Model parameters, estimates

The third example shows how the uncertainties in plant measurements compromise the model parameter estimates. Minimal temperature differences, veiy low conversions, and hmited separations are all instances where errors in the measurements will have a greater impact on the parameter estimate. 

Model parameters estimated by linear regression, weighted linear regression, and unweighted non-linear regression are shown in Table B-1. 

Duever, T.A., S. E. Keeler, P.M. Reilly, J.H. Vera, and P.A. Williams, "An Application of the Error-In-Variables Model-Parameter Estimation from van Ness-type Vapour-Liqud Equilibrium Experiments", Chem. Eng Sci., 42, 403-412 (1987). 

Model parameter estimation by laboratory, microcosm, or pilot plant studies followed by field application. 

Buzzi-Ferraris, G., and Donati, G. 1974. A powerful method for Hougen-Watson model parameter estimation with integral conversion data. Chem. Eng. Sci. 29 1504-9. 

The relative efficiencies have also been obtained by comparing these relative errors to the smallest value of the other estimates for each case studied. The smaller the relative error, the better the model parameter estimation the larger the relative efficiency, the better the estimator. Results are listed in Table 1 for the uniform and t2 distributions. 

Model validation is a process that involves establishing the predictive power of a model during the study design as well as in the data analysis stages. The predictive power is estimated through simulation that considers distributions of PK, PD, and study-design variables. A robust study design will provide accurate and precise model-parameter estimations that are insensitive to model assumptions. 

Li H, Watanabe K, Auslander D, Spear RC. 1994. Model parameter estimation and analysis Understanding parametric structure. Ann Biomed Eng 22 97-1 II. 

The ANOVA table shown in Table 2.14 indicates that there was no significant lack-of-fit of the model. Parameter estimates and t-statistics for this model are shown in Table 2.15. 

Hayes, K. F., Redden, G., Ela, W. Leckie, J. O. 1991. Surface complexation models an evaluation of model parameter estimation using FITEQL and oxide mineral titration data. Journal of Colloid and Interface Science, 142, 448-469. 

Since the orthogonal collocation or OCFE procedure reduces the original model to a first-order nonlinear ordinary differential equation system, linearization techniques can then be applied to obtain the linear form (72). Once the dynamic equations have been transformed to the standard state-space form and the model parameters estimated, various procedures can be used to design one or more multivariable control schemes. 

Figure 18. Values of Gazs, 1 calculated from solution model parameters estimated by fitting the phase diagram. Data are from references 144 (-),...

Figure 20. Values of GW11 versus reciprocal temperature. Values were calculated with simple-solution model parameters estimated by a Jit to the combined data set (— —) and nearly coincident with the recommended values, liquidus data only (—), liquidus and activity data (— —), and liq-uidus and enthalpy of mixing data ( ) The recommended values are indicated by —.

Table 14.4 Cetuximab population pharmacokinetic analysis final model parameter estimates.

Value/origin of model parameters Estimated based on data available Estimated using combined datasets or taken from different sources (e.g. databases, literature, own experiments)... 

Variability and standard error of model parameters Estimated Estimated or approximated or unknown... 

This chapter presents an overview of reactive absorption, which is one of the most important industrial reactive separation operations. Industrially relevant systems and equipment are highlighted, the modeling basics and peculiarities are detailed, and the methods of model parameter estimation are discussed. Both steady-state and dynamic modeling issues are addressed. The implementation of the theoretical description is illustrated with a number of up-to-date applications and validated against laboratory-, pilot- and industrial-scale experiments. 

Despite highly developed computer technologies and numerical methods, the application of new-generation rate-based models requires a high computational effort, which is often related to numerical difficulties. This is a reason for the relatively limited application of modeling methods described above to industrial problems. Therefore, a further study in this field - as well as in the area of model parameter estimation - is required in order to bridge a gap and to provide process engineers with reliable, consistent, robust and user-friendly simulation tools for reactive absorption operations. 

Another optimization approach was followed by Wagner [68 ]. Wagner developed a methodology for performing simultaneous model parameter estimation and source characterization, in which he used an inverse model as a non-linear maximum likelihood estimation problem. The hydrogeologic and source parameters were estimated based on hydraulic head and contaminant concentration measurements. In essence, this method is minimizing the following ... 

The process of research in chemical systems is one of developing and testing different models for process behavior. Whether empirical or mechanistic models are involved, the discipline of statistics provides data-based tools for discrimination between competing possible models, parameter estimation, and model verification for use in this enterprise. In the case where empirical models are used, techniques associated with linear regression (linear least squares) are used, whereas in mechanistic modeling contexts nonlinear regression (nonlinear least squares) techniques most often are needed. In either case, the statistical tools are applied most fruitfully in iterative strategies. 

NLLS or CNLS starts with the selection of the equivalent circuit, followed by the initial value estimation for all the model parameters. Estimation of the initial values is one of the most difficult tasks in the analysis of an equivalent circuit model. A good initial value estimation needs a sohd understanding of the element behaviours in the circuit. If the initial estimations are far from the real values , the optimum fit may not be found. An estimated value within a factor of ten of the true value is a good start for determining a model parameter [7],... 

Thus far, the transport model, after incorporation of equilibrium or kinetic retention, was used in a calibration mode where, along with nonlinear least-squares approximation, a best fit of the model to the experimental BTC was attempted. This resulted in a set of model parameter estimates that provided the best fit of the BTC for a... 

L. L. Oliveira and E. Biscaia Catalytic cracking kinetic models. Parameter estimation and model evaluation. Industrial and Engineering Chemistry Research, 28, 264-271 (1989). 

Rheological model (a) Is it appropriate for the experimental data (b) How reliable is the model parameter estimation software Has the reliability of the software been checked (c) What are you looking for in the data (e.g., effect of temp.) (d) Compare experimental data with a model s predictions because values often do not indicate the appropriateness of the model for the selected data ... 

Figure 5. Solubility isotherms of lipid components at 323 K plotted using model parameters estimated using Equation 2.

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