Abstract

This manuscript provides a detailed synopsis of the contemporary advancements in the nascent area of real-time structural damage detection for vibrating systems. The paper mainly focuses on the theoretical development and engineering applications of algorithms that are based on first-order perturbation (FOP) techniques applied to vibration responses. The importance of this work stems from the fact that recent developments in the field of online structural health monitoring (SHM) have given rise to algorithms that are computationally complex and, consequently, are not amenable to real-time implementation. In this paper, we discuss and demonstrate the FOP-based algorithms in the light of all the contemporary nonadaptive/nonrecursive techniques to establish their relevance. We review 216 papers in this regard. The efficacy, efficiency, robustness, and the applicability of the FOP family of algorithms are highlighted in light of several experimental, theoretical, and field studies.

References

References
1.
Farrar
,
C. R.
, and
Worden
,
K.
,
2007
, “
An Introduction to Structural Health Monitoring
,”
Philos. Trans. R. Soc. London A
,
365
(
1851
), pp.
303
315
.10.1098/rsta.2006.1928
2.
Balageas
,
D.
,
Fritzen
,
C.-P.
, and
Güemes
,
A.
,
2006
,
Structural Health Monitoring
, Vol.
493
,
Wiley
,
Hoboken, NJ
.
3.
Farrar
,
C. R.
, and
Worden
,
K.
,
2012
,
Structural Health Monitoring: A Machine Learning Perspective
,
Wiley
,
Hoboken, NJ
.
4.
Doebling
,
S. W.
,
Farrar
,
C. R.
, and
Prime
,
M. B.
,
1998
, “
A Summary Review of Vibration-Based Damage Identification Methods
,”
Shock Vib. Dig.
,
30
(
2
), pp.
91
105
.10.1177/058310249803000201
5.
Yan
,
Y. J.
,
Cheng
,
L.
,
Wu
,
Z. Y.
, and
Yam
,
L. H.
,
2007
, “
Development in Vibration-Based Structural Damage Detection Technique
,”
Mech. Syst. Signal Process.
,
21
(
5
), pp.
2198
2211
.10.1016/j.ymssp.2006.10.002
6.
Nair
,
K. K.
,
Kiremidjian
,
A. S.
, and
Law
,
K. H.
,
2006
, “
Time Series-Based Damage Detection and Localization Algorithm With Application to the ASCE Benchmark Structure
,”
J. Sound Vib.
,
291
(
1–2
), pp.
349
368
.10.1016/j.jsv.2005.06.016
7.
Sharman
,
K.
, and
Friedlander
,
B.
,
1984
, “
Time-Varying Autoregressive Modeling of a Class of Nonstationary Signals
,”
IEEE International Conference on Acoustics, Speech, and Signal Processing
(
ICASSP'84
),
San Diego, CA
,
Mar. 19–21
, pp.
227
230
.10.1109/ICASSP.1984.1172536
8.
Ratcliffe
,
C. P.
,
1997
, “
Damage Detection Using a Modified Laplacian Operator on Mode Shape Data
,”
J. Sound Vib.
,
204
(
3
), pp.
505
517
.10.1006/jsvi.1997.0961
9.
Mirmomeni
,
M.
,
Lucas
,
C.
,
Araabi
,
B. N.
,
Moshiri
,
B.
, and
Bidar
,
M. R.
,
2011
, “
Recursive Spectral Analysis of Natural Time Series Based on Eigenvector Matrix Perturbation for Online Applications
,”
IET Signal Process.
,
5
(
6
), pp.
515
526
.10.1049/iet-spr.2009.0278
10.
Zimmerman
,
D. C.
, and
Kaouk
,
M.
,
1992
, “
Eigenstructure Assignment Approach for Structural Damage Detection
,”
AIAA J.
,
30
(
7
), pp.
1848
1855
.10.2514/3.11146
11.
Rytter
,
A.
,
1993
, “
Vibrational Based Inspection of Civil Engineering Structures
,” Ph.D. dissertation, Aalborg University, Aalborg, Denmark.
12.
Spencer
,
B. F.
, Jr.
, and
Nagarajaiah
,
S.
,
2003
, “
State of the Art of Structural Control
,”
J. Struct. Eng.
,
129
(
7
), pp.
845
856
.10.1061/(ASCE)0733-9445(2003)129:7(845)
13.
Bodeux
,
J. B.
, and
Golinval
,
J. C.
,
2014
, “
Application of ARMAV Models to the Identification and Damage Detection of Mechanical and Civil Engineering Structures
,”
Smart Mater. Struct.
,
10
(
3
), pp.
479
489
.10.1088/0964-1726/10/3/309
14.
Worden
,
K.
, and
Dulieu-Barton
,
J. M.
,
2004
, “
An Overview of Intelligent Fault Detection in Systems and Structure
,”
Struct. Health Monit.
,
3
(
1
), pp.
85
98
.10.1177/1475921704041866
15.
Krishnan
,
M.
,
Bhowmik
,
B.
,
Tiwari
,
A. K.
, and
Hazra
,
B.
,
2017
, “
Online Damage Detection Using Recursive Principal Component Analysis and Recursive Condition Indicators
,”
Smart Mater. Struct.
,
26
(
8
), p.
085017
.10.1088/1361-665X/aa7220
16.
Lovera
,
M.
,
Gustafsson
,
T.
, and
Verhaegen
,
M.
,
2000
, “
Recursive Subspace Identification of Linear and Non-Linear Wiener State-Space Models
,”
Automatica
,
36
(
11
), pp.
1639
1650
.10.1016/S0005-1098(00)00103-5
17.
Hou
,
J.
,
Jankowski
,
Ł.
, and
Ou
,
J.
,
2013
, “
An Online Substructure Identification Method for Local Structural Health Monitoring
,”
Smart Mater. Struct.
,
22
(
9
), p.
095017
.10.1088/0964-1726/22/9/095017
18.
Lee
,
D. S.
,
Park
,
J. M.
, and
Vanrolleghem
,
P. A.
,
2005
, “
Adaptive Multiscale Principal Component Analysis for On-Line Monitoring of a Sequencing Batch Reactor
,”
Mech. Syst. Signal Process.
,
116
(
2
), pp.
195
210
.10.1016/j.jbiotec.2004.10.012
19.
Kato
,
T.
,
2013
,
Perturbation Theory for Linear Operators
, Vol.
132
,
Springer Science & Business Media
,
Berlin
.10.1007/978-3-642-66282-9
20.
Sibson
,
R.
,
1979
, “
Studies in the Robustness of Multidimensional Scaling: Perturbational Analysis of Classical Scaling
,”
J. R. Stat. Soc., Ser. B
,
41
(
2
), pp.
217
229
.10.1111/j.2517-6161.1979.tb01076.x
21.
Krishnan
,
M.
,
Bhowmik
,
B.
,
Hazra
,
B.
, and
Pakrashi
,
V.
,
2018
, “
Real Time Damage Detection Using Recursive Principal Components and Time Varying Auto-Regressive Modeling
,”
Mech. Syst. Signal Process.
,
101
, pp.
549
574
.10.1016/j.ymssp.2017.08.037
22.
Bhowmik
,
B.
,
Krishnan
,
M.
,
Hazra
,
B.
, and
Pakrashi
,
V.
,
2018
, “
Real Time Unified Single and Multi-Channel Structural Damage Detection Using Recursive Singular Spectrum Analysis
,”
Struct. Health Monit.
,
18
(
2
), pp.
563
589
.10.1177/1475921718760483
23.
Mottershead
,
J. E.
, and
Friswell
,
M. I.
,
1993
, “
Model Updating in Structural Dynamics: A Survey
,”
J. Sound Vib.
,
167
(
2
), pp.
347
375
.10.1006/jsvi.1993.1340
24.
Hazra
,
B.
, and
Narasimhan
,
S.
,
2010
, “
Wavelet-Based Blind Identification of the UCLA Factor Building Using Ambient and Earthquake Responses
,”
Smart Mater. Struct.
,
19
(
2
), p.
025005
.10.1088/0964-1726/19/2/025005
25.
Kunwar
,
A.
,
Jha
,
R.
,
Whelan
,
M.
, and
Janoyan
,
K.
,
2013
, “
Damage Detection in an Experimental Bridge Model Using Hilbert–Huang Transform of Transient Vibrations
,”
Struct. Control Health Monit.
,
20
(
1
), pp.
1
15
.10.1002/stc.466
26.
