Result Verification and Uncertainty Management in Engineering Applications
University of Duisburg-Essen, Germany
Verified methods can have different uses in engineering applications. On the one hand, they are able to demonstrate the correctness of results obtained on a computer using a certain model of the considered system or process. On the other hand, we can represent bounded parameter uncertainty in a natural way with their help. This allows us to study models and make statements about them over whole parameter ranges instead of their (possibly incidental) point values. However, whole processes cannot be feasibly verified in all cases, the reasons ranging from inherent difficulties (e.g., for chaotic models) to problems caused by dependency and wrapping to drawbacks arising simply from choosing the wrong verified technique. In this talk, we give a detailed overview of how verified methods -- sometimes in combinations with other techniques -- improve the quality of simulations in engineering. We start by providing a general view on the role of verified methods in the verification/validation systematics and the modeling and simulation cycle for a given process. After that, we point out what concepts and tools are necessary to successfully apply verified methods, including not yet (fully) implemented ones that would be nonetheless advantageous. Finally, we consider several applications from (bio)mechanics and systems control which exemplify the general approach and focus on different usage areas for verified methods.