Newton-Raphson Iteration Method Research Articles

A coupled finite element approach to spatially resolved lithium plating and stripping in three-dimensional anode microstructures of lithium-ion cells

In this article, we present a coupled finite element approach to spatially resolved lithium plating and stripping in three-dimensional anode microstructures of lithium-ion cells. The local film thickness of plated lithium at the anode-electrolyte interface is treated as a primary variable in addition to the lithium concentration and the electric potential inside both electrodes as well as the lithium concentration and the electrochemical potential inside the electrolyte. We take the electric resistance of plated lithium into account when evaluating the Butler–Volmer charge transfer kinetics at the anode-electrolyte interface. The overall system of nonlinear equations resulting from discretization in time and space is solved in a monolithic, implicit fashion by the iterative Newton–Raphson method. To ensure stable and fast convergence especially during the final stages of lithium stripping, we introduce a novel regularization technique characterized by a trigonometrical regularization function for the purpose of discontinuity removal, and we show that our regularization is indeed necessary and effective while being superior to an existing one from the literature in several respects. The linear solver is derived from an advanced, physics-oriented preconditioning and solution technique established in one of our previous publications. In a large number of numerical examples, we thoroughly study two different lithium-ion cells involving up to approximately 2.3 million degrees of freedom. We thereby prove that our modeling and simulation approach is straightforwardly applicable to large and complex problem setups, and that it is capable of capturing lithium plating and stripping during continuous cell cycling without any interruptions in the corresponding simulations. Besides validating our implementation and examining various electrochemical properties of lithium plating and stripping, we also demonstrate that our approach is physically plausible and sensitive to overcharging, fast charging, and low-temperature charging as the three major causes of lithium plating. Unlike existing and widely used approaches based on geometric homogenization via morphological model parameters such as the porosity and the tortuosity, our approach offers the opportunity to detect spatial inhomogeneities in the propagation and distribution of plated lithium within anode microstructures. Accurate and in-depth numerical investigations of lithium plating and stripping are thus enabled as a potent alternative to elaborate and often costly experimental studies.

Rigid-Flexible Coupling Dynamics Modeling of Spatial Crank-Slider Mechanism Based on Absolute Node Coordinate Formulation

In order to study the influence of compliance parts on spatial multibody systems, a rigid-flexible coupling dynamic equation of a spatial crank-slider mechanism is established based on the finite element method. Specifically, absolute node coordinate formulation (ANCF) is used to formulate a three-dimensional, two-node flexible cable element. The rigid-flexible coupling dynamic equation of the mechanism is derived by the Lagrange multiplier method and solved by the generalized α method and Newton–Raphson iteration method combined. Comparison of the kinematics and dynamics response between rigid-flexible coupling system and pure rigid system implies that the flexible part causes a certain degree of nonlinearity and reduces the reaction forces of joints. The elastic modulus of the flexible part is also important to the dynamics of the rigid-flexible multibody system. With smaller elastic modulus, the motion accuracy and reaction forces become lower.

Interval current injection method for harmonic analysis in distribution systems: An approach using the Krawczyk operator

This paper presents a novel deterministic method for an interval analysis of a harmonic load flow algorithm. In the proposed approach, the current injection method is used for determining harmonic voltages in a distribution network by the iterative Newton-Raphson method. Based on the deterministic Jacobian matrix, the Krawczyk operator is applied in order to calculate interval results, being possible to obtain upper and lower limits of harmonic voltage magnitudes and total harmonic distortion at each system bus of the network. The 33-bus test system is used for the computational simulations to prove the viability and efficiency of the proposed method assuming the introduction of non linear loads into the power grid. Results are compared with Monte Carlo simulations to validate the use of the proposed methodology. The main contribution of the article is the development of a new technique for determining interval harmonic voltages and currents in power systems based on the concept of interval arithmetic in an advantageous computational time.

