Coefficient of model uncertainty

In some cases, in particular for non-linear analysis or the design of coimections, the effect of the randomness of the intensity of the actions and the uncertainty associated with the analytical procedures, e.g. the models used in the calculations, should be considered separately. This may be achieved by the application of a coefficient of model uncertainty. Cm, appUed either to the actions or to the internal forces and moments, or incorporated in the design expression or condition to be satisfied, provided that the purpose and value of such a factor are defined where used. 

For FRP composite design, such uncertainties in the assessment of the structural response to actions can vary more than for other structural materials. Nevertheless, it is desirable for the same or a similar set of partial safety factors for permanent actions and variable actions to be used in the EUROCOMP Design Code as in the Eurocodes generally. Therefore, in the EUROCOMP Design Code, the supplementary yc,2 and yg,2 factors are, wherever possible, incorporated into the design expressions for conditions that must be satisfied for compliance with the EUROCOMP Design Code by means of the coefficient of model uncertainty (see 22.2.5). 

The coefficient of model uncertainty is variously denoted as C, Cx or K in the text or, exceptionally, for approximate formulae, is incorporated in the numeric coefficients. 

These equations identify the dominant source and loss processes for HO and H02 when NMHC reactions are unimportant. Imprecisions inherent in the laboratory measured rate coefficients used in atmospheric mechanisms (for instance, the rate constants in Equation E6) can, themselves, add considerable uncertainty to computed concentrations of atmospheric constituents. A Monte-Carlo technique was used to propagate rate coefficient uncertainties to calculated concentrations (179,180). For hydroxyl radical, uncertainties in published rate constants propagate to modelled [HO ] uncertainties that range from 25% under low-latitude marine conditions to 72% under urban mid-latitude conditions. A large part of this uncertainty is due to the uncertainty (la=40%) in the photolysis rate of 0(3) to form O D, /j. 

For turbulent flow in single-phase systems, the predicted temperature profile is not changed significantly if the Peclet number is assumed to be infinite. Therefore, in turbulent two-phase systems the second-order terms in Eqs. (9) probably do not have a significant effect on the resulting temperature profiles. In view of the uncertainties in the present state of the art for determining the holdups and the heat-transfer coefficients, the inclusion of these second-order terms is probably not justified, and the resulting first-order equations should adequately model the process. 

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. 

Mathematical model that describes the relationship between random variables (usually x and y) by means of regression coefficients and their uncertainties as well as uncertainties of model and the prediction. 

Although the coefficients of determination and the correlation coefficients are conceptually simple and attractive, and are frequently used as a measure of how well a model fits a set of data, they are not, by themselves, a good measure of the effectiveness of the factors as they appear in the model, primarily because they do not take into account the degrees of freedom. Thus, the value of R can usually be increased by adding another parameter to the model (until p =J), but this increased R value does not necessarily mean that the expanded model offers a significantly better fit. It should also be noted that the coefficient of determination gives no indication of whether the lack of perfect prediction is caused by an inadequate model or by purely experimental uncertainty. 

In general, the coefficients of variation decrease with smaller values of 02. This is definitely desirable since it indicates that for higher expected profits there is diminishing uncertainty in the model, thus signifying model and solution robustness. It is also observed that for values of 02 approximately greater than or equal to 2, the coefficient of variation remain at a static value of 0.5237, thus indicating overall stability and a minimal degree of uncertainty in the model. 

The Effect of Imperfect Sampling. Let St be the random variable which estimates the true value of the lognormally distributed random variable (x). The value of (St) is determined by sampling (x) and analyzing with a process which has inherent uncertainty associated with it. The uncertainty is described by the coefficient of variation of the analysis, CV. If CV < 0.3, then %) can be modelled adequately as a lognormally distributed random varible characterized by GM and GSV as defined below (1). 

Estimates of modeled parameters of particular oceanic processes of the carbon cycle range widely. For instance, from the data of various authors the estimates of assimilation of carbon from the hydrosphere in the process of photosynthesis range from 10 GtC/yr to 155 GtC/yr. The value 127.8 GtC/yr is most widely used. However, because of large variations in these estimates, calculation of the C31 coefficient is fraught with great uncertainty therefore, specifying it requires numerical experiments using other, more accurate data. 

Since the dynamics of a batch reactor is characterized by a unitary relative order, the GMC law can be adopted [6, 14, 22, 40, 42, 65], In order to cope with model uncertainties, adaptive GMC approaches have been developed [56, 60, 62] in [27] some unknown quantities—namely, the effect of the heat released by the reaction and the heat transfer coefficient—are estimated by adopting the nonlinear adaptive observer proposed in [24] in [63], an ANN-based GMC approach is presented for semi-batch processes with relative order higher than one. 

Often there are cases where the submodels are poorly known or misunderstood, such as for chemical rate equations, thermochemical data, or transport coefficients. A typical example is shown in Figure 1 which was provided by David Garvin at the U. S. National Bureau of Standards. The figure shows the rate constant at 300°K for the reaction HO + O3 - HO2 + Oj as a function of the year of the measurement. We note with amusement and chagrin that if we were modelling a kinetics scheme which incorporated this reaction before 1970, the rate would be uncertain by five orders of magnitude As shown most clearly by the pair of rate constant values which have an equal upper bound and lower bound, a sensitivity analysis using such poorly defined rate constants would be useless. Yet this case is not atypical of the uncertainty in rate constants for many major reactions in combustion processes. 

Within the Standard Model, ae is not sensitive to the short-distance effects. Thus ae is used primarily to test the renormalization theory of QED. Our current goal for ae is to calculate the coefficient of the a4 term to a precision of 0.01. This corresponds to the uncertainty of 0.3 x 10-12 in ae. With the matching improvement in experiment, this will provide a with a precision of 10-9 or better. How far can we go beyond this It is certainly feasible and desirable to improve it further by another factor of 4. This is just a matter of computer time. (It will require about 10 million hours of computing time.) However, improving the a4 term much further will not make sense until the tenth-order term is evaluated or estimated reliably which will be of the order of... 

The stochastic error is expressed in (9.23) by the variance Var [Aj (t)] and co-variance Cov [Nj (t) Nk (t)] that did not exist in the deterministic model. This error could also be named spatial stochastic error, since it describes the process uncertainty among compartments for the same t and it depends on the number of drug particles initially administered in the system. For the sake of simplicity, assume riQi = uq for each compartment i. From the previous relations, the coefficient of variation CVj (t) associated with a time curve Nj (t) in compartment 3 is... 

Central to Bayesian approaches is the treatment of model parameters, such as the vector of regression coefficients (3, as random variables. Uncertainty and expert knowledge about these parameters are expressed via a prior distribution. The observed data give rise to a likelihood for the parameters. The likelihood and... 

In all three documents concern is raised about the validity and relevance of models used to predict exposures, such as EUSES, which rely on the substance s lipophilicity as estimated by its octanol-water partitioning coefficient (Kow) and other chemical characteristics. The reason for this is that these models are generally not applicable to substances with a very high lipophilicity. Furthermore, the determination of some main physico-chemical properties such as lipophilicity, water solubility and vapour pressure is also stated as sources of uncertainty for substances with very high lipophilicity. 

For simply producing the magnitude of observed excesses, both dynamic melting models and transport models are viable. The largest uncertainty in either type of model is the appropriate partition coefficients (and D as a function of pressure) as these control the inferences on the porosity through the parameter D (f>. The more stringent tests on these models, however, come from the observed correlations... 

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