水文序列相依变异识别的RIC定阶准则——以自回归模型为例

水文过程相依性是水文变异的主要表现形式之一,应用自回归模型对其进行拟合时合理确定模型阶数是一个难点问题。本文在分析AIC和BIC准则的基础上,提出了一种以原序列与其相依成分的相关系数作为拟合度指标,同时借用信息熵形式的函数式,作为模型不确定性度量指标的自回归模型定阶准则(简称RIC准则)。以AR(1)、AR(2)、AR(3)和AR(4)模型为例进行统计试验,将不同序列长度下该准则的定阶准确率与其他定阶准则进行比较,试验结果表明,RIC准则对于上述模型均具有较好的适应性,且定阶准确率远高于AIC准则,其中对于前三阶模型RIC准则优于BIC准则,但四阶模型略低于BIC准则。RIC准则的优势是可以同时满足模型定阶、相依程度分级与模型检验的需求,将其应用于实测水文序列分析,结果显示,该准则能较准确地识别自回归模型的阶数,且符合提出的"相依有变异而残差无变异的最小阶数"的检验标准。     

高阶统计量地震子波估计建模

本文在反射系数序列为非高斯、平稳和统计独立的随机过程,地震子波为非因果、混合相位的假设条件下,分别应用滑动平均(MA)和自回归滑动平均(ARMA)模型对地震记录进行建模,并采用运算代价较小的基于高阶累积量的线性化求解方法——累积量矩阵方程法进行了子波提取和模型适应性的研究。数值模拟结果和实际地震数据处理结果表明:自回归滑动平均(ARMA)模型比滑动平均(MA)模型具有参数节省、模型更为高效的特点;累积量矩阵方程法可以有效地压制加性高斯噪声,但对累积量样本估计的准确性要求较高;如果累积量样本估计的误差和方差适度,结合自回归滑动平均(ARMA)模型描述的累积量矩阵方程法可以高效、准确地估计出地震子波。     

基于非线性规划的指数自回归模型的辨识

讨论了指数自回归模型的辨识问题，证明了该模型最小二乘估计的目标函数的非凸性，并给出了使该函数为凸的条件，最后给出了辨识该模型的算法及该算法的收敛性，并以数值例子加以说明。     

混合门限自回归模型在长期水文预报中的应用

在长期水文预报中主要应用两类方法,它们是多元分析法和时间序列分析法,这两种方法各有其局限性;应用混合门限自回归模型模拟水文时间序列可以考虑诸多因素,能避免以上两方法的局限性,并在实践中得到检验.     

Spectral estimation of video signals

Spectrum analyzers are ubiquitous in laboratory work concerning one dimensional signals. This is because linear operators are best examined in the frequency domain. Linear operators, such as linear filters, DCT coders, line shufflers, etc., dominate also the video systems scenario. Their frequency domain study is as appropriate and informative as it is in the case of their one-dimensional counterparts. This paper considers the problems associated with the introduction of two well-known spectral estimation techniques, the periodogram and AR estimates, to the context of television signals. The potential for application of spectral estimation to video problems is exemplified by a number of applications related to the fields of enhanced quality television and HDTV. Special attention is paid to the computational aspects, whose effective solution conditions the practical applicability of the proposed spectral estimation techniques.R. Rinaldo is currently at the Department of Electrical and Computer Engineering of the University of California, Berkeley.     

A time series approach to fatigue crack propagation

The inherently nonlinear phenomenon of fatigue crack propagation is modeled as a linear random process. To a first approximation, simple, nonstationary time series models are introduced and standard techniques for determining the parameters of autoregressive integrated moving-average processes are applied. Multiplicative time series models are next utilised for the representation of a group of crack history curves. Implementation of the models on the Virkler experimental data set yields satisfactory results. Reliable Gaussian approximations to the distribution of the time required by a crack to reach a specified critical length are obtained, and the usefulness of the approach is demonstrated when updating lifetime predictions after periodic inspections.     

Dynamic analysis of the NPP pressure sensor system

The aim of the work was to develop on-line methods of control and diagnostics of pressure sensors at a NPP. The analysis was carried out along two lines:

1. i) The detection system including the sensor itself was modeled theoretically to obtain and study its transfer function, and to establish correspondence between the spectral characteristics of the pressure signal.

2. ii) The numerical processing of the signal using the AR technique to reconstruct the transfer function and evaluate the system's response, to a step impulse, as well as the spectral analysis. The hydraulic model presented indicate that the spectral lines observed at 10 Hz are due to longitu-dinal oscillations of water in the system branches, while the response time of the detection system is effectively the time of signal retardation in the porous ceramic diaphragms of the δ-cell of the sensor itself.

     

基于多尺度自回归模型体系的混凝土坝位移预报及工程应用

针对混凝土坝位移监测数据的时频非线性特征严重影响到数值模型预报精度的难题,通过小波技术解析原型数据中多重交叉环境驱动的效应实况,有机结合非线性自回归模型(Nonlinear Autoregressive Model with Exogenous Input, NARX)和差分整合移动平均自回归模型(Autoregressive Integrated Moving Average Model, ARIMA),建立了多尺度组合机制下的自回归模型体系,解决了内蕴复杂混沌特性的监测序列的信息挖掘难点。工程实例分析表明,所建模型的拟合精度及预测能力均得以提升,相比于传统模型具有较好的抗噪性和鲁棒性。此外,所建立的计算模型经一定的优化和拓展,亦可推广应用于其它水工建筑物的效应预报分析。     

TESTING CHANGE-POINTS IN THE EXPLOSIVE GAUSSIAN AUTOREGRESSIVE PROCESSES

Abstract. A functional limit theorem with a particular function class and topology is derived for non-ergodic type time series. This limit theorem allows us to study the asymptotic law of the associated likelihood ratio test (LRT) statistic for testing the presence of a change in the covariance parameter in the explosive Gaussian autoregressive model. We show that the level of the LRT cannot be approximated without introducing appropriate normalization. The limit law of a particular weighted likelihood ratio test is examined through a simulation study and is compared with the well-known Kolmogorov distribution obtained in the stationary case; we conclude that for practical applications when the root is really close to unity one can use the same thresholds as in the stationary case. This procedure is applied to the study of three real time series known to be non-stationary.     

Estimation in Random Coefficient Autoregressive Models

Abstract. We propose the quasi‐maximum likelihood method to estimate the parameters of an RCA(1) process, i.e. a random coefficient autoregressive time series of order 1. The strong consistency and the asymptotic normality of the estimators are derived under optimal conditions.