Iterative Numerical Algorithm Research Articles

Reducing plug flow effect on measured rheological results of cement-based materials: Image analysis and numerical iteration approach

The rheological properties of cement-based materials (CBM) significantly influence their workability and application in construction. Despite the common use of coaxial cylinder rheometers for measuring these properties, challenges arise, particularly at low shear rates due to plug flow within the tested samples. This study aims to investigate the impact of plug flow on rheological property measurements of CBM and proposes strategies to enhance measurement accuracy. An image analysis method and a novel numerical iteration algorithm were proposed in this study to address plug flow effects. Three series fresh cement paste with different fluidities were prepared to conduct the rheological tests. Through the image analysis method, actual shear radii at different rotor speeds were measured. The corresponding rheological parameters were determined and compared using the complete shear assumption, the image analysis method, and numerical iteration algorithm, respectively. The results indicated the great influence of plug flow on rheological results, especially at low shear rates and low fluidities, highlighting the need for its consideration in rheological parameters calculations. Moreover, the proposed numerical iteration algorithm was verified to calculate the incomplete shear state of CBM and improve the measurement accuracy of rheological parameters. The extensions and limitations of the numerical iteration algorithm in its application were discussed further.

Simulation of fiber-induced melt pressure fluctuations within large scale polymer composite deposition beads

The process-structure-property relationship in Large Area Additive Manufacturing (LAAM) technology is an ongoing area of research as the inherent microstructural properties (chiefly fibers and voids) affect the performance of printed parts. Unfortunately, we currently lack adequate understanding of micro void nucleation and evolution during the LAAM and fused deposition modelling (FDM) processes. Modeling of the polymer melt flow during the extrusion process is important in understanding the underlying microstructural formation and associated properties of the print, that determines the part performance in service conditions. In this paper we compute fiber-induced local pressure fluctuations which may promote void formation in the bead’s microstructure. On a macro-scale, we determine flow fields of a purely viscous, Newtonian planar polymer deposition flow through a LAAM nozzle which are utilized on a micro-scale model where we simulate the evolution of a single ellipsoidal fiber along streamlines obtained from the macro-model. On the micro-scale, we determine instantaneous values of the translational and rotational velocities of the rigid ellipsoidal fiber that satisfies a balance of hydrodynamic forces and couples on the fiber’s surface based on a Newton Raphson algorithm and we track the fiber’s motion along the flow path via an explicit numerical iterative algorithm. Model verification is achieved by benchmarking results with solutions from well-known Jeffery’s equation of motion of a particle in homogeneous simple shear flow. We account for rotary diffusivity due to short-range fiber-fiber interaction in the FEA simulation by determining an effective fluid domain size representative of the interaction coefficient of the melt flow through a correlation analysis that yields an equivalent steady state orientation based on the Advani-Tucker equation. We also consider different possible motions of the fiber along individual LAAM flow paths from a given set of random initial fiber conditions to determine pressure bounds on the fiber surface along each streamline. For improved computational efficiency, calculations are carried out with respect to the fiber’s local coordinate axes to overcome the rigor of adaptive remeshing during the quasi-transient analysis. Results show low pressure extremes near the fiber’s surface which varies across the printed bead as well as through its thickness. Discussion is provided to gain insight into the effect of low-pressure extremes on micro void formation, particularly at the nozzle exit and during die swell/expansion.

An accelerated scheme for solving inhomogeneous elasticity in phase-field method and application to Ni-based multi-component alloys

On the way towards realistic predictions of various material properties for engineering structural materials, efficient computational simulations of microstructural evolution play an indispensable role. In the present work, an in-house phase-field code with inhomogeneous elasticity has been developed aiming to deal with precipitation processes for multi-component alloys with high efficiency. Two different numerical iterative algorithms, named as Model A and B, are implemented to solve inhomogeneous elastic equations. The resulting simulated morphology and energy evolutions under different conditions show consistency for these two algorithms. In order to perform simulation efficiently, a parallel technique based on CUDA (Computer Unified Device Architecture) architecture is used, which greatly improves the computational efficiency. After estimating the computational efficiency of different acceleration techniques for different grid sizes, Model A is extended to simulate concentration and morphology evolutions in the precipitation and rafting processes of γ′ phase in a Ni-based five-component alloy of Ni−Co−Al−Mo−W. Meanwhile, the CALPHAD method and related databases are linked to provide thermodynamic and diffusivity data. Finally, the computation costs of the parallel technique for different simulation scales are explored, testifying that this technique is capable of performing larger scale simulations for multi-component multi-phase structural materials.

