用序贯法对反应速率模型中的参数作精确估算

对一个确定的模型,不仅要确定参数的估算值,还必须了解其可靠性。为了缩小参数的不定性,降低参数间的相关性,以扩大模型拟合的适定性和准确度,本文讨论了参数精确估算的序贯设计过程。 文内还详细讨论了精估参数的实验设计准则——最小联合置信容积准则和形状准则,以及序贯设计的实用价值。以氨合成为例,用序贯法精确估算了反应速度模型中的参数。这一模型是在序贯判别过程中选定的。把精估结果用于拟合大型生产过程的实测数据,得到了满意的结果。     

关于模型筛选的适应性准则问题——兼与“用序贯法判别在‘A’系催化剂上氨合成反应的速率模型”的作者商榷

<正>一、引言 序贯法是一新的实验设计方法,文献“用序贯法判别在‘A’系催化剂上氨合成反应的速率模型”将序贯法应用到实际中去,并取得较为理想的效果。本文拟对模型筛选的适应性准则这一问题作进一步的探讨。     

工程项目中地基土的地震液化判别分析

本文以山西省忻州市工程实例为载体采用标准贯入试验法对拟建场址地基土地震液化特征进行了判别,判别结果符合本地区历史工程实践经验。通过整个判别过程的详细计算,对采用标准贯入试验法判别地震液化影响进行了深入的分析。     

在S101型钒催化剂上二氧化硫氧化过程的本征动力学研究

本文叙述了在等温良好的二段反应器内,在细颗粒S101型钒催化剂上二氧化硫氧化过程的本征动力学的研究结果。在模拟工业条件下进行了广泛的动力学数据测定,第一次成功地将序贯法用于二氧化硫氧化过程动力学的研究,根据十组基本实验数据,用非线性最小二乘法求出竞争模型的参数估算值。利用离散度最大原理选择补充实验条件,从十一个竞争模型中筛选出适定的等效模型。应用最小联合置信容积准则精估了模型参数。在全操作区内,推荐的二氧化硫氧化过程的本征速率方程式是:     

PA6材料拉-扭组合的力学特征及屈服准则的试验研究

为了研究PA6在拉-扭组合作用下的力学特征、屈服准则及强度条件,利用电子拉-扭试验机对PA6材料进行了6种加载速率下的拉-扭组合变形试验,得到了相应的正应力与正应变、切应力与切应变的关系曲线;通过试验验证了Mises屈服准则可作为PA6材料的拉-扭屈服准则;基于最小二乘法建立Mises屈服准则中应力偏张量的第二不变量关于PA材料密度、声波速率、拉伸加载速率、扭转加载速率的拟合模型。由该拟合模型,可以不做加载破坏试验,即可建立PA6的拉-扭屈服准则,得到拉-扭屈服时的相当应力,并通过该屈服准则建立强度条件,可进行相应的PA6拉-扭强度计算。     

钒催化剂上二氧化硫氧化过程的本征动力学模型

在二段反应器内,模拟工业条件下,测定了细颗粒S101型钒催化剂上二氧化硫氧化过程的数据,并首次将序贯法应用于二氧化硫氧化过程动力学的研究.将基本实验测定的数据,用非线型最小二乘法回归,算出模型的参数估算值,利用离散度最大原理选择补充实验条件,从十一个竞争模型中筛选出适定的最佳模型.应用最小联合置信容积准则精估了模型参数.推荐S101型钒催化剂上二氧化硫氧化过程的本征动力学速率方程是     

用序贯法研究乙醇脱水制乙烯的速率模型

用序贯法研究乙醇脱水制乙烯的速率模型刘雁，丛津生，邹仁（河北工业大学化工系，天津３００１３０）关键词：乙醇，乙烯，脱水，序贯法１前言乙烯是一种重要的基本有机化工原料，其生产有多种途径。目前大部分国家采用石油烃裂解，但不少国家还采用了乙醇催化脱水法。乙...     

