Iterative Technique Research Articles

Modified couple stress and artificial intelligence examination of nonlinear buckling in porous variable thickness cylinder micro sport structures

This investigation focuses on the nonlinear behavior of porosity-dependent functionally graded (FG) truncated conical small-scale structures. The modified coupled stress theory, as well as the energy method, are applied to generate the nonlinear partial differential equations (PDEs) related to buckling analysis of simply supported nonuniform micro-cylindrical structures. The material dispersion is gradually changed along the length of the structures between the Nickel and concrete, while the porosity voids are scattered in the radial direction, and the external radius of the structure decreases along the length direction via nonlinear mathematic equations applicable in sports structures. The PDEs are numerically solved via the generalized differential quadrature method (GDQM) coupled with the numerical iterative technique. In this particular context, the aim is to predict nonlinear results using a newly developed methodology that employs artificial neural networks (ANNs). The predictions generated by this approach will be compared against previously obtained data and validated to ensure their accuracy and reliability. The ANN methodology is expected to provide a more robust and comprehensive framework for predicting nonlinear results, which would be helpful in a variety of settings, from scientific research to engineering applications.

The Adaptive Optimal Output Feedback Tracking Control of Unknown Discrete-Time Linear Systems Using a Multistep Q-Learning Approach

This paper investigates the output feedback (OPFB) tracking control problem for discrete-time linear (DTL) systems with unknown dynamics. To solve this problem, we use an augmented system approach, which first transforms the tracking control problem into a regulation problem with a discounted performance function. The solution to this problem is derived using a Bellman equation, based on the Q-function. In order to overcome the challenges of unmeasurable system state variables, we employ a multistep Q-learning algorithm that surpasses the advantages of the policy iteration (PI) and value iteration (VI) techniques and state reconstruction methods for output feedback control. As such, the requirement for an initial stabilizing control policy for the PI method is removed and the convergence speed of the learning algorithm is improved. Finally, we demonstrate the effectiveness of the proposed scheme using a simulation example.

Optimizing residential demand response in Ghana through iterative techniques and home appliance trend analysis

This study examines the concept of demand response in household appliance use. Its primary aim is to explore the factors influencing electricity consumption behavior and employ K-means clustering to group households, estimating daily electricity consumption patterns. This understanding is essential for the development of effective demand response strategies within the Greater Accra Region, Ghana. The research leveraged metrics, such as the Silhouette Score and principal component analysis to ensure the quality of the clustering process, effectively combining qualitative and quantitative data. Insights were enhanced by incorporating consumer behavior surveys to better comprehend appliance use trends and optimize demand response strategies. The findings emphasize differences in voltage, intensity, power consumption, and smart meter data among different household clusters. Notably, clusters 1 and 3 emerge as high energy consumers, particularly in water and cold appliances. These insights offer valuable guidance for targeted energy management and optimization strategies. This study underscores the significance of using consumer behavior insights to enhance and optimize demand response programs, providing essential guidance to energy stakeholders, particularly in Ghana, for the efficient optimization of electricity consumption and the successful implementation of demand response initiatives.

Reinforcement learning strategies using Monte-Carlo to solve the blackjack problem

Blackjack is a classic casino game in which the player attempts to outsmart the dealer by drawing a combination of cards with face values that add up to just under or equal to 21 but are more incredible than the hand of the dealer he manages to come up with. This study considers a simplified variation of blackjack, which has a dealer and plays no active role after the first two draws. A different game regime will be modeled for everyone to ten multiples of the conventional 52-card deck. Irrespective of the number of standard decks utilized, the game is played as a randomized discrete-time process. For determining the optimum course of action in terms of policy, we teach an agent-a decision maker-to optimize across the decision space of the game, considering the procedure as a finite Markov decision chain. To choose the most effective course of action, we mainly research Monte Carlo-based reinforcement learning approaches and compare them with q-learning, dynamic programming, and temporal difference. The performance of the distinct model-free policy iteration techniques is presented in this study, framing the game as a reinforcement learning problem.

