二级不可逆反应半分批操作的渐近解

对半分批反应器中等温进行的二级不可逆反应Ａ＋Ｂ→Ｐ进行了分析，在限制性反应物Ａ一次投料，反应物Ｂ连续恒速流加情况下，导出了非线性物料衡算微分方程的渐近解，即ＭＡ＝（Ｖｏ／ｋ）（１＋βｔ）＾ｓ／（Ｖ０／ｋＭＡ０＋Ｎ／Σｎ＝０ｆ＾（ｎ）（０）／（ｋｃｂ０）＾（ｎ＋１）ｅｘｐ（ＫＣｂｏ＾ｔ）－ＮΣｎ－０ｆ＾（ｎ）（ｔ）／（ＫＣｂ０）＾（ｎ＋１）本文将渐近解的结果与数值解的结果进行了比较，二者极为吻合。渐     

用于估计动力学参数的微型反应装置

动力学参数估值的较好方法是使用微型反应器进行测定．本文讨论了多种实验用的微型反应器，它们可适用于很宽的流作状态．使用温度范围在0-1000℃以上，压力范围为0．1～10MPa或更高．     

浆态F—T法宏观反应动力学的参数估计

利用浆态床 F-T 合成反应,经长周期试验数据估算宏观反应动力学参数。用多组分数学模型,考虑了反应器内催化剂浓度间歇变化,并引入催化剂活性修正因子,采用正交排列与单纯形方法进行计算。最后用得到的动力学参数进行模拟计算,合成气转化率预报值与实测值相对误差2.5%,最大误差7.7%。可以认为采用的数学模型及动力学参数可以描述用沉淀铁催化剂,进行浆态床 F-T 合成反应的结果。     

ESTIMATION OF AUTOREGRESSIVE PARAMETERS AND ORDER SELECTION FOR ARMA MODELS

Abstract. A quick algorithm for obtaining estimates of autoregressive parameters for autoregressive moving-average model is presented. The algorithm is recursive in the orders, and can be used for model selection by providing a criterion and a two-way table of certain partial covariances. Consistency and asymptotic normality of the estimates are shown.     

A GENERALIZED LEAST-SQUARES APPROACH FOR ESTIMATION OF AUTOREGRESSIVE MOVING-AVERAGE MODELS

Abstract. In this paper we present a generalized least-squares approach for estimating autoregressive moving-average (ARMA) models. Simulation results based on different model structures with varying numbers of observations are used to contrast the performance of our procedure with that of maximum likelihood estimates. Existing software packages can be utilized to derive these estimates.     

A GROUP-INTERACTION CONTRIBUTION APPROACH. A NEW STRATEGY FOR THE ESTIMATION OF PHYSICO-CHEMICAL PROPERTIES OF BRANCHED ISOMERS

The methods based on the Group Contribution Concept usually fail when one attempts to estimate the physico-chemical properties of different branched isomers of a given compound. We present a new concept, the Group-Interaction Contribution Approach (GIC) which considers the contribution of the different interactions between groups present in a molecule instead of the contribution of structural groups.

This approach allows differentiation between branched isomers, thus leading to different values of the physico-chemical properties. The GIC Approach can be easily implemented in current correlations based on the group contribution concept.

The estimates of enthalpy of formation, normal boiling temperature and critical temperature of a series of 51 saturated hydrocarbons showed clearly that the GIC concept leads to very good estimations for branched isomers.     

A LINEAR ESTIMATION PROCEDURE FOR THE PARAMETERS OF AUTOREGRESSIVE MOVING-AVERAGE PROCESSES

Abstract. A linear estimation procedure for the parameters of autoregressive moving-average processes is proposed. The basic idea is to write the spectrum for the moving-average part as a linear function of a properly selected set of parameters and to use Chiu's weighted least-squares procedure to reduce the problem to a weighted linear least-squares problem. The proposed procedure finds estimates by solving systems of linear equations and does not need optimization programs. An one-step estimate is also suggested. It is shown that the estimates are asymptotically equal to the commonly used 'approximate' maximum likelihood estimate described in the paper. For Gaussian processes, the estimates obtained by the proposed procedures are asymptotically efficient.     

THE ESTIMATION OF PARAMETERS FOR AUTOREGRESSIVE MOVING AVERAGE MODELS

Abstract. This paper provides some new and improved versions of an earlier procedure for the estimation of parameters for autoregressive moving average models suggested by the author (1979). Some numerical examples of the application of the procedure are also given.     

