Newton-Raphson Algorithm Research Articles

A standard thermodynamic-based extension of the Modified Cam-Clay soil model and its applications

For mechanical behaviours of granular soils considered here (sands, silts and stiff clays), we propose a thermodynamic-based formulation which relies on the Modified Cam-Clay constitutive model. To this end, and in the framework of Generalized Standard Materials (GSM) framework, we introduce a free energy and a yield criterion (or equivalently a dissipation potential) which account for an isotropic nonlinear elastic behaviour and a volumetric hardening law. Based on available works with coupled hardening laws for von Mises plasticity, we propose for pressure-sensitive materials a new nonlinear deviatoric hardening preserving the well-known critical state existence.Taking advantage of the GSM framework, we establish an incremental variational formulation of the model whose solution obeys to a minimization principle. This has required an approximation of the incremental dissipation. The resulting equations are detailed for the use of an implicit resolution scheme with a standard Newton–Raphson algorithm. The constitutive model parameters are calibrated on a pool of experimental data on isotropic, shearing and triaxial tests on loose sand specimen. The investigations of the model responses allow to better predict the nonlinear regimes of soils specimen on monotonic and cyclic loading paths. Numerical finite element simulations finally underline the predictive capabilities of the model on structures.

An advanced beam-column element for analysis of frames in fires

A novel advanced fiber beam-column element, which utilizes the stability functions and the fiber distributed plasticity model to capture the geometric and material nonlinearities, is proposed for the first time to predict the nonlinear inelastic thermo-mechanical behaviors of framed structures in fires by using the Fortran programming language. The element stiffness matrix is integrated via the Gauss-Lobatto numerical integration scheme, and geometric nonlinearity is considered by using the stability functions and a geometric matrix for P-δ and P-Δ effects, respectively. A nonlinear thermal incremental-iterative solution scheme based on the Newton-Raphson algorithm is also developed and operated to solve the nonlinear problems due to thermal expansion and material degradation in fires. The proposed element has the novelty of simultaneously taking advantage of the benefits of the stability functions with low computational cost and the capacity of tracing the gradual space spread of plasticity of the fiber model. At the moment it is not possible for the normal beam-column element in commercial software that allows for considering the effects of temperature to provide both low computational cost and accurate representation of the spread of plasticity. To demonstrate the proposed element's capacity in dealing with various scenarios, it will be investigated with both uniform fire, compartment fire, and localized fire with members made of steel and concrete. The accuracy of the proposed element is verified by comparing the obtained results with those from test data and the Abaqus program. Results show that the proposed element can provide exact solutions with excellent computational performance, which is more significantly effective than the traditional finite element in commercial software like Abaqus.

Inference and optimal censoring scheme for a competing-risks model with type-II progressive censoring

ABSTRACT For statistical inference of competing risks under type-II progressive censoring, lifetimes are modeled by an inverted exponential Rayleigh distribution, which allows the use of a non-monotonic hazard function. Maximum-likelihood estimators for all parameters exist and are unique. The Newton-Raphson algorithm and maximum stochastic expectation each provide estimates. Confidence intervals result from the Fisher matrix and the asymptotic normality of maximum-likelihood estimators. For small samples, the Bootstrap estimators of the parameters do not need to be asymptotically normal. In addition, the Monte Carlo method with the Metropolis-Hastings algorithm and importance sampling allow for Bayesian estimation, with the associated highest posterior-density intervals. The Bayesian method takes account of prior information, contrary to the frequentist method. The Bootstrap method improves the precision of the estimation, especially in the case of small sample sizes. The estimated range obtained by Bootstrap is between 20% and 60% smaller than that obtained by maximum likelihood. Frequentist and Bayesian estimations using the inverted exponentiated Rayleigh distribution under type-II progressive censoring allow for fitting empirical mouse mortality data and obtaining parameter estimates of this distribution. A quantile-dependent criterion and a quantile-independent criterion are used to determine the optimal censoring and to design the experiment.

