A new look at the response surface method for reliability analysis using chaos theory     

Youliang Ding  Aiqun Li  Yang Deng 《地震工程与工程振动(英文版)》2008,7(3):329-335

To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.  相似文献   

强震地面运动的混沌特性分析     

杨迪雄  杨丕鑫 《地震学刊》2009,(3):252-260

引入非线性动力学理论和混沌时间序列分析方法考察强震地面运动加速度时程的非线性特征。首先采用功率谱分析法、主成份分析法和Cao方法定性判断地震动加速度时程具有混沌特性,然后应用混沌时间序列分析方法定量计算了30条地震动加速度时程的三个非线性特征参数。计算表明,这些地震动时程的关联维数为2．0～4．0的分数维,Kolmogorov熵K2为大于零的有限正值,最大Lyapunov指数在o～i．0之间。结果说明,强震地面运动具有混沌特性,地震动的高度不规则和复杂性是地震过程强非线性的反映。  相似文献   

黄河流域泥沙时序混沌特征——地理学综合研究的一种尝试(英文)     

马建华  孙艳丽  楚纯洁 《地理学报(英文版)》2010,20(2):219-230

The sediment content of the Yellow River is resulted from the interactions of natural, economic,and social factors,so it includes some evolutive information of the Yellow River Basin system.Sediment contents from 1952 to 2007 on Toudaoguai,Tongguan,Huayuankou and Lijin sections along the river are chosen as the study time series,and correlation dimensions(D2),Kolmogorov entropies(K2),and Hurst indexes(H)of the time series were calculated.Correlation dimensions on Toudaoguai,Tongguan,Huayuankou,and Lijin sec...  相似文献   

Chaotic characters of the Yellow River Basin based on the sediment time series: An attempt to integrated research in geography     

MA Jianhua  SUN Yanli  CHU Chunjie 《地理学报》2010,20(2):219-230

The sediment content of the Yellow River is resulted from the interactions of natural, economic, and social factors, so it includes some evolutive information of the Yellow River Basin system. Sediment contents from 1952 to 2007 on Toudaoguai, Tongguan, Huayuankou and Lijin sections along the river are chosen as the study time series, and correlation dimensions (D2), Kolmogorov entropies (K2), and Hurst indexes (H) of the time series were calculated. Correlation dimensions on Toudaoguai, Tongguan, Huayuankou, and Lijin sections are 3.24, 5.69, 6.57 and 7.34 respectively, and the Kolmogorov entropies are 0.13, 0.37, 0.40 and 0.38 respectively, which indicates that the systems controlled by different sections along the Yellow River are chaotic systems and the chaotic degrees increase gradually from the upper to lower section. The average predictable period of the sediment contents is 8 years on Toudaoguai section and 3 years on the other sections with the reciprocals of the Kolmogorov entropies. The more obvious the chaotic degree is, the shorter the average predictable period is. Hurst indexes on the sections are above 0.5, with the maximum of 0.86 on Tongguan section and the minimum of 0.68 on Toudaoguai section, which indicates that the time series have persistent trends in the average predictable period. Eight state variables and two control parameters are necessary to construct the dynamic model of the Yellow River Basin system.  相似文献   

A Symplectic Mapping Model for the Study of 2:3 Resonant Trans-Neptunian Motion     

K. G. Hadjifotinou  John D. Hadjidemetriou 《Celestial Mechanics and Dynamical Astronomy》2002,84(2):135-157

A symplectic mapping is constructed for the study of the dynamical evolution of Edgeworth-Kuiper belt objects near the 2:3 mean motion resonance with Neptune. The mapping is six-dimensional and is a good model for the Poincaré map of the real system, that is, the spatial elliptic restricted three-body problem at the 2:3 resonance, with the Sun and Neptune as primaries. The mapping model is based on the averaged Hamiltonian, corrected by a semianalytic method so that it has the basic topological properties of the phase space of the real system both qualitatively and quantitatively. We start with two dimensional motion and then we extend it to three dimensions. Both chaotic and regular motion is observed, depending on the objects' initial inclination and phase. For zero inclination, objects that are phase-protected from close encounters with Neptune show ordered motion even at eccentricities as large as 0.4 and despite being Neptune-crossers. On the other hand, not-phase-protected objects with eccentricities greater than 0.15 follow chaotic motion that leads to sudden jumps in their eccentricity and are removed from the 2:3 resonance, thus becoming short period comets. As inclination increases, chaotic motion becomes more widespread, but phase-protection still exists and, as a result, stable motion appears for eccentricities up to e = 0.3 and inclinations as high as i = 15°, a region where plutinos exist.  相似文献   

