高中学业水平考试试题难度模型建构*

利用主成分分析方法厘清试题难度影响因素之间的关系,进而从问题表征、问题解决和结果输出等3个维度上建立了影响高中学业水平考试试题难度的主要因素。通过编写高中学业水平考试测试题进行实证研究,建立影响因素常见呈现类型的难易赋值规则。选用机器学习的线性回归方法建构试题难度分析模型,并使用高考化学江苏卷部分试题的实测难度数据进行校验,模型难度预测值和高考难度实测值具有较好的拟合度,表明模型具有较好的应用价值和推广意义。     

Improving the neural network method for finite element model updating using homogenous distribution of design points

In developing a neural network technique for a finite element model updating, researchers have been shown that the number of training samples and their quality, significantly affect the accuracy of the NN predication. In this study, based on the genetic algorithm (GA) method, we reduce the number of analyses required to develop the training pairs and reduce the amount of time for training the NN. In the other words, a uniform distribution of design points inside the design space will be obtained by means of this approach. To validate the efficiency of GA sample selection, random generation (RG) method is used for comparison. Two comparisons are made based on a numerical and experimental example. One is updated from 10 degrees of freedom lumped parameters system and the other is updated from a free–free beam using test data. The results indicate that the GA sample selection can reduce the number of training samples without affecting the accuracy of the NN predication. In our present study, also, the advantages of using frequency response function (FRF) data as input to the NN are kept and the drawback of having too many frequency points is overcome by the application of principal component analyses (PCA).     

基于半参数回归模型的最小一乘局部线性算法

根据最小一乘准则,推导出最小一乘局部线性估计的计算方法,并通过对模拟数据的计算和分析,对比最小一乘核算法和最小二乘局部线性算法,验证了最小一乘局部线性算法是一种有效的,稳健的估计方法,并且有降低边界效应的作用．     

不等式约束条件下回归模型的参数估计及检验

本文研究了具有不等式约束条件的回归模型的参数估计，给出了检验的统计量和一个实例．     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.     

Multivariate Liouville distributions

A random vector (X₁, …, X_n), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x₁ + … + x_n)x₁^a₁.1 … x_n^a_n.1 with thea_i all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a comprehensive treatment of the Liouville distributions is provided. The results pertain to stochastic representations, transformation properties, complete neutrality, marginal and conditional distributions, regression functions, and total positivity and reverse rule properties. Further, these topics are utilized in various characterizations of the Dirichlet and inverted Dirichlet distributions. Matrix analogs of the Liouville distributions are also treated, and many of the results obtained in the vector setting are extended appropriately.     

双层PLS算法及其在近红外光谱分析中的应用

针对近红外光谱数据局部效应显著,变量个数多,且彼此间常存在严重的复共线性,并与样品组分含量呈非线性关系,构建了一种双层非线性偏最小二乘回归 (DNPLSR)算法。它将非线性回归和偏最小二 乘(PLS)相结合,先在外层由PLS从样本数据中提取成分,并实现每对成分间的非线性映射,再在内层实施PLS算法,将外层因变量成分的拟合误差反馈计算转换权向量的增量,进一步修正转换权向量,以使外层所提取的成分对因变量具有更优的解释能力。最后,将该法应用于80个谷物样品的水组分含量与其近红外光谱的定量关系建模,效果良好,显示出很强的学习能力,所建模型的预报性能也优于其他方法。     

油菜叶片的光谱特征与叶绿素含量之间的关系研究

叶绿素是作物生长中的重要因素,是植物营养胁迫、光合作用能力和生长状况的良好指示剂。实时、可靠的作物营养诊断是进行科学施肥管理的基础,也是实践精细农业的关键技术之一。采用便携式可见-近红外光谱仪,在室外自然光照条件下对不同氮肥水平下油菜叶片的光谱特性进行了研究,并根据作物特有的光谱特征,采用逐步回归分析方法建立了油菜叶片的叶绿素含量与红边位置和绿峰位置之间的定量分析模型。结果表明,将红边位置、绿峰位置二者作为自变量时,建立的模型效果优于采用单一的红边位置为自变量时建立的模型效果。其相关系数分别为0.863和0.848;校正标准偏差SEC分别为5.273和5.459, 说明采用红边位置和绿峰位置这两个参数更能很好地预测叶片的叶绿素含量。     

~(252)Cf自发裂变中子发射率符合测量的回归分析

~(252)Cf同位素源具有标准的自发裂变中子能谱,但由于其半衰期较短,应用中常需要对源强进行标定修正.随着源年龄增加,来自源中~(250)Cf和~(248)Cm自发裂变的影响愈加凸显,不能简单按~(252)Cf的衰变规律计算源中子发射率,而通过锰浴活化的间接测量方法周期较长,且在源强低于10~4 n/s时误差较大.最近,基于中子多重性计数的源强绝对测量算法已得到验证.本文进一步从点模型假设的测量方程出发,在将符合计数率与总中子计数率关联的基础上,分别对符合计数率随源位置、符合门宽的变化关系进行回归分析,提取变化过程的特征系数,建立了两种避规效率变化的~(252)Cf中子发射率测量方法,并基于JCC-51型中子符合测量装置开展实验验证.结果表明:两种回归分析方法的测量值均与标称值的修正结果在2%的偏差范围内一致;反推求得装置中轴线上的探测效率也与基于MCNPX程序的蒙特卡罗模拟计算值相符.研究结果可为活度信息不明的~(252)Cf源强标定及符合测量装置的效率刻度提供便携准确的实验方法.     

能量色散X射线荧光光谱检测土壤重金属砷、锌、铅和铬

利用X射线荧光光谱检测土壤重金属砷、锌、铅和铬元素的含量。通过分析仪器检出限和准确度,得出仪器适用性良好。然后,利用二维相关同步光谱获得重金属元素的X射线荧光光谱能谱范围和变量数,得出铅元素的能谱范围分别为10.380~10.740和12.435~12.900 keV,砷元素的能量范围是10.380~10.740和11.610~11.880 keV,铬元素的能量范围是5.310~5.520和5.805~6.015 keV, 锌元素的能量范围是8.520~8.805和9.555~9.630 keV,铅、砷、铬和锌的变量数分别为57,44,30和26。最后,根据获得的能谱范围,采用偏最小二乘回归方法建立重金属元素的X射线荧光光谱定量分析模型,得出砷元素的模型性能最佳,其次是铅、锌和铬,预测相关系数都高于0.92。研究表明,利用二维相关光谱获得的能谱范围有助于提高模型的预测性能和便携式X射线荧光光谱检测仪器适用于土壤重金属的原位监测。