定时截尾数据最佳线性无偏估计方法

提出定时截尾数据最佳线性无偏估计方法.针对工程中常见的位置-尺度分布族,给出定时截尾情况下分布参数的最佳线性无偏点估计公式及其协方差矩阵,得到分布参数的置信区间、百分位值和百分率的点估计及其置信上、下限.详细讨论Weibull分布和对数正态分布定时截尾数据的最佳线性无偏估计问题.与目前工程中常用的极大似然估计(maximum likelihood estimation,MLE)方法相比,文中方法所得估计量不但在大样本而且在小样本情况下也具有最佳无偏性质,且计算简单、精度高,便于工程应用.     

最佳无偏整体估计方法

提出一种最佳无偏整体估计方法,给出整体参数的估计量及其协方差公式,建立正态分布、Weibull分布和极值分布等位置-尺度分布族的点估计与区间估计。传统的回归分析只适用于正态分布和完全数据,最佳无偏整体估计方法则将回归分析推广到工程中常见的位置-尺度分布族和截尾数据的情况。该方法可以将不同条件(状态)下的试验数据作为一个整体进行统计推断,能够全面开发利用不同条件下试验数据之间的横向信息,使其可利用的信息量远远大于只能分别在各自条件下对试验数据进行处理的传统最佳线性无偏估计方法。最佳无偏整体估计方法对一种条件下只有一个失效数据的情况也能进行分析,传统最佳线性无偏估计方法则要求在一种条件下有较多的失效数据,因此前者具有小样本性质;并且前者的参数估计量是所有条件下顺序统计量的线性函数,后者的参数估计量只是一种条件下顺序统计量的线性函数,所以前者的参数估计量具有更好的正态分布特性。大量Monte Carlo模拟和工程应用表明,在试样数相同的情况下,文中方法比传统方法具有更高的精度,而在精度相同的情况下,则可节省大量试样。     

估计疲劳寿命三参数P-S-N曲线的新方法

由于不同应力水平下对数疲劳寿命的方差不等,因而不同应力水平下的对数疲劳数据不满足最小二乘估计的Gauss-Markov假设条件,此时采用常规最小二乘法估计的三参数P-S-N曲线不是统计意义下的最佳线性无偏估计,而加权最小二乘法则可以给出异方差条件下的最佳线性无偏估计.为此基于加权最小二乘和Bootstrap方法提出一种疲劳寿命三参数P-S-N曲线估计方法,在所提方法中,Bootstrap方法被用来确定不同应力水平下疲劳试验寿命数据的协方差矩阵对角线元素,避免迭代确定加权最小二乘法中的权矩阵.对三种材料的四组疲劳试验寿命数据进行分析的结果表明,所提方法具有工程实用性,传统最小二乘法由于忽略了Gauss-Markov假设条件可能得到偏危险的结果,而由于所提方法得到的是最佳线性无偏估计,因而在子样容量增大时将趋于估计的真值,并且参数估计的方差将是最小的.     

机械产品可用度的区间估计公式

本文介绍了机械产品可用度的点估计和区间估计方法。在“能工作时间”和“不能工作时间”均服从指数分布或均服从正态分布,“能工作时间”服从指数分布和“不能工作时间”服从对数正态分布的三种情况下,给出了可用度和不可用度的区间估计公式。     

无偏估计拆分算法在数控加工中心主轴热误差建模中的应用

针对多元线性回归无偏估计算法在处理具有多重共线性的机床热误差数据建模中出现的模型参数估计失真问题,提出了一种用于处理共线性数据的无偏估计拆分算法。该算法将建模过程分成多个步骤完成,每步只对一个自变量进行回归,从而达到弱化自变量共线性的目的。以Leaderway-V450型数控加工中心为实验对象,根据在不同季度内测量的多批次空转实验数据,将无偏估计拆分算法与传统多元线性回归的模型精度和稳健性进行了验证。研究结果显示,无偏估计拆分模型的预测精度和稳健性远优于经典多元线性回归模型,尤其对于跨季度数据预测,该算法优势更大。     

区间统计量及其分布

提出区间统计量和区间秩统计量的概念,建立其概率密度函数和联合分布函数,给出区间统计量的均值、方差、协方差和区间秩统计量的平均秩、中位秩、百分位秩计算公式。区间统计量是对顺序统计量的补充,当失效数据较少难以统计分析时,可以通过区间统计量增加其数据,提高统计分析的精度。在此基础上,提出一种区间数据最佳线性无偏估计方法,并对正态分布、极值分布、Weibull分布等常用的位置一尺度分布进行讨论,该方法能够对产品贮存寿命进行小样本预测和可靠性评定。     

