By Peter Englezos
A reference and textbook supplying readers with an important optimization tools for parameter estimation in chemical engineering. The CD-ROM positive factors Fortran desktop courses for fixing equation platforms and different issues of Microsoft Excel and Sigma Plot. comprises over 900 equations in all.
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Additional resources for Applied Parameter Estimation for Chemical Engineers
20) where A is a constant quantity. The maximum likelihood estimates of the unknown parameters are obtained by maximizing the Loglikelihood function. At this point let us assume that the covariance matrices (Zj) of the measured responses (and hence of the error terms) during each experiment are known precisely. ,N) is rather unrealistic. 21. This approach can actually aid us in establishing guidelines for the selection of the weighting matrices Q; in least squares estimation. d) normally with zero mean and variance, Og .
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.
40) The above implicit formulation of maximum likelihood estimation is valid only under the assumption that the residuals are normally distributed and the model is adequate. From our own experience we have found that implicit estimation provides the easiest and computationally the most efficient solution to many parameter estimation problems. , 1990). 41) If the assumption of normality is grossly violated, ML estimates of the parameters can only be obtained using the "error-in-variables" method where besides the parameters, we also estimate the true (error-free) value of the measured variables.