Iterative Technique Research Articles

Optimisation of asymmetries in mm-wave single-element fractal antenna for gain-bandwidth enhancement

ABSTRACT In this study, a low-loss substrate was used to create an Asymmetric Irregular Hexagonal Fractal (AIHF) mm-wave antenna. The antenna consists of an Asymmetric Defected Ground Structure (ADGS) attached to the bottom of a 0.55λ0 ×0.40λ0 ×0.032λ0 mm3 substrate and an Irregular Hexagonal Fractal (IHF) patch on top of the substrate. The proposed fractal technique is unique and based on fractal-slot 3-stage iterations. The IHF patch is created by etching seven fractals arranged symmetrically about the y-axis, one of which has a central 1/3rd (scaling) iteration factor and six hexagonal fractals that are 1/9th of the parent 0th order iteration. On the patch, these fractal slots are evenly spaced out. By etching an Asymmetric Cascaded Double Dumbbell (ACDD) slot on the ground plane, an ADGS is created. With this etching in the patch and ground, a gain of > 5.0 dBi for a −10 dB S11 bandwidth of 4.655 GHz (32.84–37.215 GHz), a recorded peak gain of 13.4 dBi is at 33.55 GHz and an average radiation efficiency of 87.75% is achieved. Using the High-Frequency Structure Simulator (HFSS), the width of ADGS, the position of ACDD on ADGS, and the dimensions of etched fractals are optimised through a pattern search parametric iterative technique. These results are validated using the Vector Network Analyser (VNA), and the Anechoic Chamber and it is revealed that they agree well with the simulated results. The designed AIHF antenna’s RLC electrical equivalent circuit modelling is presented along with evaluated R, L, and C values.

A novel Noor iterative method of operators with property (E)$$ (E) $$ as concerns convex programming applicable in signal recovery and polynomiography

This work proposes a novel Noor iterative scheme, called CT‐iteration, to approximate the fixed points in the new context of generalized nonexpansive mappings with property . We establish the strong and weak convergence results in a uniformly convex Banach space. Additionally, numerical examples of the iterative technique are demonstrated using a signal recovery application in a compressed sensing situation. Furthermore, we show the use of the proposed method to generate polynomiographs. The proposed algorithm has been implemented and tested via numerical simulation in MATLAB. The simulation results show the effectiveness of the proposed algorithm.

Fixed Point Theorems in Extended Convex Quasi s-metric Spaces

In this work, through the convex structure, we introduce the concept of the extended convex quasi s-metric spaces. In addition, through Mann's iterative technique, we theorize the existence of a unique fixed point for two types of contraction mapping in extended convex quasi s-metric spaces.

Numerical optimization of longitudinal collimator geometry for novel x-ray field.

A novel X-ray field produced by an ultrathin conical target is described in the literature. However, the optimal design for an associated collimator remains ambiguous. Current optimization methods using Monte Carlo calculations restrict the efficiency and robustness of the design process. A more generic optimization method that reduces parameter constraints while minimizing computational load is necessary. A numerical method for optimizing the longitudinal collimator hole geometry for a cylindrically-symmetrical X-ray tube is demonstrated and compared to Monte Carlo calculations. 
Approach: The X-ray phase space was modelled as a four-dimensional histogram differential in photon initial position, final position, and photon energy. The collimator was modelled as a stack of thin washers with varying inner radii. Simulated annealing was employed to optimize this set of inner radii according to various objective functions calculated on the photon flux at a specified plane. 
Main results: The analytical transport model used for optimization was validated against Monte Carlo calculations using Geant4 via its wrapper, TOPAS. Optimized collimators and the resulting photon flux profiles are presented for three focal spot sizes and five positions of the source. Optimizations were performed with multiple objective functions based on various weightings of precision, intensity, and field flatness metrics. Finally, a select set of these optimized collimators, plus a parallel-hole collimator for comparison, were modelled in TOPAS. The evolution of the radiation field profiles are presented for various positions of the source for each collimator.
Significance: This novel optimization strategy proved consistent and robust across the range of X-ray tube settings regardless of the optimization starting point. Common collimator geometries were re-derived using this algorithm while simultaneously optimizing geometry-specific parameters. The advantages of this strategy over iterative Monte Carlo-based techniques, including computational efficiency, radiation source-specificity, and solution flexibility, make it a desirable optimization method for complex irradiation geometries. &#xD.

