chaotic mapping
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Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 28
Author(s):  
Guijuan Wang ◽  
Xinheng Wang ◽  
Zuoxun Wang ◽  
Chunrui Ma ◽  
Zengxu Song

Accurate power load forecasting has an important impact on power systems. In order to improve the load forecasting accuracy, a new load forecasting model, VMD–CISSA–LSSVM, is proposed. The model combines the variational modal decomposition (VMD) data preprocessing method, the sparrow search algorithm (SSA) and the least squares support vector machine (LSSVM) model. A multi-strategy improved chaotic sparrow search algorithm (CISSA) is proposed to address the shortcomings of the SSA algorithm, which is prone to local optima and a slow convergence. The initial population is generated using an improved tent chaotic mapping to enhance the quality of the initial individuals and population diversity. Second, a random following strategy is used to optimize the position update process of the followers in the sparrow search algorithm, balancing the local exploitation performance and global search capability of the algorithm. Finally, the Levy flight strategy is used to expand the search range and local search capability. The results of the benchmark test function show that the CISSA algorithm has a better search accuracy and convergence performance. The volatility of the original load sequence is reduced by using VMD. The optimal parameters of the LSSVM are optimized by the CISSA. The simulation test results demonstrate that the VMD–CISSA–LSSVM model has the highest prediction accuracy and stabler prediction results.


Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2364
Author(s):  
Shangbin Jiao ◽  
Chen Wang ◽  
Rui Gao ◽  
Yuxing Li ◽  
Qing Zhang

The probability of the basic HHO algorithm in choosing different search methods is symmetric: about 0.5 in the interval from 0 to 1. The optimal solution from the previous iteration of the algorithm affects the current solution, the search for prey in a linear way led to a single search result, and the overall number of updates of the optimal position was low. These factors limit Harris Hawks optimization algorithm. For example, an ease of falling into a local optimum and the efficiency of convergence is low. Inspired by the prey hunting behavior of Harris’s hawk, a multi-strategy search Harris Hawks optimization algorithm is proposed, and the least squares support vector machine (LSSVM) optimized by the proposed algorithm was used to model the reactive power output of the synchronous condenser. Firstly, we select the best Gauss chaotic mapping method from seven commonly used chaotic mapping population initialization methods to improve the accuracy. Secondly, the optimal neighborhood perturbation mechanism is introduced to avoid premature maturity of the algorithm. Simultaneously, the adaptive weight and variable spiral search strategy are designed to simulate the prey hunting behavior of Harris hawk to improve the convergence speed of the improved algorithm and enhance the global search ability of the improved algorithm. A numerical experiment is tested with the classical 23 test functions and the CEC2017 test function set. The results show that the proposed algorithm outperforms the Harris Hawks optimization algorithm and other intelligent optimization algorithms in terms of convergence speed, solution accuracy and robustness, and the model of synchronous condenser reactive power output established by the improved algorithm optimized LSSVM has good accuracy and generalization ability.


PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0260725
Author(s):  
Jiahao Fan ◽  
Ying Li ◽  
Tan Wang

Metaheuristic optimization algorithms are one of the most effective methods for solving complex engineering problems. However, the performance of a metaheuristic algorithm is related to its exploration ability and exploitation ability. Therefore, to further improve the African vultures optimization algorithm (AVOA), a new metaheuristic algorithm, an improved African vultures optimization algorithm based on tent chaotic mapping and time-varying mechanism (TAVOA), is proposed. First, a tent chaotic map is introduced for population initialization. Second, the individual’s historical optimal position is recorded and applied to individual location updating. Third, a time-varying mechanism is designed to balance the exploration ability and exploitation ability. To verify the effectiveness and efficiency of TAVOA, TAVOA is tested on 23 basic benchmark functions, 28 CEC 2013 benchmark functions and 3 common real-world engineering design problems, and compared with AVOA and 5 other state-of-the-art metaheuristic optimization algorithms. According to the results of the Wilcoxon rank-sum test with 5%, among the 23 basic benchmark functions, the performance of TAVOA has significantly better than that of AVOA on 13 functions. Among the 28 CEC 2013 benchmark functions, the performance of TAVOA on 9 functions is significantly better than AVOA, and on 17 functions is similar to AVOA. Besides, compared with the six metaheuristic optimization algorithms, TAVOA also shows good performance in real-world engineering design problems.