A self-adaptive relaxed primal-dual iterative algorithm for solving the split feasibility and the fixed point problem

In this paper, we introduce a new numerical simulation iterative algorithm to solve the split feasibility problem and the fixed point problem with demicontractive mappings. Our algorithm mainly involves primal-dual iterative, relaxed projection, inertial technique and self-adaptive step size. Under reasonable conditions, the strong convergence of our algorithm is established. Moreover, we provide some numerical simulation examples to demonstrate the efficiency of our iterative algorithm compared to existing algorithms in the other literature.

Ultracycles consisting of macrocycles

Presented here is a one-pot strategy starting from rationally designed macrocyclic precursors for the diverse construction of sophisticated ultracycles. The type and amount of the base were found to significantly influence the macrocyclization outcome. The use of 4.0 equiv. CsF resulted in ultracycles of both types A and B while the presence of CsF larger than 6.0 equiv. produced only type B ultracycles. Existence of anion template increased the total yields and affected the distribution of the ultracycles. The ultracycles can accommodate large organic dicarboxylates anions via multiple anion–π and hydrogen bonds, and show selectivity to the size-matched heptanedioate (C72−). Based on all possible species and relevant equilibrium constants as well as material and charge balances, a numerical iterative algorithm was developed and applied to fit the association constants of B2H with dicarboxylates from glutarate (C52−) to octanedioate (C82−), which gave association constants up to 103 L/mol.

Bifurcation and Chaotic Behavior of Duffing System with Fractional-Order Derivative and Time Delay

In this paper, the abundant nonlinear dynamical behaviors of a fractional-order time-delayed Duffing system under harmonic excitation are studied. By constructing Melnikov function, the necessary conditions of chaotic motion in horseshoe shape are detected, and the chaos threshold curve is obtained by comparing the results obtained through the Melnikov theory and numerical iterative algorithm. The results show that the trend of change is the same, which confirms the accuracy of the chaos threshold curve. It could be found that when the excitation frequency ω is larger than a certain value, the Melnikov theory is not valid for these values. Furthermore, by numerical simulation, some numerical results are obtained, including phase portraits, the largest Lyapunov exponents, and the bifurcation diagrams, Poincare maps, time histories, and frequency spectrograms at some typical points. These numerical simulation results show that the system exhibits some new complex dynamical behaviors, including entry into the state of chaotic motion from single period to period-doubling bifurcation and chaotic motion and periodic motion alternating under the necessary condition of chaotic occurrence. In addition, the effects of time delay, fractional-order coefficient, fractional order, linear viscous damping coefficient, and linear stiffness coefficient on the chaotic threshold curve are discussed, respectively. Those results reveal that there exist abundant nonlinear dynamic behaviors in this fractional-order system, and by adjusting these parameters reasonably, the system could be transformed from chaotic motion to non-chaotic motion.

Modeling the dynamic magneto-mechanical response of magnetic shape memory alloys based on Hamilton’s principle: The numerical algorithm

