Sensitivity Analysis of Structural Dynamic Behavior Based on the Sparse Polynomial Chaos Expansion and Material Point Method

This paper presents a framework for constructing surrogate models for sensitivity analysis of structural dynamics behavior.Physical models involving deformation,such as collisions,vibrations,and penetration,are devel-oped using the material point method.To reduce the computational cost of Monte Carlo simulations,response surface models are created as surrogate models for the material point system to approximate its dynamic behavior.An adaptive randomized greedy algorithm is employed to construct a sparse polynomial chaos expansion model with a fixed order,effectively balancing the accuracy and computational efficiency of the surrogate model.Based on the sparse polynomial chaos expansion,sensitivity analysis is conducted using the global finite difference and Sobol methods.Several examples of structural dynamics are provided to demonstrate the effectiveness of the proposed method in addressing structural dynamics problems.

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.

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.

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.

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.

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.

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.

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.

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.

LOCAL CHAOS CHARACTERISTICS IN A SELF ASPIRATED REVERSED FLOW JET LOOP REACTOR

The local chaos characteristics of the time series pressure fluctuations of gas liquid two phase flow in a self aspirated reversed flow jet loop reactor are studied by the deterministic chaos analysis technique. It is found that the estimated local largest Lyapunov exponent is positive in all cases and the profile is similar to that of the local fractal dimension in this reactor. The positive largest Lyapunov exponent shows that the reactor is a nonlinear chaotic system. The obvious distribution indicates that the local nonlinear characteristic parameters such as the Lyapunov exponent and the fractal dimension could be applied to further study the flow characteristics such as the flow regine transitions and flow structures of the multi phase reactors.

Test analysis on relationship between anti-vibration performanceand chaos characteristics of vehicle suspension

Based on the primary principle of anti-vibration on vehicles, a chaos description on the vibration in suspensions is put forward. The vibration curve of the suspensions of test vehicles is obtained based on the data from a test rig for vehicle braking vs. suspension anti-vibration efficiency. The system parameters such as first inherent frequency and damp rate, as well as the chaos parameters such as the minimum embedding dimension and correlation dimension, are calculated by the vibration curve. The relationship among anti-vibration performance, chaos parameters and system parameters of vehicle suspension is presented. The research results show that the minimum embedding dimension Mmin can be used to estimate the change of the anti-vibration performance of the front suspension of the off-road jeep. The smaller Min is, the worse anti-vibration performance is. The corresponding stiffness and damp of the front suspension of the off-road jeep is smaller. Correlation dimension D2 can be used to identify different suspension types such as those of the off-road jeep and the car. The D2 of the off-road jeep is larger than the one of the car.

再掀“革命”风暴——Last Chaos

两年前，韩国NAKO开发的《混乱冒险》曾冲入韩国网游排行榜前三甲，进入中国后却被《天堂》远远抛在身后。闭关两年后，NAKO带着它的最新作品Last Chaos再次进军中国网游市场，并指名挑战《天堂Ⅱ》！这款游的画面、风格都与《天堂Ⅱ》十分相像，如果只看画面，很容易误认为是《天堂Ⅱ》中的新角色或新装扮。

Ceremony Chaos

在各种颁奖典礼、演唱会等仪式上．出现过不少小插曲，有的温馨感人，有的搞笑幽默，有的令人费解疑惑。有的让人措手不及，这些小插曲让人印象深刻。

New chaotic system and its hyperchaos generation

To seek for lower-dimensional chaotic systems that have complex topological attractor structure with simple algebraic system structure, a new chaotic system of three-dimensional autonomous ordinary differential equations is presented. The new system has simple algebraic structure, and can display a 2-scroll attractor with complex topological structure, which is different from the Lorenz＇s, Chen＇s and Lu¨＇s attractors. By introducing a linear state feedback controller, the system can be controlled to generate a hyperchaotic attractor. The novel chaotic attractor, hyperchaotic attractor and dynamical behaviors of corresponding systems are further investigated by employing Lyapunov exponent spectrum, bifurcation diagram, Poincar′e mapping and phase portrait, etc., and then verified by simulating an experimental circuit.

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.

Application of Chaos in Genetic Algorithms

Through replacing Gaussian mutation operator in real-coded genetic algorithm with a chaotic mapping, wepresent a genetic algorithm with chaotic mutation. To examine this new algorithm, we applied our algorithm to functionoptimization problems and obtained good results. Furthermore the orbital points' distribution of chaotic mapping andthe effects of chaotic mutation with different parameters were studied in order to make the chaotic mutation mechanismbe utilized efficiently.