On the topology of basins of convergence linked to libration points in the modified R3BP with oblateness

We numerically investigate the effect of oblateness parameter on the topology of basins of convergence connected with the equilibrium points in the restricted three-body problem when the test particle is an oblate spheroid, and the influence of the gravitational potential from the belt is taken into consideration. Additionally, the primaries are also not spherical in shape, on the contrary, it is oblate or prolate spheroid. The parametric variation of the equilibrium points, their stability, and the regions of possible motion are illustrated as the function of the parameters involved. The domain of convergence, on the several two dimensional planes, are unveiled by applying the bi-variate version of the Newton–Raphson iterative method. In addition, we perform a systematic investigation in an order to show how the used parameters affect the topology as well as the degree of fractality of basins of convergence. Moreover, it is also unveiled that how the region of the convergence is related with the number of the required iterations to achieve the desired accuracy with the corresponding probability distribution.

Numerical investigation into hydraulic fracture initiation and breakdown pressures considering wellbore compliance based on the boundary element method

There is a wealth of experimental evidence that fracture initiation and breakdown pressures differ depending on in-situ stress status, rock properties, and injection conditions. However, the mechanism is not fully understood from a theoretical modeling perspective. In this study, a fully coupled plain-strain fracture model is proposed to interpret the mechanism of fracture initiation and breakdown pressures. The fracture model consists of fracture initiation and propagation governed by linear elastic fracture mechanics. The effects of wellbore compliance (or compressibility), solid-fluid coupling, and fracture multiscale propagation behavior are fully considered. The solid-fluid coupling equations are solved using the Newton–Raphson iterative method. The explicit time marching method is used to capture the fracture initiation process. An implicit time-stepping with the fracture tip asymptotic solution is used to capture fracture propagation fronts. The model is validated against the analytical solutions of the plane-strain model. Sensitivity analysis demonstrates that the initiation pressure mainly depends on rock properties, especially the fracture toughness. The peak pressure (breakdown pressure) is related to rock properties and injection conditions and usually occurs before the peak of the pressurization rate is reached. It increases with the injection rate, fluid viscosity, Young's modulus, and fracture toughness. The dimensionless inlet flux into the fracture can be used to determine the fracture initiation pressure. The pressurization rate during the fracture initiation stage is constant and can be used to assess wellbore compliance. Using a low injection rate and a low-viscosity fluid is beneficial to capturing the fracture initiation pressure. This study can help understand fracture initiation and propagation and interpret hydraulic fracture initiation and breakdown pressures.

Performance of textured foil journal bearing considering the influence of relative texture depth

Both foil structure and surface texturing have been widely used to improve bearing performance. However, there is little research on their combination, namely, textured gas foil bearing. This paper adopts the Reynolds equation as the pressure governing equation of bump-type foil journal bearing to study the influence of textures located on the top foil. The Newton-Raphson iterative method and the perturbation method are employed to obtain static and dynamic characteristics, respectively. Thereafter, based on three texture distribution types, further analysis about the effect of the relative texture depth and the textured portion is carried out. The results indicate that an appropriate arrangement of textures could improve the performance of gas foil bearing. For #1 texture distribution, the maximum increment of load capacity could exceed 10% when ω = 1.4 × 105 r/min, ε = 0.2.

Finite-element modeling of partially prestressed concrete beams with unbonded tendon under monotonic loadings

