelastic beams

This work focuses on mathematically studying thermoelastic damping (TED) and frequency shift (FS) in micro-scale piezoelectro-magneto-thermoelastic (PEMT) composite beams composed of BaTiO3-CoFe2O4 combination. Pertaining to cutting-edge micro-technologies implemented in several engineering/scientific applications now-a-days, micro-scale doubly clamped (CC), doubly simply supported (SS), clamped-free (CF), and clamped-simply supported (CS) beams are extensively analyzed. The beams are modeled following the linear Euler-Bernoulli assumptions. The first two eigenvalues of all beams are numerically obtained using Newton-Raphson method. The closed-form expressions of TED and FS of all beams are derived analytically. The influences of Classical dynamical coupled (CL), Lord-Shulman (LS) & Green-Lindsay (GL) thermoelasticity theories, beam dimensions, BaTiO3 volume fraction (Ω f ), and the first two modes (M 1 & M 2) on the TED & FS are meticulously analyzed. Critical thickness (CrTh), critical length (CrLt), and TED (inverse Quality factor) of the beams are numerically obtained and studied. Among other key outcomes, the existence of a critical value of Ω f is established in the range Ω f ∈ [0.5, 0.55], at which, the TED and FS display a drastic change in their natures. The outcomes of the present analysis may find immense potential uses in the design and development of PEMT composite micro-beams, and their applications in several areas such as supporting/stiffening other micro/nanostructures, construction works, sensitive sensing applications, etc.

Feedback control system design for force-sensing concentric tube-based surgical robot: Kinematics using Bernstein polynomials

A novel force sensing module integrated into a concentric tube robot (CTR) was proposed for vitreoretinal surgery in our previous work, and this robot was able to provide tip force information to the operating surgeon. However, when the force-sensing module was integrated, the property of the tube changed, and the conventional modeling-based control algorithm proved to be unsuitable for the force-sensing concentric tube robot (FSCTR). In this work, we have proposed a shape optimization algorithm for the FSCTR to prevent snapping issue while providing an adequate workspace. A corollary actuation system was used to control the FSCTR. The forward kinematics of the FSCTR consisted of rigid body motion and shape variation, where the shape variation was determined using Bernstein polynomials. Inverse kinematics was derived using the Newton–Raphson method. A feedback controller was designed to compensate for the error caused by rigid body motion. Several experiments were conducted to evaluate the performance of the proposed control system. The experimental accuracy of the proposed forward kinematics was 0.15 ± 0.16 mm, and this result was superior to that of the torsionally compliant model. The accuracy of the inverse kinematics was 0.55 ± 0.24 mm, and the accuracy of point targeting under feedback control was 0.12 ± 0.05 mm. Overall, the results of this study indicate that the proposed motion control system satisfies the standards required for vitreoretinal surgery.

Adaptive Precoding for Aeronautical Communication Systems in Public Channels

The family of aeronautical communication systems is considered as one of the core technologies for the beyond-the-fifth-generation (B5G) networks, thus attracting rapidly increasing attention from both industry and academia. In this paper, a new multiple-input multiple-output (MIMO) precoding scheme is proposed for aeronautical communication systems, where the transmit power for the aerial user equipment (UE) approaching the target cell is maximized based on the direction information. Specifically, we first transform the precoding optimization problem into a linear programming problem, and then develop two algorithms to derive the precoders for two transmission modes, namely the multi-stream and single-stream transmissions. For the multi-stream case, an algorithm based on manifold optimization is proposed, which guarantees the equal power allocation for each antenna. For the single-stream case, we derive a precoder by a numerically stable algorithm that extends the Newton-Raphson method. Simulation results show that the proposed precoding schemes can improve the link performance of the UEs with known directions, while ensuring that the performance of the UEs with unknown directions can still be close to that achievable by conventional schemes.

Parallel Computing of Thermo-Fluid Modeling Related to the FSW Process

This paper is devoted to the numerical computation of a steady-state thermo-fluid modeling related to the Friction Stir Welding Process in a two-dimensional cylindrical geometry. It analyzes the efficiency of the implementation on parallel architectures of two finite-difference schemes on a structured grid. The first one applies the Newton-Raphson method to compute a numerical solution of this non-linear elliptic type equation, and uses an iterative sparse solver. The second one is based on a time-marching approach converging to the steady state solution thanks to a time-explicit computation. Their respective performance is presented and discussed. Some numerical simulation results are presented to validate the proposed approach.

