Application of profile likelihood function to the uncertainty analysis of hydrometeorological extreme inference

Profile likelihood function is introduced to analyze the uncertainty of hydrometeorological extreme inference and the theory of estimating confidence intervals of the key parameters and quantiles of extreme value distribution by profile likelihood function is described. GEV (generalized extreme value) distribution and GP (generalized Pareto) distribution are used respectively to fit the annual maximum daily flood discharge sample of the Yichang station in the Yangtze River and the daily rainfall sample in 10 big cities including Guangzhou. The parameters of the models are estimated by maximum likelihood method and the fitting results are tested by probability plot, quantile plot, return level plot and density plot. The return levels and confidence intervals of flood and rainstorm in different return periods are calculated by profile likelihood function. The results show that the asymmetry of the profile likelihood function curve increases with the return period, which can reflect the effect of the length of sample series and return periods on confidence interval. As an effective tool for estimating confidence interval of the key parameters and quantiles of extreme value distribution, profile likelihood function can lead to a more accurate result and help to analyze the uncertainty of extreme values of hydrometeorology.     

极值-I型风速预测的Bayes方法

为提高极值-I型风速预测精度,在Jeffreys准则的基础上,采用Bayes估计中的Lindley近似方法推导极值-I型风速预测表达式.采用Monte Carlo法产生服从极值-I型分布的伪风速母样,基于伪风速母样分别采用基于Bayes理论和最大似然估计理论的极值-I型风速预测方法进行风速预测,并与伪风速母样的理论值进行对比分析.结果表明:与最大似然估计法相比,采用基于Bayes理论建立的极值-I型风速预测模型进行风速预测的精度更高,且精度随着伪风速母样样本量的增加而提高,位置参数先验样本数量的增加以及先验方差的增大对计算精度没有影响.     

基于贝叶斯方法的实时洪水校正模型

简述了实时洪水校正方法的研究进展,提出并建立了基于贝叶斯方法的实时洪水校正模型. 该模型用先验分布考虑水文资料的不确定性,用似然函数描述模型结构和参数的不确定性,将两者综合得到预报流量的后验分布. 选用江西省白云山水库的雨洪资料对模型进行探讨与检验,采用可变遗忘因子最小二乘递推算法估计先验分布和似然函数的参数,以后验分布密度函数的均值作为结果发布. 结果表明该法不仅可显著的提高洪水预报精度,还给出预报区间估计值,实现了预报与决策的有机耦合.     

一种桥梁实测小样本数据的区间优化方法——灰自助抽样与灰色系统理论相结合

针对农村公路桥梁的非概率可靠性评估中现场实测获得的数据属于小样本、贫信息且概率分布未知而难以精确估计参数变化区间这一问题,提出将灰自助抽样与基于灰色系统理论的区间估计方法相结合对桥梁实测的小样本数据进行区间估计。该方法通过自助法产生多组相似样本后利用灰色预测模型减小其误差,再通过基于灰色系统理论的区间估计方法计算各样本的灰色置信区间,并通过取交集的方式排除随机误差对结果的影响来获得更为精确的置信区间。最后将实测桥梁混凝土强度数据作为小样本数据,计算3种区间估计方法的区间估计结果,结果证明了本文所提方法的合理性及有效性。     

基于改进贝叶斯的重型数控机床可靠性研究

重型数控机床在机械加工领域占据重要地位,因此提高其可靠性以及加工精度,对我国工业发展有重要意义。重型数控机床具有结构复杂、故障溯源困难、样本少、数据不足等缺点,因此对其进行可靠性研究比较困难。针对这一问题,采用双参数的威布尔分布建立机床的可靠性模型,引入贝叶斯理论对其进行参数估计,并通过马尔科夫链蒙特卡洛方法(MCMC)计算参数估计结果。对贝叶斯参数估计法中的待估参数进一步分析,得到多层次的贝叶斯模型,并通过参数仿真实验分析其准确性。采用标准均方根误差值及置信区间宽度进行模型优劣的对比,结果表明,改进后的贝叶斯方法参数估计结果精度更优,更有利于建立机床可靠性模型。     

基于不确定性分析的视觉里程计优化

通过推导视觉里程计中运动参数估计的不确定度,分析了视觉里程计的定位精度.采用矩阵扰动理论,准确计算了基于最小二乘法运动估计算法给出的6个自由度运动参数估计的不确定性,此方法的计算复杂度为O(1).采用扩展卡尔曼滤波器对视觉里程计和惯性测量单元数据进行融合优化,获得了更加准确的机器人定位和姿态信息.融合实验结果表明,融合后的闭合误差比单一的视觉里程计闭合误差减少近49.5%.     

