Piecewise Linear Chaotic Map Research Articles

PMSOMA: optical microscope algorithm based on piecewise linear chaotic mapping and sparse adaptive exploration

The optical microscope algorithm (OMA) is a metaheuristic algorithm that draws inspiration from the magnifying functionality of optical microscopes. This study introduces an enhanced variant of OMA, termed PMSOMA, designed to mitigate the original version's limitations, notably its slow convergence rates and vulnerability to local optima. PMSOMA integrates a piecewise linear chaotic map to refine population initialization and augment diversity, alongside a sparse adaptive exploration mechanism to bolster search efficacy. The performance of PMSOMA was rigorously tested using a suite of 50 benchmark functions, the CEC2017 test suite, feature selection datasets, and three classical engineering challenges. The empirical findings confirm that PMSOMA surpasses both the original OMA and competing algorithms by delivering superior solutions, accelerating convergence, and demonstrating enhanced robustness in convergence.

Optimization of a photovoltaic/wind/battery energy-based microgrid in distribution network using machine learning and fuzzy multi-objective improved Kepler optimizer algorithms

In this study, a fuzzy multi-objective framework is performed for optimization of a hybrid microgrid (HMG) including photovoltaic (PV) and wind energy sources linked with battery energy storage (PV/WT/BES) in a 33-bus distribution network to minimize the cost of energy losses, minimizing the voltage oscillations as well as power purchased minimization from the HMG incorporated forecasted data. The variables are microgrid optimal location and capacity of the HMG components in the network which are determined through a multi-objective improved Kepler optimization algorithm (MOIKOA) modeled by Kepler’s laws of planetary motion, piecewise linear chaotic map and using the FDMT. In this study, a machine learning approach using a multilayer perceptron artificial neural network (MLP-ANN) has been used to forecast solar radiation, wind speed, temperature, and load data. The optimization problem is implemented in three optimization scenarios based on real and forecasted data as well as the investigation of the battery's depth of discharge in the HMG optimization in the distribution network and its effects on the different objectives. The results including energy losses, voltage deviations, and purchased power from the HMG have been presented. Also, the MOIKOA superior capability is validated in comparison with the multi-objective conventional Kepler optimization algorithm, multi-objective particle swarm optimization, and multi-objective genetic algorithm in problem-solving. The findings are cleared that microgrid multi-objective optimization in the distribution network considering forecasted data based on the MLP-ANN causes an increase of 3.50%, 2.33%, and 1.98%, respectively, in annual energy losses, voltage deviation, and the purchased power cost from the HMG compared to the real data-based optimization. Also, the outcomes proved that increasing the battery depth of discharge causes the BES to have more participation in the HMG effectiveness on the distribution network objectives and affects the network energy losses and voltage deviation reduction.

New PID parameter tuning based on improved dung beetle optimization algorithm

AbstractIn this paper, a proportional‐integral‐derivative (PID) controller parameter optimization method based on the improved dung beetle optimization (IDBO) algorithm is proposed, which improves the balance between the global exploration and local exploitation capabilities of the dung beetle optimization (DBO) and significantly enhances the convergence speed and optimization accuracy. Initially, the dung beetle population is initialized using piecewise linear chaotic map (PWLCM) chaotic mapping in order to increase its variety and the DBO algorithm's capacity for global exploration. Furthermore, adaptive weighting in the DBO algorithm is now balanced between the capabilities of local exploitation and global exploration with the addition of adaptive weights. After that, in order to improve the DBO algorithm's capacity for local exploitation, a triangle wandering strategy is included during the dung beetle reproductive phase. Finally, using both Lévy flying wandering and greedy strategy (GS) together make it easier to take advantage of opportunities in both local and global areas. The outcomes of the traditional benchmark function test demonstrate a significant improvement in both convergence speed and optimization accuracy when the particle swarm optimization (PSO), DBO, grey wolf optimization (GWO), and sparrow search algorithm (SSA) algorithms are compared. The performance index function incorporates an overshooting penalty term to prevent the overshooting phenomenon in the control system. Simulation experiments are carried out for the DC motor control system, and the time domain performance, frequency domain performance, and robustness performance of the closed‐loop control system with ZN‐PID, Lambda‐PID, PSO‐PID, and IDBO‐PID rectified PID controller parameters are comparatively analyzed, which verifies the validity and practicability of the IDBO algorithm.

