A comparison of reduced-order modelling techniques for application in hyperthermia control and estimation

Abstract

Reduced-order modelling techniques can make important contributions in the control and state estimation of large systems. In hyperthermia, reduced—order modelling can provide a useful tool by which a large thermal model can be reduced to the most significant subset of its full—order modes, making real—time control and estimation possible. Two such reduction methods, one based on modal decomposition and the other on balanced realization, are compared in the context of simulated hyperthermia heat transfer problems. The results show that the modal decomposition reduction method has three significant advantages over that of balanced realization. First, modal decomposition reduced models result in less error, when compared to the full-order model, than balanced realization reduced models of similar order in problems with low or moderate advec—tive heat transfer. Second, because the balanced realization based methods require a priori knowledge of the sensor and actuator placements, the reduced-order model is not robust to changes in sensor or actuator locations, a limitation not present in modal decomposition. Third, the modal decomposition transformation is less demanding computationally. On the other hand, in thermal problems dominated by advective heat transfer, numerical instabilities make modal decomposition based reduction problematic. Modal decomposition methods are therefore recommended for reduction of models in which advection is not dominant and research continues into methods to render balanced realization based reduction more suitable for real—time clinical hyperthermia control and estimation.

Key Words:

• Reduced-order modelling
• hyperthermia
• balanced realization
• control
• estimation