Internal Iterations Research Articles

Foundations of iterated star maps and their use in combinatorics

We develop a framework for nonstandard analysis that gives foundations to the interplay between external and internal iterations of the star map, and we present a few examples to show the strength and flexibility of such a nonstandard technique for applications in combinatorial number theory.

An Iteratively Extended Target Tracking by Using Decorrelated Unbiased Conversion of Nonlinear Measurements.

Extended target tracking (ETT) based on random matrices typically assumes that the measurement model is linear. However, nonlinear measurements (such as range and azimuth) depending on locations of a series of unknown scattering centers always exist in many practical tracking applications. To address this issue, this paper proposes an iteratively extended target tracking based on random matrices by using decorrelated unbiased conversion of nonlinear measurements (ETT-IDUCM). First, we utilize a decorrelated unbiased converted measurement (DUCM) method to convert nonlinear measurements depending on unknown scatters of target extent in polar coordinates into the ones in Cartesian coordinates with equivalent measurement noise covariances. Subsequently, a novel method, combining iteratively extended Kalman filter (IEKF) updates with variational Bayesian (VB) cycles is developed for precise estimation of the target's kinematic state and extension. This method leverages the synergy between external IEKF iterations, which use the estimated state as a new prediction and input for DUCM, and internal VB iterations, which realize a closed-form approximation of the joint posterior probability. This approach progressively enhances estimation accuracy. Simulation results demonstrate the ETT-IDUCM algorithm's superior precision in estimating the target's kinematic state and extension compared to existing methods.

Topology Optimization and Efficiency Evaluation of Short-Fiber-Reinforced Composite Structures Considering Anisotropy

The current study aims to develop a methodology for obtaining topology-optimal structures made of short fiber-reinforced polymers. Each iteration of topology optimization involves two consecutive steps: the first is a simulation of the injection molding process for obtaining the fiber orientation tensor, and the second is a structural analysis with anisotropic material properties. Accounting for the molding process during the internal iterations of topology optimization makes it possible to enhance the weight efficiency of structures—a crucial aspect, especially in aerospace. Anisotropy is considered through the fiber orientation tensor, which is modeled by solving the plastic molding equations for non-Newtonian fluids and then introduced as a variable in the stiffness matrix during the structural analysis. Structural analysis using a linear anisotropic material model was employed within the topology optimization. For verification, a non-linear elasto-plastic material model was used based on an exponential-and-linear hardening law. The evaluation of weight efficiency in structures composed of short-reinforced composite materials using a dimensionless criterion is addressed. Experimental verification was performed to confirm the validity of the developed methodology. The evidence illustrates that considering anisotropy leads to stiffer structures, and structural elements should be oriented in the direction of maximal stiffness. The load-carrying factor is expressed in terms of failure criteria. The presented multidisciplinary methodology can be used to improve the quality of the design of structures made of short fiber-reinforced composites (SFRC), where high stiffness, high strength, and minimum mass are the primary required structural characteristics.

On the number of subproblem iterations per coupling step in partitioned fluid‐structure interaction simulations

AbstractIn literature, the cost of a partitioned fluid‐structure interaction scheme is typically assessed by the number of coupling iterations required per time step, while ignoring the internal iterations within the nonlinear subproblems. In this work, we demonstrate that these internal iterations have a significant influence on the computational cost of the coupled simulation. Particular attention is paid to how limiting the number of iterations within each solver call can shorten the overall run time, as it avoids polishing the subproblem solution using unconverged coupling data. Based on systematic parameter studies, we investigate the optimal number of subproblem iterations per coupling step. In addition, this work proposes a new convergence criterion for partitioned algorithms that is based solely on the number of subproblem iterations required to reach the subproblem residual tolerances and therefore does not require any additional convergence tolerance for the coupling loop.