Astroza
,
R.
,
Ebrahimian
,
H.
, and
Conte
,
J. P.
,
2015
, “
Material Parameter Identification in Distributed Plasticity FE Models of Frame-Type Structures Using Nonlinear Stochastic Filtering
,”
J. Eng. Mech.
,
141
(
5
), p.
04014149
.10.1061/(ASCE)EM.1943-7889.0000851
27.
Nasrellah
,
H. A.
, and
Manohar
,
C. S.
,
2011
, “
Particle Filters for Structural System Identification Using Multiple Test and Sensor Data: A Combined Computational and Experimental Study
,”
Struct. Control Health Monit.
,
18
(
1
), pp.
99
120
.10.1002/stc.361
28.
Chatzis
,
M. N.
,
Chatzi
,
E. N.
, and
Smyth
,
A. W.
,
2015
, “
An Experimental Validation of Time Domain System Identification Methods With Fusion of Heterogeneous Data
,”
Earthquake Eng. Struct. Dyn.
,
44
(
4
), pp.
523
547
.10.1002/eqe.2528
29.
Azam
,
S. E.
,
Ghisi
,
A.
, and
Mariani
,
S.
,
2012
, “
Parallelized Sigma-Point Kalman Filtering for Structural Dynamics
,”
Comput. Struct.
,
92
, pp.
193
205
.10.1016/j.compstruc.2011.11.004
30.
Behmanesh
,
I.
, and
Moaveni
,
B.
,
2015
, “
Probabilistic Identification of Simulated Damage on the Dowling Hall Footbridge Through Bayesian Finite Element Model Updating
,”
Struct. Control Health Monit.
,
22
(
3
), pp.
463
483
.10.1002/stc.1684
31.
Brownjohn
,
J.-M.
,
Xia
,
P.-Q.
,
Hao
,
H.
, and
Xia
,
Y.
,
2001
, “
Civil Structure Condition Assessment by FE Model Updating: Methodology and Case Studies
,”
Finite Elem. Anal. Des.
,
37
(
10
), pp.
761
775
.10.1016/S0168-874X(00)00071-8
32.
Jaksic
,
V.
,
Mandic
,
D. P.
,
Ryan
,
K.
,
Basu
,
B.
, and
Pakrashi
,
V.
,
2016
, “
A Comprehensive Study of the Delay Vector Variance Method for Quantification of Nonlinearity in Dynamical Systems
,”
R. Soc. Open Sci.
,
2
, p.
150493
.10.1098/rsos.150493
33.
Jaksic
,
V.
,
O Shea
,
R.
,
Cahill
,
P.
,
Murphy
,
J.
,
Mandic
,
D. P.
, and
Pakrashi
,
V.
,
2015
, “
Dynamic Response Signatures of a Scaled Model Platform for Floating Wind Turbines in an Ocean Wave Basin
,”
Philos. Trans. R. Soc. A
,
373
(
2035
), p.
20140078
.10.1098/rsta.2014.0078
34.
Jaksic
,
V.
,
Wright
,
C. S.
,
Murphy
,
J.
,
Afeef
,
C.
,
Ali
,
S. F.
,
Mandic
,
D. P.
, and
Pakrashi
,
V.
,
2015
, “
Dynamic Response Mitigation of Floating Wind Turbine Platforms Using Tuned Liquid Column Dampers
,”
Philos. Trans. R. Soc. A
,
373
(
2035
), p.
20140079
9.10.1098/rsta.2014.0079
35.
Koh
,
B. H.
,
Dharap
,
P.
,
Nagarajaiah
,
S.
, and
Phan
,
M. Q.
,
2005
, “
Real-Time Structural Damage Monitoring by Input Error Function
,”
AIAA J.
,
43
(
8
), pp.
1808
1814
.10.2514/1.14008
36.
Safak
,
E.
, and
Hudnut
,
K.
,
2006
, “
Real-Time Structural Monitoring and Damage Detection by Acceleration and GPS Sensors
,”
Eighth U.S. National Conference on Earthquake Engineering
,
San Francisco, CA
,
Apr. 18–22
.
37.
Wahab
,
M. M.-A.
, and
De Roeck
,
G.
,
1999
, “
Damage Detection in Bridges Using Modal Curvatures: Application to a Real Damage Scenario
,”
J. Sound Vib.
,
226
(
2
), pp.
217
235
.10.1006/jsvi.1999.2295
38.
Kessler
,
S. S.
,
Spearing
,
S. M.
, and
Soutis
,
C.
,
2002
, “
Damage Detection in Composite Materials Using Lamb Wave Methods
,”
Smart Mater. Struct.
,
11
(
2
), p.
269
.10.1088/0964-1726/11/2/310
39.
Ostachowicz
,
W. M.
,
2008
, “
Damage Detection of Structures Using Spectral Finite Element Method
,”
Comput. Struct.
,
86
(
3–5
), pp.
454
462
.10.1016/j.compstruc.2007.02.004
40.
Jaishi
,
B.
, and
Ren
,
W.-X.
,
2005
, “
Structural Finite Element Model Updating Using Ambient Vibration Test Results
,”
J. Struct. Eng.
,
131
(
4
), pp.
617
628
.10.1061/(ASCE)0733-9445(2005)131:4(617)
41.
Zimmerman
,
D. C.
, and
Kaouk
,
M.
,
1994
, “
Structural Damage Detection Using a Minimum Rank Update Theory
,”
ASME J. Vib. Acoust.
,
116
(
2
), pp.
222
231
.10.1115/1.2930416
42.
Jaishi
,
B.
, and
Ren
,
W.-X.
,
2006
, “
Damage Detection by Finite Element Model Updating Using Modal Flexibility Residual
,”
J. Sound Vib.
,
290
(
1–2
), pp.
369
387
.10.1016/j.jsv.2005.04.006
43.
Balsamo
,
L.
, and
Betti
,
R.
,
2015
, “
Data-Based Structural Health Monitoring Using Small Training Data Sets
,”
Struct. Control Health Monit.
,
22
(
10
), pp.
1240
1264
.10.1002/stc.1744
44.
Skolnik
,
D.
,
Lei
,
Y.
,
Yu
,
E.
, and
Wallace
,
J. W.
,
2006
, “
Identification, Model Updating, and Response Prediction of an Instrumented 15-Story Steel-Frame Building
,”
Earthquake Spectra
,
22
(
3
), pp.
781
802
.10.1193/1.2219487
45.
Fritzen
,
C. P.
, and
Bohle
,
K.
,
2001
, “
Application of Model-Based Damage Identification to a Seismically Loaded Structure
,”
Smart Mater. Struct.
,
10
(
3
), pp.
452
458
.10.1088/0964-1726/10/3/305
46.
Teughels
,
A.
, and
De Roeck
,
G.
,
2005
, “
Damage Detection and Parameter Identification by Finite Element Model Updating
,”
Rev. Eur. Génie Civ.
,
9
(
1–2
), pp.
109
158
.10.1080/17747120.2005.9692748
47.
Hajela
,
P.
, and
Soeiro
,
F. J.
,
1990
, “
Structural Damage Detection Based on Static and Modal Analysis
,”
AIAA J.
,
28
(
6
), pp.
1110
1115
.10.2514/3.25174
48.
An
,
Y.
, and
Ou
,
J.
,
2013
, “
Experimental and Numerical Studies on Model Updating Method of Damage Severity Identification Utilizing Four Cost Functions
,”
Struct. Control Health Monit.
,
20
(
1
), pp.
107
120
.10.1002/stc.480
49.
Lee
,
E.-T.
, and
Eun
,
H.-C.
,
2014
,
A Model-Based Substructuring Method for Local Damage Detection of Structure Shock and Vibration
,
Hindawi Publishing
,
London
.10.1155/2014/390769
50.
Curadelli
,
R. O.
,
Riera
,
J. D.
,
Ambrosini
,
D.
, and
Amani
,
M. G.
,
2008
, “
Damage Detection by Means of Structural Damping Identification
,”
Eng. Struct.
,
30
(
12
), pp.
3497
3504
.10.1016/j.engstruct.2008.05.024
51.
Pandey
,
A. K.
,
Biswas
,
M.
, and
Samman
,
M. M.
,
1991
, “
Damage Detection From Changes in Curvature Mode Shapes
,”
J. Sound Vib.
,
145
(
2
), pp.
321
332
.10.1016/0022-460X(91)90595-B
52.
