Chaotic Variables Research Articles

Sensorless Speed Estimation of Induction Motors through Signal Analysis Based on Chaos Using Density of Maxima.

Three-phase induction motors are widely used in various industrial sectors and are responsible for a significant portion of the total electrical energy consumed. To ensure their efficient operation, it is necessary to apply control systems with specific algorithms able to estimate rotation speed accurately and with an adequate response time. However, the angular speed sensors used in induction motors are generally expensive and unreliable, and they may be unsuitable for use in hostile environments. This paper presents an algorithm for speed estimation in three-phase induction motors using the chaotic variable of maximum density. The technique used in this work analyzes the current signals from the motor power supply without invasive sensors on its structure. The results show that speed estimation is achieved with a response time lower than that obtained by classical techniques based on the Fourier Transform. This technique allows for the provision of motor shaft speed values when operated under variable load.

Chaos-Enhanced Archimede Algorithm for Global Optimization of Real-World Engineering Problems and Signal Feature Extraction

Optimization algorithms play a crucial role in a wide range of fields, from designing complex systems to solving mathematical and engineering problems. However, these algorithms frequently face major challenges, such as convergence to local optima, which limits their ability to find global, optimal solutions. To overcome these challenges, it has become imperative to explore more efficient approaches by incorporating chaotic maps within these original algorithms. Incorporating chaotic variables into the search process offers notable advantages, including the ability to avoid local minima, diversify the search, and accelerate convergence toward optimal solutions. In this study, we propose an improved Archimedean optimization algorithm called Chaotic_AO (CAO), based on the use of ten distinct chaotic maps to replace pseudorandom sequences in the three essential components of the classical Archimedean optimization algorithm: initialization, density and volume update, and position update. This improvement aims to achieve a more appropriate balance between the exploitation and exploration phases, offering a greater likelihood of discovering global solutions. CAO performance was extensively validated through the exploration of three distinct groups of problems. The first group, made up of twenty-three benchmark functions, served as an initial reference. Group 2 comprises three crucial engineering problems: the design of a welded beam, the modeling of a spring subjected to tension/compression stresses, and the planning of pressurized tanks. Finally, the third group of problems is dedicated to evaluating the efficiency of the CAO algorithm in the field of signal reconstruction, as well as 2D and 3D medical images. The results obtained from these in-depth tests revealed the efficiency and reliability of the CAO algorithm in terms of convergence speeds, and outstanding solution quality in most of the cases studied.

Review: Fractal Geometry in Precipitation

Rainfall, or more generally the precipitation process (flux), is a clear example of chaotic variables resulting from a highly nonlinear dynamical system, the atmosphere, which is represented by a set of physical equations such as the Navier–Stokes equations, energy balances, and the hydrological cycle, among others. As a generalization of the Euclidean (ordinary) measurements, chaotic solutions of these equations are characterized by fractal indices, that is, non-integer values that represent the complexity of variables like the rainfall. However, observed precipitation is measured as an aggregate variable over time; thus, a physical analysis of observed fluxes is very limited. Consequently, this review aims to go through the different approaches used to identify and analyze the complexity of observed precipitation, taking advantage of its geometry footprint. To address the review, it ranges from classical perspectives of fractal-based techniques to new perspectives at temporal and spatial scales as well as for the classification of climatic features, including the monofractal dimension, multifractal approaches, Hurst exponent, Shannon entropy, and time-scaling in intensity–duration–frequency curves.

Chaotic Binarization Schemes for Solving Combinatorial Optimization Problems Using Continuous Metaheuristics

Chaotic maps are sources of randomness formed by a set of rules and chaotic variables. They have been incorporated into metaheuristics because they improve the balance of exploration and exploitation, and with this, they allow one to obtain better results. In the present work, chaotic maps are used to modify the behavior of the binarization rules that allow continuous metaheuristics to solve binary combinatorial optimization problems. In particular, seven different chaotic maps, three different binarization rules, and three continuous metaheuristics are used, which are the Sine Cosine Algorithm, Grey Wolf Optimizer, and Whale Optimization Algorithm. A classic combinatorial optimization problem is solved: the 0-1 Knapsack Problem. Experimental results indicate that chaotic maps have an impact on the binarization rule, leading to better results. Specifically, experiments incorporating the standard binarization rule and the complement binarization rule performed better than experiments incorporating the elitist binarization rule. The experiment with the best results was STD_TENT, which uses the standard binarization rule and the tent chaotic map.

