Iterative Method Research Articles

AN EFFICIENT ITERATIVE METHOD TO SIMULATE THE VARYING STATIC RECEPTANCE OF A THIN-WALLED WORKPIECE

This paper introduces an accelerated iterative Conjugate Gradient method (CG-method) for simulating the varying static receptance of a thin-walled workpiece. The proposed approach enhances computational efficiency by computing an optimal initial displacement guess for a given cutter location. This guess is based on the previously calculated displacement vector from the preceding cutter location, serving as the start iteration vector for the CG-method. The validation of efficiency gains through this method is demonstrated by a significant reduction in computation time for a numerical example. Moreover, to ensure the accuracy of the accelerated iterative CG-method, comparisons are made with the Cholesky method. The results confirm the precision of the proposed approach.

Iterative Method with Inertia for Variational Inequalities on Hadamard Manifolds with Lower Bounded Curvature

Iterative Method with Inertia for Variational Inequalities on Hadamard Manifolds with Lower Bounded Curvature

Development of an efficient vehicle-to-grid method for massive electric vehicle aggregation

The growing adoption of renewable energy and electric vehicles (EVs) has contributed to environmental sustainability; nevertheless, integration of these products into the power grid has become complex owing to their unpredictable nature and variable energy demands. A significant challenge lies in the realization of large-scale, coordinated control of EVs to serve as an alternative to traditional energy storage systems. This challenge is underscored by the complexity of optimization in large-scale cooperative control problems and the difficulty in reducing such problems to an easily manageable and practical level in real-world application. In response to these challenges, a practical mechanism for the integration of EVs into a vehicle-to-grid concept is proposed in this study. In this approach, the constraints involved in merging multiple EVs into a fictitious clustered energy storage unit, which are often neglected, are given renewed focus. An iterative multi-stage optimization method is introduced that includes an EV aggregation clustering model, multi-tier optimization model, and recursive framework. Here, marked efficacy for larger EV fleets is demonstrated for this method, providing optimal charging and discharging schedules for each vehicle while a high degree of precision is maintained. With the proposed technique, validated through numerous case studies using historical data, the global optimum solution is largely approximated, with a marginal deviation of 4 %. In addition, robustness of the model is demonstrated under varying pricing scenarios, with a computation time that increases in a linear manner, rather than exponentially, as the number of EVs increases. Meanwhile, compared with conventional methods, the technique proposed in this study has the capacity to fulfill the charging demands of all users with reduced charging expense, demonstrating the high precision and efficacy of the technique.

An Enhanced Real-time Iterative Compensation Method for Fast Tool Servos with Resonance Suppression

An Enhanced Real-time Iterative Compensation Method for Fast Tool Servos with Resonance Suppression

NUMERICAL TREATMENT OF LINEAR VOLTERRA INTEGRO DIFFERENTIAL EQUATIONS USING VARIATIONAL ITERATION ALGORITHM WITH COLLOCATION

To numerically solve the linear Volterra integro-differential equation, this study employs fourth-kind Chebyshev polynomials and the variational iteration algorithm with collocation, which is a combination of the variational iteration strategy and collocation technique. By applying fourth-kind Chebyshev polynomials to the variational iteration method with collocation for solving Volterra integro-differential equations, mathematical problems with a broad range of multidisciplinary applications are addressed, and numerical techniques that produce more accurate and efficient results are developed. The recommended method is then used, and the fourth-kind Chebyshev polynomials generated for the given integro-differential equation serve as the trial functions for the approximation. As a result, the suggested method's significance probably goes beyond a particular equation or application, as it contributes to the larger field of mathematical modeling and numerical analysis. Research methods employing a variational iteration algorithm with collocation aim to provide general techniques that can be applied to a wide range of problems. Additionally, numerical examples were provided to highlight the applicability and dependability of the proposed methodology. The mathematical computations were carried out using the Maple 18 software.

