This paper describes a nonlinear deterministic estimator based on cumulants for the extraction of modal parameters. The signal analysed is composed of multiple exponentially damped real sinusoids in unknown additive noise. Cumulants reduce significantly the effects of noise and are also an efficient way of compressing the sampled data. In modal analysis a sensor may be unable to detect some modes of vibration due to its location. Cumulants estimated from real data sampled at different locations and instances are added directly together. This average cumulant function will contain the eigenvalues for all excited modes of vibration. Finding the frequencies and corresponding damping factors is therefore reduced to solving a single average cumulant function. The performance of the proposed estimator is examined and compared with the Eigensystem Realization Algorithm via simulations.

Issue Section:
Research Papers
Topics:
Algorithms, Damping, Eigenvalues, Engineering simulation, Modal analysis, Noise (Sound), Sensors, Signals, Simulation, Vibration
1.
Ibrahim
S. R.
, and
Mikulcik
E. C.
, “
A Time Domain Modal Vibration Test Technique
,”
The Shock and Vibration Bulletin
, Vol.
43
, No.
4
, pp.
21
–
37
,
1973
.
2.
Void
H.
,
Kundrat
J.
,
Rocklin
G.
, and
Russell
R.
, “
A Multi-modal Estimation Algorithm for Mini-computers
,”
SAE Transactions
, Vol.
91
, No.
1
, pp.
815
–
821
,
1982
.
3.
Juang
J-N.
, and
Pappa
R. S.
, “
An Eigensystem Realization Algorithm for Modal Parameter Identification and Model Reduction
,”
J. of Guidance
, Vol.
8
, No.
5
, pp.
620
–
627
,
1985
.
4.
Hollkamp
J. J.
, and
Batill
S. M.
, “
Structural Identification Using Order Overspecified Time-series Models
,”
ASME Journal of Dynamic Systems Measurement Control
, Vol.
114
, pp.
27
–
33
, March
1992
.
5.
Bresler
Yoram
, and
Macovski
Albert
, “
Exact Maximum Likelihood Parameter Estimation of Superimposed Exponential Signals in Noise
,”
IEEE Transactions on Acoustics, Speech, and Signal Processing
, Vol.
34
, No.
5
, pp.
1081
–
1089
, October
1986
.
6.
Anderson
John M. M.
,
Giannakis
Georgios B.
, and
Swami
Ananthram
, “
Harmonic Retrival Using Higher Order Statistics: A Deterministic Formulation
,”
IEEE Transactions on Signal Processing
, Vol.
43
, No.
8
, pp.
1880
–
1889
, August
1995
.
7.
Mendel
Jerry M.
, “
Tutorial on Higher-order Statistics (Spectra) in Signal Processing and System Theory: Theoretical Results and Some Applications
,”
Proceedings of the IEEE
, Vol.
79
, No.
3
, pp.
278
–
305
, March
1991
.
8.
Cook, R. D., Malkus, D. S., and Plesha, M. E., Concepts and Applications of Finite Element Analysis, John Wiley & Sons, Singapore, 1989.
9.
Umapathi
Reddy V.
, and
Biradar
L. S.
, “
SVD-based Information Theoretic Criteria for Detection of the Number of Damped/Undamped Sinusoids and Their Performance Analysis
,”
IEEE Transactions on Signal Processing
, Vol.
41
, No.
9
, pp.
2872
–
2881
, September
1993
.
10.
Hua
Yingbo
, and
Sarkar
Tapan K.
, “
Matrix Pencil Method for Estimating Parameters of Exponentially Damped/Undamped Sinusoids in Noise
,”
IEEE Transactions on Acoustics, Speech, and Signal Processing
, Vol.
38
, No.
5
, pp.
814
–
824
, May
1990
.
11.
Starer
David
, and
Nehorai
Arye
, “
Newton Algorithms for Conditional and Unconditional Maximum Likelihood Estimation of the Parameters of Exponential Signals in Noise
,”
IEEE Transactions on Signal Processing
, Vol.
40
, No.
6
, pp.
1528
–
1534
, June
1992
12.
Steedly
William M.
, and
Moses
Randolph L.
, “
The cramer-rao Bound for Pole and Amplitude Coefficient Estimates of Damped Exponential Signals in Noise
,”
IEEE Transactions on Signal Processing
, Vol.
41
, No.
3
, pp.
1305
–
1318
, March
1993
.
13.
Papadopoulos
Christos K.
, and
Nikias
Chrysostomos L.
, “
Parameter Estimation of Exponentially Damped Sinusoids Using Higher Order Statistics
,”
IEEE Transactions on Acoustics, Speech, and Signal Processing
, Vol.
38
, No.
8
, pp.
1424
–
1435
, August
1990
.
14.
Ljung, Lennard, System Identification: Theory for the User, Prentice Hall, Englewood Cliffs, New Jersey, 1987.
15.
Hua
Yingbo
, “
The Most Efficient Implementation of the IQML Algorithm
,”
IEEE Transactions on Signal Processing
, Vol.
42
, No.
8
, pp.
2203
–
2204
, August
1994
.
16.
Juang
J-N.
, and
Pappa
R. S.
, “
Effects of Noise on Modal Parameters Identified by die Eigensystem Realization Algorithm
,”
J. of Guidance
, Vol.
9
, No.
3
, pp.
294
–
303
,
1986
.
This content is only available via PDF.
Copyright © 1998
 by The American Society of Mechanical Engineers
You do not currently have access to this content.