The stability and statistic of domain decomposition algorithm with mini-batch learning for optimal transport

The Wasserstein distance in the optimal transport (OT) model is being widely used in machine learning applications due to its mathematical and geometric properties. Since the entropic regularization OT is a convex problem, and for its large-scale problems, many algorithms have been proposed. Existing methods mainly adopt iterative random projection techniques to approximate the Wasserstein distance in the OT model. In this paper, we employ the entropic domain decomposition algorithm with mini-batch learning to calculate the entropic regularization OT problem and investigate the stability of this algorithm. The algorithm performs on different cells of the domain instead of using the projection technique and it is based on a mini-batch loss function. The corresponding solution in each iteration is derived from the dual problem of entropic regularized OT on each decomposed cell. Once the solutions to the dual problem on all decomposed cells are obtained, the corresponding transport plan in each iteration can be obtained. We show that the transport plan computed by its dual variables is admissible, and we also give the sub-gradient approximation result. In addition, we exploit the statistical concentration result of the subsampled mini-batch Wasserstein distance on decomposed cells. Finally, the numerical experiments validate that the proposed algorithm can save computational time further.

Full wave modeling of radio-frequency beams in tokamaks in the electron cyclotron frequency range

Simulation of full wave, without paraxial approximation, high-resolution solution of wave equations in frequency domain in the electron cyclotron resonance (ECR) frequency range for realistic Tokamak plasma parameters became possible by using recently formulated hybrid iterative algorithm [Svidzinski et al., Phys. Plasmas 25, 082509 (2018)] for numerically solving discretized wave equations. This approach combines time evolution and iterative relaxation techniques into iteration cycles. This algorithm is implemented in 2D code FullWave, solving wave equations in Tokamaks in cold and hot plasma models, and it has been tested in 3D full wave iterative RF beams simulation tool, which is presently being developed to model 3D ECRH RF beams in fusion devices using dynamic grid adaptation. The results of 2D full wave modeling, assuming specified toroidal mode number, of ECRH RF beams in DIII-D plasma, performed in the cold and hot plasma models for outboard and top launch scenarios using FullWave are presented. Nonlocal hot plasma response model, based on accurate numerical solution of linearized Vlasov equation, is used to model beam propagation and absorption in the 2nd electron cyclotron harmonic region. Demonstration of capability of the hybrid iterative algorithm to model ECRH RF beams in 3D is made by simulating a substantial part of realistic beam in DIII-D, launched from outboard side of the machine. All relevant physics of RF beam propagation, most of which is not captured in paraxial approximation, such as beam's divergence, interference between the X and O modes in the beam, X-O mode conversion, beam splitting into the X and O mode beams, transformation of beam's cross section, and absorption at the 2nd electron cyclotron harmonic, is captured in the simulations. A numerical technique to find an optimal beam polarization at the launcher to launch a nearly pure X or O mode beam in plasma is developed and tested.

Bayesian reconstruction of Cartesian product graph signals with general patterns of missing data

In this paper, we address the challenge of signal reconstruction on Cartesian product graphs, which frequently arises in applications where node-level data may be corrupted by equipment failure or difficult to reliably collect. A recent approach to Graph Signal Reconstruction (GSR) is to formulate it as a Bayesian inference problem, where the underlying signal is presumed to be smooth with respect to the graph topology. However, the resulting linear system derived from this model specification is often intractable to solve directly for general Cartesian product graphs. To overcome this limitation, we introduce two robust and efficient iterative procedures for computing the posterior mean. The first method is a stationary iterative technique based on matrix splitting, while the second employs a conjugate gradient approach with a symmetric graph-spectral preconditioner. We provide a theoretical and numerical comparison of the convergence behaviour of these algorithms, demonstrating that the optimal choice depends on the model hyperparameters. Finally, we propose a novel supervised learning-based technique, enhanced by an active learning strategy, for estimating the posterior marginal variance. This circumvents the need to to instantiate, invert or decompose large matrices directly in memory and results in an R2 statistic of over 0.95 on a synthetic test data set. This paper contributes to the development of advanced signal reconstruction techniques applicable in various domains, including large-scale sensor networks and social network analysis.

