**7. Diagnosis with system identification techniques**

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 widely used nowadays in the GPA. The techniques compute estimates <sup>ˆ</sup> Θ as a result of distance minimization between simulated and measured values of the monitored variables. This minimization problem can be written as

$$\stackrel{\hat{\bullet}}{\vec{\Theta}} = \arg\min \left\| \vec{Y} - \vec{Y}(\vec{\mathcal{U}}, \vec{\Theta}) \right\|. \tag{15}$$

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 current estimate depends on previous ones.

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 values 0.02-0.03 of the regularization parameter were recommended.

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

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is verified on maintenance data of the GT1. The comparison of the modified and original identification procedures has shown that the proposed procedure has better properties. Such a model can be widely used in monitoring systems as well.

Another way to get more exact estimates is to use the option of the diagnosis at transients and to identify the dynamic model as shown in (Loboda & Hernandez Gonzalez, 2002).

As shown above, the considered system identification-based approach can be realized for the same options as the pattern recognition-based approach. Additionally, the principal problems of the latter (such as inadequacy of the baseline model and inaccurate fault simulation) are also typical for the system identification-based approach. Thus, they are alternative approaches for all steps of a total fault localization process. Furthermore, it can also be demonstrated that with this approaches the stages of fault detection and prognostics can be realized. In this way, we can consider these two approaches as applicable for all gas path analysis methods.
