Chaotic Map Research Articles

A visual security multi-key selection image encryption algorithm based on a new four-dimensional chaos and compressed sensing

In this article, a visual security image encryption algorithm based on compressed sensing is proposed. The algorithm consists of two stages: the compression and encryption stage and the embedding stage. The key streams in the compression and encryption stage are generated by a newly constructed four-dimensional discrete chaotic map, while the Gaussian measurement matrix is generated by a Chebyshev map, and both of their generations are related to the feature code of the carrier image, which enhances the security of the ciphertext. In the compression and encryption stage, a scrambling-cyclic shift-diffusion encryption structure is adopted for the compressed image in which the shift number in the cyclic shift stage and the diffusion key streams are dynamically changed according to each pixel value, so the algorithm can resist chosen plaintext attack. In the embedding stage, the carrier image is first subjected to integer wavelet transform to obtain the high-frequency and low-frequency components of the image, and then the intermediate ciphertext information is embedded into its high-frequency components. Finally, the carrier image is subjected to inverse integer wavelet transform to obtain a visually secure ciphertext image. The experimental results and security analysis indicate that the encryption scheme has a large key space, high decryption key sensitivity, similar histogram distribution between the carrier image and the visual security ciphertext image, and good robustness to noise attacks.

A new image encryption approach that uses an improved Hill-Vigenère method and chaotic maps

A new image encryption approach that uses an improved Hill-Vigenère method and chaotic maps

On New Symmetric Fractional Discrete-Time Systems: Chaos, Complexity, and Control

This paper introduces a new symmetric fractional-order discrete system. The dynamics and symmetry of the suggested model are studied under two initial conditions, mainly a comparison of the commensurate order and incommensurate order maps, which highlights their effect on symmetry-breaking bifurcations. In addition, a theoretical analysis examines the stability of the zero equilibrium point. It proves that the map generates typical nonlinear features, including chaos, which is confirmed numerically: phase attractors are plotted in a two-dimensional (2D) and three-dimensional (3D) space, bifurcation diagrams are drawn with variations in the derivative fractional values and in the system parameters, and we calculate the Maximum Lyapunov Exponents (MLEs) associated with the bifurcation diagram. Additionally, we use the C0 algorithm and entropy approach to measure the complexity of the chaotic symmetric fractional map. Finally, nonlinear 3D controllers are revealed to stabilize the symmetric fractional order map’s states in commensurate and incommensurate cases.

Fault diagnosis method for hydropower unit via the incorporation of chaotic quadratic interpolation optimized deep learning model

Hydro-turbine fault diagnosis is crucial for hydropower plants’ safe and stable operation. This paper proposes a deep learning model for hydro-turbine fault diagnosis based on chaotic quadratic interpolation optimization (CQIO). Chaotic mapping optimizes the initial population of the QIO algorithm by introducing randomness and diversity, improving the algorithm’s performance and stability. The CQIO is used to calculate the optimal hyperparameter combinations for CNN-LSTM models. It can improve the model’s stability and reduce computational resource consumption. The results show that the fault accuracy of the proposed method reaches 96.7% and 93.6%, respectively, which is higher than the CNN, LSTM, CNN-LSTM, and QIO-CNN-LSTM models. Notably, the diagnostic accuracy about impact faults exceeds that of wear faults, with the latter exhibiting an augmented diagnostic accuracy as sediment increases.

Pseudo-random number generation based on spatial chaotic map of Logistic type and its cryptographic application

The pseudo-random number generator (PRNG) based on chaos has been widely used in the fields of digital communication, cryptography and computer simulation. In this paper, we study a new PRNG based on spatial surface chaotic system (SSCS), which is constructed based on coupling mapping lattice (CML) and one-dimensional Logistic chaotic map. To verify the performance of this generator, we study its nonlinear dynamic properties, including the Lyapunov exponent, ergodicity and bifurcation phenomena. Moreover, we analyze the cryptographic properties such as key space, key sensitivity, correlation, histogram and information entropy, while performing NIST SP800-22 test and TestU01 test for the randomness of this system. Theoretical analysis and numerical simulation results show that the PRNG proposed in this paper has good complexity, ergodicity, sensitivity and randomness. Moreover, the key space can increase dynamically with the increase of encrypted data, especially suitable for the protection of big data such as multimedia, which is more advantageous than most existing chaotic mapping. The results of this paper will provide a new idea for the study of chaotic cryptography, and motivate the study of new discrete chaotic models with desirable statistical properties.