Analysis and numerical simulation of fractional Bloch model arising in magnetic resonance imaging using novel iterative technique

Analysis and numerical simulation of fractional Bloch model arising in magnetic resonance imaging using novel iterative technique

Dual-quaternion-based iterative algorithm of the three dimensional coordinate transformation

Nowadays a unit quaternion is widely employed to represent the three-dimensional (3D) rotation matrix and then applied to the 3D similarity coordinate transformation. A unit dual quaternion can describe not only the 3D rotation matrix but also the translation vector meanwhile. Thus it is of great potentiality to the 3D coordinate transformation. The paper constructs the 3D similarity coordinate transformation model based on the unit dual quaternion in the sense of errors-in-variables (EIV). By means of linearization by Taylor's formula, Lagrangian extremum principle with constraints, and iterative numerical technique, the Dual Quaternion Algorithm (DQA) of 3D coordinate transformation in weighted total least squares (WTLS) is proposed. The algorithm is capable to not only compute the transformation parameters but also estimate the full precision information of computed parameters. Two numerical experiments involving an actual geodetic datum transformation case and a simulated case from surface fitting are demonstrated. The results indicate that DQA is not sensitive to the initial values of parameters, and obtains the consistent values of transformation parameters with the quaternion algorithm (QA), regardless of the size of the rotation angles and no matter whether the relative errors of coordinates (pseudo-observations) are small or large. Moreover, the DQA is advantageous to the QA. The key advantage is the improvement of estimated precisions of transformation parameters, i.e. the average decrease percent of standard deviations is 18.28%, and biggest decrease percent is 99.36% for the scaled quaternion and translations in the geodetic datum transformation case. Another advantage is the DQA implements the computation and precision estimation of traditional seven transformation parameters (which still are frequent used yet) from dual quaternion, and even could perform the computation and precision estimation of the scaled quaternion.Graphical

Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative

Abstract This study demonstrates the use of fractional calculus in the field of epidemiology, specifically in relation to dengue illness. Using noninteger order integrals and derivatives, a novel model is created to examine the impact of temperature on the transmission of the vector–host disease, dengue. A comprehensive strategy is proposed and illustrated, drawing inspiration from the first dengue epidemic recorded in 2009 in Cape Verde. The model utilizes a fractional-order derivative, which has recently acquired popularity for its adaptability in addressing a wide variety of applicable problems and exponential kernel. A fixed point method of Krasnoselskii and Banach is used to determine the main findings. The semi-analytical results are then investigated using iterative techniques such as Laplace-Adomian decomposition method. Computational models are utilized to support analytical experiments and enhance the credibility of the results. These models are useful for simulating and validating the effect of temperature on the complex dynamics of the vector–host interaction during dengue outbreaks. It is essential to note that the research draws on dengue outbreak studies conducted in various geographic regions, thereby providing a broader perspective and validating the findings generally. This study not only demonstrates a novel application of fractional calculus in epidemiology but also casts light on the complex relationship between temperature and the dynamics of dengue transmission. The obtained results serve as a foundation for enhancing our understanding of the complex interaction between environmental factors and infectious diseases, leading the way for enhanced prevention and control strategies to combat global dengue outbreaks.

An AI-based framework for earthquake relief demand forecasting: A case study in Türkiye

Accurately forecasting the demand for relief assistance is crucial for efficient post-disaster relief operations. This paper presents an AI-based framework for earthquake relief demand forecasting, aiming to optimize the distribution of emergency resources. To identify higher-risk areas, the framework integrates historical earthquake data with socioeconomic information. This information aids in identifying regions that require immediate relief assistance. The initial dataset for relief demand quantification includes essential parameters such as Latitude, Longitude, Population, Demand, Supply, Cost, Deaths, Injuries, Infrastructural Damage, and Cascading Disaster. By analyzing these inputs and factors, AI algorithms can quantify the relief demand scenario accurately, resulting in accurate and reliable forecasts of relief supply requirements. The iterative ML techniques in generating comprehensive data for Türkiye greatly enhance the quality and accuracy of relief demand prediction. The prediction models used in the framework, namely Least Angle Regression and Linear Regression, demonstrate exceptional performance in forecasting relief demand. They achieve a remarkable R2 score of 1, indicating a perfect fit to the data, and a Loss Error function value of zero, signifying highly accurate predictions. Additionally, the Decision Tree algorithm showcases strong capabilities in iterative learning, achieving an accuracy rate of 88.99 %. In addition to providing valuable insights for tailored relief strategies, the framework extends beyond relief demand by predicting outcomes such as casualties, injuries, and infrastructure damage. With a comprehensive understanding of the earthquake’s impact, relief organizations can strategize their response and allocate resources accordingly. The thorough methodology and innovative application of ML algorithms within our pioneering AI-based framework significantly contribute to the field. This signifies a fundamental shift in the approach to envisioning and executing relief operations following seismic events.