Yan
,
A. M.
,
Kerschen
,
G.
,
De Boe
,
P.
, and
Golinval
,
J. C.
,
2005
, “
Structural Damage Diagnosis Under Varying Environmental Conditions—Part I: A Linear Analysis
,”
Mech. Syst. Signal Process.
,
19
(
4
), pp.
847
864
.10.1016/j.ymssp.2004.12.002
53.
Hearn
,
G.
, and
Testa
,
R. B.
,
1991
, “
Modal Analysis for Damage Detection in Structures
,”
J. Struct. Eng.
,
117
(
10
), pp.
3042
3063
.10.1061/(ASCE)0733-9445(1991)117:10(3042)
54.
Pandey
,
A. K.
, and
Biswas
,
M.
,
1994
, “
Damage Detection in Structures Using Changes in Flexibility
,”
J. Sound Vib.
,
169
(
1
), pp.
3
17
.10.1006/jsvi.1994.1002
55.
Ciang
,
C. C.
,
Lee
,
J. R.
, and
Bang
,
H. J.
,
2008
, “
Structural Health Monitoring for a Wind Turbine System: A Review of Damage Detection Methods
,”
Meas. Sci. Technol.
,
19
(
12
), p.
122001
.10.1088/0957-0233/19/12/122001
56.
Salawu
,
O. S.
,
1997
, “
Detection of Structural Damage Through Changes in Frequency: A Review
,”
Eng. Struct.
,
19
(
9
), pp.
718
723
.10.1016/S0141-0296(96)00149-6
57.
Zou
,
Y.
,
Tong
,
L.
, and
Steven
,
G. P.
,
2000
, “
Vibration-Based Model-Dependent Damage (Delamination) Identification and Health Monitoring for Composite Structures—A Review
,”
J. Sound Vib.
,
230
(
2
), pp.
357
378
.10.1006/jsvi.1999.2624
58.
Kim
,
J. T.
,
Ryu
,
Y.-S.
,
Cho
,
H.-M.
, and
Stubbs
,
N.
,
2003
, “
Damage Identification in Beam-Type Structures: Frequency-Based Method versus Mode-Shape-Based Method
,”
Eng. Struct.
,
25
(
1
), pp.
57
67
.10.1016/S0141-0296(02)00118-9
59.
Carden
,
E. P.
, and
Fanning
,
P.
,
2004
, “
Vibration Based Condition Monitoring: A Review
,”
Struct. Health Monit.
,
3
(
4
), pp.
355
377
.10.1177/1475921704047500
60.
Fan
,
W.
, and
Qiao
,
P.
,
2011
, “
Vibration-Based Damage Identification Methods: A Review and Comparative Study
,”
Struct. Health Monit.
,
10
(
1
), pp.
83
111
.10.1177/1475921710365419
61.
Li
,
Y. Y.
, and
Chen
,
Y.
,
2013
, “
A Review on Recent Development of Vibration-Based Structural Robust Damage Detection
,”
Struct. Eng. Mech.
,
45
(
2
), pp.
159
168
.10.12989/sem.2013.45.2.159
62.
Sadhu
,
A.
, and
Hazra
,
B.
,
2013
, “
A Novel Damage Detection Algorithm Using Time-Series Analysis-Based Blind Source Separation
,”
Shock Vib.
,
20
(
3
), pp.
423
438
.10.1155/2013/237805
63.
Posenato
,
D.
,
Lanata
,
F.
,
Inaudi
,
D.
, and
Smith
,
I.-F.
,
2008
, “
Model-Free Data Interpretation for Continuous Monitoring of Complex Structures
,”
Adv. Eng. Inf.
,
22
(
1
), pp.
135
144
.10.1016/j.aei.2007.02.002
64.
Yang
,
J. N.
,
Lei
,
Y.
,
Lin
,
S.
, and
Huang
,
N.
,
2004
, “
Hilbert-Huang Based Approach for Structural Damage Detection
,”
J. Eng. Mech.
,
130
(
1
), pp.
85
95
.10.1061/(ASCE)0733-9399(2004)130:1(85)
65.
Nigro
,
M. B.
,
Pakzad
,
S. N.
, and
Dorvash
,
S.
,
2014
, “
Localized Structural Damage Detection: A Change Point Analysis
,”
Comput.-Aided Civ. Infrastruct. Eng.
,
29
(
6
), pp.
416
432
.10.1111/mice.12059
66.
Posenato
,
D.
,
Kripakaran
,
P.
,
Inaudi
,
D.
, and
Smith
,
I.-F.
,
2010
, “
Methodologies for Model-Free Data Interpretation of Civil Engineering Structures
,”
Comput. Struct.
,
88
, pp.
467
482
.10.1016/j.compstruc.2010.01.001
67.
Laory
,
I.
,
Trinh
,
T. N.
, and
Smith
,
I.-F.
,
2011
, “
Evaluating Two Model-Free Data Interpretation Methods for Measurements That Are Influenced by Temperature
,”
Adv. Eng. Inf.
,
25
(
3
), pp.
495
506
.10.1016/j.aei.2011.01.001
68.
Yam
,
L. H.
,
Yan
,
Y. J.
, and
Jiang
,
J. S.
,
2003
, “
Vibration-Based Damage Detection for Composite Structures Using Wavelet Transform and Neural Network Identification
,”
Compos. Struct.
,
60
(
4
), pp.
403
412
.10.1016/S0263-8223(03)00023-0
69.
Peeters
,
B.
,
Maeck
,
J.
, and
De Roeck
,
G.
,
2001
, “
Vibration-Based Damage Detection in Civil Engineering: Excitation Sources and Temperature Effects
,”
Smart Mater. Struct.
,
10
(
3
), pp.
518
527
.10.1088/0964-1726/10/3/314
70.
Rucka
,
M.
, and
Wilde
,
K.
,
2006
, “
Application of Continuous Wavelet Transform in Vibration Based Damage Detection Method for Beams and Plates
,”
J. Sound Vib.
,
297
(
3–5
), pp.
536
550
.10.1016/j.jsv.2006.04.015
71.
Fugate
,
M. L.
,
Sohn
,
H.
, and
Farrar
,
C. R.
,
2001
, “
Vibration-Based Damage Detection Using Statistical Process Control
,”
Mech. Syst. Signal Process.
,
15
(
4
), pp.
707
721
.10.1006/mssp.2000.1323
72.
Hou
,
Z.
,
Noori
,
M.
, and
Amand
,
R. S.
,
2000
, “
Wavelet-Based Approach for Structural Damage Detection
,”
J. Eng. Mech.
,
126
(
7
), pp.
677
683
.10.1061/(ASCE)0733-9399(2000)126:7(677)
73.
Deraemaeker
,
A.
,
Reynders
,
E.
,
De Roeck
,
G.
, and
Kullaa
,
J.
,
2008
, “
Vibration-Based Structural Health Monitoring Using Output-Only Measurements Under Changing Environment
,”
Mech. Syst. Signal Process.
,
22
(
1
), pp.
34
56
.10.1016/j.ymssp.2007.07.004
74.
Feng
,
L.
,
Yi
,
X.
,
Zhu
,
D.
,
Xie
,
X.
, and
Wang
,
Y.
,
2015
, “
Damage Detection of Metro Tunnel Structure Through Transmissibility Function and Cross Correlation Analysis Using Local Excitation and Measurement
,”
Mech. Syst. Signal Process.
,
60
, pp.
59
74
.10.1016/j.ymssp.2015.02.007
75.
Fitzgerald
,
B.
,
Arrigan
,
J.
, and
Basu
,
B.
,
2010
, “
Damage Detection in Wind Turbine Blades Using Time-Frequency Analysis of Vibration Signals
,”
IEEE International Joint Conference on Neural Networks
(
IJCNN
),
Barcelona, Spain
,
July 18–23
, pp.
1
5
.10.1109/IJCNN.2010.5596790
76.
Li
,
H.
,
Deng
,
X.
, and
Dai
,
H.
,
2007
, “
Structural Damage Detection Using the Combination Method of EMD and Wavelet Analysis
,”
Mech. Syst. Signal Process.
,
21
(
1
), pp.
298
306
.10.1016/j.ymssp.2006.05.001
77.
Xu
,
Y. L.
, and
Chen
,
J.
,
2004
, “
Structural Damage Detection Using Empirical Mode Decomposition: Experimental Investigation
,”
J. Eng. Mech.
,
130
(
11
), pp.
