Dealing with Model Uncertainty

The workshop recognized the importance of dealing with model uncertainty but did not evaluate the alternative approaches in detail. Further work is required to identify instances of model nncertainty for pesticide risk assessment and to develop guidance on how to deal with it. Some possible approaches are briefly discussed below. 

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Several approaches exist for dealing with model uncertainty ... 

A common approach to deal with model uncertainty is model set expansion (Zio and Apostolakis, 1996). According to this approach, the characteristics of the system under consideration are analyzed and models are created in an attempt to emulate the system based on goodness-of-fit criteria (Reinert and Apostolakis, 2006). The models may use different assumptions and require different inputs. These models are then combined to produce a meta-model of the system. Several methods have been proposed regarding the construction of the meta-model. AU rely on expert opinion. In the Bayesian approach, the combination of the individual models is carried out using Bayes theorem (Droguett and Mosleh, 2008). This method is theoretically very attractive dne to its mathematical rigor and ability to incorporate both objective and subjective information in a probabilistic representation. 

In the present contribution a MPC scheme is proposed for the operational management of a FISC, which naturally permits to deal with input uncertainty, as well as unexpected events, which can disrupt the system operations. This article is structured as follows. In section 2 a description of a typical FISC along with the required features of the corresponding operational planning model is provided. In section 3 the basics of the proposed MPC scheme are outlined. In section 4 experimental results for typical operative scenarios are discussed. A Conclusions and Future Work Section closes the article. 

The rock stress predictions, based on database information and numerical modelling, were satisfactory and helped to focus attention on the key factors involved. In particular, the use of numerical modelling assists in evaluating potential stress changes in the vicinity of fracture zones. Methods of dealing with conceptual uncertainty and spatial variability of stress were successfully introduced into the rock stress characterization and predictive methodology. 

In this framework, deterministic approaches cannot cope with the inherent randomness of the processes and any predictive model for the evolution of the littoral zone over years or decades has to be based upon statistic tools capable of dealing with the uncertainty of the prognosis. 

All these methods pretend to represent the intuitive way an expert deals with uncertainty. Whether this is true remains an open question. No method has yet been evaluated thoroughly. Modelling uncertainty to obtain a reasonable reliability measure for the conclusions remains one of the major unsolved issues in expert system technology. Therefore, it is important that in the expert system a mechanism is provided to define its boundaries, within which it is reasonably safe to accept the conclusions of the expert system. 

Fuzzy logic is often referred to as a way of "reasoning with uncertainty." It provides a well-defined mechanism to deal with uncertain and incompletely defined data, so that one can make precise deductions from imprecise data. The incorporation of fuzzy ideas into expert systems allows the development of software that can reason in roughly the same way that people think when confronted with information that is ragged around the edges. Fuzzy logic is also convenient in that it can operate on not just imprecise data, but inaccurate data, or data about which we have doubts. It does not require that some underlying mathematical model be constructed before we start to assess the data. 

In addition to the overview of models that are used for adsorption at the oxide-electrolyte interface, examples for the application of these models were discussed. It has been stated that there is a great deal of uncertainty associated with models of the oxide-electrolyte interface, and, in the opinion of the author, it is better to cast uncertainty in terms of a simple model than in terms of a complex model. 

This appendix presents a review of experimental work in the field of packed-bed combustion of biomass. It deals with the measurement methods used to analyse the thermochemical conversion of the biomass. This implies that thermochemical conversion studies of coal is outside the scope of this literature study. Wood stove research is not considered in this review either. Of special interest in this survey is the choice of sought physical quantities (target quantities) and measurands of interest in each study and how they are modelled and verified, and if uncertainty analysis is carried out. 

Cullen, A.C. and H.C. Frey. 1999. Probabilistic Techniques in Exposure Assessment A Handbook for Dealing with Variability and Uncertainty in Models and Inputs. New York Plenum Publishing Corporation. 

A probabilistic risk assessment (PRA) deals with many types of uncertainties. In addition to the uncertainties associated with the model itself and model input, there is also the meta-uncertainty about whether the entire PRA process has been performed properly. Employment of sophisticated mathematical and statistical methods may easily convey the false impression of accuracy, especially when numerical results are presented with a high number of significant figures. But those who produce PR As, and those who evaluate them, should exert caution there are many possible pitfalls, traps, and potential swindles that can arise. Because of the potential for generating seemingly correct results that are far from the intended model of reality, it is imperative that the PRA practitioner carefully evaluates not only model input data but also the assumptions used in the PRA, the model itself, and the calculations inherent within the model. This chapter presents information on performing PRA in a manner that will minimize the introduction of errors associated with the PRA process. 

If a consensus is reached, the user is more confident. A critical situation may appear in case of conflicting results. A simple approach is to adopt a conservative strategy and get the worst case. A different strategy may be to associate a higher uncertainty to the predictions in case of disagreement. A third strategy is to develop a suitable system capable to deal with multiple inputs. This is the case of the above-mentioned hybrid models, which needs a specific study for the optimization of the final results. 

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