Comparison of Simplex Designs for Quadratic Mixture Models

Designs for quadratic regression are considered when the possible values of the controlable variable are mixtures x = (x ₁, x ₂, …, x _{q + 1}) of nonnegative components x _i with Σ ^{q + 1} ₁ x _i = 1. The designs that are optimum with respect to the D-, A-, and E-optimality criteria are compared in their performance relative to these and other criteria. Computational routines for obtaining these designs are developed, and the geometry of optimum structures is discussed. Except when q = 2, the A-optimum design is supported by the vertices and midpoints of edges of the simplex, as is the case for the previously known D-optimum design. Although the E-optimum design requires more observation points, it is more robust in its efficiency, under variation of criterion: but all three designs perform reasonably well in this sense.     

Global Sensitivity Analysis for Mixture Experiments

A mixture experiment is characterized by having two or more inputs that are specified as a percentage contribution to a total amount of material. In such situations, the input variables are correlated because they must sum to one. Consequently, additional care must be taken when fitting statistical models or visualizing the effect of one or more inputs on the response. In this article, we consider the use of a Gaussian process to model the output from a computer simulator taking a mixture input. We introduce a procedure to perform global sensitivity analysis of the code output providing main effects and revealing interactions. The resulting methodology is illustrated using a function with analytically tractable results for comparison, a chemical compositional simulator, and a physical experiment. Supplementary materials providing assistance with implementing this methodology are available online.     

最优混料试验轴设计

混料试验设计被广泛地应用在工农业生产和科学研究中。本文讨论了三、四分量二阶可加混料模型的最优轴设计问题,使用对称的轴设计,获得了它们的轴设计类上的D-,A-最优轴设计。     

Some Percentile Estimators for Weibull Parameters

A percentile estimator for the shape parameter of the Weibull distribution, based on the 17th and 97th sample percentiles, is proposed which is asymptotically about 66% efficient when compared with the MLE (maximum likelihood estimator). A two-observation percentile estimator, based on the 40th and 82nd sample percentiles, for the scale parameter when the shape parameter is unknown is asymptotically about 82y0 efficient when compared with the MLE. The 24th and 93rd sample percentiles yield asymptotically about 41ye jointly efficient percentile estimators for both the scale and shape parameters in a class of two-observation percentile estimators when compared with their MLEs. Some other simple percentile estimators for these parameters are also briefly discussed. Finally, asymptotic properties of these estimators are investigated and their application in statistical inference problems is mentioned.     

混料试验设计中置换阵的性质及其应用

为解决由于高维混料试验的设计阵的形式复杂且计算难度大的问题,使用高阶混料格点作为支撑集,提出了置换阵的定义。首先讨论了由置换阵构造出设计阵的方法;进而由此推导出信息矩阵与相关矩阵的显示表达;然后探索了置换阵的行列式、迹和特征值等方面的性质;最后通过实例验证置换阵用于设计分析的有效性,并进一步分析了利用置换阵构造高阶混料格点集和最优设计的必要性和可行性。     

Sequentially Generated Second Order Quasi D-Optimal Designs for Experiments With Mixture and Process Variables

Second order designs for experiments with mixture and process variables are proposed. They are constructed on the basis of continuous D-optimal designs by use of a three-stage procedure for sequentially generating optimal designs. The determinants of the information matrices of the designs obtained are very near to those of continuous D-optimal designs. Tables of discrete quasi D-optimal designs for q + r ≤ 7 are given, where q is the number of mixture components and r is the number of process variables. The experimenter can choose the number of trials N within the interval k ≤ N ≤ min(2k, k + 20), where k is the number of model coefficients. An application of the proposed designs in an investigation of truck tire properties is given.     

Using a Genetic Algorithm to Generate D‐optimal Designs for Mixture Experiments

We propose and develop a genetic algorithm (GA) for generating D‐optimal designs where the experimental region is an irregularly shaped polyhedral region. Our approach does not require selection of points from a user‐defined candidate set of mixtures and allows movement through a continuous region that includes highly constrained mixture regions. This approach is useful in situations where extreme vertices (EV) designs or conventional exchange algorithms fail to find a near‐optimal design. For illustration, examples with three and four components are presented with comparisons of our GA designs with those obtained using EV designs and exchange‐point algorithms over an irregularly shaped polyhedral region. The results show that the designs produced by the GA perform better than, if not as well as, the designs produced by the exchange‐point algorithms; however, the designs produced by the GA perform better than the designs produced by the EV. This suggests that GA is an alternative approach for constructing the D‐optimal designs in problems of mixture experiments when EV designs or exchange‐point algorithms are insufficient. Copyright © 2012 John Wiley & Sons, Ltd.     

Correlation for the Carbon Dioxide and Water Mixture Based on The Lemmon–Jacobsen Mixture Model and the Peng–Robinson Equation of State

Models representing the thermodynamic behavior of the CO₂–H₂O mixture have been developed. The single-phase model is based upon the thermodynamic property mixture model proposed by Lemmon and Jacobsen. The model represents the single-phase vapor states over the temperature range of 323–1074 K, up to a pressure of 100 MPa over the entire composition range. The experimental data used to develop these formulations include pressure–density–temperature-composition, second virial coefficients, and excess enthalpy. A nonlinear regression algorithm was used to determine the various adjustable parameters of the model. The model can be used to compute density values of the mixture to within ±0.1%. Due to a lack of single-phase liquid data for the mixture, the Peng–Robinson equation of state (PREOS) was used to predict the vapor–liquid equilibrium (VLE) properties of the mixture. Comparisons of values computed from the Peng–Robinson VLE predictions using standard binary interaction parameters to experimental data are presented to verify the accuracy of this calculation. The VLE calculation is shown to be accurate to within ±3 K in temperature over a temperature range of 323–624 K up to 20 MPa. The accuracy from 20 to 100 MPa is ±3 K up to ±30 K in temperature, being worse for higher pressures. Bubble-point mole fractions can be determined within ±0.05 for CO₂.     