Data analysis of non-linear radiative electro-periodic MHD flow past a stretching sheet with activation energy impact

Electro-periodic Magneto-hydrodynamics (EPMHD), activation energy, and non-linear radiation are pivotal elements in engineering and industry also contribute to advancements in fields like heat transfer, materials science, and chemical engineering. Through similarity transformation, governing partial differential equations simplify into ordinary differential equations. Precise computational solutions are derived using the Nachtsheim-Swigert shooting iteration method (NSSIM) and the reliable 6th-order Runge-Kutta integration algorithm (RKIA). The profiles of velocities, temperatures, concentrations, skin friction, heat and mass transfer rate are presented by graphically. The novel aspect of this research is that thermal performance is enhanced by non-linear radiation by around 2.28%, whereas linear radiation only produces a 0.28% improvement in thermal performance. Also the mass transfer rate experiences a decrease of about 25.76% with increasing chemical reactions in the presence of activation energy and a more substantial 62.22% reduction in its absence, notably showing a comparatively milder decline of 36.46% in the presence of activation energy than in its absence. Furthermore, this study yields three novel linear regression equations, skillfully derived from the numerical and graphical results. This research have practical applications in understanding and optimizing processes involving fluid dynamics, such as the behavior of certain materials or substances subjected to stretching or deformation.

A Novel Iterative Method to Find the Moore-Penrose Inverse of a Tensor with Einstein Product

A Novel Iterative Method to Find the Moore-Penrose Inverse of a Tensor with Einstein Product

A penta-linear backbone model for unbonded post-tensioned concrete masonry shear walls

Unbonded post-tensioned concrete masonry (UPCM) shear walls are an effective seismic force resisting system due to their ability to mitigate expected damage through their self-centering capabilities. A few design procedures were proposed to predict the in-plane flexural response of UPCM walls, albeit following only basic mechanics and/or extensive iterative methods. Such procedures, however, may not be capable of capturing the complex nonlinear relationships between different parameters that affect UPCM walls’ behavior or are tedious to be adopted for design practice. In addition, the limited datasets used to validate these procedures may cast doubt on their accuracy and validity for new, unseen data, further hindering their adoption by practitioners and design standards. To address these issues, an experimentally-validated nonlinear numerical model was adopted in this study and subsequently employed to simulate 95 UPCM walls with different design parameters to compensate for the lack of relevant experimental data in the current literature. Guided by mechanics and using this database, an evolutionary algorithm, multigene genetic programming (MGGP), was adopted to uncover the relationships controlling the response of UPCM walls, and subsequently develop simplified closed-form wall behavior prediction expressions. Specifically, through integrating MGGP and basic mechanics, a penta-linear backbone model was developed to predict the load-displacement backbone for UPCM walls up to 20% strength degradation. Compared to existing predictive procedures, the prediction accuracy of the developed model and its closed-form nature are expected to facilitate better understanding of such wall behaviors and subsequently open the gate to further incorporate other experimental and numerical results to ultimately incorporate UPCM in mainstream designs in the near future.

A new identification of Lagrange multipliers to study solutions of nonlinear Caputo–Fabrizio fractional problems

This research aims to provide a new identification of Lagrange multipliers using a novel hybrid method based on the Khalouta transform method and the variational iteration method and to study the solutions of nonlinear fractional problems. This method is called Khalouta variational iteration method (KHVIM). The fractional derivative is considered in Caputo–Fabrizio sense. The uniqueness and convergence results are investigated using Banach fixed point theorem. The results are obtained in the form of successive approximations corresponding to the proposed problem. To demonstrate the accuracy and effectiveness of the proposed method, three different nonlinear fractional partial differential equations are provided. Approximate solutions of the fractional equations were obtained. These solutions quickly converged to exact solutions with lower computational cost. Furthermore, the method used in this study is more generalized and allows our results to be more extensive and cover several new and existing fractional problems in the literature.

A fast analysis algorithm for structural vibration modal sensitivity

Vibration modal sensitivity analysis has a wide range of applications in structural optimization design, model correction, fault detection, and reliability analysis. The existing methods for calculating modal sensitivity mainly include modal superposition method, Nelson’s method, and some improved algorithms derived from them. However, the existing algorithms have the drawback of low computational efficiency when applied to modal sensitivity analysis of the large-scale structures. In view of this, the objective of this work is to develop a fast modal sensitivity analysis method that can more efficiently calculate the modal sensitivity of the large structures with thousands of degrees of freedom. This new sensitivity analysis technique integrates Sherman-Morrison-Woodbury formula, subspace iteration and forward-difference to achieve the goal of fast calculation. The innovations of the proposed method mainly include the following aspects. Firstly, the Sherman-Morrison-Woodbury formula is used to quickly calculate the perturbed flexibility matrix due to the minor modification in the structure. Then, the perturbed flexibility matrix is introduced into the subspace iteration method to calculate the perturbed modal parameters. Finally, the forward-difference algorithm is used to calculate the modal sensitivity. Two numerical examples are used to verify the superiority of the proposed modal sensitivity algorithm. Taking the 1952-bar structure as an example, the calculation time of the proposed algorithm is only 8.3 % and 18.2 % of that of the existing approximate modal superposition method and the improved Nelson’s method, respectively. In terms of calculation accuracy, the results obtained by the proposed method are exactly the same as the exact solution when the perturbation scale is set to 10−5. It is found that the proposed method significantly reduces computation time compared to the existing methods on the premise that the calculation accuracy is basically unchanged.

