组合取样的误差理论研究及其Monte Carlo模拟

基于多项分布理论,建立了组合取样方差与取样总体中各子区的大小及其组分含量之间的关系和计算公式,探讨了组合取样常数的物理意义.以颗粒物质为例,探讨了组合取样的逻辑质量单元的概念及其意义,为确定组合取样中的份样质量提供了理论依据.本文对于完善组合取样误差理论,保证组合取样的质量均具有重要意义.     

应用Monte Carlo模拟法探讨分层性物质的组合取样精度

应用MonteCarlo模拟法研究了分层性物质的组合取样精度,探讨了组合样中组分含量的分布规律、组合取样方差的分布规律、组合取样方差估计值的精度与组合样本数目之间的关系等.考察了组分含量服从正态分布、均匀随机分布及多项分布的分层性总体.结果表明,当样本数目较多时,组合取样误差规律对于不同原始分布的总体是相似的.     

参数法和非参数法估计组合样中被测组分含量的置信区间

本文以散装生铁块的随机样本分析结果为基础,应用Ｍｏｎｔｅ Ｃａｒｌｏ模拟法考察了组合样本中Ｓｉ、Ｍｎ,Ｃ,Ｓ,Ｐ含量（或份样平均值）的分布情况,研究了组分含量的置信区间,对参数法和非参数法的结果进行了比较。结果表明,对近似符合正态分布的原始总体或当组合样中的份样数目较多时,两种方法所估计的置信区间相近。但对偏离正态分布（或ｔ－分布）的总体且组合样中的份样数目较少时,非参数法较参数法的结果更符合实际     

计算机模拟地质化验室分样及取样常数Ks的估算

提出了计算机模拟地质化验室取样过程,考察取样误差与取样量、样品粒度之间关系,并估算取样常数。实验所得的误差与取样量之间的关系与Ingamells的取样方程一致,取样常数及取样常数和样品粒度关系式也与Ingamells推导的相符。由于计算机模拟是一颗颗取样,不用预设分布模式,不存在分析方法误差和分样操作误差的叠加,误差完全是因样品本身不均匀产生的。而且计算机模拟运算速度快,参数变换方便,使模拟更接近样品实际,能满足地质化验室的应用。     

取样方差估计值的精度与样本数目之间的关系

通过数学推导建立了取样方差估计值的精度与样本数目之间的定量关系。实验也证明,取样方差估计值的标准偏差与样本数目的平方根之积可近似为一常数。应用蒙特卡罗技术模拟随机取样,对该关系式进行了验证,并探讨了取样方差估计值的分布规律,表明其规律对于组分含量服从正态分布,均匀随机分布及多项分布总体是相似的。     

进口铜冶炼渣的取样及其分析试样的制备

针对大吨位量进口铜冶炼渣的不均匀性且有不能破碎的金属颗粒的存在，根据统计学及概率论的基础原理和实际经验提出了新的取样及制样方法，对整批铜冶炼渣渣料，以500t为一个取样单元，每个单元中取份样50～60个。根据渣料的粒径大小，决定每一份样的质量，粒径在20-50mm之间者，取份样量为4kg，粒径在10-20mm之间者，取份样量为2kg。将每一个取样单元所取的份样充分混合均匀作为副样，将每一副样进行粉碎，研磨并按需要多次缩分。收集在规定粒径条件下不能破碎的金属颗粒，并分别装在样袋中，另将通过100μm粒径的渣样收集于另一样袋，分别对不同样袋中铜，银，金的含量进行测定。按统计方法计算3元素的加权平均值，并最终得到整批渣料中上述3元素的含量。按所提出的方法，对两船进口的两批铜冶炼渣进行取样、制样并分析了其中铜、银及金的含量，所得结果与国外实验室的结果相吻合。     

计算机模拟取样确定标准物质的最小取样量

本文提出用计算机模拟取样对不同的取样量重复进行测试多次,统计其检测结果的标准偏差,做出标准偏差s对取样量m的拟合曲线,再计算最小取样量。设计的模式是一颗一颗地取样,这样不存在取样操作及测试过程带来的误差,操作是可行的,结果是可靠的。计算机运算速度快,参数转换方便,也可以取毫克甚至亚毫克样进行实验。只要有足够的岩矿鉴定的资料,可以模拟不同状态下的样品取样过程。     

二元颗粒混合物按质量取样的误差研究

二元颗粒混合物的随机取样方式有两种：一是按颗粒数目取样,二是按质量取样本文对二元颗粒混合物按质量取样的误差进行了深入研究,详细分析了混合物的各种参对被测组分含量取样误差的影响,应用Ｍｏｎｔｅ Ｃａｒｌｏ技术对取样进行了模拟。以颗粒药品的二元混合物为例对按颗粒数目取样和按质量取样的误差进行了比较。此项研究对于分析取样理论和应用具有重要的价值。     

