# Download e-book for iPad: Applied Parameter Estimation for Chemical Engineers by Peter Englezos

By Peter Englezos

ISBN-10: 0585434204

ISBN-13: 9780585434209

ISBN-10: 082479561X

ISBN-13: 9780824795610

This publication determines adjustable parameters in mathematical versions that describe regular kingdom or dynamic platforms, offering crucial optimization equipment used for parameter estimation. It makes a speciality of the Gauss-Newton strategy and its adjustments for structures and strategies represented via algebraic or differential equation types.

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**Extra info for Applied Parameter Estimation for Chemical Engineers (Chemical Industries)**

**Sample text**

E.. 2c) A single experiment consists of the measurementof each of the m response variables for a given set of values of the n independent variables. For each experiment, the measured output vector which can be viewed as a random variable is comprised of the deterministic part calculated by the model (Equation 2. 3 represents only measurement errors. As such, it can often be assumed to be normally distributed with zero mean (assuming there is no bias present in the measurement). In reallife the vector E, incorporates not only the experimental error but also any inaccuracyof the mathematical model.

This approach can actually aid us i n establishing guidelines for the selection of the weighting matrices QIin least squares estimation. Case I: Let us consider the stringent assumption that the error terms in each response variable and for each experiment (qj, i=l,. N; j=l,. d) normally with zero mean and variance, 0: . 23) where I is the m x m identity matrix. 21 yields . 24) Obviously minimization of SML(k)in the above equation does not require the prior knowledge of the common factor 0:. Therefore, under these conditions the ML estimation is equivalent to simple LS estimation (QI=l).

The user-supplied weighting matricesdiffer from experiment to experiment. Of course, it is not at all clear how one shouldselect the weighting matrices Q,, i=l,. ,N, even for cases where a constant weighting matrix Q is used. Practical guidelines for the selection of Q can be derived fiom Maximum Likelihood {ML) considerations. 4MaximumLikelihood(ML)Estimation If the mathematical modelof the processunder consideration is adequate, it is very reasonable to assume that the measured responses fiom the ith experiment are normally distributed.

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