By Peter Englezos
A reference and textbook offering readers with crucial optimization equipment for parameter estimation in chemical engineering. The CD-ROM good points Fortran laptop courses for fixing equation platforms and different issues of Microsoft Excel and Sigma Plot. comprises over 900 equations in all.
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Extra resources for Applied Parameter Estimation for Chemical Engineers
13) As in algebraic models, the error term accounts for the measurement error as well as for all model inadequacies. In dynamic systems we have the additional complexity that the error terms may be autocorrelated and in such cases several modifications to the objective function should be performed. Details are provided in Chapter 8. In dynamic systems we may have the situation where a series of runs have been conducted and we wish to estimate the parameters using all the data simultaneously. For example in a study of isothermal decomposition kinetics, measurements are often taken over time for each run which is carried out at a fixed temperature.
1 Inference on the Parameters The least squares estimator has several desirable properties. 19a. ) are the degrees of freedom, namely the total number of measurements minus the number of unknown parameters. 32a) or where a is the selected probability level in Fisher's F-distribution and ^Nm-p 's obtained from the F-distribution tables with VI=P and v2=(Nw-p) degrees of freedom. 33) where t ^ / 2 is obtained from the tables of Student's T-distribution with v=Nm-p degrees of freedom. The standard error of parameter k,, c k .
26c) where a2 is an unknown scaling factor. 25 are totally unknown, the ML parameter estimates can only be obtained by the determinant criterion presented later in this chapter. Case III: Generalized LS estimation will yield ML estimates whenever the errors are distributed with variances that change from experiment to experiment. ,N. e. 29) where o2 is an unknown scaling factor. 30) The above choice has the computational disadvantage that the weights are a function of the unknown parameters. 20) over k and the unknown variances.