Suppression and synchronization of chaos in uncertain time-delay physical system

The mechanical horizontal platform(MHP)system exhibits a rich chaotic behavior.The chaotic MHP system has applications in the earthquake and offshore industries.This article proposes a robust adaptive continuous control(RACC)algorithm.It investigates the control and synchronization of chaos in the uncertain MHP system with time-delay in the presence of unknown state-dependent and time-dependent disturbances.The closed-loop system contains most of the nonlinear terms that enhance the complexity of the dynamical system;it improves the efficiency of the closed-loop.The proposed RACC approach(a)accomplishes faster convergence of the perturbed state variables(synchronization errors)to the desired steady-state,(b)eradicates the effect of unknown state-dependent and time-dependent disturbances,and(c)suppresses undesirable chattering in the feedback control inputs.This paper describes a detailed closed-loop stability analysis based on the Lyapunov-Krasovskii functional theory and Lyapunov stability technique.It provides parameter adaptation laws that confirm the convergence of the uncertain parameters to some constant values.The computer simulation results endorse the theoretical findings and provide a comparative performance.

Probabilistic analysis of tunnel face seismic stability in layered rock masses using Polynomial Chaos Kriging metamodel

Face stability is an essential issue in tunnel design and construction.Layered rock masses are typical and ubiquitous;uncertainties in rock properties always exist.In view of this,a comprehensive method,which combines the Upper bound Limit analysis of Tunnel face stability,the Polynomial Chaos Kriging,the Monte-Carlo Simulation and Analysis of Covariance method(ULT-PCK-MA),is proposed to investigate the seismic stability of tunnel faces.A two-dimensional analytical model of ULT is developed to evaluate the virtual support force based on the upper bound limit analysis.An efficient probabilistic analysis method PCK-MA based on the adaptive Polynomial Chaos Kriging metamodel is then implemented to investigate the parameter uncertainty effects.Ten input parameters,including geological strength indices,uniaxial compressive strengths and constants for three rock formations,and the horizontal seismic coefficients,are treated as random variables.The effects of these parameter uncertainties on the failure probability and sensitivity indices are discussed.In addition,the effects of weak layer position,the middle layer thickness and quality,the tunnel diameter,the parameters correlation,and the seismic loadings are investigated,respectively.The results show that the layer distributions significantly influence the tunnel face probabilistic stability,particularly when the weak rock is present in the bottom layer.The efficiency of the proposed ULT-PCK-MA is validated,which is expected to facilitate the engineering design and construction.

Random-injection-based two-channel chaos with enhanced bandwidth and suppressed time-delay signature by mutually coupled lasers: Proposal and numerical analysis

Simultaneous bandwidth(BW) enhancement and time-delay signature(TDS) suppression of chaotic lasing over a wide range of parameters by mutually coupled semiconductor lasers(MCSLs) with random optical injection are proposed and numerically investigated. The influences of system parameters on TDS suppression(characterized by autocorrelation function(ACF) and permutation entropy(PE) around characteristic time) and chaos BW are investigated. The results show that, with the increasing bias current, the ranges of parameters(detuning and injection strength) for the larger BW(> 20 GHz) are broadened considerably, while the parameter range for optimized TDS(< 0.1) is not shrunk obviously.Under optimized parameters, the system can simultaneously achieve two chaos outputs with enhanced BW(> 20 GHz)and perfect TDS suppression. In addition, the system can generate two-channel high-speed truly physical random number sequences at 200 Gbits/s for each channel.

Control of Halo-Chaos in Beam Transport Network via Neural Network Adaptation with Time-Delayed Feedback

Subject of the halo-chaos control in beam transport networks （channels） has become a key concerned issue for many important applications of high-current proton beam since 1990＇. In this paper, the magnetic field adaptive control based on the neural network with time-delayed feedback is proposed for suppressing beam halo-chaos in the beam transport network with periodic focusing channels. The envelope radius of high-current proton beam is controlled to reach the matched beam radius by suitably selecting the control structure and parameter of the neural network, adjusting the delayed-time and control coefficient of the neural network.

On fractional discrete financial system:Bifurcation,chaos,and control

The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets.This paper introduces a new three-dimensional(3D)fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders.As such,we evaluate when the equilibrium points are stable or unstable at various fractional orders.We use many numerical methods,phase plots in 2D and 3D projections,bifurcation diagrams and the maximum Lyapunov exponent.These techniques reveal that financial maps exhibit chaotic attractor behavior.This study is grounded on the Caputo-like discrete operator,which is specifically influenced by the variance of the commensurate and incommensurate orders.Furthermore,we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy algorithm.Additionally,we offer nonlinear-type controllers to stabilize the fractional financial map.The numerical results of this study are obtained using MATLAB.

