用序贯法判别“A”系催化剂上氨合成反应的速率模型

本文详细讨论了用序贯法对“A”系催化剂上氨合成反应的速率模型最佳判别的过程;对不同速率模型中的参数进行初估,按设定的准则作序贯判别,最后选出优惠的模型方程。 文中还讨论了最小二乘法的选择;判别过程的具体技术问题及模型的判别准则。     

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     

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:     

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。     

用时间域最小二乘拟合法研究萃取柱中的轴向混合

本文以非理想脉冲注入的扰动-响应技术,进行萃取柱轴向混合的研究。各种参数估值方法的比较表明,时间域最小二乘拟合法较为精确。本文还讨论了参数估值的不定性问题和计算时间问题。在标准结构的脉冲筛板柱内研究了脉冲振幅和频率对轴向混合系数的影响。     

二元混合物蒸馏塔的图解设计

<正> 在作可行性研究时,为了估算工程费用常需迅速计算出蒸馏塔的大致尺寸。若用传统方法估算蒸馏塔的尺寸,不但很费力,而且常常并不需要如此精确。分离二元混合物的蒸馏塔的设计参数可用本文介绍的算图迅速而方便地确定。算图还提供了水蒸汽和冷却水耗量的估算方法。本文还介绍了为获得塔的初步尺寸必须通过计算的参数,并举例对估算步骤作了具体说明。     

随机建模与油藏数值模拟技术在油田开发中的应用

在油田地质建模研究中,综合应用地质、地震和测井资料建立构造模型。以构造模型提供的地层格架,采用随机建模中序贯指示模拟的方法建立沉积微相模型。在此基础上,按相控建模的思路,选择地质统计学克里金方法中的球形变差函数模型对研究区储层参数进行模拟,建立了储层参数模型,为油藏数值模拟提供了精确的三维数据体。油藏数值模拟是定量描述剩余油分布的重要手段,可以较为准确全面的确定油藏中纵向及平面上剩余油的分布情况,并给出具体数值,为优化调整挖潜方案提供技术指导。     

固定式海洋平台底层甲板高度计算方法

依据API RP 2A-WSD、ISO 19902-2007、海上固定平台安全规则以及壳牌DEP标准的推荐做法,总结了依据海洋环境条件确定固定式海洋平台底层甲板高度的准则和计算方法。对设计重现期、潮汐、空气间隙、最大波峰高程等参数的定义、选取、计算方法进行了描述。结合具体工程实例的环境参数,详细说明了各参数计算过程,为总体设计中底层甲板高度的估算或精确计算提供参考。     

高二区莲花油层储层建模研究

在辽河盆地东部凹陷高二区储层地质建模研究中,综合应用地质、地震和测井资料建立构造模型。以构造模型提供的地层格架,采用随机建模中序贯指示模拟的方法建立沉积微相模型。在此基础上,按相控建模的思路,选择地质统计学克里金方法中的球形变差函数模型对研究区储层参数进行模拟,建立了储层参数模型,为油藏数值模拟提供了精确的三维数据体。     

基于剩余使用寿命预测的替换时间和备件订购时间联合决策

针对带有状态监测的单部件系统, 基于剩余使用寿命预测信息, 考虑了替换时间和备件订购时间的联合决策。首先, 利用实时状态监测信息对剩余使用寿命分布函数进行预测;然后, 分别建立了该预测信息下的序贯优化模型和联合优化模型;最后, 进行了实验研究, 利用实际的轴承加速寿命实验对序贯决策和联合决策的效果进行比较。结果表明, 联合决策比序贯决策要好, 同时还避免了序贯决策中决策结果无法实施的问题。     

A SEQUENTIAL PROCEDURE FOR PRECISE ESTIMATION OF PARAMETERS IN KINETIC MODEL

For a determined mathematical model,it is not only necessary to obtain the estimates of parameters,but also their reliabilites.The present work deals with a sequential statistical design strategy for anexperimental program to obtain precise parameter estimetes for a nonlinear kinetic model.It aims at de-creasing the indeterminatness of the parameter estimates,in reducing the correlation between parameterestimates,and in inceasing the adequacy and accuracy of the model.The paper discusses the experimental design criterion for precise parameter estimates-the minimun vol-ume design criterion and the spherical shape design criterion,and the practical value of a sequential statis-tical design strategy.At last,an example was performed to precise estimate the parameters in the kinetic model of ammoniasynthesis reaction which was selected as being adequate in the previous work.Comparison of the results from the industrial unit and the corresponding values calculated with themodel using the estimates of parameters reveals the reasonable reliability of the model.     

Sequential statistical design strategy in a kinetic study of propylene oxidation

A sequential design strategy was used to direct an experimental kinetic study of propylene oxidation over bismuth molybdate. Two statistical criteria were used to design experiments. The first is a joint criterion for the dual problem of model discrimination and parameter estimation which was proposed by Hill et al. (1968), but which to the best of our knowledge has not been tested in an experimental program. Using this joint criterion design, it was demonstrated that both the objectives of model discrimination and precise parameter estimation were effectively accomplished. After model discrimination had been achieved, a design strategy for further improvement in parameter precision was found, as expected, to be effective for that purpose.     

