A method of measurement selection is introduced that relies on parameter signatures to assess the identifiability of dynamic model parameters by different outputs. A parameter signature is a region in the time-scale plane wherein the sensitivity of the output with respect to one model parameter is much larger than the rest of the output sensitivities. Since a parameter signature can be extracted when the corresponding output sensitivity is independent of the others, the ability to extract parameter signatures is indicative of parameter identifiability by the output and used here for output/measurement selection. The purpose of this paper is to introduce a strategy for measurement selection by parameter signatures and to demonstrate its applicability to the transient decks of turbojet engines. The validity of the selected outputs in providing observability to all the engine model parameters is independently verified by successful estimation of parameters by nonlinear least-squares estimation.

1.
Simon
,
D. L.
,
Gang
,
S.
,
Hunter
,
G. W.
,
Guo
,
T. -H.
, and
Semega
,
K. J.
, 2004, “
Sensor Needs for Control and Health Management of Intelligent Aircraft Engines
,”
NASA
Report No. TM-2004-213202.
2.
Ljung
,
L.
, and
Glad
,
T.
, 1994, “
On Global Identifiability for Arbitrary Model Parametrizations
,”
Automatica
0005-1098,
30
(
2
), pp.
265
276
.
3.
Urban
,
L. A.
, and
Volponi
,
A. J.
, 1992, “
Mathematical Methods of Relative Engine Performance Diagnostics
,”
SAE Trans.
0096-736X,
101
, pp.
2025
2050
.
4.
Doel
,
D. L.
, 1994, “
TEMPER—A Gas-Path Analysis Tool for Commercial Jet Engines
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
116
(
1
), pp.
82
89
.
5.
Luppold
,
R. H.
,
Roman
,
J. R.
,
Gallops
,
G. W.
, and
Kerr
,
L. J.
, 1989, “
Estimating In-Flight Engine Performance Variations Using Kalman Filter Concepts
,” AIAA Paper No. AIAA-89-2584.
6.
Kerr
,
L. J.
,
Nemec
,
T. S.
, and
Gallops
,
G. W.
, 1991, “
Real-Time Estimation of Gas Turbine Engine Damage Using a Control Based Kalman Filter Algorithm
,” ASME Paper 91-GT-216.
7.
Mathioudakis
,
K.
,
Kamboukos
,
Ph.
, and
Stamatis
,
A.
, 2002, “
Turbofan Performance Deterioration Tracking Using Nonlinear Models and Optimization Techniques
,”
ASME J. Turbomach.
0889-504X,
124
, pp.
580
587
.
8.
Brotherton
,
T.
, and
Volponi
,
A.
,
Luppold
,
R.
, and
Simon
,
D. L.
, 2003, “
eSTORM: Enhanced Self Tuning On-Board Real-Time Engine Model
,”
Proceedings of the 2003 IEEE Aerospace Conference
.
9.
Kobayashi
,
I.
,
Simon
,
D. L.
, and
Litt
,
J. S.
, 2005, “
Application of a Constant Gain Extended Kalman Filter for In-Flight Estimation of Aircraft Engine Performance Parameters
,”
Army Research Laboratory
Report No. ARL-TR-2955.
10.
Kamboukos
,
P.
,
Oikonomou
,
P.
,
Stamatis
,
A.
, and
Mathioudakis
,
K.
, 2001, “
Optimizing Effectiveness of Mixed Turbofans by Means of Adaptive Modelling and Choice of Appropriate Monitoring Parameters
,” AGARD RTO-MP-79: Ageing Mechanisms and Control, No. 9, Manchester, UK.
11.
Mushini
,
R.
, and
Simon
,
D.
, 2005, “
On Optimization of Sensor Selection for Aircraft Gas Turbine Engine
,”
Proceedings of 18th International Conference on Systems Engineering
, pp.
9
18
.
12.
Bechini
,
G.
,
Ameyugo
,
G.
,
Marinai
,
L.
, and
Singh
,
R.