This paper is the second part of a variational modeling work on the dynamic magneto-mechanical response of magnetic shape memory alloys (MSMA). In the first part of this series work, the governing equations system for modeling the dynamic response of MSMA samples has been derived based on Hamilton’s principle, which contains the Maxwell’s equations, the magneto-mechanic equations, the evolution equations of internal variables and the twin interface motion criteria. In this paper, we aim to conduct comprehensive numerical simulations on the dynamic magneto-mechanical response of MSMA samples. To solve the governing system, the space–time finite element method is applied and a double-loop iterative numerical algorithm is proposed. By using this algorithm, the independent variables in the governing system and the motion of twin interfaces in the MSMA sample can be determined separately and iteratively. Besides that, a specific discretization of the sample is adopted to simplify the calculation of variant state distribution in the sample. To show the efficiency of the numerical algorithm, the magneto-mechanical response of a MSMA sample in stress-assisted dynamic field loading tests and field-assisted dynamic mechanical loading tests are studied. Based on the numerical results, some global response curves of the MSMA sample are plotted, which show good consistency with the experimental results. Furthermore, the current configuration of the sample and the distributions of some important physical fields in the sample can be simulated. The current work will be helpful for the design of novel actuators or energy harvesters with MSMA.

Deep fuzzy mapping nonparametric model for real-time demand estimation in water distribution systems: A new perspective.

Hydraulic modeling has been recognized as a valuable tool for improving the design, operation, and management of water distribution systems (WDSs) as it allows engineers to simulate and analyze behaviors of WDSs in real time and help them make scientific decisions. The informatization of urban infrastructure has motivated the real-time fine-grained control of WDSs, making it one of the hotspots in recent years, thereby putting higher requirements on WDS online calibration in terms of efficiency and accuracy, especially when dealing with large-complex WDSs. To achieve this purpose, this paper proposes a novel approach (i.e., deep fuzzy mapping nonparametric model (DFM)) from a new perspective for developing a real-time WDS model. To our knowledge, this is the first work that considers uncertainties in modeling problems using fuzzy membership functions and establishes the precise inverse mapping from pressure/flow sensors to nodal water consumption for a given WDS based on the proposed DFM framework. Unlike most traditional calibration methods that require time to optimize model parameters, the DFM approach has a unique analytical solution derived through rigorous mathematical theory, thus the DFM is computationally fast as a result of sensibly handling the problems whose solutions typically require iterative numerical algorithms and large computational time. The proposed method is applied to two case studies and the results obtained show that it can produce a real-time estimation of nodal water consumption with higher accuracy, computational efficiency, and robustness relative to traditional calibration methods.

Radiofrequency Sensing Method and Algorithm of Inhomogeneous Conductive Structures

The paper proposes a method and algorithm for frequency probing of the internal inhomogeneous structure of electrically conductive objects based on the skin effect for diagnostics and control. The essence of the method consists in frequency control of electromagnetic field penetration depth into an electrically conductive object, and according to the measured frequency characteristic of the surface impedance, the profiles of electrophysical parameters characterizing the structural properties of the medium under study. An electrical model of an inhomogeneous medium with distributed RL parameters has been developed on the basis of electrodynamic presentations. The relationship of resistance and inductance linear parameters of the electrical model with the local parameters of the conductive medium results from their relationship with the electrical resistivity and magnetic permeability of the medium. The mathematical model of an inhomogeneous conducting medium is based on the Riccati equation with respect to the impedance characteristics of the medium. The mathematical statement of the probing problem is formulated as an inverse operator problem solution of mathematical physics. A numerical iterative algorithm for inhomogeneous medium frequency sensing based on Tikhonov regularized solution of the inverse problem is proposed. The proposed algorithm can also be extended to probe the internal structure of semiconductor and low-conducting objects containing a capacitive component in the impedance. The results of numerical simulation of the proposed algorithm for various distributions of inhomogeneity in the frequency characteristics of the impedance, measured with a known error, are presented. Solutions to various control and measurement problems in thermophysical applications based on the proposed method are given in the patents of the authors.

