Fuzzy finite element analysis of heat conduction problems with uncertain parameters

In this article we have used four different global optimisation algorithms for interval finite element analysis of (non)linear heat conduction problems: (i) sequential quadratic programming (SQP), (ii) a scatter search method (SSm), (iii) the vertex algorithm, and (iv) the response surface method (RSM). Their performance was compared based on a thermal sterilisation problem and a food freezing problem. The vertex method proved to be by far the fastest method but is only effective if the solution is a monotonic function of the uncertain parameters. The RSM was also fast albeit much less than the vertex method. Both SQP and SSm were considerably slower than the former methods; SQP did not converge to the real solution in the food freezing test problem. The interval finite element method was used as a building block for a fuzzy finite element analysis based on the α-cuts method. The RSM fuzzy finite element method was identified as the fastest algorithm among all the tested methods. It was shown that uncertain parameters may cause large uncertainties in the process variables. The algorithms can be used to obtain more realistic modelling of food processes that often have significant uncertainty in the model parameters.