Harnessing Online Knowledge Transfer for Enhanced Search and Rescue Decisions via Multi-Agent Reinforcement Learning

In the rapidly evolving domain of the Internet of Things (IoT), devices play an instrumental role in high-stakes scenarios like search and rescue (SAR) operations. Traditional decision-making processes within SAR missions often struggle to cope with the dynamic and unpredictable nature of such environments, leading to inefficiencies and delayed responses. This paper aims to explore the potential of multi-agent reinforcement learning (MARL) to improve the decision-making process within SAR operations underpinned by IoT. Functional, current methods are limited by their static decision frameworks and inability to adapt in real time to the chaotic variables present in SAR situations. We introduced a novel MARL framework and compared its performance against benchmark strategies, specifically the multi-agent deep deterministic policy gradient (MADDPG) approach. Uniquely enhanced by online knowledge transfer, the framework leverages the capabilities of the deep deterministic policy gradient (DDPG) method. The preliminary findings underscore the proposed framework’s superior efficiency and speed in SAR contexts. Our research highlights MARL’s transformative potential, positing it as a groundbreaking strategy for IoT-based decision making in high-pressure SAR environments with suggestions for further studies in varied real-world scenarios.

From Collatz Conjecture to chaos and hash function

The non-linear property of Chaos is a promising approach to information security, and many accomplishments have been made by combining Chaos with several sub-security domains, including chaos-based stream ciphers, block ciphers, image encryption, and hash functions. Most Chaos-based hash functions are insecure or inefficient due to their dependence on complex, attacked multi-dimensional maps or uncertain, weak one-dimensional maps like logistic and tent. The Collatz Conjecture is a mystery that has stumped mathematicians for decades and still has not been solved. This paper aims to introduce a novel approach to addressing current security challenges by utilizing our generalized Collatz process to create a chaos-based hash function. By leveraging the unpredictable behaviour of the Collatz sequence, the proposed hash function aims to enhance ergodicity and entropy properties, thereby making it well-suited for cryptographic applications. In the proposed method, the chaotic variables are governed by cryptographic keys, crucial in generating data sequences. These sequences are then utilized within the diffusion and confusion structures of the hashing function. The design of the chaos-hash model is carefully optimized to exhibit desirable characteristics such as randomness, collision resistance, uniformity, sensitivity to initial conditions, speed, and resistance against cryptanalysis.The primary goal of this research is to develop a robust and efficient chaos-based hash function that addresses the requirements of cryptographic systems. By incorporating the Collatz process and carefully considering key-controlled variables, the proposed model aims to offer enhanced security properties while meeting the necessary criteria for a reliable and effective hashing mechanism. The effectiveness and dependability of the proposed hash function are evaluated by comparing it with two well-known hash algorithms, namely SHA-3 and SHA-2, as well as several other Chaos-based hash algorithms. Through comprehensive evaluations conducted under various circumstances and with different datasets, the suggested hash function consistently outperforms the state-of-the-art alternatives. Experiments involving diverse input scenarios consistently demonstrate that the proposed hash function surpasses the performance of the current leading alternatives. Its superior performance is observed across various evaluation metrics, confirming its effectiveness in generating reliable and secure hash values. The results obtained from the comparative analysis highlight the superiority of the proposed hash function over existing alternatives, validating its potential as a robust solution for various cryptographic applications.

Reconstruction, forecasting, and stability of chaotic dynamics from partial data.