Variational Data Assimilation and its Decoupled Iterative Numerical Algorithms for Stokes–Darcy Model

Variational Data Assimilation and its Decoupled Iterative Numerical Algorithms for Stokes–Darcy Model

A species richness estimator for sample‐based incidence data sampled without replacement

Abstract The accurate estimation of species richness in a target region is still a statistical challenge, especially in a highly heterogeneous community. Most richness estimators have been developed based on the assumption that data are randomly sampled with replacement or that data are sampled from an infinite population. However, in reality, most sampling schemes in the field are implemented as sampling without replacement (SWOR). As such, estimators derived based on sampling with replacement may cause overestimation as the sampling fraction increases and not converge to the true richness as the sampling fraction approaches one. Sample‐based incidence data, in which the sampling unit is a plot, and only the presence or absence of a species in each chosen plot is recorded, is one of the most commonly used data types for assessing species diversity in ecological studies. In this manuscript, according to sample‐based incidence data collected through SWOR, a new richness estimator is proposed using a truncated beta‐binomial mixture model. The new estimator was obtained through the moment approach, which avoids using iterative numerical algorithms for parameter estimation and presents a closed‐form estimator as an alternative to the maximum likelihood method. Although the newly proposed method is a parametric‐based richness estimator, similar to nonparametric estimators, only the rare species in the sample (i.e. the frequencies of uniques and duplicates) are required to estimate undetected richness. Based on the hypothetical models, the statistical performances of the proposed estimator are evaluated under varying degrees of heterogeneity and different mean species detection rates. Compared to other widely used nonparametric and parametric estimators, the simulation results indicate that the proposed estimator has a smaller bias and lower root mean square error when the sampling fraction is greater than 10%, particularly in highly heterogeneous communities. In addition, one ForestGEO permanent forest plot dataset is used to evaluate and compare the proposed approach with other estimators discussed in the study. The results demonstrate that the proposed estimator, in comparison to other widely used estimators, produces less biased estimate of true richness, along with more accurate 95% confidence interval.

Closed-Form Implicit Models for Efficient Simulation of Power Electronics

This document describes novel closed-form implicit (CF-implicit) models of switched-mode power converters, which feature implicit integration but require no iterative numerical solving algorithm for evaluation because they are explicitly solved in CF prior to model execution. The derived models capture the large-signal dynamic behavior of the power converters, so their use and accuracy are not limited to any one set of operating conditions. These models can be directly implemented in any computational environment, including directly on an existing embedded controller. Since no iterative solver is required, the models are highly computationally efficient and have a very predictable worst case execution time (WCET), which makes them especially suitable for real-time (RT) modeling applications, such as hardware-in-the-loop (HIL) simulation or digital twins (DTs). The model derivation process is demonstrated by example on a two-stage power converter, and computational expense is analyzed. A discussion of model error is also included.

Energy‐efficient semi‐supervised learning framework for subchannel allocation in non‐orthogonal multiple access systems

AbstractNon‐orthogonal multiple access (NOMA) is considered a key candidate technology for next‐generation wireless communication systems due to its high spectral efficiency and massive connectivity. Incorporating the concepts of multiple‐input‐multiple‐output (MIMO) into NOMA can further improve the system efficiency, but the hardware complexity increases. This study develops an energy‐efficient (EE) subchannel assignment framework for MIMO‐NOMA systems under the quality‐of‐service and interference constraints. This framework handles an energy‐efficient co‐training‐based semi‐supervised learning (EE‐CSL) algorithm, which utilizes a small portion of existing labeled data generated by numerical iterative algorithms for training. To improve the learning performance of the proposed EE‐CSL, initial assignment is performed by a many‐to‐one matching (MOM) algorithm. The MOM algorithm helps achieve a low complex solution. Simulation results illustrate that a lower computational complexity of the EE‐CSL algorithm helps significantly minimize the energy consumption in a network. Furthermore, the sum rate of NOMA outperforms conventional orthogonal multiple access.

Research on fast forward kinematics of an offset-type flexible micro-motion Delta parallel mechanism