基于地震数据结构梯度张量属性的采空区识别方法     

陈强  许玉莹  曾维望 《中国煤炭地质》2013,(7):42-47

通过介绍结构张量矩阵构建及其特征向量与特征值的算法原理,提出了利用梯度结构张量矩阵特征值计算Chaos及其边缘属性,以提高不同类型采空区三维地震资料解释精度的技术思路,并讨论了在地震数据结构张量chaos、边缘检测属性计算中的关键环节。实例分析表明,chaos和边缘属性可以精细描述不同类型采空区的地震反射结构特征变化规律:工作面采空区可形成明显的杂乱反射结构,平面呈连续密实的团块状或宽条带状异常;巷道采空区则表现为微波状弯曲反射结构,具有串珠状、短而弯曲的线状、窄条状平面特征。基于地震数据梯度结构张量算法的属性分析是精细识别和解释采空区的一个有效工具。  相似文献   

Chaotic mixing of tracer and vorticity by modulated travelling Rossby waves     

R. T. Pierrehumbert 《地球物理与天体物理流体动力学》2013,107(1-4):285-319

Abstract

We consider the mixing of passive tracers and vorticity by temporally fluctuating large scale flows in two dimensions. In analyzing this problem, we employ modern developments stemming from properties of Hamiltonian chaos in the particle trajectories; these developments generally come under the heading “chaotic advection” or “Lagrangian turbulence.” A review of the salient properties of this kind of mixing, and the mathematics used to analyze it, is presented in the context of passive tracer mixing by a vacillating barotropic Rossby wave. We then take up the characterization of subtler aspects of the mixing. It is shown the chaotic advection produces very nonlocal mixing which cannot be represented by eddy diffusivity. Also, the power spectrum of the tracer field is found to be k ^{? l} at shortwaves—precisely as for mixing by homogeneous, isotropic two dimensional turbulence,—even though the physics of the present case is very different. We have produced two independent arguments accounting for this behavior.

We then examine integrations of the unforced barotropic vorticity equation with initial conditions chosen to give a large scale streamline geometry similar to that analyzed in the passive case. It is found that vorticity mixing proceeds along lines similar to passive tracer mixing. Broad regions of homogenized vorticity ultimately surround the separatrices of the large scale streamline pattern, with vorticity gradients limited to nonchaotic regions (regions of tori) in the corresponding passive problem.

Vorticity in the chaotic zone takes the form of an arrangement of strands which become progressively finer in scale and progressively more densely packed; this process transfers enstrophy to small scales. Although the enstrophy cascade is entirely controlled by the large scale wave, the shortwave enstrophy spectrum ultimately takes on the classical k ^{? l} form. If one accepts that the enstrophy cascade is indeed mediated by chaotic advection, this is the expected behavior. The extreme form of nonlocality (in wavenumber space) manifest in this example casts some doubt on the traditional picture of enstrophy cascade in the Atmosphere, which is based on homogeneous two dimensional turbulence theory. We advance the conjecture that these transfers are in large measure attributable to large scale, low frequency, planetary waves.

Upscale energy transfers amplifying the large scale wave do indeed occur in the course of the above-described process. However, the energy transfer is complete long before vorticity mixing has gotten very far, and therefore has little to do with chaotic advection. In this sense, the vorticity involved in the enstrophy cascade is “fossil vorticity,” which has already given up its energy to the large scale.

We conclude with some speculations concerning statistical mechanics of two dimensional flow, prompted by our finding that flows with identical initial energy and enstrophy can culminate in very different final states. We also outline prospects for further applications of chaotic mixing in atmospheric problems.  相似文献   

天然大地电磁场时间序列的分形特征     

严家斌  刘贵忠 《煤田地质与勘探》2007,35(2):66-69

分形理论是分析和研究自然界中具有“自相似性”、“自仿射性”不规则形体的重要手段。分形维是描述这种分形体的定量参数,反映了系统的复杂性与本质特征。利用相空间重建理论与G-P算法对大地电磁场的时间序列进行相空间重构,表明大地电磁场时间序列相空间的吸引子是存在的,大地电磁场虽然看似随机的天然信号,事实上它是具有内在确定性的随机信号。实例分析表明,大地电磁场时间序列关联维数与地下介质特征密切相关,能定性地反映介质的电性分布与结构特征。   相似文献