1279
1288
.10.1061/(ASCE)0733-9399(2004)130:11(1279)
78.
Kesavan
,
K. N.
, and
Kiremidjian
,
A. S.
,
2012
, “
A Wavelet-Based Damage Diagnosis Algorithm Using Principal Component Analysis
,”
Struct. Control Health Monit.
,
19
(
8
), pp.
672
685
.10.1002/stc.462
79.
Yang
,
Y.
, and
Nagarajaiah
,
S.
,
2014
, “
Blind Identification of Damage in Time-Varying Systems Using Independent Component Analysis With Wavelet Transform
,”
Mech. Syst. Signal Process.
,
47
(
1–2
), pp.
3
20
.10.1016/j.ymssp.2012.08.029
80.
Pakrashi
,
V.
,
Basu
,
B.
, and
O'Connor
,
A.
,
2007
, “
Structural Damage Detection and Calibration Using a Wavelet–Kurtosis Technique
,”
Eng. Struct.
,
29
(
9
), pp.
2097
2108
.10.1016/j.engstruct.2006.10.013
81.
Pakrashi
,
V.
,
O'Connor
,
A.
, and
Basu
,
B.
,
2007
, “
A Study on the Effects of Damage Models and Wavelet Bases for Damage Identification and Calibration in Beams
,”
Comput.-Aided Civ. Infrastruct. Eng.
,
22
(
8
), pp.
555
569
.10.1111/j.1467-8667.2007.00510.x
82.
Hazra
,
B.
,
Sadhu
,
A.
,
Roffel
,
A. J.
, and
Narasimhan
,
S.
,
2012
, “
Hybrid Time-Frequency Blind Source Separation Towards Ambient System Identification of Structures
,”
Comput.-Aided Civ. Infrastruct. Eng.
,
27
(
5
), pp.
314
332
.10.1111/j.1467-8667.2011.00732.x
83.
Poncelet
,
F.
,
Kerschen
,
G.
,
Golinval
,
J. C.
, and
Verhelst
,
D.
,
2007
, “
Output-Only Modal Analysis Using Blind Source Separation Techniques
,”
Mech. Syst. Signal Process.
,
21
(
6
), pp.
2335
2358
.10.1016/j.ymssp.2006.12.005
84.
Antoni
,
J.
,
2005
, “
Blind Separation of Vibration Components: Principles and Demonstrations
,”
Mech. Syst. Signal Process.
,
19
(
6
), pp.
1166
1180
.10.1016/j.ymssp.2005.08.008
85.
Morovati
,
V.
, and
Kazemi
,
M. T.
,
2013
, “
Detection of Sudden Structural Damage Using Blind Source Separation and Time–Frequency Approaches
,”
Smart Mater. Struct.
,
42
(
8
), pp.
1221
1242
.10.1088/0964-1726/25/5/055008
86.
Zang
,
C.
,
Friswell
,
M. I.
, and
Imregun
,
M.
,
2004
, “
Structural Damage Detection Using Independent Component Analysis
,”
Struct. Health Monit.
,
3
(
1
), pp.
69
83
.10.1177/1475921704041876
87.
Sohn
,
H.
, and
Farrar
,
C. R.
,
2001
, “
Damage Diagnosis Using Time Series Analysis of Vibration Signals
,”
Smart Mater. Struct.
,
10
(
3
), pp.
446
451
.10.1088/0964-1726/10/3/304
88.
Musafere
,
F.
,
Sadhu
,
A.
, and
Liu
,
K.
,
2016
, “
Towards Damage Detection Using Blind Source Separation Integrated With Time-Varying Auto-Regressive Modeling
,”
Smart Mater. Struct.
,
25
(
1
), p.
015013
.10.1088/0964-1726/25/1/015013
89.
Nair
,
K. K.
, and
Kiremidjian
,
A. S.
,
2007
, “
Time Series Based Structural Damage Detection Algorithm Using Gaussian Mixtures Modeling
,”
ASME J. Dyn., Syst., Meas., Control
,
129
(
3
), pp.
285
293
.10.1115/1.2718241
90.
Misra
,
M.
,
Yue
,
H. H.
,
Qin
,
S. J.
, and
Ling
,
C.
,
2002
, “
Multivariate Process Monitoring and Fault Diagnosis by Multi-Scale PCA
,”
Comput. Chem. Eng.
,
26
(
9
), pp.
1281
1293
.10.1016/S0098-1354(02)00093-5
91.
Messina
,
A.
,
Williams
,
E. J.
, and
Contursi
,
T.
,
1998
, “
Structural Damage Detection by a Sensitivity and Statistical-Based Method
,”
J. Sound Vib.
,
216
(
5
), pp.
791
808
.10.1006/jsvi.1998.1728
92.
Hassani
,
H.
,
2010
,
A Brief Introduction to Singular Spectrum Analysis
(Optimal Decisions in Statistics and Data Analysis), Vol. 13,
UK
.http://ssa.cf.ac.uk/ssa2010/a_brief_introduction_to_ssa.pdf
93.
Golyandina
,
N.
, and
Zhigljavsky
,
A.
,
2013
, “
Singular Spectrum Analysis for Time Series
,”
Earthquake Eng. Struct. Dyn.
,
44
(
6
), pp.
831
848
.10.1007/978-3-642-34913-3
94.
Feeny
,
B.
,
2002
, “
On Proper Orthogonal co-Ordinates as Indicators of Modal Activity
,”
J. Sound Vib.
,
255
(
5
), pp.
805
817
.10.1006/jsvi.2001.4120
95.
Jolliffe
,
I. T.
,
1986
,
Principal Component Analysis and Factor Analysis
, Principal Component Analysis (Springer Series in Statistics)
Springer
,
New York
, pp.
115
128
.10.1007/978-1-4757-1904-8_7
96.
Tipping
,
M. E.
, and
Bishop
,
C. M.
,
1999
, “
Probabilistic Principal Component Analysis
,”
J. R. Stat. Soc.: Ser. B
,
61
(
3
), pp.
611
622
.10.1111/1467-9868.00196
97.
Gharibnezhad
,
F.
,
Mujica
,
L. E.
, and
Rodellar
,
J.
,
2015
, “
Applying Robust Variant of Principal Component Analysis as a Damage Detector in the Presence of Outliers
,”
Mech. Syst. Signal Process.
,
50
, pp.
467
479
.10.1016/j.ymssp.2014.05.032
98.
Yu
,
L.
,
Zhu
,
J. H.
, and
Yu
,
L. L.
,
2013
, “
Structural Damage Detection in a Truss Bridge Model Using Fuzzy Clustering and Measured FRF Data Reduced by Principal Component Projection
,”
Adv. Struct. Eng.
,
16
(
1
), pp.
207
217
.10.1260/1369-4332.16.1.207
99.
Zang
,
C.
, and
Imregun
,
M.
,
2001
, “
Structural Damage Detection Using Artificial Neural Networks and Measured FRF Data Reduced Via Principal Component Projection
,”
J. Sound Vib.
,
242
(
5
), pp.
813
827
.10.1006/jsvi.2000.3390
100.
Wang
,
X.
,
Hu
,
N.
,
Fukunaga
,
H.
, and
Yao
,
Z. H.
,
2001
, “
Structural Damage Identification Using Static Test Data and Changes in Frequencies
,”
Eng. Struct.
,
23
(
6
), pp.
610
621
.10.1016/S0141-0296(00)00086-9
101.
Abdo
,
M.
, and
Hori
,
M.
,
2002
, “
A Numerical Study of Structural Damage Detection Using Changes in the Rotation of Mode Shapes
,”
J. Sound Vib.
,
251
(
2
), pp.
227
239
.10.1006/jsvi.2001.3989
102.
Elsner
, J. B.
, and
Tsonis
,
A. A.
,
2013
,
Singular Spectrum Analysis: A New Tool in Time Series Analysis
,
Springer Science & Business Media
,
Berlin
.10.1007/978-1-4757-2514-8
103.
Liu
,
K.
,
Law
,
S. S.
,
Xia
,
Y.
, and
Zhu
,
X. Q.
,
2014
, “
Singular Spectrum Analysis for Enhancing the Sensitivity in Structural Damage Detection
,”
J. Sound Vib.
,
333
(
2
), pp.
392
417
.10.1016/j.jsv.2013.09.027
104.
