Uncertainty Analysis General Conclusions

In this chapter various methods applicable for sensitivity and uncertainty analyses were reviewed, and the usual definitions of uncertainty information, as given in chemical kinetic databases, were summarised. The uncertainty of chemical kinetic models, calculated from the uncertainty of parameters, was presented, for examples of simulations of a methane flame model. In this section the general features of the various uncertainty analysis methods are reviewed and some general conclusions are made. 

Ideally, an uncertainty analysis method has the following features  

Not surprisingly, such an ideal method that is applicable to all model types does not exist, since the requirements of the various features described above have trade-offs against each other. In reality, the comprehensive analysis of a model may require the combined application of several methods (Tebes-Stevens and Valocchi 2000 Ratto and Paladino 2000). In particular, common practice is to use computationally cheaper methods to screen out unimportant parameters and then subsequently to perform a global analysis on a subset of important input parameters. The features of various available methods are summarised in Table 5.2. 

The FAST method and the computation of the SoboT sensitivity indices do not provide the joint pdf of the model results, but do give information about 

Metamodel or response surface-based methods perhaps provide the best balance between computational intensity and information about the partial variances due to input parameter imcertainties. In many cases, the development of an accurate metamodel can be achieved using a far smaller sample size than that required by FAST or Sobol s basic method. The metamodel is then used for calculating global sensitivity indices. In common with the Sobol method, HDMR, for example, is based on the analysis of variance. Where higher-order terms ( 2) in the HDMR expansion are weak, global sensitivity indices can be achieved using a relatively small quasi-random sample even for large parameter systems. 

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The lack of precision in the above analysis is a consequence of the lack of good GPC calibrants for the polysilanes and the fact that the polymers are substantially non-linear. These factors result in a large margin of uncertainty in the estimates of molecular size by GPC. In addition, the peak areas in the DEPT spectra are not proportional to the number of silicons for different types of H substitution, therefore there is a large margin of uncertainty in the estimate of DPn using this data. Despite these uncertainties, the general conclusion is reasonably well founded. 

Although the measurement uncertainties limit the conclusions which can be drawn from these results, the data set proved useful for the determination of general Influences on rainwater composition In the Seattle area and for the demonstration of the application of these exploratory data analysis techniques. Current efforts to collect and analyze aerosol and rainwater samples over meteorologically appropriate time scales with precise analytical techniques are expected to provide better resolution of the factors controlling the composition of rainwater. 

The previous discussion is quantitatively valid only for the angles and indices of refraction presented, but the analysis and conclusions would qualitatively hold for a general combination of angles and indices of refraction. Also, in practice the uncertainty introduced by the refractive index effect requires that a range of ratio combinations be used in the three-angle discrimination test rather than two exact ratios, but the advantages are still present. The method can also determine refractive indices when inversed. 

There Is one general conclusion I do feel quite comfortable In drawing. Far too much risk assessment that Is done as slngle-value-best-estlmate analysis should In fact be done as probabilistic analysis. There are undoubtedly several reasons for this. Performing probabilistic analysis can get analytically messy. Obtaining subjective Judgmental estimates of uncertain coefficients can be awkward uid Is subject to a variety of pitfalls. And, idille most people appesu to be quite comfortable with such basic notions of uncertainty as "odds" unless care Is taken, the results of probabilistic analysis can become somewhat difficult to communicate to a semi-technical or non-technical audience. 

It is very clear from the complexity of the situations described in the case studies of the last two chapters, that simple factors of safety, load factors, partial factors or even notional probabilities of failure can cover only a small part of a total description of the safety of a structure. In this chapter we will try to draw some general conclusions from the incidents described as well as others not discussed in any detail in this book. The conclusions will be based upon the general classification of types of failure presented in Section 7.2. Subjective assessments of the truth and importance of the checklist of parameter statements within that classification are analysed using a simple numerical scale and also using fuzzy set theory. This leads us on to a tentative method for the analysis of the safety of a structure yet to be built. The method,however, has several disadvantages which can be overcome by the use of a model based on fuzzy logic. At the end of the chapte(, the discussion of the various possible measures of uncertainty is completed. 

When the analysis is complete, the analyst must translate the results into terms that can be understood by others—preferably by the general public. A most important feature of any result is its limitations. What is the statistical uncertainty in reported results If you took samples in a different manner, would you obtain the same results Is a tiny amount (a trace) of analyte found in a sample really there or is it contamination Only after we understand the results and their limitations can we draw conclusions. 

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