Optimization of Variational Mode Decomposition-Convolutional Neural Network-Bidirectional Long Short Term Memory Rolling Bearing Fault Diagnosis Model Based on Improved Dung Beetle Optimizer Algorithm

(1) Background: Rolling bearings are important components in mechanical equipment, but they are also components with a high failure rate. Once a malfunction occurs, it will cause mechanical equipment to malfunction and may even affect personnel safety. Therefore, studying the fault diagnosis methods for rolling bearings is of great significance and is also a current research hotspot and frontier. However, the vibration signals of rolling bearings usually exhibit nonlinear and non-stationary characteristics, and are easily affected by industrial environmental noise, making it difficult to accurately diagnose bearing faults. (2) Methods: Therefore, this article proposes a rolling bearing fault diagnosis model based on an improved dung beetle optimizer (DBO) algorithm-optimized variational mode decomposition-convolutional neural network-bidirectional long short-term memory (VMD-CNN-BiLSTM). Firstly, an improved DBO algorithm named CSADBO is proposed by integrating multiple strategies such as chaotic mapping and cooperative search. Secondly, the optimal parameter combination of VMD was adaptively determined through the CSADBO algorithm, and the optimized VMD algorithm was used to perform modal decomposition on the bearing vibration signal. Then, CNN-BiLSTM was used as the model for fault classification, and hyperparameters of the model were optimized using the CSADBO algorithm. (3) Results: Finally, multiple experiments were conducted on the bearing dataset of Case Western Reserve University, and the proposed method achieved an average diagnostic accuracy of 99.6%. (4) Conclusions: Experimental comparisons were made with other models to verify the effectiveness of the proposed model. The experimental results show that the proposed model based on an improved DBO algorithm optimized VMD-CNN-BiLSTM can effectively be used for rolling bearing fault diagnosis, with high diagnostic accuracy, and can provide a theoretical reference for other related fault diagnosis problems.

Enhancing biometric authentication security through the novel integration of graph theory encryption and chaotic logistic mapping

Enhancing biometric authentication security through the novel integration of graph theory encryption and chaotic logistic mapping

Research on a Distributed Photovoltaic Two-Level Planning Method Based on the SCMPSO Algorithm

In response to challenges such as voltage limit violations, excessive currents, and power imbalances caused by the integration of distributed photovoltaic (distributed PV) systems into the distribution network, this study proposes at two-level optimization configuration method. This method effectively balances the grid capacity and reduces the active power losses, thereby decreasing the operating costs. The upper-level optimization enhances the distribution network’s capacity by determining the siting and sizing of distributed PV devices. The lower-level aims to reduce the active power losses, improve the voltage stability margins, and minimize the voltage deviations. The upper-level planning results, which include the siting and sizing of the distributed PV, are used as initial conditions for the lower level. Subsequently, the lower level feeds back its optimization results to further refine the configuration. The model is solved using an improved second-order oscillating chaotic map particle swarm optimization algorithm (SCMPSO) combined with a second-order relaxation method. The simulation experiments on an improved IEEE 33-bus test system show that the SCMPSO algorithm can effectively reduce the voltage deviations, decrease the voltage fluctuations, lower the active power losses in the distribution network, and significantly enhance the power quality.