Chao
,
S. H.
, and
Loh
,
C. H.
,
2014
, “
Application of Singular Spectrum Analysis to Structural Monitoring and Damage Diagnosis of Bridges
,”
Struct. Infrastruct. Eng.
,
10
(
6
), pp.
708
727
.10.1080/15732479.2012.758643
105.
Lakshmi
,
K.
,
Rao
,
A.
, and
Gopalakrishnan
,
N.
,
2016
, “
Singular Spectrum Analysis Combined With ARMAX Model for Structural Damage Detection
,”
Struct. Control Health Monit.
,
24
(
9
), p.
e1960
.10.1002/stc.1960
106.
Carniel
,
R.
,
Barazza
,
F.
,
Tárraga
,
M.
, and
Ortiz
,
R.
,
2006
, “
On the Singular Values Decoupling in the Singular Spectrum Analysis of Volcanic Tremor at Stromboli
,”
Nat. Hazards Earth Syst. Sci.
,
6
(
6
), pp.
903
909
.10.5194/nhess-6-903-2006
107.
Garcia
,
D.
, and
Trendafilova
,
I.
,
2014
, “
Singular Spectrum Analysis for Identifying Structural Nonlinearity Using Free-Decay Responses. Application for Delamination Detection and Diagnosis in Composite Laminates
,”
26th International Conference on Noise and Vibration Engineering
,
Leuven, Belgium
,
Sept. 15–17
.
108.
Loh
,
C. H.
, and
Chao
,
S. H.
,
2012
, “
Application of Singular Spectrum Analysis to Bridge Structure Health Monitoring and Damage Detection
,”
ASME
Paper No. SMASIS2012-7905.10.1115/SMASIS2012-7905
109.
Kilundu
,
B.
,
Chiementin
,
X.
, and
Dehombreux
,
P.
,
2011
, “
Singular Spectrum Analysis for Bearing Defect Detection
,”
ASME J. Vib. Acoust.
,
133
(
5
), p.
051007
.10.1115/1.4003938
110.
Chao
,
S. H.
,
Loh
,
C. H.
, and
Tseng
,
M. H.
,
2014
, “
Structural Damage Assessment Using Output-Only Measurement: Localization and Quantification
,”
J. Intell. Mater. Syst. Struct.
,
25
(
9
), pp.
1097
1106
.10.1177/1045389X13498318
111.
Murotani
,
K.
, and
Sugihara
,
K.
,
2005
, “
New Spectral Decomposition Method for Three-Dimensional Shape Models and Its Applications
,”
ASME J. Comput. Inf. Sci. Eng.
,
5
(
4
), pp.
277
282
.10.1115/1.2052849
112.
Hu
,
Z. X.
,
Huang
,
X.
,
Wang
,
Y.
, and
Wang
,
F.
,
2018
, “
Extended Smooth Orthogonal Decomposition for Modal Analysis
,”
ASME J. Vib. Acoust.
,
140
(
4
), p.
041008
.10.1115/1.4039240
113.
Liu
,
L.
, and
Yang
,
Y.
,
2015
, “
Singular Spectrum Analysis and Its Application in Lamb Wave-Based Damage Detection
,”
J. Vibroeng.
,
17
(
7
), pp.
3561
3571
.https://www.jvejournals.com/article/15988
114.
De Oliveira
,
M. A.
, and
Inman
,
D. J.
,
2015
,
PCA-Based Method for Damage Detection Exploring Electromechanical Impedance in a Composite Beam, Structural Health Monitoring
,
SAGE Publications
,
Thousand Oaks, CA
.10.12783/SHM2015/94
115.
Mujica
,
L. E.
,
Ruiz
,
M.
,
Pozo
,
F.
,
Rodellar
,
J.
, and
Güemes
,
A.
,
2014
, “
A Structural Damage Detection Indicator Based on Principal Component Analysis and Statistical Hypothesis Testing
,”
Smart Mater. Struct.
,
23
(
2
), p.
025014
.10.1088/0964-1726/23/2/025014
116.
Yao
,
R.
, and
Pakzad
,
S. N.
,
2012
, “
A Structural Damage Detection Indicator Based on Principal Component Analysis and Statistical Hypothesis Testing
,”
Mech. Syst. Signal Process.
,
31
, pp.
355
368
.10.1016/j.ymssp.2012.02.014
117.
Farooq
,
U.
, and
Feeny
,
B. F.
,
2008
, “
Smooth Orthogonal Decomposition for Modal Analysis of Randomly Excited Systems
,”
J. Sound Vib.
,
316
(
1–5
), pp.
137
146
.10.1016/j.jsv.2008.02.052
118.
Kerschen
,
G.
,
Golinval
,
J. C.
,
Vakakis
,
A. F.
, and
Bergman
,
L. A.
,
2005
, “
The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview
,”
Nonlinear Dyn.
,
41
(
1–3
), pp.
104
116
.10.1007/s11071-005-2803-2
119.
Feeny
,
B. F.
, and
Liang
,
Y.
,
2003
, “
Interpreting Proper Orthogonal Modes of Randomly Excited Vibration Systems
,”
J. Sound Vib.
,
265
(
5
), pp.
953
966
.10.1016/S0022-460X(02)01265-8
120.
Kerschen
,
G.
, and
Golinval
,
J. C.
,
2002
, “
Physical Interpretation of the Proper Orthogonal Modes Using the Singular Value Decomposition
,”
J. Sound Vib.
,
249
(
5
), pp.
849
865
.10.1006/jsvi.2001.3930
121.
Kerschen
,
G.
,
Poncelet
,
F.
, and
Golinval
,
J. C.
,
2007
, “
Physical Interpretation of Independent Component Analysis in Structural Dynamics
,”
Mech. Syst. Signal Process.
,
21
(
4
), pp.
1561
1575
.10.1016/j.ymssp.2006.07.009
122.
Feeny
,
B. F.
,
2002
, “
On the Proper Orthogonal Modes and Normal Modes of Continuous Vibration Systems
,”
ASME J. Vib. Acoust.
,
124
(
1
), pp.
157
160
.10.1115/1.1421352
123.
Nguyen
,
V. H.
, and
Golinval
,
J. C.
,
2010
, “
Fault Detection Based on Kernel Principal Component Analysis
,”
Eng. Struct.
,
32
(
11
), pp.
3683
3691
.10.1016/j.engstruct.2010.08.012
124.
De Boe
,
P.
, and
Golinval
,
J. C.
,
2003
, “
Principal Component Analysis of a Piezosensor Array for Damage Localization
,”
Struct. Health Monit.
,
2
(
2
), pp.
137
144
.10.1177/1475921703002002005
125.
Schölkopf
,
B.
,
Smola
,
A.
, and
Müller
,
K. R.
,
1998
, “
Nonlinear Component Analysis as a Kernel Eigenvalue Problem
,”
Neural Comput.
,
10
(
5
), pp.
1299
1319
.10.1162/089976698300017467
126.
Yan
,
A. M.
,
Kerschen
,
G.
,
De Boe
,
P.
, and
Golinval
,
J. C.
,
2005
, “
Structural Damage Diagnosis Under Varying Environmental Conditions—Part II: Local PCA for Non-Linear Cases
,”
Mech. Syst. Signal Process.
,
19
(
4
), pp.
865
880
.10.1016/j.ymssp.2004.12.003
127.
Li
,
W.
,
Yue
,
H. H.
,
Valle-Cervantes
,
S.
, and
Qin
,
S. J.
,
2000
, “
Recursive PCA for Adaptive Process Monitoring
,”
J. Process Control
,
10
(
5
), pp.
471
486
.10.1016/S0959-1524(00)00022-6
128.
Ljung
,
L.
, and
Söderström
,
T.
,
1983
,
Theory and Practice of Recursive Identification
,
MIT Press
,
Cambridge, MA
.10.1002/oca.4660060109
129.
Ding
,
F.
, and
Chen
,
T.
,
2005
, “
Identification of Hammerstein Nonlinear ARMAX Systems
,”
Automatica
,
41
(
9
), pp.
1479
1489
.10.1016/j.automatica.2005.03.026
130.
Chen
,
S. A.
,
Billings
,
S. A.
, and
Grant
,
P. M.
,
1992
, “
Recursive Hybrid Algorithm for Non-Linear System Identification Using Radial Basis Function Networks
,”
Int. J. Control
,
55
(
5
), pp.
1051
1070
.10.1080/00207179208934272
131.
Azam
,
S. E.
,
Chatzi
,
E.