Numerical Prediction of Ship Resistance Based on Volume of Fluid Implicit Multi-Step Method

The Volume of Fluid (VOF) method is used in two-phase fluid flow problems of ship hydrodynamic calculations, to capture the motion and distribution of the gas–liquid free surface. To ensure solution stability and accuracy, numerical simulations typically require separate mesh refinement for the free surface or a reduced time step, resulting in a significant increase in solution time. This study aims to compare the drag and vessel attitude change calculations of the VOF implicit multi-step method with the traditional single-step method, and to verify the feasibility of the method in the numerical prediction of ship resistance and flow field analysis. The results show that an implicit multi-step method with a reasonable number of internal iterations could obtain results close to those of the single-step method with a reduced time step, and the error in trim angle was relatively large, about 2%, but the solving time was only about half that of the latter. The method could also capture the shape and location of waves on the hull, especially in the vicinity of the ship, while the distribution of the waves in the far field differed from those in the experiments to some extent.

Design of a optimization algorithm for binary classification

In the present work, the design of a system to classify data is carried out, using the Scrum methodology. The validation was carried out by expert judgment, having favorable results in terms of different criteria such as; integrity, ease of use, innovation, and scalability. Regarding the development of the functional elements of the system, it was obtained; he developed the architecture of the system, the database, and the prototypes, among other points considered. From the implementation of the system, the equation of a classifying plane in three-dimensional space will be obtained, as well as the number of internal iterations that the algorithm develops, the estimated execution time, and the graph of the plane. This system is based on a recently introduced symmetric cone proximal multiplier algorithm to solve separable optimization problems, this algorithm made an application for classification-related support vector machines.

Design Structure Matrix Approach Applied to Lunar Habitat Design

Lunar habitat design is a complex endeavor characterized by complicated task-composition, numerous internal iterations, and intense task-coupling. The design process of assembled building in terrestrial construction and the system composition of lunar habitats have been constructed. However, there is insufficient experience to fully understand lunar habitat design missions and likewise there is insufficient coordination between architects and various disciplines. The task flow for sequencing optimization can be determined using a design structure matrix (DSM), which is widely used in engineering. The DSM can reveal necessary interfaces within the lunar habitat system as per relevant interface variables and processes. By decomposing the lunar habitat design process, an initial activity-based DSM is established in the present study. Informational interactions between each design task and its respective intensity are statistically investigated to clarify them across the four dimensions of energy, space, materials, and information. A sequencing algorithm is applied to optimize the design process. Finally, 20 design tasks of lunar habitat design are clarified among four phases: Pre-planning, spatial design, environmental design, and optimization. Related disciplines should coordinate in the design process according to the optimization results, and use the optimized task coupling relationship to build the requirement model and design model in an orderly manner to improve the design efficiency.

The Simulation of the Nonlinear Consolidation of Porous Media

In this paper, the general formulation of the problem of coupled deformation of a porous deformable medium with a fluid flowing through the pores is formulated, mathematically investigated and numerically implemented within the framework of physical and geometric nonlinearity. We present the formulation of the problem in velocities of solid phase displacements and the rate of pore pressure change in differential and variational forms. A phenomenological approach was used to formulate the mechanical model. The equations of the coupled consolidation model were derived from the general conservation laws of continuum mechanics using spatial averaging over a representative volume element. The consolidation model took into account the change in the porosity and permeability of the medium during deformation. The equations of filtration and porosity change, originally presented in Euler approach, were reformulated in Lagrangian coordinates of the solid phase using the relative fluid velocity according to ALE (Arbitrary Lagrangian - Eulerian) approach. The Gâteaux differentiation technique was used to linearize the variational equilibrium equations. For spatial discretization of the saddle system of equations, the finite element method (FEM) was used: quadratic serendipity elements for approximating the equilibrium equations and Brick type elements for approximating the filtration equation. To solve the system of equilibrium and filtration equations, a generalization of the implicit scheme with internal iterations at each time step by the Uzawa method was used. The results of numerical simulation of elastoplastic deformation of a water-saturated soil under load with fluid outflow are presented. To simulate the constitutive relations of elastoplastic deformation of soil under short-term loads, a generalization of S.S. Grigoryan's model to large deformations is proposed. The calculations were carried out in our own program code. The developed consolidation model can be used to simulate the formation of tracking ruts and unevenness of natural roads, as well as to calculate the uneven settlement of engineering structures.