A Metaheuristic Approach to Parameter Estimation of a Flexible Parametric Mixture Cure Rate Model with Interval-Censored Data

A flexible parametric mixture cure model, called bi-lognormal cure rate model or simply BLN model, is defined and studied. The BLN model can be effectively used to analyze survival dataset in the presence of long-term survivors, especially when the dataset presents the underlying phenomenon of latent competing risks or when there is evidence that a bimodal hazard function is appropriated to described it, which are advantages over other cure rate models found in the literature. We discuss the maximum likelihood estimation for the model parameters considering interval-censored data through the differential evolution algorithm that is a nature-inspired computing metaheuristic used for global optimization of functions defined in multidimensional spaces. This approach is also used because the likelihood function of the model is multimodal and the direct application of gradient methods in this case is not ideal, since such methods are local search methods with a high chance of getting stuck at a local maximum when the starting point is chosen outside the basin of attraction of a global maximum. In addition, a simulation study was implemented to compare the performance of differential evolution algorithm with the performance of the Newton-Raphson algorithm in terms of bias, root mean square error, and the coverage probability of the asymptotic confidence intervals for the parameters. Finally, an application of the BLN model to real data is presented to illustrate that it can provide a better fit than other mixture cure rate models.

An Adaptive Method for Likelihood Optimization in Linear Mixed Models Under Constrained Search Spaces

Linear mixed effects models are highly flexible in handling correlated data by considering covariance matrices that explain variation patterns between and within clusters. For these covariance matrices, there exist a wide list of possible structures proposed by researchers in multiple scientific areas. Maximum likelihood is the most common estimation method in linear mixed models and it depends on the structured covariance matrices for random effects and errors. Classical methods used to optimize the likelihood function, such as Newton-Raphson or Fisher's scoring, require analytical procedures to obtain parametrical restrictions to guarantee positive definiteness for the structured matrices and it is not, in general, an easy task. To avoid dealing with complex restrictions, we propose an adaptive method that incorporates the so-called Hybrid Genetic Algorithms with a penalization technique based on minimum eigenvalues to guarantee positive definiteness in an evolutionary process which discards non-viable cases. The proposed method is evaluated through simulations and its performance is compared with that of Newton-Raphson algorithm implemented in SAS® PROC MIXED V9.4.

Model-based cylinder radius and permeability estimation using eddy current testing

The material quality of metallic cylinders including microstructure is reflected in their physical properties. Eddy current testing techniques play an important role in the measurement of metallic cylinder measurement. In this paper, a cylinder radius and permeability estimation method is proposed based on the combined analytical and optimisation method. The Dodd and Deeds analytical model has been first simplified, which suggests an approximate linear relationship between the cylinder radius, permeability and coil inductance. Based on the proposed relation, the pre-estimated radius and permeability are used as the initial guess for the modified Newton–Raphson algorithm to solve the least squares problem between the measured and calculated coil inductance spectra. This method avoids the local minimum issue that occurs otherwise, to some extent. The effectiveness of the proposed method has been evaluated by numerical simulations and experiments, which indicates that fast estimation can be achieved with high accuracy.

MANA Formulation Based Load Flow Solution for DC Distribution Networks

This paper presents an efficient load-flow (LF) solution method for direct current distribution networks (DC-DNs). The principles of this method are based on the modified-augmented-nodal-analysis (MANA) formulation and Newton-Raphson (NR) algorithm. The guaranteed convergence and quadratic convergence conditions are also formulated using Kantorovich’s theorem. The modified IEEE 33 bus test feeder is simulated to test the proposed method and compare its performance with Laplacian Matrix based LF methods, Holomorphic Embedding LF method (HE-LFM) and classical Gauss-Seidel (GS) solution. Apart from the comparisons with these numerical methods the accuracy of the proposed method is also validated with Electromagnetic Transients (EMT) results. The proposed method offers much better convergence properties with a faster simulation speed.

Consumer willingness to pay for vanilla using contingent valuation analysis

Objective: To show the willingness to pay a premium for vanilla from the Totonacapan region through contingent valuation analysis for the strengthening of vanilla in the local market. Design/methodology/approach: To contingent valuation methodology (CV) was followed to estimate the WTP, based on consumer surveys in the Totonacapan region. The information analysis was carried out by the XLSTAT 2019 software through logistic regression of the willingness to pay data in a binary response with a confidence interval of 95% and with 100 iterations, and maximization of the likelihood function with the Newton-Raphson algorithm. Results: The results indicate that 55.63% of the consumers agree that certification increases the potential to pay a premium; the accessibility of vanilla is important for 66.56% of consumers; previous experience with the brands and product behavior is paramount for 56.95% of all consumers; regarding the origin of vanilla, it is important for 65.23% of consumers. Findings/conclusions: Production by small-scale local producers is an appreciated quality because it is related with the symbolic dimension and is appreciated by 68.54% of consumers.