改性沥青混合料拌和与压实温度确定方法综述

改性沥青混合料拌和与压实温度对沥青路面的设计和施工质量有很大影响,进而影响沥青路面的使用性能.介绍了4种具有代表性的确定改性沥青混合料拌和与压实温度的方法,分别为Yildirim法(Y法)、Bahia法(B法)、Shenoy法(S法)和Azari法(A法),阐明并论述了这4种方法的优缺点及适用范围.     

有限混合体模型上的自动模型选择:一种崭新的数据建模方式

在数据建模和分析中,有限混合体模型被广泛地使用着。然而,如何仅仅针对一组来自于某个有限混合体模型的数据选择出分量或聚类的个数则依然是一个非常困难的问题。由于分量个数是混合体模型的规模度量,其选择问题被称为有限混合体的模型选择问题。最近,针对有限混合体模型,特别是高斯混合模型,一种自动模型选择学习机制逐步发展成熟起来。这种新的机制能够在学习参数的过程中自动地完成模型选择,为数据的建模与分析提供了一种新的思路与途径。本文将对于高斯混合模型或一般有限混合体模型的自动模型选择学习算法及其典型应用进行综述与总结。首先,我们综述了基于贝叶斯阴阳机和谐学习原则的自动模型选择学习算法。然后,我们描述了另一种基于熵惩罚的自动模型选择学习算法。最后,我们给出了自动模型选择学习算法的一些典型的应用。     

厅堂音质设计响度评价新参量质疑

厅堂音质设计中响度是最基本的评价参量之一,目前通常采用相对强感（又称强度因子）G（dB）作为评价响度的参量。吴硕贤等人（2001）则认为这一参量不足以说明听众的真实感受,提出用乐队齐奏强音标志段（fone）的平均声压级协作为评价音乐厅内响度的新物理指标为好,亚可用Barton的简单修正公式进行估算厅内各处切的分布。从实用意义、客观测定、音质设计预估等方面,对此新评价参量作出剖析和评论,以说明其存在的问题和不可行性。     

也谈"军事计量测量标准价值分析"

就价值分析的内涵和操作要点,以及价值分析在计量领域的应用等方面,对本刊曾发表过的"军事计量测量标准价值分析"一文中的某些提法和分析提出几点不同的看法.     

用于现场条件下识别模态参数的几种时域模型及其比较

在现场条件下,当无法测量存在的自然激振力时,只能采用时域方法.本文介绍了用于现场条件下在时域内识别模态参数的多重积分模型.为了说明采用多重积分模型的必要性,还简要介绍了差分模型和多重微分模型,并进行了相应的比较.鉴于多重积分模型的一些特点,本文建议优先采用.     

水平微翅管内二元混合制冷剂流动沸腾阻力特性研究

对非共沸混合工质R32／R134a在水平微翅管内流动沸腾阻力特性进行了实验研究,分析了影响压特性的一些因素,讨论了混合物在水平微翅管内流动沸腾的流动阻力特点和规律。通过对试验数据的拟合,按分相模型计算了加速阻力,并建立了预测摩擦阻力的关联式,计算结果与实验较吻合。     

Some estimates on solutions of mixed problems for mixtures

Abstract

Our study is dedicated to a composite, which, in fact, is a mixture of two thermoelastic micropolar bodies. We formulate the mixed initial boundary value problem in this context and define the domain of influence for given data. For any solution of the mixed problem we associate a measure and prove a second-order differential inequality for it. Based on the maximum principle for the heat equation and on the second-order differential inequality, we establish an estimate which proves that the thermal and the mechanical effects, at large distance from the domain of influence, are dominated by an exponential decay.     

基于局部多项式拟合非时齐扩散模型参数的局部估计（英文）

本文主要研究一类非时齐扩散模型中参数的局部估计,此类问题是期权定价和风险管理中必要的组成部分.漂移参数和扩散参数是期权定价和风险管理中的关键性变量.首先,基于离散观测样本,利用局部多项式拟合,得到了漂移参数的局部多项式复合分位回归估计,并证明了其渐近性质.然后,考虑到扩散参数是非负的,本文利用对数局部多项式拟合,得到了扩散参数的局部多项式估计,并讨论了扩散项估计的渐近偏差、渐近方差和渐近正态性.最后,分别对漂移参数和扩散参数的估计采用了不同的带宽参数.模拟结果表明,本文所得到的局部复合分位回归估计比局部最小二乘估计的拟合效果更好.     

基于离散元方法的沥青混合料力链演化及分布量化分析

为了研究沥青混合料内部颗粒间力链的演化及分布规律,以AC-13沥青混合料作为研究对象,利用离散元方法重构沥青混合料数字试件,模拟简单性能试验,提取试件内部颗粒间的力链信息进行力链演化、概率分布和角度分布分析。结果表明,通过比较预测结果和实测结果,基于离散元方法重构的AC-13沥青混合料细观模型用于模拟其细观力学特性是可行的。试件内部力链空间分布具有各向异性,以垂直方向的压力力链为主,承受大部分的半正弦荷载。法向力链概率分布随加载时间的变化规律基本一致,法向接触力与平均法向接触力比值f最小时,概率分布出现最大值,f=1.75时,概率分布再次达到峰值,然后逐渐减小并趋于稳定。法向力链角度分布主要位于90°和270°附近,第一、二象限的角度分布比例远大于第三、四象限,60~120°、30~150°中法向力链角度分布比例均大于70%,最小为72.733%。