Bed expansion at backwashing in pressurised porous media filters for drip irrigation: Numerical simulations and analytical equations

Actions for improving the energy efficiency of pressurised porous media filters used in drip micro-irrigation require methods to properly determine the behaviour of both filtration and backwashing modes. The latter is essentially a fluidisation process. Though many authors have analysed fluidised bed columns, very few studies have dealt with the backwashing of granular media filters used in agriculture. The purpose of the present work was 1) to validate a computational fluid dynamics (CFD) model to simulate the backwashing regime, and 2) to assess the extent of analytical expressions for determining the expanded bed height. Experimental data were obtained using a laboratory filter for two types of porous media at superficial velocities <150 m h −1 . The CFD model used the Eulerian–Eulerian approach, and its sensitivity was investigated in a simplified two-dimensional domain. A modified three-dimensional model effectively reproduced the bed expansion for most of the experimental conditions using large time steps (0.025 s) and few internal iterations (20). Well-known analytical equations overestimated the expanded bed height at superficial velocities <150 m h −1 , but the recent RIO 1 model proposed by Kramer et al. (2020) showed very good predictive capacities. Two analytical expressions based on basic principles were developed, providing a trend which was also close to observations and a lower bound for the expanded bed height value. These conclusions were confirmed by analysing external data obtained using commercial pressurised sand filters. • The backwashing mode of a pressurised granular media filter was investigated. • The CFD model reproduced the fluidised bed behavior for superficial velocities <150 m h −1 . • The set-up of the CFD model required a case-by-case analysis. • A new analytical equation to determine the expanded bed height was obtained. • An equation to estimate the minimum expanded bed height was developed.

Deep Learning Approach for the Detection of Noise Type in Ancient Images

Recent innovations in digital image capturing techniques facilitate the capture of stationary and moving objects. The images can be easily captured via high-end digital cameras, mobile phones and other handheld devices. Most of the time, captured images vary compared to actual objects. The captured images may be contaminated by dark, grey shades and undesirable black spots. There are various reasons for contamination, such as atmospheric conditions, limitations of capturing device and human errors. There are various mechanisms to process the image, which can clean up contaminated image to match with the original one. The image processing applications primarily require detection of accurate noise type which is used as input for image restoration. There are filtering techniques, fractional differential gradient and machine learning techniques to detect and identify the type of noise. These methods primarily rely on image content and spatial domain information of a given image. With the advancements in the technologies, deep learning (DL) is a technology that can be trained to mimic human intelligence to recognize various image patterns, audio files and text for accuracy. A deep learning framework empowers correct processing of multiple images for object identification and quick decision abilities without human interventions. Here Convolution Neural Network (CNN) model has been implemented to detect and identify types of noise in the given image. Over the multiple internal iterations to optimize the results, the identified noise is classified with 99.25% accuracy using the Proposed System Architecture (PSA) compared with AlexNet, Yolo V5, Yolo V3, RCNN and CNN. The proposed model in this study proved to be suitable for the classification of mural images on the basis of every performance parameter. The precision, accuracy, f1-score and recall of the PSA are 98.50%, 99.25%, 98.50% and 98.50%, respectively. This study contributes to the development of mural art recovery.

Utilizing a "Crawl, Walk, Run" Training Model to Enhance Field Sanitation Capabilities for Peacekeeping Forces: A Recommendation for the Department of Defense Global Health Engagement Enterprise.

