By Peter Englezos
This e-book determines adjustable parameters in mathematical types that describe regular country or dynamic platforms, providing crucial optimization tools used for parameter estimation. It specializes in the Gauss-Newton technique and its variations for platforms and strategies represented through algebraic or differential equation types.
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Extra info for Applied Parameter Estimation for Chemical Engineers (Chemical Industries)
A higher degree of confidence is gained if the adjustable parameters are found from independent sources. , the determination of the unknown parameters). In the formulation of the parameter estimation problem we must answer two questions: (a) what typeof mathematical model dowe have? In this chapter we address both these questions. Although the primary focus of this book is the treatment of mathematical models that are nonlinear with respect to the parameters (nonlinear regression)consideration to linear models(linear regression) will also be given.
1) 23 Chapter 3 24 which can be readily handled by linear least squares estimation. In this model, k is the p-dinlensional parameter vector, x is the rz-cl'itnensionul vector of independent variables (regressor variables), y is the m-dimensionnl vector of dependent variables (response variables) and F(x,) is an mxp dirnensionnl matrix which depends only on x, and is independent of the parameters. This matrix is also the sensitivihf coefficients matrix that plays a very important role in nonlinear regression.
35. This is particularly true when the expression is highly nonlinear. For example, this situation arises in the estimation of parameters for nonlinear thermodynamic models and i n the treatment of potentiometric titration data (Sutton and MacGregor, 1977; Sachs. , 1990a, 1990b). ,)through the error propagation law. 37) The diagonal elements of the covariance matrix(E,) can be obtained From, where the partial derivatives are evaluated at the conditions of the it” experiment. As a result, the elements of the covariance matrix (E,) change from experiment to Formulation of the Parameter Estimation Problem ’ 21 experiment even if we assume that the variance of the measurement error is constant.
Applied Parameter Estimation for Chemical Engineers (Chemical Industries) by Peter Englezos