Provably convergent Newton–Raphson methods for recovering primitive variables with applications to physical-constraint-preserving Hermite WENO schemes for relativistic hydrodynamics

The relativistic hydrodynamics (RHD) equations have three crucial intrinsic physical constraints on the primitive variables: positivity of pressure and density, and subluminal fluid velocity. However, numerical simulations can violate these constraints, leading to nonphysical results or even simulation failure. Designing genuinely physical-constraint-preserving (PCP) schemes is very difficult, as the primitive variables cannot be explicitly reformulated using conservative variables due to relativistic effects. In this paper, we propose three efficient Newton–Raphson (NR) methods for robustly recovering primitive variables from conservative variables. Importantly, we rigorously prove that these NR methods are always convergent and PCP, meaning they preserve the physical constraints throughout the NR iterations. The discovery of these robust NR methods and their PCP convergence analyses are highly nontrivial and technical. Our NR methods are versatile and can be seamlessly incorporated into any RHD schemes that require the recovery of primitive variables. As an application, we apply them to design PCP finite volume Hermite weighted essentially non-oscillatory (HWENO) schemes for solving the RHD equations. Our PCP HWENO schemes incorporate high-order HWENO reconstruction, a PCP limiter, and strong-stability-preserving time discretization. We rigorously prove the PCP property of the fully discrete schemes using convex decomposition techniques. Moreover, we suggest the characteristic decomposition with rescaled eigenvectors and scale-invariant nonlinear weights to enhance the performance of the HWENO schemes in simulating large-scale RHD problems. Several demanding numerical tests are conducted to demonstrate the robustness, accuracy, and high resolution of the proposed PCP HWENO schemes and to validate the efficiency of our NR methods.

Coupled thermo-hydro-mechanical-phase field modelling for hydraulic fracturing in thermo-poroelastic media

This study presents a coupled thermo-hydro-mechanical-phase field model, grounded in a thermodynamic framework, to elucidate the process of hydraulic fracture evolution in thermo-poroelastic media. The thermo-poroelastic characteristics of the rock exhibit variations contingent upon the phase field value. Consequently, the energy stored within the fluid and rock becomes a function of the phase field values, leading to the formulation of novel phase field evolution equations. For discretizing the thermal-hydrodynamic-mechanical-phase field model, the finite element method is employed. An interleaved scheme is utilized to concurrently solve for displacement, pressure, phase field, and temperature. The corresponding iterative structure is established using the Newton–Raphson method. Several hydraulic fracturing scenarios are investigated to showcase the potential and versatility of the presented model. These scenarios include: a) investigating the impact of different reservoir temperatures on hydraulic fracture propagation, b) analyzing the effects of intersection angle and reservoir temperature on fracture propagation in naturally fractured reservoirs, and c) examining the influence of reservoir temperature on hydraulic fracture propagation in grain-scale polymineral rock.

Using Lie Derivatives with Dual Quaternions for Parallel Robots

We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how actuators affect an end effector in parallel robots, and make it explicit in the two cases case of Stewart Platforms, and cable-driven parallel robots. We also show how to use Lie derivatives with the Newton-Raphson Method to solve the forward kinematic problem for over constrained parallel actuators. Finally, we derive the equations of motion of the end effector in dual quaternion form, which include the effect of inertia from the actuators.

Numerical simulation for two species time fractional weakly singular model arising in population dynamics

ABSTRACT In this work, we analyze and develop an efficient numerical scheme for the Lotka–Volterra competitive population dynamics model involving fractional derivative of order . The fractional derivative is defined in the Caputo sense. The solution exhibits a weak singularity near Using the L1 technique, the fractional operator is discretized. The differential equations are reduced to a system of nonlinear algebraic equations. To solve the corresponding nonlinear system, we employed the generalized Newton–Raphson method. The presence of singularities creates a layer at the origin, and as a result, the proposed scheme fails to achieve its optimal convergence on a uniform mesh. To accelerate the rate of convergence, we used a graded mesh with a suitably chosen grading parameter. The stability analysis and error estimates are derived on a maximum norm. Finally, numerical experiments are conducted to show the validity and applicability of the proposed scheme.

Three-dimensional flow of hybrid nanofluid through Darcy-Forchheimer porous surface: A Legendre wavelet collocation approach

The main objective of the present study is to obtain the solution of 3D Darcy-Forchheimer flow of hybrid nanofluid (MoS2-GO/H2O) over stretchable surface using a novel Legendre Wavelet Collocation Method (LWCM). The transformed model is a semi-infinite boundary value problem of nonlinear coupled system of Ordinary Differential Equation (ODEs). Using special transformation in a space coordinate, the model is converted into finite domain of boundary value problem. Then, LWCM is implemented and problem is converted into system of algebraic equations. Now, the solution of algebraic equations is obtained by Newton-Raphson method. The ratio of volume fraction of GO and MoS2 are taken as 6% and 8% respectively. The outcomes disclose that the heat transfer rate and both drag forces regularly rises with increase in volume fraction of MoS2 and GO. Moreover, the heat transfer outlines of MoS2-GO/H2O constantly decreased when the fluid motion is in suction region, while the skin friction coefficients are increased. To validate the results obtained by the LWCM, a comparison is made with exact solution as well as with earlier published numerical results.