System identification techniques are often used to determine the parameters required to define a model of a linear time invariant (LTI) system. The Cramer–Rao bound can be used to validate those parameters in order to ensure that the system model is an accurate representation of the system. Unfortunately, the Cramer–Rao bound is only valid for LTI systems and is not valid for linear time periodic (LTP) systems such as a helicopter rotor in forward flight. This paper describes an extension of the Cramer–Rao bound to LTP systems and demonstrates the methodology for a simple LTP system.

1.
Kunz
,
D. L.
,
McNulty
,
M. J.
,
Sorensen
,
J. L.
, and
McCauley
,
K.
, 1995, “
Effects of Age and Use on Apache Main Rotor Support Characteristics
,”
Proceedings of the AIAA/ASME/ASCE/AHS/ACS 36th Structures, Structural Dynamics, and Materials Conference
, AIAA Paper No. 95-1229.
2.
Miller
,
N. A.
, and
Kunz
,
D. L.
, 2006, “
A Comparison of Main Rotor Smoothing Adjustments Using Linear and Neural Network Algorithms
,”
Proceedings of the 62nd Annual Forum of the American Helicopter Society
, pp.
1317
1322
.
3.
Taitel
,
H. J.
,
Danai
,
K.
, and
Gauthier
,
D.
, 1995, “
Helicopter Track and Balance With Artificial Neural Nets
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
117
(
2
), pp.
226
231
.
4.
Wroblewski
,
D.
,
Branhof
,
R. W.
, and
Cook
,
T.
, 2001, “
Neural Networks for Smoothing of Helicopter Rotors
,”
Proceedings of the 57th Annual Forum of the American Helicopter Society
, pp.
1587
1594
.
5.
Kaletka
,
J.
,
Tischler
,
M. B.
,
Von Grunhagen
,
W.
, and
Fletcher
,
J. W.
, 1991, “
Time and Frequency Domain Identification and Verification of Bo-105 Dynamic Models
,”
J. Am. Helicopter Soc.
0002-8711,
36
(
4
), pp.
25
38
.
6.
de Leeuw
,
J. H.
, 1991, “
Identification Techniques: Model Structure and Time Domain Methods
,”
AGARD Lecture Series 178: Rotorcraft System Identification
, NATO, Paper No. AGARD-LS-178, p.
10
.
7.
Padfield
,
G. D.
,
Thorne
,
R.
,
Murray-Smith
,
D.
,
Black
,
C.
, and
Caldwell
,
A. E.
, 1985, “
UK Research Into System Identification for Helicopter Flight Mechanics
,”
Proceedings of the 11th European Rotorcraft Forum
, Paper No. 82.
8.
Tischler
,
M. B.
, 1991, “
Identification Techniques: Frequency Domain Methods
,”
AGARD Lecture Series 178: Rotorcraft System Identification
, NATO, Paper No. AGARD-LS-178, p.
10
.
9.
Tischler
,
M. B.
, 1989, “
Advancements in Frequency Domain Methods for Rotorcraft System Identification
,”
Vertica
0360-5450,
13
(
3
), pp.
327
342
.
10.
Hwang
,
S.
, 1997, “
Frequency Domain System Identification of Helicopter Rotor Dynamics Incorporating Models With Time Periodic Coefficients
,” Ph.D. thesis, University of Maryland, College Park, MD.
11.
Maine
,
R.
, and
Iliff
,
K.
, 1981, “
The Theory and Practice of Estimating the Accuracy of Dynamic Flight-Determined Coefficients
,” National Aeronautics and Space Administration, Dryden Flight Research Center, Reference Publication 1077.
12.
Jones
,
C.
, and
Celi
,
R.
, 1995, “
Determination of Helicopter Rotor Damping From Simulated Data Using Frequency Domain System Identification
,”
Proceedings of the AIAA/ASME/ASCE/AHS/ACS 36th Structures, Structural Dynamics, and Materials Conference
.
13.
Cramr
,
H.
, 1946,
Mathematical Methods of Statistics
,
Princeton University Press
,
Princeton, NJ
.
14.
Kay
,
S. M.
, 1993,
Fundamentals of Statistical Signal Processing: Estimation Theory
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
15.
Wereley
,
N.
, 1991, “
Analysis and Control of Linear Periodically Time Varying Systems
,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
16.
Mannchen
,
T.
, 2003, “
Helicopter Vibration Reduction Using Robust Control
,” Ph.D. thesis, Institut füur Flugmechanik und Flugregelung, Universitäat Stuttgart.
17.
Johnson
,
W.
, 1994,
Helicopter Theory
,
Dover
,
New York
.
18.
Hwang
,
S.
, and
Wereley
,
N.
, 1996, “
Frequency Domain System Identification of Helicopter Blades With Trailing Edge Flaps
,”
AIAA/ASME/AHS Adaptive Structures Forum
.
You do not currently have access to this content.