Applied Parameter Estimation for Chemical Engineers by Peter Englezos

By Peter Englezos

This ebook determines adjustable parameters in mathematical types that describe regular country or dynamic platforms, featuring an important optimization equipment used for parameter estimation. It makes a speciality of the Gauss-Newton strategy and its variations for platforms and tactics represented by means of algebraic or differential equation versions.

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Example text

In several cases, the measurements could even be pools of several species present in the reactor. ,N. The initial condition x0, is also chosen by the experimentalist and it is assumed to be precisely known. It represents a very important variable from an experimental design point of view. 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.

7) where e; is the m- dimensional vector of residuals from the ith experiment. 2 using the estimated parameter values instead of their true values that yield the error terms EJ. The LS objective function takes the form, where Q, is an mxm user-supplied weighting matrix. d) normally with zero mean and variance, 0^ . Namely, £(Sj) = 0 and COK(Sj) = a ^ I where I is the mxm identity matrix. ,m) are independently distributed normally with zero mean and constant variance. ,v m are known constants. 13) Generalized Least Squares (GLS) Estimation In this case we minimize a weighted SSE with non-constant weights.

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. 32) ) In addition, the corresponding estimate of the unknown covariance is E = — It is worthwhile noting that Box and Draper (1965) arrived at the same determinant criterion following a Bayesian argument and assuming that L is unknown and that the prior distribution of the parameters is noninformative.

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