Remaining useful life estimation based on Wiener degradation processes with random failure threshold

Remaining useful life(RUL) estimation based on condition monitoring data is central to condition based maintenance(CBM). In the current methods about the Wiener process based RUL estimation, the randomness of the failure threshold has not been studied thoroughly. In this work, by using the truncated normal distribution to model random failure threshold(RFT), an analytical and closed-form RUL distribution based on the current observed data was derived considering the posterior distribution of the drift parameter. Then, the Bayesian method was used to update the prior estimation of failure threshold. To solve the uncertainty of the censored in situ data of failure threshold, the expectation maximization(EM) algorithm is used to calculate the posteriori estimation of failure threshold. Numerical examples show that considering the randomness of the failure threshold and updating the prior information of RFT could improve the accuracy of real time RUL estimation.     

Satellite precipitation product: Applicability and accuracy evaluation in diverse region

Satellite precipitation products, e.g., Tropical Rainfall Measuring Mission version-07(hereafter TRMM) and its successor Integrated Multi-Satellite Retrievals for Global Precipitation Measurement(hereafter IMERG) are being used at a global scale for rainfall estimation. Recently, SM2RAIN-ASCAT(hereafter SM2RAIN) is a novel addition to satellite-based precipitation products which gives the rainfall estimates from the knowledge of soil moisture state and is based on ‘bottom to top' approach. A comparative assessment of any newly developed product or a new version of the product is quite vital for algorithm developers and users. Hence, this research work was carried out to evaluate the accuracy and applicability of SM2RAIN, in comparison to in-situ data, TRMM, and IMERG in diverse regions of Pakistan. The comparative analysis was performed on a temporal scale(daily and monthly) and seasonal scale(spring, autumn, summer, and winter) using five performance metrics namely, root mean square error(RMSE), correlation coefficient(CC), false alarm ratio(FAR), the probability of detection(POD), and critical success index(CSI). The results showed that:(1) SM2RAIN is a better rainfall estimation product in the dry region(having avg.CC0.35), however, less effective in hilly and mountainous terrain having high rainfall intensity;(2) SM2RAIN provides more satisfactory estimates in winter and autumn seasons, while relative poor in the summer season;(3) SM2RAIN performs better in terms of rainfall detection with an average POD of 0.61;(4) the overall performance of SM2RAIN is very convincing and it was concluded that SM2RAIN can be a feasible satellite product for most of the areas of Pakistan. It is noteworthy here to mention that this could be the preliminary assessment of SM2RAIN in diverse climatic zones of Pakistan.     

增强操作工况识别可靠性的概率PLS-ELM方法

针对分类阈值任意给定和临近边界区域操作工况识别可靠性低问题,提出基于贝叶斯理论的概率偏最小二乘极限学习机（p-PLS-ELM)分类算法.偏最小二乘被嵌入到极限学习机框架内,通过提取隐含层正交潜在变量,避免共线性引起输出权值系数不稳定,降低输出预报值的不确定性,改善分类编码输出预报模型的鲁棒性和稳定性.应用非线性最小二乘方法估计每类条件概率密度函数的参数,结合概率密度函数和贝叶斯定理,计算每类输出预报值后验概率作为分类可靠性测度.采用该方法在某污水处理厂进行实验验证.实验结果表明,基于概率PLS-ELM方法的污水处理操作工况识别可靠性和准确性相对优于PLS-ELM方法.     

制造误差的灰自助动态预报

综合考虑灰色系统理论和Bootstrap统计理论的信息预报特点,建立制造误差的灰自助动态预报模型GBM(1,1),以解决信息预报中存在的一些问题。GBM(1,1) 在灰微分建模时进行Bootstrap再抽样,更多地挖掘系统信息,从而更准确地预报系统真值及其分布区间的瞬态变化状况。在计算机仿真中,研究了各种随机误差系统例如正态分布、瑞利分布、均匀分布、三角分布以及混合分布等系统的预报问题,也涉及到一些系统误差例如上升趋势、下降趋势和周期趋势等误差的预报问题。在实际试验中,研究了滚动轴承套圈磨削圆度误差的预报问题。计算机仿真和试验研究表明,GBM(1,1)允许小的数据样本以及各种类型的随机误差与系统误差存在,预报的准确率可以达到95%以上。     

可靠性模型自助参数估计法

为了提高可靠性模型参数估计精度,在分析传统可靠性模型的基础上,指出传统的最小二乘法估计和逐次线性概似估计因受随机变量假设分布的限制存在一定的局限性.用自助法给出了可靠性模型的参数估计,包括点估计和区间估计.计算结果表明:自助法所得参数的估计区间、标准差及模型标准残差均小于传统回归法所得结果.在可靠性模型参数估计中,自助参数估计法通过增加模拟次数可快速逼近参数真值,方法快速、有效,可提高模型精度.     

