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This paper extends previous work on model order reduction based on singular value decomposition. It is shown how the decrease in estimator variance must be balanced against the bias on the estimate inevitably introduced by solving the inverse problem in a reduced order space. A proof for the decrease in estimator variance by means of multi-point analysis is provided. The proof relies on comparing the Cramer-Rao lower bound of the single point and the multi-point estimators. Model order selection is discussed in the presence of a varying degree of a priori parameter information, through the use of a regularization parameter. Simulation results on the SR-30 turbojet engine indicate that the theoretically attainable multi-point improvements are difficult to realize in practical jet engine applications.

A Study on Engine Health Monitoring in the Frequency DomainMost of the techniques developed to date for module performance analysis rely on steadystate measurements from a single operating point to evaluate the level of deterioration of an engine. One of the major difficulties associated with this estimation problem comes from its underdetermined nature. It results from the fact that the number of health parameters e.Kceeds the number of available sensors. Among the panel of remedies to this issue, a few authors have inve.itigated the potential of using data collected during a transient operation of the engine. A major outcome of these studies is an improvement in the assessed health condition. The present study proposes a framework that formalizes this observation for a given class of input signals. The analysis is performed in the frequency domain, following the lines of .n'stem identification theory. More specifically, the mean-squared estimation error is shown to drastically decrease when using transient input signals. This study is conducted with an engine model representative of a commercial turbofan. Statement of the ProblemThe scope of this section is to present the theoretical foundation of the methodology developed to show the benefit of using transient signals for diagnosis. First, the model relating the observa- Journal of Engineering for Gas Turbines and Power

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