Exploring the Julia and Mandelbrot sets of [formula omitted] using a four-step iteration scheme extended with [formula omitted]-convexity

Iterative approaches have been established to be fundamental for the creation of fractals. This paper introduces an approach to visualize Julia and Mandelbrot sets for a complex function of the form Q(z)=zp+logct for all z∈ℂ, where p∈N∖{1},t∈[1,∞),c∈ℂ∖{0}, using a four-step iteration scheme extended with s-convexity. The study introduces an escape criteria for generating Julia and Mandelbrot sets using a four-step iterative method. It investigates how changes in the iteration parameters influence the shape and color of the resulting Julia and Mandelbrot sets. This approach can generate a wide range of captivating fractals and analyze them through numerical experiments.

On the soft tissue ultrasound elastography using FEM based inversion approach.

Elastography is a medical imaging modality that enables visualization of tissue stiffness. It involves quasi-static or harmonic mechanical stimulation of the tissue to generate a displacement field which is used as input in an inversion algorithm to reconstruct tissue elastic modulus. This paper considers quasi-static stimulation and presents a novel inversion technique for elastic modulus reconstruction. The technique follows an inverse finite element framework. Reconstructed elastic modulus maps produced in this technique do not depend on the initial guess, while it is computationally less involved than iterative reconstruction approaches. The method was first evaluated using simulated data (in-silico) where modulus reconstruction's sensitivity to displacement noise and elastic modulus was assessed. To demonstrate the method's performance, displacement fields of two tissue mimicking phantoms determined using three different motion tracking techniques were used as input to the developed elastography method to reconstruct the distribution of relative elastic modulus of the inclusion to background tissue. In the next stage, the relative elastic modulus of three clinical cases pertaining to liver cancer patient were determined. The obtained results demonstrate reasonably high elastic modulus reconstruction accuracy in comparison with similar direct methods. Also it is associated with reduced computational cost in comparison with iterative techniques, which suffer from convergence and uniqueness issues, following the same formulation concept. Moreover, in comparison with other methods which need initial guess, the presented method does not require initial guess while it is easy to understand and implement.

Deep unfolding as iterative regularization for imaging inverse problems

Deep unfolding methods have gained significant popularity in the field of inverse problems as they have driven the design of deep neural networks (DNNs) using iterative algorithms. In contrast to general DNNs, unfolding methods offer improved interpretability and performance. However, their theoretical stability or regularity in solving inverse problems remains subject to certain limitations. To address this, we reevaluate unfolded DNNs and observe that their algorithmically-driven cascading structure exhibits a closer resemblance to iterative regularization. Recognizing this, we propose a modified training approach and configure termination criteria for unfolded DNNs, thereby establishing the unfolding method as an iterative regularization technique. Specifically, our method involves the joint learning of a convex penalty function using an input-convex neural network to quantify distance to a real data manifold. Then, we train a DNN unfolded from the proximal gradient descent algorithm, incorporating this learned penalty. Additionally, we introduce a new termination criterion for the unfolded DNN. Under the assumption that the real data manifold intersects the solutions of the inverse problem with a unique real solution, even when measurements contain perturbations, we provide a theoretical proof of the stable convergence of the unfolded DNN to this solution. Furthermore, we demonstrate with an example of magnetic resonance imaging reconstruction that the proposed method outperforms original unfolding methods and traditional regularization methods in terms of reconstruction quality, stability, and convergence speed.