Use of Inverter-Based Air Conditioners to Provide Voltage Regulation Services in Unbalanced Distribution Networks

The large-scale integration of photovoltaic generation and electric vehicles results in over-voltage, under-voltage, and voltage unbalance problems in three-phase distribution networks. The power consumption of the air conditioners (ACs) is large among the daily electrical appliances and can be regulated to provide voltage regulation services. To protect occupants' privacy and utilize the existing dispatch strategy of the battery, we propose a thermal battery equivalent model of the inverter-based AC to regulate the active power and provide a voltage regulation service. Moreover, an improved Newton-Raphson power-flow algorithm is developed to reduce the computational burden. The affinity propagation method is applied to cluster ACs according to different operating states. Thus, the ACs' operating frequencies are adjusted to reset the corresponding operating power. The feasibility of the thermal battery equivalent model and voltage regulation algorithm is verified based on case studies utilizing the revised IEEE 33-node three-phase power distribution network.

Electrical load flow analysis of Auchi distribution network without load shedding

The occurrence of loadshedding under normal operating condition in Distribution Network caused a lot of inconveniences to the consumer. However, there is need to examine the state of the distribution network to know the performance without load shedding under normal condition. This research examines the state of Auchi distribution network without load shedding. In order to achieve the aim of the research data was obtained from the distribution company, the modelling of the distribution network obtained was done using ETAP and the load flow simulation was done using Newton Raphson Algorithm to determine the power flow in the network, Bus voltage, losses along the line and transformer losses. The results of the study show that at 80% loading of the transformers in the network, the voltage supply to the consumer is bad under normal condition, since the two out of three 33 kV bus voltages is below the acceptable range of plus or minus 5% of the nominal voltage. Likewise, almost all 11 kV and 0.415kV voltages in the network is below the acceptable limit of plus or minus 10% of the nominal voltage. Furthermore, the result indicates that active power loss in the network is 0.2MW which is very high. This research therefore recommends that the voltage profile of AUCHI distribution network needs improvement in order to improve the quality of supply. Also, since the supply from the grid is be allocated based on the generating capacity this research also recommends that DISCO in charge of Auchi distribution network should also considering the usage of DG in the network which can perform a dual purpose of voltage improvement and addition of power supplied.

The Influence of GPL Reinforcements on the Post-Buckling Behavior of FG Porous Rings Subjected to an External Pressure

The work focuses on the post- buckling behavior of functionally graded graphene platelet (FG-GPL)-reinforced porous thick rings with open-cell internal cavities under a uniform external pressure. The generalized rule of mixture and the modified Halpin–Tsai model are here used to evaluate the effective mechanical properties of the ring. Three types of porosity patterns are assumed together with five different GPL distributions as reinforcement across the ring thickness. The theoretical formulation relies on a 2D-plane stress linear elasticity theory and Green strain field in conjunction a virtual work principle to derive the nonlinear governing equations of the post-buckling problem. Unlike the simple ring models, 2D elasticity considers the thickness stretching. The finite element model combined with an iterative Newton–Raphson algorithm is used to obtain the post-buckling path of the ring up to the collapse. A systematic investigation evaluates the effect of the weight fraction of nanofillers, the coefficient of porosity, porosity distribution, and the GPLs distribution on the deep post-buckling path of the ring. Based on the results, it is found that the buckling value and post-buckling strength increase considerably (by approximately 80%) by increasing the weight fraction of the nanofiller of about 1%.

Time series reconciliation through flexible least squares estimation

In the paper we optimize a procedure developed recently to reconcile time series by flexible least squares. In the previous version of the procedure the author assumed prior knowledge of the weighting parameter μ of Kalaba and Tesfatsion’s so-called “incompatibility cost function”. In the new version, this parameter is estimated from the sample using an iterative method based on the Newton-Raphson algorithm. We test the improved method by reconciling the monthly growth rates of the Monthly Economic Activity Estimator (EMAE) of Argentina with the quarterly growth rates of the Gross Domestic Product. The results suggest that optimal levels of μ would be close to 1 (thevalue suggested by Kalaba and Tesfatsion as prior value) but estimating μ from the sample instead of keeping it fixed at 1 hardly modifies the reconciled series.

