Arrhythmia Detection by Using Chaos Theory with Machine Learning Algorithms

Heart monitoring improves life quality.Electrocardiograms(ECGs or EKGs)detect heart irregularities.Machine learning algorithms can create a few ECG diagnosis processing methods.The first method uses raw ECG and time-series data.The second method classifies the ECG by patient experience.The third technique translates ECG impulses into Q waves,R waves and S waves(QRS)features using richer information.Because ECG signals vary naturally between humans and activities,we will combine the three feature selection methods to improve classification accuracy and diagnosis.Classifications using all three approaches have not been examined till now.Several researchers found that Machine Learning(ML)techniques can improve ECG classification.This study will compare popular machine learning techniques to evaluate ECG features.Four algorithms—Support Vector Machine(SVM),Decision Tree,Naive Bayes,and Neural Network—compare categorization results.SVM plus prior knowledge has the highest accuracy(99%)of the four ML methods.QRS characteristics failed to identify signals without chaos theory.With 99.8%classification accuracy,the Decision Tree technique outperformed all previous experiments.

Improved PSO algorithm based on chaos theory and its application to design flood hydrograph

The deficiencies of basic particle swarm optimization （bPSO） are its ubiquitous prematurity and its inability to seek the global optimal solution when optimizing complex high-dimensional functions. To overcome such deficiencies, the chaos-PSO （COSPSO） algorithm was established by introducing the chaos optimization mechanism and a global particle stagnation-disturbance strategy into bPSO. In the improved algorithm, chaotic movement was adopted for the particles＇ initial movement trajectories to replace the former stochastic movement, and the chaos factor was used to guide the particles＇ path. When the global particles were stagnant, the disturbance strategy was used to keep the particles in motion. Five benchmark optimizations were introduced to test COSPSO, and they proved that COSPSO can remarkably improve efficiency in optimizing complex functions. Finally, a case study of COSPSO in calculating design flood hydrographs demonstrated the applicability of the improved algorithm.

Prediction method for risks of coal and gas outbursts based on spatial chaos theory using gas desorption index of drill cuttings

Based on the evolution of geological dynamics and spatial chaos theory, we proposed the advanced prediction an advanced prediction method of a gas desorption index of drill cuttings to predict coal and gas outbursts. We investigated and verified the prediction method by a spatial series data of a gas desorption index of drill cuttings obtained from the 113112 coal roadway at the Shitai Mine. Our experimental results show that the spatial distribution of the gas desorption index of drill cuttings has some chaotic charac- teristics, which implies that the risk of coal and gas outbursts can be predicted by spatial chaos theory. We also found that a proper amount of sample data needs to be chosen in order to ensure the accuracy and practical maneuverability of prediction. The relative prediction error is small when the prediction pace is chosen carefully. In our experiments, it turned out that the optimum number of sample points is 80 and the optimum prediction pace 30. The corresponding advanced prediction pace basically meets the requirements of engineering applications.

A Novel 2D Hyperchaotic with a Complex Dynamic Behavior for Color Image Encryption

The generation method of the key stream and the structure of the algorithm determine the security of the cryptosystem.The classical chaotic map has simple dynamic behavior and few control parameters,so it is not suitable for modern cryptography.In this paper,we design a new 2D hyperchaotic system called 2D simple structure and complex dynamic behavior map(2D-SSCDB).The 2D-SSCDB has a simple structure but has complex dynamic behavior.The Lyapunov exponent verifies that the 2D-SSCDB has hyperchaotic behavior,and the parameter space in the hyperchaotic state is extensive and continuous.Trajectory analysis and some randomness tests verify that the 2D-SSCDB can generate random sequences with good performance.Next,to verify the excellent performance of the 2D-SSCDB,we use the 2D-SSCDB to generate a keystream for color image encryption.In the encryption algorithm,the encryption algorithm scrambles and diffuses simultaneously,increasing the cryptographic system’s security.The horizontal correlation,vertical correlation,and diagonal correlation of ciphertext are−0.0004,−0.0004 and 0.0007,respectively.The average information entropy of the ciphertext is 7.9993.In addition,the designed encryption algorithm reduces the correlation between the three channels of the color image.Security analysis shows that the color image encryption algorithm designed using 2DSSCDB has good security,can resist standard attack methods,and has high efficiency.

