Sensitivity parameters, values

Preliminary Analysis The purpose of the preliminary analyses is to develop estimates for the model parameter values and to estabhsh the model sensitivity to the underlying database and plant and model uncertainties. This will estabhsh whether the unit test will actually achieve the desired results. 

The goal here is to determine the (relative) effect of a variation in a given parameter value on the model prediction. Let y= u(X, 0) + e be the considered model, with y 6 V and 0 6 0 c V . We study the sensitivity of the modeling function u with respect to the parameter 0 by means of the (absolute)... 

Figure 3.6c Sensitivity analysis correlations of time points with parameter values. Each curve refers to one model structural parameter a (+), b (open circles), and Vo ( ).

Sensitivity analysis is a very important tool in analysing the relative importance of the model parameters and in the design of experiments for their optimal determination. In many cases, it is be found that a model may be rather insensitive to a particular parameter value in the region of main interest, and then the parameter obviously does not need to be determined very accurately. 

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. 

Figure 5 A sensitivity analysis for the Barber-Cushinan model for the uptake of P by maize in Raub soil. The. sensitivity was analysed by halving and doubling each parameter value in turn while keeping all other parameters at their standard values. (From Ref. 103.)...

Figure 6 Sensitivity analysis of maize seedlings to some model parameter values during the first 10 days of uptake. The curves show how phosphorus flux (F) into the roots responds to differential perturbation to the parameters, a (i.e., 5F/8a). (Model parameters are given in Table 1.)...

Therefore, instead of modifying the normal equations, we propose a direct approach whereby the conditioning of matrix A can be significantly improved by using an appropriate section of the data so that most of the available sensitivity information is captured for the current parameter values. To be able to determine the proper section of the data where sensitivity infonnation is available, Kalo-gerakis and Lulls (1983b) introduced the Information Index for each parameter, defined as... 

The current version of CalTOX (CalTOX4) is an eight-compartment regional and dynamic multimedia fugacity model. CalTOX comprises a multimedia transport and transformation model, multi-pathway exposure scenario models, and add-ins to quantify and evaluate variability and uncertainty. To conduct the sensitivity and uncertainty analyses, all input parameter values are given as distributions, described in terms of mean values and a coefficient of variation, instead of point estimates or plausible upper values. 

Due to the tetrahedral arrangement of the windows within the cage, tetrahedral jumps of the cations are feasible. This jump model is confirmed by the averaged parameters obtained by lineshape simulations of the broad lines at 295 and 813 K. Cq is reduced at 813 K to about half of its original value at 295 K, and the averaged asymmetry parameter, (77), is 1. Especially (77) is a very sensitive parameter on jump angle due to the steepness of the curve in Fig. 8a. 

The E-Z Solve software also has a sweep feature that allows the user to perform sensitivity analyses and examine a variety of design outcomes for a specified range of parameter values. Consequently, it is also a powerful design and optimization tool. 

Step 6. You should always be aware of the sensitivity of the optimal answer, that is, how much the optimal value of C changes when a variable such as D changes or a coefficient in the objective function changes. Parameter values usually contain errors or uncertainties. Information concerning the sensitivity of the optimum to changes or variations in a parameter is therefore very important in optimal process design. For some problems, a sensitivity analysis can be carried out analytically, but in others the sensitivity coefficients must be determined numerically. 

Lorazepam The PK-PD modeling of the psychomotor and mnesic effects of a single 2 mg oral dose of lorazepam in healthy volunteers showed that the parameter values derived from PK/PD modeling, and especially the EC values, may provide sensitive indices that can be used, rather than the raw data derived from PD measurements, to compare CNS effects of benzodiazepines... 

Furthermore, as mentioned above the screening of the dipole field by the conduction electrons can be represented by an image dipole inside the metal. This complex of the chemisorbed molecule and its image has a vibration frequency different from that of the free molecule. The electrodynamic interaction between a dipole and its image has been discussed in many works. The theoretical problem is that the calculated frequency shift is extremely sensitive to the position of the image plane (Fig. 3a). One can with reasonable parameter values obtain a downward frequency shift of the order of 5-50 cm S but the latest work indicates that the shift due to this interaction is rather small. 

The RGA is useful for avoiding poor pairings. If the diagonal element in the RGA is negative, the system may show integral instability the same situation that we discussed in the use of the Niederlinski index. Very large values of the RGA indicate that the system can be quite sensitive to changes in the parameter values. 

---