Implementing Newton-Raphson Method Algorithm in 6 Programming Languages’ Solution to Van Der Waals Equation of State

Newton’s method can be implemented for the Van der Waals equation of state (VDW EOS) and its derivatives. Application of programming language in chemical engineering is not new but however limited in practice, as it is not included in the curriculum of students of tertiary institutions across the globe. Finding roots through iteration for the VDW EOS can be described as interesting and simple using C++, FORTRAN, R, MATLAB, Java and Python languages; even though a perfect programming language does not exist. In this work, the coding syntax in the six languages employed to solve parameters in VDW EOS differs in terms of simplicity and user-friendliness. Notwithstanding, all of them proves to be an adaptable software, capable of solving chemical engineering problems leading to nonlinear relations

An Improved Slicing Technique for Finite Line Contacts in the Modeling of Rolling Element Bearings

Abstract Mechanical system often involves the finite line contact of key components such as rolling element bearings and gear pairs. Different contact models have been developed to predict the load–displacement relationship and contact pressure distribution, but there usually exists a tradeoff between the accuracy of simulation results and computational cost. An improved slicing technique is presented in this work. According to the half-space theory, a tri-linear fitting model is developed to express the load–displacement relationship and coupling behavior in slices of contact region, which is originally controlled by a spatial convolution. The improved slicing technique is thus formulated based on the tri-linear model. A modified Newton–Raphson algorithm is adopted to solve the free boundary problem of the improved slicing technique. The improved slicing technique is validated to be able to correctly predict the load–displacement relationships and the contact pressure distributions of different contact profiles, especially for contact pressure concentrations which other slicing techniques are unable to predict accurately. The computation speed of the proposed method is much faster than the semi-analytical method and is of the same order of other slicing technique. The high accuracy and low computational cost enable the proposed method to be applied in the on-line calculation of rolling element bearings and other sophisticated mechanical systems.

Numerical Modeling of Static Hysteresis Phenomena Using a Vector Extension of the Loss Surface Model

This paper proposes a vector extension of the Loss Surface model for numerically modelling hysteretic phenomena in electromagnetic device simulations with isotropic ferromagnetic materials. The vectorization strategy is based on Mayergoyz’s approach. The developed model has been implemented in the 2D finite element code. To handle the non linear problem solved with the Newton-Raphson algorithm, a suitable method is proposed for the approximation of the reluctivity tensor. Several test cases from TEAM problem 32 were investigated for validation. The results are in good agreement with measurements combining accuracy and short computation times.

A Fast and Efficient Estimation of the Parameters of a Model of Accident Frequencies via an MM Algorithm

In this paper, we consider a multivariate statistical model of accident frequencies having a variable number of parameters and whose parameters are dependent and subject to box constraints and linear equality constraints. We design a minorization-maximization (MM) algorithm and an accelerated MM algorithm to compute the maximum likelihood estimates of the parameters. We illustrate, through simulations, the performance of our proposed MM algorithm and its accelerated version by comparing them to Newton-Raphson (NR) and quasi-Newton algorithms. The results suggest that the MM algorithm and its accelerated version are better in terms of convergence proportion and, as the number of parameters increases, they are also better in terms of computation time.

B2C3NetF2: Breast cancer classification using an end‐to‐end deep learning feature fusion and satin bowerbird optimization controlled Newton Raphson feature selection

AbstractCurrently, the improvement in AI is mainly related to deep learning techniques that are employed for the classification, identification, and quantification of patterns in clinical images. The deep learning models show more remarkable performance than the traditional methods for medical image processing tasks, such as skin cancer, colorectal cancer, brain tumour, cardiac disease, Breast cancer (BrC), and a few more. The manual diagnosis of medical issues always requires an expert and is also expensive. Therefore, developing some computer diagnosis techniques based on deep learning is essential. Breast cancer is the most frequently diagnosed cancer in females with a rapidly growing percentage. It is estimated that patients with BrC will rise to 70% in the next 20 years. If diagnosed at a later stage, the survival rate of patients with BrC is shallow. Hence, early detection is essential, increasing the survival rate to 50%. A new framework for BrC classification is presented that utilises deep learning and feature optimization. The significant steps of the presented framework include (i) hybrid contrast enhancement of acquired images, (ii) data augmentation to facilitate better learning of the Convolutional Neural Network (CNN) model, (iii) a pre‐trained ResNet‐101 model is utilised and modified according to selected dataset classes, (iv) deep transfer learning based model training for feature extraction, (v) the fusion of features using the proposed highly corrected function‐controlled canonical correlation analysis approach, and (vi) optimal feature selection using the modified Satin Bowerbird Optimization controlled Newton Raphson algorithm that finally classified using 10 machine learning classifiers. The experiments of the proposed framework have been carried out using the most critical and publicly available dataset, such as CBIS‐DDSM, and obtained the best accuracy of 94.5% along with improved computation time. The comparison depicts that the presented method surpasses the current state‐of‐the‐art approaches.