Colossal Kerr nonlinearity without absorption in a five-level atomic medium

In this work, we present an analytical method to achieve giant Kerr nonlinearity without absorption in a five-level atomic medium. By using iterative perturbation technique on density matrix equations, we have derived the analytical expressions of nonlinear susceptibility and Kerr nonlinear coefficient in the presence of spontaneously generated coherence (SGC) and relative phase between applied laser fields. It shows that, this five-level atomic medium exhibits multiple electromagnetically induced transparency (EIT) at three different frequencies, at the same time, the Kerr nonlinear coefficient is enhanced around three transparent spectral regions; in each such EIT region appears a pair of positive–negative peaks of Kerr nonlinear coefficient. In particular, these nonlinear peaks are moved to the center of the EIT windows via SGC. This means that the Kerr nonlinear coefficient is enhanced with completely suppressed absorption at different transparency frequencies. Furthermore, the magnitude and the sign of the Kerr nonlinear coefficient are easily controlled according to the SGC strength, the coupling laser intensity, and the relative phase between applied laser fields. Such a giant nonlinear medium can be useful for photonic devices working in the resonant frequency region without absorption. As a typical application, this giant Kerr nonlinear material has been applied to an interferometer for the formation of optical bistability, and showed the appearance of OB at the resonant frequency with significantly reduced threshold intensity and OB width.

Designing an optimal hybrid microgrid system using a leader artificial rabbits optimization algorithm for domestic load in Guelmim city, Morocco

This research endeavor strives to conceptualize a hybrid microgrid tailored for household consumption in Guelmim City, situated in the southern region of Morocco. In pursuit of this objective, a groundbreaking and enhanced algorithm, denoted as the Leader Artificial Rabbits Optimization Algorithm, is introduced. The efficacy of this innovative algorithm is initially validated by means of an exhaustive performance assessment involving a comprehensive comparison with the original version of the algorithm as well as other contemporary optimization methodologies. This comparative analysis encompasses the evaluation of the algorithms across 23 benchmark functions. The outcomes clearly exhibit that the developed algorithm outperforms both the original iteration and other optimization techniques in terms of both convergence speed and solution quality. Subsequent to this validation, the proposed algorithm is applied to the specific project at hand. The resulting outcomes are juxtaposed with those derived from other optimization strategies. This comparative evaluation serves to underscore the effectiveness of the suggested approach. The outcome of this comparison highlights a net present cost of $106,821, based on the microgrid configuration employing PV/wind/diesel/battery. Additionally, the cost of energy is estimated at approximately $0.11 per kWh, accompanied by a reliability rate of 5 % and an availability rate of 95 %.

Fast X-ray/CT image registration based on perspective projection triangular features

X-ray/CT image registration plays a pivotal role in enhancing surgical navigation success rates. However, challenges stemming from sparse and noisy X-ray image features, coupled with the complexities of multi-parameter optimization, impose limitations on existing methods in terms of registration accuracy and efficiency. In response, this paper presents an innovative approach—a fast X-ray/CT image registration method based on perspective projection triangular features(F-PPTF). By leveraging the conformal nature of perspective projection, the proposed method constructs perspective projection triangular features with rotation, translation, and scale invariance using point feature descriptors. Diverging from multi-parameter iterative optimization techniques, this approach achieves the decoupling of the six transformation parameters. This decoupling simplifies computational intricacies, thereby facilitating swift registration. Experimental evaluations conducted on synthetic and real X-ray images reveal an average rotational absolute error of 0.41°, an average translational absolute error of 1.16 mm, and an average registration time of 14.89 s. In comparison to conventional registration methodologies, the method presented in this paper demonstrates pronounced superiority in terms of both registration accuracy and efficiency, thereby exhibiting heightened potential for broader applicability.

HSS-progressive interpolation for Loop and Catmull–Clark Subdivision Surfaces

Loop and Catmull–Clark subdivision schemes are the most popular and commonly employed approximation subdivision schemes. However, some features of the given mesh are lost in their refinement process. Thus, the subdivision surfaces of Loop and Catmull–Clark schemes does not interpolate the vertices of the given mesh and shrink in some cases. This paper proposed new progressive iterative approximation (PIA) formats based on Hermitian and skew-Hermitian splitting iteration technique (HSS). The proposed method named H-PIA and its weighted version called WH-PIA force the limit surface of Loop and Catmull–Clark subdivision schemes to interpolate the vertices of the given mesh. The approximate optimal weight of WH-PIA is given, and the convergence of H-PIA and WH-PIA are proved. Various test examples are provided to illustrate the efficiency and effectiveness of the proposed H-PIA and WH-PIA. Experimental results demonstrate that the rate of convergence of H-PIA and WH-PIA are faster than that of the PIA and weighted PIA (W-PIA), respectively.