氯氧化铋反应结晶动力学研究

在铋盐水解制备氯氧化铋的反应结晶过程中,控制氯氧化铋晶体成核和生长速率可影响氯氧化铋晶体的形貌、粒径和分散性。为此,选用间歇动态法研究了氯氧化铋晶体成核与生长动力学,采用矩量变换法建立了结晶过程动力学模型,并用最小二乘法对实验数据进行多元线性回归,获取了动力学模型参数。研究结果表明：当氯氧化铋晶体粒度≥3 μm时,其晶体生长速率符合粒度无关生长模型;晶浆悬浮密度和过饱和度对成核速率均有显著影响;溶液过饱和度对成核速率的影响较生长速率的影响更为显著。     

陶瓷原料分类的Bayes判别分析法

将Bayes判别分析法应用于陶瓷原料分类中,建立了陶瓷原料分类识别的Bayes判别分析模型.模型选用陶瓷原料的9种化学成分作为分类识别的判别因子;将陶瓷原料分为4个类别并作为Bayes判别分析的4个正态总体;以陶瓷原料样本实测数据作为训练样本,建立Bayes线性判别函数;以Bayes线性判别函数计算待判样品的Bayes判别函数值,以最大值对应的总体作为样品所归属的总体;最后以回代法对判别准则进行评价以检验模型的优良性.实例研究表明,Bayes判别分析模型回判估计误判率为0,因而是陶瓷原料分类识别的一种有效方法,可在生产实际中应用和推广.     

竞争模型的逐点甄别方法

基于残差的随机性，提出了蕴涵展伸不确定度参数的目标偏差二阶矩最小准则并与序贯设计中的散度最大准则进行比较，表明目标偏差二阶矩最小准则能逐点甄别竞争模型并弥补散度最大准则的不足之处。     

Sequential experimental design based on multiobjective optimization procedures

Model-based sequential experimental designs are frequently applied for discrimination of rival models and/or estimation of precise model parameters. Although the development and use of a single design criterion to perform the simultaneous model discrimination and precise parameter estimation seem appealing, published material indicates that previous attempts to develop such a single design criterion have not been successful. Despite that, this problem has rarely been analyzed with the help of multiobjective optimization procedures. In this work, a multiobjective optimization method based on the particle swarm optimization procedure is used to build the Pareto fronts in experimental design problems where distinct design criteria used for discrimination of rival models and/or estimation of precise model parameters are considered simultaneously. It is shown through the rigorous analysis of the Pareto sets that both design objectives are frequently conflicting, which means that optimum discrimination of rival models and estimation of precise model parameters cannot be performed simultaneously in many cases. However, it is also shown that the use of the posterior covariance matrix of estimated model parameters for model discrimination makes the design of experiments for the simultaneous optimum model discrimination and estimation of model parameters possible in many experimental design problems.     

Discrimination of rival kinetic models in heterogeneous catalysis by the dynamic behaviour of products

The transient response method has been applied to discriminate between rival kinetic models derived from the conventional Hougen-Watson procedure in heterogeneous catalysis, by using some old data for the NO-CO reaction, dehydrogenation of sec-butanol, hydrogenation of phenol, and dehydrogenation of tert-butanol. A computer technique is commonly used for the simulation of the transient response curves of products caused by the concentration jump of reactants in a flow type reactor. The shapes of the calculated response curves are of various characteristic types (depending on the given model) which allow for easy discrimination between rival kinetic models. The difficulty of the discrimination in some particular models is also discussed.     

