Iterative Optimization Method Research Articles

A new approach for design of constant modulus discrete phase radar waveform with low WISL

This paper deals with the constant modulus waveform design for a cognitive radar in an effort to achieve the desired Auto-Correlation Function (ACF). The Weighted Integrated Sidelobe Level (WISL) of ACF is considered as a figure of merit accounting for the finite alphabet constraint. By introducing an auxiliary variable, an Inexact Alternating Direction Penalty Method (IADPM) framework is developed to solve the resultant non-convex and, in general, NP-hard problem. In each iteration, it converts the original problem into two subproblems which are solved by an analytic technique and a fast Iterative Sequential Quartic Optimization (ISQO) method, respectively, while locally increasing the involved penalty factor. In particular, the developed procedure can well overcome the non-convergence issue of Alternating Direction Method of Multipliers (ADMM) as it is proved to be convergent for any initialization under some mild conditions. Finally, the WISL, auto-correlation performance, and convergence speed of the proposed technique are evaluated against the state-of-the-art methods. Results show that our proposal outperforms the competitive counterparts with reference to the achieved WISL value and provides the favorable performance-complexity balance.

Optimal control on the attitude rotation of a flexible satellite model base on tetrahedral configured reaction wheels

The increase in demand for performance for satellite capabilities has pushed the design of the system to be more power consuming. Currently, most of the satellite design are equipped with large solar panel in order to produce sufficient power. Thus, this translates to a higher flexibility in the satellite which makes the satellite prone to vibratory motion. The primary cause of vibratory motion in satellite is the attitude rotation. Reaction wheel is a widely used attitude rotation actuator for a satellite Commonly, the reaction wheels are configured in the tetrahedral form. This causes uneven maximum torque at any direction. Hence, an iterative optimal control method is applied using GPOPS toolbox to achieve minimum time of rotation with low level of induced vibratory motion. The optimized control is compared with the Eigen-axis Quaternion Feedback control to observe the performance of the optimal control. Depending on the direction of attitude manoeuvre, the optimal control has shown an improvement between 3.49% to 25.11% in manoeuvre time. Overall, the optimal control outperformed the traditional the Eigen-axis Quaternion Feedback control.

An iterative approach to optimize loudspeaker placement for multi-zone sound field reproduction

Various array patterns, such as circular, linear, and arc-shaped arrays, have been used in multi-zone sound field reproduction, but most of them are based on empirical rather than judicious selection. This article proposes an iterative optimization method to select the loudspeaker positions from a large set of candidate locations. Both the number and locations of the loudspeakers can be designed with superior performance. Both single-frequency and broadband simulations based on the acoustic contrast control method are performed to validate the proposed scheme, and the performance of the optimized array is compared with that of an arc-shaped array and that of an array optimized with an existing method.

Impact of Sea‐Ice Model Complexity on the Performance of an Unstructured‐Mesh Sea‐Ice/Ocean Model under Different Atmospheric Forcings

AbstractWe have equipped the unstructured‐mesh global sea‐ice and ocean model FESOM2 with a set of physical parameterizations derived from the single‐column sea‐ice model Icepack. The update has substantially broadened the range of physical processes that can be represented by the model. The new features are directly implemented on the unstructured FESOM2 mesh, and thereby benefit from the flexibility that comes with it in terms of spatial resolution. A subset of the parameter space of three model configurations, with increasing complexity, has been calibrated with an iterative Green's function optimization method to test the impact of the model update on the sea‐ice representation. Furthermore, to explore the sensitivity of the results to different atmospheric forcings, each model configuration was calibrated separately for the NCEP‐CFSR/CFSv2 and ERA5 forcings. The results suggest that a complex model formulation leads to a better agreement between modeled and the observed sea‐ice concentration and snow thickness, while differences are smaller for sea‐ice thickness and drift speed. However, the choice of the atmospheric forcing also impacts the agreement of the FESOM2 simulations and observations, with NCEP‐CFSR/CFSv2 being particularly beneficial for the simulated sea‐ice concentration and ERA5 for sea‐ice drift speed. In this respect, our results indicate that parameter calibration can better compensate for differences among atmospheric forcings in a simpler model (i.e., sea‐ice has no heat capacity) than in more realistic formulations with a prognostic sea‐ice thickness distribution and sea ice enthalpy.

