Chaotic Tent Map Research Articles

Research on Combination of Distributed Generation Placement and Dynamic Distribution Network Reconfiguration Based on MIBWOA

This paper aims to address the combination of distributed generation placement and dynamic distribution network reconfiguration. Herein, a multi-strategy multi-objective improved black widow algorithm is proposed. A model is established, which considers the objectives of minimizing active power loss, voltage deviation, and carbon emission. The proposed algorithm significantly enhances the traversal capability and search speed by employing Cubic–Tent chaotic mapping, involving a novel formula with the fusion of optimal genes, and employing an adaptive mutation of Wald mutation and elite reverse learning mixing. The DeepSCN is employed to forecast the distributed generation (DG) output power and distribution network load. Through various test functions, the capability of the proposed algorithm is demonstrated. Whether single-objective or multi-objective, the algorithm has excellent performance. To showcase the practicality and effectiveness of the model and approach, a simulation experiment was performed on the IEEE-33 node configuration. The solution set provided by MIBWOA can reduce active network loss to improve operating efficiency, increase voltage offset to make operation more stable, and reduce carbon emissions to make operation more environmentally friendly. The proposed algorithm shows excellent performance in distributed generation placement and distribution network reconfiguration compared with the comparison algorithms. The results show that the solution proposed by MIBWOA can enhance the real-time operational parameters of the distribution network with considerable efficiency.

DETDO: An adaptive hybrid dandelion optimizer for engineering optimization

Dandelion Optimizer (DO) is a recently proposed swarm intelligence algorithm that coincides with the process of finding the best reproduction site for dandelion seeds. Compared with the classical Meta-heuristic algorithms, DO exhibits strong competitiveness, but it also has some drawbacks. In this paper, we proposed an adaptive hybrid dandelion optimizer called DETDO by combining three strategies of adaptive tent chaotic mapping, differential evolution (DE) strategy, and adaptive t-distribution perturbation to address the shortcomings of weak DO development, easy to fall into local optimum and slow convergence speed. Firstly, the adaptive tent chaos mapping is used in the initialization phase to obtain a uniformly distributed high-quality initial population, which helps the algorithm to enter the correct search region quickly. Secondly, the DE strategy is introduced to increase the diversity of dandelion populations to avoid algorithm stagnation, which improves the exploitation capability and the accuracy of the optimal solution. Finally, adaptive t-distribution perturbation around the elite solution successfully balances the exploration and exploitation phases while improving the convergence speed through a reasonable conversion from Cauchy to Gaussian distribution. The proposed DETDO is compared with classical or advanced optimization algorithms on CEC2017 and CEC2019 test sets, and the experimental results and statistical analysis demonstrate that the algorithm has better optimization accuracy and speed. In addition, DETDO has obtained the best results in solving six real-world engineering design problems. Finally, DETDO is applied to two bar topology optimization cases. Under a series of complex constraints, DETDO produces a lighter bar structure than the current scheme. It further illustrates the effectiveness and applicability of DETDO in practical problems. The above results mean that DETDO with strong competitiveness will become a preferred swarm intelligence algorithm to cope with optimization problems.

3D Content Encryption Using Multi-Level Chaotic Maps

Nowadays, 3D content is becoming an essential part of multimedia applications, when the 3D content is not protected, hackers may attack and steal it. This paper introduces a proposed scheme that provides high protection for 3D content by implementing multiple levels of security with preserving the original size using weight factor (w). First level of security is implemented by encrypting the texture map based on a 2D Logistic chaotic map. Second level is implemented by shuffling vertices (confusion) based on a 1D Tent chaotic map. Third level is implemented by modifying the vertices values (diffusion) based on a 3D Lorenz chaotic map. Results illustrate that the proposed scheme is completely deform the entire 3D content according to Hausdorff Distance (HD) approximately around 100 after the encryption process. It provides a high security against brute force attack because it has large key space equal to 10165 and secret key sensitivity using NPCR near 99:6% and UACI near 33:4%. The histogram and HD indicate the decrypted 3D content is identical to the origin where HD values approximate zero.

