By Peter Englezos

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

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**Sample text**

Besides the minimization of the objective function (a weighted sum of errors) the mathematical model of the physical process includes a set of constrains that must also be satisfied. In general these are either equality or inequality constraints. In order to avoidunnecessary complications in thepresentation of the material, constrained parameterestimation is presented exclusively i n Chapter 9. I 3 Computation of Parameters in Linear Models - Linear Regression Linear models with respect to the parameters represent the simplest case of parameter estimation from a computational pointof view because there is no need for iterative computations.

The interaction parameters are usuallyestimatedfromtheregression of binary vapor-liquid equilibrium (VLE) data. Such data consist of sets o f temperature, pressure and liquid and vapor phase mole fractions for one of the components. Typical examples such as the ones mentioned above, are used throughout this book and they cover most of the applications chemical engineers are faced with. In addition to the problem definition, the mathematical developtnent and the numerical results, the implementation of each algorithm is presented in detail and computer listings of selected problems are given in the attached CD.

The category of algebraic equation models is quite general and it encompassesmany types of engineering models. For example, any discrefe cfynamic model described by a set of difference eqzrations falls in this category for parameter estimation purposes. ic in nature or even conlbinations of the two. Although on-line techniques are available for the estimation of parameters in sampled data systems, off-line techniques , Formulation Parameter Estimation of the 11 Probleiii such as the ones emphasized in this book are very useful and they can be employed when all the data are used together after the experiment is over.