2021 ◽  
Vol 11 (23) ◽  
pp. 11192
Author(s):  
Xiaoxu Yang ◽  
Jie Liu ◽  
Yi Liu ◽  
Peng Xu ◽  
Ling Yu ◽  
...  

Aiming at the problems of the basic sparrow search algorithm (SSA) in terms of slow convergence speed and the ease of falling into the local optimum, the chaotic mapping strategy, adaptive weighting strategy and t-distribution mutation strategy are introduced to develop a novel adaptive sparrow search algorithm, namely the CWTSSA in this paper. In the proposed CWTSSA, the chaotic mapping strategy is employed to initialize the population in order to enhance the population diversity. The adaptive weighting strategy is applied to balance the capabilities of local mining and global exploration, and improve the convergence speed. An adaptive t-distribution mutation operator is designed, which uses the iteration number t as the degree of freedom parameter of the t-distribution to improve the characteristic of global exploration and local exploration abilities, so as to avoid falling into the local optimum. In order to prove the effectiveness of the CWTSSA, 15 standard test functions and other improved SSAs, differential evolution (DE), particle swarm optimization (PSO), gray wolf optimization (GWO) are selected here. The compared experiment results indicate that the proposed CWTSSA can obtain higher convergence accuracy, faster convergence speed, better diversity and exploration abilities. It provides a new optimization algorithm for solving complex optimization problems.


2021 ◽  
Vol 2095 (1) ◽  
pp. 012017
Author(s):  
Jiliang Jin ◽  
Liyun Xing ◽  
Miao Yang ◽  
Jianqiang Shen ◽  
Yuqi Dong

Abstract To verify the advantages of deterministic matrix applied to power line carrier communication (PLCC) based on compressed sensing (CS). This article analyzed the research status of commonly used deterministic measurement matrices, and made simulation comparison. It is found that different types of deterministic measurement matrices generated based on chaotic mapping had higher reconstruction accuracy and higher reconstruction efficiency than Gaussian random matrix. Then, according to simulation results and the characteristics of PLCC signal, the Chebyshev sparse circulant (CSC) measurement matrix was designed by combining eighth-order Chebyshev chaotic and the idea of sparse and circulant. Actual circuit measurement shows that when compression rate was 40% and 60%, the reconstruction loss of CSC is 0.72dB and 0.49dB higher than that of Chebyshev chaotic measurement matrix and Chebyshev circulate measurement matrix, respectively. Obviously, the CSC measurement matrix designed in this paper can effectively improve the reconstruction accuracy.


2021 ◽  
Vol 2066 (1) ◽  
pp. 012011
Author(s):  
Xianglian Xue ◽  
Haiyan Jin

Abstract This paper studies the current situation of image compression encryption and analyzes the influence of low frequency (DC coefficient) and high frequency (AC coefficient) on image structure in DCT transformation. Based on this, a novel image security protection method based on DCT compression theory and hyper-chaotic mapping is proposed. First, the position of the pixel of the original image is disturbed, and converts the image from spatial domain into frequency domain by the two-dimensional DCT transformation and quantization. Second, change the pixel values by modifying the values of the sign bit of AC coefficient and DC coefficient. At last, the encrypted image is obtained by carrying out inverse quantization, inverse transformation and reverse operation by bit.