ABSTRACTIntroductionDoD Global Health Engagement (GHE) planners can follow a number of models to effectively plan and execute successful GHE activities. One recommendation that could provide a significant return on investment for the DoD GHE enterprise is to utilize a “Crawl, Walk, Run” training model to build or enhance a specific medical capability for a Partner Nation (PN). Through the African Peacekeeping Rapid Response Partnership (APRRP) program, U.S. military medical subject matter experts serving as instructors for a Field Sanitation Course (FSC) delivered to the Senegalese Armed Forces (SAF), gained first-hand experience of the positive outcomes that resulted from incorporating this training model into the DoD GHE process.Materials and MethodsThe SAF completed three APRRP-led, in-person FSC iterations: May 2019 (crawl phase), September 2019 (walk phase), and February 2020 (run phase). Approximately 1 year after the completion of the in-person FSCs, in the midst of the COVID-19 pandemic, USU’s CGHE offered a Field Sanitation Virtual Engagement to augment the FSC, emphasize specific field sanitation topics, and discuss lessons learned with the SAF on the deployment of their Level 2 Hospital.ResultsBefore deploying their Level 2 Hospital during the COVID-19 pandemic, the SAF conducted a base camp assessment and found multiple ways to apply the knowledge and skills learned through the APRRP FSC to address issues related to waste management, pest control, and personal protective measures to protect against COVID-19. The SAF’s progress in strengthening and institutionalizing their field sanitation capabilities can be seen by their execution of their own variation of the FSC—in preparation for their deployment, the SAF conducted three of their own FSCs, which closely resembled the APRRP-administered course.ConclusionsThe “Crawl, Walk, Run” training model demonstrates an excellent teaching method that develops PN instructors so they can train more personnel in the long-term, thus building both capacity and capability. This gives the PN the opportunity to sustainably institutionalize a course, allowing them to continue training it in perpetuity. Implementing this training model flexibly to adapt to the differing needs of each PN and each line of effort would increase the success of DoD GHE activities when training PNs. It would also ensure the PN has the capability to sustainably institutionalize a course and can independently train future cohorts through internal iterations of the course.

N-SVRG: Stochastic Variance Reduction Gradient with Noise Reduction Ability for Small Batch Samples

The machine learning model converges slowly and has unstable training since large variance by random using a sample estimate gradient in SGD. To this end, we propose a noise reduction method for Stochastic Variance Reduction gradient (SVRG), called N-SVRG, which uses small batches samples instead of all samples for the average gradient calculation, while performing an incremental update of the average gradient. In each round of iteration, a small batch of samples is randomly selected for the average gradient calculation, while the average gradient is updated by rounding of the past model gradients during internal iterations. By suitably reducing the batch size B, the memory storage as well as the number of iterations can be reduced. The experiments are compared with the state-of-the-art Mini-Batch SGD, AdaGrad, RMSProp, SVRG and SCSG, and it is demonstrated that N-SVRG outperforms SVRG and SASG, and is on par with SCSG. Finally, by exploring the relationship between the small values of different parameters n. B and k and the effectiveness of the algorithm, we prove that our N-SVRG algorithm has some stability and can achieve sufficient accuracy even in the case of small batch size. The advantages and disadvantages of various methods are experimentally compared, and the stability of N-SVRG is explored by parameter settings.

An iterative method for solving difference problems of gas dynamics in the mixed Euler-Lagrangian variables

The method proposed is intended to solve implicit conservative operator difference schemes for a grid initial-boundary value problems on a simplex grid for a system of equations of gas dynamics in the mixed Euler-Lagrangian variables. To find a solution to such a scheme at a time step, it is represented as a single equation for a nonlinear function of two arguments from space – the direct product of the grid spaces of gas-dynamic quantities. To solve such an equation, a combination of the generalized Gauss-Seidel iterative method (external iterations) and an implicit two-layer iteration scheme (internal iterations at each external iteration) is used. The feature of the method is that, the equation, which is solved by internal iterations, is obtained from the equation of the difference scheme using symmetrization – such a non-degenerate linear transformation that the function in this equation has a self-adjoint positive Frechet derivative.