Controlling Beam Halo-Chaos via Time-Delayed Feedback

The study of controlling high-current proton beam halo-chaos has become a key concerned issue for manyimportant applications. In this paper, time-delayed feedback control method is proposed for beam halo-chaos. Particle incell simulation results show that the method is very effective and has some advantages for high-current beam experimentsand engineering.

Can spatial planning in the Polish Carpathians be enforced? How spatial chaos indicators depict a gap between scientific knowledge and practice

Despite their strategic hydrological importance for neighbouring areas,the Polish Carpathians are experiencing spatial chaos,which may weaken their adaptability to the progressive climate change.The article attempts to answer the question of whether spatial planning,which is supposed to guarantee spatial order,fulfils its role and whether the knowledge of the natural conditions of spatial development is respected in the spatial planning process.Using GIS techniques,up to 238 communes were analysed in terms of their spatial coverage,the degree of scattered settlement,and the violation of natural barriers by location of buildings in areas that are threatened with mass movements or floods;by settlement on excessively inclined slopes and in areas with adverse climatic conditions.Spearman non-parametric rank correlation analysis and the multidimensional Principal Component Analysis(PCA)technique were performed to investigate relations between spatial chaos indicators and the planning situation.The analysis of the data has revealed that spatial planning does not fulfil its role.Serious errors in location of buildings have been noted even though the communes are covered by local spatial development plans.Scientific knowledge is not sufficiently transferred into planning documents,and bottom-up initiatives cannot replace systemic solutions.There is a need for strengthening the role of environmental studies documents in the spatial planning system.This would facilitate the transfer of scientific knowledge into the planning process and help to protect mountain areas.The development of a special spatial strategy for the Polish Carpathians in compliance with the Carpathian Convention is also recommended.

基于小样本下改进ChaosNet的轴承故障诊断

为解决在训练样本不足条件下,轴承故障特征提取困难的问题,提出一种基于改进神经混沌学习(neurochaos learning+AdaBoost,NL-AdaBoost)的轴承故障诊断新方法。首先,对时域振动信号进行快速傅里叶变换(fast fourier transform,FFT)提取频域特征,拼接时频域信号获得一维特征样本;其次,输入信号产生对混沌GLS神经元的激励,形成ChaoFEX特征,馈送至集成学习分类器(AdaBoost);随后,选取轴承故障特征样本,对样本集做k折交叉验证,获得模型最优超参数值,将其应用于测试集进行模型分类能力验证;最后,在小样本对比实验中,与4种常见深度学习算法比较模型的macro F1-score。实验结果证明,在低训练样本条件下,NL-AdaBoost模型具有良好的准确性和泛化能力。

Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.

Three-dimensional pseudo-dynamic reliability analysis of seismic shield tunnel faces combined with sparse polynomial chaos expansion

To address the seismic face stability challenges encountered in urban and subsea tunnel construction,an efficient probabilistic analysis framework for shield tunnel faces under seismic conditions is proposed.Based on the upper-bound theory of limit analysis,an improved three-dimensional discrete deterministic mechanism,accounting for the heterogeneous nature of soil media,is formulated to evaluate seismic face stability.The metamodel of failure probabilistic assessments for seismic tunnel faces is constructed by integrating the sparse polynomial chaos expansion method(SPCE)with the modified pseudo-dynamic approach(MPD).The improved deterministic model is validated by comparing with published literature and numerical simulations results,and the SPCE-MPD metamodel is examined with the traditional MCS method.Based on the SPCE-MPD metamodels,the seismic effects on face failure probability and reliability index are presented and the global sensitivity analysis(GSA)is involved to reflect the influence order of seismic action parameters.Finally,the proposed approach is tested to be effective by a engineering case of the Chengdu outer ring tunnel.The results show that higher uncertainty of seismic response on face stability should be noticed in areas with intense earthquakes and variation of seismic wave velocity has the most profound influence on tunnel face stability.

Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring

This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.

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.

Chaos and Its Impulsive Control in Chua's Oscillator via Time-Delay Feedback

A novel framework for chaos and its impul-sive control in Chua＇s oscillator via time-delay feedback is presented.The exponential stability of impulsive control Chua＇s oscillator via time-delay feedback is considered,and some novel conditions are obtained.Then a novel impulsive controller design procedure is proposed.Simulation experiments are provided to demonstrate the feasibility and effectiveness of our method finally.