对数正态分布下基于LSM航空陀螺电机寿命预测

为了准确预测航空陀螺电机寿命,利用对数正态分布函数来描述其寿命分布,采用最小二乘法(LSM)估计了对数均值、对数标准差及加速参数,对陀螺电机寿命是否服从对数正态分布进行了K-S检验,并利用自行开发的寿命预测软件计算出平均寿命和中位寿命。结果表明,航空陀螺电机寿命满足对数正态分布,其寿命特征和温度应力的关系符合阿伦尼斯方程,预测出的陀螺电机寿命精度较高,利用精确计算的加速参数可实现在短时间(10 h)内估算其寿命,为航空陀螺电机设计提供技术参考。     

多点失效时结构寿命可靠度的计算方法

复杂结构的疲劳断裂破坏往往是多点的,并且各点之间具有一定的相关性,因此,已有的单点寿命可靠度的计算方法不适用于多点疲劳断裂寿命可靠性评估问题.文中针对多点失效疲劳寿命和裂纹扩展寿命为正态或对数正态分布的情况,并且计及不同失效点疲劳寿命间和裂纹扩展寿命间相关的特征,推导出一种新的可进行数值计算的积分表达式.在进行具体的数值积分时,用重要抽样(importance sampling)的概念提高积分效率.该方法能解决结构多点失效寿命可靠度的计算问题.理论与算例表明方法是有效的.该方法的原理也可推广于其他非正态与非对数正态分布的情况.     

威布尔分布特征寿命最好线性无偏估计方法的改进

采用蒙特卡洛方法对国家标准ＧＢ２６８９．４－８１寿命试验和加速寿命试验中威布尔分布参数的最好线性无偏估计法（ＢＬＵＥ）作了进一步验算。结果表明，两参数威布尔分布特征寿命的点估计结果是有偏的，且在某些场合下会产生很大的偏差。进而分析了其产生偏差的原因，提出了一种修偏方法，并编制出包括修偏在内的两参数威布尔分布参数的最好线性无偏估计程序。     

基于FA-LN-BiGRU的机械设备剩余寿命区间预测方法

针对数据驱动融合模型存在前后模型不匹配、关键信息丢失等问题,提出了一种端对端的预测方法,即基于特征注意力机制的对数正态分布和双向门控循环单元融合（feature attention-lognorm-bidirectional gated recurrent unit, 简称FA-LN-BiGRU）的剩余寿命区间预测方法。首先,利用特征注意力机制从多维度、非线性和大规模的传感器信号中提取出关键特征向量;其次,采用BiGRU网络从前向和后向2个方向对注意力加权特征的时变特性进行建模学习,并通过最大似然估计损失函数来训练网络参数,获得网络隐含状态输出向量的概率分布;最后,计算出基于对数正态分布的概率密度函数,实现设备剩余寿命（remaining useful life,简称RUL）不确定性的衡量。分析结果表明,对于运行条件复杂和故障模式多变的多维监测数据,所提方法能够深入挖掘性能退化信息,有效提高机械设备剩余寿命点预测和区间预测的准确度和可靠性。     

Unbiased linear property estimation for spheres,from sections exhibiting overprojection and truncation

In the biological sciences, stereological techniques are frequently used to infer changes in structural parameters (volume fraction, for example) between samples from different populations or subject to differing treatment regimes. Non-homogeneity of these parameters is virtually guaranteed, both between experimental animals and within the organ under consideration. A two-stage strategy is then desirable, the first stage involving unbiased estimation of the required parameter, separately for each experimental unit, the latter being defined as a subset of the organ for which homogeneity can reasonably be assumed. In the second stage, these point estimates are used as data inputs to a hierarchical analysis of variance, to distinguish treatment effects from variability between animals, for example. Techniques are therefore required for unbiased estimation of parameters from potentially small numbers of sample profiles. This paper derives unbiased estimates of linear properties in one special case—the sampling of spherical particles by transmission microscopy, when the section thickness is not negligible and the resulting circular profiles are subject to lower truncation. The derivation uses the general integral equation formulation of Nicholson (1970); the resulting formulae are simplified, algebraically, and their efficient computation discussed. Bias arising from variability in slice thickness is shown to be negligible in typical cases. The strategy is illustrated for data examining the effects, on the secondary lysosomes in the digestive cells, of exposure of the common mussel to hydrocarbons. Prolonged exposure, at 30 μg 1^?1 total oil-derived hydrocarbons, is seen to increase the average volume of a lysosome, and the volume fraction that lysosomes occupy, but to reduce their number.     