Purpose The partially prestressed concrete beam with unbonded tendon is still an active field of research because of the difficulty in analyzing and understanding its behavior. The finite-element (FE) simulation of such beams using numerical software is very scarce in the literature and therefore this study is taken to demonstrate the modeling aspects of unbonded partially prestressed concrete (UPPSC) beams. This study aims to present the three-dimensional (3-D) nonlinear FE simulations of UPPSC beams subjected to monotonic static loadings using the numerical analysis package ANSYS. Design/methodology/approach The sensitivity study is carried out with three different mesh densities to obtain the optimum elements that reflect on the load–deflection behavior of numerical models, and the model with optimum element density is used further to model all the UPPSC beams in this study. Three half-symmetry FE model is constructed in ANSYS parametric design language domain with proper boundary conditions at the symmetry plane and support to achieve the same response as that of the full-scale experimental beam available in the literature. The linear and nonlinear material behavior of prestressing tendon and conventional steel reinforcements, concrete and anchorage and loading plates are modeled using link180, solid65 and solid185 elements, respectively. The Newton–Raphson iteration method is used to solve the nonlinear solution of the FE models. Findings The evolution of concrete cracking at critical loadings, yielding of nonprestressed steel reinforcements, stress increment in the prestressing tendon, stresses in concrete elements and the complete load–deflection behavior of the UPPSC beams are well predicted by the proposed FE model. The maximum discrepancy of ultimate moments and deflections of the validated FE models exhibit 13% and −5%, respectively, in comparison with the experimental results. Practical implications The FE analysis of UPPSC beams is done using ANSYS software, which is a versatile tool in contrast to the experimental testing to study the stress increments in the unbonded tendons and assess the complete nonlinear response of partially prestressed concrete beams. The validated numerical model and the techniques presented in this study can be readily used to explore the parametric analysis of UPPSC beams. Originality/value The developed model is capable of predicting the strength and nonlinear behavior of UPPSC beams with reasonable accuracy. The load–deflection plot captured by the FE model is corroborated with the experimental data existing in the literature and the FE results exhibit good agreement against the experimentally tested beams, which expresses the practicability of using FE analysis for the nonlinear response of UPPSC beams using ANSYS software.

Multiple hydraulic fractures growth from a highly deviated well: A XFEM study

A fully coupled extended finite element (XFEM) model is presented to investigate the effect of different well types (highly deviated and horizontal wells) on simultaneous growth of multiple fractures. The importance of the use of deviated wells is briefly described and the governing equations for multi-cluster hydraulic fracturing in a saturated porous media are stated. The weak forms of both stress equilibrium and fluid mass continuity equations are turned into a system of linear equations through XFEM-type enrichments in space and Newmark scheme in time, which are solved by Newton-Raphson iteration method. In addition, the secant method is employed to impose the pressure continuity and mass conservation conditions at the fracture-well intersections. A numerical example with considering the simultaneous propagation of four hydraulic fractures is first adopted to validate the proposed numerical model. Several examples are then employed to investigate the influence of operational parameter, deviation angle, fracture spacing, placement and number on final fracture patterns. Numerical results show that coefficient of variation in multiple fracture heights for high-angle well is lower than that for horizontal well for all fracture placements. The opposite growth directions for two neighboring fractures, partially arising from the height difference at fracture-well intersection points, can reduce the stress shadow effect, thus promoting uniform growth of multiple fractures. Those results potentially unveil the causes for higher oil and gas production rates measured after multi-cluster hydraulic fracturing along highly deviated wells.

Scanning Radar Forward-Looking Superresolution Imaging Based on the Weibull Distribution for a Sea-Surface Target

To realize high azimuth resolution for sea-surface targets, this paper proposes a superresolution imaging method that relies on the Weibull distribution. The proposed method introduces the generalized Gaussian distribution and Weibull distribution to represent the statistical distribution function of the target prior information and sea clutter, respectively. The corresponding objective function was derived under the maximum a posteriori (MAP) criterion. To address the nonlinearity of the objective function, this paper adopts the NewtonRaphson iterative method to resolve it. Simulations and experimental data assessment indicate that the proposed method has superior superresolution imaging performance compared with other traditional superresolution methods for sea-surface target imaging.