Conversational AI

Abstract: Conversational AI systems are becoming increasingly popular across many industries and are transforming the way people interact with technology. For a more authentic, human-like connection and a smooth user experience, these systems should combine text-based interactions with multimodal capabilities. The authors of this work suggest a new approach to improving conversational AI systems' usability by combining speech and visual analysis. By combining visual and auditory processing capabilities, AI systems can better understand human inquiries and instructions. Both visual data and speech can be better understood with the use of computer vision algorithms and natural language processing techniques, respectively. Conversational AI systems can provide more accurate and tailored replies by integrating many modalities to better grasp human intent and context. The development of multimodal conversational AI presents a significant difficulty in ensuring the smooth integration of voice and visual processing units. A strong architectural design and advanced algorithms are necessary for the simultaneous synchronization and comprehension of data from several modalities in real-time. The system needs to keep track of the conversation's context even when it switches between different forms of communication so it can keep providing fair and relevant responses all through the engagement. Customization is key to making multimodal conversational AI better for users. Based on user data and preferences, the system may tailor interactions to offer more relevant ideas and support. Users are more invested in the AI system over time, and they have a better experience overall because to customization. Ensuring the privacy and security of important audiovisual data is of the utmost importance while building multimodal conversational AI. Strong encryption, anonymization technologies, and compliance with data protection regulations are vital for user privacy and system confidence. Continuous improvement is key to the success of multimodal conversational AI systems. The feedback from users can help the developers improve the system and add new features. Thanks to this iterative technique, the AI system stays flexible and can adjust to changing consumer preferences. By combining voice and picture processing, conversational AI systems have a great deal of promise for improving the user experience. Through the integration of visual and auditory signals, these systems have the ability to comprehend user intent more accurately, provide customized experiences, and completely transform the way humans engage with technology.

Progress and Opportunities for Machine Learning in Materials and Processes of Additive Manufacturing.

In recent years, there has been widespread adoption of machine learning (ML) technologies to unravel intricate relationships among diverse parameters in various additive manufacturing (AM) techniques. These ML models excel at recognizing complex patterns from extensive, well-curated datasets, thereby unveiling latent knowledge crucial for informed decision-making during the AM process. The collaborative synergy between ML and AM holds the potential to revolutionize the design and production of AM-printed parts. This review delves into the challenges and opportunities emerging at the intersection of these two dynamic fields. It provides a comprehensive analysis of the publication landscape for ML-related research in the field of AM, explores common ML applications in AM research (such as quality control, process optimization, design optimization, microstructure analysis, and material formulation), and concludes by presenting an outlook that underscores the utilization of advanced ML models, the development of emerging sensors, and ML applications in emerging AM-related fields. Notably, ML has garnered increased attention in AM due to its superior performance across various AM-related applications. It is envisioned that the integration of ML into AM processes will significantly enhance 3D printing capabilities across diverse AM-related research areas.

Iterative solutions for nonlinear equations via fractional derivatives: adaptations and advances

In recent years, the utilization of fractional calculus has witnessed a notable surge across various scientific and engineering domains. This manuscript delves into the exploration of adapted iterative techniques tailored for solving nonlinear equations, capitalizing on the diverse range of derivatives available for addressing different problem contexts. We scrutinize previously developed iterative methods, enhancing their efficacy by introducing an auxiliary parameter to the root search process for nonlinear equations (NLE), alongside a fixed order of fractional derivatives. The selection of the auxiliary parameter is confined to the interval (0,1] for convenience. A thorough convergence analysis is conducted, employing a fractional power series expansion of f(x) in terms of fractional derivatives. Subsequently, a series of NLEs is solved to showcase and contrast the efficiency of our proposed methods with established iterative techniques. This refined abstract aims to succinctly elucidate the objectives and contributions of our study, providing readers with a clearer understanding of the manuscript's scope and significance.

