Mapping Correlation Dimension along the Wall Region of a High-Flux Gas-Solid Riser Using Embedded Solid Concentration Time Series

Analysis of the entrance and wall dynamics of a high-flux gas-solid riser was conducted using embedded solid concentration time series collected from a 76 mm internal diameter and 10 m high riser of a circulating fluidized bed (CFB) system. The riser was operated at 4.0 to 10.0 m/s air velocity and 50 to 550 kg/m2s solids flux of spent fluid catalytic cracking (FCC) catalyst particles with 67 μm mean diameter and density of 1500 kg/m3. Data were analyzed using prepared FORTRAN 2008 code to get correlation integral followed by determination of correlation dimensions with respect to the hyperspherical radius and their profiles, plots of which were studied. It was found that correlation dimension profiles at the centre have single peak with higher values than the wall region profiles. Towards the wall, these profiles have double or multiple peaks showing bifractal or multifractal flow behaviors. As the velocity increases the wall region profiles become random and irregular. Further it was found that, as the height increases the correlation dimension profiles shift towards higher hyperspherical radius at the centre and towards lower hyperspherical radius in the wall region at r/R = 0.81. The established method of mapping correlation dimension profiles in this study forms a suitable tool for analysis of high-flux riser dynamics compared to other analyses approaches. However, further analysis is recommended to other gas-solid CFB riser of different dimensions operated at high-flux conditions using the established method.

Nonlinear Deterministic Chaos in Benue River Flow Daily Time Sequence

The Various physical mechanisms governing river flow dynamics act on a wide range of temporal and spatial scales. This spatio-temporal variability has been believed to be influenced by a large number of variables. In the light of this, an attempt was made in this paper to examine whether the daily flow sequence of the Benue River exhibits low-dimensional chaos;that is, if or not its dynamics could be explained by a small number of effective degrees of freedom. To this end, nonlinear analysis of the flow sequence was done by evaluating the correlation dimension based on phase space reconstruction and maximal Lyapunov estimation as well as nonlinear prediction. Results obtained in all instances considered indicate that there is no discernible evidence to suggest that the daily flow sequence of the Benue River exhibit nonlinear deterministic chaotic signatures. Thus, it may be conjectured that the daily flow time series span a wide dynamical range between deterministic chaos and periodic signal contaminated with additive noise;that is, by either measurement or dynamical noise. However, contradictory results abound on the existence of low-dimensional chaos in daily streamflows. Hence, it is paramount to note that if the existence of low-dimension deterministic component is reliably verified, it is necessary to investigate its origin, dependence on the space-time behavior of precipitation and therefore on climate and role of the inflow-runoff mechanism.

工业多元时序数据质量评估方法

现有的数据质量评估(DQA)方法通常只从特定数据质量维度(DQD)的基本概念分析,忽略了能够反映数据质量(DQ)关键信息的细粒度的子维度对评估结果的影响。针对上述问题,提出一种工业多元时序数据质量评估(IMTSDQA)方法。首先,对于待评估的DQD,如完整性、规范性、一致性、唯一性和准确性等进行细粒度划分,考虑同一DQD内或不同DQD间各子维度的相关性以确定这些子维度的度量;其次,对完整性的属性完整性、记录完整性、数值完整性,规范性的类型规范性、精度规范性,一致性的顺序一致性、逻辑一致性,唯一性的属性唯一性、记录唯一性,准确性的范围准确性、数值准确性等子维度进行权重分配,进而充分挖掘DQD的深层次信息,从而获得反映DQ详情的评估结果。实验结果表明,与现有的基于框架定性分析、依据DQD基本定义构建模型的方法相比,IMTSDQA能更详细、更全面地评估DQ,且不同DQD的评估结果更能客观准确地反映DQ问题。

Trispectrum and correlation dimension analysis of magnetorheological damper in vibration screen

In order to improve the screening efficiency of vibrating screen and make vibration process smooth,a new type of magnetorheological (MR) damper was proposed. The signals of displacement in the vibration process during the test were collected. The trispectrum model of autoregressive (AR) time series was built and the correlation dimension was used to quantify the fractal characteristics during the vibration process. The result shows that,in different working conditions,trispectrum slices are applied to obtaining the information of non-Gaussian,nonlinear amplitude?frequency characteristics of the signal. Besides,there is correlation between the correlation dimension of vibration signal and trispectrum slices,which is very important to select the optimum working parameters of the MR damper and vibrating screen. And in the experimental conditions,it is found that when the working current of MR damper is 2 A and the rotation speed of vibration motor is 800 r/min,the vibration screen reaches its maximum screening efficiency.