, and
Papadimitriou
,
C.
,
2015
, “
A Dual Kalman Filter Approach for State Estimation Via Output-Only Acceleration Measurements
,”
Mech. Syst. Signal Process.
,
60–61
, pp.
866
886
.10.1016/j.ymssp.2015.02.001
132.
Yang
,
J. N.
,
Lin
,
S.
,
Huang
,
H.
, and
Zhou
,
L.
,
2006
, “
An Adaptive Extended Kalman Filter for Structural Damage Identification
,”
Struct. Control Health Monit.
,
13
(
4
), pp.
849
867
.10.1002/stc.84
133.
Zhou
,
L.
,
Wu
,
S.
, and
Yang
,
J. N.
,
2008
, “
Experimental Study of an Adaptive Extended Kalman Filter for Structural Damage Identification
,”
J. Infrastruct. Syst.
,
14
(
1
), pp.
42
51
.10.1061/(ASCE)1076-0342(2008)14:1(42)
134.
Chatzi
,
E. N.
,
Smyth
,
A. W.
, and
Masri
,
S. F.
,
2010
, “
Experimental Application of On-Line Parametric Identification for Nonlinear Hysteretic Systems With Model Uncertainty
,”
Struct. Saf.
,
32
(
5
), pp.
326
337
.10.1016/j.strusafe.2010.03.008
135.
Azam
,
S. E.
,
Chatzi
,
E. N.
,
Papadimitriou
,
C.
, and
Smyth
,
A. W.
,
2017
, “
Experimental Validation of the Kalman-Type Filters for Online and Real-Time State and Input Estimation
,”
J. Vib. Control
,
23
(
15
), pp.
2494
2519
.10.1177/1077546315617672
136.
Chatzi
,
E. N.
, and
Smyth
,
A. W.
,
2009
, “
The Unscented Kalman Filter and Particle Filter Methods for Nonlinear Structural System Identification With Non-Collocated Heterogeneous Sensing
,”
Struct. Control Health Monit.
,
16
(
1
), pp.
99
123
.10.1002/stc.290
137.
Watkins
,
D. S.
,
1982
, “
Understanding the QR Algorithm
,”
SIAM Rev.
,
24
(
4
), pp.
427
440
.10.1137/1024100
138.
Byers
,
R.
,
1986
, “
A Hamiltonian QR Algorithm
,”
SIAM J. Sci. Stat. Comput.
,
7
(
1
), pp.
212
229
.10.1137/0907015
139.
Braman
,
K.
,
Byers
,
R.
, and
Mathias
,
R.
,
2002
, “
The Multishift QR Algorithm—Part I: Maintaining Well-Focused Shifts and Level 3 Performance
,”
SIAM J. Matrix Anal. Appl.
,
23
(
4
), pp.
929
947
.10.1137/S0895479801384573
140.
Golub
,
G. H.
, and
Van Loan
,
C. F.
,
2012
,
Matrix Computations
, Vol.
3
,
JHU Press
,
Baltimore, MD
.
141.
Cullum
,
J. K.
, and
Willoughby
,
R.
,
2002
,
Lanczos Algorithms for Large Symmetric Eigenvalue Computations: Vol. 1: Theory
, Vol.
41
,
SIAM
,
Philadelphia, PA
.10.1137/1.9780898719192
142.
Paige
,
C. C.
,
1980
, “
Accuracy and Effectiveness of the Lanczos Algorithm for the Symmetric Eigenproblem
,”
Linear Algebra Its Appl.
,
34
, pp.
235
258
.10.1016/0024-3795(80)90167-6
143.
Mistarihi
,
M. Z.
,
2013
,
Sensor-Based Nonlinear and Nonstationary Dynamic Analysis of Online Structural Health Monitoring
, Doctoral dissertation,
Oklahoma State University
,
Stillwater, OK
.
144.
Hassani
,
H.
,
Xu
,
Z.
, and
Zhigljavsky
,
A.
,
2011
, “
Singular Spectrum Analysis Based on the Perturbation Theory
,”
Nonlinear Anal.: Real World Appl.
,
12
(
5
), pp.
2752
2766
.10.1016/j.nonrwa.2011.03.020
145.
Mattsson
,
P.
,
Zachariah
,
D.
, and
Stoica
,
P.
,
2016
, “
Recursive Identification Method for Piecewise ARX Models: A Sparse Estimation Approach
,”
IEEE Trans. Signal Process.
,
64
(
19
), pp.
5082
5093
.10.1109/TSP.2016.2595487
146.
Voegtlin
,
T.
,
2005
, “
Recursive Principal Components Analysis
,”
Neural Networks
,
18
(
8
), pp.
1051
1063
.10.1016/j.neunet.2005.07.005
147.
Han
,
S.
, and
Feeny
,
B. F.
,
2002
, “
Enhanced Proper Orthogonal Decomposition for the Modal Analysis of Homogeneous Structures
,”
Modal Anal.
,
8
(
1
), pp.
19
40
.10.1177/1077546302008001518
148.
Nagarajaiah
,
S.
, and
Basu
,
B.
,
2009
, “
Output Only Modal Identification and Structural Damage Detection Using Time Frequency & Wavelet Techniques
,”
Earthquake Eng. Eng. Vib.
,
8
(
4
), pp.
583
605
.10.1007/s11803-009-9120-6
149.
Clement
,
S.
,
Bellizzi
,
S.
,
Cochelin
,
B.
, and
Ricciardi
,
G.
,
2014
, “
Sliding Window Proper Orthogonal Decomposition: Application to Linear and Nonlinear Modal Identification
,”
J. Sound Vib.
,
333
(
21
), pp.
5312
5323
.10.1016/j.jsv.2014.05.035
150.
Sobczyk
,
K.
, and
Spencer
,
B.
, Jr.
,
2012
,
Random Fatigue: From Data to Theory
,
Academic Press
,
New York
.
151.
Sobczyk
,
K.
,
2006
, “
Stochastic Dynamics and Reliability of Degrading Systems
,”
Bull. Pol. Acad. Sci.
,
54
(
1
), pp.
125
136
.https://pdfs.semanticscholar.org/f36b/8fc63ff3542012dc79f3fd19d75b507e5999.pdf
152.
Sobczyk
,
K.
, and
Trebicki
,
J.
,
2000
, “
Stochastic Dynamics With Fatigue-Induced Stiffness Degradation
,”
Probab. Eng. Mech.
,
15
(
1
), pp.
91
99
.10.1016/S0266-8920(99)00012-0
153.
Kantz
,
H.
,
Schreiber
,
T.
,
Hoffmann
,
I.
,
Buzug
,
T.
,
Pfister
,
G.
,
Flepp
,
L. G.
,
Simonet
,
J.
,
Badii
,
R.
, and
Brun
,
E.
,
1993
, “
Nonlinear Noise Reduction: A Case Study on Experimental Data
,”
Phys. Rev. E
,
48
(
2
), pp.
1529
1538
.10.1103/PhysRevE.48.1529
154.
Just
,
W.
,
Kantz
,
H.
,
Rödenbeck
,
C.
, and
Helm
,
M.
,
2001
, “
Stochastic Modelling: Replacing Fast Degrees of Freedom by Noise
,”
J. Phys. A: Math. Gen.
,
34
(
15
), pp.
3199
3123
.10.1088/0305-4470/34/15/302
155.
Cahill
,
P.
,
Hazra
,
B.
,
Karoumi
,
R.
,
Mathewson
,
A.
, and
Pakrashi
,
V.
,
2018
, “
Vibration Energy Harvesting Based Monitoring of an Operational Bridge Undergoing Forced Vibration and Train Passage
,”
Mech. Syst. Signal Process.
,
106
, pp.
265
283
.10.1016/j.ymssp.2018.01.007
156.
Reynders
,
E.
,
Wursten
,
G.
, and
De Roeck
,
G.
,
2014
, “
Output-Only Structural Health Monitoring in Changing Environmental Conditions by Means of Nonlinear System Identification
,”
Struct. Health Monit.
,
13
(
1
), pp.
82
93
.10.1177/1475921713502836
157.
Avendaño-Valencia
,
L. D.
,
Chatzi
,
E. N.
,
Koo
,
K. Y.
, and
Brownjohn
,
J. M.
,
2017
, “
Gaussian Process Time-Series Models for Structures Under Operational Variability
,”
Front. Built Environ.
,
3
, p.
