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TECHNICAL PAPERS: Gas Turbines: Controls, Diagnostics, and Instrumentation

# Artificial Intelligence for the Diagnostics of Gas Turbines—Part II: Neuro-Fuzzy Approach

[+] Author and Article Information
R. Bettocchi, M. Pinelli, P. R. Spina, M. Venturini

ENDIF Engineering Department in Ferrara, University of Ferrara, Via Saragat, 1-44100 Ferrara, Italy

The criterion for ending the process is:
• If $Pk*>εaP1*$then $(x)k*$ is accepted as a cluster center and the clustering process is continued
• else if $Pk*<εrP1*$then $(x)k*$ is rejected and the clustering process is stopped
• else if $εaP1*≥Pk*≥εrP1*$then
•   if $(dmin∕ra)+(Pk*∕P1*)≥1$then $(x)k*$ is accepted as a cluster center and the clustering process is continued
•   else $(x)k*$ is rejected, $Pk*$ is set to 0, the data with the next highest potential is selected as the new $(x)k*$ and the test is repeated
•   end if
• end if
The parameter $dmin$ is the shortest distance between $(x)k*$ and all previously found cluster centers.
J. Eng. Gas Turbines Power 129(3), 720-729 (Sep 08, 2006) (10 pages) doi:10.1115/1.2431392 History: Received December 02, 2005; Revised September 08, 2006

## Abstract

In the paper, neuro-fuzzy systems (NFSs) for gas turbine diagnostics are studied and developed. The same procedure used previously for the setup of neural network (NN) models (Bettocchi, R., Pinelli, M., Spina, P. R., and Venturini, M., 2007, ASME J. Eng. Gas Turbines Power, 129(3), pp. 711–719) was used. In particular, the same database of patterns was used for both training and testing the NFSs. This database was obtained by running a cycle program, calibrated on a $255MW$ single-shaft gas turbine working in the ENEL combined cycle power plant of La Spezia (Italy). The database contains the variations of the Health Indices (which are the characteristic parameters that are indices of gas turbine health state, such as efficiencies and characteristic flow passage areas of compressor and turbine) and the corresponding variations of the measured quantities with respect to the values in new and clean conditions. The analyses carried out are aimed at the selection of the most appropriate NFS structure for gas turbine diagnostics, in terms of computational time of the NFS training phase, accuracy, and robustness towards measurement uncertainty during simulations. In particular, adaptive neuro-fuzzy inference system (ANFIS) architectures were considered and tested, and their performance was compared to that obtainable by using the NN models. An analysis was also performed in order to identify the most significant ANFIS inputs. The results obtained show that ANFISs are robust with respect to measurement uncertainty, and, in all the cases analyzed, the performance (in terms of accuracy during simulations and time spent for the training phase) proved to be better than that obtainable by multi-input/multioutput (MIMO) and multi-input/single-output (MISO) neural networks trained and tested on the same data.

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Copyright © 2007 by American Society of Mechanical Engineers
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## Figures

Figure 7

Influence of the number of training patterns in the presence of measurement errors: comparison between ANFISs trained with data not corrupted with measurement errors (Tr U) and with data corrupted with measurement errors (Tr C) (nMF=3 in all cases)

Figure 8

Influence of the number of training patterns in the presence of measurement errors: comparison of ANFISs (nMF=3), MIMO, and MISO NNs, all trained with data corrupted with measurement errors

Figure 9

Influence of the number of inputs (5, 6, and 15) and of the input space partitioning algorithm (gp: grid partition; sc: subtractive clustering); training data corrupted with measurement errors

Figure 1

Two-crisp-input Mamdani FLS with two MFs for each input

Figure 2

Two-crisp-input two-rule Sugeno FLS

Figure 3

ANFIS architecture equivalent to a first-order two-input single-output Sugeno FLS with two MFs for each input and two rules

Figure 4

FIAT Avio 701F gas turbine model

Figure 5

Influence of the number of training patterns

Figure 6

Influence of the number of training patterns: comparison of ANFISs (nMF=9), MISO, and MIMO neural networks

Figure 10

Influence of the input space partitioning algorithm (gp: grid partition; sc: subtractive clustering) for six-input ANFIS trained with data corrupted with measurement errors

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