Age Dependence of the Menstrual Cycle Correlation Dimension

Time series analysis, based on the idea that female reproductive endocrine physiology can be construed as a nonlinear dynamical system in a chaotic trajectory, is performed to measure the correlation dimension of the menstrual cycle data from subjects in two different age cohorts. The dimension is computed using a method proposed by Judd (Physica D, vol. 56, 1992, pp. 216-228) that does not assume the correlation dimension to be necessarily constant for all appropriate time scales of the system’s strange attractor. Significant time scale differences are found in the behavior of the dimension between the two age cohorts, but at the shortest time scales the correlation dimension converges to the same value, approximately 5.5, in both cases.

The Research of Fractal Characteristics of the Electrocardiogram in a Real Time Mode

The article presents the results of recent investigations into Holter monitoring of ECG, using non-linear analysis methods. This paper discusses one of the modern methods of time series analysis--a method of deterministic chaos theory. It involves the transition from study of the characteristics of the signal to the investigation of metric （and probabilistic） properties of the reconstructed attractor of the signal. It is shown that one of the most precise characteristics of the functional state of biological systems is the dynamical trend of correlation dimension and entropy of the reconstructed attractor. On the basis of this it is suggested that a complex programming apparatus be created for calculating these characteristics on line. A similar programming product is being created now with the support of RFBR. The first results of the working program, its adjustment, and further development, are also considered in the article.

A novel method to identify the scaling region for chaotic time series correlation dimension calculation

To obtain more accurate correlation dimension estimations for chaotic time series, a novel scaling region identification method is developed. First, points that obviously do not belong to the scaling region associated with the whole double logarithm correlation integral curve are removed using the K-means algorithm. Second, a point-slope-error algorithm is developed to recognize a possible scaling region. Third, the K-means algorithm is used again to further remove a small interval of interfering points in the possible scaling region to obtain a more precise scaling region. The correlation dimension of four typical chaotic attractors and five curves generated by the Weierstrass-Mandelbrot fractal function were calculated using the proposed method. These calculated values were very close to the respective theoretical fractal dimensions. Moreover, the effectiveness of our method in identifying the scaling region was compared with existing methods. Results show that our method can distinguish the scaling region objectively, accurately, automatically and quickly, making estimations of the correlation dimension more precise and affording significant improvements in nonlinear analysis.

Measuring Nonlinear Dependence Between Time Series Based on Correlation Dimension

In this paper, it is proved that the correlation dimension estimate of a nonlinear dynamical system with its multivariate observation series is the same as that with its univariate observation series. Based on this result, an inference method is presented, and the Nonlinear Dependence Coefficient is defined. This method is designed for testing nonlinear dependence between time series, and can be used in economic analysis and forecasting. Numerical results show the method is effective.

月降雨量时间序列中的混沌现象

降雨是水文水资源系统的输入 ,研究它的演变特性 ,对于水文水资源系统的预报、模拟是十分重要的。以四川省 6个水文站的月降雨量时间序列为例 ,通过混沌理论分析方法 ,探讨降雨系统的混沌特性。研究表明 ,降水系统中混沌现象是可能存在的。

混沌理论及在水科学中的应用与存在的问题

在简要介绍表征系统混沌特征常用方法的基础上,认为混沌理论在水科学中的应用主要集中在水文时间序列性质的判定和非线性预测模型研究上,并就这两方面的国内外研究进展进行了综述。通过对其应用中存在的主要问题:延迟时间的确定、数据量大小、噪声等进行分析和讨论,认为水科学问题中混沌的假设是合理的。但对于任何有限长度和受噪声干扰的时间序列来说,严格判定其相空间是确定性系统还是随机系统几乎是不可能的,纯粹的混沌和纯粹的随机都只是数学上的一种理想状态。因此,对于所研究的水科学问题是否存在混沌现象,仅采用单一的方法所取得的结论,不能作为判定依据,而仅表明可能存在混沌特征。所以有必要采用多种研究方法,综合刻划某一水科学问题中的混沌迹象,判定该序列是以混沌成分为主还是以随机性成分为主。提出分形上的混沌动力系统以及混沌与神经网络相结合的方法,可为水科学问题的研究能提供一些新的思路。

0-1测试方法的径流时间序列混沌特性应用

径流时间序列混沌特性识别的常用方法是基于相空间重构的关联维数法、最大Lyapunov指数法和Kolmogorov熵法。引入一种新的时间序列混沌特性识别方法:0-1混沌测试方法。该方法直接应用于时间序列不需要相空间重构,并且通过量化指标Kc是否接近于0或1来识别时间序列的混沌特性。以Logistic映射生成的序列、金沙江流域和美国Umpqua河多年日径流序列为研究对象,首先利用0-1混沌测试方法进行了混沌特性识别和判定;然后基于相空间重构,运用相空间重构、伪最近邻点法、关联维数方法、最大Lyapunov指数法和Kolmogorov熵5种非线性研究方法分析了这两列径流时间序列混沌特性。研究结果表明0-1混沌测试方法简单有效。以上方法交互验证了该两列径流时间序列存在低维混沌特性。