Analytical modeling of the lateral stiffness of a spline coupling considering teeth engagement and influence on rotor dynamics

Spline couplings are widely used to transfer rotary motion in rotatory machinery. The local stiffness nonlinearity caused by spline engaging teeth may significantly affect rotordynamics; however, it is usually ignored in most analyses. In this paper, a fully analytical model that can comprehensively account for engaging teeth is first proposed to fast determine the nonlinear stiffness of the spline coupling. Compared with the results of the finite element (FE) model, the results of the proposed model show good agreement but have higher computational efficiency. In addition, the nonlinear mechanism of the spline coupling is revealed, and the effects of the spline length and torque are studied. By introducing the proposed analytical model, a dynamic model of splined rotors is developed. To address the modal solving problem of splined rotors, a modal analysis strategy is proposed based on the Newton-Raphson iteration method. Finally, the modal frequencies, modal shapes and resonance responses of the splined rotor are investigated. The energy-dependent characteristics and softening nonlinearity of splined rotors are highlighted through rotordynamics analysis.

Study of power flow in electricity system using extreme learning machine

Load Flow or Power Flow Analysis in the power system in used to determine the power system parameters such as voltage, current, active power, and reactive power contained in the power grid. The method that has long been used in the calculation of load flow or power flow is the Newton-Raphson iteration method. As for its development, to complete the power flow study, it is carried out by implementing the Artificial Intelligence method, one of which is the Extreme Learning Machine method. This method is used in the simulation of the simple 39 Bus system calculation from IEEE. In this Extreme Learning Machine, the testing analysis is carried out with 2 inputs, 1 hidden layer, 5 neurons, and 2 outputs and the number of datasets is 39 to produce MAE and MAPE respectively 2.02 and 0.76% and with a very fast processing time of 0.010s

On the axisymmetric restricted five-body problem within the frame of variable mass: The convex case

The present manuscript reveals the existence and stability of the libration points (LPs) in the axisymmetric restricted five-body problem (AR5BP) in which mass of the fifth particle varies with respect to time as per Jeans’ law. It has been assumed that the four bodies Pi with masses mi,i=1,2,…,4 (when m3=m4=m˜) form an axisymmetric convex configuration. The system of differential equations which govern the motion of the test particle (whose mass is variable) moving under the gravitational influence of the four primaries, have been presented, indeed, these equations are different from those of the test particle with constant mass in the AR5BP. We have determined the in-plane and out-of-plane LPs along with their linear stability. Furthermore, it is observed that the existence of these LPs depends not only on the angle parameters α and β but also on the parameters occur due to variation in mass namely γ(0<γ≤1) and σ(0≤σ≤2.2, a proportionality constant occurs in Jeans’ law). Moreover, we have investigated the evolution of the regions of possible motion as function of variable mass parameters where the fifth body can move freely. The topology of the basins of convergence (BoC) linked with the LPs as function of σ is unveiled by deploying the bivariate version of Newton-Raphson (NR) iterative method, and, in order to measure the uncertainty of the basins, the basin entropy is also evaluated. The co-relations between the domains of basins of convergence (DoBoC) and the required number of iterations to achieve predefined accuracy, and also with the corresponding probability distributions are illustrated.

Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

Estimating the Catenary Parameter for Catenary Shape Using the Newton Raphson Iterative Method as a Tool for Extended Reach Well Buildup Section Design

The catenary well profile was first used to design extended reach well buildup section in 1985, ever since then a number of wells have been constructed using this profile. It towers over the constant build (circular arc) profile in terms of advantages. Prominent of which is the reduction of torque and drag. This advantage was restrained by the catenary parameter “a”, as “a” determines the shape or trajectory of a catenary shape in any given circumstance. We proffered a solution to estimating the catenary parameter “a” using the Newton-Raphson iteration method for linear equations. This method makes it easy to calculate “a” for almost every desired catenary shape. Also after estimating the values for “a” we went ahead to calculate tensions that will produce that calculated catenary parameter “a” as the parameter is the product of tension at the end of the string and inverse of unit weight. This method of catenary parameter prediction has been used to design overhead electrical cables and predict the extent of sagging of this cables. We used it here to design the path or trajectory of an extended reach well with satisfactory success. Results from the study shows that the use of the Newton-Raphson iterative method for the estimation of catenary parameter “a” for buildup section design of extended reach wells makes it easy for engineers to plan catenary trajectories with available materials and also removes the uncertainties that are inherent in predicting the shape of the trajectory. Keywords : Caternary, String, well, Newton-Raphson, Extended Reach well DOI: 10.7176/JETP/11-5-04 Publication date: October 31 st 2021