On the Kantorovich Theory for Nonsingular and Singular Equations

We develop a new Kantorovich-like convergence analysis of Newton-type methods to solve nonsingular and singular nonlinear equations in Banach spaces. The outer or generalized inverses are exchanged by a finite sum of linear operators making the implementation of these methods easier than in earlier studies. The analysis uses relaxed generalized continuity of the derivatives of operators involved required to control the derivative and on real majorizing sequences. The same approach can also be implemented on other iterative methods with inverses. The examples complement the theory by verifying the convergence conditions and demonstrating the performance of the methods.

An adversarial example attack method based on predicted bounding box adaptive deformation in optical remote sensing images

Existing global adversarial attacks are not applicable to real-time optical remote sensing object detectors based on the YOLO series of deep neural networks, which makes it difficult to improve the adversarial robustness of single-stage detectors. The existing methods do not work well enough in optical remote sensing images, which may be due to the mechanism of adversarial perturbations is not suitable. Therefore, an adaptive deformation method (ADM) was proposed to fool the detector into generating wrong predicted bounding boxes. Building upon this, we introduce the Adaptive Deformation Method Iterative Fast Gradient Sign Method (ADM-I-FGSM) and Adaptive Deformation Mechanism Projected Gradient Descent (ADM-PGD) against YOLOv4 and YOLOv5. ADM method can obtain the deformation trend values based on the length-to-width ratio of the prediction box, and the adversarial perturbation trend generated based on these trend values has better adversarial effect. Through experiments, we validate that our approach exhibits a higher adversarial success rate compared to the state-of-the-art methods. We anticipate that our unveiled attack scheme will aid in the evaluation of adversarial resilience of these models.

Analytical solution for single-pixel ptychography through linear modeling

Amplitude-modulated single-pixel ptychography (SPP) enables non-interferometric complex-field imaging of objects. However, the conventional iterative and nondeterministic reconstruction methods, based on the ptychography algorithm, pose challenges in fully understanding the role of critical optical parameters. In response, this paper introduces an innovative analytical approach that establishes a theoretical foundation for the uniqueness of SPP reconstruction results. The proposed method conceptualizes SPP as a system of linear equations in the frequency domain, involving both object and modulated illumination. Solving this equation system reveals a determined solution for the complex object, providing an alternative to iterative and nondeterministic techniques. Through a series of simulations, this approach not only validates the uniqueness of SPP reconstruction, but also explores key properties influencing accuracy.

Improved Mixture Correntropy Cubature Kalman Filter for Attitude Estimation

Abstract This work proposes an algorithm based on improved mixture correntropy cubature Kalman filtering (IMC-CKF) to address the issues of low accuracy and susceptibility to complex noise and outlier interference in inertial navigation attitude estimation. First, a combination of Gaussian kernel and Cauchy kernel is suggested to construct mixture correntropy to tackle the problem of single kernel-based correntropy being insufficient to confronted with complex noise. Second, the model fitting loss based on mean square error and measurement fitting loss based on mixture correntropy are used to establish the objective function. The maximum correntropy criterion (MCC) replaces the minimum mean square error (MMSE) criterion, and the fixed-point iteration method is used to solve the objective function, deriving the mixture correntropy matrix to adjust the measurement noise variance. Finally, the semi-trapezoidal membership function is used to determine the mixture correntropy coefficient. Accordingly, the algorithm can adaptively select the proportions of each kernel function according to the respective noise interference situation. Simulations and dynamic–static experiments have been conducted, and the algorithm has been compared with single kernel-based correntropy algorithms and other robust algorithms to confirm its superior precision and stability under complex noise and outlier interference.