The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i) infer the dynamics of unobserved (hidden) chaotic variables (full-state reconstruction); (ii) time forecast the evolution of the full state; and (iii) infer the stability properties of the full state. The tasks are performed with long short-term memory (LSTM) networks, which are trained with observations (data) limited to only part of the state: (i) the low-to-high resolution LSTM (LH-LSTM), which takes partial observations as training input, and requires access to the full system state when computing the loss; and (ii) the physics-informed LSTM (PI-LSTM), which is designed to combine partial observations with the integral formulation of the dynamical system's evolution equations. First, we derive the Jacobian of the LSTMs. Second, we analyze a chaotic partial differential equation, the Kuramoto-Sivashinsky, and the Lorenz-96 system. We show that the proposed networks can forecast the hidden variables, both time-accurately and statistically. The Lyapunov exponents and covariant Lyapunov vectors, which characterize the stability of the chaotic attractors, are correctly inferred from partial observations. Third, the PI-LSTM outperforms the LH-LSTM by successfully reconstructing the hidden chaotic dynamics when the input dimension is smaller or similar to the Kaplan-Yorke dimension of the attractor. The performance is also analyzed against noisy data. This work opens new opportunities for reconstructing the full state, inferring hidden variables, and computing the stability of chaotic systems from partial data.

Heterogeneous Coexisting Attractors and Large-Scale Amplitude Control in a Simple Memristive Neural Network

This paper proposes a simple ring memristive neural network (MNN) with self-connection, bidirectional connection and a single memristive synapse. Compared with some existing MNNs, the most distinctive feature of the proposed MNN is that it can generate heterogeneous coexisting attractors and large-scale amplitude control. Various kinds of heterogeneous coexisting attractors are numerically found in the MNN, including chaos with a stable point, chaos with a limit cycle, a limit cycle with a stable point. By increasing the parameter values, the chaotic variables of the MNN can be accordingly increased and their corresponding areas are extremely wide, yielding parameter-dependent large-scale amplitude control. A circuit implementation platform is established and the obtained results demonstrate its validity and reliability.

Deep learning of model- and reanalysis-based precipitation and pressure mismatches over Europe

Physically based numerical weather prediction and climate models provide useful information for a large number of end users, such as flood forecasters, water resource managers, and farmers. However, due to model uncertainties arising from, e.g., initial value and model errors, the simulation results do not match the in situ or remotely sensed observations to arbitrary accuracy. Merging model-based data with observations yield promising results benefiting simultaneously from the information content of the model results and observations. Machine learning (ML) and/or deep learning (DL) methods have been shown to be useful tools in closing the gap between models and observations due to the capacity in the representation of the non-linear space–time correlation structure. This study focused on using UNet encoder–decoder convolutional neural networks (CNNs) for extracting spatiotemporal features from model simulations for predicting the actual mismatches (errors) between the simulation results and a reference data set. Here, the climate simulations over Europe from the Terrestrial Systems Modeling Platform (TSMP) were used as input to the CNN. The COSMO-REA6 reanalysis data were used as a reference. The proposed merging framework was applied to mismatches in precipitation and surface pressure representing more and less chaotic variables, respectively. The merged data show a strong average improvement in mean error (~ 47%), correlation coefficient (~ 37%), and root mean square error (~22%). To highlight the performance of the DL-based method, the results were compared with the results obtained by a baseline method, quantile mapping. The proposed DL-based merging methodology can be used either during the simulation to correct model forecast output online or in a post-processing step, for downstream impact applications, such as flood forecasting, water resources management, and agriculture.

Forecasting chaotic weather variables with echo state networks and a novel swing training approach

Physical systems like weather variables, the behavior of oceanic bodies, economic variables, and similar systems possess a considerable amount of chaos, and deducing predictive patterns from them is almost not feasible. Forecasting weather parameters has always been a major objective due to several reasons, but observably not all weather variables are equally influential. Parameters like temperature, humidity, and radiation, though easier to predict due to obvious patterns, are found to be less impactful in practical circumstances. But variables that are more turbulent and difficult to model, like wind flow, cloud cover, sea level pressure, etc. are very influential in the context of managing disasters like cyclones, estimating trades, estimating power generation and many other causes. In this study, the aim is to accurately forecast the horizontal wind velocity field which individually considers the longitudinal and latitudinal components of velocity and sea level pressure over a certain region. Initial attempts in this domain used to be purely mathematical with deterministic results, but predicting real phenomena by overpowering the chaos required enormous computational overhead. The results obtained were not satisfactory. With the evolution of statistical modeling, machine learning and deep learning, these systems were majorly formulated as spatiotemporal forecasting problems. Modified deep learning approaches like ConvLSTM, transformer-based models, CNN-GRU models, and others were applied on the spatiotemporal prediction problem producing more accurate results as compared to the primary methods. But the introduction of reservoir computing framework once again invoked the possibilities of improvements in this domain. An instance of reservoir computing, known as the echo state Network (ESN) was found to simulate and learn the complex dynamics of physical systems with significantly less effort. This boiled down to be a major motivation behind this paper. In this study, we have selected two regions over the Indian peninsula and the Mexican gulf and collected hourly data of horizontal wind velocity and sea level pressure with a spatial granularity of 0.25 degrees on these regions. This data has been used to train our proposed model which is an echo state network and convolution-based encoder–decoder architecture. The model forecasts the same parameters over the same spatial zone for some forecast horizons. The results have been rigorously compared with potential baselines where the ESN was replaced by conventional recurrent networks, and it was observed that our proposed approach outperforms all the other baselines.