Analysis on stationary window of oblique detonation wave in methane-air mixture

In order to obtain the standing conditions and stationary range of oblique detonation wave in methane-air combustible mixture, we use the Newton-Raphson iteration method to solve the perfect gas flow conservation equations of oblique detonation wave based on detonation theory. We investigate the variation laws of the oblique detonation stationary window and internal mechanism under different methane-air equivalence ratio, incoming flow velocity, initial pressure and initial temperature. The oblique detonation polar curve can be separated into three sections, each of which has different flow characteristics corresponding to different wave morphology. Among them, a stationary oblique detonation wave can be formed when the wedge angle is larger than the wedge angle of Chapman-Jouguet state oblique detonation wave, and smaller than the maximum wedge angle corresponding to the oblique detonation wave without detached. The wedge angle range is called the stationary window of the oblique detonation wave. We found that the oblique detonation is more easily formed when the methane-air mixture is under the oxygen-enriched condition, and the range of oblique detonation wave stationary window becomes larger as the incoming velocity increases. The changes of initial pressure and temperature have little influence on the stationary window. The change law of the stationary window of oblique detonation wave corresponds to the change law of Mach number behind CJ oblique detonation wave. In addition, the standing conditions are mainly related to the coupling of the incoming mixture kinetic energy and heat release.

Photovoltaic Maximum Penetration Limits on Medium Voltage Overhead and Underground Cable Distribution Feeders: A Comparative Study

This paper investigates the maximum photovoltaic (PV) penetration limits on both overhead lines and underground cables medium voltage radial distribution system. The maximum PV penetration limit is estimated considering both bus voltage limit (1.05 p.u.) and feeder current ampacity (1 p.u.). All factors affect the max PV penetration limit are investigated in detail. Substation voltage, load percentage, load power factor, and power system frequency (50 Hz or 60 Hz) are analyzed. The maximum PV penetration limit associated with overhead lines is usually higher than the value associated with the underground cables for high substation voltage (substation voltage = 1.05 and 1.04 p.u.). The maximum PV penetration limit decreases dramatically with low load percentage for both feeder types but still the overhead lines accept PV plant higher than the underground cables. Conversely, the maximum PV penetration increases with load power factor decreasing and the overhead lines capability for hosting PV plant remains higher than the capability of the underground cables. This paper proved that the capability of the 60-Hz power system for hosting the PV plant is higher than the capability of 50 Hz power system. MATLAB software has been employed to obtain all results in this paper. The Newton-Raphson iterative method was the used method to solve the power flow of the investigated systems.

A Comparison of Generalized Unified Power Flow Controller and Load Tap Changing Transformer for Voltage Stability Enhancement in a Power System

The continuous increase in power demand and huge power losses in modern power systems have been a growing concern to power utilities. Such phenomenon often results in epileptic power supply, power system instability, supply fluctuations and security problems in many parts of the globe. Identification of suitable places for the installation of reactive power compensators to minimize voltage drop and system power losses in a power system becomes imperative. In this paper, the Newton-Raphson iterative method was used for the power flow solution of the 28 bus Nigerian 330KV grid system. The Generalized Unified Power flow Controller (GUPFC) is installed at identified weak load buses of the Nigerian 28-bus power system to reduce the losses and voltage drop of the system. A comparative analysis of the GUPFC with Load Tap Changing Transformers (LTCT) is also performed. Result obtained shows that the GUPFC can largely (effectively) improve the system power stability and selectively balance the power flow of multi-lines power flows when placed at identified weak buses compared with LTCT. Thus, GUPFC can be used to reduce overall power losses along transmission lines as well as improve stability overall reliability of the power grid system.