Classification of high-dimensional imbalanced biomedical data based on spectral clustering SMOTE and marine predators algorithm

The research of biomedical data is crucial for disease diagnosis, health management, and medicine development. However, biomedical data are usually characterized by high dimensionality and class imbalance, which increase computational cost and affect the classification performance of minority class, making accurate classification difficult. In this paper, we propose a biomedical data classification method based on feature selection and data resampling. First, use the minimal-redundancy maximal-relevance (mRMR) method to select biomedical data features, reduce the feature dimension, reduce the computational cost, and improve the generalization ability; then, a new SMOTE oversampling method (Spectral-SMOTE) is proposed, which solves the noise sensitivity problem of SMOTE by an improved spectral clustering method; finally, the marine predators algorithm is improved using piecewise linear chaotic maps and random opposition-based learning strategy to improve the algorithm’s optimization seeking ability and convergence speed, and the key parameters of the spectral-SMOTE are optimized using the improved marine predators algorithm, which effectively improves the performance of the over-sampling approach. In this paper, five real biomedical datasets are selected to test and evaluate the proposed method using four classifiers, and three evaluation metrics are used to compare with seven data resampling methods. The experimental results show that the method effectively improves the classification performance of biomedical data. Statistical test results also show that the proposed PRMPA-Spectral-SMOTE method outperforms other data resampling methods.

A Robust Zero-Watermarking Scheme in Spatial Domain by Achieving Features Similar to Frequency Domain

In recent years, there has been a substantial surge in the application of image watermarking, which has evolved into an essential tool for identifying multimedia material, ensuring security, and protecting copyright. Singular value decomposition (SVD) and discrete cosine transform (DCT) are widely utilized in digital image watermarking despite the considerable computational burden they involve. By combining block-based direct current (DC) values with matrix norm, this research article presents a novel, robust zero-watermarking approach. It generates a zero-watermark without attempting to modify the contents of the image. The image is partitioned into non-overlapping blocks, and DC values are computed without applying DCT. This sub-image is further partitioned into non-overlapping blocks, and the maximum singular value of each block is calculated by matrix norm instead of SVD to obtain the binary feature matrix. A piecewise linear chaotic map encryption technique is utilized to improve the security of the watermark image. After that, the feature image is created via XOR procedure between the encrypted watermark image and the binary feature matrix. The proposed scheme is tested using a variety of distortion attacks including noise, filter, geometric, and compression attacks. It is also compared with the other relevant image watermarking methods and outperformed them in most cases.

An optimization method for wireless sensor networks coverage based on genetic algorithm and reinforced whale algorithm.

In response to the problem of coverage redundancy and coverage holes caused by the random deployment of nodes in wireless sensor networks (WSN), a WSN coverage optimization method called GARWOA is proposed, which combines the genetic algorithm (GA) and reinforced whale optimization algorithm (RWOA) to balance global search and local development performance. First, the population is initialized using sine map and piecewise linear chaotic map (SPM) to distribute it more evenly in the search space. Secondly, a non-linear improvement is made to the linear control factor 'a' in the whale optimization algorithm (WOA) to enhance the efficiency of algorithm exploration and development. Finally, a Levy flight mechanism is introduced to improve the algorithm's tendency to fall into local optima and premature convergence phenomena. Simulation experiments indicate that among the 10 standard test functions, GARWOA outperforms other algorithms with better optimization ability. In three coverage experiments, the coverage ratio of GARWOA is 95.73, 98.15, and 99.34%, which is 3.27, 2.32 and 0.87% higher than mutant grey wolf optimizer (MuGWO), respectively.