基于改进的C-C方法的相空间重构参数选择

针对混沌时间序列相空间重构C-C方法的三点不足,提出了一种基于改进的C-C方法的确定最优时延与嵌入窗的新算法。在关联积分计算过程中引入了权衡计算精度与速度的可调参数,合理选择该参数,能在不严重损失估计精度的前提下,大大加快计算速度。在理论分析的基础上,用所提出的算法对三种混沌序列进行相空间重构,仿真结果表明该算法对最优时延的选择更准确,对最优嵌入窗的选取更可靠。

地下水水位时间序列中的混沌特征

利用相空间重构技术、G -P算法以及Wolf提出的从单变量中提取Lyapunov指数的方法 ,分别计算了太原盆地 4组地下水水位时间序列的关联维数和Lyapunov指数。结果揭示在自然状态下 ,太原盆地某些孔隙潜水和孔隙承压水水位变化存在明显的混沌特征。这不仅为以后建立水位预测模型提供了理论依据 ,并且也为运用分形理论研究地质参数的时空变异性以及含水层结构的自相似性提供了进一步的支持。

陕北黄土高原气候干旱特性的混沌研究

在阐述了混沌系统的复杂特性以及关联维数的计算原理基础上,以陕北黄土高原地区气候干旱日持续时段分布为例,具体介绍了如何利用关联维数来判别其混沌性以及如何从单变量时间序列中提取其关联维数,提出了判断陕北黄土高原地区气候干旱混沌特性及其控制简单易行的方法。

从混沌时间序列同时计算关联维和Kolmogorov熵

在ＧＰ算法的基础上提出用最小二乘法从时间序列同时计算出关联维和Ｋｏｌｍｏｇｏｒｏｖ熵的方法。对混沌系统，从本方法得出的关联维是最优的，同时也得到了Ｋｏｌｍｏｇｏｒｏｖ熵的稳定估计。并用Ｒｏｓｌｅｒ吸引子和Ｌｏｒｅｎｚ吸引子为例证实了这一算法。

地震过程动力学行为和可预报性问题研究

本文提出了地震事件时序概念,找到了通过对实际地震观测资料的分析来有效地研究地震系统动力学行为和可预报性问题的方法.从实例分析观测资料的结果发现,被分析的这些地震系统混沌吸引子关联维数d_2为3.2—7.5,二阶Renyi熵K_2为0.019—0.052.这表明这些地震过程存在着已知变量数目范围的确定性规律,是可以预报的,但可预报时间有限.由K_2可以估算在一定预报精度要求下,对未来地震的可预报时间长度(本文震例中最长为一个月左右).这套分析方法对认识地震过程动力学行为及可预报性问题都有重要意义.

多变量时间序列复杂系统的相空间重构

根据单变量时间序列相空间重构思想 ,提出了多变量时间序列描述的复杂系统的相空间延迟重构方法 .对每一分量的时间序列 ,分别利用互信息最小法确定最佳延迟时间间隔 ,最小嵌入维数的选取方法是单变量时间序列情况下虚假邻点法的推广 .给出了q阶广义关联积分和q阶广义关联维数的计算公式 ,并证明了广义关联维数与所用范数无关 .计算了Lorenz系统按前 2个变量进行重构时的最佳延迟时间间隔和最小嵌入维数 .计算结果表明 。

东北地区月降雨时间序列的混沌特性研究

运用混沌分析的重构相空间技术 ,以东北地区四大水库控制流域的月降雨时间序列为例 ,估算出饱和相关维数与最大李雅谱诺夫指数 ,探讨了月降水量的可预报性问题。研究表明

洞庭湖区月降雨序列的混沌特性识别及预测研究

基于相空间重构思想,采用最大Laypunov指数法确定洞庭湖区岳阳水文站30 a的月降雨序列具有明显的混沌特性。应用混沌径向基函数神经网络预测月降雨量,预测精度远远低于时间序列分解模型,并表现出高度的无规律性。定量分析了噪声对混沌预测精度的影响,表明监测误差是影响混沌预测精度的一个重要因素,提高数据精度是提高混沌预测精度的一个有效方法。

金沙江流域月径流时间序列的混沌分析

在介绍重构相空间技术的主要定量指标（关联维数D2和柯尔莫奇诺夫熵）的基础上，以长江上游金沙江流域小黄瓜园站和蔡家村站的月径流时间序列为例详细说明了求取时间序列中的混沌特征数的方法；并且采用主分量分析（PCA分布）方法进一步验证了两个站的径流序列具有混沌特性。得到金沙江流域径流序列的预测年限不应超过7～9个月，为金沙江流域径流预测提供了科学的依据。