An ideal point method for the design of compromise experiments to simultaneously estimate the parameters of rival mathematical models

When several rival mathematical models are proposed for one and the same process, experimental design techniques are available to design optimal discriminatory experiments. Because these techniques are model-based, it is important that the model predictions are not too uncertain. Therefore, model discrimination may become more efficient and effective if this uncertainty is reduced first. This can be achieved by performing experiments designed to increase the accuracy of the parameter estimates and, thus, the model predictions. However, performing such an additional experiment for each rival model may undermine the overall goal of optimal experimental design, which is to minimize the experimental effort. This paper deals with the design of a so-called compromise experiment, which is an experiment that is not optimal for each of the rival models, but sufficiently informative to improve the overall accuracy of the parameters of all rival models. For this purpose, the problem is approached as a multi-objective optimization problem and the ideal point method is proposed to design the compromise experiment. This method searches for the experiment that is as close as possible to the optimal experiments of the individual rival models. The method is applied to a case study where nine rival models are competing to describe the kinetics of an enzymatic reaction, and the obtained results show that the ideal method is capable of designing a compromise experiment.     

A new approach for sequential experimental design for model discrimination

Model discrimination procedures are useful tools for selection of the best mathematical models to be used to represent a specific chemical process. The present paper presents and discusses a new sequential discrimination procedure, which makes use of model probabilities and concentrates the efforts on models with higher probabilities. Model probabilities are determined based on simple statistical arguments. Four numerical examples illustrate the application of the proposed discrimination procedure. The obtained results indicate that the new procedure is able to discriminate kinetic models with fewer experiments when compared to other procedures and also indicates when model discrimination is not possible and, thus, when the sequential design must be halted. Furthermore, the speed of the proposed discrimination procedure can be controlled by tuning a design parameter which reflects the analyst's mood (confidence) towards the discrimination problem and allows for increase or decrease of the number of experiments required for model discrimination during the sequential procedure.     

Sequential design including initial experimental runs for a kinetic study of propylene oxidation

A sequential design strategy for selecting experimental runs to obtain model discrimination and precise parameter estimation is tested via a simulation study of propylene oxidation kinetics. The strategy is used to design all runs including the preliminary ones which were arbitrarily chosen by earlier researchers. To design initial runs, crude initial parameter guesses may be used in the rival models until least squares estimates can be calculated. Even under conditions of very bad initial guesses and high error variances, this procedure selects whichever model is the correct one and estimates with precision its parameters, in fewer runs than previously reported.     

A new sequential experimental design procedure for discriminating among rival models

A new procedure to be used in the sequential design of experiments for discriminating among rival models is presented. The procedure consists of a new design criterion and a model adequacy test based on statistical principles. The method is illustrated with examples and compared to previous methods.     

Modeling of thermal cracking kinetics—II: Cracking of iso-butane,of n-butane and of mixtures ethane—propane—n-butane

Molecular reaction schemes for the pyrolysis of isobutane and normal butane were derived from experimental products distributions, radical mechanisms and thermodynamic principles. The associated parameters were estimated by non linear regression using a Marquardt routine for the minimization of a suitable objective function. The discrimination between the rival models was based on physical criteria, statistical tests and the closeness of fit. The prediction of the product distributions of the cracking of binary mixtures of normal and isobutane, n-butane and ethane, n-butane and propane and the ternary mixtures of n-butane, propane and ethane was based upon a model obtained from the superposition of the models for single component cracking.     

USING POWER-LAW RATE EXPRESSION PARAMETERS FOR DISCRIMINATION AMONG MECHANISTIC MODELS IN RATE DATA REGRESSION

Langmuir-Hinshelwood (or Hougen-Watson) type rate expressions are most often used in modeling reaction rate data. In cases when there are tens of possible rival models, effective discrimination between them requires that most of the inadequate models be discarded as early as possible in the discrimination process.

In this paper, the relationship between power-law and Hougen and Watson type rate expressions was studied. It was found that there is a clear mathematical connection between the two types of rate expressions. This connection can be utilized in order to discriminate between feasible and infeasible models, using only the numerical values of the power-law rate expression parameters. This way most of the inadequate mechanisms can be discarded after fitting the data to a single (power-law) model.

The 95% confidence intervals of the parameters have proven to be key statistical variables in determining the adequacy of both power-law and mechanistic models. Using the data and results of Hougen and Watson (1947), it is shown that they rejected valid mechanisms and accepted invalid ones because they did not take into account the confidence intervals on the parameters.