In this paper, the time-varying autoregressive (TVAR) model is integrated with the K-means—clustering technique to detect the damage in the steel moment-resisting frame. The damage is detected in the frame using nonstationary acceleration response of the structure excited using ambient white noise. The proposed technique identifies and quantifies the damage in the beam-to-column connection and column-to-column splice plate connection caused due to loosening of the connecting bolts. The algorithm models the nonstationary acceleration time history and evaluates the TVAR coefficients (TVARCs) for pristine and damage states. These coefficients are represented as a cluster in the TVARC subspace and segregated and classified using K-means—segmentation technique. The K-means—approach is adapted to simultaneously perform partition clustering and remove outliers. Eigenstructure evaluation of the segregated TVARC cluster is performed to detect the temporal damage. The topological and statistical parameters of the TVARC clusters are used to quantify the magnitude of the damage. The damage is quantified using the Mahalanobis distance (MD) and the Itakura distance (ID) serving as the statistical distance between the healthy and damage TVARC clusters. MD calculates a multidimensional statistical distance between two clusters using the covariance between the state vectors, whereas ID measures the dissimilarity of the autoregressive (AR) parameter between reference state and unknown states. These statistical distances are used as damage-sensitive feature (DSF) to detect and quantify the initiation and progression of the damage in the structure under ambient vibrations. The outcome of both the DSFs corroborate with the experimental investigation, thereby improving the robustness of the algorithm by avoiding false damage alarms.

References

1.
Bruneau
,
M.
,
Uang
,
C.-M.
, and
Whittaker
,
A.
,
1998
,
Ductile Design of Steel Structures
, Vol.
389
,
McGraw-Hill
,
New York
.
2.
AISC
,
1999
, “
Specification for Structural Steel Buildings
,”
Chicago
, p.
27
.
3.
AISC
,
2010
, “
Seismic Provisions for Structural Steel Buildings
,”
Chicago
.
4.
AISC
,
2010
, “
Prequalified Connections for Special and Intermediate Steel Moment Frames for Seismic Applications
,”
Chicago
.
5.
ASCE
,
2010
, “
Minimum Design Loads for Buildings and Other Structures, Standard ASCE/SEI 7-10
,”
Reston, VA
.
6.
Amezquita-Sanchez
,
J. P.
, and
Adeli
,
H.
,
2016
, “
Signal Processing Techniques for Vibration-Based Health Monitoring of Smart Structures
,”
Arch Comput. Methods Eng.
,
23
(
1
), pp.
1
15
.
7.
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
.
8.
Farrar
,
C. R.
, and
Worden
,
K.
,
2007
, “
An Introduction to Structural Health Monitoring
,”
Philos. Trans. Royal Soc. A
,
365
(
1851
), pp.
303
315
.
9.
Wang
,
D.
, and
Haldar
,
A.
,
1997
, “
System Identification With Limited Observations and Without Input
,”
J. Eng. Mech.
,
123
(
5
), pp.
504
511
.
10.
Hayes
,
M. H.
,
2009
,
Statistical Digital Signal Processing and Modeling
,
John Wiley & Sons
,
New York
.
11.
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
.
12.
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
,”
Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences
,
London, UK
,
Mar. 8, pp. 904-995
.
13.
Taha
,
M. R.
,
Noureldin
,
A.
,
Lucero
,
J. L.
, and
Baca
,
T. J.
,
2006
, “
Wavelet Transform for Structural Health Monitoring: A Compendium of Uses and Features
,”
Struct. Health Monit.
5
(
3
), pp.
267
295
.
14.
Lakshmi
,
K.
,
Rao
,
A. R. M.
, and
Gopalakrishnan
,
N.
,
2017
, “
Singular Spectrum Analysis Combined With ARMAX Model for Structural Damage Detection
,”
Struct. Control Health Monit.
,
24
(
9
), p.
e1960
.
15.
Lu
,
Y.
, and
Gao
,
F.
,
2005
, “
A Novel Time-Domain Auto-Regressive Model for Structural Damage Diagnosis
,”
J. Sound Vib.
,
283
(
3–5
), pp.