, 2005, “
Gas Path Diagnostics: The Importance of Measurement Selection in the Monitoring Process
,”
Proceedings of the 17th International Symposium on Air Breathing Engines
, Munchen, Germany, Paper No. ISABE-2005-1281.
13.
Sowers
,
T.
,
Kopasakis
,
G.
, and
Simon
,
D. L.
, 2008, “
Application of the Systematic Sensor Selection Strategy for Turbofan Engine Diagnostics
,” ASME Paper No. GT2008-50525.
14.
Borguet
,
S.
, and
Leonard
,
O.
, 2008, “
The Fisher Information Matrix as a Relevant Tool for Sensor Selection in Engine Health Monitoring
,”
Int. J. Rotating Mach.
1023-621X,
2008
, p.
784749
.
15.
Espana
,
M. D.
, and
Gilyard
,
G. B.
, 1993, “
On the Estimation Algorithm Used in Adaptive Performance Optimization of Turbofan Engines
,”
NASA
Report No. TM 4551.
16.
Provost
,
M. J.
, 2003, “
Observability Analysis for Successful Diagnosis of Gas Turbine Faults
,”
Von Karman Institute Lecture Series, VKI LS
, Jan. 13–17.
17.
Li
,
Y. G.
, 2003, “
A Gas Turbine Diagnostic Approach With Transient Measurements
,”
Proc. Inst. Mech. Eng., Part A
0957-6509,
217
(
2
), pp.
169
177
.
18.
Merrington
,
G. L.
, 1989, “
Fault Diagnosis of Gas Turbine Engines From Transient Data
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
111
, pp.
237
243
.
19.
Merrington
,
G. L.
, 1994, “
Fault Diagnosis in Gas Turbine Using a Model-Based Technique
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
116
, pp.
374
380
.
20.
Léonard
,
O.
,
Borguet
,
S.
, and
Dewallef
,
P.
, 2008, “
Adaptive Estimation Algorithm for Aircraft Engine Performance Monitoring
,”
J. Propul. Power
0748-4658,
24
(
4
), pp.
763
769
.
21.
Gupta
,
S.
,
Ray
,
A.
,
Sarkar
,
S.
, and
Yasar
,
M.
, 2008, “
Fault Detection and Isolation in Aircraft Gas Turbine Engines. Part 1: Underlying Concept
,”
Proc. Inst. Mech. Eng., Part G: J. Aeropace Engineering
,
222
, pp.
307
318
.
22.
Gupta
,
S.
,
Ray
,
A.
,
Sarkar
,
S.
, and
Yasar
,
M.
, 2008, “
Fault Detection and Isolation in Aircraft Gas Turbine Engines. Part 2: Validation on a Simulation Test Bed
,”
Proc. Inst. Mech. Eng., Part G: J. Aeropace Engineering
,
222
, pp.
319
330
.
23.
Müller
,
P.
, and
Weber
,
H.
, 1972, “
Analysis and Optimization of Certain Qualities of Controllability and Observability of Linear Dynamic Systems
,”
Automatica
0005-1098,
8
, pp.
237
246
.
24.
Mehra
,
R. K.
, 1976, “
Optimization of Measurement Schedules and Sensor Designs for Linear Dynamic Systems
,”
IEEE Trans. Autom. Control
0018-9286,
21
(
1
), pp.
55
64
.
25.
Mehra
,
R. K.
, 1974, “
Optimal Input Signals for Parameter Estimation in Dynamic Systems—Survey and New Results
,”
IEEE Trans. Autom. Control
0018-9286,
19
(
6
), pp.
753
768
.
26.
Kumar
,
S.
, and
Seinfeld
,
J. H.
, 1978, “
Optimal Location of Measurements in Tubular Reactors
,”
Chem. Eng. Sci.
0009-2509,
33
, pp.
1507
1516
.
27.
Bagajewicz
,
M. J.
, 1997, “
Design and Retrofit of Sensor Networks in Process Plants
,”
AIChE J.
0001-1541,
43
(
9
), pp.
2300
2306
.
28.
Wouwer
,
A. V.
,
Point
,
N.
,
Porteman
,
S.
, and
Remy
,
M.