Pencegahan Penyakit Kusta di Lingkungan Hutan Tropis Lembab Kalimantan Melalui Pemodelan Geographically Weighted Poisson Regression

Geographically Weighted Poisson Regression (GWPR) model is a regression model developed from Poisson regression which is applied to spatial data. Parameter estimation of the GWPR model is done at each observation location using spatial weighting. This study goal is to obtain the GWPR model and the factors influencing the number of leprosy cases in each regency(municipality) on Kalimantan Island in 2018. Spatial weighting was obtained by using the adaptive bisquare kernel function and optimal bandwidth was determined by using Generalized Cross-Validation (GCV) criteria. The data of this study was secondary data namely the number of leprosy cases in 56 regency on Kalimantan Island in 2018. The parameter estimation method of GWPR model is Maximum Likelihood Estimation (MLE). The results of analysis showed that maximum likelihood estimator is obtained by using the Newton-Raphson iterative method and the factors affecting the number of leprosy cases in each regency were different and locally. The factors influencing locally were the number of health facilities, the number of health workers, the number of male population and population density.

Analisis Faktor-Faktor Yang Berpengaruh Terhadap Pencemaran Air Sungai Mahakam Menggunakan Pemodelan Geographically Weighted Logistic Regression Pada Data Dissolved Oxygen

Geographically Weighted Logistic Regression (GWLR) model is a local model of the logistic regression model applied to spatial data. Parameter estimation is performed at each observation location using spatial weighting. The spatial weighting is calculated by using an adaptive tricube function and bandwidth optimum was obtained based on Generalized Cross Validation (GCV) criteria. The purpose of this study was to obtain a GWLR model on the water pollution indicator Dissolve Oxygen (DO) in Mahakam River in East Kalimantan Province and to find factors affecting the probability of the Mahakam River water was not polluted based on DO indicator. The research data is secondary obtained from Environmental Department of East Kalimantan. The parameter estimation method was Maximum Likelihood Estimation (MLE). The research result showed that the closed form of ML estimator could not be found analytically and it can be approximed by using Newton-Raphson iterative methods. Based on the result of partial hypothesis test, the factors influencing the probability of the Mahakam River water was not polluted is different for every observation location. They were phosphate consentration, total dissolved solid and nitrite consentration. The factor influencing globally was total dissolved solid.

Analisis Faktor-Faktor yang Mempengaruhi Jumlah Kasus Tuberkulosis di Indonesia Menggunakan Model Geographically Weighted Poisson Regression

Tuberculosis is a contagious disease suffered by humans caused by mycobacterium tuberculosis bacteria. Tuberculosis in Indonesia must be eradicated both preventive and treatment. One effort that can be given to the community to reduce tuberculosis cases is by providing information on the factors that influence tuberculosis cases through Geographically Weighted Poisson Regression (GWPR) modeling. The number of tuberculosis cases in Indonesia is a count data with a small chance of occurrence so that it is suspected to have a Poisson distribution. Cases of tuberculosis are spatial data (spatial heterogeneity). The purpose of this study is to determine the GWPR model of the number of tuberculosis cases in Indonesia and determine the factors that influence tuberculosis cases in Indonesia. The research data are secondary data obtained from the Indonesian Ministry of Health. Parameter estimation method is Maximum Likelihood Estimation (MLE). Spatial weighting is calculated by using the Adaptive Gaussian weighting function and the optimum bandwidth is determined by using the Cross-Validation (CV) criteria. The research results showed that the exact Maximum Likelihood (ML) estimator could not be obtained analytically and the approximation of ML estimator was obtained by using the Newton-Raphson iterative method. Based on the results of the parameter testing of GWPR model, it was concluded that the factors affecting the number of tuberculosis cases were local and varied in 34 provinces. The factor affecting locally are the number of poor people, the percentage of houses unfit for habitation, the percentage of districts/cities that do not have a PHBS policy and the percentage of TPM not meeting health requirements, meanwhile factors influencing globally are the number of poor people.