In this paper, a fast numerical iterative algorithm is proposed based on the Pseudo-Rigid-Body-Model and geometric method to deal with the problem of the offset-type flexible Delta mechanism forward kinematics with multiple solutions and without analytical solutions. In forward kinematics, the quartic kinematic equations are reduced to quadratic ones by variable substitution. As the simplest nonlinear equations, quadratic equations can be represented by the coefficient matrices which is suitable for computer calculation. And due to the operational properties of the matrix, the updating and iterative process in the steps of Newton’s method can be simplified and improved to solve the forward kinematics more efficiently. The convergence and singularity of the proposed iterative algorithm are also analysed. By controlling the offset-type flexible micro-motion Delta parallel mechanism to move along three different expected spatial trace curves and measuring the displacements, the experiment results show that the Root Mean Square Error between the measured values and the expected values of linear positioning is 0.9177 μm for 37.4166 μm. Moreover, it is proved by numerical examples that the proposed iterative algorithm takes only 0.53 ms on average to solve the forward kinematic problems. The calculation time is reduced by 90.3% on average compared to the traditional Newton’s method, which provides a feasible solution for real-time control based on forward kinematics.

Kinematics Modeling and Singularity Analysis of a 6-DOF All-Metal Vibration Isolator Based on Dual Quaternions

Driven by the need for impact resistance and vibration reduction for mechanical devices in extreme environments, an all-metal vibration isolator with 6-degree-of-freedom (6-DOF) motion that is horizontally symmetrical was developed. Its stiffness and damping ability are provided by oblique springs in symmetrical arrangement and a metal–rubber elasto-porous damper. The spring is symmetrically distributed in the center axis of the support load surface. It is necessary to investigate the kinematics and the singularity before conducting multi-body dynamics analysis of the vibration isolator. Based on the theory of dual quaternions, the forward kinematics equations of the isolator were successively derived for theoretical kinematics modeling. In addition, an enhanced Broyden numerical iterative algorithm was developed and applied to the numerical solution of the forward kinematics equations of the vibration isolator. Compared with the traditional rotation-matrix method and Newton–Raphson method, the computational efficiency of the enhanced Broyden numerical iterative algorithm was increased by 680% and 290%, respectively. This was due to the enhanced algorithm without the calculations of any inverse matrix and forward kinematics equations. Finally, according to the forward kinematics Jacobian matrix, the position-singularity trajectory at a given orientation and the orientation-singularity space at a given position are calculated, which provides a basis for the algorithm of the 6-DOF vibration isolator to avoid singular positions and orientations.

Blaze: A High performance Big Data Computing System for High Energy Physics

High energy physics (HEP) is moving towards extremely high statistical experiments and super-large-scale simulation of theory. In order to handle the challenge of rapid growth of data volumes, distributed computing and storage frameworks in Big Data area like Hadoop and Spark make computations easy to scale out. While the programming model based on in-memory RDD assumes that workload performs only local computation and rare message exchange, it’s inefficient at some HEP use cases, because several scientific computations, such as partial wave analysis (PWA) and lattice quantum chromodynamics (LQCD), are based on numerical linear algebra and iterative algorithms that rely on message passing between tasks. In this paper, we present a computing system (Blaze) that modifies Spark to support OpenMPI, and performs as a unified system that integrates MPI in DAG and provides task scheduling policy. The results indicate that the insufficient expressiveness in Spark model are supplemented by inter-task message passing. Additionally, Blaze also empowers MPI with the ability of data-locality computing and provides a solution of fault tolerance.

Targets Spatial Coordinates Calculation in Angle-Difference Rangefinder Passive Location Complexes by Numerical Iterative Methods

This paper presents the analysis results of the iterative numerical algorithms use for roots calculating of nonlinear equations systems ( Levenberg-Marquardt , Newton’s algorithm , modified Newton’s algorithm , sequential iterations and gradient descent ) describing the process of spatial rectangular coordinates calculating of radio emission sources in the angle-difference-rangefinder passive location complexes with different configurations ( containing from 2 to 4 receivers ). The main objectives of the work include determining optimal number of receiving points and choosing the most effective way to transform the coordinates of the observed parameters vector (a set of range differences and angular coordinates estimates of objects emitting radio signals in relation to the receiver spatial location of the system ) into a measured parameters vector ( spatial rectangular coordinates of the observation object ). The criteria for further comparison of the using analyzed algorithms results were determined by the following characteristics : working area of the passive location complex ( the part of the space within which the targets coordinates estimates deviation from their true values does not exceed the maximum allowable values ); average error of calculating the target spatial coordinates in the working area ; number of coordinate calculating stages of radio sources in the s tudied part of the space . The results of a comparative analysis of the obtained numerical values by the selected criteria allowed us to conclude that the optimal implementation is the implementation of the angle-difference-rangefinder passive location complexes consisting of four receiving points and the use of the Levenberg-Marquardt algorithm for calculating the spatial coordinates of radio emission sources .