, 2000, “
An Approach to the Selection of Optimal Sensor Locations in Distributed Parameter Systems
,”
J. Process Control
0959-1524,
10
, pp.
291
300
.
29.
Chmielewski
,
D. J.
,
Palmer
,
T.
, and
Manousiouthakis
,
V.
, 2002, “
On the Theory of Optimal Sensor Placement
,”
AIChE J.
0001-1541,
48
(
5
), pp.
1001
1012
.
30.
Muske
,
K. R.
, and
Georgakis
,
C.
, 2003, “
Optimal Measurement System Design for Chemical Processes
,”
AIChE J.
0001-1541,
49
(
6
), pp.
1488
1494
.
31.
Udwadia
,
F. E.
, 1994, “
Methodology for Optimum Sensor Locations for Parameter Identification in Dynamic Systems
,”
J. Eng. Mech.
0733-9399,
120
(
2
), pp.
368
390
.
32.
Shi
,
Z. Y.
,
Law
,
S. S.
, and
Zhang
,
L. M.
, 2000, “
Optimum Sensor Placement for Structural Damage Detection
,”
J. Eng. Mech.
0733-9399,
126
, pp.
1173
1179
.
33.
Papadimitriou
,
C.
,
Beck
,
J. L.
, and
Au
,
S. -K.
, 2000, “
Entropy-Based Optimal Sensor Location for Structural Model Updating
,”
J. Vib. Control
1077-5463,
6
, pp.
781
800
.
34.
Xia
,
Y.
, and
Hao
,
H.
, 2000, “
Measurement Selection for Vibration-Based Structural Damage Identification
,”
J. Sound Vib.
0022-460X,
236
(
1
), pp.
89
104
.
35.
Mathioudakis
,
K.
, and
Kamboukos
,
Ph.
, 2006, “
Assessment of the Effectiveness Gas Path Diagnostic Schemes
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
128
, pp.
57
63
.
36.
Ehlers
,
J.
, and
Diop
,
A.
, 2007, “
Sensor Selection and State Estimation for Wind Turbine Controls
New York
,”
Proceedings of the 45th AIAA Aerospace Science Meeting and Exhibit
, Reno, NV, Jan. 8–11.
37.
Danai
,
K.
, and
McCusker
,
J. R.
, 2009, “
Parameter Estimation by Parameter Signature Isolation in the Time-Scale Domain
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
131
(
4
), p.
041008
.
38.
Goodwin
,
G. C.
, and
Payne
,
R. L.
, 1977,
Dynamic System Identification: Experiment Design and Data Analysis
,
Academic
,
New York
.
39.
Qureshi
,
Z. H.
,
Ng
,
T. S.
, and
Goodwin
,
G. C.
, 1980, “
Optimum Experiment Design for Identification of Distributed Parameter Systems
,”
Int. J. Control
0020-7179,
31
(
1
), pp.
21
29
.
40.
Fedorov
,
V. V.
, and
Khabarov
,
V.
, 1986, “
Duality of Optimal Designs for Model Discrimination and Parameter Estimation
,”
Biometrika
0006-3444,
73
(
1
), pp.
183
190
.
41.
Jackson
,
J. E.
, 1991,
A User’s Guide to Principle Components
,
Wiley
,
New York
.
42.
Seber
,
G. A. F.
, and
Wild
,
C. J.
, 1989,
Nonlinear Regression
,
Wiley
,
New York
.
43.
Mallat
,
S.
, and
Hwang
,
W. L.
, 1992, “
Singularity Detection and Processing With Wavelets
,”
IEEE Trans. Inf. Theory
0018-9448,
38
(
2
), pp.
617
643
.
44.
Mallat
,
S.
, 1998,
A Wavelet Tour of Signal Processing
, 2nd ed.,
Academic
,
San Diego
.
45.
Thomaseth
,
K.
, and
Cobelli
,
C.
, 1997, “
Parameter Information Content During Model Identification Experiments
,”
Proceedings of IFAC Symposium on Modeling and Control in Biomedical Systems
, Warwick, UK.
You do not currently have access to this content.