DOA method based on CSI and improved neural network

Abstract In wireless communication systems, accurate estimation of signal direction has always been a key research area. Channel State Information (CSI) is an important parameter that can be used to estimate the Direction of Arrival (DOA) of a signal. In order to improve the accuracy and robustness of DOA estimation, this study aims to explore a DOA estimation method based on CSI and improved neural networks. Firstly, the role of CSI in localization technology and related theories are detailed. Subsequently, the application of neural network-based fingerprint matching algorithms, including BP neural networks, Whale Optimization Algorithm (WOA), and chaotic mapping techniques, is analyzed. In light of this, an improved BP neural network integrating chaotic mapping and adaptive weighting is proposed to improve the positioning accuracy and convergence rate of the algorithm. Finally, through the collection and training of experimental data, an algorithm proposed in this article achieves a test set accuracy of 96.4286% and a training set accuracy of 82.7243%. The better training effect is obtained, which verifies the efficacy and superiority of the proposed approach.

Chaotic RIME optimization algorithm with adaptive mutualism for feature selection problems

The RIME optimization algorithm is a newly developed physics-based optimization algorithm used for solving optimization problems. The RIME algorithm proved high-performing in various fields and domains, providing a high-performance solution. Nevertheless, like many swarm-based optimization algorithms, RIME suffers from many limitations, including the exploration-exploitation balance not being well balanced. In addition, the likelihood of falling into local optimal solutions is high, and the convergence speed still needs some work. Hence, there is room for enhancement in the search mechanism so that various search agents can discover new solutions. The authors suggest an adaptive chaotic version of the RIME algorithm named ACRIME, which incorporates four main improvements, including an intelligent population initialization using chaotic maps, a novel adaptive modified Symbiotic Organism Search (SOS) mutualism phase, a novel mixed mutation strategy, and the utilization of restart strategy. The main goal of these improvements is to improve the variety of the population, achieve a better balance between exploration and exploitation, and improve RIME's local and global search abilities. The study assesses the effectiveness of ACRIME by using the standard benchmark functions of the CEC2005 and CEC2019 benchmarks. The proposed ACRIME is also applied as a feature selection to fourteen various datasets to test its applicability to real-world problems. Besides, the ACRIME algorithm is applied to the COVID-19 classification real problem to test its applicability and performance further. The suggested algorithm is compared to other sophisticated classical and advanced metaheuristics, and its performance is assessed using statistical tests such as Wilcoxon rank-sum and Friedman rank tests. The study demonstrates that ACRIME exhibits a high level of competitiveness and often outperforms competing algorithms. It discovers the optimal subset of features, enhancing the accuracy of classification and minimizing the number of features employed. This study primarily focuses on enhancing the equilibrium between exploration and exploitation, extending the scope of local search.

Advanced color image encryption using third-order differential equations and three-dimensional logistic map

Image encryption stands out as a crucial technique employed to securely transmit images across the Internet. In this paper, we introduce a novel algorithm for encrypting color images. The algorithm is built upon the principles of differential equations, XOR operations, and chaotic maps. First, the plain image is three-dimensional pixel shuffled via a logistic map. Afterward, the differential equations are used as a mathematical tool for encrypting images. The third-order ordinary differential equations are used to encrypt the shuffled images. The color values of the plain image are considered coefficients for the independent variable X. Subsequently, an alternate matrix of the same size is generated using a three-dimensional logistic map, taking into account its color values as the exponents linked to the independent variable X. A set of third-order differential equations emerged, containing an equivalent number of elements as the color values present in the plain image. This set of differential equations is addressed in the following manner: combining XOR and integration three times with respect to the independent variable X for each set of obtained differential equations while treating the integration constant as zero. Ultimately, a set of ordinary equations involving the independent variable X is derived, where the coefficients of X represent color values for the cipher image. The results from experiments and the security analysis affirm the resilience of the proposed algorithm against established security attacks. It exhibits a substantial key space, heightened key sensitivity, and a strong encryption effect.