Effect of metal oxide arrester on the chaotic oscillations in the voltage transformer with nonlinear core loss model using chaos theory

In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlin- ear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester （MOA） is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifur- cations such as period doubling bifurcation （PDB）, saddle node bifurcation （SNB）, Hopf bifurcation （HB）, and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are il- lustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.

Research on Stream Cipher Model Based on Chaos Theory

Chaos is a similar and random process which is very sensitive to initial value in deterministic system. It is a performance of nonlinear dynamical system with built-in randomness. Combined with the advantages and disadvantages of the present chaos encryption model, the paper proposes a chaotic stream cipher model based on chaos theory, which not only overcomes finite precision effect, but also improves the randomness of chaotic system and output sequence. The Sequence cycle theory generated by the algorithm can reach more than 10600 at least, which completely satisfies the actual application requirements of stream cipher system.

Research on General Permutation Encryption Module Based on Chaos Theory

Replacement and substitution encryption are two basic types of encryption historically. The classical encryption algorithm has been compromised now, but they still can play special role for modem cryptnlogy. For example, in digital image encryption system, substitution can disrupt the original order of the images and eliminate the correlation of image information which not only can realize security of images, but also can resist intentional attack and destruction of clipping and noise. And transposition transformation is introduced into the design of block ciphers. The substitution has the feature of high efficiency and resistance, which makes it meet the specific requirements of encryption. So substitution cypher can be applied to modern encryption system.

A Color Image Encryption Scheme Based on Singular Values and Chaos

The security of digital images transmitted via the Internet or other public media is of the utmost importance.Image encryption is a method of keeping an image secure while it travels across a non-secure communication medium where it could be intercepted by unauthorized entities.This study provides an approach to color image encryption that could find practical use in various contexts.The proposed method,which combines four chaotic systems,employs singular value decomposition and a chaotic sequence,making it both secure and compression-friendly.The unified average change intensity,the number of pixels’change rate,information entropy analysis,correlation coefficient analysis,compression friendliness,and security against brute force,statistical analysis and differential attacks are all used to evaluate the algorithm’s performance.Following a thorough investigation of the experimental data,it is concluded that the proposed image encryption approach is secure against a wide range of attacks and provides superior compression friendliness when compared to chaos-based alternatives.

FLIGHT CONFLICT FO RECASTING BASED ON CHAOTIC TIME SERIES

In order to grasp the evolution of flight conflict amount accurately and to forecast the amount, chaos in flight conflicts is studied. Firstly, a fault tree of flight conflicts is established based on the man-machine-environ- ment system engineering theory. The chaotic characteristics of flight conflict are analyzed from the qualitative point of view. Secondly, an improved chaotic algorithm for the largest Lyapunov exponent is proposed based on the small-data method and the wavelet de-noising theory. Chaos in flight conflict time series is identified by the improved chaotic algorithm from the quantitative point of view. Finally, a case study by the chaos forecasting al- gorithm is performed and the results are evaluated by the gray error checking ： Correlative value of posterior error is 0. 220 9〈0. 35, and micro-error probability is 0. 985 3〉0.95. Such results show the chaos forecasting algo- rithm is effective, thus it is feasible to analyze and forecast flight conflict by chaotic theory.

