对输电线路冰凌重现期的浅见

冰凌重现期是确定输电线路设计冰厚的重要参数,2008年1～2月特大冰害事故后,相应的规程得到了修订,冰凌重现期有所提高,但目前实测覆冰数据较少,很难采用极值Ⅰ型进行准确的统计分析。本文根据云南的具体情况,对输电线路冰凌重现期及设计冰厚的选取提出一些粗浅的看法。     

广义Pareto分布参数的Bootstrap置信区间及应用

针对广义Pareto分布应用于超阈值数据拟合时尾部数据较少的情况,将参数的极大似然估计与Bootstrap方法相结合,给出参数的Bootstrap置信区间。Bootstrap置信区间计算方法既可以通过重复抽样充分利用样本信息,又可以避免样本较少时估计量方差偏大的情况。理论证明参数的Bootstrap置信区间是渐近有效的。数值模拟结果表明在一定的置信度下,置信区间的区间长度和覆盖率比较合理。应用建立的Pareto模型对巴颜喀拉地震带震级数据进行分析,结果表明在相同的置信度下,采用Bootstrap方法计算的置信区间比由近似协方差矩阵计算的区间长度更短,这为广义Pareto模型描述地震震级分布的适用性提供了支撑。     

渤海海冰工程设计参数分布

利用渤海历史资料建立由气温、水温、冰期和冰厚表达平整冰层温度、盐度、密度的垂直剖面,进而获得冰的孔隙率垂直剖面。在此基础上通过渤海冰力学参数同孔隙率的试验关系计算出相应冰层峰值压缩强度、峰值弯曲强度、峰值剪切强度和弹性模量。将渤海历史资料归纳的冬季气温分布、水温分布和不同重现期冰厚度分布资料放入渤海1/6经度和1/6纬度的网格内,从而获得渤海不同重现期平整冰层的物理和力学参数分布。作为实例,给出渤海25、50、100年重现期的平整冰层设计厚度分布、压缩强度分布、弯曲强度分布、剪切强度分布和弹性模量分布。     

确定飞机最大抖振设计载荷的长期极值估计方法

确定飞机在抖振工况下的限制载荷是现代飞机动强度设计分析的关键步骤之一。运用次序统计和长期极值估计理论的极值Ⅰ型分布和Ⅲ型分布,在风洞试验数据基础上,分别应用最小二乘法和最大似然估计法进行极值模型的参数估计,并根据预设的重现期指标进行了某型飞机尾部结构抖振设计载荷的极值估计。探讨了极值分布概率模型、估计方法和样本数量对抖振载荷极值估计结果的影响。提出了实现准确有效极值估计的样本数量基本要求的指标,根据该指标可以确定最小振动响应采集时间,以指导测试方案和数据处理方法的制定。实例分析结果表明:极值Ⅲ型分布能够较好地估计抖振试验数据的极值(相对误差在±5%以内),且进行分布模型的参数估计时,最大似然法的精度略高于最小二乘法。对比分析的结果也表明,应用传统的3σ准则进行随机振动结构的限制载荷设计可能偏危险,不适于工程应用。     

响应变量随机缺失下的变系数部分线性模型的经验似然推断

本文考虑了响应变量随机缺失下的变系数部分线性模型的估计问题。利用经验似然方法,给出了参数部分的调整经验似然比函数,证明其渐近服从标准卡方分布。进而构造了参数部分的置信域,得到了其极大经验似然估计的最优参数收敛速度和渐近半参数有效界。模拟结果表明调整经验似然方法优于未调整的经验似然方法。     

双参数Rayleigh分布环境因子的经验Bayes估计及应用

本文针对Rayleigh分布位置参数已知的情形,给出了Rayleigh分布环境因子的极大似然估计和经验Bayes估计,并将环境因子的估计结果应用于Rayleigh部件的可靠性评估,给出了该部件可靠度函数与失效率的估计。最后的随机模拟例子表明,经验Bayes估计优于极大似然估计,并且在考虑环境因子的情形下,Rayleigh部件可靠性指标的估计优于未考虑环境因子时的估计。     

基于极大似然估计的多参考点模态参数识别方法

在考虑随机噪声的情况下,实现了一种基于极大似然估计的多参考点频域模态参数识别方法。该方法采用频响函数的右矩阵分式模型,通过噪声的协方差矩阵对误差向量加权,使用离散时间域中基函数改善数值求解性态。模态参数的估计过程分为两步:首先由基于最小二乘估计的polyLSCF算法获取迭代初值,然后通过Gauss-Newton方法对极大似然函数进行迭代优化,得到精度更高的模态参数识别结果。采用GARTEUR仿真算例对所给出的方法进行了验证,结果表明:在高噪声情况下,利用噪声信息的极大似然估计方法能够显著提高模态参数的识别精度,特别是阻尼的识别精度。     

