Poincaré maps for detecting chaos in fractional-order systems with hidden attractors for its Kaplan-Yorke dimension optimization

<abstract><p>The optimization of fractional-order (FO) chaotic systems is challenging when simulating a considerable number of cases for long times, where the primary problem is verifying if the given parameter values will generate chaotic behavior. In this manner, we introduce a methodology for detecting chaotic behavior in FO systems through the analysis of Poincaré maps. The optimization process is performed applying differential evolution (DE) and accelerated particle swarm optimization (APSO) algorithms for maximizing the Kaplan-Yorke dimension ($ D_{KY} $) of two case studies: a 3D and a 4D FO chaotic systems with hidden attractors. These FO chaotic systems are solved applying the Grünwald-Letnikov method, and the Numba just-in-time (jit) compiler is used to improve the optimization process's time execution in Python programming language. The optimization results show that the proposed method efficiently optimizes FO chaotic systems with hidden attractors while saving execution time.</p></abstract>

Mission Planning of GEO Active Debris Removal Based on Revolver Mode

The mission planning of active debris removal (ADR) of revolver mode on geosynchronous orbit (GEO) is studied in this paper. It is assumed that there are one service satellite, one space depot, and some pieces of space debris in the ADR mission. The service satellite firstly rendezvouses with the debris and then releases the thruster deorbit kits (TDKs), which are carried with the satellite, to push the debris to the graveyard orbit. Space depot will provide replenishment for the service satellite. The purpose of this mission planning is to optimize the ADR sequence of the service satellite, which represents the chronological order, in which the service satellite approaches different debris. In this paper, the mission cost will be stated firstly, and then a mathematical optimization model is proposed. ADR sequence and orbital transfer time are used as designed variables, whereas the fuel consumption in the whole mission is regarded as objective for optimizing, and a specific number of TDKs is also a new constraint. Then, two-level optimization is proposed to solve the mission planning problem, which is low-level for finding optimal transfer orbit using accelerated particle swarm optimization (APSO) algorithm and up-level for finding best mission sequence using immune genetic (IGA) algorithm. Numerical simulations are carried out to demonstrate the effectiveness of the model and the optimization method. Results show that TDK number influences the fuel consumption through impacting the replenishing frequency and TDK redundancy. To reduce fuel consumption, the TDK number should be optimized and designed with suitable replenishing frequency and minimum TDK redundancy.

A Novel Approach for Image Denoising and Performance Analysis using SGO and APSO

Image denoising is essential to extract the information contained in an image without errors. A technique of using both wavelets and evolutionary computing tools is proposed to denoise and to improve the image quality. An adaptive thresholding-based wavelet denoising technique in the threshold function is coordinated by novel social group optimization (SGO) and accelerated particle swarm optimization (APSO) is proposed. The simulation oriented experimentation is taken out employing MATLAB and the analysis is carried out using the image property metrics similar to peak signal to noise ratio (PSNR), mean square error (MSE) and other structural similarity index metrics (SSIM).

Feasible Optimal Solutions of Electromagnetic Cloaking Problems by Chaotic Accelerated Particle Swarm Optimization

The optimization problem of cloaking a perfectly electric conducting or dielectric spherical core is investigated. The primary excitation is due to an external magnetic dipole. The chaotic accelerated particle swarm optimization (CAPSO) algorithm is adjusted and applied to this optimization problem. The optimization variables are the radii, the permittivities and the permeabilities of a small number of spherical shells covering the core. Several feasible optimal designs are obtained, which exhibit perfect or almost perfect cloaking performance for all angles of observation. These optimal designs correspond to two, three or four spherical coating layers composed of ordinary materials. Detailed parametric investigations of the cloaking mechanism with respect to the type and radius of the core and the location of the primary dipole are carried out. The presented optimization procedure and the reported results are expected to be useful in applications like scattering and characterization of optical particles as well as in designing low-profile receiving antennas.

System Identification of Dampers Using Chaotic Accelerated Particle Swarm Optimization

Aims: Different chaotic APSO-based algorithms are developed to deal with high non-linear optimization problems. Then, considering the difficulty of the problem, an adaptation of these algorithms is presented to enhance the algorithm. Background: : Particle swarm optimization (PSO) is a population-based stochastic optimization technique suitable for global optimization with no need for direct evaluation of gradients. The method mimics the social behavior of flocks of birds and swarms of insects and satisfies the five axioms of swarm intelligence, namely proximity, quality, diverse response, stability, and adaptability. There are some advantages to using the PSO consisting of easy implementation and a smaller number of parameters to be adjusted; however, it is known that the original PSO had difficulties in controlling the balance between exploration and exploitation. In order to improve this character of the PSO, recently, an improved PSO algorithm, called the accelerated PSO (APSO), was proposed, and preliminary studies show that the APSO can perform superiorly. Objective: This paper presents several chaos-enhanced accelerated particle swarm optimization methods for high non-linear optimization problems. Method: Some modifications to the APSO-based algorithms are performed to enhance their performance. Then, the algorithms are employed to find the optimal parameters of the various types of hysteretic Bouc-Wen models. The problems are solved by the standard PSO, APSO, different CAPSO, and adaptive CAPSO, and the results provide the most useful method. Result: Seven different chaotic maps have been investigated to tune the main parameter of the APSO. The main advantage of the CAPSO is that there is a fewer number of parameters compared with other PSO variants. In CAPSO, there is only one parameter to be tuned using chaos theory. Conclusion: To adapt the new algorithm for susceptible parameter identification algorithm, two series of Bouc-Wen model parameters containing standard and modified Bouc-Wen models are used. Performances are assessed on the basis of the best fitness values and the statistical results of the new approaches from 20 runs with different seeds. Simulation results show that the CAPSO method with Gauss/mouse, Liebovitch, Tent, and Sinusoidal maps performs satisfactorily. Other: The sub-optimization mechanism is added to these methods to enhance the performance of the algorithm.