FSR-SPD: an efficient chaotic multi-image encryption system based on flip-shift-rotate synchronous-permutation-diffusion operation

Images are a crucial component in contemporary data transmission. Numerous images are transmitted daily through the open-source network. This paper presents a multi-image encryption scheme that utilises flip-shift-rotate synchronous-permutation-diffusion (FSR-SPD) processes to ensure the security of multiple images in a single encryption operation. The proposed encryption technique distinguishes itself from current multi-image encryption methods by utilising SPD operation and rapid FSR-based pixel-shuffling and diffusion operation. The SPD is a cryptographic technique that involves the simultaneous application of permutation and diffusion methods. The FSR-based process involves the manipulation of pixels through three different operations, namely flipping, shifting, and rotating. In the process of encryption, the image components of red, green, and blue colours are merged into a single composite image. The large image is partitioned into non-overlapping blocks of uniform size. The SPD technique is employed to tackle each specific block. The encryption method is efficient and expeditious as it exhibits high performance with both FSR and SPD procedures. The method employs a single, fixed-type, one-dimensional, piecewise linear chaotic map (PWLCM) for both the permutation and diffusion phases, resulting in high efficiency in both software and hardware. The proposed method is assessed using key space, histogram variance, neighbouring pixel correlation, information entropy, and computational complexity. The proposed method has a much bigger key space than the comparative method. Compared to comparison approaches, the suggested solution reduces encrypted picture histogram variance by 6.22% and neighbouring pixel correlations by 77.78%. Compared to the comparison technique, the proposed scheme has a slightly higher information entropy of 0.0025%. Other multiple-color image encryption methods are more computationally intensive than the suggested method. Computer simulations, security analysis, and comparison analysis evaluated the proposed methodology. The results show it outperforms multiple images encrypting methods.

Fiber orientation and boundary stiffness optimization of laminated cylindrical shells with elastic boundary for maximum the fundamental frequency by an improved sparrow search algorithm

In this paper, a multivariate improved sparrow search algorithm (MCSSA) is proposed for maximizing the fundamental frequency of composite laminated cylindrical shells and preventing vibrational resonance. The mathematical model for analyzing the fundamental frequency of composite laminated cylindrical shells in free vibration is established based on the first-order shear deformation theory (FSDT). A fundamental frequency optimization model for composite laminated cylindrical shells with elastic boundary is formulated, considering the influence of fiber orientation and boundary stiffness, with the objective of maximizing the fundamental frequency. In the optimization process, in response to the shortcomings of the sparrow search algorithm, Piecewise Linear Chaotic Map (PWLCM), tracking learning strategy, opposition-based learning strategy (OBL) and elite retention strategy are introduced for improvement to obtain the MCSSA with better overall performance for model optimization. The effectiveness and applicability of the algorithm improvements are demonstrated by comparing MCSSA with the whale optimization algorithm (WOA), sparrow search algorithm (SSA), and pelican optimization algorithm (POA) using 13 standard test functions and 2 composite laminated cylindrical shell cases. The numerical calculation results show that the shells optimized with MCSSA have higher fundamental frequency. MCSSA is an effective candidate for solving such problems.

Safe-LBP: A visually meaningful image encryption scheme based on LBP and compressive sensing

Recently, some visually meaningful image encryption schemes have been proposed to protect the visual security of images. However, much of the existing literature on visual image encryption ignores the features of cover images. To address the above issues, this paper proposes a content-adaptive visual image encryption scheme based on piecewise linear chaotic map (PWLCM), compressive sensing (CS), and safe local binary pattern (Safe-LBP). First of all, the plain image are sparse by applying discrete wavelet transform (DWT). Secondly, the cipher data is obtained by encrypting and compressing the sparse matrix using Arnold scrambling and CS. Next, we design a new LBP operator to discover appropriate embedding place in the cover image, which tremendously improves the imperceptibility of the cipher image. Finally, the visually meaningful steganographic image is obtained by embedded all cipher data through the least significant bit (LSB) method. Simulations and comparisons show that the proposed algorithm has excellent visual security and decryption quality and proves its robustness against various types of noises and data loss.