关于模糊环境中统计参数估计

利用了模糊随机变量理论探讨多元统计分析中模型环境下总体分布未知参数的估计方法，定义新的多维模糊数据，给出参数的一致估计，无偏估计及极大似然估计的定义及相关性质。     

缺失数据下两线性模型中响应变量分位数差异的经验似然置信区间

总体差异的比较是医学,经济和教育领域中经常遇到的课题,本文讨论缺失数据情形下两线性模型中响应变量分位数差异的经验似然置信区间的构造。我们采用分数线性回归填补法对响应变量的缺失值进行补足,得到两线性回归模型的"完全"样本数据,在此基础上构造响应变量分位数差异的对数经验似然比统计量,在一定条件下证明了统计量的极限分布为加权χ12,并利用此结果构造分位数差异的经验似然置信区间。模拟结果表明在分数填补下得到的置信区间具有较高的覆盖精度。     

三参数威布尔分布在风机载荷外推中的应用

本文通过极大似然法、双线性回归法、相关系数法及概率权重矩法的威布尔估计算法对风机载荷相关变量(叶根面内弯矩、叶根面外弯矩及叶尖挠度)进行载荷外推,并通过极大似然值对该几种方法进行比较,提出适合风机载荷变量的估计算法,为使用三参数威布尔分布对风机载荷外推提供了一定的参考。     

Parameter and Quantile Estimation for the Generalized Pareto Distribution

The generalized Pareto distribution is a two-parameter distribution that contains uniform, exponential, and Pareto distributions as special cases. It has applications in a number of fields, including reliability studies and the analysis of environmental extreme events. Maximum likelihood estimation of the generalized Pareto distribution has previously been considered in the literature, but we show, using computer simulation, that, unless the sample size is 500 or more, estimators derived by the method of moments or the method of probability-weighted moments are more reliable. We also use computer simulation to assess the accuracy of confidence intervals for the parameters and quantiles of the generalized Pareto distribution.     

New predictions of extreme keel depths and scour frequencies for the Beaufort Sea using ice thickness statistics

In 1983 Wadhams proposed a technique for calculating scour return periods and pipeline burial depths for scour avoidance for the coastal Beaufort Sea. The technique combined extreme keel depth predictions based on submarine data with the use of observed distributions of scour widths and incision depths, to calculate the extreme incision depth with a given return period for a pipeline of given length laid across the seabed. The Beaufort Sea submarine dataset used to illustrate the application of the technique was obtained in 1976 from a regime consisting largely of multi-year ice. In recent years first-year ice has come to dominate the southern Beaufort Sea, so we replaced the 1976 statistics with data from a winter 2007 survey of the same region by the submarine HMS “Tireless”. Holding other scour geometry parameters constant, we calculated new return periods and burial depths and found large changes which appear to be reflected in the results of recent resurveys of regions subject to ice scour. We reflect on the likelihood that these more moderate conditions will continue to prevail in the future.     

平均时距对良态风气候地区极值风速的影响研究

在风气候分析中,风速观测历史数据一般来源于各气象站的归档测量,但不同气象站采用的平均时距并不统一,这导致基于风速观测历史数据的极值风速预测过程存在平均时距的转换问题。该文对美国11座处于良态风气候地区城市气象站记录的风速连续观测数据,进行处理得到不同时距下平均风速序列,并将改进独立风暴法与极值I型分布模型相结合分析得到各重现期的风速极值,分析了平均时距对极值风速预测结果的影响。研究结果表明:在良态风气候地区,一定重现期的极值风速随平均时距的增大而减小,近似呈指数律衰减;平均时距对极值风速的影响规律基本不受极值风速重现期的影响; 1 min平均时距下的极值风速比10 min平均时距极值风速大19%左右。基于这些结果,拟合给出了良态风气候地区不同平均时距极值风速的转换关系式。     

Reliability analysis of Weibull multicomponent system with stress-dependent parameters from accelerated life data

In this paper, reliability estimation of multicomponent system under a multilevel accelerated life testing. When the lifetime of components follows Weibull distribution, the problem of point and interval estimates are discussed from different perspectives. Under a general life-stress assumption that there are multiple nonconstant and stress-dependent scale and shape parameters, the maximum likelihood estimates of unknown parameters along with associated existence and uniqueness are established. Approximate confidence intervals are constructed correspondingly via expected Fisher information matrix. Furthermore, some pivotal quantities are constructed and alternative generalized point and interval estimates are also proposed for comparison. In addition, predictive intervals for the lifetime of the multicomponent system are discussed under classical and generalized pivotal approaches, respectively. The results show that the proposed generalized estimates are superior to the conventional likelihood approach in terms of the accuracy. A real data example is carried out to illustrate the implementations of the proposed methods.     