A CNN-LSTM-Based Fusion Separation Deep Neural Network for 6G Ultra-Massive MIMO Hybrid Beamforming

In the sixth-generation (6G) cellular networks, hybrid beamforming would be a real-time optimization problem that is becoming progressively more challenging. Although numerical computation-based iterative methods such as the minimal mean square error (MMSE) and the alternative manifold optimization (Alt-Min) can already attain near-optimal performance, their computational cost renders them unsuitable for real-time applications. However, recent studies have demonstrated that machine learning techniques like deep neural networks (DNN) can learn the mapping done by those algorithms between channel state information (CSI) and near-optimal resource allocation and then approximate this mapping in near real-time. In light of this, we investigate various DNN architectures for beamforming challenges in the terahertz (THz) band for ultra-massive multiple-input multiple-output (UM-MIMO) and explore their contextual mathematical modeling. Specifically, we design a sophisticated 1D convolutional neural network, and long short-term memory (1D CNN-LSTM) based fusion-separation scheme, which can approach the performance of the Alt-Min algorithm in terms of spectral efficiency (SE) for fully connected structures and, at the same time, use significantly less computational effort. Simulation results indicate that the proposed system can attain almost the same level of SE as that of the numerical iterative algorithms while incurring a substantial reduction in computational cost. Our DNN-based approach also exhibits exceptional adaptability to diverse network setups and high scalability. Although the current model only addresses the fully connected hybrid architecture, our approach can also be expanded to address a variety of other beamforming topologies.

Dynamic analysis of beams vibrating on nonlinear poroelastic multi‐layered continuum

AbstractThe paper presents a framework for analysis of beams interacting with nonlinear‐poroelastic, layered continuums (e.g., clayey soils) when subjected to time‐dependent loads. The poroelastic layered continuum is characterized by a nonlinear‐elastic constitutive relationship that relates the secant shear modulus to the induced shear strain. The Biot's theory of consolidation is combined with a dynamic beam‐continuum interaction model to develop the analysis. The vertical consolidation settlement of the beam and the excess pore pressure in the porous continuum are assumed to be products of separable functions, and the extended Hamilton's principle of least action is applied to obtain the differential equations governing the inertial consolidation motion of the beam‐continuum system and the dissipation of excess pore pressure. An iterative numerical algorithm is used to solve these coupled differential equations following one‐dimensional finite element analysis in which the implicit Wilson‐Θ time integration scheme is used to obtain the time history of beam and continuum responses. The novelty of the framework is that it rigorously takes into account the nonlinear poroelastic soil‐structure interaction within a dynamic time‐integration framework with minimal computational resources. The characteristics of this newly developed model are illustrated through examples.

An effective Fourier spectral phase-field approach for ferroelectric materials

In this article, we propose an efficient iterative numerical algorithm applying a Fourier spectral method to accurately compute the coupled elasto–electrostatic equilibrium equations in ferroelectric microstructures. The method is implemented for a phase-field model for domain pattern formation and domain kinetics evolution in tetragonal perovskite ferroelectrics, that uses spontaneous polarization as order parameter and includes the piezoelectric effect in the constitutive equation. The scheme is based on a two-scale homogenization approach, introducing local perturbations for stress and dielectric displacement. Green’s functions are derived in Fourier space for the coupled constitutive equations. Furthermore, using model parameters for BaTiO3 we investigate domain formation in 2D and 3D, and the polarization switching process starting from a critical nucleus subjected to an applied electric field and compressive stress. The simulation results based on the proposed method reveal that for polarization switching under external fields, intermediately appearing domains with 90° rotated polarization are formed, that reduce electrostatic or elastic strain energy.