Inverse Design for Silicon Photonics: From Iterative Optimization Algorithms to Deep Neural Networks

Silicon photonics is a low-cost and versatile platform for various applications. For design of silicon photonic devices, the light-material interaction within its complex subwavelength geometry is difficult to investigate analytically and therefore numerical simulations are majorly adopted. To make the design process more time-efficient and to improve the device performance to its physical limits, various methods have been proposed over the past few years to manipulate the geometries of silicon platform for specific applications. In this review paper, we summarize the design methodologies for silicon photonics including iterative optimization algorithms and deep neural networks. In case of iterative optimization methods, we discuss them in different scenarios in the sequence of increased degrees of freedom: empirical structure, QR-code like structure and irregular structure. We also review inverse design approaches assisted by deep neural networks, which generate multiple devices with similar structure much faster than iterative optimization methods and are thus suitable in situations where piles of optical components are needed. Finally, the applications of inverse design methodology in optical neural networks are also discussed. This review intends to provide the readers with the suggestion for the most suitable design methodology for a specific scenario.

Multiple Crack Detection in Thick-walled Pipes Using Artificial Bee Colony Algorithm

An analytical method for diagnosis of cracks in thick-walled pipes with a circular hollow section is investigated in this study. In the proposed method, the defect is assumed to be a non-leaking crack, which is modeled by a massless linear spring with infinitesimal length at the crack location. In order to find the cracks in the pipe, the vibration-based method related to the modal properties of the pipe is utilized. In the modal analysis, the mass and stiffness matrices influence the dynamic properties of the pipe. It is assumed that the mass matrix remains unchanged after the crack initiation, while the corresponding stiffness matrix changes. The stiffness matrix of a cracked element can be formulated by the finite element method with two unknown parameters: location and depth of the crack. Using the eigensolution for an undamped dynamic system to formulate the objective function yields to a complicated optimization problem, which can be solved by an iterative numerical optimization method. Among the optimization approaches, the Artificial Bee Colony (ABC) algorithm is a simple and flexible technique for minimizing the objective function. In this paper, the analytical model is utilized to find the size and position of cracks in a pipe using the ABC algorithm and subsequently some numerical examples are examined in order to assess the accuracy of the method. The results show that the proposed method is able to acceptably estimate the location and depth of multiple cracks in the straight pipes as well as curved ones.

Dynamic event‐triggered sliding mode security control for Markovian jump systems: Learning‐based iteration optimization method

AbstractThis work investigates the sliding mode control (SMC) of Markovian jump systems under communication constraints subject to unavailable states and deception attack. To reduce the information communication, a dynamic event‐triggered (DET) scheme is employed to regulate the transmission of measured outputs, in which the transmitted signals may be maliciously attacked. Meanwhile, a mode estimator is utilized to estimate the unavailable system mode. Then, an asynchronous static output‐feedback SMC law is co‐designed with the DET strategy, by which the influence of deception attacks can be completely accommodated and the closed‐loop systems are ensured to be stochastically ultimate bounded. Moreover, a learning‐based iteration optimization algorithm is developed to minimize the convergence domain. Finally, the numerical simulations are given to illustrate the proposed control scheme.

Joint Optimization for Coordinated Charging Control of Commercial Electric Vehicles Under Distributed Hydrogen Energy Supply

The transition to the zero-carbon power system is underway accelerating recently. Hydrogen energy and electric vehicles (EVs) are promising solutions on the supply and demand sides. This brief presents a novel architecture that includes hydrogen production stations, fast-charging stations, and commercial EVs. The proposed architecture jointly optimizes the hydrogen energy dispatch and the EV charging location selection and is formulated by a time-varying bilevel bipartite graph (T-BBG) model. We develop a bilevel iteration optimization method combining the linear programming (LP) and the Kuhn–Munkres (KM) algorithm to solve the joint problem whose optimality is proved theoretically. The effectiveness of the proposed architecture on reducing the operating cost is verified via case studies in Shanghai. The proposed method outperforms other strategies and improves the performance by at least 13%, which shows the potential economic benefits of the joint architecture. The convergence and impact of parameters are assessed.