模型估计对序数响应轮廓控制图的影响

复杂制造或服务过程的质量特性可用函数关系即轮廓描述.针对序数响应轮廓的监控,基于非参数回归模型提出了广义似然比控制图.在受控模型未知且需要估计的现实情况下,采用局部线性核估计、样条和Newton Raphson 3种模型估计方法,并考虑不同的样本量、估计方法的不同参数设置,研究模型估计对控制图性能的影响.仿真以及案例分...     

Input and state estimation for linear systems with a rank-deficient direct feedthrough matrix

The problem of joint input and state estimation for linear stochastic systems with a rank-deficient direct feedthrough matrix is discussed in this paper. Results from previous studies only solve the state estimation problem; globally optimal estimation of the unknown input is not provided. Based on linear minimum-variance unbiased estimation, a five-step recursive filter with global optimality is proposed to estimate both the unknown input and the state. The relationship between the proposed filter and the existing results is addressed. We show that the unbiased input estimation does not require any new information or additional constraints. Both the state and the unknown input can be estimated under the same unbiasedness condition. Global optimalities of both the state estimator and the unknown input estimator are proven in the minimum-variance unbiased sense.     

A thinning algorithm for GPS-based unbiased FIR estimation of a clock TIE model

A thinning algorithm is proposed for real-time unbiased finite impulse response (FIR) estimation of the local clock time interval error (TIE) model (time error, fractional frequency offset, linear frequency drift rate, etc.) employing GPS-based sawtooth measurements. We show that the approach allows obtaining practically optimal estimates of the clock states, by large horizons (number of the points in the average). The algorithm is applied to the TIE measurements allowing for different time steps and averaging horizons for each of the clock states and compared to the three state Kalman filter. It is demonstrated that, in the presence of the sawtooth noise induced by the GPS receiver, the unbiased FIR estimates with thinning out fit the clock states better than the Kalman filter, in terms of the Allan deviation and precision time protocol deviation.     

The use of quadrats and test systems in stereology,including magnification corrections

At present a model-free, design-based theory of unbiased estimation, and a model-based one of linear unbiased estimation of minimum variance, are available for stereology. The main developments rest upon the nested scheme {section (quadrat)}, whence the raw data are expressible in terms of area, length and number. The main aim of this paper is to complete the available model-based theory by introducing the step in which sections are analysed by point-counting via coherent test systems (CTSs). Using this development, the stereologist should be able to handle raw point and intersection counts optimally, in order to find the best estimator of a ratio R in a given specimen in a wide range of circumstances. The latter include, for instance, the use of different CTSs on different sections and of double CTSs on each section, as well as the case—(not uncommon in electron microscopy)—in which different sections from the same sample are observed at slightly different magnifications but analysed by quadrats (via automatic or semi-automatic image analysers, for instance), or CTSs of fixed sizes. The main conclusion pertaining to the latter case is that the estimators obtained via section-wise magnification corrections are in general superior to those corrected via a global, average magnification. In order to illustrate the methodology, a synthetic numerical example, and a real one, are given.     

Estimation of subcellular organelle volume from ultrathin sections through centrioles with a discretized version of the vertical rotator

A method for the fast and efficient estimation of the volume (but not surface area) of subcellular organelles is presented. It consists of a rotator/coaxial-section approach based on the Pappus theorem and represents a discretized version of the vertical rotator where, instead of measuring intercept lengths, the points in distance classes are counted. Centrioles serve as a unique reference 'double-point' with constant size allowing unbiased cell selection from the whole population with equal probability and without the disector application. The sandwich-like method of sample preparation allows comparison of control and experimental cases with the same errors caused by overlapping and overprojection. Test experiments demonstrated that the vertical discretized rotator was an efficient and precise tool for the estimation of volume and that a few independent sections of unknown thickness were sufficient for the quantification of one experimental point.     

滚动直线导轨副寿命试验方法

针对滚动直线导轨副的寿命问题,对其寿命试验方法进行了研究。介绍了滚动直线导轨副寿命试验装置的组成结构和功能,根据试验装置提出了滚动直线导轨副的恒定应力加速寿命试验方法。在此基础上采用最优线性无偏估计法对试验数据进行了处理。对形状参数和特征寿命的估计值进行了计算和分析。对具体型号的滚动直线导轨副,给出其加速寿命试验方法示例。