A stochastic dynamic load identification algorithm is proposed for an uncertain dynamic system with correlated random system parameters. The stochastic Green's function is adopted to establish the relationship between the Gaussian excitation and the response. The Green's function is approximated by the second-order perturbation method, and orthogonal polynomial chaos bases are adopted to replace the corresponding bases in the Tayler series. The stochastic system responses and the stochastic forces are then represented by the polynomial chaos expansion (PCE) and the Karhunen–Loève expansion (KLE), respectively. A unified probabilistic framework for the stochastic dynamic problem is formulated based on the PCE. The stochastic load identification problem of an uncertain dynamic system is then transformed into a stochastic load identification problem of an equivalent deterministic system with the orthogonality of the PCE. Numerical simulations and experimental studies with a cantilever beam under a concentrate stochastic force are conducted to estimate the statistical characteristics of the stochastic load from the stochastic structural response samples. Results show that the proposed method has good accuracy in the identification of force's statistics when the level of uncertainty in the system parameters is not small. Large errors in the identified statistics may occur when the correlation in the random system parameters is neglected. Different correlation lengths for the random system parameters are investigated to show the effectiveness and accuracy of the proposed method.

References

References
1.
Sanchez
,
J.
, and
Benaroya
,
H.
,
2014
, “
Review of Force Reconstruction Techniques
,”
J. Sound Vib.
,
333
(
14
), pp.
2999
3018
.
2.
Liu
,
Y.
, and
Shepard
,
W. S.
, Jr.
,
2005
, “
Dynamic Force Identification Based on Enhanced Least Squares and Total Least-Squares Schemes in the Frequency Domain
,”
J. Sound Vib.
,
282
(
1–2
), pp.
37
60
.
3.
Law
,
S. S.
,
Chan
,
T. H. T.
, and
Zeng
,
Q. H.
,
1997
, “
Moving Force Identification: A Time Domain Method
,”
J. Sound Vib.
,
201
(
1
), pp.
1
22
.
4.
Qiao
,
B.
,
Zhang
,
X.
,
Wang
,
C.
,
Zhang
,
H.
, and
Chen
,
X.
,
2016
, “
Sparse Regularization for Force Identification Using Dictionaries
,”
J. Sound Vib.
,
368
, pp.
71
86
.
5.
Liu
,
J.
,
Meng
,
X.
,
Jiang
,
C.
,
Han
,
X.
, and
Zhang
,
D.
,
2016
, “
Time-Domain Galerkin Method for Dynamic Load Identification
,”
Int. J. Numer. Meth. Eng.
,
105
(
8
), pp.
620
640
.
6.
Qiao
,
B.
,
Zhang
,
X.
,
Luo
,
X.
, and
Chen
,
X.
,
2015
, “
A Force Identification Method Using Cubic B-Spline Scaling Functions
,”
J. Sound Vib.
,
337
, pp.
28
44
.
7.
Law
,
S. S.
,
Wu
,
S. Q.
, and
Shi
,
Z. Y.
,
2008
, “
Moving Load and Prestress Identification Using Wavelet-Based Method
,”
ASME J. Appl. Mech.
,
75
(2), p.
021014
.
8.
Lu
,
Z. R.
, and
Law
,
S. S.
,
2006
, “
Force Identification Based on Sensitivity in Time Domain
,”
ASCE J. Eng. Mech.
,
132
(
10
), pp.
1050
1056
. x
9.
Lourens
,
E.
,
Reynders
,
E.
,
De Roeck
,
G.
,
Degrande
,
G.
, and
Lombaert
,
G.
,
2012
, “
An Augmented Kalman Filter for Force Identification in Structural Dynamics
,”
Mech. Syst. Signal Process.
,
27
, pp.
446
460
.
10.
Nordstrom
,
L. J. L.
,
2006
, “
A Dynamic Programming Algorithm for Input Estimation on Linear Time-Variant Systems
,”
Comput. Methods Appl. Mech. Eng.
,
195
(
44–47
), pp.
6407
6427
.
11.
Jiang
,
D.
,
Li
,
Y. B.
,
Fei
,
Q. G.
, and
Wu
,
S. Q.
,
2015
, “
Prediction of Uncertain Elastic Parameters of a Braided Composite
,”
Compos. Struct.
,
126
, pp.
123
131
.
12.
Li
,
Y. B.
,
Mulani
,
S. B.
,
Fei
,
Q. G.
,
Wu
,
S. Q.
, and
Zhang
,
P.