Multiple Hybrid of Lambda Iteration and Bee Colony Optimization Method for Solving Economic Dispatch Problem

Multiple Hybrid of Lambda Iteration and Bee Colony Optimization Method for Solving Economic Dispatch Problem

A Family of Optimal Eighth Order Iteration Functions for Multiple Roots and Its Dynamics

In this manuscript, we present a new general family of optimal iterative methods for finding multiple roots of nonlinear equations with known multiplicity using weight functions. An extensive convergence analysis is presented to verify the optimal eighth order convergence of the new family. Some special cases of the family are also presented which require only three functions and one derivative evaluation at each iteration to reach optimal eighth order convergence. A variety of numerical test functions along with some real-world problems such as beam designing model and Van der Waals’ equation of state are presented to ensure that the newly developed family efficiently competes with the other existing methods. The dynamical analysis of the proposed methods is also presented to validate the theoretical results by using graphical tools, termed as the basins of attraction.

Energy-Efficient Communications in Unmanned Aerial Relaying Systems

Due to flexible deployment and low cost, an unmanned aerial relaying (UAR) system has been considered as a promising aerial communication platform to complement current terrestrial infrastructure in some scenarios like temporary hotspots, disaster areas, and complex terrains. However, practical UAR systems may not be able to provide ubiquitous and high-quality wireless connections, mainly due to the limited on-board energy of unmanned aerial vehicles (UAVs). Consequently, the UAVs are unable to hover in the sky for a long time, thus having to land frequently for energy replenishment. To save UAVs' energy, we propose a joint communication and placement design for energy-efficient communications in a multi-hop UAR system. Specifically, we formulate the Energy Consumption Rate minimization problem, called ECR, by jointly considering routing, data rate, transmission power, and UAV position. Since ECR is a non-convex nonlinear programming, we propose an iterative optimization method to solve ECR iteratively by first reducing ECR into two sub-problems ECR-C and ECR-P and then solving them sequentially at an iteration. Specifically, we develop an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\epsilon$</tex-math></inline-formula> -bounded approximation algorithm to solve ECR-C with a performance guarantee, and reformulate ECR-P as a global consensus optimization problem solved by an ADMM (alternating direction method of multipliers) method. Particularly, all UAVs locally update their own positions in parallel, reducing the computation and implementation complexity significantly. Extensive simulation results show the energy efficiency improvement by up to 20% compared with other existing algorithms.

Research on Multibeam Pattern Synthesis of Time Modulated Array Based on Convex Optimization

An efficient multibeam pattern synthesis method for time modulated array (TMA) is proposed in this paper. The aim of this method is to generate a beam pattern on the specified sideband of TMA. The pattern synthesis problem is divided into two stages. In the first stage, the sequential convex optimization method is used to suppress the sidelobe of the center frequency and reduce the amplitude dynamic range ratios (DRR). In the second stage, the iterative convex optimization method is used to realize the multibeam pattern synthesis in the sideband. Owing to the introduction of convex optimization, the proposed method could be more efficient than approaches using a global optimization algorithm. The proposed method is capable of realizing pattern synthesis under different DRR constraints and different beam radiation directions. Numerical examples of two beams and four beams patterns of 1000-element time modulated linear array verify the effectiveness of the proposed method.