An Improved Synthesis of Sparse Planar Arrays Using Density-Weighted Method and Chaos Sparrow Search Algorithm

This paper presents an improved approach for the synthesis of sparse planar arrays using density-weighted method and chaos sparrow search algorithm (CSSA) with multiple constraints. The approach consists of two stages and has an efficient way in dealing with multiple constraints, including the array aperture, number of elements, and minimum spacing between adjacent elements. In the first step, a density-weighted method is implemented to generate a thinned array structure by introducing the weighted coefficient based on the distribution function of a uniform full array to the elements, which can reduce the time and improve the efficiency of the optimization of sparse matrices. On the basis of a density-weighted array, tent chaotic mapping is introduced to initialize the population, then sparrow search algorithm (SSA) is used to further optimize the location of each element of the array antenna to search for the global optimal solution. As a consequence, the proposed method exhibits improved flexibility with respect to other analytical techniques, and reduces the computational cost of the optimization algorithm. Numerical validation results demonstrate the effectiveness and reliability of the proposed method, showing that it can achieve better results than existing methods in the design of sparse planar array arrangements.

Even symmetric chaotic and skewed maps as a technique in video encryption

The massive growth and use of digital multimedia through computer networks, including video and images, have increased the demand for protecting this digital data. To secure digital video, video encryption is frequently utilized. In this paper, a brand-new video scrambling technique based on two chaotic linearly symmetric maps and one chaotic tent map that has been twisted is suggested. The permutation procedure moves every frame pixel's position using a P-box created by permuting a linearly symmetric chaotic sequence. The diffusion technique employs both linearly symmetric chaos maps and distorted tent maps to create key streams. The keystream closely resembles simple frames because the pixels in the permuted frame indicate which of the two even symmetric chaos maps is replicated each time for the following byte. The information entropy, histogram, neighboring pixel correlation and sensitivity analysis, number of pixels changing regions (NPCR), and unified mean change intensity are used to thoroughly evaluate the recommended method's capacity to improve performance and security (UACI). Comparatively to other methods, the suggested algorithm is resistant to clipping, salt and pepper noise, speckle noise rotation assaults, and clipping. This positive outcome indicates that the plan can be successfully implemented for secure video communication applications.

Efficient Image Encryption Scheme Using Novel 1D Multiparametric Dynamical Tent Map and Parallel Computing

In order to ensure reliable and secure image exchange, chaotic systems are often considered for their good performance in information security. In this work, we first propose an extended version of a chaotic tent map (TM)—the multiparametric 1D tent map (MTM). The latter contains six control parameters defined over an unlimited range. These parameters strongly influence the MTM output when they are slightly modified by ∓10−13, which makes MTM stronger than the existing TM and other 1D chaotic maps in terms of security key space. Then, this paper proposes a simple, yet powerful method to make uniform the distribution of chaotic sequence values, making the latter suitable for use in cryptosystems. Next, a new image cryptosystem is introduced based on MTM and parallel computing. This computing mode is incorporated to boost the security level of our scheme and to speed up its runtime. Indeed, in only one running round, our encryption scheme generates a security key of space equal to 1078×n with n indicating the number of the available CPU cores. Therefore, the suggested scheme achieves a good trade-off between safety and efficiency. The results of the performed comparisons and numerical experiments indicate on the one hand that MTM exhibits good chaotic characteristics in comparison to its original version. On the other hand, the suggested cryptosystem demonstrates good strength against various kinds of attacks (brute force, statistical, classical, noise, differential, etc.). Furthermore, comparison with similar schemes indicate that the proposed scheme is competitive in terms of execution time and superior in terms of security level.