Motion compensated cone-beam CT reconstruction using an a priori motion model from CT simulation: a pilot study

Objective. To combat the motion artifacts present in traditional 4D-CBCT reconstruction, an iterative technique known as the motion-compensated simultaneous algebraic reconstruction technique (MC-SART) was previously developed. MC-SART employs a 4D-CBCT reconstruction to obtain an initial model, which suffers from a lack of sufficient projections in each bin. The purpose of this study is to demonstrate the feasibility of introducing a motion model acquired during CT simulation to MC-SART, coined model-based CBCT (MB-CBCT). Approach. For each of 5 patients, we acquired 5DCTs during simulation and pre-treatment CBCTs with a simultaneous breathing surrogate. We cross-calibrated the 5DCT and CBCT breathing waveforms by matching the diaphragms and employed the 5DCT motion model parameters for MC-SART. We introduced the Amplitude Reassignment Motion Modeling technique, which measures the ability of the model to control diaphragm sharpness by reassigning projection amplitudes with varying resolution. We evaluated the sharpness of tumors and compared them between MB-CBCT and 4D-CBCT. We quantified sharpness by fitting an error function across anatomical boundaries. Furthermore, we compared our MB-CBCT approach to the traditional MC-SART approach. We evaluated MB-CBCT’s robustness over time by reconstructing multiple fractions for each patient and measuring consistency in tumor centroid locations between 4D-CBCT and MB-CBCT. Main results. We found that the diaphragm sharpness rose consistently with increasing amplitude resolution for 4/5 patients. We observed consistently high image quality across multiple fractions, and observed stable tumor centroids with an average 0.74 ± 0.31 mm difference between the 4D-CBCT and MB-CBCT. Overall, vast improvements over 3D-CBCT and 4D-CBCT were demonstrated by our MB-CBCT technique in terms of both diaphragm sharpness and overall image quality. Significance. This work is an important extension of the MC-SART technique. We demonstrated the ability of a priori 5DCT models to provide motion compensation for CBCT reconstruction. We showed improvements in image quality over both 4D-CBCT and the traditional MC-SART approach.

On the implementation in Abaqus of the global–local iterative coupling and acceleration techniques

This paper presents results and convergence study of the Global–Local Iterative Coupling through the implementation in the commercial software Abaqus making use of the co-simulation engine. A hierarchical modeling and simulation approach is often required to alleviate modeling burdens. Particular focus has been devoted here on convergence acceleration and performance optimization. Two applications in statics with nonlinear material behavior and geometrically nonlinear formulation are considered here: first a holed curved plate under traction with elastic–plastic material, then a pre-stressed bolted joint connecting two plates between each other and subjected to traction load. Three different convergence acceleration techniques are compared in terms of convergence performance and accuracy. An inexact solver strategy is proposed to improve computing time performance. The results show promising results for the coupling technology and constitute a step forward in the availability of non-intrusive multi-scale modeling capabilities for complex structures and assemblies.

Correcting Hardening Artifacts of Aero-Engine Blades with an Iterative Linear Fitting Technique Framework.

Aero engines are the key power source for aerospace vehicles. Cermet turbine blades are the guarantee for the new-generation fighters to improve aero-engine overall performance. X-ray non-destructive reconstruction can obtain the internal structure and morphology of cermet turbine blades. However, the beam hardening effect causes artifacts in objects and affects the reconstruction quality, which is an issue that needs to be solved urgently. This study proposes a hardening-correction framework for industrial computed tomography (ICT) images based on iterative linear fitting. First, an iterative binarization was performed to improve the penetration length accuracy of the forward projection. Then, the proposed linear fitting technology combined with the Hermite function model is derived and analyzed to obtain suitable parameters of blade data. Finally, the fitting curves of the blade data, using the proposed method and the traditional polynomial fitting method, were analyzed and compared and were used to correct the engine turbine blade projection data to reconstruct different groups of tomographic images. Different groups of tomographic images were analyzed using three quantitative image quality evaluation indicators. The results show that the root-mean-square error (RMSE) of the tomographic image obtained by the proposed framework is 0.0133, which is lower than that of the compared method. The peak signal-to-noise ratio (PSNR) is 37.7050 dB and the feature structural similarity (FSIM) is 0.9881, which are both higher than that of the compared method. The proposed method improves the hardening-artifact-correction capability and can obtain higher-quality images, which provides new ideas for the development of imaging and detection of new-generation aero-engine turbine blades.