Fabrication and characterization of an L3 nanocavity designed by an iterative machine-learning method

Optical nanocavities formed by defects in a two-dimensional photonic crystal (PC) slab can simultaneously realize a very small modal volume and an ultrahigh quality factor (Q). Therefore, such nanocavities are expected to be useful for the enhancement of light–matter interaction and slowdown of light in devices. In the past, it was difficult to design a PC hole pattern that makes sufficient use of the high degree of structural freedom of this type of optical nanocavity, but very recently, an iterative optimization method based on machine learning was proposed that efficiently explores a wide parameter space. Here, we fabricate and characterize an L3 nanocavity that was designed by using this method and has a theoretical Q value of 29 × 106 and a modal volume of 0.7 cubic wavelength in the material. The highest unloaded Q value of the fabricated cavities is 4.3 × 106; this value significantly exceeds those reported previously for an L3 cavity, i.e., ≈2.1 × 106. The experimental result shows that the iterative optimization method based on machine learning is effective in improving cavity Q values.

GroupRegNet: a groupwise one-shot deep learning-based 4D image registration method

Accurate deformable four-dimensional (4D) (three-dimensional in space and time) medical images registration is essential in a variety of medical applications. Deep learning-based methods have recently gained popularity in this area for the significantly lower inference time. However, they suffer from drawbacks of non-optimal accuracy and the requirement of a large amount of training data. A new method named GroupRegNet is proposed to address both limitations. The deformation fields to warp all images in the group into a common template is obtained through one-shot learning. The use of the implicit template reduces bias and accumulated error associated with the specified reference image. The one-shot learning strategy is similar to the conventional iterative optimization method but the motion model and parameters are replaced with a convolutional neural network and the weights of the network. GroupRegNet also features a simpler network design and a more straightforward registration process, which eliminates the need to break up the input image into patches. The proposed method was quantitatively evaluated on two public respiratory-binned 4D-computed tomography datasets. The results suggest that GroupRegNet outperforms the latest published deep learning-based methods and is comparable to the top conventional method pTVreg. To facilitate future research, the source code is available at https://github.com/vincentme/GroupRegNet.

Comparative study of generalized couette flow of couple stress fluid using optimal homotopy asymptotic method and new iterative method

In this research work, we have studied the steady generalized Couette flow of couple stress fluid between two parallel plates considering the non-isothermal effects. The governing equations that are, continuity, momentum and energy equations are reduced to ordinary differential equations. The Optimal Homotopy Asymptotic Method (OHAM) and New Iterative Method (NIM) are used to solve this coupled system of differential equations. Using the said methods, we have obtained expressions for velocity profile, temperature distribution, volume flux, average velocity and shear stress. The results of OHAM and NIM are compared numerically as well as graphically and a tremendous agreement is attained.

Self-Calibration of Inertial Sensor Arrays

A maximum likelihood estimator is presented for self-calibrating both accelerometers and gyroscopes in an inertial sensor array, including scale factors, misalignments, biases, and sensor positions. By simultaneous estimation of the calibration parameters and the motion dynamics of the array, external equipment is not required for the method. A computational efficient iterative optimization method is proposed where the calibration problem is divided into smaller subproblems. Further, an identifiability analysis of the calibration problem is presented. The analysis shows that it is sufficient to know the magnitude of the local gravity vector and the average scale factor gain of the gyroscopes, and that the array is exposed to two types of motions for the calibration problem to be well defined. The proposed estimator is evaluated by real-world experiments and by Monte Carlo simulations. The results show that the parameters can be consistently estimated and that the calibration significantly improves the accuracy of the motion estimation. This enables on-the-fly calibration of small inertial sensors arrays by simply twisting them by hand.

A new efficient technique for solving modified Chua\u2019s circuit model with a new fractional operator

Chua’s circuit is an electronic circuit that exhibits nonlinear dynamics. In this paper, a new model for Chua’s circuit is obtained by transforming the classical model of Chua’s circuit into novel forms of various fractional derivatives. The new obtained system is then named fractional Chua’s circuit model. The modified system is then analyzed by the optimal perturbation iteration method. Illustrations are given to show the applicability of the algorithms, and effective graphics are sketched for comparison purposes of the newly introduced fractional operators.