基于贝叶斯理论的不确定度评定

传统的测量不确定评定是A类、B类评定,与这两类评定方法不同,提出了一种基于贝叶斯理论的测量不确定度评定方法.此方法综合了历史信息和当前样本信息,通过建立贝叶斯模型得出后验分布,从而进行测量不确定度评定.通过实例说明,贝叶斯评定比A类评定更为合理.     

边坡稳定不确定性分析的贝叶斯方法

在边坡稳定分析中,存在着各种不确定性因素,传统的稳定性分析模型很难得到合理的预测结果.尝试应用贝叶斯理论对边坡工程模型的不确定性进行分析,并借用蒙特卡洛方法对随机样本进行模拟抽样,从而描述其不确定性.贝叶斯方法充分利用了各种信息,使得到的结果更加合理,贝叶斯方法是描述模型不确定性的一个有力工具.边坡算例分析结果表明贝叶斯方法能够很好地描述边坡稳定不确定性.     

贝叶斯网络在模型诊断中的应用

把贝叶斯网络引入到模型诊断框架中,依据观测量,研究了一种建立系统贝叶斯网络观测模型的方法。利用网络观测模型,可计算系统诊断解的后验概率,从而找出系统最可能的故障组件。最后,以卫星两轴姿态控制系统为例,应用本文方法进行了分析。     

工程结构作用极值分析方法研究

由于对工程结构所承受的各类作用进行极值分析,是确定作用的设计值以及服役结构的作用评估值的重要依据,针对目前的作用极值分析方法,主要在3个方面展开了探讨,即作用的截口分布的估计、最大值分布的估计以及估计结果的不确定性的评估等,发现了这些环节所存在的一些问题和缺陷：作用截口分布的估计缺乏客观性,而且估计的准确性不足;采用随机过程模型计算作用的最大值分布是不合适的;在极值的分析中缺乏对于不确定性的必要的估计,同时也存在一些细节上的欠妥之处。最后针对主要的问题提出了建议：采用阈值模型估计作用的底分布,采用点过程模型直接估计最大值的广义极值分布,并且考虑估计的不确定性选择适当的估计。     

逐步增加定数截尾下Weibull 分布恒加试验的Bayes估计

基于逐步增加定数截尾样本,对累积失效模型(简称CE模型)下,Weibull分布恒定应力加速寿命试验(简称恒加试验)进行了Bayes统计分析,利用Gibbs抽样给出了该模型的Bayes估计。最后,通过模拟例子表明Bayes估计有效而实用。     

Method of time delay measurement based on fast maximum likelihood for pulsar pulse profile

The time delay of the pulsar integrated pulse profile relative to the standard pulse profile is one of the important observations in an X-ray pulsar-based navigation system, with the measuring accuracy directly affecting the the pulsar-based navigation system. In order to improve the measuring accuracy of the time delay of the pulsar integrated pulse profile and reduce the computation complexity, a method called fast maximum likelihood (FML) estimation is proposed in this paper, which first distills the pulse profile of the X-ray pulsar by the epoch folding. Then, the likelihood function is estimated to obtain the time delay of the pulsar integrated pulse profile. This paper also improves the fast maximum likelihood time delay estimation by narrowing the phase interval of the standard pulse profile and combines rough estimation with accurate estimation to effectively compute the time delay. Real pulsar data observed by the Rossi X-ray Timing Explorer (RXTE) are used to validate the effectiveness of the proposed method from the aspects of the observed time and computational complexity. Compared with the Taylor FFT algorithm, the measurement accuracy of the proposed method can be significantly improved while keeping the total computational complexity.     

瑞利分布恒定应力加速寿命试验的贝叶斯估计

基于定数截尾样本, 对 CE 模型下瑞利分布恒定应力加速寿命试验进行了贝叶斯统计分析, 利用蒙特卡洛计 算积分法给出了该模型的贝叶斯估计的近似算法, 最后通过模拟比较表明贝叶斯估计更加精准有效。     

基于Bootstrap滤波的非线性系统的识别

Bootstrap滤波是一种基于贝叶斯状态估计和蒙特卡罗方法的新的海波方法，相对于经典的卡尔曼滤波而言，它不受状态方程须为线性以及状态与噪声须是高斯分布的限制，具有很强的适应性。对贝叶斯估计及Bootstrap滤波方法在非线性系统识别中的应用进行了分析与数值模拟，计算结果表明了该方法的有效性和实用性。