Abstract

Selecting the proper set of degrees-of-freedom (DoFs) is essential in inverse blocked force calculation. Including too many degrees-of-freedom in the computation can lead to overfitting, resulting in inaccurate force estimations and poor prediction quality. The discrepancy arises from errors within the dataset, such as measurement noise or other artifacts. This article presents a solution to the overfitting problem, introducing the X-DoF procedure to automatically identify the relevant subset of blocked force degrees-of-freedom. Its effectiveness is showed through numerical and experimental validation and compared against regularization techniques.

Issue Section:
Research Papers
Keywords:
active vibration and noise control, dynamics, structural acoustics, system identification
Topics:
Degrees of freedom, Noise (Sound), Dynamics (Mechanics), Polynomials, Sensors, Excitation, Errors

References

1.
Van der Seijs
,
M.
,
De Klerk
,
D.
, and
Rixen
,
D. J.
,
2016
, “
General Framework for Transfer Path Analysis: History, Theory and Classification of Techniques
,”
Mech. Syst. Signal Process.
,
68
, pp.
217
–
244
.
Google Scholar
Crossref
Search ADS
 
2.
Elliott
,
A.
, and
Moorhouse
,
A. T.
,
2008
, “
Characterisation of Structure Borne Sound Sources From Measurement In-situ
,”
J. Acoust. Soc. Am.
,
123
(
5
), p.
3176
.
Google Scholar
Crossref
Search ADS
 
3.
De Klerk
,
D.
,
2009
, “
Dynamic Response Characterization of Complex Systems Through Operational Identification and Dynamic Substructuring
,” Ph.D. thesis,
Delft University of Technology
,
Delft, The Netherlands
.
4.
Magrans
,
F.
,
2009
, “
Path Analysis
,”
Proceedings of the NAG/DAGA Conference
,
Rotterdam, The Netherlands
,
Mar. 23–26
, pp.
768
–
771
.
5.
Van der Seijs
,
M.
,
Rixen
,
D.
, and
Klerk
,
D.
,
2013
, “
An Improved Methodology for the Virtual Point Transformation of Measured Frequency Response Functions in Dynamic Substructuring
,”
4th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering
,
Kos Island, Greece
,
June 12–14
, Vol.
4
, pp.
4334
–
4347
.
Google Scholar
Crossref
Search ADS
 
6.
Haeussler
,
M.
,
Mueller
,
T.
,
Pasma
,
E.
,
Freund
,
J.
,
Westphal
,
O.
, and
Voehringer
,
T.
,
2020
, “
Component Tpa: Benefit of Including Rotational Degrees of Freedom and Over-Determination
,”
Proceedings of the International Conference on Noise and Vibration Engineering
,
Leuven, Belgium
,
Sept. 7–9
, pp.
7
–
9
.
7.
Van der Seijs
,
M.
,
2016
, “
Experimental Dynamic Substructuring: Analysis and Design Strategies for Vehicle Development
,” Ph.D. thesis,
TU Delft
,
Delft, The Netherlands
.
8.
Meggitt
,
J.
,
Moorhouse
,
A.
, and
Elliott
,
A.
,
2018
, “
On the Problem of Describing the Coupling Interface Between Sub-structures: An Experimental Test for “Completeness
,”
Dynamics of Coupled Structures, Volume 4: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018
,
Orlando, FL
,
March
,
Springer
, pp.
171
–
182
.
Google Scholar
Crossref
Search ADS
 
9.
Everitt
,
B. S.
, and
Skrondal
,
A.
,
2010
,
The Cambridge Dictionary of Statistics
,
Cambridge University Press
,
Cambridge
.
Google Scholar
Crossref
Search ADS
 
10.
Brunton
,
S. L.
, and
Kutz
,
J. N.
,
2022
,
Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control
, 2nd ed.,
Cambridge University Press
,
Cambridge
.
Google Scholar
Crossref
Search ADS
 
11.
Haeussler
,
M.
,
2021
, “
Modular Sound & Vibration Engineering by Substructuring
,” Ph.D. thesis,
Technische Universität München
,
Munich, Germany
.
12.
Wernsen
,
M.
,
2017
, “
Observability and Transferability of In-Situ Blocked Force Characterisation
,” Master’s thesis,
Delft University of Technology
,
Delft, The Netherlands
.
13.
Hansen
,
P. C.
,
1987
, “
The Truncated SVD as a Method for Regularization
,”
BIT Num. Math.
,
27
(
4
), pp.
534
–
553
.
Google Scholar
Crossref
Search ADS
 
14.
Moorhouse
,
A.
,
2003
, “
Compensation for Discarded Singular Values in Vibro-Acoustic Inverse Methods
,”
J. Sound Vib.
,
267
(
2
), pp.
245
–
252
.
Google Scholar
Crossref
Search ADS
 
15.
Hoerl
,
A. E.
, and
Kennard
,
R. W.
,
1970
, “
Ridge Regression: Biased Estimation for Nonorthogonal Problems
,”
Technometrics
,
12
(
1
), pp.
55
–
67
.
Google Scholar
Crossref
Search ADS
 
16.
Pati
,
Y. C.
,
Rezaiifar
,
R.
, and
Krishnaprasad
,
P. S.
,
1993
, “
Orthogonal Matching Pursuit: Recursive Function Approximation With Applications to Wavelet Decomposition
,”
Proceedings of 27th Asilomar Conference on Signals, Systems and Computers
,
Pacific Grove, CA
,
Nov. 1–3
,
IEEE
, pp.
40
–
44
.
Google Scholar
Crossref
Search ADS
 
17.
Tibshirani
,
R.
,
1996
, “
Regression Shrinkage and Selection Via the Lasso
,”
J. R. Stat. Soc. Series B: Stat. Methodol.
,
58
(
1
), pp.
267
–
288
.
Google Scholar
Crossref
Search ADS
 
18.
Chen
,
S.
,
Billings
,
S. A.
, and
Luo
,
W.
,
1989
, “
Orthogonal Least Squares Methods and Their Application to Non-linear System Identification
,”
Int. J. Control.
,
50
(
5
), pp.
1873
–
1896
.
Google Scholar
Crossref
Search ADS
 
19.
Blumensath
,
T.
, and
Davies
,
M. E.
,
2007
, “
On the Difference Between Orthogonal Matching Pursuit and Orthogonal Least Squares
,” University of Southampton, Signal Processing & Control Group, Southampton, UK
20.
Mallows
,
C. L.
,
2000
, “
Some Comments on Cp
,”
Technometrics
,
42
(
1
), pp.
87
–
94
.
21.
Hurvich
,
C. M.
, and
Tsai
,
C. -L.
,
1993
, “
A Corrected Akaike Information Criterion for Vector Autoregressive Model Selection
,”
J. Seri. Anal.
,
14
(
3
), pp.
271
–
279
.
Google Scholar
Crossref
Search ADS
 
22.
Schwarz
,
G.
,
1978
, “
Estimating the Dimension of a Model
,”
Ann. Stat.
,
6
(
2
), pp.
461
–
464
.
Google Scholar
Crossref
Search ADS
 
Copyright © 2024 by ASME
You do not currently have access to this content.