Modeling sensitivity analysis

Kilduff, J.E., Karanfil, T., and Weber, W.,Jr (1998). Competitive effects ofnon-displacable organic compounds on trichloroethylene uptake by activated carbon. I. Thermodynamic predictions and model sensitivity analysis. /. Colloid Interface Sd., 205, 271-9. 

Theoretically, the stability of HOOCl intermediate and its stmctural isomers have been studied by Franciso et al. [70], and Lee and Rendell [71]. Sumathi and Peyerimhoff [72] calculated the potential energy surface (PES) of the reaction and concluded that reaction (6b) was less important because of the high barrier. Dubey et al. [73] performed a box-model sensitivity analysis using the recommended value [74] of k(, and found that the transition state (see TS5 in Fig. 17 later) for HCl production must lie at least... 

Keywords large SOFC generator, experimental activity, design of experiment, regression models, sensitivity analysis, polarization effects. 

Fig. 12. Model sensitivity analysis. Sutfur retention as a function of air ratio X.

In the evaluation of the model, sensitivity analysis, i.e. the change in model output due to uncertainties in parameter values, is important. 

Sensitivity Analysis When solving differential equations, it is frequently necessary to know the solution as well as the sensitivity of the solution to the value of a parameter. Such information is useful when doing parameter estimation (to find the best set of parameters for a model) and for deciding if a parameter needs to be measured accurately. See Ref. 105. 

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. 

Once the model parameters have been estimated, analysts should perform a sensitivity analysis to establish the uniqueness of the parameters and the model. Figure 30-9 presents a procedure for performing this sensitivity analysis. If the model will ultimately be used for exploration of other operating conditions, analysts should use the results of the sensitivity analysis to estabhsh the error in extrapolation that will result from database/model interactions, database uncertainties, plant fluctuations, and alternative models. These sensitivity analyses and subsequent extrapolations will assist analysts in determining whether the results of the unit test will lead to results suitable for the intended purpose. 

The Important Sequence Model module does sensitivity studies and importance rankings for about a thousand highest frequency sequences. The analyst zooms to the most frequent plant damage category, to the most frequent sequences in that category, to the most important top event, to the most important split fraction, and to the most important cutsets. If sensitivity analysis is needed on the model as a whole, a menu option, "CLONE a Model," makes a copy of the model, c hange,s are made, and results compared. 

Once the model was complete, it was adjusted to a steady state condition and tested using historic carbon isotope data from the atmosphere, oceans and polar ice. Several important parameters were calculated and chosen at this stage. Sensitivity analysis indicated that results dispersal of the missing carbon - were significantly influenced by the size of the vegetation carbon pool, its assimilation rate, the concentration of preindustrial atmospheric carbon used, and the CO2 fertilization factor. The model was also sensitive to several factors related to fluxes between ocean reservoirs. 

The modeling of steady-state problems in combustion and heat and mass transfer can often be reduced to the solution of a system of ordinary or partial differential equations. In many of these systems the governing equations are highly nonlinear and one must employ numerical methods to obtain approximate solutions. The solutions of these problems can also depend upon one or more physical/chemical parameters. For example, the parameters may include the strain rate or the equivalence ratio in a counterflow premixed laminar flame (1-2). In some cases the combustion scientist is interested in knowing how the system mil behave if one or more of these parameters is varied. This information can be obtained by applying a first-order sensitivity analysis to the physical system (3). In other cases, the researcher may want to know how the system actually behaves as the parameters are adjusted. As an example, in the counterflow premixed laminar flame problem, a solution could be obtained for a specified value of the strain... 

Once a model has been fitted to the available data and parameter estimates have been obtained, two further possible questions that the experimenter may pose are How important is a single parameter in modifying the prediction of a model in a certain region of independent variable space, say at a certain point in time and, moreover. How important is the numerical value of a specific observation in determining the estimated value of a particular parameter Although both questions fall within the domain of sensitivity analysis, in the following we shall address the first. The second question is addressed in Section 3.6 on optimal design. 

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 ( ).

In the described MC simulation, the action of several simultaneous sources of variation is considered. The explanation of the different time courses of parameter influence on volume size between sensitivity and MCCC analyses lies in the fact that classic sensitivity analysis considers variations in model output due exclusively to the variation of one parameter component at a time, all else being equal. In these conditions, the regression coefficient between model output and parameter component value, in a small interval around the considered parameter, is approximately equal to the partial derivative of the model output with respect to the parameter component. 

Iman RL, Helton JC, Campbell JE. An approach to sensitivity analysis of computer models Part II—Ranking of input variables, response surface validation, distribution effect and technique synopsis. / Quality Technol 1981 13 232-40. 

Bayesian networks for multivariate reasoning about cause and effect within R D with a flow bottleneck model (Fig. 11.6) to help combine scientific and economic aspects of decision making. This model can, where research process decisions affect potential candidate value, further incorporate simple estimation of how the candidate value varies based on the target product profile. Factors such as ease of dosing in this profile can then be causally linked to the relevant predictors within the research process (e.g., bioavailability), to model the value of the predictive methods that might be used and to perform sensitivity analysis of how R D process choices affect the expected added... 

Nestorov lA, Aarons LJ, Rowland M. Physiologically based pharmacokinetic modeling of a homologous series of barbiturates in the rat a sensitivity analysis. / Pharmacokinet Biopharm 1997 25 413-47. 

In all analyses, there is uncertainty about the accuracy of the results that may be dealt with via sensitivity analyses [1, 2]. In these analyses, one essentially asks the question What if These allow one to vary key values over clinically feasible ranges to determine whether the decision remains the same, that is, if the strategy initially found to be cost-effective remains the dominant strategy. By performing sensitivity analyses, one can increase the level of confidence in the conclusions. Sensitivity analyses also allow one to determine threshold values for these key parameters at which the decision would change. For example, in the previous example of a Bayesian evaluation embedded in a decision-analytic model of pancreatic cancer, a sensitivity analysis (Fig. 24.6) was conducted to evaluate the relationship... 

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. 

In a silane-hydrogen discharge the feedstock gases SiHa and H2 take part in all the processes that occur. A large number of reactions have been proposed (see e.g. Kushner [190]). Nienhuis et al. [191] have performed a sensitivity analysis in their self-consistent fluid model, from which a minimum set of reactions have been extracted for a typical low-pressure RF discharge. Tables II and III list these reactions. They will be used in the plasma models described in subsequent sections. The review articles on silane chemistry by Perrin et al. [192] and on hydrogen by Phelps [193] and Tawara et al. [194] have been used. The electron collision data are compiled in Figure 13 [189]. 

Sensitivity analysis. A possible cause for the discrepancy between experiment and model is an error in the elementary parameters (reaction coefficients, cross sections, and transport coefficients) which are obtained from the literature. With a sensitivity study it is possible to identify the most important processes [189]. 

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.)...

Table VII shows a sensitivity analysis on the SWRRB model. It can be seen that the intensity of the rainfall is one of the most important parameters affecting runoff.

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