2021 ◽  
Vol 2079 (1) ◽  
pp. 012027
Author(s):  
Xudong Ren ◽  
Wanbo Yu

Abstract In order to improve the complexity of chaotic mapping and the security of image encryption algorithms, this paper proposes a new coupled three-dimensional chaotic system based on sine mapping and lorenz mapping. Based on this chaotic system, a new color image encryption algorithm is proposed, which performs index position scrambling and Arnold scrambling on the bit plane of the plaintext image, and then performs an XOR diffusion operation on the scrambled ciphertext to obtain the final ciphertext image. Simulation experiments show that the algorithm has a large key space, a small image correlation coefficient, an information entropy value of 7.9921, and a good encryption effect.


Processes ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1806
Author(s):  
Yuedong Zhang ◽  
Yuanbin Mo

The optimal solution of the chemical dynamic optimization problem is the basis of automatic control operation in the chemical process, which can reduce energy consumption, increase production efficiency, and maximize economic benefit. In this paper, a modified sailfish optimizer (MSFO) combined with an equal division method is proposed for solving chemical dynamic optimization problems. Based on the basic sailfish optimizer, firstly, the tent chaotic mapping strategy is introduced to disturb the initialization of sailfish and sardine populations to avoid the loss of population diversity. Secondly, an adaptive linear reduction strategy of attack parameters is proposed to enhance the exploration and exploitation ability of sailfish. Thirdly, the updating formula of sardine position is modified, and the global optimal solution is used to attract all sardine positions, which can avoid the premature phenomenon of the algorithm. Eventually, the MSFO is applied to solve six classical optimization cases of chemical engineering to evaluate its feasibility. The experimental results are analyzed and compared with other optimization methods to prove the superiority of the MSFO in solving chemical dynamic optimization problems.


Author(s):  
Костянтин Станіславович Васюта ◽  
Уляна Романівна Збежховська ◽  
Валерій Валерійович Слободянюк ◽  
Ірина Вікторівна Захарченко ◽  
Олександр Леонтійович Кащишин ◽  
...  

The subject of the research is the processes of formation and processing of signals with orthogonal frequency divisionand multiplexing (OFDM) of chaotic sequences to ensure the stealthiness of data transmission. The research synthesizes the method for increasing the stealthiness of information transmission systems based on signals with OFDM-modulation on the basis of forming an analytical signal and chaotic mapping of Chebyshev polynomial. It would enable ensuring reliable information protection in radio transmission systems that use signals with OFDM-modulation, at the cost of the high level of structural and independent and Identically distributed (IID) (the degree of signal masking under noise) stealthiness of the signals. The tasks are to investigate the effectiveness of the developed method for increasing the stealthiness of information transmission systems by numerical assessment of the level of structural and IID-stealthiness and the quality of recovery of the masked information on the receiving side. The methods used are for the formation and processing of chaotic subcarriers in the signal with OFDM-modulation – methods of nonlinear dynamics, approaches to the formation of analytical chaotic signal and methods of the statistical theory of observation processing; to assess the level of structural and IID-stealthiness – steganography theory, a method of nonlinear time series analysis based on the use of BDS-statistics. The following results are obtained: the method for increasing the stealthiness of information transmission systems based on the use of signals with OFDM-modulation and chaotic subcarriers has been synthesized, has also evaluated the level of structural and IID-stealthiness of signals, that generated using the proposed method. It is established that compared with systems that use harmonic signals with OFDM-modulation, chaotic signals with OFDM-modulation can provide a higher level of IID-stealthiness. It was confirmed by the obtained results of visual, frequency, statistical and dynamic analysis. To assess the level of structural stealthiness, the expenditure of detecting the generated signals with a given probability has been estimated. The obtained results showed that the level of structural stealthiness increased by 2…2.5 times. It has shown that to ensure the required level of recovery of the generated signal, the signal-to-noise ratio at the input of the receiver must be greater than 4 dB. Conclusions. The scientific novelty of the obtained results lies in the following: for the first time, the method of subcarrier formation for signals with OFDM-modulation based on the use of analytical signal and Chebyshev polynomial of the first kind of tertiary is obtained. The proposed method provides the required level of structural and IID-stealthiness of information transmission systems, compared with conventional methods of signal generation with OFDM-modulation, due to the similarity of the generated signals with “white” noise. 


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