69
.10.3389/fbuil.2017.00069
158.
Soong
,
T. T.
,
Reinhorn
,
A. M.
,
Aizawa
,
S.
, and
Higashino
,
M.
,
1994
, “
Recent Structural Applications of Active Control Technology
,”
J. Struct. Control
,
1
(
1–2
), pp.
1
21
.10.1002/stc.4300010101
159.
Ormondroyd
,
J.
,
1928
, “
The Theory of the Dynamic Vibration Absorber
,”
ASME J. Appl. Mech.
,
50
, pp.
9
22
.
160.
Red
,
B.
, and
Welbourn
,
D. B.
,
1952
, “
The Problem of the Dynamic Vibration Absorber
,”
Engineering
,
174
, p.
769
.
161.
Guo
,
H.
,
Qiu
,
C.
, and
Vaswani
,
N.
,
2014
, “
An Online Algorithm for Separating Sparse and Low-Dimensional Signal Sequences From Their Sum
,”
IEEE Trans. Signal Process.
,
62
(
16
), pp.
4284
4297
.10.1109/TSP.2014.2331612
162.
Qiu
,
C.
,
Vaswani
,
N.
,
Lois
,
B.
, and
Hogben
,
L.
,
2014
, “
Recursive Robust PCA or Recursive Sparse Recovery in Large but Structured Noise
,”
IEEE Trans. Inf. Theory
,
60
(
8
), pp.
5007
5039
.10.1109/TIT.2014.2331344
163.
Nagarajaiah
,
S.
, and
Yang
,
Y.
,
2017
, “
Modeling and Harnessing Sparse and Low–Rank Data Structure: A New Paradigm for Structural Dynamics, Identification, Damage Detection, and Health Monitoring
,”
Struct. Control Health Monit.
,
24
(
1
), p.
e1851
.10.1002/stc.1851
164.
Kutz
,
J. N.
,
2013
,
Data-Driven Modeling and Scientific Computation: Methods for Complex Systems and Big Data
,
Oxford University Press
,
Oxford, UK
.
165.
Prabhu
,
R. S.
,
Balasubramaniam
,
M. S.
,
Behera
,
A. K.
,
Bhattacharya
,
A.
,
Rajagopalan
,
V.
,
D'Souza
,
P.
, and
Badami
,
V. V.
,
2016
, “
Methods and Systems for Monitoring Health of Blades
,” U.S. Patent No. 9,250,153.
166.
Gul
,
M.
, and
Catbas
,
F. N.
,
2009
, “
Statistical Pattern Recognition for Structural Health Monitoring Using Time Series Modeling: Theory and Experimental Verifications
,”
Mech. Syst. Signal Process.
,
23
(
7
), pp.
2192
2204
.10.1016/j.ymssp.2009.02.013
167.
Loeve
,
M.
,
1963
,
Probability Theory
,
Van Nostrand
,
Princeton, NJ
.
168.
Narasimha
,
R.
,
2011
, “
Kosambi and Proper Orthogonal Decomposition
,”
Resonance
,
16
(
6
), pp.
574
581
.10.1007/s12045-011-0062-8
169.
Kosambi
,
D. D.
,
2016
,
Statistics in Function Space
,
Springer
,
Berlin
, pp.
115
123
.
170.
Karhunen
,
K.
,
1946
, “
Zur Spektraltheorie Stochastischer Prozesse
,”
Ann. Acad. Sci. Fennicae, AI
,
34
.
171.
Han
,
S.
, and
Feeny
,
B. F.
,
2003
, “
Application of Proper Orthogonal Decomposition to Structural Vibration Analysis
,”
Mech. Syst. Signal Process.
,
17
(
5
), pp.
989
1001
.10.1006/mssp.2002.1570
172.
Lumley
,
J. L.
,
2007
,
Stochastic Tools in Turbulence
,
Academic Press
,
New York
.
173.
Feeny
,
B. F.
,
1997
, “
Interpreting Proper Orthogonal Modes in Vibrations
,” Proceedings of DET, Vol. 97.
174.
Feeny
,
B. F.
, and
Kappagantu
,
R.
,
1998
, “
On the Physical Interpretation of Proper Orthogonal Modes in Vibrations
,”
J. Sound Vib.
,
211
(
4
), pp.
607
616
.10.1006/jsvi.1997.1386
175.
Kappagantu
,
R.
, and
Feeny
,
B. F.
,
1999
, “
An ‘Optimal’ Modal Reduction of a System With Frictional Excitation
,”
J. Sound Vib.
,
224
(
5
), pp.
863
877
.10.1006/jsvi.1999.2165
176.
Yadalam
,
V. K.
, and
Feeny
,
B. F.
,
2011
, “
Reduced Mass-Weighted Proper Decomposition for Modal Analysis
,”
ASME J. Vib. Acoust.
,
133
(
2
), p.
024504
.10.1115/1.4002960
177.
Kappagantu
,
R.
, and
Feeny
,
B. F.
,
2000
, “
Part 1: Dynamical Characterization of a Frictionally Excited Beam
,”
Nonlinear Dyn.
,
22
(
4
), pp.
317
333
.10.1023/A:1008344005183
178.
Kappagantu
,
R.
, and
Feeny
,
B. F.
,
2000
, “
Part 2: Proper Orthogonal Modal Modeling of a Frictionally Excited Beam
,”
Nonlinear Dyn.
,
23
(
1
), pp.
1
11
.10.1023/A:1008303406091
179.
Ravindra
,
B.
,
1999
,
On the Physical Interpretation of Proper Orthogonal Modes in Vibrations
,
Academic Press
,
New York
.
180.
Kerschen
,
G.
,
Feeny
,
B. F.
, and
Golinval
,
J. C.
,
2003
, “
On the Exploitation of Chaos to Build Reduced-Order Models
,”
Comput. Methods Appl. Mech. Eng.
,
192
(
13–14
), pp.
1785
1795
.10.1016/S0045-7825(03)00206-8
181.
Wang
,
Z.
,
Lin
,
R. M.
, and
Lim
,
M. K.
,
1997
, “
Structural Damage Detection Using Measured FRF Data
,”
Comput. Methods Appl. Mech. Eng.
,
147
(
1–2
), pp.
187
197
.10.1016/S0045-7825(97)00013-3
182.
Chelidze
,
D.
, and
Zhou
,
W.
,
2006
, “
Smooth Orthogonal Decomposition-Based Vibration Mode Identification
,”
J. Sound Vib.
,
292
(
3–5
), pp.
461
473
.10.1016/j.jsv.2005.08.006
183.
Groth
,
A.
, and
Ghil
,
M.
,
2015
, “
Monte Carlo Singular Spectrum Analysis (SSA) Revisited: Detecting Oscillator Clusters in Multivariate Datasets
,”
J. Climatol.
,
28
(
19
), pp.
7873
7893
.10.1175/JCLI-D-15-0100.1
184.
Oropeza
,
V.
, and
Sacchi
,
M.
,
2011
, “
Simultaneous Seismic Data Denoising and Reconstruction Via Multichannel Singular Spectrum Analysis
,”
Geophysics
,
76
(
3
), pp.
V25
V32
.10.1190/1.3552706
185.
Hsieh
,
W. W.
, and
Wu
,
A.
,
2012
, “
Nonlinear Multichannel Singular Spectrum Analysis of the Tropical Pacific Climate Variability Using a Neural Network Approach
,”
J. Geophys. Res.: Oceans
,
10
(
7
), pp.
903
909
.10.1029/2001JC000957
186.
Huang
,
W.
,
Wang
,
R.
,
Yuan
,
Y.
,
Gan
,
S.
, and
Chen
,
Y.
,
2016
, “
Signal Extraction Using Randomized-Order Multichannel Singular Spectrum Analysis
,”
Geophysics
,
82
(
2
), pp.
V69
V84
.10.1190/geo2015-0708.1
187.
Rangelova
,
E.
,
Sideris
,
M. G.
, and
Kim
,
J. W.
,
2012
, “
On the Capabilities of the Multi-Channel Singular Spectrum Method for Extracting the Main Periodic and Non-Periodic Variability From Weekly GRACE Data
,”
J. Geodynam.
,
54
, pp.
64
78
.10.1016/j.jog.2011.10.006
188.
Richman
,
M. B.
,
1986
, “
Rotation of Principal Components
,”
J. Climatol.
,
6
(
3
), pp.
293
335
.10.1002/joc.3370060305
189.
