In this paper, feed-forward recurrent neural networks (RNNs) with a single hidden layer and trained by using a back-propagation learning algorithm are studied and developed for the simulation of compressor behavior under unsteady conditions. The data used for training and testing the RNNs are both obtained by means of a nonlinear physics-based model for compressor dynamic simulation (simulated data) and measured on a multistage axial-centrifugal small-size compressor (field data). The analysis on simulated data deals with the evaluation of the influence of the number of training patterns and of each RNN input on model response, both for data not corrupted and corrupted with measurement errors, for different RNN configurations, and different values of the total delay time. For RNN models trained directly on experimental data, the analysis of the influence of RNN input combination on model response is repeated, as carried out for models trained on simulated data, in order to evaluate real system dynamic behavior. Then, predictor RNNs (i.e., those that do not include among the inputs the exogenous inputs evaluated at the same time step as the output vector) are developed and a discussion about their capabilities is carried out. The analysis on simulated data led to the conclusion that, to improve RNN performance, the adoption of a one-time delayed RNN is beneficial, with an as-low-as-possible total delay time (in this paper, $0.1s$) and trained with an as-high-as possible number of training patterns (at least 500). The analysis of the influence of each input on RNN response, conducted for RNN models trained on field data, showed that the single-step-ahead predictor RNN allowed very good performance, comparable to that of RNN models with all inputs (overall error for each single calculation equal to 1.3% and 0.9% for the two test cases considered). Moreover, the analysis of multi-step-ahead predictor capabilities showed that the reduction of the number of RNN calculations is the key factor for improving its performance over a significant time horizon. In fact, when a high test data sampling time is chosen (in this paper, $0.24s$), prediction errors were acceptable (lower than $1.9%$).

1.
Parlos
,
A. G.
,
Chong
,
K. T.
, and
Atiya
,
A. F.
, 1994, “
Application of the Recurrent Multilayer Perceptron in Modeling Complex Process Dynamics
,”
IEEE Trans. Neural Netw.
1045-9227,
5
(
2
), pp.
255
266
.
2.
Torella
,
G.
, and
Lombardo
,
G.
, 1996, “
Neural Networks for the Diagnostics of Gas Turbine Engines
,” ASME Paper No. 96-TA-39.
3.
Kanelopoulos
,
K.
,
Stamatis
,
A.
, and
Mathioudakis
,
K.
, 1997, “
Incorporating Neural Networks Into Gas Turbine Performance Diagnostics
,” ASME Paper No. 97-GT-35.
4.
Bettocchi
,
R.
,
Spina
,
P. R.
, and
Torella
,
G.
, 2002, “
Gas Turbine Health Indices Determination by Using Neural Networks
,” ASME Paper No. GT-2002-30276.
5.
,
J.
,
Genrup
,
M.
,
Loberg
,
A.
, and
,
M.
, 2003, “
Fault Diagnosis System for an Industrial Gas Turbine by Means of Neural Networks
,”
Proc. of International Gas Turbine Congress 2003 (IGTC’03)
, Tokyo, Nov. 2–7,
GTSJ
, Tokyo, Paper No. IGTC2003Tokyo TS-001.
6.
Bettocchi
,
R.
,
Pinelli
,
M.
,
Spina
,
P. R.
, and
Venturini
,
M.
, 2005, “
Artificial Intelligence for the Diagnostics of Gas Turbines. Part I: Neural Network Approach
,” ASME Paper No. GT2005-68026.
7.
Volponi
,
A. J.
,
DePold
,
H. R.
,
Ganguli
,
R.
, and
Daguang
,
C.
, 2000, “
The Use of Kalman Filter and Neural Networks Methodologies in Gas Turbine Performance Diagnostics: A Comparative Study
,” ASME Paper No. 2000-GT-0547.
8.
DePold
,
H. R.
, and
Gass
,
F. D.
, 1999, “
The Application of Expert Systems and Neural Networks to Gas Turbine Prognostics and Diagnostics
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
121
, pp.
607
612
.
9.
Sampath
,
S.
, and
Singh
,
R.
, 2004, “
An Integrated Fault Diagnostics Model Using Genetic Algorithm and Neural Networks
,” ASME Paper No. GT-2004-53914.