On anisotropic parabolic equation with nonstandard growth order

ABSTRACT In this paper, the existence and the uniqueness of an evolutionary anisotropic p i ( x ) -Laplacian equation with a damping term are studied. If the damping term is with a subcritical index, by the Di Giorgi iteration technique, the L ∞ -estimate of the weak solutions can be obtained. The existence of weak solution is proved by the renormalized solution method, and how the anisotropic characteristic of the considered equation affect the L ∞ -estimate of the weak solutions is revealed. The uniqueness is true strongly depending on subcritical index of the damping term, and this result goes beyond previous efforts in the literature (Bertsch M, Dal Passo R, Ughi M: Discontinuous viscosity solutions of a degenerate parabolic equation. Trans Amer Math Soc. 1990;320:779–798; Li Z, Yan B, Gao W. Existence of solutions to a parabolic p ( x ) − Laplace equation with convection term via L ∞ − Estimates. Electron J Differ Equ. 2015;46:1–21; Zhang Q, Shi P. Global solutions and self-similar solutions of semilinear parabolic equations with nonlinear gradient terms. Nonlinear Anal. 2010;72:2744–2752; Zhou W, Cai S. The continuity of the viscosity of the Cauchy problem of a degenerate parabolic equation not in divergence form. J Jilin University (Natural Sci.). 2004;42:341–345), etc.

Projection-based reduced order modeling of an iterative scheme for linear thermo-poroelasticity

This paper explores an iterative approach to solve linear thermo-poroelasticity problems, with its application as a high-fidelity discretization utilizing finite elements during the training of projection-based reduced order models. One of the main challenges in addressing coupled multi-physics problems is the complexity and computational expenses involved. In this study, we introduce a decoupled iterative solution approach, integrated with reduced order modeling, aimed at augmenting the efficiency of the computational algorithm. The iterative technique we employ builds upon the established fixed-stress splitting scheme that has been extensively investigated for Biot’s poroelasticity. By leveraging solutions derived from this coupled iterative scheme, the reduced order model employs an additional Galerkin projection onto a reduced basis space formed by a small number of modes obtained through proper orthogonal decomposition. The effectiveness of the proposed algorithm is demonstrated through numerical experiments, showcasing its computational prowess.

An iteration method for solving elliptic equations

In this paper, we use a natural iteration technique to prove the existence of solutions to nonlinear Dirichlet problems. Among the examples included is the prescribed mean curvature equation. The nature of the technique allows applications to unbounded domains, as we show with domains of the form Rn−1×(−d/2,d/2).

Fixed point and endpoint theorems of multivalued mappings in convex $ b $-metric spaces with an application

<abstract><p>In this paper, we investigated several new fixed points theorems for multivalued mappings in the framework $ b $-metric spaces. We first generalized $ S $-iterative schemes for multivalued mappings to above spaces by means of a convex structure and then we developed the existence of fixed points and approximate endpoints of the multivalued contraction mappings using iteration techniques. Furthermore, we introduced the modified $ S $-iteration process for approximating a common endpoint of a multivalued $ \alpha_{s} $-nonexpansive mapping and a multivalued mapping satisfying conditon $ (E^{'}) $. We also showed that this new iteration process converges faster than the $ S $-iteration process in the sense of Berinde. Some convergence results for this iterative procedure to a common endpoint under some certain additional hypotheses were proved. As an application, we applied the $ S $-iteration process in finding the solution to a class of nonlinear quadratic integral equations.</p></abstract>

Adaptive spline surface fitting with arbitrary topological control mesh.

Reconstructing a spline surface from a given arbitrary topological triangle mesh is a fundamental and challenging problem in computer-aided design and engineering. This paper introduces a novel surface fitting method utilizing G-NURBS capable of handling control meshes with arbitrary topologies. This method employs adaptive control point adjustment, guided by the geometric attributes of the input model, ensuring precise representation of sharp features such as edges and corners. Two primary strategies are employed: a parameter correspondence approach designed for sharp features and a control mesh iterative refinement technique that incorporates geometrical feature information. The proposed method has been tested and evaluated on various CAD models to demonstrate its effectiveness. This method can achieve higher fitting accuracy while faithfully preserving the geometrical features with fewer control points.