Given the fact that in parameter estimation we normally have a relatively smooth LS objective function, we do not need to be exceptionally concerned about local optima (although this may not be the case for ill-conditioned estimation problems). This is particularly true if we have a good idea of the range where the parameter values should be. As a result, it may be more efficient to consider using a value for NR which is a function of the number of unknown parameters. For example, we may consider [Pg.80]

Given an EoS, the objective of the parameter estimation problem is to compute optimal values for the interaction parameter vector, k, in a statistically correct and computationally efficient manner. Those values are expected to enhance the correlational ability of the EoS without compromising its ability to predict the correct phase behavior. [Pg.229]

STUDY EXECUTION AND IMPACT ON PARAMETER ESTIMATION EFFICIENCY [Pg.324]

The random variable values 0 are more centered around the population parameter than the 02 ones (i.e. estimations). This means that the average error made in multiple population parameter estimation by means of 0 will be smaller than when we do the same for 02. The 0 estimation can be said to be more efficient. [Pg.32]

Central composite designs are relatively efficient for small numbers of factors. Efficiency in this case means obtaining the required parameter estimates with little wasted effort. One measure of efficiency is the efficiency value, E [Pg.249]

Serth, R.W, B. Srikanth, and S.J. Maronga, Gross Error Detection and Stage Efficiency Estimation in a Separation Process, AlChE Journal, 39(10), 1993, 1726-1731. (Physical model development, parameter estimation) [Pg.2545]

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]

These partial derivatives provide a lot of information (ref. 10). They show how parameter perturbations (e.g., uncertainties in parameter values) affect the solution. Identifying the unimportant parameters the analysis may help to simplify the model. Sensitivities are also needed by efficient parameter estimation procedures of the Gauss - Newton type. Since the solution y(t,p) is rarely available in analytic form, calculation of the coefficients Sj(t,p) is not easy. The simplest method is to perturb the parameter pj, solve the differential equation with the modified parameter set and estimate the partial derivatives by divided differences. This "brute force" approach is not only time consuming (i.e., one has to solve np+1 sets of ny differential equations), but may be rather unreliable due to the roundoff errors. A much better approach is solving the sensitivity equations [Pg.279]

The solution developed is able to solve the scheduling problem very efficiently, resulting in good and realistic schedules. Of course, the solution quality depends to a great deal on how well the parameter estimation matches with the production process. More illustrations on the solution can be found in [5]. [Pg.107]

Consider all alternatives for estimation in terms of reliability, accuracy, time required, and cost efficiency. Develop predictive models that allow for in silico screening, rather than necessitating prior synthesis of compound. Analyze literature for both pharmacokinetic and toxicokinetic parameter estimation, to identify models that already exist or ones that could be suitably modified for the parameter of interest [Pg.263]

Three parameters thus need to be estimated, namely the scalar factor a, the compression factor c, and the shift d. Parameter b was dropped for two reasons (1) the effect of this exponent is to be explored, so it must remain fixed during a parameter-fitting calculation, and (2) the parameter estimation decreases in efficiency for every additional parameter. Therefore the model takes on the form [Pg.209]

In summary while conceptually appealing, the application of complex multi-solute models for Sr sorption to zeolite is in the early stages of development. While preliminary results are encouraging, additional work is required to develop more efficient computational methods and develop an improved database for parameter estimation. The remainder of this section focuses on the simpler retardation factor approach. [Pg.130]

The relative efficiencies have also been obtained by comparing these relative errors to the smallest value of the other estimates for each case studied. The smaller the relative error, the better the model parameter estimation the larger the relative efficiency, the better the estimator. Results are listed in Table 1 for the uniform and t2 distributions. [Pg.228]

The PULSAR units are high efficiency static aerators that have been developed for municipal wastewater treatment plants and have successfully been used over extended periods of time without any operational problems such as unstable operation or plugging up during intermittent operation of the air pumps (Chourda-kis, 1999). Data have been collected from a pilot plant unit at the Wastewater Treatment plant of the Industrial Park (Herakleion, Crete). A series of experiments were conducted for the determination of the mass transfer coefficient (kLa) and are shown in Figure 17.4. The data are also available in tabular form as part of the parameter estimation input files provided with the enclosed CD. [Pg.327]

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