10.
Bettocchi
,
R.
,
Pinelli
,
M.
,
Spina
,
P. R.
, and
Venturini
,
M.
, 2005, “
Artificial Intelligence for the Diagnostics of Gas Turbines. Part II: Neuro-Fuzzy Approach
,” ASME Paper No. GT2005-68027.
11.
Simani
,
S.
,
Fantuzzi
,
C.
, and
Spina
,
P. R.
, 1998, “
Application of a Neural Network in Gas Turbine Control Sensor Fault Detection
,”
Proc. of 1998 IEEE International Conference on Control Applications
, Trieste, Italy,
IEEE
,
New York
, pp.
182
186
.
12.
Botros
,
K. K.
,
,
Kibria
,
G.
, and
Glover
,
A.
, 2000, “
A Demonstration of Artificial Neural Networks Based Data Mining for Gas Turbine Driven Compressor Stations
,” ASME Paper No. 2000-GT-0351.
13.
Fink
,
D. A.
,
Cumpsty
,
N. A.
, and
Greitzer
,
E. M.
, 1992, “
Surge Dynamics in a Free-Spool Centrifugal Compressor System
,”
ASME J. Turbomach.
0889-504X,
114
, pp.
321
332
.
14.
Hale
,
A. A.
, and
Davis
,
M. W.
, 1992, “
DYNamic Turbine Engine Compressor Code DYNTECC—Theory and Capabilities
,” AIAA Paper No. AIAA-92-3190.
15.
Blotemberg
,
W.
, 1993, “
A Model for the Dynamic Simulation of a Two-Shaft Industrial Gas Turbine With Dry Low Nox Combustor
,” ASME Paper No. 93-GT-355.
16.
Bettocchi
,
R.
,
Spina
,
P. R.
, and
Fabbri
,
F.
, 1996, “
Dynamic Modeling of Single-Shaft Industrial Gas Turbine
,” ASME Paper No. 96-GT-332.
17.
Bianchi
,
M.
,
Peretto
,
A.
, and
Spina
,
P. R.
, 1998, “
Modular Dynamic Model of Multi-Shaft Gas Turbine and Validation Test
,”
Proc. of The Winter Annual Meeting of ASME
,
ASME
,
New York
, Vol.
AES-38
, pp.
73
81
.
18.
Camporeale
,
S. M.
,
Fortunato
,
B.
, and
Mastrovito
,
M.
, 2002, “
A High-Fidelity Real-Time Simulation Code of Gas Turbine Dynamics for Control Applications
,” ASME Paper No. GT-2002-30039.
19.
Theotokatos
,
G.
, and
Kyrtatos
,
N. P.
, 2003, “
Investigation of a Large High-Speed Diesel Engine Transient Behaviour Including Compressor Surging and Emergency Shutdown
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
125
, pp.
580
589
.
20.
Tveit
,
G. B.
,
Bjorge
,
T.
, and
Bakken
,
L. E.
, 2005, “
Impact of Compressor Protection System on Rundown Characteristics
,” ASME Paper No. GT2005-68436.
21.
Venturini
,
M.
, 2005, “
Development and Experimental Validation of a Compressor Dynamic Model
,”
ASME J. Turbomach.
0889-504X,
127
(
3
), pp.
599
608
.
22.
Morini
,
M.
,
Pinelli
,
M.
, and
Venturini
,
M.
, 2006, “
Development of a One-Dimensional Modular Dynamic Model For The Simulation of Surge in Compression Systems
,” ASME Paper No. GT2006-90134.
23.
Venturini
,
M.
, 2006, “
Simulation of Compressor Transient Behavior Through Recurrent Neural Network Models
,”
ASME J. Turbomach.
0889-504X,
128
(
4
), pp.
1
11
.
24.
Bozzi
,
L.
,
Crosa
,
G.
, and
Trucco
,
A.
, 2003, “
Simplified Simulation Block Diagram of Twin-Shaft Gas Turbines
,” ASME Paper No. GT-2003-38679.
25.
Ohanian
,
S.
, and
Kurz
,
R.
