Arora, N., Biegler, L. T., 2001. Redescending estimators for Data Reconciliation and Parameter Estimation. Comput. Chem. Eng. 25, 1585. [Pg.506]

Using the method just described, the van Laar equation, and a parameter estimation computer program with the objective function of Eq. 10.2-16, we find. [Pg.540]

If we consider the relative merits of the two forms of the optimal reconstructor, Eq. s 16 and 17, we note that both require a matrix inversion. Computationally, the size of the matrix inversion is important. Eq. 16 inverts an M x M (measurements) matrix and Eq. 17 a P x P (parameters) matrix. In a traditional least squares system there are fewer parameters estimated than there are measurements, ie M > P, indicating Eq. 16 should be used. In a Bayesian framework we are hying to reconstruct more modes than we have measurements, ie P > M, so Eq. 17 is more convenient. [Pg.380]

FIGURE 16.5 Saccadic eye movement in response to a 15° target movement. Solidline is the prediction of the saccadic eye movement model with the final parameter estimates computed using the system identification techniques. Dots are the data. (From Enderle, J.D. and Wolfe, J.W. 1987. IEEE Trans. Biomed. Eng. 34 43-55. With permission.) [Pg.260]

Parameter Estimation. WeibuU parameters can be estimated using the usual statistical procedures however, a computer is needed to solve readily the equations. A computer program based on the maximum likelihood method is presented in Reference 22. Graphical estimation can be made on WeibuU paper without the aid of a computer however, the results caimot be expected to be as accurate and consistent. [Pg.13]

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. [Pg.21]

Because of these limitations, different models may appear to describe the unit operation equally well. Analysts must discriminate among various models with the associated parameter estimates that best meet the end-use criteria for the model development. There are three principal criteria forjudging the suitability of one model over another. In addition, there are ancillary criteria like computing time and ease of use that may also contribute to the decision but are not of general concern. [Pg.2578]

Experimental isotherm data for the adsorption of four solutes, phenol, p-bromophenol, p-toluene sulfonate, and dodecyl benzene sulfonate onto activated carbon are shown in Figures 1 to 4. The isotherm constants are estimated using a nonlinear parameter estimation program, and are shown in Table 1. The parameter estimation program uses the principal axis method to obtain the parameters, a, b and 3 that will minimize the sum of the squares of the differences between experimental and computed isotherm data. [Pg.30]

These problems refer to models that have more than one (w>l) response variables, (mx ) independent variables and p (= +l) unknown parameters. These problems cannot be solved with the readily available software that was used in the previous three examples. These problems can be solved by using Equation 3.18. We often use our nonlinear parameter estimation computer program. Obviously, since it is a linear estimation problem, convergence occurs in one iteration. [Pg.46]

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