Inverse Modeling of Radiative Transfer by Two-Stream Approximation using the Luus-Jaakola Method

The simulation of terrestrial ecosystem processes, using numerical biosphere-atmosphere models that can be coupled to the Atmospheric Models, assist in a better diagnosis and forecast of climate and weather. To be able to represent a particular region, biome or ecosystem, the model parameters need to be adjusted for local conditions. This work aims to assess the Luus-Jaakola (LJ) method in the optimization of the parameters in a two-stream radiative transfer model applied to a vegetation canopy. Solar radiation components (incident, S↓, and reflected, S↑) were measured above a sugarcane crop in a Tropical region from February 17 to 24, 2006. Among the combinations of internal and external iterations evaluated for Luss-Jaakola method, 60/30 (external/internal) iterations presented more precise albedo (∝ = S↑/S↓) simulated (r^2 = 0.7386) and, for the accuracy of the simulated ∝, even though the 60/40 combination had the smallest percentual error (6.40%), the 60/30 combination was 0.03% higher. The precision and accuracy of S↑ was greater with the parameters obtained by the inverse problem with the combination of 60/30 (external/internal) iterations respectively. In general, the behavior of simulated S↑ at the top of the canopy was underestimated compared to the observed S↑, especially in the early morning. For the simulated ∝ at the top of the canopy, the model's overestimation was observed at the lowest values of albedo. When the largest albedos are observed, only at the beginning of the day the model underestimated the values. As shown by the tests result, the parameters optimized by Luus-Jaakola method have an adequate representation of the observed data.

A Distributed Power Transfer Limit Calculation Method for Multi-Area Interconnection Power Networks

For multi-area interconnected power networks, each subarea may be operated by independent regulator, who oppose to open the access of private information such as network topology to the others. For this case, this study proposes a decomposition-coordination strategy to calculate power transfer limit (PTL) considering both saddle node bifurcation (SNB) and limit-induced bifurcation (LIB). The external coordination equations are derived based on the sensitivity analysis of boundary buses at tie-lines, to express the power exchange of subareas and the consistent boundary state variables. Power Flow (PF) results for each subarea system are separately calculated followed by the adjustment of tie-lines' PF injected into boundary buses according to the external coordination. Then the alternation between internal and external iterations, for which operators of subareas are not required to share private network information, could generate the same results as conventional PF that relies on the complete information. Moreover, an improved Continuation PF (CPF) model that includes the prediction of the PF of area tie-lines is proposed. The point of collapse (POC) method is employed to calculate PTL involving the SNB of the interconnected networks to improve the accuracy of the algorithm. Case studies demonstrate the effectiveness and reliability of the proposed method.

A CFD-DEM-IBM method for Cartesian grid simulation of gas-solid flow in complex geometries

The use of CFD-DEM method to accurately simulate gas-solid flows in complex geometries is challenging, mainly due to the complexity related to the use of unstructured computational grids. In order to solve this problem, researchers have simulated gas-solid fluidized beds with complex geometries using CFD-DEM-IBM method with Cartesian grids. In present study the gas-solid flows in complex geometries were simulated using Cartesian grids following the basic idea of CFD-DEM-IBM method (De Jong et al., 2012), where the interactions between gas phase and complex geometries were firstly modelled using the immersed boundary method (IBM) implemented by Tuković and Jasak (2012) in OpenFOAM®. It was found that the computational efficiency is quite low. To improve the efficiency of the CFD-DEM-IBM solver, a new IBM method was then proposed by removing the neighboring immersed boundary cells from the interpolated extended stencil in the reconstruction of the velocity and pressure fields near the wall, and further proposing a new zero-gradient boundary condition to replace the original Neumann boundary condition for reconstructing the pressure field. Single-phase flow past a stationary cylinder, single-phase pipe flow, gas-solid flow in a cylindrical fluidized bed and fluidized bed with immersed tubes were simulated with four different IBM imposition methods to assess the accuracy and efficiency of sharp-interface CFD-DEM-IBM solver. It was shown that (i) the results of CFD-DEM-IBM simulations agree well with the reported experimental, analytical and/or numerical results available in literature; and (ii) the computational efficiency of newly proposed CFD-DEM-IBM solver is one or two order of magnitudes faster than that of the original IBM of Tuković and Jasak (2012) in OpenFOAM®, due to the fact that internal iterations are not needed anymore during the reconstruction of velocity and pressure fields.

