Recent work on gas turbine diagnostics based on optimisation techniques advocates two different approaches: 1) Stochastic optimisation, including Genetic Algorithm techniques, for its robustness when optimising objective functions with many local optima and 2) Gradient based methods mainly for their computational efficiency. For smooth and single optimum functions, gradient methods are known to provide superior numerical performance. This paper addresses the key issue for method selection, i.e. whether multiple local optima may occur when the optimisation approach is applied to real engine testing. Two performance test data sets for the RM12 low bypass ratio turbofan engine, powering the Swedish Fighter Gripen, have been analysed. One set of data was recorded during performance testing of a highly degraded engine. This engine has been subjected to Accelerated Mission Testing (AMT) cycles corresponding to more than 4000 hours of run time. The other data set was recorded for a development engine with less than 200 hours of operation. The search for multiple optima was performed starting from more than 100 extreme points. Not a single case of multi-modality was encountered, i.e. one unique solution for each of the two data sets was consistently obtained. The RM12 engine cycle is typical for a modern fighter engine, implying that the obtained results can be transferred to, at least, most low bypass ratio turbofan engines. The paper goes on to describe the numerical difficulties that had to be resolved to obtain efficient and robust performance by the gradient solvers. Ill conditioning and noise may, as illustrated on a model problem, introduce local optima without a correspondence in the gas turbine physics. Numerical methods exploiting the special problem structure represented by a non-linear least squares formulation is given special attention. Finally, a mixed norm allowing for both robustness and numerical efficiency is suggested.
Gas Turbine Performance Forecast and Assessment: GE LM2500 in Outlook