## 2 Models for SOFC and their Verification Degree
### Verification and Validation Assessment Verification Degree  
Nowadays, it is agreed [5] to consider development processes in engineering as comprising analysis, formalization, simulation, and optimisation (calibration) steps, the relations between which are characterized by the verification and validation (V&V) cycle. The cycle can be reiterated any number of times so that the task of design and formalization turns into system optimisation/calibration (including customizing) after the initial round is completed. The first stage of the cycle is to analyse the real world problem and to develop a conceptual and a formal model for it. During this phase, _qualification_ is carried out, defined as \"determination of adequacy of the conceptual model to provide an acceptable level of agreement for the domain of intended application\" [5]. The second stage consists in implementing the formal model, in most cases using a computer. Here, _verification_ is necessary, that is, making sure that the formal model is implemented correctly in the sense established by requirements devised at the previous stage. The third stage of the cycle is simulation. _Validation_ needs to be carried out at this stage, the task of which is to compare the outcomes of the computerized model or the prototype to reality, establish the degree of similarity, and address model fidelity. An important distinction made clear by the V&V cycle is that between the concepts of verification and validation, the exact meaning of which often depends on the considered application area. In essence, to verify a model means to prove that the model is built and simulated with the correct methods whereas the term validation denotes showing the degree of its similarity to the reality [25]. A precondition for this kind of analysis is that features of the real world problem, with respect to which the comparison is carried out, are identified at the stage of qualification. In this paper, we focus mainly on verification with the help of interval methods. However, in general, methods with result verification such as interval analysis might also offer assistance at the qualification and validation stages (cf. [26]). At the second stage of the cycle, traditional V&V methodologies (concentrating on formal verification) suggest using benchmarks in the cases where no theoretical proof of the model and algorithm accuracy is possible and interpreting the outcome of the process of interest on these. In [6; 15; 16], we proposed to shift the focus on the process itself. Helped by appropriate questionnaires, users subdivide their processes into smaller tasks and classify the input/output data and algorithms, which allows us to assign a certain initial verification degree from the four-tier hierarchy shown below to the (sub-)process. Note that this hierarchy highlights our process-oriented understanding of the V&V analysis as presented in [6; 15; 16]. After that, the initial degree can be improved and uncertainty quantified by using a selection of specialized data types and tools. Here, interoperability with respect to data types, algorithms and used hardware is highly relevant. On the one hand, interoperable software would allow us to compute the solution in several ways in parallel and compare/interpret the outcome of these different computational models (cf. Section 4). On the other hand, a combination of different kinds of tools in one interconnected package would help to solve problems a single tool might not have the necessary means for. A computerized system model (CSM) associated with a given real-life system has the verification degree C4 to C1 if [16]:  
* The CSM uses standard floating point or fixed point arithmetic (the lowest verification degree). * The CSM is meaningfully subdivided into its constituent parts; the numerical implementation uses at least standardized IEEE 754 floating point arithmetic; and sensitivity analysis is carried out for uncertain parameters or uncertainty is propagated through the subsystems using traditional methods (e.g., Monte-Carlo).