An Adaptive Lion Swarm Optimization Algorithm Incorporating Tent Chaotic Search and Information Entropy

This paper proposes an improved adaptive lion swarm optimization (LSO) algorithm integrating the chaotic search strategy and information entropy to address the problem that the standard LSO algorithm has slow convergence and easily falls into the local optimum in later iterations. At first, an adaptive factor is introduced to improve tent chaotic mapping and used for population position initialization to enhance population diversity and realize uniform traversal while ensuring random distribution, ultimately improving the global search ability. Second, to address the problem that the cub selection strategy is blind, resulting in insufficient traversal in the early stage, a dynamic step-size perturbation factor is established using the second-order norm and information entropy. Adaptive parameters are used to dynamically adjust the selection probability of different cub behaviors based on the number of iterations to suppress the premature convergence of the algorithm. Finally, tent chaotic search is employed to adaptively adjust the search range and improve the individuals with poor fitness through multiple neighborhood points of the local optimal solution, further improving the algorithm’s search speed and accuracy. Experimental results on 18 benchmark functions revealed that the proposed algorithm yields superior performance in terms of convergence speed, optimization accuracy, and ability to jump out of the local optimal solution compared with the standard LSO, gray wolf optimizer, and particle swarm optimization algorithms. Furthermore, the improved LSO algorithm was used to optimize the initial weights and thresholds of the BP neural network, and the effectiveness of the proposed algorithm was further verified by studying the house price prediction problem using two real-world datasets.

Leveraging Metaheuristic Unequal Clustering for Hotspot Elimination in Energy-Aware Wireless Sensor Networks

Wireless sensor networks (WSNs) are becoming a significant technology for ubiquitous living and continue to be involved in active research because of their varied applications. Energy awareness will be a critical design problem in WSNs. Clustering is a widespread energy-efficient method and grants several benefits such as scalability, energy efficiency, less delay, and lifetime, but it results in hotspot issues. To solve this, unequal clustering (UC) has been presented. In UC, the size of the cluster differs with the distance to the base station (BS). This paper devises an improved tuna-swarm-algorithm-based unequal clustering for hotspot elimination (ITSA-UCHSE) technique in an energy-aware WSN. The ITSA-UCHSE technique intends to resolve the hotspot problem and uneven energy dissipation in the WSN. In this study, the ITSA is derived from the use of a tent chaotic map with the traditional TSA. In addition, the ITSA-UCHSE technique computes a fitness value based on energy and distance metrics. Moreover, the cluster size determination via the ITSA-UCHSE technique helps to address the hotspot issue. To demonstrate the enhanced performance of the ITSA-UCHSE approach, a series of simulation analyses were conducted. The simulation values stated that the ITSA-UCHSE algorithm has reached improved results over other models.

The Performance of Electronic Current Transformer Fault Diagnosis Model: Using an Improved Whale Optimization Algorithm and RBF Neural Network

With the widely application of electronic transformers in smart grids, transformer faults have become a pressing problem. However, reliable fault diagnosis of electronic current transformers (ECT) is still an open problem due to the complexity and diversity of fault types. In order to solve this problem, this paper proposes an ECT fault diagnosis model based on radial basis function neural network (RBFNN) and optimizes the model parameters and the network size of RBFNN simultaneously via an improved whale optimization algorithm (WOA) to improve the classification accuracy and robustness of RBFNN. Since the classical WOA is easy to fall into a locally optimal performance, a hybrid multi-strategies WOA algorithm (CASAWOA) is proposed for further improvement in optimization performance. Firstly, we introduced the tent chaotic map strategy to improve the population diversity of WOA. Secondly, we introduced nonlinear convergence factor and adaptive inertia weight to enhance the exploitation ability of the WOA. Finally, on the premise of ensuring the convergence speed of the algorithm, we modified the simulated annealing mechanism in order to prevent premature convergence. The benchmark function tests show that the CASAWOA outperforms other state-of-the-art WOA algorithms in terms of convergence speed and exploration ability. Furthermore, to validate the performance of ECT fault diagnosis model based on CASAWOA-RBFNN, a comprehensive analysis of eight fault diagnosis methods is conducted based on the ECT fault samples collected from the detection circuit. The experimental results show that the CASAWOA-RBFNN achieves an accuracy of 97.77% in ECT fault diagnosis, which is 9.8% better than WOA-RBF and which shows promising engineering practicality.

