**5. Recognition technique selection**

On basis of the probabilistic indices *P* → and *P* , three recognition techniques are optimized and compared in paper (Loboda & Yepifanov, 2006) in order to choose the best one and give recommendations on its practical use. Two techniques, the Bayesian approach and multilayer perceptron (type of neural networks), have shown similarly good results. The difference of the probabilities *P* estimated for each technique was only about 0.6% in different conditions of technique application.

Preliminary calculations have shown that the distinguishability of fault classes can change by up to 6% when real errors are replaced by simulated errors. Thus, the diagnostic performance estimated with simulated noise can be inaccurate. The case was also investigated when the errors for the learning and validation set were extracted from different time portions of real data. The loss of diagnosability for this case was found drastic: from *P* = 90% - 94% in the previous cases to *P* = 59%. It has happened because real deviation errors included into the validation set increased a lot in comparison with the learning set errors. The increase of the errors occurred because the baseline model is adequate on the reference set data but loses its accuracy on the subsequently recorded data. Such a problem seems to be very probable in real

diagnosis and we should be careful to avoid or mitigate it.

Fig. 5. 3D plot of four fault classes with simulated sensor errors

**5. Recognition technique selection** 

different conditions of technique application.

On basis of the probabilistic indices *P*

recommended for a final precise estimation of gas turbine diagnosability.

→

Although the proposed scheme is more realistic, it cannot automatically replace existing noise simulation modes. This new scheme is more complex for realization. Additionally, it needs both the thermodynamic model and extensive real data, two things rarely available together. In this way, the proposed scheme of deviation error representation can rather be

Thus, we completed the analysis of different improvements of a convenient fault

and compared in paper (Loboda & Yepifanov, 2006) in order to choose the best one and give recommendations on its practical use. Two techniques, the Bayesian approach and multilayer perceptron (type of neural networks), have shown similarly good results. The difference of the probabilities *P* estimated for each technique was only about 0.6% in

and *P* , three recognition techniques are optimized

classification. Let us now consider the problem of choosing a recognition technique.

To continue the comparison of recognition techniques, paper (Loboda, Feldshteyn et al., 2011) compares two network types: a multilayer perceptron (MLP) and a radial basis network (RBN). To draw firm conclusions on the networks' applicability, comparative calculations were repeated for different variations of diagnostic conditions. In particular, two different engines were chosen as test cases. The comparison results are shown in Table 2. It can be seen that the differences between the techniques are very smal. On average for all cases presented in the table for the GT1, the RBN gains 0.0009 (0.09%) only.


Table 2. Probabilities *P* for the networks compared on GT1 data

The comparison was repeated for an aircraft turbofan engine denoted as GT3. The corresponding average probability increment was found to be 0.0028 (0.28%). In this way, an advantage of the radial basis network in the application to the analyzed turbofan seems to be a little more notable than in the case of the industrial gas turbine. By way of summing up the comparison results, the conclusion is that the radial basis network is a little more accurate than the perceptron, however the difference can be considered as insignificant.

The comparison of recognition techniques has been completed in paper (Estrada Moreno & Loboda, 2011), in which the MLP and probabilistic neural network (PNN) are compared. The comparison under different diagnostic conditions has revealed that the diagnosis by the PNN is less reliable. However, the averaged difference of the probability is not greater than 0.5%. Once more we can state that the compared techniques are practically equal in accuracy.

The fact that the fault recognition performances of four different recognition techniques, namely, Bayessian approach, MLP, RBN, and PNN, are very close is worthy of some discussion. What explanation can be provided for this? We believe that all four techniques are sophisticated enough and are well suited for solving this specific problem – gas turbine fault recognition. No one of these techniques can further enhance diagnostic accuracy because the accuracy achieved is near the theoretical accuracy level that is inherent to the solving problem: gas turbine fault recognition with the given classification. Following this idea, we suppose that within the approach used and the classification accepted no other recognition technique will be capable to considerably enhance diagnostic accuracy. Instead, all efforts should be made to reduce fault class intersections, for example, by reducing measurement inaccuracy, installing more sensors in the gas path, and decreasing deviation errors. The options of multipoint diagnosis and diagnosis during transient operation will also result in a higher diagnostic accuracy.

Gas Turbine Diagnostics 209

When simulating the diagnostic processes at transients, we were unable to take into account some peculiarities that complicate the real diagnosis at transients, such as a turbine temperature sensor's dynamic error and an unequal dynamic warm-up of rotor and stator parts. That is why our conclusions regarding the diagnosis at transients cannot be

Thus, the modes and options to enhance the diagnosis methods based on the pattern recognition theory have been analysed in details in sections 4-6. In contrast, the next section gives a general description of the other main diagnostic approach using system

The gas turbine diagnosis based on system identification means the identification of the thermodynamic models, namely nonlinear static model, linear model, and dynamic model, given by equations (1) - (3). The techniques to identify the nonlinear static model are most

distance minimization between simulated and measured values of the monitored variables.

\* arg min ( , ) *Y YU*

The estimates contain information on a current technical state of each engine component. This drastically simplifies a subsequent diagnostic decision. Furthermore, the diagnosis is not limited by a rigid classification as in the case of the pattern recognition-based approach. Among the system identification techniques applied to diagnose gas turbines, the Kalman filter is by far widely used. The details its application can be found, for example, in (Volponi et al., 2003). The alignment of the estimates is provided by the Kalman filter because its

Other computational scheme is maintained in (Loboda, 2007). Independent estimations are obtained by a special inverse procedure within the multipoint option. With data registered through a prolonged period, successive estimates are computed and analyzed in time to get more reliable results. Within this scheme, a regularizing identification procedure is proposed and verified on simulated and real data in (Loboda et al., 2005). The verification has shown that the regularization of the estimated state parameters makes the identification procedure more stable and reduces an estimation scatter. On the other hand, the regularization shifts mean values of the estimates and should be applied carefully. The

Next diagnostic development of the gas turbine identification is presented in (Loboda, 2007). The idea is proposed to develop in the basis of the thermodynamic model a new model that takes gradual engine performance degradation in consideration. Two purposes are achieved identifying such a model. The first purpose consists in creating the model of a gradually degraded engine while the second is to have a baseline function of high accuracy. The idea

Θ= − Θ . (15)

→ → →→→

Θ 

as a result of

considered as the sole argument for choosing a proper diagnostic option.

widely used nowadays in the GPA. The techniques compute estimates <sup>ˆ</sup>

∧

values 0.02-0.03 of the regularization parameter were recommended.

**7. Diagnosis with system identification techniques** 

This minimization problem can be written as

current estimate depends on previous ones.

identification techniques.