Interval Estimation for the Smaller-the-Better Type of Signal-to-Noise Ratio using Bootstrap Method

The signal-to-noise ratio is an indicator, introduced by Taguchi, for evaluating the experimental data in robust design. Estimating the confidence interval of the signal-to-noise ratio is an important topic in data analysis of robust design. Calculating the confidence interval for a parameter usually needs the assumption about the underlying distributions. Bootstrapping is a nonparametric, but computer-intensive estimation method. In this article, we present the results of a simulation study on the behavior of three 95% bootstrap confidence intervals (i.e., SB, PB, and BCPB) for estimating the smaller-the-better signal-to-noise ratio when the data are from either a normal distribution or one of the Burr distributions. A detailed discussion of the simulation results is presented and some recommendations are given.     

An additive Chen-Weibull distribution and its applications in reliability modeling

In this article, we introduce a new lifetime distribution with increasing and bathtub-shaped failure rates. Some statistical properties of the proposed distribution are studied. We use the method of maximum likelihood for estimating the model parameters and reliability characteristics and discuss the interval estimates using asymptotic confidence intervals and bootstrap confidence intervals on one hand, and we provide Bayes estimators and highest posterior density intervals for the parameters via Hamiltonian Monte Carlo simulation method on the other hand. We demonstrate the superiority of the proposed distribution by fitting two reliability data sets well-known from references.     

Inference for two-parameter Rayleigh competing risks data under generalized progressive hybrid censoring

In this paper, a competing risks model based on the generalized progressive hybrid censored two-parameter Rayleigh distributions is studied under the assumption that the lifetime distributions of failure causes are identically distributed with same location and different scale parameters. We obtain maximum likelihood estimates of unknown parameters with associated existence uniqueness. The approximate confidence intervals are constructed using the asymptotic distribution of maximum likelihood estimates via the observed information matrix. Further, Bayes point estimates and the highest probability density credible intervals of unknown parameters are presented, and the Gibbs sampling technique is used to approximate corresponding estimates. A Monte Carlo simulation study is conducted to compare the accuracy of proposed estimates. Finally, a real-life example is presented for illustration purpose.     

Bayesian Analysis in Partially Accelerated Life Tests for Weighted Lomax Distribution

Accelerated life testing has been widely used in product life testing experiments because it can quickly provide information on the lifetime distributions by testing products or materials at higher than basic conditional levels of stress, such as pressure, temperature, vibration, voltage, or load to induce early failures. In this paper, a step stress partially accelerated life test (SS-PALT) is regarded under the progressive type-II censored data with random removals. The removals from the test are considered to have the binomial distribution. The life times of the testing items are assumed to follow length-biased weighted Lomax distribution. The maximum likelihood method is used for estimating the model parameters of length-biased weighted Lomax. The asymptotic confidence interval estimates of the model parameters are evaluated using the Fisher information matrix. The Bayesian estimators cannot be obtained in the explicit form, so the Markov chain Monte Carlo method is employed to address this problem, which ensures both obtaining the Bayesian estimates as well as constructing the credible interval of the involved parameters. The precision of the Bayesian estimates and the maximum likelihood estimates are compared by simulations. In addition, to compare the performance of the considered confidence intervals for different parameter values and sample sizes. The Bootstrap confidence intervals give more accurate results than the approximate confidence intervals since the lengths of the former are less than the lengths of latter, for different sample sizes, observed failures, and censoring schemes, in most cases. Also, the percentile Bootstrap confidence intervals give more accurate results than Bootstrap-t since the lengths of the former are less than the lengths of latter for different sample sizes, observed failures, and censoring schemes, in most cases. Further performance comparison is conducted by the experiments with real data.     

Statistical inference for constant-stress accelerated life tests with dependent competing risks from Marshall-Olkin bivariate exponential distribution

This paper considers a constant-stress accelerated dependent competing risks model under Type-II censoring. The dependent structure between competing risks is modeled by a Marshall-Olkin bivariate exponential distribution, and the accelerated model is described by the power rule model. The point and interval estimation of the model parameters and the reliability function under the normal usage condition at mission time are obtained by using the maximum likelihood estimation method and the bootstrap sampling technique. Moreover, the pivotal quantities based estimation are adopted to estimate the model parameters and the generalized confidence intervals. As a comparison, we also consider the Bayes estimation and the highest posterior density credible intervals for the model parameters based on conjugate priors and importance sampling method, respectively. To illustrate the proposed methodology, a Monte Carlo simulation is used to study the performances of different estimation methods. Finally, a dataset is analyzed for illustrative purpose and a comparison with the original results is also given.