Chaotic Artificial Algae Algorithm for Solving Global Optimization With Real-World Space Trajectory Design Problems

AbstractThe artificial algae algorithm (AAA) is a recently introduced metaheuristic algorithm inspired by the behavior and characteristics of microalgae. Like other metaheuristic algorithms, AAA faces challenges such as local optima and premature convergence. Various strategies to address these issues and enhance the performance of the algorithm have been proposed in the literature. These include levy flight, local search, variable search, intelligent search, multi-agent systems, and quantum behaviors. This paper introduces chaos theory as a strategy to improve AAA's performance. Chaotic maps are utilized to effectively balance exploration and exploitation, prevent premature convergence, and avoid local minima. Ten popular chaotic maps are employed to enhance AAA's performance, resulting in the chaotic artificial algae algorithm (CAAA). CAAA's performance is evaluated on thirty benchmark test functions, including unimodal, multimodal, and fixed dimension problems. The algorithm is also tested on three classical engineering problems and eight space trajectory design problems at the European Space Agency. A statistical analysis using the Friedman and Wilcoxon tests confirms that CAA demonstrates successful performance in optimization problems.

CMRLCCOA: Multi-Strategy Enhanced Coati Optimization Algorithm for Engineering Designs and Hypersonic Vehicle Path Planning.

The recently introduced coati optimization algorithm suffers from drawbacks such as slow search velocity and weak optimization precision. An enhanced coati optimization algorithm called CMRLCCOA is proposed. Firstly, the Sine chaotic mapping function is used to initialize the CMRLCCOA as a way to obtain better-quality coati populations and increase the diversity of the population. Secondly, the generated candidate solutions are updated again using the convex lens imaging reverse learning strategy to expand the search range. Thirdly, the Lévy flight strategy increases the search step size, expands the search range, and avoids the phenomenon of convergence too early. Finally, utilizing the crossover strategy can effectively reduce the search blind spots, making the search particles constantly close to the global optimum solution. The four strategies work together to enhance the efficiency of COA and to boost the precision and steadiness. The performance of CMRLCCOA is evaluated on CEC2017 and CEC2019. The superiority of CMRLCCOA is comprehensively demonstrated by comparing the output of CMRLCCOA with the previously submitted algorithms. Besides the results of iterative convergence curves, boxplots and a nonparametric statistical analysis illustrate that the CMRLCCOA is competitive, significantly improves the convergence accuracy, and well avoids local optimal solutions. Finally, the performance and usefulness of CMRLCCOA are proven through three engineering application problems. A mathematical model of the hypersonic vehicle cruise trajectory optimization problem is developed. The result of CMRLCCOA is less than other comparative algorithms and the shortest path length for this problem is obtained.

Research on Multi-Objective Optimization Scheduling Strategy for Cascaded Small Hydropower Stations Based on Improved HBA

Abstract Effective optimization scheduling strategy is the premise and key to improving the power generation and capacity benefits of cascade small hydropower stations (CSHS). However, the power generation of CSHS is significantly affected by complex hydraulic and electrical constraints. To effectively solve this problem, an improved honey badger algorithm (HBA) is proposed by updating the mutation strategy and introducing non-dominated sorting to achieve the multi-objective optimization scheduling solution of CSHS. The following improvements have been made to the standard HBA: Firstly, the Tent chaotic mapping is applied to the population initialization stage, its strong ergodicity and randomness ensure the randomness of the initialization stage and improve the global search ability of CSHS scheduling. Secondly, the powerful optimization ability and fast convergence speed of the Golden-Sine strategy make updating and mutation more efficient, greatly enhancing the local search ability of CSCH scheduling. And then combining the non-dominated sorting of the non-dominated sorting genetic algorithm-II (NSGA-II), an improved multi-objective Honey Badger Algorithm (IMOHBA) is further proposed to achieve multi-objective solutions for CSCH scheduling. Finally, abundant field experiments were tested for validation. The results expressed that compared to other algorithms, the effect of IMOHBA in CSHS scheduling can further increase power generation, while also improving the peak shaving ability of CSHS.

