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** Iterative procedure for parameter **

Fig. 2.29 Iterative procedure for parameter estimation, sensitivity analysis and experimentation. |

Point wise calculation of multi-component isotherm qA(cA,CB), qB(cA,cB) for the given mixture composition (cA,cB) by means of a parameter estimation problem (iterative procedure) [Pg.40]

With more than two variables the L terms are simply expanded to include more terms. For a two-parameter equation the size of the matrix remains 2. For a six-parameter equation with two variables, the size of the matrix is a symmetrical 6x6. Thus, only 27 sums need be calculated. The 6x6 square matrix is inverted and multiplied by the 1x6 matrix to obtain corrections in the six parameters. These are then adjusted and the process iterated to convergence. The iteration is controlled with a Visual Basic Macro. The rigorous inclusion of estimates for parameters from other experiments is easily incorporated into this procedure. The parameters and errors must be input. Next the program simply adds terms to the appropriate sums. For example, if the value of a has been determined to be ax with an uncertainty of sa, then the quantity 1 / (sa sa) is added to [a a ] and this quantity is multiplied by (aest —ax) and added to /-oa ] The adjustment is made as before, as are the parameters and uncertainties obtained. This has been demonstrated by Wentworth, Hirsch, and Chen [Chapt. 5, 37], [Pg.344]

Model parameters are usually determined from expterimental data. In doing this, sensitivity analysis is valuable in identifying the experimental conditions that are best for the estimation of a particular model parameter. In advanced software packages for parameter estimation, such as SIMUSOLV, sensitivity analysis is provided. The resulting iterative procedure for determining model parameter values is shown in Fig. 2.39. [Pg.114]

Iteration for Coexisting Densities. Orthobaric densities near the critical point generally cannot be obtained accurately from isochoric PpT data by extrapolation to the vapor-pressure curve because the isochore curvatures become extremely large near the critical point. The present, nonanalytic equation of state, however, can be used to estimate these densities by a simple, iterative procedure. Assume that nonlinear parameters in the equation of state have been estimated in preliminary work. For data along a given experimental isochore (density), it is necessary merely to find the coexistence temperature, Ta(p), by trial (iteration) for a best, least-squares fit of these data. [Pg.360]

** Iterative procedure for parameter **

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