Fractional multivariate grey Bernoulli model combined with improved grey wolf algorithm: Application in short-term power load forecasting

The accurate prediction of power load is helpful to make reasonable power generation plans and scientific dispatching schemes and achieve the goal of energy saving and emission reduction.There are many factors influencing the power load, and there may be a nonlinear relationship between the power load and these influencing factors. A new fractional multivariate grey Bernoulli model, referred to as MFGBM (q, r, N), is developed in this article for the short-term prediction of power load. The fractional differential equation and fractional accumulation generation are integrated into MFGBM (q, r, N). Second, this paper improves the grey wolf algorithm to better optimize many parameters in the model. The algorithm is improved by using a chaotic Tent map to optimize the initial population composition, adding inertia weights to change the position vector of the grey wolf, and introducing a nonlinear function and Lévy flight to enhance local exploitation and global exploration ability. Finally, this paper selects the daytime and nighttime power loads in Australia and takes the electricity price, humidity, and temperature as the influencing factors to validate the prediction capability of MFGBM (q, r, N). Our findings indicate that MFGBM (q, r, N) is highly applicable to short-term power system prediction.

Multi-objective capacity optimization configuration of independent wind-photovoltaic- hydrogen-battery system based on improved MOSSA algorithm

Under the background of large-scale and rapid development of renewable energy, in order to improve the economic benefit of the system and ensure the reliability of the system, this paper introduces hydrogen production and energy storage into the independent wind/photovoltaic/hydrogen/storage capacity optimization configuration method. In order to minimize the total planning cost and self-sufficiency rate of system power supply, a capacity optimization allocation model was established. On the basis of this model, the Multi-objective Salp Swarm Algorithm (MOSSA) was improved in Algorithm structure, Tent chaotic mapping was introduced to initialize the population, and the positions of leaders and followers were updated based on the adaptive spiral search strategy. The validity of the algorithm is verified by test function. Finally, the specific example is solved by MATLAB programming, and the improved multi-objective Salp Swarm Algorithm (IMOSSA) is used to obtain the capacity configuration scheme, which provides reference for the optimization design of independent photovoltaic hydrogen storage system.

Prediction of CO2 storage performance in reservoirs based on optimized neural networks

Accurate prediction of CO2 geological storage performance is of great guiding significance for oilfield development and management. The use of artificial neural networks is an effective method; however, insufficient data and certain errors caused by difficulties encountered during the measurement process make the traditional neural network fall into local optimization or overfitting. Therefore, in this study an optimized back propagation (BP) neural network based on the lion swarm optimization (LSO) algorithm was proposed. Firstly, the LSO algorithm was improved by combining a tent chaotic map and differential evolution to enhance its optimization capability. Secondly, the improved algorithm was used to obtain the optimal initial weights and thresholds of BP neural networks. Finally, by using the normalized sample data obtained by numerical simulation, five dimensionless variables were introduced to predict the CO2 storage performance in reservoirs. Experimental results demonstrated that the proposed model yields a faster convergence speed and higher prediction accuracy compared with four existing neural networks. The root mean square errors on the training and test sets were 0.0234 and 0.0254, respectively, and the absolute error of more than 95% of the data was within 5%, which shows that the proposed method is feasible and effective in predicting the CO2 storage performance and can serve as a good guide in oilfield development projects.

Parameter Estimation of Fractional-Order Chaotic Power System Based on Lens Imaging Learning Strategy State Transition Algorithm

Parameter identification of fractional-order chaotic power systems is a multidimensional optimization problem that plays a decisive role in the synchronization and control of fractional-order chaotic power systems. In this paper, a state transition algorithm based on the lens imaging learning strategy is proposed for parameter identification of fractional-order chaotic power systems. Taking a fractional-order six-dimensional chaotic power system mathematical model as an example, the mathematical model and chaotic state are analyzed. First, the Tent chaotic mapping is used to initialize the population, thus increasing population diversity. The randomness and ergodicity of the Tent chaotic sequence are used to enhance the global searching ability of the algorithm. Second, a maturity index is employed to determine population maturity. The lens imaging learning strategy is used to suppress the premature convergence of the state transition algorithm effectively and help the population jump out of local optima. Finally, the improved state transition algorithm is used to identify the parameters of the fractional-order six-dimensional chaotic power system model. The proposed improved state transition algorithm shows high estimation accuracy and convergence speed, and is superior to the traditional state transition and particle swarm optimization algorithms. The simulation results show that the parameters of the fractional-order chaotic power system are identified accurately even in the presence of white noise, demonstrating the strong robustness and versatility of the proposed algorithm.