Stability prediction of roadway surrounding rock using INGO-RF

In order to more accurately classify the stability of roadway surrounding rock and identify dangerous areas in a timely manner to prevent roadway collapse and other disasters, an INGO-RF roadway surrounding rock stability prediction model is proposed. This model combines the improved Northern Gok algorithm (INGO) and Random Forest (RF) based on the analysis of influencing factors of roadway surrounding rock stability. First, three strategies were employed to enhance the Northern Gob algorithm (NGO): Logistic chaotic mapping, refraction reverse learning, and improved sine and cosine. Subsequently, INGO was utilized to optimize the number of decision trees and the minimum number of leaf nodes for RF species in order to improve the prediction accuracy of RF. Secondly, a data set consisting of 34 groups of roadway surrounding rock data is selected. The input indexes of the model include roof strength, two-wall strength, floor strength, burial depth, roadway pillar width, ratio of direct roof thickness to mining height, and surrounding rock integrity. Meanwhile, surrounding rock stability is considered as the output index. Particle swarm optimization backpropagation neural network (PSO-BPNN), genetic algorithm optimization support vector machine (GA-SVM), Sparrow search algorithm optimization RF (SSA-RF) models were introduced to compare the prediction results with the INGO-RF model, and the results showed that: INGO-RF model has the best performance in the comparison of various performance indicators. Compared with other models, the accuracy rate (Ac) in the test set has increased by 0.12∼0.4, the accuracy rate (Pr) has increased by 0.07∼0.65, and the recall rate (Re) has increased by 0.08∼0.37. The harmonic mean (F1-Score) of the recall rate increased by 0.08∼0.52, the mean absolute error (MAE) decreased by 0.1428∼0.4285, the mean absolute percentage error (MAPE) decreased by 7.15%∼28.57%, and the root mean square error (RMSE) decreased by 0.1565∼0.3779. Finally, the data on surrounding rock conditions of roadways in multiple mining areas in Shanxi Province were collected to test the INGO-RF model. The results indicate that the predicted outcomes closely align with the actual results, demonstrating a certain level of reliability and stability. It shows that it can better meet the practical needs of engineering and avoid the occurrence of mine disasters.

Optimization of Power Prediction of BP Network with Improved Pelican Algorithm

Abstract In view of the large fluctuation of photovoltaic output power affected by different weather, accurate prediction of photovoltaic output power is particularly important for the safe and stable operation of power system. Firstly, the pelican optimization algorithm ( POA ) is improved in the following three aspects : adding Circle chaotic map to make the population evenly distributed, introducing mutation factor to expand the search range of pelican when approaching prey, adding adaptive weight and firefly disturbance to avoid falling into local optimum in the water surface flight stage ; then, in order to improve the prediction accuracy of BP algorithm, the improved pelican algorithm ( IPOA ) is used to optimize the weights and thresholds of BP neural network, and the IPOA-BP photovoltaic power prediction model is built to improve the accuracy of power prediction. Finally, this paper tests the prediction performance of IPOA-BP, POA-BP and basic BP power prediction models in sunny, cloudy and rainy days through experiments. The experimental results demonstrate that the IPOA-BP prediction model outperforms both the POA-BP and traditional BP neural network models under various weather conditions.

Emergent order in adaptively rewired networks.

We explore adaptive link change strategies that can lead a system to network configurations that yield ordered dynamical states. We propose two adaptive strategies based on feedback from the global synchronization error. In the first strategy, the connectivity matrix changes if the instantaneous synchronization error is larger than a prescribed threshold. In the second strategy, the probability of a link changing at any instant of time is proportional to the magnitude of the instantaneous synchronization error. We demonstrate that both these strategies are capable of guiding networks to chaos suppression within a prescribed tolerance, in two prototypical systems of coupled chaotic maps. So, the adaptation works effectively as an efficient search in the vast space of connectivities for a configuration that serves to yield a targeted pattern. The mean synchronization error shows the presence of a sharply defined transition to very low values after a critical coupling strength, in all cases. For the first strategy, the total time during which a network undergoes link adaptation also exhibits a distinct transition to a small value under increasing coupling strength. Analogously, for the second strategy, the mean fraction of links that change in the network over time, after transience, drops to nearly zero, after a critical coupling strength, implying that the network reaches a static link configuration that yields the desired dynamics. These ideas can then potentially help us to devise control methods for extended interactive systems, as well as suggest natural mechanisms capable of regularizing complex networks.

