Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.

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.

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.

A novel variable-order fractional chaotic map and its dynamics

In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.

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.

Multi-Level Image Segmentation Combining Chaotic Initialized Chimp Optimization Algorithm and Cauchy Mutation

To enhance the diversity and distribution uniformity of initial population,as well as to avoid local extrema in the Chimp Optimization Algorithm(CHOA),this paper improves the CHOA based on chaos initialization and Cauchy mutation.First,Sin chaos is introduced to improve the random population initialization scheme of the CHOA,which not only guarantees the diversity of the population,but also enhances the distribution uniformity of the initial population.Next,Cauchy mutation is added to optimize the global search ability of the CHOA in the process of position(threshold)updating to avoid the CHOA falling into local optima.Finally,an improved CHOA was formed through the combination of chaos initialization and Cauchy mutation(CICMCHOA),then taking fuzzy Kapur as the objective function,this paper applied CICMCHOA to natural and medical image segmentation,and compared it with four algorithms,including the improved Satin Bowerbird optimizer(ISBO),Cuckoo Search(ICS),etc.The experimental results deriving from visual and specific indicators demonstrate that CICMCHOA delivers superior segmentation effects in image segmentation.

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.

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.

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.

具有食饵避难所的离散捕食者-食饵模型的余维二分支分析

In this paper,a discrete predator-prey model with prey refuge is investigated.It is proved that the model undergoes codimension-2 bifurcations associated with 1:2 and 1:3 resonances.The bifurcation diagrams and phase portraits show that the model has some interesting complex dynamical behaviors,such as limit cycle,periodic solutions,chaos and codimension-1 bifurcations.

Nonlinear Dynamics Behaviors of a Rotor Roller Bearing System with Radial Clearances and Waviness Considered

A rotor system supported by roller beatings displays very complicated nonlinear behaviors due to nonlinear Hertzian contact forces, radial clearances and bearing waviness. This paper presents nonlinear bearing forces of a roller bearing under four-dimensional loads and establishes 4-DOF dynamics equations of a rotor roller bearing system. The methods of Newmark-β and of Newton-Laphson are used to solve the nonlinear equations. The dynamics behaviors of a rigid rotor system are studied through the bifurcation, the Poincar è maps, the spectrum diagrams and the axis orbit of responses of the system. The results show that the system is liable to undergo instability caused by the quasi-periodic bifurcation, the periodic-doubling bifurcation and chaos routes as the rotational speed increases. Clearances, outer race waviness, inner race waviness, roller waviness, damping, radial forces and unbalanced forces-all these bring a significant influence to bear on the system stability. As the clearance increases, the dynamics behaviors become complicated with the number and the scale of instable regions becoming larger. The vibration frequencies induced by the roller bearing waviness and the orders of the waviness might cause severe vibrations. The system is able to eliminate non-periodic vibration by reasonable choice and optimization of the parameters.

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.

基于相对增益和改进粒子群算法的PSS与直流调制协调策略

现有电力系统稳定器(power system stabilizer,PSS)和直流调制多使用本地信号作为控制器反馈输入信号,控制器间的交互作用可能降低甚至破坏系统稳定性。提出了一种基于广域测量信号的PSS与直流调制协调策略,首先通过留数法选择对于振荡模态可观性较强的广域信号作为阻尼控制器备选反馈信号;其次通过相对增益方法选择使PSS和直流调制交互影响最小的备选信号作为最佳反馈信号;而后设计分散控制器,并运用基于混沌和差分进化的混合粒子群优化算法对PSS和直流调制控制器参数进行协调优化。最后,通过EPRI 36节点系统仿真验证了协调策略的正确性和有效性。

VIBRO-IMPACTS OF A SLENDER CANTILEVER BEAM WITH A LUMPED TIP MASS BETWEEN TWO RIGID STOPS

This paper presents a dynamic analysis of vibro impacts of a slender cantilever beam carrying a lumped tip mass between two rigid stops subjected to horizontal harmonic excitation of basement. This vibro impacting system is a simplified model for the vibro impacts between the shell of a flying vehicle and its interior components. The dynamic equation of vibro impacting system is established on the basis of the Galerkin method, the Lagrange method and the Newton rule of collision. The effects of excitation frequency, excitation amplitude and the clearance between the tip mass and a stop on system dynamics are numerically investigated. The nonlinear dynamics, especially various chaotic motions, are observed by using the Poincaré section. Numerical results show that the longterm behavior of system mainly depends on the above three parameters, and there exist a series of processes and corresponding reverse processes, during which a periodic motion undergoes period doubling bifurcation and then becomes chaotic motion, or vice versa.

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。

中国及邻近地区地磁长期变化分析

利用2010.0—2016.0年中国国际地磁交换台站和中国邻近地区共14个地磁台站的X,Y,Z分量观测数据,结合世界资料中心发布的静扰日数据,计算了台站十日静日午夜均值,并进行三次多项式拟合,得到X,Y,Z分量的长期变化和年变率。同时,利用CHAOS-6和IGRF-12模型计算了2010.0—2016.0年F分量的长期变化,分别得到了CHAOS-6及IGRF-12模型计算值与台站观测值的差值。结果表明:同一地区的台站X,Y,Z分量变化趋势基本一致;Z分量的平均年变率与X,Y分量相比偏大;CHAOS-6和IGRF-12模型描述的F分量的长期变化与台站观测值之间的差值的绝对值分别为4.8～253.7 nT和0.9～420.0 nT。产生上述误差的原因主要是CHAOS-6和IGRF-12模型是描述全球地磁场的模型,而地磁场及其长期变化具有显著的区域特征和局部特征。

Stochastic Analysis of Interconnect Delay in the Presence of Process Variations

Process variations can reduce the accuracy in estimation of interconnect performance. This work presents a process variation based stochastic model and proposes an effective analytical method to estimate interconnect delay. The technique decouples the stochastic interconnect segments by an improved decoupling method. Combined with a polynomial chaos expression （PCE）, this paper applies the stochastic Galerkin method （SGM） to analyze the system response. A finite representation of interconnect delay is then obtained with the complex approximation method and the bisection method. Results from the analysis match well with those from SPICE. Moreover, the method shows good computational efficiency, as the running time is much less than the SPICE simulation＇s.

CHAOTIC TRANSDUCER

Utilizing the character of chaos, the sensitivity to the initial conditions, the concept and the structure of so-called chaotic transducer based on Tent map is provided in this paper creatively. The possibility of applying the basic theory of symbolic dynamics to the measurement is presented and proved. Then, the theoretical model of chaotic transducer is realized by using the switched capacitor and the basic experimental results are given. The transducer has such characters as high sensitivity, resolution, the simple structure and combining signal amplification with A/D. The new area of the application of chaos is exploited. Meanwhile, it provides a new method of exploring the structure of new type transducer.

INTERNET TRAFFIC DATA FLOW FORECAST BY RBF NEURAL NETWORK BASED ON PHASE SPACE RECONSTRUCTION

Characteristics of the Internet traffic data flow are studied based on the chaos theory. A phase space that is isometric with the network dynamic system is reconstructed by using the single variable time series of a network flow. Some parameters, such as the correlative dimension and the Lyapunov exponent are calculated, and the chaos characteristic is proved to exist in Internet traffic data flows. A neural network model is construct- ed based on radial basis function （RBF） to forecast actual Internet traffic data flow. Simulation results show that, compared with other forecasts of the forward-feedback neural network, the forecast of the RBF neural network based on the chaos theory has faster learning capacity and higher forecasting accuracy.