Research on Control Strategy of Buck Converter Based on Particle Swarm Optimization Fuzzy PID

Because buck converter is a typical non-minimum phase system, the traditional PID algorithm has the disadvantages of low control accuracy and high system overshoot, while fuzzy PID control only slightly improves the control effect. Therefore, this paper designs a control strategy based on particle swarm optimization fuzzy PID algorithm to enhance the control effect of the buck converter and combines chaotic variables to optimize the quality of the initial particle swarm. Finally, Matlab simulation experiments verify that the control strategy of fuzzy PID optimization using particle swarm optimization combined with chaotic variables has the advantages of short response time, high stability, and low system overshoot compared with the traditional PID algorithm and fuzzy PID algorithm.

Chaos follow the leader algorithm: Application to data classification

Classification is the process of systematically arranging the data into multiple groups, which gives a better understanding of large datasets. Considerable research has been carried out on data classification to develop a predictive model with high accuracy. This paper introduces chaos in the Follow the leader (FTL) optimization algorithm to achieve global optima for imbalanced data classification problems. In the FTL algorithm, the random parameter ω may not give enough exploration to the particles, which may lead to local stagnation problems. One of the solutions to this problem can be the replacement of the random parameter ω by a chaotic variable. For a detailed study on the chaotic behavior of ω in FTL, the algorithm is implemented with ten different chaotic maps and tested on twenty-four standard benchmark functions. Thereafter, the best chaos FTL (cFTL) algorithm is tested on six different complex real engineering problems and compared with ten meta-heuristic algorithms. Moreover, to further validate the performance of cFT, it has been applied to ten standard classification datasets collected from UCI and Kaggle data repositories. The obtained results show that cFTL outperforms FTL and other meta-heuristic algorithms.

A chaos-based block cipher based on an enhanced logistic map and simultaneous confusion-diffusion operations

Over the years, there has been considerable interest in the area of chaos-based encryption due to the fact that cryptographic algorithms and chaotic maps share a wide-range of similar characteristics. The majority of chaos-based ciphers were designed for encrypting digital images and vast amounts of data. This paper proposes a new chaos-based block cipher algorithm (CBCA) based on an improved logistic chaotic map. To strengthen the performance of the classical logistic chaotic map, a new chaotification method based on a multiplicative inverse function is used which leads to improved properties such as ergodicity and entropy, both of which are desirable for cryptographic applications. The secret key is used to perturb the chaotic variables, and these perturbed variables are used to produce data sequences for the block cipher’s diffusion and confusion structures. The permutation (diffusion) structure is controlled by an ergodic chaotic map, while the substitution (confusion) structure is controlled by the chaotic points themselves. This new ergodicity-based diffusion approach provides higher security and efficiency. The proposed algorithm not only possess good statistical properties provided by the enhanced chaotic map, but it is also key sensitive and uniformly distributed. Statistical evaluation of the proposed algorithm was performed using text and images as inputs to depict its capability to secure various types of media. The performance of the proposed cipher is then compared to other recently proposed algorithms in literature. The performance comparison indicates that CBCA is efficient, secure and that it can be used to encrypt both small and large amounts of data.