Generating Li-Yorke chaos in a stable continuous-time T-S fuzzy model via time-delay feedback control

This paper investigates the chaotification problem of a stable continuous-time T S fuzzy system. A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique. Then, the asymptotically approximate relationship between the controlled continuous-time T-S fuzzy system with time-delay and a discrete-time T-S fuzzy system is established. Based on the discrete-time T-S fuzzy system, it proves that the chaos in the discrete- time T-S fuzzy system satisfies the Li-Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem. Finally, the effectiveness of the proposed chaotic anticontrol method is verified by a practical example.

CHAOS-6模型描述的中国地区地磁长期变化及误差分析

根据CHAOS-6模型,计算了2015年中国地区28个地磁台站的地磁年度变化以及2008.0—2016.5年成都、格尔木、兰州、泰安和通海5个地磁台站的地磁长期变化。分析比较了地磁台站实际观测值与CHAOS-6模型计算值之间的差异,得到两者差值的均值及均方误差。结果表明:CHAOS-6模型描述的中国地区地磁长期变化与地磁台站实际观测的地磁长期变化趋势基本一致,但存在一定的差异,28个台站的磁偏角(D)、磁倾角(I)、地磁总强度(F)、北向分量(X)、东向分量(Y)、水平分量(H)、垂直分量(Z)差值的均值和均方误差的平均值分别为-0.9'/1.7',-29.3'/0.8',-116.3 nT/10.2 nT,264.7 nT/13.6 nT,-27.7 nT/15.0 nT,265.2 nT/13.7 nT,-356.9 nT/8.0 nT。因此,在使用CHAOS-6模型研究中国地区区域问题时,应充分考虑模型的误差大小。

A Robust Low Power Chaos-Based Truly Random Number Generator

This paper presents a low power,truly random number generator （TRNG） based on a simple chaotic map of the Bernoulli shift,which is extended to remain robustness in implementation. The map is realized by switched-current techniques that can fully integrate it in a cryptosystem on a chip. A pipelined architecture post-processed by a simple XOR circuit is used to improve the entropy. The TRNG is fabricated in an HJTC 0.18μm CMOS mixed signal process,and the statistical properties are investigated by measurement results. The power consumption is only 1.42mW and the truly random output bit rate is 10Mbit/s.

MODEL FOR CHAOS CONTROL OF REGIONAL Ec-R-Ev SYSTEM

In order to realize the coordination oriented management of the economy resource environment(Ec R Ev) composite system,its optimal aggregate coordinating measurement model is established.A self learning method is presented,which combines the optimizing technology and stability analysis together to achieve a tradeoff between the optimizing objective and system stability.So a model for chaos control of the composite system based on coordination is proposed.

SIMULATION STUDY OF CHAOS IN DC-DC CONVERTER

A DC DC buck converter c on trolled by naturally sampled, constant frequency PWM is considered. The existe nce of chaotic solutions and the output performance of the system under differen t circuit parameters are studied. The transforming pattern of system behavior fr om steady state to chaotic is discovered by the cascades of period doubling bi furcation and the cascades of periodic orbit in V I phase space. Accordingl y, it is validated that change of values of the circuit parameters may lead DC DC converter to chaotic motion. Performances of the output ripples fro m steady state to chaotic are analyzed in time and frequency domains respective ly. Some important conclusions are helpful for opt imization design of DC DC converter.

时空Chaos研究中的CML模型

通过对有关差分格式的稳定性分析,我们提出了一类新的格点耦合映射(CML)模型,数值试验表明:我们提出的CML模型是一类有效的研究时空复杂性的模型,特别是对于强耦合系统.

基于RS-Chaos-LSSVM的鱼雷航向控制研究

基于典型的非线性系统的鱼雷航向控制存在不确定性因素,尝试提出基于RS-Chaos-LSSVM的航向控制方案。Chaos在线优化LSSVM模型参数,确保控制的精度。为提高控制的实时快速性,采用RS理论消除冗余信息,用约简后的规则集对Chaos-LSSVM模型进行训练控制,满足较好的快速性;RS-Chaos-LSSVM与RS-LSSVM控制器仿真表明,该方法提高了鱼雷航向控制的实时精确性,且对于海流海浪干扰具有良好的自适应抗干扰能力。