1031
1049
.
16.
Bodeux
,
J.-B.
, and
Golinval
,
J.-C.
,
2001
, “
Application of ARMAV Models to the Identification and Damage Detection of Mechanical and Civil Engineering Structures
,”
Smart Mater. Struct.
,
10
(
3
), pp.
479
.
17.
Omenzetter
,
P.
, and
Brownjohn
,
J. M. W.
,
2006
, “
Application of Time Series Analysis for Bridge Monitoring
,”
Smart Mater. Struct.
,
15
(
1
), p.
129
.
18.
Sohn
,
H.
,
Czarnecki
,
J. A.
, and
Farrar
,
C. R.
,
2000
, “
Structural Health Monitoring Using Statistical Process Control
,”
J. Struct. Eng.
,
126
(
11
), pp.
1356
1363
.
19.
Yao
,
R.
, and
Pakzad
,
S. N.
,
2012
, “
Autoregressive Statistical Pattern Recognition Algorithms for Damage Detection in Civil Structures
,”
Mech. Syst. Signal Process.
,
31
, pp.
355
368
.
20.
Sohn
,
H.
,
Farrar
,
C. R.
,
Hunter
,
N. F.
, and
Worden
,
K.
,
2001
, “
Structural Health Monitoring Using Statistical Pattern Recognition Techniques
,”
ASME J. Dyn. Syst. Meas. Control
,
123
(
4
), pp.
706
711
.
21.
Worden
,
K.
,
Farrar
,
C. R.
,
Haywood
,
J.
, and
Todd
,
M.
,
2008
, “
A Review of Nonlinear Dynamics Applications to Structural Health Monitoring
,”
Struct. Control Health Monit.
15
(
4
), pp.
540
567
.
22.
Farrar
,
C. R.
, and
Worden
,
K.
,
2012
,
Structural Health Monitoring: a Machine Learning Perspective
,
John Wiley & Sons
,
New York
.
23.
Yang
,
J. N.
, and
Huang
,
H.
,
2007
, “
Sequential Non-Linear Least-Square Estimation for Damage Identification of Structures With Unknown Inputs and Unknown Outputs
,”
Int. J. Nonlin. Mech.
,
42
(
5
), pp.
789
801
.
24.
Smyth
,
A. W.
,
Masri
,
S. F.
,
Kosmatopoulos
,
E. B.
, and
Chassiakos
,
A. G.
,
2002
, “
Development of Adaptive Modeling Techniques for Non-Linear Hysteretic Systems
,”
Int. J. Nonlin. Mech.
,
37
(
8
), pp.
1435
1451
.
25.
Ling
,
X.
, and
Haldar
,
A.
,
2004
, “
Element Level System Identification With Unknown Input With rayleigh Damping
,”
J. Eng. Mech.
,
130
(
8
), pp.
877
885
.
26.
Wang
,
D.
, and
Haldar
,
A.
,
1994
, “
Element-Level System Identification With Unknown Input
,”
J. Eng. Mech.
,
120
(
1
), pp.
159
176
.
27.
Namdeo
,
V.
, and
Manohar
,
C.
,
2007
, “
Nonlinear Structural Dynamical System Identification Using Adaptive Particle Filters
,”
J. Sound Vib.
,
306
(
3–5
), pp.
524
563
.
28.
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
.
29.
Rajan
,
J. J.
, and
Rayner
,
P. J.
,
1996
, “
Generalized Feature Extraction for Time-Varying Autoregressive Models
,”
IEEE Trans. Signal Process.
,
44
(
10
), pp.
2498
2507
.
30.
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
.
31.
Musafere
,
F.
,
Sadhu
,
A.
, and
Liu
,
K.
,
2016
, “Time-Varying System Identification Using a Hybrid Blind Source Separation Method,”
Structural Health Monitoring, Damage Detection & Mechatronics
,
Wicks
Alfred
, and
Niezrecki
Christopher
, eds.,
Springer
,
New York
, pp.
99
104
.
32.
