近50年大黑河流域气候水文要素变化趋势及突变分析

基于大黑河流域6个气象站1966～2013年气温、降水量、蒸发皿蒸发量、相对湿度和日照时数长期数据系列,采用气候倾向率和滑动t检验法分析了近50年大黑河流域气象要素的变化趋势及变异年份。结果表明,大黑河流域整体呈现暖干气候倾向,气温呈显著增高趋势,变化率为0.43～0.57℃/10a,气温增温变点大致出现了两次,分别在1986、1997年;降水量和蒸发量多呈不显著减少趋势,降水量先减(1981年)后增(1990年),蒸发皿蒸发量先减(1986年)后增(1996年);相对湿度、日照时数多呈显著减小趋势。     

Performance study of change-point detection thresholds for cumulative sum statistic in a sequential context

Sequential detection is based on a recursive statistic and a threshold it must reach to report a change. In this paper, we consider the score-based cumulative sum statistic and propose to evaluate the detection performance of some thresholds on simulated data. Three thresholds come from the literature: the Wald constant, the empirical constant, and the conditional empirical instantaneous threshold (the latter two are built by a simulation-based procedure). Two new thresholds are built by a simulation-based procedure: the first one is instantaneous, the second is a dynamical version of the previous one. The thresholds' performance measured by an estimation of the mean time between false alarm (MTBFA) and the average detection delay (ADD) are evaluated on independent and autocorrelated data for several scenario, according to the detection objective and the real change in the data. The simulations allow us to compare the difference between the thresholds' results and to see that their performances prove to be robust when a parameter of the prechange regime is misestimated or when the data independence assumption is violated. We found also that the conditional empirical threshold is the best at minimizing the detection delay while maintaining the given false alarm rate. However, on real data, we suggest to use the dynamic instantaneous threshold because it is the easiest to build for practical implementation.     

Bayesian Quickest Detection in Sensor Arrays

Abstract

We study Bayesian quickest detection problems with sensor arrays. An underlying signal is assumed to gradually propagate through a network of several sensors, triggering a cascade of interdependent change-points. The aim of the decision maker is to centrally fuse all available information to find an optimal detection rule that minimizes Bayes risk. We develop a tractable continuous-time formulation of this problem focusing on the case of sensors collecting point process observations and monitoring the resulting changes in intensity and type of observed events. Our approach uses methods of nonlinear filtering and optimal stopping and lends itself to an efficient numerical scheme that combines particle filtering with a Monte Carlo–based approach to dynamic programming. The developed models and algorithms are illustrated with plenty of numerical examples.     

漳河水库入库径流序列R/S分析

依据漳河水库1963～2008年入库径流资料,利用法对其未来变化趋势进行了分析。结果表明:①H0.5,即入库径流过去的一个增长或减少趋势意味着将来的一个减少或增长趋势,未来年径流量可能呈现持续下降的趋势;②1995年为流域径流系列的突变点,对前后两个序列的特征值进行统计分析,均具有明显的差异,已经不符合"一致性"的要求;③流域人类活动日趋频繁,使得流域下垫面条件发生了较大的变化,对于漳河水库入库径流量变化有较大的影响。     

ON THE PARTIAL SUMS OF RESIDUALS IN AUTOREGRESSIVE AND MOVING AVERAGE MODELS

Abstract. The limiting process of partial sums of residuals in stationary and invertible autoregressive moving-average models is studied. It is shown that the partial sums converge to a standard Brownian motion under the assumptions that estimators of unknown parameters are root- n consistent and that innovations are independent and identically distributed random variables with zero mean and finite variance or, more generally, are martingale differences with moment restrictions specified in Theorem 1. Applications for goodness-of-fit and change-point problems are considered. The use of residuals for constructing nonparametric density estimation is discussed.     

基于变点方法的软件可靠性分析

简述软件危机及其引发的软件可靠性问题,讨论软件可靠性的变点分析理论,结合Schneidewind模型提出软件可靠性变点分析的极大似然方法,并将其应用于一个实际的软件失效数据集,采用积分变换的U-图准则进行检验,结果证明了该软件可靠性变点分析方法的有效性和统计意义.     

水文变异综合诊断方法及其应用研究

提出了一种水文时间变异综合诊断方法。首先采用Hurst系数等方法对序列进行初步检验，判断序列是否存在变异；然后用多种检验方法对序列进行详细诊断，得到多种检验结果；最后对检验结果评分，计算综合权重，找出权重最大的点，并结合实际水文调查分析对该点进行确认，从而得到最可能变异点。该方法已应用于潮白河45a径流量变异分析中，解决了单一检验方法检验结果不合理、多种检验方法检验结果不一致的问题。     

水文序列变异点检验方法的性能比较分析

通过设计的水文变异序列生成器生成满足P-型分布及统计参数,用统计实验的方法比较分析了10种常用水文序列变异点检验方法对3类变异序列的性能检验。结果表明,秩和检验、Brown-Forsythe、有序聚类、滑动T检验、Bayesian、里海哈林检验方法对均值变异类序列检验效果明显,滑动F检验法对变差系数CV变异序列检验效率优于其他方法,各方法对偏态系数CS变异序列检验效率较低。     

基于变点探测的功率振荡数据挖掘

针对当前功率小幅振荡数据挖掘的不足,引入了变点探测方法判断系统是否发生振荡、主要参与机组以及振荡何时进入平稳阶段,从而提出了一种新的大电网功率振荡特征挖掘方法。该方法通过在海量广域测量系统(WAMS)数据中挖掘电网振荡信息,根据变点探测方法获取的极值特性区分弱阻尼的低频振荡以及强阻尼快速衰减过程,并在弱阻尼振荡情况下确定Prony分析时间窗的起点,从而获取更为准确的振荡模式和强相关机组信息。通过新英格兰10机39节点系统仿真和河南电网WAMS实测振荡数据挖掘验证了所提方法的有效性,结果表明该方法能够从海量数据中有效挖掘大电网振荡特征,并准确识别系统模式信息。     

An Accurate Method for Determining the Pre-Change Run Length Distribution of the Generalized Shiryaev-Roberts Detection Procedure

Abstract

Change-of-measure is a powerful technique in wide use across statistics, probability, and analysis. Particularly known as Wald's likelihood ratio identity, the technique enabled the proof of a number of exact and asymptotic optimality results pertaining to the problem of quickest change-point detection. Within the latter problem's context we apply the technique to develop a numerical method to compute the generalized Shiryaev–Roberts (GSR) detection procedure's pre-change run length distribution. Specifically, the method is based on the integral equations approach and uses the collocation framework with the basis functions chosen to exploit a certain change-of-measure identity and a specific martingale property of the GSR procedure's detection statistic. As a result, the method's accuracy and robustness improve substantially, even though the method's theoretical rate of convergence is shown to be merely quadratic. A tight upper bound on the method's error is supplied as well. The method is not restricted to a particular data distribution or to a specific value of the GSR detection statistic's head start. To conclude, we offer a case study to demonstrate the proposed method at work, drawing particular attention to the method's accuracy and its robustness with respect to three factors: (1) partition size (rough vs. fine), (2) change magnitude (faint vs. contrast), and (3) average run length (ARL) to false alarm level (low vs. high). Specifically, assuming independent standard Gaussian observations undergoing a surge in the mean, we employ the method to study the GSR procedure's run length's pre-change distribution, its average (i.e., the usual ARL to false alarm), and its standard deviation. As expected from the theoretical analysis, the method's high accuracy and robustness with respect to the foregoing three factors are confirmed experimentally. We also comment on extending the method to handle other performance measures and other procedures.