Precise parameter estimation for chemical batch reactions in heterogeneous medium

A sequential experimental strategy for precise parameter estimation has been used in the case of liquid-liquid dispersions in batch-stirred tank reactors where slow chemical reactions take place. The mathematical model for a batch reaction in a stirred tank reactor is formulated as a system of non-linear differential equations standing for the mass balance of each component. Physical kinetic parameters and chemical kinetic parameters which arise from this model are estimated simultaneously. The estimation problem is posed as a weighted least squares problem and solved by using a standard Levenberg-Marquardt algorithm. In this work, we intend to show how it is possible to develop efficient experimental design strategies that lead to an accurate estimation of the parameters involved in phenomenological models and most particularly in kinetic models. Three design criteria for designing the experiments have been employed in order to increase the precision on the parameter estimates of the model. A standard non-linear sequential quadratic programming method ensures the determination of the operating conditions which define the experimental design. The well-known alkaline hydrolysis of esters in aqueous phase has been treated as a numerical application example.     

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.     

Sequential statistical design strategy in an experimental kinetic study

The value of using a sequential statistical design strategy is illustrated through its use in an experimental kinetic study of the oxidation of o-xylene over a vanadium oxide catalyst. The rate of oxidation of o-xylene was determined in a differential reactor over the following ranges of conditions: 270 to 300°C, (0.5 to 3.5) x 10^-4 g.mole o-xylene/1., (1.0 to 10.0) x 10^-3 g.mole oxygen/1. The statistical design strategy for precise parameter estimation was found to be effective in increasing the precision of the parameter estimates, in reducing the correlation between parameter estimates and in showing the magnitude of this problem, and in providing a reliable prediction of the value of carrying out additional runs.     

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.     

Iterative model-based experimental design for spherical agglomeration processes

Spherical agglomeration (SA) is a process intensification strategy, which can reduce the number of unit operations in pharmaceutical manufacturing. SA merges drug substance crystallization with drug product wet granulation, reducing capital, and operating costs. However, SA is a highly nonlinear process, thus for its efficient operation model-based design and control strategies are beneficial. These require the development of a high-fidelity process model with appropriately estimated parameters. There are two major problems associated with the development of a high-fidelity process models—(i) selection of the appropriate model corresponding to the underlying process mechanisms, and (ii) accurate estimation of the parameters. This work focuses on the identification of the best fitting model that correlates with experimental observations using cross-validation experiments. Further, an iterative model-based experimental design strategy is developed, which uses D-optimal experimental design criterion to minimize the number of experiments necessary to obtain accurate parameter estimates.     

A sequential experimental design procedure for precise parameter estimation based upon the shape of the joint confidence region

A sequential experimental design procedure which aims at obtaining precise parameter estimates of the mathematical model is proposed and illustrated. The design criterion modifies the shape of the joint confidence hyperellipsoid, rather than its volume. It consists of identifying those experimental conditions for the next experiment which maximize the smallest eigenvalue of X^TX, resulting in maximal contraction of the largest principal axis of the confidence hyperellipsoid. The conditions to be fulfilled for applicability of the criterion are that the mathematical model has to be sufficiently linear in the parameters in the vicinity of the maximum likelihood (least squares) parameter estimates and that the unobservable experimental error is distributed according to N(O, Iσ²).     

Precise parameter estimation in reaction modelling — sensitivity in choosing experimental conditions

A sequential experimental design developed by Box and coworkers was reviewed and the sensitivity of experimental conditions in increasing the preciseness of parameter estimates was examined. Continuous kinetic data were utilized for the examination. It is found that experimental conditions are in some cases rather sinsitive and slightly deviated experimental conditions from those specified by the criterion may induce some difficulty in reducing the size of confidence region of parameter estimates.     

Kinetic parameter estimation from TGA: Optimal design of TGA experiments

This work presents a general methodology to determine kinetic models of solid thermal decomposition with thermogravimetric analysis (TGA) instruments. The goal is to determine a simple and robust kinetic model for a given solid with the minimum of TGA experiments. From this last point of view, this work can be seen as an attempt to find the optimal design of TGA experiments for kinetic modelling. Two computation tools were developed. The first is a nonlinear parameter estimation procedure for identifying parameters in nonlinear dynamical models. The second tool computes the thermogravimetric experiment (here, the programmed temperature profile applied to the thermobalance) required in order to identify the best kinetic parameters, i.e. parameters with a higher statistical reliability. The combination of the two tools can be integrated in an iterative approach generally called sequential strategy. The application concerns the thermal degradation of cardboard in a Setaram TGA instrument and the results that are presented demonstrate the improvements in the kinetic parameter estimation process.