Kopsaftopoulos
,
F. D.
, and
Fassois
,
S. D.
,
2013
, “
A Functional Model Based Statistical Time Series Method for Vibration Based Damage Detection, Localization, and Magnitude Estimation
,”
Mech. Syst. Signal Process.
,
39
(
1–2
), pp.
143
161
.
33.
Jain
,
A. K.
,
2010
, “
Data Clustering: 50 Years Beyond K-Means
,”
Pattern Recognit. Lett.
,
31
(
8
), pp.
651
666
.
34.
Chawla
,
S.
, and
Gionis
,
A.
,
2013
, “
k-Means—: A Unified Approach to Clustering and Outlier Detection
,”
Proceedings of the 2013 SIAM International Conference on Data Mining
,
Austin, TX
,
May 2, pp. 189-197
.
35.
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
.
36.
Gul
,
M.
, and
Catbas
,
F. N.
,
2011
, “
Structural Health Monitoring and Damage Assessment Using a Novel Time Series Analysis Methodology With Sensor Clustering
,”
J. Sound Vib.
,
330
(
6
), pp.
1196
1210
.
37.
Pamwani
,
L.
, and
Shelke
,
A.
,
2018
, “
Damage Detection Using Dissimilarity in Phase Space Topology of Dynamic Response of Structure Subjected to Shock Wave Loading
,”
ASME J. Nondestr. Eval. Diagn. Progn. Eng. Syst.
,
1
(
4
), p.
041004
.
38.
Zheng
,
H.
, and
Mita
,
A.
,
2009
, “
Localized Damage Detection of Structures Subject to Multiple Ambient Excitations Using Two Distance Measures for Autoregressive Models
,”
Struct. Health Monit.
,
8
(
3
), pp.
207
222
.
39.
Musafere
,
F.
,
Sadhu
,
A.
, and
Liu
,
K.
,
2015
, “
Towards Damage Detection Using Blind Source Separation Integrated With Time-Varying Auto-Regressive Modeling
,”
Smart Mater. Struct.
,
25
(
1
), p.
015013
.
40.
Nguyen
,
D. P.
,
Wilson
,
M. A.
,
Brown
,
E. N.
, and
Barbieri
,
R.
,
2009
, “
Measuring Instantaneous Frequency of Local Field Potential Oscillations Using the Kalman Smoother
,”
J. Neurosci. Methods
,
184
(
2
), pp.
365
374
.
41.
Grenier
,
Y.
,
1983
, “
Time-Dependent ARMA Modeling of Nonstationary Signals
,”
IEEE Trans. Acoust. Speech Signal Process.
,
31
(
4
), pp.
899
911
.
42.
Linde
,
Y.
,
Buzo
,
A.
, and
Gray
,
R.
,
1980
, “
An Algorithm for Vector Quantizer Design
,”
IEEE Trans. Commun.
,
28
(
1
), pp.
84
95
.
43.
De Maesschalck
,
R.
,
Jouan-Rimbaud
,
D.
, and
Massart
,
D. L.
,
2000
, “
The Mahalanobis Distance
,”
Chemom. Intell. Lab. Syst.
,
50
(
1
), pp.
1
18
.
44.
Kong
,
X.
,
Thakor
,
N.
, and
Goel
,
V.
,
1995
, “
Characterization of EEG Signal Changes via Itakura Distance
,”
Proceedings of 17th International Conference of the Engineering in Medicine and Biology Society
,
Montreal, Quebec, Canada
,
Sept. 20–23
.
45.
Muthuswamy
,
J.
, and
Thakor
,
N. V.
,
1998
, “
Spectral Analysis Methods for Neurological Signals
,”
J. Neurosci. Methods
,
83
(
1
), pp.
1
14
.
46.
Kong
,
X.
,
Goel
,
V.
, and
Thakor
,
N.
,
1995
, “
Quantification of Injury-Related EEG Signal Changes Using Itakura Distance Measure
,”
1995 International Conference on Acoustics, Speech, and Signal Processing
,
Detroit, MI
,
May 9–12
.
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