Optimal Voltage Recovery Learning Control for Microgrids with N-Distributed Generations via Hybrid Iteration Algorithm

Considering that the nonlinearity and uncertainty of the microgrid model complicate the derivation and design of the optimal controller, an adaptive dynamic programming (ADP) algorithm is designed to solve the model-free non-zero-sum game. By combining the advantages of policy iteration and value iteration, an optimal learning control scheme based on hybrid iteration is constructed to provide stringent real power sharing for the nonlinear and coupled microgrid systems with N-distributed generations. First, using non-zero-sum differential game strategy, a novel distributed secondary voltage recovery consensus optimal control protocol is built using a hybrid iteration method to realize the voltage recovery of microgrids. Then, the data of the system state and input are gathered along a dynamic system trajectory and a data-driven optimal controller learns the game solution without microgrid physics information, enhancing convenience and efficiency in practical applications. Furthermore, the convergence analysis is given in detail, and it is proved that the control protocol can converge to the optimal solution so as to ensure the stability of the voltage recovery of the microgrid system. Convergence analysis proves the convergence of the the protocol to the optimal solution, ensuring voltage recovery stability. Simulation results validate the feasibility and effectiveness of the proposed scheme.

Improved dragonfly optimization algorithm based on quantum behavior for multi-objective optimization of ethylene cracking furnace

Ethylene is one of the important basic raw materials for the modern chemical production, accounting for over 75 % of petrochemical products. And the ethylene cracking furnace is subject to coking problems that can impede the thermal conductivity of the reaction tube. Therefore, an improved multi-objective dragonfly optimization algorithm based on quantum behavior is proposed. The particle evolutionary model introduces the quantum bound state δ-potential well model, which improves the global convergence ability and the convergence speed of the dragonfly optimization algorithm. In addition, the calculation formulas for parameters are improved by introducing natural logarithm and the iterative search method is changed to a triple search. Moreover, the global convergence and local search ability of the quantum behavior enhancement algorithm is assisted by adaptively selecting the search strategy according to the current number of iterations of the improved dragonfly algorithm. Compared with other multi-objective optimization algorithms on the ZDT and CEC test functions, the proposed algorithm has good global convergence and local search capabilities in terms of the inverted general distance. Finally, the proposed algorithm is applied in the multi-objective optimization of an ethylene cracking furnace, with the ethylene yield and the propylene yield as optimization objectives. The experimental results show that the ethylene yield can be increased by 1.5498 %, while the propylene yield decreases by only 0.0081 %, which proves that the proposed algorithm achieves better effect in optimizing the main product yield under fixed cycle adjustment operating conditions compared to original operating conditions.

Low-rank generalized alternating direction implicit iteration method for solving matrix equations

Low-rank generalized alternating direction implicit iteration method for solving matrix equations

NetHD: Neurally Inspired Integration of Communication and Learning in Hyperspace

The 6G network, the next‐generation communication system, is envisaged to provide unprecedented experience through hyperconnectivity involving everything. The communication should hold artificial intelligence‐centric network infrastructures as interconnecting a swarm of machines. However, existing network systems use orthogonal modulation and costly error correction code; they are very sensitive to noise and rely on many processing layers. These schemes impose significant overhead on low‐power internet of things devices connected to noisy networks. Herein, a hyperdimensional network‐based system, called , is proposed, which enables robust and efficient data communication/learning. exploits a redundant and holographic representation of hyperdimensional computing (HDC) to design highly robust data modulation, enabling two functionalities on transmitted data: 1) an iterative decoding method that translates the vector back to the original data without error correction mechanisms, or 2) a native hyperdimensional learning technique on transmitted data with no need for costly data decoding. A hardware accelerator that supports both data decoding and hyperdimensional learning using a unified accelerator is also developed. The evaluation shows that provides a bit error rate comparable to that of state‐of‐the‐art modulation schemes while achieving 9.4 faster and 27.8 higher energy efficiency compared to state‐of‐the‐art deep learning systems.

Multi-step-length gradient iterative method for separable nonlinear least squares problems

Multi-step-length gradient iterative method for separable nonlinear least squares problems

Fixed-Point Iteration Method for Uncertain Parameters in Dynamic Response of Systems with Viscoelastic Elements

Fixed-Point Iteration Method for Uncertain Parameters in Dynamic Response of Systems with Viscoelastic Elements