Synchronization of Monostatic Radar Using a Time-Delayed Chaos-Based FM Waveform

There is no doubt that chaotic systems are still attractive issues in various radar applications and communication systems. In this paper, we present a new 0.3 GHz mono-static microwave chaotic radar. It includes a chaotic system based on a time-delay to generate and process frequency modulated (FM) waveforms. Such a radar is designed to extract high-resolution information from the targets. To generate a continuous FM signal, the chaotic signal is first modulated using the voltage control oscillator (VCO). Next, the correct value for the loop gain (G) is carefully set when utilizing the Phase-Locked Loop (PLL) at the receiver, so that the instantaneous frequency that reflects a chaotic state variable can be reliably recovered. In this system, the PLL synchronization and radar correlation are enough to recover the echo signal and detect the target. The finding indicates that the system can be implemented with no need to use the complete self-synchronization or complex projective synchronization schemes as compared to the existing chaotic radar systems. The simulation results show that the short-time cross-correlation of the transmitted and reconstructed waveforms is good and satisfactory to detect the target under various signal-to-noise ratio (SNR) levels and with less complexity in the design.

Improved Ephemeral Search and Nepenthes Algorithms for Diminution of True Power Loss

In this paper Improved Ephemeral Search Algorithm and Nepenthes Algorithm are used for solving the power loss lessening problem. Ephemeral Search Algorithm is physics-based algorithm that mimics the ephemeral actions of switching circuits which made by one or more intermediary switching expedients (like inductor and capacitor circuits). Actions of inductor and capacitor circuits are mathematically formulated to design the algorithm. To improve the convergence rate of the algorithm and Improved Ephemeral Search Algorithm has been designed by integrating chaotic opposition learning approach (to engender superior preliminary populations). Logistic chaos possesses arbitrary, ergodic, and systematic characteristics and chaotic variables used for optimization exploration which features the algorithm to evade local optimum, endorse the population multiplicity. Subsequently an adaptive inertia weighting approach is used (to balance exploration and exploitation capability with good convergence speed) then a neighbour learning (dimension) approach is utilized (to uphold the population assortment with every iteration of weight pursuing). Learning between neighbours (dimensional), modernizing the coordinates of the present entity by means of some data (dimensional) of adjacent entities and the data (dimensional) of an entity is arbitrarily chosen from the total population. Then in this paper Nepenthes Algorithm for solving power loss lessening problem. Nepenthes Algorithm is moulded based on the deeds of Nepenthes plant. Certain plants enthral the prey for reproduction deprived of killing them and quite a few restrain or kill the intruders for protection obstinacies conversely do not digest the physical bodies. Although several plants do engross the nutrients from the numb faunas, hitherto they do not have the competence to kill it. They simply eat the physical bodies found in the topsoil or on the surface of leaf. Every entity is structured rendering to its fitness value in uphill order mode. The highest p Nepenthes plant solutions of the systematized population are measured as the "p Nepenthes plant" plants, NP; however, the left-over solutions (p prey) are the victim (prey). The method of combination is obligatory to simulate the atmosphere of each Nepenthes plant and its victim (prey). In the course of the combination method, the Victim (prey) with the outstanding fitness is allotted to the Rank one Nepenthes plant. In the same way, the consequent preys are allotted to consecutive Nepenthes plants, consistently. When fascination rate is mediocre to the produced capricious value, the prey is successful to spurt from the ploy and Nepenthes plant withstands to propagate. Authenticity of the Ephemeral Search Algorithm, Improved Ephemeral Search Algorithm and Nepenthes Algorithm are substantiated in IEEE 30 bus system. Actual power loss lessening is reached. Proportion of actual power loss lessening is augmented

A novel chaotic teaching learning based optimization algorithm and its application in optimization of extreme learning machine

Recent ten years, the teaching learning based optimization algorithm (TLBO) has been widely concerned and successfully applied to solve various constraints and non-constraints problems. However, its convergence accuracy and convergence speed should be further improved. Therefore, a novel chaotic teaching learning based optimization algorithm (called CTLBO) is proposed. Firstly, chaotic variables are applied to initialize population individuals for increasing the diversity of population. Secondly, a kind of self-adaptive acceleration coefficient is introduced into teaching phase to enhance the convergence speed and solution quality. Finally, two population updating mechanisms are proposed to balance the exploration and exploitation capabilities in the learning phase. One is neighbor elitist search mechanism, another is chaos optimization mechanism. The performance of CTLBO is compared with five state-of-the-art optimization algorithms by several CEC mathematical problems. The experiment results show that the CTLBO yields better convergence rate than other algorithms on most testing functions. Additionally, the proposed CTLBO is applied to optimize the model parameters of extreme learning machine(ELM) and the tuned ELM is adopted to establish the NOx emissions model. Experiment results reveal that the NOx emissions model has good accuracy and meets the engineering requirement.