The Unreasonable Effectiveness of the Chaotic Tent Map in Engineering Applications

From decimal expansion of real numbers to complex behaviour in physical, biological and human-made systems, deterministic chaos is ubiquitous. One of the simplest examples of a nonlinear dynamical system that exhibits chaos is the well known 1-dimensional piecewise linear Tent map. The Tent map (and their skewed cousins) are instances of a larger family of maps namely Generalized Luröth Series (GLS) which are studied for their rich number theoretic and ergodic properties. In this work, we discuss the unreasonable effectiveness of the Tent map and their generalizations (GLS maps) in a number of applications in electronics, communication and computer engineering. To list a few of these applications: (a) GLS-coding: a lossless data compression algorithm for i.i.d sources is Shannon optimal and is in fact a generalization of the popular Arithmetic Coding algorithm used in the image compression standard JPEG2000; (b) GLS maps are used as neurons in the recently proposed Neurochaos Learning architecture which delivers state-of-the-art performance in classification tasks; (c) GLS maps are ideal candidates for chaos-based computing since they can simulate XOR, NAND and other gates and for dense storage of information for efficient search and retrieval; (d) Noise-resistant versions of GLS maps are useful for signal multiplexing in the presence of noise and error detection; (e) GLS maps are shown to be useful in a number of cryptographic protocols - for joint compression and encryption and also for generating pseudo-random numbers. The unique properties and rich features of the Tent Map (GLS maps) that enable these wide variety of engineering applications will be investigated. A list of open problems are indicated as well.

Improved coyote optimization algorithm for parameter estimation of lithium-ion batteries

This paper studies the parameter estimation of fractional order equivalent circuit model of lithium-ion batteries. Since intelligent optimization algorithms can achieve parameters with high accuracy by transforming the parameter estimation into optimization problem, coyote optimization algorithm is taken in this paper by modifying two key steps so as to improve the accuracy and convergence speed. Firstly, tent chaotic map is introduced to avoid falling into local optimum and enhance population diversity. Secondly, dual strategy learning is employed to improve the searching ability, accuracy and convergence speed. Non-parametric statistical significance is tested by 6 benchmark functions with the comparison of other 5 optimization algorithms. Furthermore, the proposed algorithm is applied to identify the fractional order model of the Samsung ICR18650 (2600 mAh) and compared with conventional coyote optimization algorithm and particle swarm algorithm, which declared the excellence in identification accuracy.

Near-Ground Delivery Drones Path Planning Design Based on BOA-TSAR Algorithm

With the advancement of technology and the rise of the unmanned aerial vehicle industry, the use of drones has grown tremendously. For drones performing near-ground delivery missions, the problem of 3D space-based path planning is particularly important in the autonomous navigation of drones in complex spaces. Therefore, an improved butterfly optimization (BOA-TSAR) algorithm is proposed in this paper to achieve the autonomous pathfinding of drones in 3D space. First, this paper improves the randomness strategy of the initial population generation in the butterfly optimization algorithm (BOA) via the Tent chaotic mapping method, by means of the removal of the short-period property, which balances the equilibrium of the initial solutions generated by the BOA algorithm in the solution space. Secondly, this paper improves the shortcomings of the BOA algorithm in terms of slower convergence, lower accuracy, and the existence of local optimal stagnation when dealing with high-dimensional complex functions via adaptive nonlinear inertia weights, a simulated annealing strategy, and stochasticity mutation with global adaptive features. Finally, this paper proposes an initial population generation strategy, based on the 3D line of sight (LOS) detection method, to further reduce the generation of path interruption points while ensuring the diversity of feasible solutions generated by the BOA algorithm for paths. In this paper, we verify the superior performance of BOA-TSAR by means of simulation experiments. The simulation results show that BOA-TSAR is very competitive among swarm intelligence (SI) algorithms of the same type. At the same time, the BOA-TSAR algorithm achieves the optimal path length measure and smoothness measure in the path-planning experiment.