过程质谱仪测量气体浓度快速变化过程的应用研究

通过实验研究了微型流化床多阶段原位反应分析仪( MFB-MIRA)检测快速气固反应气体逸出过程的适应性。研究表明,取样毛细管的伴热性能对在线测量的稳定性有重要影响。基于所得规律,将精密温控器配置于毛细管的伴热系统,毛细管温度的控制精度达到±0.2℃,从而实现了取样流量和腔室真空度的稳定化。实测结果表明,改造后在线测量的周期性波动消失,稳定性显著提高。空气中O2测量响应的波动度和30 s相对标准偏差由1.9％和0.5％,优化至1.4％和0.2％。同时还开发了精确控制取样点绝对压力的调节装置,使取样点绝对压力的控制精度达到±0.02 kPa。实验结果表明,取样点绝对压力与过程质谱仪的响应呈正相关,准确控制取样点绝对压力非常必要。本研究提高了过程质谱仪测量结果的准确性和重复性,提升了MFB-MIRA分析快速气固反应的适应性,进而拓宽了MFB-MIRA及过程质谱仪可靠应用的范围。     

渐进取样法及其应用

提出了渐进取样法,通过样本数目的累积,使总方差估计值达到所需的精度。应用Ｍｏｎｔｅ Ｃａｒｌｏ模拟技术考察了满足一定取样精度的样本数目及其偏差。将该方法应用于散装生铁块中Ｓｉ、Ｍｎ、Ｃ、Ｓ、Ｐ含量分析的取样,结果令人满意。该项研究对于大宗货物的实际随机取样具有重要参考价值。     

Effect of missing values in estimation of mean of auto-correlated measurement series

Sampling and uncertainty of sampling are important tasks, when industrial processes are monitored. Missing values and unequal sources can cause problems in almost all industrial fields. One major problem is that during weekends samples may not be collected. On the other hand a composite sample may be collected during weekend. These systematically occurring missing values (gaps) will have an effect on the uncertainties of the measurements. Another type of missing values is random missing values. These random gaps are caused, for example, by instrument failures. Pierre Gy's sampling theory includes tools to evaluate all error components that are involved in sampling of heterogeneous materials. Variograms, introduced by Gy's sampling theory, have been developed to estimate the uncertainty of auto-correlated process measurements. Variographic experiments are utilized for estimating the variance for different sample selection strategies. The different sample selection strategies are random sampling, stratified random sampling and systematic sampling. In this paper both systematic and random gaps were estimated by using simulations and real process data. These process data were taken from bark boilers of pulp and paper mills (combustion processes). When systematic gaps were examined a linear interpolation was utilized. Also cases introducing composite sampling were studied. Aims of this paper are: (1) how reliable the variogram is to estimate the process variogram calculated from data with systematic gaps, (2) how the uncertainty of missing gap can be estimated in reporting time-averages of auto-correlated time series measurements. The results show that when systematic gaps were filled by linear interpolation only minor changes in the values of variogram were observed. The differences between the variograms were constantly smallest with composite samples. While estimating the effect of random gaps, the results show that for the non-periodic processes the stratified random sampling strategy gives more reliable results than systematic sampling strategy. Therefore stratified random sampling should be used while estimating the uncertainty of random gaps in reporting time-averages of auto-correlated time series measurements.     

Quality control of sampling: proof of concept

Quality control in sampling has been demonstrated as practicable in sampling procedures that require the combination of sample increments to form a composite sample. The proposed method requires no sampling resources or use of time beyond those normally used. Increments are allocated at random into two half-sized composites, each of which is analysed separately. The absolute difference between the two results is plotted on a one-sided control chart, which is interpreted like a Shewhart chart. In commonly prevailing circumstances the analytical precision is negligible and the chart represents sampling precision alone.     

Soil sampling uncertainty on arable fields estimated from reference sampling and a collaborative trial

On three fields of arable land of (3–6)×10⁴ m², simple reference sampling was performed by taking up to 195 soil increments from each field applying a systematic sampling strategy. From the analytical data reference values for 15 elements were established, which should represent the average analyte mass fraction of the areas. A “point selection standard deviation” was estimated, from which a prediction of the sampling uncertainty was calculated for the application of a standard sampling protocol (X-path across the field, totally 20 increments for a composite sample). Predicted mass fractions and associated uncertainties are compared with the results of a collaborative trial of 18 experienced samplers, who had applied the standard sampling protocol on these fields. In some cases, bias between reference and collaborative values is found. Most of these biases can be explained by analyte heterogeneity across the area, in particular on one field, which was found to be highly heterogeneous for most nutrient elements. The sampling uncertainties estimated from the reference sampling were often somewhat smaller compared to those from the collaborative trial. It is suspected that the influence of sample preparation and the variation due to sampler were responsible for these differences. For the applied sampling protocol, the uncertainty contribution from sampling generally is in the same range as the uncertainty contribution from analysis. From these findings, some conclusions were drawn, especially about the consequences for a sampling protocol, if in routine sampling a demanded “certainty of trueness” for the measurement result should be met.     

固体分层取样方案的最优化设计

本文首次从理论上探讨了取得量对分层取样误差的影响,提出了总取样量一定时各层的最佳取样量和最小取样方差的计算公式,从而为分层取样的最佳取样方案设计提供了理论依据。