Cryptanalysis of Some Self-Synchronous Chaotic Stream Ciphers and Their Improved Schemes

In this paper, a cryptanalysis method that combines a chosen-ciphertext attack with a divide-and-conquer attack by traversing multiple nonzero component initial conditions (DCA-TMNCIC) is proposed. The method is used for security analysis of [Formula: see text]-D ([Formula: see text]) self-synchronous chaotic stream ciphers that employ a product of two chaotic variables and three chaotic variables ([Formula: see text]-D SCSC-2 and [Formula: see text]-D SCSC-3), taking 3-D SCSC-2 as a typical example for cryptanalysis. For resisting the combinational effect of the chosen-ciphertext attack and DCA-TMNCIC, several improved chaotic cipher schemes are designed, including 3-D SCSC based on a nonlinear nominal system (3-D SCSC-NNS) and [Formula: see text]-D SCSC based on sinusoidal modulation ([Formula: see text]-D SCSC-SM ([Formula: see text])). Theoretical security analysis validates the improved schemes.

Image encryption algorithm based on dynamic DNA coding operations and 3D chaotic systems

This paper presents a new image encryption algorithm based on 3D chaotic system and deoxyribonucleic acid (DNA) coding. It uses two keys, an external one of 128 bits long and an internal one of 64 gray values coming from the plain image. The initial conditions come from the two keys and vary from one line of the image to the other and from one image to the other and consequently the sequences of substitutions too. In general, in image encryption based on 3D chaotic systems, each chaotic variable is used independently of the others in one phase of the encryption. Here we use the zigzag process to combine the sequences from all the variables before using them simultaneously in the encryption process. DNA coding generally uses one of the 24 DNA rules and one of the 16 join operations to perform the encryption. Here we use all the 24 rules dynamically as well as the 16 join operations in the encryption. Also we apply the chaotic permutation on DNA chain. The logical DNA operations are used according to an algorithm similar to that of the Fast Walsh Transform (FWT) in those 24 DNA rules. The algorithm has been evaluated. It has good statistical properties of cipher images. The proposed system presents high sensitivity on the encryption-decryption keys and on the plain images. These latter features make the proposed algorithm very efficient, robust and resistant against brute force attacks and good for the future secure image communication.

RETRACTED ARTICLE: Emotional interpretation using chaotic cuckoo public sentiment variations on textual data from Twitter

The number of client share assessments on Twitter is an important stage for checking and perusing public sentiment. Such checking and review can offer data for choice making in different areas. In these canvases, we move further to translate estimation variants for machine learning algorithms. In trendy, the chaotic variable has unique characters, and firstly chaotic Levy flight is included in the proposed meta-heuristic for successfully delivering new arrangements. Secondly, the psychology version of feeling and confused grouping presented stream acknowledgment choice in the cuckoo search algorithm. Furthermore, we propose an LDA model and Modified Latent Dirichlet Allocation (M-LDA). These M-LDA subjects pick most advisor tweets for changed topics and build up a new setup known as the Emotional Chaotic Cuckoo Search LDA model. The proposed obligations, including discovering point, contrast among two arrangements of documents.

An Improved Chaos Quantum Immune Algorithm for Power Generation Expansion Planning

In this paper, a new chaos quantum immune algorithm is proposed, which combines the ergodicity of chaos search and the efficiency of quantum computation into the immune optimization algorithm. In this algorithm, antibodies in the algorithm population are encoded by quantum bits and replaced by quantum revolving gate. At the same time, in order to evolve the quantum bits of the corresponding phase, we introduce two different chaotic variables into the quantum revolving gate. Among them, local search is realized by using a small number of excellent clones; the excellent clone with relatively large amplitude realizes global search. The convergence of this method is verified. At the end of the paper, a simulation example is used to show that compared with the existing methods, The improved immune algorithm has a great improvement in the efficiency of solving the problem, at the same time, it also improves the convergence efficiency.