Guiding iterative optimisation methods to a predefined kind of optima for unconstrained optimisation problems

One of the most fundamental issues in the field of mathematical optimisation is the convergence of an iterative optimisation method and by this we are referring to two things. First, will the method find an optimum and second, will this optimum be a local one or a global one? A recently proposed technique (Nikolakakou et al., 2015b) that is used in order to lessen the dependence a locally convergent iterative optimisation method has on the initial guess, is exploited in this paper. A way so that such a method may be guided to a predefined kind of minimum (local or global) is presented. Well known test functions were used for experimentation. Statistical analysis was conducted by applying a logistic regression classification model on data arisen from the numerical results which confirmed that iterative optimisation methods can be guided to a predefined kind of optimum.

ВПРОВАДЖЕННЯ СИСТЕМ ПІДТРИМКИ ПРИЙНЯТТЯ РІШЕНЬ ЩОДО УПРАВЛІННЯ ДОМЕННОЮ ПЛАВКОЮ В УМОВАХ МЕТАЛУРГІЙНОГО ВИРОБНИЦТВА ПрАТ “ДКХЗ“

The aim of the work is to increase the level of automation of blast furnace production through the development and implementation of new systems to support decision-making on the management of blast furnace smelting in changing technological and fuel conditions. The article presents a description of three decision support systems (DSS) in the mode of an adviser to the technological personnel of blast furnaces, which were implemented by the Iron and Steel Institute or underwent pilot testing as part of the automated control system of the blast furnace shop of the metallurgical production of PrJSC "Dniprovskyi Coke Plant" (Kamianske). The first DSS for managing the thermal state was implemented in 2021, it includes the entire list of information necessary for personnel in a convenient and compact form, generates recommendations in case of technology deviations and, in case of incorrect actions of the personnel, signals the need for correct actions. The main recommendations of the system are to correct the raceway adiabatic flame temperature, coke consumption when its characteristics and ore load change. Using the system allows both reducing the specific coke consumption and preventing unplanned downtime. The second DSS for controlling the distribution of fuel additives over air tuyeres is based on information on thermal loads determined on water-cooled elements of tuyere tools. The main recommendations of the system are to adjust the amount of injected pulverized coal fuel on individual tuyeres in order to ensure a uniform distribution of the raceway adiabatic flame temperature around the circumference of the blast furnace and, as a result, the energy efficiency of blast furnace smelting. The third DSS for adjusting the parameters of the charging mode is based on information from the means of controlling the temperatures of the gas flow above the surface of the charge in the blast furnace. The functioning of this system is based on determining the reference curves for the distribution of the gas flow along the furnace radii, corresponding to the minimum consumption of coke and maximum productivity, and on the search for solutions by direct and iterative optimization methods, which allow, by adjusting the loading parameters, to ensure a rational distribution of charge materials and gas flow in the furnace.

Particle Size Characterization in Liquid–Solid Dispersion With Aggregates by Broadband Ultrasound Attenuation

Ultrasound attenuation methods for particle size characterization generally assume that the dispersed phases are uniformly dispersed in the continuous phase. However, the aggregation of particles in dispersions affects ultrasound attenuation, which limits the estimation accuracy of the attenuation model. A broadband ultrasound method is proposed, which utilizes a fractal approach to address the acoustic attenuation influence of particle aggregation. First, a chirp-based swept-frequency mode is designed to demodulate the ultrasonic attenuation at a low time cost to ensure the consistency of multifrequency attenuation. Next, considering the effect of particle aggregation on attenuation, the ultrasound attenuation model based on Faran scattering theory is modified by the fractal approach. Then, the inversion of particle size characterization is formulated as an optimization problem of nonlinear and nonconvex functions. An iterative optimization method is proposed to solve the ill-posed inverse problem, in which covariance matrix adaptive evolutionary strategy (CMA-ES) is developed as its inverse solver, and the fractal modified attenuation model is developed as its forward solver. Finally, the experiments were carried out with a mixture of micron-sized polystyrene particles and water. Experimental results indicate that the attenuation predicted by the proposed attenuation model is in good agreement with that measured in liquid–solid dispersion with particle aggregation, and the effectiveness of CMA-ES based on multiple distribution functions is verified for the inversion of particle size characterization.