Aggarwal
,
C. C.
, and
Yu
,
P. S.
,
2001
, “
Outlier Detection for High Dimensional Data
,”
ACM Sigmoid Record
,
30
(
2
), pp.
37
46
.10.1145/376284.375668
190.
Hamilton
,
J. D.
,
1994
,
Time Series Analysis
, Vol.
2
,
Princeton University Press
,
Princeton, NJ
.
191.
Hazra
,
B.
,
Sadhu
,
A.
, and
Narasimhan
,
S.
,
2016
, “
Fault Detection of Gearboxes Using Synchro-Squeezing Transform
,”
J. Vib. Control
,
23
(
19
), pp.
3108
3127
.10.1177/1077546315627242
192.
Hot
,
A.
,
Kerschen
,
G.
,
Foltête
,
E.
, and
Cogan
,
S.
,
2012
, “
Detection and Quantification of Non-Linear Structural Behavior Using Principal Component Analysis
,”
Mech. Syst. Signal Process.
,
26
, pp.
104
116
.10.1016/j.ymssp.2011.06.006
193.
Cusumano
,
J. P.
, and
Chatterjee
,
A.
,
2000
, “
Steps Towards a Qualitative Dynamics of Damage Evolution
,”
Int. J. Solids Struct.
,
37
(
44
), pp.
6397
6417
.10.1016/S0020-7683(99)00042-6
194.
Borga
,
M.
, and
Knutsson
,
H.
,
2001
, “
A Canonical Correlation Approach to Blind Source Separation
,” Linköping University, Linköping, Sweden, Report No. LiU-IMT-EX-0062.
195.
Cichocki
,
A.
, and
Amari
,
S.
,
2002
,
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
,
Wiley
,
Hoboken, NJ.
.10.1002/0470845899
196.
Ghosh
,
S. J.
,
Manohar
,
C. S.
, and
Roy
,
D.
,
2008
, “
A Sequential Importance Sampling Filter With a New Proposal Distribution for State and Parameter Estimation of Nonlinear Dynamical Systems
,”
Proc. R. Soc. London A
,
464
(
2089
), pp.
25
47
.10.1098/rspa.2007.0075
197.
Roy
,
D.
, and
Rao
,
G. V.
,
2017
,
Stochastic Dynamics, Filtering and Optimization
,
Cambridge University Press
,
Cambridge, UK
.10.1017/9781316863107
198.
Johnson
,
E. A.
,
Lam
,
H. F.
,
Katafygiotis
,
L. S.
, and
Beck
,
J. L.
,
2004
, “
Phase I IASC-ASCE Structural Health Monitoring Benchmark Problem Using Simulated Data
,”
J. Eng. Mech.
,
130
(
1
), pp.
3
15
.10.1061/(ASCE)0733-9399(2004)130:1(3)
199.
Ray
,
W. C.
, and
Joseph
,
P.
,
2003
,
Dynamics of Structures
,
Computers and Structures
,
Berkeley, CA
.
200.
Worden
,
K.
, and
Cross
,
E. J.
,
2018
, “
On Switching Response Surface Models, With Applications to the Structural Health Monitoring of Bridges
,”
Mech. Syst. Signal Process.
,
98
, pp.
139
156
.10.1016/j.ymssp.2017.04.022
201.
Spiridonakos
,
M. D.
,
Chatzi
,
E. N.
, and
Sudret
,
B.
,
2016
, “
Polynomial Chaos Expansion Models for the Monitoring of Structures Under Operational Variability
,”
ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng.
,
2
(
3
), p.
B4016003
.10.1061/AJRUA6.0000872
202.
Kullaa
,
J.
,
2011
, “
Distinguishing Between Sensor Fault, Structural Damage, and Environmental or Operational Effects in Structural Health Monitoring
,”
Mech. Syst. Signal Process.
,
25
(
8
), pp.
2976
2989
.10.1016/j.ymssp.2011.05.017
203.
Shi
,
H.
,
Worden
,
K.
, and
Cross
,
E. J.
,
2016
, “
A Nonlinear Cointegration Approach With Applications to Structural Health Monitoring
,”
J. Phys.: Conf. Ser.
,
744
(
1
), p.
012025
.10.1088/1742-6596/744/1/012025
204.
Snowdon
,
J. C.
,
1959
, “
Steady-State Behavior of the Dynamic Absorber
,”
J. Acoust. Soc. Am.
,
31
(
8
), pp.
1096
1103
.10.1121/1.1907832
205.
Falcon
,
K. C.
,
Stone
,
B. J.
,
Simcock
,
W. D.
, and
Andrew
,
C.
,
1967
, “
Optimization of Vibration Absorbers: A Graphical Method for Use on Idealized Systems With Restricted Damping
,”
J. Mech. Eng. Sci.
,
9
(
5
), pp.
374
381
.10.1243/JMES_JOUR_1967_009_058_02
206.
Ioi
,
T.
, and
Ikeda
,
K.
,
1978
, “
On the Dynamic Vibration Damped Absorber of the Vibration System
,”
Bull. JSME
,
21
(
151
), pp.
64
71
.10.1299/jsme1958.21.64
207.
Warburton
,
G. B.
, and
Ayorinde
,
E. O.
,
1980
, “
Optimum Absorber Parameters for Simple Systems
,”
Earthquake Eng. Struct. Dyn.
,
8
(
3
), pp.
197
217
.10.1002/eqe.4290080302
208.
Thompson
,
A. G.
,
1981
, “
Optimum Tuning and Damping of a Dynamic Vibration Absorber Applied to a Force Excited and Damped Primary System
,”
J. Sound Vib.
,
77
(
3
), pp.
403
415
.10.1016/S0022-460X(81)80176-9
209.
Azam
,
S. E.
,
Ghisi
,
A.
, and
Mariani
,
S.
,
1982
, “
Optimum Absorber Parameters for Various Combinations of Response and Excitation Parameters
,”
Earthquake Eng. Struct. Dyn.
,
10
(
3
), pp.
381
401
.
210.
Vickery
,
B. J.
,
Isyumov
,
N.
, and
Davenport
,
A. G.
,
1983
, “
The Role of Damping, Mass and Acceleration
,”
J. Wind Eng. Ind. Aerodyn.
,
11
(
1–3
), pp.
285
294
.10.1016/0167-6105(83)90107-1
211.
Tsai
,
H. C.
, and
Lin
,
G. C.
,
1993
, “
Optimum Tuned-Mass Dampers for Minimizing Steady-State Response of Support-Excited and Damped Systems
,”
Earthquake Eng. Struct. Dyn.
,
22
(
11
), pp.
957
973
.10.1002/eqe.4290221104
212.
Schmitendorf
,
W. E.
,
2000
, “
Designing Tuned Mass Dampers Via Static Output Feedback: A Numerical Approach
,”
Earthquake Eng. Struct. Dyn.
,
29
(
1
), pp.
127
137
.10.1002/(SICI)1096-9845(200001)29:1<127::AID-EQE910>3.0.CO;2-Y
213.
Hazra
,
B.
,
Sadhu
,
A.
,
Lourenco
,
R.
, and
Narasimhan
,
S.
,
2010
, “
Re-Tuning Tuned Mass Dampers Using Ambient Vibration Measurements
,”
Smart Mater. Struct.
,
92
, p.
115002
.10.1088/0964-1726/19/11/115002
214.
Rana
,
R.
, and
Soong
,
T. T.
,
1998
, “
Parametric Study and Simplified Design of Tuned Mass Dampers
,”
Eng. Struct.
,
20
(
3
), pp.
193
204
.10.1016/S0141-0296(97)00078-3
215.
Huang
,
N. E.
,
Shen
,
Z.
,
Long
,
S. R.
,
Wu
,
M. C.
,
Shih
,
H. H.
,
Zheng
,
Q.
,
Yen
,
N. C.
,
Tung
,
C. C.
, and
Liu
,
H. H.
,
1998
, “
The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis
,”
Proc. R. Soc. London, Ser. A
,
454
(
1971
), pp.
903
995
.10.1098/rspa.1998.0193
216.
Peng
,
Z. K.
,
Tse
,
P. W.
, and
Chu
,
F. L.
,
2005
, “
An Improved Hilbert-Huang Transform and Its Application in Vibration Signal Analysis
,”
J. Sound Vib.
,
286
(
1–2
), pp.
187
205
.10.1016/j.jsv.2004.10.005
You do not currently have access to this content.