Hamiltonian Monte Carlo based elastic full-waveform inversion of wide-angle seismic data

Summary Full-waveform inversion (FWI) of seismic data provides quantitative constraints on subsurface structures. Despite its widespread success, FWI of data around the critical angle is challenging because of the abrupt change in amplitude and phase at the critical angle and the complex waveforms, especially in the presence of a sharp velocity contrast, such as at the Moho transition zone (MTZ). Furthermore, the interference of refracted lower crustal (Pg) and upper mantle (Pn) arrivals with the critically reflected Moho (PmP) arrivals in crustal and mantle studies makes the application of conventional FWI based on linearized model updates difficult. To address such a complex relationship between the model and data, one should use an inversion method based on a Bayesian formulation. Here, we propose to use a Hamiltonian Monte Carlo (HMC) method for FWI of wide-angle seismic data. HMC is a non-linear inversion technique where model updates follow the Hamiltonian mechanics while using the gradient information present in the probability distribution, making it similar to iterative gradient techniques like FWI. It also involves procedures for generating distant models for sampling the posterior distribution, making it a Bayesian method. We test the performance and applicability of HMC based elastic FWI by inverting the non-linear part of the synthetic seismic data from a three-layer and a complex velocity model, followed by the inversion of wide-angle seismic data recorded by two ocean bottom seismometers (OBS’s) over a 70 Ma old oceanic crustal segment in the equatorial Atlantic Ocean. The inversion results from both synthetic and real data suggest that HMC based FWI is an appropriate method for inverting the non-linear part of seismic data for crustal studies.

Robust residual-guided iterative reconstruction for sparse-view CT in small animal imaging.


We introduce a robust image reconstruction algorithm named Residual-guided Golub-Kahan Iterative Reconstruction Technique (RGIRT) designed for sparse-view computed tomography (CT), which aims at iterative reconstruction for a limited number of projection views.

Approach:
RGIRT utilizes an inner-outer dual iteration framework, with a flexible least square QR (FLSQR) algorithm implemented in the inner iteration and a restarted iterative scheme applied in the outer iteration. The inner FLSQR employs a flexible Golub-Kahan bidiagonalization method to reduce the size of the inverse problem, and a weighted generalized cross-validation method to adaptively estimate the regularization hyper-parameter. The inner iteration efficiently yields the intermediate reconstruction result, while the outer iteration minimizes the residual and refines the solution by using the result obtained from the inner iteration.

Main results:
The reconstruction performance of RGIRT is evaluated and compared to other reference methods (FBPConvNet, SART-TV, and FLSQR) using projection data from both numerical phantoms and real experimental Micro-CT data. The experimental findings, from testing various numbers of projection views and different noise levels, underscore the robustness of RGIRT. Meanwhile, theoretical outcomes confirm the convergence of our approach. 

Significance:
We propose a robust iterative reconstruction algorithm for X-ray CT scans with sparse projection views, thereby shortening scanning time and mitigating excessive ionizing radiation exposure to small animals. &#xD.

Field Experiment as a Tool to Verify The Effectiveness of Prototype Track Structure Components Aimed at Reducing Railway Noise Nuisance

The almost unlimited possibilities of modern computational tools create the temptation to study phenomena related to the operation of engineering objects exclusively using complex numerical simulations. However, the fascination with multi-parametric complex computational models, whose solutions are obtained using iterative techniques, may result in qualitative discrepancies between reality and virtual simulations. The need to verify on real objects the conclusions obtained from numerical calculations is therefore indisputable. The enormous cost and uniqueness of large-scale test stands significantly limit the possibility of conducting tests under real conditions. The solution may be an experiment focused on testing features relevant to the given task, while minimising the dimensions of the objects under consideration. Such conditions led to the concept of conducting a series of field experiments to verify the effectiveness of prototype track components, which were developed using numerical simulations to reduce the noise caused by passing trains. The main aim of this study is to examine the acoustic efficiency of prototype porous concrete sound absorbing panels, in relation to the ballasted and ballastless track structures. Presented results of the proposed unconventional experiments carried out on an improvised test stand using the recorded acoustic signals confirm the effectiveness of the developed vibroacoustic isolators.

