On the reduction of the overestimation in verified simulation by model reformulation

Many process engineering problems have critical bounds (quality, safety or environmental) that must be satisfied at all times. In a dynamic optimisation algorithm guaranteed bounds on the dynamic variables of the models that describe processes are needed in order to solve the problem to global optimality in a rigorous way. Hence, verified bounds are a key step in the optimisation algorithm. Recently there has been a focus on obtaining bounds which are as tight as possible while being a close representation of the reachable set. The dependency problem and the wrapping effect, which are the main contributors to the overestimation, have been tackled a number of ways. However, the construction of tight bounds is still an issue for practical applications. In this paper reformulation techniques for dynamic models are investigated. Emphasis is put on the reduction of the number of repetitions of a variable in the model. A search on directed acyclic graphs (DAGs) is performed using the Mathematica 10 symbolic functions and the result is used in an interval Taylor series with contractors. The effectiveness of the technique presented is demonstrated with a chemical reaction case study. The results show that the dependency problem is alleviated and in turn reduction of the overestimation is obtained.