,
2017
, “
Vibro-Acoustic Analysis Under Stationary and Non-Stationary Random Excitations With KLE/FEM/BEM
,”
Aerosp. Sci. Technol.
,
66
, pp.
203
215
.
13.
Granger
,
S.
, and
Perotin
,
L.
,
1999
, “
An Inverse Method for the Identification of a Distributed Random Excitation Acting on a Vibrating Structure Part 1: Theory
,”
Mech. Syst. Signal Process.
,
13
(
1
), pp.
53
65
.
14.
Jia
,
Y.
,
Yang
,
Z.
,
Guo
,
N.
, and
Wang
,
L.
,
2015
, “
Random Dynamic Load Identification Based on Error Analysis and Weighted Total Least Squares Method
,”
J. Sound Vib.
,
358
, pp.
111
123
.
15.
Wu
,
S. Q.
, and
Law
,
S. S.
,
2012
, “
Statistical Moving Load Identification Including Uncertainties
,”
Probab. Eng. Mech.
,
29
, pp.
70
78
.
16.
Schuëller
,
G. I.
, and
Pradlwarter
,
H. J.
,
2009
, “
Uncertain Analysis of Complex Structural Systems
,”
Int. J. Numer. Methods Eng.
,
80
(
6–7
), pp.
881
913
.
17.
Wu
,
S. Q.
, and
Law
,
S. S.
,
2010
, “
Moving Force Identification Based on Stochastic Finite Element Model
,”
Eng. Struct.
,
32
(
4
), pp.
1016
1027
.
18.
Zhang
,
E.
,
Antoni
,
J.
, and
Feissel
,
P.
,
2012
, “
Bayesian Force Reconstruction With an Uncertain Model
,”
J. Sound Vib.
,
331
(
4
), pp.
798
814
.
19.
Han
,
S. L.
, and
Kinoshita
,
T.
,
2012
, “
Investigation of a Stochastic Inverse Method to Estimate an External Force: Application to a Wave-Structure Interaction
,”
Math. Probl. Eng.
,
2012
, p.
175036
.
20.
Liu
,
J.
,
Sun
,
X.
,
Han
,
X.
,
Jiang
,
C.
, and
Yu
,
D.
,
2015
, “
Dynamic Load Identification for Stochastic Structures Based on Gegenbauer Polynomial Approximation and Regularization Method
,”
Mech. Syst. Signal Process.
,
56–57
, pp.
35
54
.
21.
Liu
,
J.
,
Sun
,
X.
,
Li
,
K.
,
Jiang
,
C.
, and
Han
,
X.
,
2015
, “
A Probability Density Function Discretization and Approximation Method for the Dynamic Load Identification of Stochastic Structures
,”
J. Sound Vib.
,
357
, pp.
74
94
.
22.
Ghanem
,
R. G.
, and
Spanos
,
P. D.
,
1997
, “
Spectral Techniques for Stochastic Finite Elements
,”
Arch. Comput. Methods Eng.
,
4
(
1
), pp.
63
100
.
23.
Tikhonov
,
A. N.
, and
Arsenin
,
V. Y.
,
1977
, “
Solution of Ill-Posed Problems
,”
SIAM Rev.
,
21
(
2
), pp.
266
267
.
24.
Golub
,
G.
,
Heath
,
M.
, and
Wahba
,
G.
,
1979
, “
Generalized Cross-Validation as a Method for Choosing a Good Ridge Parameter
,”
Technometrics
,
21
(
2
), pp.
215
223
.
25.
Mehrez
,
L.
,
Moens
,
D.
, and
Vandepitte
,
D.
,
2012
, “
Stochastic Identification of Composite Material Properties From Limited Experimental Databases, Part I: Experimental Database Construction
,”
Mech. Syst. Signal Process.
,
27
, pp.
471
483
.
26.
Imregun
,
M.
,
Visser
,
W. J.
, and
Ewins
,
D. J.
,
1995
, “
Finite Element Model Updating Using Frequency Response Function Data—I: Theory and Initial Investigation
,”
Mech. Syst. Signal Process.
,
9
(
2
), pp.
187
202
.
27.
Mehrez
,
L.
,
Doostan
,
A.
,
Moens
,
D.
, and
Vandepitte
,
D.
,
2012
, “
Stochastic Identification of Composite Material Properties From Limited Experimental Databases, Part II: Uncertainty Modelling
,”
Mech. Syst. Signal Process.
,
27
, pp.
484
498
.
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