Extragradient methods with dual inertial steps for solving equilibrium problems

ABSTRACT The primary focus of this study is how to expedite the convergence rate of the extragradient method by tactfully choosing inertial parameters and building up the step-size rule. To achieve this goal, we introduce three improvements to Korpelevich's extragradient method. These improvements include the use of dual inertial steps as well as a self-adaptive step-size rule. The proposed iterative techniques are employed for solving equilibrium problems in real Hilbert spaces. Initially, we establish the results for weak convergence of the proposed methods, assuming the involved bifunction to be both pseudomonotone and Lipschitz-type continuous. Subsequently, we demonstrate linear convergence in scenarios where the bifunction is strongly pseudomonotone and Lipschitz-type continuous. Finally, we present multiple numerical experiments to illustrate the practical effectiveness of the proposed methods.

Modified Tseng Method for Solving Pseudomonotone Variational Inequality Problem in Banach Spaces

This article examines the process for solving the fixed-point problem of Bregman strongly nonexpansive mapping as well as the variational inequality problem of the pseudomonotone operator. Within the context of p-uniformly convex real Banach spaces that are also uniformly smooth, we introduce a modified Halpern iterative technique combined with an inertial approach and Tseng methods for finding a common solution of the fixed-point problem of Bregman strongly nonexpansive mapping and the pseudomonotone variational inequality problem. Using our iterative approach, we develop a strong convergence result for approximating the solution of the aforementioned problems. We also discuss some consequences of our major finding. The results presented in this paper complement and build upon many relevant discoveries in the literature.

Multilayered neural network for power series‐based approximation of fractional delay differential equations

This paper trains a multilayered neural network (MLNN) for solving fractional delay differential equations (FDDEs), including nonlinear and singular types. The proposed methodology involves replacing the unknown functions in the equations with a truncated power series expansion. Subsequently, a collection of algebraic equations is solved utilizing an iterative minimization technique that leverages the capabilities of the MLNN architecture. The outcomes demonstrate that the MLNN architecture provides the required accuracy and strong stability compared to several numerical methods.

An Efficient Procedure to Compensate for the Errors Due to the Probe Mispositioning in a Cylindrical Near-Field Facility.

This paper deals with the compensation of the probe mispositioning errors occurring in a cylindrical near-field (NF) facility due to the imprecise control of the linear and azimuthal positioners allowing the cylindrical scanning and/or to their limited resolution and to defects in the rails guiding the linear motion. As a result, 3-D errors in the positioning of the probe at any sampling point, as prescribed by the adopted non-redundant representation, affect the accuracy of the NF measurements. An efficient procedure is here proposed to properly compensate for these errors. It involves two steps. The former allows one to correct the mispositioning errors due to the deviation of each actual sampling point from the nominal measurement cylinder. The latter makes use of an iterative technique to restore the NF samples at any sampling point fixed by the used non-redundant representation from the ones obtained at the previous step and affected by 2-D mispositioning errors. Once these steps have been fruitfully applied, the so-compensated NF samples are effectively interpolated through a 2-D optimal sampling interpolation (OSI) formula to accurately reconstruct the input data required to perform the traditional cylindrical near-to-far-field transformation. The OSI representation is here developed by considering an elongated antenna under test as enclosed either in a prolate spheroid or in a cylinder terminated by two half spheres (rounded cylinder) in order to make the representation effectively non-redundant. Numerical test results, which thoroughly prove the efficacy of the devised procedure in correcting even severe 3-D mispositioning errors, are reported.