Audio encryption framework based on chaotic map and DNA encoding

In this work, an audio encryption framework is proposed based on the chaos theory and DNA encoding. Traditional encryption algorithms designed for text data might not be efficient for handling the bulk data of audio files, leading to slow processing times and increased storage requirements. Striking the right balance between robust encryption and efficient processing is crucial. Additionally, some encryption methods can introduce noise or artifacts into the audio signal, impacting its clarity. Maintaining high-fidelity audio quality while ensuring strong encryption remains an ongoing area of research. Despite these challenges, the need for secure audio communication is undeniable. The RCM chaotic map is used to introduce chaotic properties in the encryption framework. A novel pseudorandom bit generator approach is proposed and used for encryption purposes. The proposed work is a symmetric encryption approach and is completely lossless. The proposed approach uses some lightweight computational procedures that make the algorithm simple and computationally less expensive which makes it suitable for real-time applications. Furthermore, the proposed approach shows significant performance and resilience against various cryptographic attacks. A new scrambling algorithm is proposed to add a layer of security. The proposed scramble algorithm uses logistic map beside the RCM map. The proposed approach achieved 98.28 % NSCR value and 33.63 % UACI values on average. The experimental outcomes are encouraging for practical applications of the proposed approach.

Multivariate short-term wind speed prediction based on PSO-VMD-SE-ICEEMDAN two-stage decomposition and Att-S2S

To counter the challenges posed by the unpredictability of wind velocities on wind energy production, a wind speed prediction model combining chaotic mapping-based particle swarm optimization with variational modal decomposition (CPSO-VMD), sample entropy (SE), improved completely integrated empirical modal decomposition with adaptive noise (ICEEMDAN) two-layer decomposition, and attention mechanism-based sequence to sequence (Att-S2S) method is proposed. Firstly, the Lasso method is employed to filter the features that significantly contribute to the wind speed data, fully considering hidden relevant information and eliminating redundant data to improve the prediction accuracy; Secondly, CPSO optimized by introducing chaotic mapping determines the parameter pairs for VMD. This facilitates an adaptive VMD breakdown of the wind speed sequence, aiding in noise removal and selection of the intrinsic mode function (IMF) with the highest sample entropy for further decomposition using ICEEMDAN. In light of this, a sequence-to-sequence method based on the attention mechanism is suggested, which may highlight the influence features' effects on IMF; Finally, the proposed model is implemented at both the Paso Robles wind farm and the Oasis wind farm for practical assessment and benchmarked against other models. Overall, the proposed model outperforms the other models in these trials.

A Universal Image Compression Sensing–Encryption Algorithm Based on DNA-Triploid Mutation

With the fast growth of information technology (IT), the safety of image transmission and the storing of images are becoming increasingly important. Traditional image encryption algorithms have certain limitations in transmission and security, so there is an urgent need for a secure and reliable image encryption algorithm. A universal compression sensing (CS) image encryption (IE) algorithm based on DNA-triploid mutation (DTM) is presented in this paper. Firstly, by using the CS algorithm, an image is compressed while obtaining a range of chaotic sequences by iteration of a chaotic map. Then, DNA sequences are generated by encoding the image and, based on the DTM, new mutant DNA sequences are generated according to specific rules. Next, the chaotic sequences are operated at the DNA level to perform confusion and diffusion operations on the image to ensure the security of the data. Finally, DNA decoding is carried out to obtain the compressed encrypted image. The simulation results show that the algorithm can effectively complete encryption and decryption of images. The performance test results show that the algorithm has a sufficiently large key space of 10587. The information entropy of the cipher image is close to 8. In summary, both simulation experiments and performance tests fully show that a high level of security and reliability for the proposed algorithm in protecting image privacy is achieved.