, 2001, “
Series or Parallel Arrangement in a Two-Unit Compressor Station
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
124
, pp.
936
941
.
26.
Bettocchi
,
R.
,
Pinelli
,
M.
,
Spina
,
P. R.
,
Venturini
,
M.
, and
Zanetta
,
G. A.
, 2006, “
Assessment of the Robustness of Gas Turbine Diagnostics Tools Based on Neural Networks
,” ASME Paper No. GT2006-90118.
27.
Jiang
,
D.
, and
Wang
,
J.
, 2000, “
On-Line Learning of Dynamical Systems in the Presence of Model Mismatch and Disturbances
,”
IEEE Trans. Neural Netw.
1045-9227,
11
(
6
), pp.
1272
1283
.
28.
Plett
,
G. L.
, 2003, “
Adaptive Inverse Control of Linear and Nonlinear Systems Using Dynamic Neural Networks
,”
IEEE Trans. Neural Netw.
1045-9227,
14
(
2
), pp.
360
376
.
29.
Parlos
,
A. G.
,
Rais
,
O. T.
, and
Atiya
,
A. F.
, 2000, “
Multi-Step-Ahead Prediction in Complex Systems Using Dynamic Recurrent Neural Networks
,”
Neural Networks
0893-6080,
13
(
7
), pp.
765
786
.
30.
Desideri
,
U.
,
Fantozzi
,
F.
,
Bidini
,
G.
, and
Mathieu
,
P.
, 1997, “
Use of Artificial Neural Networks for the Simulation of Combined Cycles Transients
,” ASME Paper No. 97-GT-442.
31.
Chiras
,
N.
,
Evans
,
C.
, and
Rees
,
D.
, 2002, “
Nonlinear Gas Turbine Modeling Using Feedforward Neural Networks
,” ASME Paper No. GT-2002-30035.
32.
Arsie
,
I.
,
Pianese
,
C.
, and
Sorrentino
,
M.
, 2002, “
Recurrent Neural Network Based Air-Fuel Ratio Observer for SI Internal Combustion Engines
,”
Proc. of ESDA 2002
, Istanbul,
ASME
, New York, Paper No. ESDA2002/APM038 ACC008.
33.
Ogaji
,
S. O. T.
,
Li
,
Y. G.
,
Sampath
,
S.
, and
Singh
,
R.
, 2003, “
Gas Path Fault Diagnosis of a Turbofan Engine From Transient Data Using Artificial Neural Networks
,” ASME Paper No. GT2003-38423.
34.
Menon
,
S.
,
Uluyol
,
O.
, and
Gupta
,
D.
, 2004, “
Turbine Engine Modeling Using Temporal Neural Networks for Incipient Fault Detection and Diagnosis
,” ASME Paper No. GT2004-53649.
35.
Haykin
,
S.
, 1999,
Neural Networks—A Comprehensive Foundation
,
2nd ed.
,
Prentice-Hall
, Englewood Cliffs, NJ.
36.
Bettocchi
,
R.
,
Pinelli
,
M.
, and
Spina
,
P. R.
, 2005, “
A MultiStage Compressor Test Facility: Uncertainty Analysis and Preliminary Test Results
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
127
(
1
), pp.
170
177
.
37.
Traverso
,
A.
,
Scarpellini
,
R.
, and
Massardo
,
A.
, 2005, “
Experimental Results and Transient Model of an Externally Fired Micro Gas Turbine Technology
,” ASME Paper No. GT2005-68100.
38.
Stiller
,
C.
,
Thorud
,
B.
, and
Bolland
,
O.
, 2005, “
Safe Dynamic Operation of a Simple SOFC/GT Hybrid System
,” ASME Paper No. GT2005-68481.
39.
Cybenko
,
G.
, 1989, “
Approximation by Superimposition of a Sigmoidal Function
,”
Math. Control, Signals, Syst.
0932-4194,
2
, pp.
303
314
.
40.
Atiya
,
A. F.
,
, and
Parlos
,
A. G.
,
, 2000, “
New Results on Recurrent Network Training: Unifying the Algorithm and Accelerating Convergence
,”
IEEE Trans. Neural Netw.
1045-9227,
11
(
3
), pp.
697
703
.