**6. Multipoint diagnosis and diagnosis at transients**

The options of one-point diagnosis, multipoint diagnosis, and diagnosis at transients have been thoroughly studied and compared in (Loboda & Feldshteyn, 2007). The same probabilistic criteria *P* → and *P* were used to compare the recognition techniques. The multipoint diagnosis means that measurements from different operating points (modes) are united to make a single diagnosis. All recognition techniques previously described in the application within the one-point option can be applied without principal changes. The dimension of patterns and diagnostic space is only increased because measurements at every operating mode can be considered as new gas turbine measured variables. In this way, a generalized deviation vector *<sup>W</sup>* \* , which unites deviations computed at all considered modes, is now a pattern to be recognised. For the investigated case of the GT3 when the engine has 5 five monitored variables and is diagnosed at 14 modes, the generalized vector *<sup>W</sup>* \* embraces 5×14=70 elemental deviations. To illustrate the effect of the multipoint option, Table 3 presents the results of the comparison of the one-point and multipoint options. The probability *P* increments contained in the line "Difference" allow to state that a positive effect from using the multipoint option is very significant. A principal part of these increments is explained by so-called averaging effect (Loboda & Feldshteyn, 2007) of the multipoint diagnosis.

From the mathematical point of view, the diagnosis under transient condition is similar to the multipoint diagnosis: every measurement section of a total transient process is considered as a new operating point and the same generalized vector *<sup>W</sup>* \* is formed. This allows comparing these two options. With the comparison results given in Table 4, one can state that the diagnosis at transients has a stable, although not very high, growth of accuracy relative to the multipoint diagnosis. This growth is probably related to the greater fault influence under dynamic conditions. As the growth is not considerable, the actions of diagnosis at transients and multipoint diagnosis are close. Consequently, the most part of the total accuracy growth at transients relative to the one-point option is produced by the averaging effect mentioned above.


Table 3. Probabilities *P* for the one-point diagnosis and multipoint diagnosis (GT3)


Table 4. Probabilities *P* for the multipoint diagnosis and diagnosis at transients (GT3)

The options of one-point diagnosis, multipoint diagnosis, and diagnosis at transients have been thoroughly studied and compared in (Loboda & Feldshteyn, 2007). The same

multipoint diagnosis means that measurements from different operating points (modes) are united to make a single diagnosis. All recognition techniques previously described in the application within the one-point option can be applied without principal changes. The dimension of patterns and diagnostic space is only increased because measurements at every operating mode can be considered as new gas turbine measured variables. In this way, a generalized deviation vector *<sup>W</sup>* \* , which unites deviations computed at all considered modes, is now a pattern to be recognised. For the investigated case of the GT3 when the engine has 5 five monitored variables and is diagnosed at 14 modes, the generalized vector *<sup>W</sup>* \* embraces 5×14=70 elemental deviations. To illustrate the effect of the multipoint option, Table 3 presents the results of the comparison of the one-point and multipoint options. The probability *P* increments contained in the line "Difference" allow to state that a positive effect from using the multipoint option is very significant. A principal part of these increments is explained by so-called averaging effect (Loboda & Feldshteyn,

From the mathematical point of view, the diagnosis under transient condition is similar to the multipoint diagnosis: every measurement section of a total transient process is considered as a new operating point and the same generalized vector *<sup>W</sup>* \* is formed. This allows comparing these two options. With the comparison results given in Table 4, one can state that the diagnosis at transients has a stable, although not very high, growth of accuracy relative to the multipoint diagnosis. This growth is probably related to the greater fault influence under dynamic conditions. As the growth is not considerable, the actions of diagnosis at transients and multipoint diagnosis are close. Consequently, the most part of the total accuracy growth at transients relative to the one-point option is produced by the

Option Single fault

Option Single fault

classification

One-point 0.7316 0.7351 Multipoint 0.8915 0.9444 Difference 0.1599 0.2093

classification

Multipoint 0.8915 0.9444 Transient 0.9032 0.9561 Difference 0.0117 0.0117

Table 4. Probabilities *P* for the multipoint diagnosis and diagnosis at transients (GT3)

Table 3. Probabilities *P* for the one-point diagnosis and multipoint diagnosis (GT3)

Multiple fault classification

Multiple fault classification

and *P* were used to compare the recognition techniques. The

**6. Multipoint diagnosis and diagnosis at transients** 

→

probabilistic criteria *P*

2007) of the multipoint diagnosis.

averaging effect mentioned above.

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

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 identification techniques.
