Impulse response functions (IRFs) and frequency response functions (FRFs) are bases for modal parameter identification of single-input, single-output (SISO) and multiple-input, multiple-out (MIMO) systems, and the two functions can be transformed from each other using the fast Fourier transform and the inverse fast Fourier transform. An efficient iterative algorithm is developed in this work to directly and accurately calculate the IRFs of SISO and MIMO systems in the time domain using relatively short input and output data series. The iterative algorithm can avoid the time-consuming inversion of a large matrix in the conventional least-square method for calculating an IRF, greatly reducing the computation time. In addition, a fitting index and an error energy decreasing coefficient are introduced to evaluate the accuracy in calculating an IRF and to provide the termination criterion for the iterative algorithm. A new coherence function is also introduced to evaluate the accuracy of calculated IRFs and FRFs at different spectral lines. Two examples are given to illustrate the effectiveness and efficiency of the methodology.

Issue Section:
Technical Briefs
Keywords:
SISO/MIMO systems, impulse response function, frequency response function, time domain, fitting index, error energy decreasing coefficient, coherence function, continuum mechanics, fast Fourier transforms, interpolation, iterative methods, mechanical engineering computing, mechanical variables measurement, MIMO systems, parameter estimation, physics computing, transient response, vibrations
Topics:
Algorithms, Errors, Fittings, Impulse (Physics), Testing

References

1.
Juang
,
J. N.
, and
Pappa
,
R.S.
, 1985, “
An Eigensystem Realization Algorithm for Modal Parameter Identification and Mode Reduction
,”
J. Guid. Control Dyn.
,
8
(
1
), pp.
620
–
627
.
2.
Peeters
,
B.
,
Guillaume
,
P.
,
Van der Auweraer
,
H.
,
Cauberghe
,
B.
,
Verboven
,
P.
, and
Leuridan
,
J.
, 2004, “
Automotive and Aerospace Applications of the PolyMAX Modal Parameter Estimation Method
,” Proceedings of the 22nd IMAC.
3.
Heylen
,
W.
,
Lammens
,
S.
, and
Sas
,
P.
, 1998,
Modal Analysis Theory and Testing
,
Katholieke Universiteit Leuven
,
Belgium
.
4.
Nakamori
,
S.
, 2002, “
Recursive Estimation of Impulse Response Function Using Covariance Information in Linear Continuous Stochastic Systems
,”
Appl. Math. Comput.
,
131
(
2
), pp.
339
–
347
.
5.
Rai
,
R. K.
,
Jain
,
M. K.
,
Mishra
,
S. K.
,
Ojha
,
C. S. P.
, and
Singh
,
V. P.
, 2007, “
Another Look at Z-transform Technique for Deriving Unit Impulse Response Function
,”
Water Resour. Manage.
,
21
, pp.
1829
–
1848
.
Crossref
Search ADS
 
6.
Chen
,
E. W.
,
Liu
,
Z. S.
, and
Wang
,
Y.
, 2005, “
Analysis of Wavelet Transform Method and Time-Domain Method for Extracting the Impulse Response Function of Structural Systems (in Chinese)
,”
J. Vib. Eng.
,
18
(
2
), pp.
189
–
194
.
7.
Ewins
,
D. J.
, 2000,
Modal Testing: Theory, Practice, and Application
, 2nd ed.,
Research Studies Press,
Baldock, Hertfordshire, England
.
8.
Kay
,
S. M.
, 1988,
Modern Spectral Estimation Theory and Application
,
Prentice-Hall, Inc.
,
Englewood Cliffs, NJ
.
9.
Brigham
,
E. O.
, 1974,
The Fast Fourier Transform
,
Prentice-Hall, Inc.
,
Englewood Cliffs, NJ
.
10.
Allemang
,
R.
,
Brown
,
D.
, and
Rost
,
R.
, 1987, “
Experimental Modal Analysis and Dynamic Component Synthesis, Vol. II: Measurement Techniques for Experimental Analysis
,” Report No. AFWAL-TR-87-3069, OH, pp.
29
–
40
.
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 by American Society of Mechanical Engineers
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