A simple iterative geometry-based interface-preserving reinitialization for the level set method

The iterative reinitialization, as an important process for the standard level set method, is flexible and straightforward in large-scale computing but has problems of interface movement and serious mass loss. Thus a simple iterative geometry-based interface-preserving reinitialization is proposed to reconstruct a signed distance function (SDF) while fixing the interface location with the combination of the external and internal iterations. The external iteration is used to restore the nature of the SDF. And the internal iteration firstly determines displacement errors of zero-level-set interpolation points via the geometric position of the interface, then the errors are redistributed iteratively to adjacent nodes until moving zero-level-set interpolation points are driven back to their original positions. The novel approach performs excellent mass conservation and shape preservation without sacrificing the simplicity of the iterative reinitialization. The accuracy and efficiency of the proposed method are validated with typical stationary interface examples and well-known benchmark cases.

Colebrook’s Flow Friction Explicit Approximations Based on Fixed-Point Iterative Cycles and Symbolic Regression

The logarithmic Colebrook flow friction equation is implicitly given in respect to an unknown flow friction factor. Traditionally, an explicit approximation of the Colebrook equation requires evaluation of computationally demanding transcendental functions, such as logarithmic, exponential, non-integer power, Lambert W and Wright Ω functions. Conversely, we herein present several computationally cheap explicit approximations of the Colebrook equation that require only one logarithmic function in the initial stage, whilst for the remaining iterations the cheap Padé approximant of the first order is used instead. Moreover, symbolic regression was used for the development of a novel starting point, which significantly reduces the error of internal iterations compared with the fixed value staring point. Despite the starting point using a simple rational function, it reduces the relative error of the approximation with one internal cycle from 1.81% to 0.156% (i.e., by a factor of 11.6), whereas the relative error of the approximation with two internal cycles is reduced from 0.317% to 0.0259% (i.e., by a factor of 12.24). This error analysis uses a sample with 2 million quasi-Monte Carlo points and the Sobol sequence.

Newton method for stationary and quasi-stationary problems for Smoluchowski-type equations

An efficient implementation of the Newton–Krylov iterative method finding numerical solutions of aggregation–fragmentation equations without spontaneous fragmentation is reported. It is based on application of fast numerical schemes for evaluation of the Smoluchowski operator associated with these equations, and structure of Jacobi matrix, allowing implementation of fast multiplication by a vector. We also propose an efficient preconditioner based on lower triangular band matrix extracted from a Jacobi matrix, resulting in a dramatic speedup of internal GMRES-based iterations between the Newton steps. We compare the efficiency of the novel method with the existing ones and demonstrate a noticeable superiority of our approach. Moreover, we show that the new method may be utilized for modeling of a wider class of aggregation–fragmentation phenomena and derive a new class of quasi-stationary solutions for aggregation–fragmentation equations source of monomers.

Computationally Efficient and Robust Nonlinear 3D Cyclic Modeling of RC Structures Through a Hybrid Finite Element Model (HYMOD)

A computationally efficient and robust simulation method is presented in this work, for the cyclic modeling of reinforced concrete (RC) structures. The proposed hybrid modeling (HYMOD) approach alleviates numerical limitations regarding the excessive computational cost during the cyclic analysis and provides a tool for the detailed simulation of the 3D cyclic nonlinear behavior of full-scale RC structures. The simplified HYMOD approach is integrated in this work with a computationally efficient cyclic concrete material model so as to investigate its numerical performance under extreme cyclic loading conditions. The proposed approach adopts a hybrid modeling concept that combines hexahedral and beam-column finite elements (FEs), in which the coupling between them is achieved through the implementation of kinematic constraints. A parametric investigation is performed through the use of the Del Toro Rivera frame joint and two RC frames with a shear wall. The proposed modeling method managed to decrease the computational cost in all numerical tests performed in this work, while it induced additional numerical stability during the cyclic analysis, in which the required number of internal iterations per displacement increment was found to be always smaller compared with the unreduced (hexahedral) model. The HYMOD provides for the first time with the required 3D detailed FE solution tools in order to simulate the nonlinear cyclic response of full-scale RC structures without hindering the numerical accuracy of the derived model nor the need of developing computationally expensive models that practically cannot be solved through the use of standard computer systems.