Nonlinear micromechanical modeling of fully coupled piezo-elastic composite under large deformation and high electric field

This paper presents mathematical modeling and predictions of effective nonlinear electro-mechanical behavior of piezoelectric materials under large deformation and high electric field. The heterogeneous inclusion problem is extended to investigate the fields dependent electro-elastic behaviors under high fields. The associated strain field dependent Green tensors are introduced. The field dependent interaction tensors, related to Eshelby’s tensors, are explicitly formulated and used to derive micromechanical models based on the Mori–Tanaka approach and the self-consistent model. Due to electric-strain field dependence nonlinear algebraic tensors equations are resulted. Iterative incremental schemes based on the Newton–Raphson algorithm are elaborated and explicit semi-analytical formulations of electric-strain field dependent effective electro-elastic moduli of piezoelectric multi-phase composites are obtained for various inclusion types. Strain and electric field’s effects on effective properties can be analyzed for various electro-elastic composites. Numerical results of field dependent effective electro-mechanical properties are given for several inclusion’s volume fraction and shapes as well as types of matrix and inclusions phases.

Efficient GPU implementation of a Boltzmann-Schrödinger-Poisson solver for the simulation of nanoscale DG MOSFETs

A previous study by Mantas and Vecil (Int J High Perform Comput Appl 34(1): 81–102, 2019) describes an efficient and accurate solver for nanoscale DG MOSFETs through a deterministic Boltzmann-Schrödinger-Poisson model with seven electron–phonon scattering mechanisms on a hybrid parallel CPU/GPU platform. The transport computational phase, i.e. the time integration of the Boltzmann equations, was ported to the GPU using CUDA extensions, but the computation of the system’s eigenstates, i.e. the solution of the Schrödinger-Poisson block, was parallelized only using OpenMP due to its complexity. This work fills the gap by describing a port to GPU for the solver of the Schrödinger-Poisson block. This new proposal implements on GPU a Scheduled Relaxation Jacobi method to solve the sparse linear systems which arise in the 2D Poisson equation. The 1D Schrödinger equation is solved on GPU by adapting a multi-section iteration and the Newton-Raphson algorithm to approximate the energy levels, and the Inverse Power Iterative Method is used to approximate the wave vectors. We want to stress that this solver for the Schrödinger-Poisson block can be thought as a module independent of the transport phase (Boltzmann) and can be used for solvers using different levels of description for the electrons; therefore, it is of particular interest because it can be adapted to other macroscopic, hence faster, solvers for confined devices exploited at industrial level.

Buoyancy-driven heat transfer performance, vorticity and fluid flow analysis of hybrid nanofluid within a U-shaped lid with heated corrugated wall

The thermal performance of alumina-copper/water hybrid nanofluid in buoyancy-driven heat transfer of a U-shaped cavity with a heated wavy wall is investigated in detail throughout this manuscript. A three-node triangular finite element method is used to solve the system by considering the Galerkin weighted residual algorithm. A Newton–Raphson algorithm with a damping coefficient is used as the convergence criterion. Numerical and experimental comparisons of previously published results are compared with the present calculations to ensure confidence in the present modeling. The physical representation of the modeling is presented through the streamlines, isotherms, and vorticity distribution. To quantify the overall heat transfer performance, the average and local Nusselt numbers are used for various combinations of parameters. It is found that the higher the cold rib dimension, the undulations, and the amplitudes of the heated corrugated walls produce a higher heat transfer rate. The inclusion of a hybrid nanofluid may inhibit the heat transfer rate when the length of the hot wall exceeds the length of the cold wall. As low as 4% and up to 16% thermal performance increase of utilizing hybrid nanofluid is observed compared to pure water in a wavy U-shaped enclosure.