SEQUENTIAL FIXED-PRECISION ESTIMATION IN STOCHASTIC LINEAR REGRESSION MODELS

ABSTRACT

The goal of this article is to address the problem of fixed-precision estimation of parameters in a linear regression setup with stochastic regressors. First in the case of a linear regression model where the regressor variable and the random errors have independent Gaussian distributions, sequential sampling schemes are proposed for fixed proportional accuracy estimation and fixed-width interval estimation of the regression-slope based on a Chebyshev inequality approach. The asymptotic second-order efficiency of these procedures is then established using the techniques developed in Aras and Woodroofe (1993)[2] Aras, G. and Woodroofe, M. 1993. Asymptotic Expansions for the Moments of a Randomly Stopped Average. Ann. Statist., 21: 503–519. [Crossref], [Web of Science ®] , [Google Scholar]. Asymptotic second-order expansions are derived for a lower bound of P (relative error < preassigned bound) in the fixed proportional accuracy estimation case and that of the coverage-probability in the interval-estimation case. In both cases, the possibility of relaxing the Gaussian assumption is explored, leading to a reconsideration of Martinsek's (1995)[15] Martinsek, A.T. 1995. Estimating a Slope Parameter in Regression with Prescribed Proportional Accuracy. Statistics and Decisions, 13: 363–377.  [Google Scholar] fixed proportional accuracy estimation and a detailed discussion of a stochastic multiple linear regression model with distribution-free errors and regressors. In this distribution-free multiple regression scenario, construction of fixed-size confidence regions for the vector of regression-parameters is considered and an asymptotically second-order efficient sequential methodology is put forward. Moderate sample-size performances of some of these procedures are investigated via simulation-studies.     

A FREQUENCY DOMAIN APPROACH FOR THE ESTIMATION OF PARAMETERS OF SPATIO‐TEMPORAL STATIONARY RANDOM PROCESSES

A frequency domain methodology is proposed for estimating parameters of covariance functions of stationary spatio‐temporal processes. Finite Fourier transforms of the processes are defined at each location. Based on the joint distribution of these complex valued random variables, an approximate likelihood function is constructed. The sampling properties of the estimators are investigated. It is observed that the expectation of these transforms can be considered to be a frequency domain analogue of the classical variogram. We call this measure frequency variogram. The method is applied to simulated data and also to Pacific wind speed data considered earlier by Cressie and Huang (1999). The proposed method does not depend on the distributional assumptions about the process.     

估算有机物基础物性的三基团参数关联式

提出T_(?)、T_m、T_c、p_c和V_c5种基础物性的三基团参数关联式,拟合了相应的基团参数值,对上述各物性估算的平均偏差分别为1.35%、8.01%、0.68%、2.73%和1.44%,准确度高于目前文献推荐的Joback法.     

A JOINT EXPERIMENTAL DESIGN PROCEDURE FOR PARAMETER ESTIMATION

A joint experimental design procedure which aims at obtaining precise parameter estimates of a given mathematical model is proposed and illustrated by means of computer simulated experiments

This criterion is found both to modify the shape of the joint confidence hyperellipsoid and to reduce its volume significantly

Therefore, it behaves as a combination of two of the most representative techniques in use today, known as the minimum volume or the shape criteria. Numerical results are given which serve to display its salient features and to compare it with the above mentioned techniques.     

试差矩阵熬及其在复杂反应动力学研究中的应用

本文提出了一种研究高维拟一级复杂反应动力学的新方法——试差矩阵法.该方法充分运用有效的数学方法和计算技术,以减少实验工作量,并能大大减少待定参数个数,提高估值精度.研究表明,该方法具有良好的方法统计特性,能耐受较大的实验误差。本文还提出了新的八碳芳烃临氢异构化和六碳组份重整体系的反应网络,应用试差矩阵法成功地研究了这两个体系的双曲型动力学模型,求取了各模型参数,模型拟合值与实验值能很好地吻合.     