Hybrid optimization algorithm based on chaos,cloud and particle swarm optimization algorithm

As for the drop of particle diversity and the slow convergent speed of particle in the late evolution period when particle swarm optimization（PSO） is applied to solve high-dimensional multi-modal functions,a hybrid optimization algorithm based on the cat mapping,the cloud model and PSO is proposed.While the PSO algorithm evolves a certain of generations,this algorithm applies the cat mapping to implement global disturbance of the poorer individuals,and employs the cloud model to execute local search of the better individuals;accordingly,the obtained best individuals form a new swarm.For this new swarm,the evolution operation is maintained with the PSO algorithm,using the parameter of pop distr to balance the global and local search capacity of the algorithm,as well as,adopting the parameter of mix gen to control mixing times of the algorithm.The comparative analysis is carried out on the basis of 4 functions and other algorithms.It indicates that this algorithm shows faster convergent speed and better solving precision for solving functions particularly those high-dimensional multi-modal functions.Finally,the suggested values are proposed for parameters pop distr and mix gen applied to different dimension functions via the comparative analysis of parameters.

Artificial Bee Colony Algorithm-based Parameter Estimation of Fractional-order Chaotic System with Time Delay

It is an important issue to estimate parameters of fractional-order chaotic systems in nonlinear science, which has received increasing interest in recent years. In this paper, time delay and fractional order as well as system's parameters are concerned by treating the time delay and fractional order as additional parameters. The parameter estimation is converted into a multi-dimensional optimization problem. A new scheme based on artificial bee colony ABC algorithm is proposed to solve the optimization problem. Numerical experiments are performed on two typical time-delay fractional-order chaotic systems to verify the effectiveness of the proposed method. © 2014 Chinese Association of Automation.

Prediction Model of Weekly Retail Price for Eggs Based on Chaotic Neural Network

This paper establishes a short-term prediction model of weekly retail prices for eggs based on chaotic neural network with the weekly retail prices of eggs from January 2008 to December 2012 in China.In the process of determining the structure of the chaotic neural network,the number of input layer nodes of the network is calculated by reconstructing phase space and computing its saturated embedding dimension,and then the number of hidden layer nodes is estimated by trial and error.Finally,this model is applied to predict the retail prices of eggs and compared with ARIMA.The result shows that the chaotic neural network has better nonlinear fitting ability and higher precision in the prediction of weekly retail price of eggs.The empirical result also shows that the chaotic neural network can be widely used in the field of short-term prediction of agricultural prices.

Optimization of HMM Parameters Based on Chaos and Genetic Algorithm for Hand Gesture Recognition

In order to prevent standard genetic algorithm (SGA) from being premature, chaos is introduced into GA, thus forming chaotic anneal genetic algorithm (CAGA). Chaos ergodicity is used to initialize the population, and chaotic anneal mutation operator is used as the substitute for the mutation operator in SGA. CAGA is a unified framework of the existing chaotic mutation methods. To validate the proposed algorithm, three algorithms, i. e. Baum-Welch, SGA and CAGA, are compared on training hidden Markov model (HMM) to recognize the hand gestures. Experiments on twenty-six alphabetical gestures show the CAGA validity.

Chaos-Based Multipurpose Image Watermarking Algorithm

To achieve the goal of image content authentication and copyright protection simultaneously, this paper presents a novel image dual watermarking method based on chaotic map. Firstly, the host image was split into many nonoverlapping small blocks, and the block-wise discrete cosine transform （DCT） is computed. Secondly, the robust watermarks, shuffled by the chaotic sequences, are embedded in the DC coefficients of blocks to achieve the goal of copyright protection. The semi-fragile watermarks, generated by chaotic map, are embedded in the AC coefficients of blocks to obtain the aim of image authentication. Both of them can be extracted without the original image. Simulation results demonstrate the effectiveness of our algorithm in terms of robustness and fragility.

Chaos and Combination Synchronization of a New Fractional-order System with Two Stable Node-foci

A new fractional-order Lorenz-like system with two stable node-foci has been thoroughly studied in this paper. Some sufficient conditions for the local stability of equilibria considering both commensurate and incommensurate cases are given. In addition, with the effective dimension less than three, the minimum effective dimension of the system is approximated as 2.8485 and is verified numerically. It should be affirmed that the linear differential equation in fractional-order Lorenzlike system appears to be less sensitive to the damping, represented by a fractional derivative, than the two other nonlinear equations. Furthermore, combination synchronization of this system is analyzed with the help of nonlinear feedback control method. Theoretical results are verified by performing numerical simulations. © 2014 Chinese Association of Automation.