Novel Integer Shmaliy Transform and New Multiparametric Piecewise Linear Chaotic Map for Joint Lossless Compression and Encryption of Medical Images in IoMTs

The discrete Shmaliy moment transform (DST) is a type of discrete orthogonal moment transform that is widely used in signal and image processing. However, DST is not suitable for lossless image applications due to its non-integer reversible nature. To overcome this limitation, we introduce the integer discrete Shmaliy transform (IDST) that performs integer-to-integer encoding, leading to a perfect and unique reconstruction of the input image. Next, a new 1D chaotic system model, the 1D multiparametric piecewise linear chaotic map (M-PWLCM), is presented as an extension of the existing 1D PWLCM. The M-PWLCM includes eight control parameters defined over an unlimited interval. To demonstrate the relevance of IDST and M-PWLCM in reversible image processing applications, they are used in a new scheme for lossless compression and encryption of medical images in the internet of medical things (IoMTs). On the one hand, the simulation results show that our scheme offers a good compression ratio and a higher level of security to resist differential attacks, brute force attacks and statistical attacks. On the other hand, the comparative analysis carried out shows the overall superiority of our scheme over similar state-of-the-art ones, both in achieving a higher compression ratio and better security when communicating medical images over unsecured IoMTs.

Color Image Encryption Algorithm Based on Cross-Spiral Transformation and Zone Diffusion

Due to their rich information, color images are frequently utilized in many different industries, but the network’s security in handling their delivery of images must be taken into account. To improve the security and efficiency of color images, this paper proposed a color image encryption algorithm based on cross-spiral transformation and zone diffusion. The proposed algorithm is based on Chen’s system and the piecewise linear chaotic map, and uses the chaotic sequences generated by them for related operations. Firstly, the R, G and B planes are extracted, and the spiral starting point of each plane is randomly selected by the chaotic sequence to implement the cross-spiral transformation. Secondly, the bit-level image matrix is constructed by the scrambled image matrix, and the bit-level chaotic matrix is constructed by the chaotic sequence. Finally, the three-dimensional matrix is divided into four zones by a dividing line, and partition diffusion is carried out to obtain the encrypted image. Simulation results and algorithm analyses indicate that the proposed algorithm has superior performance and can resist a wide range of attacks.

A Cross-Source Point Cloud Registration Algorithm Based on Trigonometric Mutation Chaotic Harris Hawk Optimisation for Rockfill Dam Construction

A high-precision three-dimensional (3D) model is the premise and vehicle of digitalising hydraulic engineering. Unmanned aerial vehicle (UAV) tilt photography and 3D laser scanning are widely used for 3D model reconstruction. Affected by the complex production environment, in a traditional 3D reconstruction based on a single surveying and mapping technology, it is difficult to simultaneously balance the rapid acquisition of high-precision 3D information and the accurate acquisition of multi-angle feature texture characteristics. To ensure the comprehensive utilisation of multi-source data, a cross-source point cloud registration method integrating the trigonometric mutation chaotic Harris hawk optimisation (TMCHHO) coarse registration algorithm and the iterative closest point (ICP) fine registration algorithm is proposed. The TMCHHO algorithm generates a piecewise linear chaotic map sequence in the population initialisation stage to improve population diversity. Furthermore, it employs trigonometric mutation to perturb the population in the development stage and thus avoid the problem of falling into local optima. Finally, the proposed method was applied to the Lianghekou project. The accuracy and integrity of the fusion model compared with those of the realistic modelling solutions of a single mapping system improved.

Multi-image encryption scheme with quaternion discrete fractional Tchebyshev moment transform and cross-coupling operation

With quaternion theory, the traditional discrete fractional Tchebyshev transform is extended to the quaternion algebra domain for multi-image processing. A new multi-image encryption scheme based on quaternion discrete fractional Tchebyshev moment transform (QDFrTMT) and the cross-coupling chaotic system is suggested. The original images are first confused by fractal sorting square matrix and sine-logistic exponential chaotic map, and then the resulting image is divided into four matrices. With the quaternion symplectic form representation, a quaternion signal can be formed by the divided matrices, which can reduce the number of the discrete fractional Tchebyshev transforms used and enhance the computational efficiency. Subsequently, the quaternion array is encrypted with the proposed QDFrTMT. To overcome the weakness of the permutation-diffusion operation based on a single chaotic map, a Logistic-sine exponential chaotic map and a piece-wise linear chaotic map are cross-coupled. The final ciphertext images can be acquired by carrying out the dual-layer encryption processes in horizontal and vertical directions. Numerical simulations and security analyses verify the effectiveness of the multi-image encryption algorithm and its strong ability to counteract common attacks.

