## 5 Steady-State Criterion Derivation from Flight Data  
The procedure proposed for establishing the criteria to be used on data collected from an operating engine is based on insights gained from the preceding discussion and the elaboration of data collected from an engine of interest. Data from a typical operating envelope will now be used to assess the different ways of applying a criterion for steady-state characterization. Data from a flight mission will be used to demonstrate the applicability of the criteria previously established to actual engine operation. The dataset used has been generated from a set of actual measured values on a civil engine, on an aircraft executing a flight among European destinations [25]. The actual data have been scaled due to confidentiality reasons. The engine model supporting the diagnosis has been scaled accordingly. The flight profile for the mission used is shown in Figure 10. In order to show the existence of non-steady operating conditions even during flight phases that may be considered as steady state, the time variation in the engine low-spool speed is plotted on the same figure. The deltas of the measured quantities have been evaluated, using the values calculated by a steady-state engine model as a reference at each operating point. The model is run using the low-spool rotational speed as a setting parameter. When the engine operates at steady state, those deltas are close to zero. During unsteady operation, the deltas obtain values that can be quite large. The evolution of \(\Delta\)Tt5 along the mission path is shown in Figure 11, where the evolution of the low-spool speed is also plotted. It is observed that when abrupt changes in the rotational speed occur, denoting transient operation, the deltas obtain also high values. Figure 10: Flight mission profile. Altitude versus flight time and corresponding low-spool speed along the flight path. Data scaled from a specific flight [25]. The deltas time series is now employed to obtain a diagnosis. A diagnosis of whether the engine is in healthy or faulty condition is sought. A diagnostic technique employing probabilistic neural networks (PNNs) [22] is applied on the time series of the measurement deltas. The PNN is a classification method, and the outcome of the diagnosis is whether the engine is healthy or faulty. It is a three-layer feed forward network that allows statistical pattern recognition based on [PERSON] decision rule [26]. The nodes of the first layer represent the available measurement deltas, which are input to the network. The nodes of the hidden layer each represent a set of measurement deltas for a known engine health condition. The set of nodes of this layer defines the set of training patterns of the network. The nodes of the output layer represent the set of possible engine health conditions that may occur. Each considered engine health condition is represented by the deviation of a group of health parameters from their nominal value due to engine fault. The set of training patterns is generated with the aid of the engine performance model. In total, 165 training patterns corresponding to specific engine health conditions that may be met in practice for this type of engine are generated. Given a set of measurement deltas, the PNN assigns a probability to each considered engine health condition; this is the node of the output layer. The engine health condition is defined as the one with the maximum estimated probability. The efficiency of the network and the adequacy of the training set are examined over a number of simulated fault cases--other than the training patterns--that show that the considered architecture can correctly discriminate patterns among the considered engine health conditions. For more information, the reader is referred to [22]. At first, the algorithm is applied to all the data points available. Although the engine is healthy, the algorithm provides a correct diagnosis for only about 75% of data points.