STOCHASTIC ANALYSIS OF AXIAL SOLIDS MIXING IN A FLUIDIZED BED

Particulate mixing systems lend themselves to a stochastic analysis due to the finite number of discrete particles involved. The physics of mixing at a single particle level can best be seen as a random process since the trajectory of the particle is influenced by many competing factors. In this work, a stochastic model for axial mixing of particles in a fluidized bed is formulated by resorting to the multivariate master equation. Configuration of the bed is cylindrical; it is divided into small axially distributed compartments. The behavior of the bed following the addition of tracer particles to the top of the bed is studied. Experimental data from Qu and Kwauk (1985) are used to estimate the single parameter in the model. Expressions are derived for the mean tracer concentration as well as its variance. The density function of the first passage time for a tracer particle to reach the bottom of the bed is derived, and other extreme value statistics are discussed. A maximum likelihood estimator of the axial dispersion coefficient based on the first passage time for a single tracer particle between two points in the bed is also derived.     

A UNIFIED APPROACH TO ARMA MODEL IDENTIFICATION AND PRELIMINARY ESTIMATION

Abstract. This paper reviews several different methods for identifying the orders of autoregressive-moving average models for time series data. The case is made that these have a common basis, and that a unified approach may be found in the analysis of a matrix G, defined to be the covariance matrix of forecast values.
The estimation of this matrix is considered, emphasis being placed on the use of high order autoregression to approximate the predictor coefficients. Statistical procedures are proposed for analysing G, and identifying the model orders.
A simulation example and three sets of real data are used to illustrate the procedure, which appears to be a very useful tool for order identification and preliminary model estimation.     

A NEW CORRELATION FOR THE PARAMETERS IN A VAN DER WAALS-TYPE EQUATION OF STATE FOR SIMPLE LIQUIDS

We present a new method based on a corresponding-states approach to evaluate the equation-of-state parameters of a van der Waals-type equation of state which is valid for simple, non-polar molecules, both spherical and non-spherical, and their mixtures. The proposed method, which has been tried on fourteen liquids, predicts well pure component liquid molar volumes over a large temperature range. The method's predictive capability of the excess thermodynamic functions (G^E, H^E, and V^E) has also been tested on fourteen liquid mixtures and the results compare favorably with those of other more sophisticated treatments.     

PERFORMANCE OF AN ANNULAR CATALYTIC THREE-PHASE REACTOR FOR A SECOND ORDER REACTION

A novel annular catalytic three-phase reactor is theoretically investigated for a second order hydrogenation reaction. The results indicate that the ratio of the gaseous reactant to the liquid reactant within the reaction zone of the annular reactor can be adjusted by changing the reactor dimensions and the concentration of the gaseous reactant in the feed. As a consequence, the annular reactor may have a significant advantage over the trickle-bed reactor with respect to the selectivities that may be achieved in the reactor.     

SENSITIVITY AND UNCERTAINTY OF PROCESS DESIGNS TO THERMODYNAMIC MODEL PARAMETERS: A MONTE CARLO APPROACH

Process simultalion relies heavily on the calculation of physical properties through thermodynamic models. The parameters in these models are subject to uncertainties that may, at first, appear to be small. However, the designs developed through use of these models can be significantly sensitive to these parameter uncertainties. Previous studies have considered special cases of design error or have involved simple sensitivity analyses close to the optimum design case. In the present work, we use Monte Carlo simulation with Latin Hypercube Sampling to quantify the probability of design errors. An example of binary distillation with phase-equilibrium calculations from a cubic equation of state is used to illustrate the technique.     

MASS TRANSFER WITH A FIRST ORDER CATALYTIC REACTION IN A THREE-PHASE SYSTEM. TRICKLE FLOW ANALYSIS IN A PERIODICALLY CURVED CATALYTIC SOLID

The present work analyzes the process of mass transfer with chemical reaction in a system formed by a periodically curved catalytic wall, which is wetted by a descending film. Through the film a limiting gaseous reactant is transferred from the stagnant gas phase to the catalyst where the chemical reaction takes place.

The film hydrodynamics is first solved with the unknown free surface through a regular perturbation technique, by expanding the resulting equations in terms of a small parameter: the ratio between the film average thickness and the wave length of the curved solid wall. Assuming that the system is isothermal and at steady state, the mass transfer of the gas is afterwards incorporated. A first order kinetics whose limiting reactant is in the gas phase occurs in the solid phase.

Once the model is established and solved, the influence of the dimensionless parameters upon the effectiveness factor and the solid-liquid Biot number is then studied; important effects are found by changing the solid surface curvature at constant flow rate and catalyst volume. Besides, changes in the flow rate, the Peclet number and the ratio between the solid average width and the film average thickness, show significant effects on the net mass transfer process.