Efficient information hiding in medical optical images based on piecewise linear chaotic maps

Efficient information hiding in medical optical images based on piecewise linear chaotic maps

Investigation of piecewise linear chaotic map as a diffusion model for image encryption

Investigation of piecewise linear chaotic map as a diffusion model for image encryption

Chaos-based optimal path planning of humanoid robot using hybridized regression-gravity search algorithm in static and dynamic terrains

The present work deals with the navigational analysis of humanoids in complex terrains by tuning the classical approach with reactive techniques. Here, the linear regression (LR)-based classical approach is merged with the gravitational search algorithm (GSA), called RGSA, and Chaos is added to achieve an optimum path. To improve upon the local traps, Chaos is introduced into the basic structure of the RGSA model to attain a global solution without effecting the higher convergence rate of the RGSA model. The Chaos further adds ergodicity to the dynamical system, gaining an optimal path length in the shortest time possible. The use of the proposed hybridization technique is found to be effective as compared to its counterparts. Various chaotic maps like the logistic map, Gauss map, piecewise linear chaotic map, and sinusoidal maps are used, and the results are compared. Also, the smoothness of the path is ensured during trajectory planning. The analysis is done in real-time lab conditions and simulation environments using single and multiple humanoids (Nao robots) with static and dynamic obstacles within the search space. The simulation for the path planning is done using the Webot software, while the choregraphe software is used for experimental path planning. The simulation and experimental work presented in the current paper shows good agreement and are within 6% acceptable limits. The proposed controller is then compared with a vision-based approach and another parallel sensor-based approach for optimum operational cost and smoother trajectory. The current work is a novel approach in which the humanoid’s interaction with the mobile robot is also analyzed. The proposed approach successfully avoided the dynamic obstacle in the form of the KHEPERA-II mobile robot. This concept can find potential applications in soccer scenarios employing mobile robots as opponent players to the Nao robots. Further, because of the lower operational cost, the proposed methodology can also be applied to other areas, such as multitasking, cooperative scheduling, power distribution systems, etc.

Ameliorating LSB Using Piecewise Linear Chaotic Map and One-Time Pad for Superlative Capacity, Imperceptibility and Secure Audio Steganography

Audio steganography hides a secret message into an audio. Existing techniques are lacking in achieving high payload, imperceptibility in addition to robustness at the same time. They also suffer from choosing the samples and even LSBs in an unpredictable fashion. Moreover, few adaptive techniques exist, besides not many embed in higher LSBs. Hence, a novel LSB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>PWLCM</i></sub> method that ameliorates LSB audio steganography is proposed. It uses piecewise linear chaotic map (PWLCM) to embed a secret message in random samples, besides selecting one of the 4-LSBs in an unsystematic way. It is noteworthy that each time a distinct sample and hence a differed 4-LSB is chosen as per different generated PWLCM. At first, Huffman coding is used to lessen the secret message size. Thereafter, to ameliorate the security of the one-time pad, random numbers are generated using PWLCM as an input key. This gives the proposed method a dual protection by amalgamating steganography with enhanced secure one-time pad. MATLAB is used to implement the proposed LSB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>PWLCM</i></sub> method and evaluate the imperceptibility between cover and stego audios against standard parameters viz. Perceptual Evaluation of Speech Quality (PESQ) and Perceptual Evaluation of Audio Quality (PEAQ). Furthermore, its imperceptibility was tested using Mean Square Error, Peak Signal to Noise Ratio, Signal-to-Noise Ratio, Percentage Root Mean Square Difference and Audio Fidelity. Exhaustive experiments on vastly used metrics affirm that the proposed method LSB <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>PWLCM</i></sub> excel prevailing methods regarding hiding capacity and imperceptibility. Furthermore, it is resistant to brute force attacks having a large key space besides its dependency on the secret message size. In addition, it effectively withstood statistical analysis, specifically histogram attack and fourth first moments. Albeit it was vigorous towards re-sampling attacks, yet it was not very robust against LSB attacks nor noise. Assuredly, it prevails over existing methods and beyond comparison when juxtaposed with them affirming its efficacy.