Nonlinear model predictive control based on hyper chaotic diagonal recurrent neural network

Nonlinear model predictive controllers(NMPC)can predict the future behavior of the under-controlled system using a nonlinear predictive model.Here,an array of hyper chaotic diagonal recurrent neural network(HCDRNN)was proposed for modeling and predicting the behavior of the under-controller nonlinear system in a moving forward window.In order to improve the convergence of the parameters of the HCDRNN to improve system’s modeling,the extent of chaos is adjusted using a logistic map in the hidden layer.A novel NMPC based on the HCDRNN array(HCDRNN-NMPC)was proposed that the control signal with the help of an improved gradient descent method was obtained.The controller was used to control a continuous stirred tank reactor(CSTR)with hard-nonlinearities and input constraints,in the presence of uncertainties including external disturbance.The results of the simulations show the superior performance of the proposed method in trajectory tracking and disturbance rejection.Parameter convergence and neglectable prediction error of the neural network(NN),guaranteed stability and high tracking performance are the most significant advantages of the proposed scheme.

CHAOTIC BEHAVIOR OF A NONLINEAR OSCILLATOR

The behavior of bifurcation and chaos in a forced oscillator containing a square nonlinear term was investigated by using Mel'nikov method and digital computer simulations. It was show that the system blows up for low damping before the motion develops into chaotic one when frequency is locked. The routes which lead to chaos are different for different frequency. After the parameters cross chaotic zone, the response of the system are also different. The three cases all depend on the values of dumping and frequency.

Feedback Control of Chaos in Delay Maps

In this paper, we discuss feedback control of a class of delay chaotic maps. Our aim is to drive the chaotic maps to its initially unstable fixed points by using linear and nonlinear state feedback control. The control is achieved by using small, bounded perturbations. Some numerical simulations are given to demonstrate the effectiveness of the proposed control method.

Chaos Analysis of Discharge Current Based on Tracking Test of Phenolic Resin

In tracking test, discharge is a complicated process and comparative tracking index (CTI) has wide varia-tion. To evaluate tracking resistance, the chaos analysis of discharge current is presented based on the tracking test of phenolic resin in accordance with IEC60112. According to the characteristics of statistical self-similarity and complexity of discharge current, the largest Lyapunov exponent is calculated, and the 2-dimensional attractor of discharge current is reconstructed. Moreover, the attractors of discharge current and recurrence plots of different discharge states are reconstructed. The results indicate that the chaos attractors have different characteristics in evo-lutionary tracks, the topological structure and grain direction of recurrence plots show significant differences. The chaos attractor can describe the tracking process, the recurrence plot can identify the tracking state clearly, while its arithmetic is simple.

High-precision chaotic radial basis function neural network model:Data forecasting for the Earth electromagnetic signal before a strong earthquake

The Earth’s natural pulse electromagnetic field data consists typically of an underlying variation tendency of intensity and irregularities.The change tendency may be related to the occurrence of earthquake disasters.Forecasting of the underlying intensity trend plays an important role in the analysis of data and disaster monitoring.Combining chaos theory and the radial basis function neural network,this paper proposes a forecasting model of the chaotic radial basis function neural network to conduct underlying intensity trend forecasting by the Earth’s natural pulse electromagnetic field signal.The main strategy of this forecasting model is to obtain parameters as the basis for optimizing the radial basis function neural network and to forecast the reconstructed Earth’s natural pulse electromagnetic field data.In verification experiments,we employ the 3 and 6 days’data of two channels as training samples to forecast the 14 and 21-day Earth’s natural pulse electromagnetic field data respectively.According to the forecasting results and absolute error results,the chaotic radial basis function forecasting model can fit the fluctuation trend of the actual signal strength,effectively reduce the forecasting error compared with the traditional radial basis function model.Hence,this network may be useful for studying the characteristics of the Earth’s natural pulse electromagnetic field signal before a strong earthquake and we hope it can contribute to the electromagnetic anomaly monitoring before the earthquake.