Design of Electric Vehicle’s Wireless Power Transfer System Based on Deep Learning Combined With Multi-Objective Optimization

During the wireless power transmission of an electric vehicle (EV), due to the influence of the compensation circuit’s manufacturing process, the driver’s operating technique, and other factors, the wireless power transfer (WPT) efficiency features strong uncertainty. The article chooses the coil group’s spatial parameters as well as the compensation circuit’s parameters as input variables, and then builds the deep learning network as the framework of uncertainty quantification, so as to obtain the relevant statistical characteristic parameters of WPT efficiency, through comparing with the calculation results of classical Monte Carlo (MC), it can be verified that the uncertainty quantification based on deep learning has almost the same solution accuracy and higher computational efficiency. At the same time, the article adopts tent chaotic mapping and adaptive inertia weight strategy to improve the traditional Aquila Optimization (AO) algorithm, then uses the improved multiobjective AO algorithm to accomplish the optimization of the WPT system’s structure. Through the comparison of improved AO and other optimization algorithms, it can be concluded that the improved AO can search out the optimal design parameter group with faster speed and higher accuracy, which provides effective guidance for the actual optimized design of the EVs WPT system.

Solving the Flexible Job Shop Scheduling Problem Using a Discrete Improved Grey Wolf Optimization Algorithm

The flexible job shop scheduling problem (FJSP) is of great importance for realistic manufacturing, and the problem has been proven to be NP-hard (non-deterministic polynomial time) because of its high computational complexity. To optimize makespan and critical machine load of FJSP, a discrete improved grey wolf optimization (DIGWO) algorithm is proposed. Firstly, combined with the random Tent chaotic mapping strategy and heuristic rules, a hybrid initialization strategy is presented to improve the quality of the original population. Secondly, a discrete grey wolf update operator (DGUO) is designed by discretizing the hunting process of grey wolf optimization so that the algorithm can solve FJSP effectively. Finally, an adaptive convergence factor is introduced to improve the global search ability of the algorithm. Thirty-five international benchmark problems as well as twelve large-scale FJSPs are used to test the performance of the proposed DIGWO. Compared with the optimization algorithms proposed in recent literature, DIGWO shows better solution accuracy and convergence performance in FJSPs at different scales.

Design and Analysis of a New Image Encryption Algorithm using Hyperchaotic System and Tent Map

Abstract: Users transfer millions of images every day in the era of information technology. Serious issues could arise if the information included in these photographs is open to unauthorised usage. There are numerous methods for protecting images. One of the most successful and well-known methods is digital image encryption. Confusion and diffusion are the two main phases of an encryption algorithm. This paper proposes a new image encryption technique that uses a hyperchaotic system and a tent chaotic map. With the help of random numbers produced by the 6D hyperchaotic system, the original image gets confused. A tent chaotic map is then used to create a key to diffuse the permuted image. Security analysis and time complexity are used to evaluate the suggested image encryption method's effectiveness. The security is tested using entropy, correlation coefficient, differential attacks, histograms, keyspace, sensitivity, noise, and data cut attacks. Additionally, the outcomes are compared using various encryption methods. The proposed method achieves a high level of security

A New Image Encryption Technique Based on Sine Map, Chaotic Tent Map, and Circulant Matrices

Image encryption is one of the sensitive areas used recently to save information over the Internet and confirms the security on a higher level. A new cryptosystem has been proposed for the encoding and decoding of images using sine map, chaotic tent map, and circulant matrices. The process involves three stages. The sine map is used for the permutation phase. In the substitution phase, the Hill cipher method together with prime circulant matrix are used and a chaotic tent map is used in the diffusion phase. The algorithm becomes impenetrable to resist differential- and statistical-type attacks. The algorithm's key space is sufficient in size to withstand brute-force attacks. This symmetric image encryption algorithm indicates good results for correlation analysis, key space analysis, entropy analysis, key sensitivity analysis, histogram analysis, number of pixel change rate (NPCR), unified average changing intensity (UACI), and peak signal-to-noise ratio (PSNR). From all these simulation results, we come to know that the constructed image encryption cryptosystem is systematic and vigorous, supplying better protection for image encryption.