Enkripsi Nilai Piksel Pada Citra Digital Dengan Algoritma Piecewise Linear Chaotic Map

The process of recording, storing and sharing digital images is very easy to do nowadays. To protect the information in the image, the image can be encrypted by scrambling the image into an unintelligible image form. The Piecewise Linear Chaotic Map algorithm is used in research to encrypt images. The trick is that the Piecewise Linear Chaotic Map algorithm generates random numbers, and these random numbers are used to randomize image pixel values using the XOR function. The application implements the Piecewise Linear Chaotic Map method to encrypt pixel values in digital images, so that only certain parties who know the key can access digital images.

Optimized Deep Learning-Enabled Hybrid Logistic Piece-Wise Chaotic Map for Secured Medical Data Storage System

Background: In recent times, medical technology has generated massive reports such as scanned medical images and electronic patient accounts. These reports are necessary to be stored in the highly secured platform for further reference. Traditional storage systems are infeasible for storing massive data. In addition, it suffers to provide secure storage and privacy protection at the time of medical services. It is necessary to provide secure storage and full utilization of personal medical records for the common people in practice. The healthcare system based on IoT enhances the support for the patients and doctors in diagnosing the sufferers at an accurate time using the monitored health data. Yet, doctors make an inappropriate decision regarding the sufferer’s sickness when the information regarding health data saved in the cloud gets lost or hacked owing to an external attack or also power failure. Hence, it is highly essential for verifying the truthfulness of the sufferer’s information regarding health data saved on the cloud.Hypothesis: The major intention of this task is to adopt a new chaotic-based healthcare medical data storage system for storing medical data (medical images) with high protection. Methodology: Initially, the input medical images are gathered from the benchmark datasets concerning different modalities. The collected medical images are enciphered by developing Hybrid Chaotic Map by adapting the 2D-Logistic Chaotic Map (2DLCM), and Piece-Wise Linear Chaotic Map (PWLCM) referred to as Hybrid Logistic Piece-Wise Chaotic Map (HLPWCM). An Optimized Recurrent Neural Network (O-RNN) is proposed for key generation using Best Fitness-based Coefficient vector improved Spotted Hyena Optimizer (BF-CSHO). The O-RNN-based key generation utilizes the extracted image features like first and second-order statistical features and the targets are acquired as a unique encrypted key, which is used for securing the medical data. The same BF-CSHO is used for improving the training algorithm (weight optimization) of RNN to minimize the Mean Absolute Error (MAE) between the cipher (encrypted) images and original images. Results: From the result analysis, the suggested BF-CSHO-RNN-HLPWCM, by considering the image size at [Formula: see text] shows 10.4%, 8.5%, 3.97%, 0.62%, 3.88%, 2.40%, and 7.82% provides better computational efficiency than LCM, PWLCM, LPWCM, PSO-RNN-HLPWCM, JA-RNN-HLPWCM, GWO-RNN-HLPWCM, and SHO-RNN-HLPWCM, respectively. Conclusion: Thus, the simulation findings show the effective efficiency of the offered method owing to the security of the stored medical data.

FTPS: Efficient fault‐tolerant dynamic phrase search over outsourced encrypted data with forward and backward privacy

SummaryWith the popularity of cloud computing, more and more users store sensitive information in cloud servers. In order to protect the data over the cloud server, symmetric encryption with keyword search has been developed and the phrase search has been proposed subsequently to overcome the inefficiency produced by single/multi‐keyword search. However, most existing phrase search schemes fails to support fault‐tolerant search which is essential to users. Therefore, this paper proposes a fault‐tolerant dynamic phrase search scheme with forward privacy and backward privacy (FTPS). Piecewise Linear Chaotic Map and minhash function are used to blur information, and Bloom filter based index is constructed to realize efficient search and dynamic update simultaneously. Security analysis proves that FTPS can properly preserve the privacy of search user, and experimental results show that FTPS is practical.