Hamzeloo,
S. R.
,
Shamshirsaz,
M.
, and
Rezaei,
S. M.
, 2012, “
Damage Detection on Hollow Cylinders by Electro-Mechanical Impedance Method: Experiments and Finite Element Modeling,” C. R. Mec.,
340(9), pp. 668–677.

[CrossRef]
Stubbs,
N.
,
Broome,
T. H.
, and
Osegueda,
R.
, 1990, “
Nondestructive Construction Error Detection in Large Space Structures,” AIAA J.,
28(1), pp. 146–152.

[CrossRef]
Stubbs,
N.
, and
Osegueda,
R.
, 1990, “
Global Non-Destructive Damage Evaluation in Solids,” Int. J. Anal. Exp. Modal Anal.,
5, pp. 67–79.

Stubbs,
N.
, and
Osegueda,
R.
, 1990, “
Global Damage Detection in Solids—Experimental Verification,” Int. J. Anal. Exp. Modal Anal.,
5, pp. 81–97.

Shiradhonkar,
S. R.
, and
Shrikhande,
M.
, 2011, “
Seismic Damage Detection in a Building Frame Via Finite Element Model Updating,” Comput. Struct.,
89(23–24), pp. 2425–2438.

Mayes,
R.
, 1991, “
Error Localization Using Mode Shapes: An Application to a Two Link Robot Arm,” Sandia National Labs., Albuquerque, NM, Report No. SAND-91-2297C; CONF-920234–1.

Jafarkhani,
R.
, and
Masri,
S. F.
, 2011, “
Finite Element Model Updating Using Evolutionary Strategy for Damage Detection,” Comput. Aided Civil Infrastruct. Eng.,
26(3), pp. 207–224.

[CrossRef]
Lee,
J. J.
,
Lee,
J. W.
,
Yi,
J. H.
,
Yun,
C. B.
, and
Jung,
H. Y.
, 2005, “
Neural Networks-Based Damage Detection for Bridges Considering Errors in Baseline Finite Element Models,” J. Sound Vib.,
280(3), pp. 555–578.

[CrossRef]
Wu,
J. R.
, and
Li,
Q. S.
, 2006, “
Structural Parameter Identification and Damage Detection for a Steel Structure Using a Two-Stage Finite Element Model Updating Method,” J. Construct. Steel Res.,
62(3), pp. 231–239.

[CrossRef]
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.

[CrossRef]
Chen,
J.-C.
, and
Garba,
J. A.
, “
On-Orbit Damage Assessment for Large Space Structures,” AIAA J.,
26(9), pp. 1119–1126.

[CrossRef]
Chen,
J.-C.
, and
Garba,
J. A.
, 1988, Structural Damage Assessment Using a System Identification Technique. Structural Safety Evaluation Based on System Identification Approaches,
Vieweg+ Teubner Verlag,
Berlin, pp. 474–492.

Sanayei,
M.
, and
Onipede,
O.
, 1991, “
Damage Assessment of Structures Using Static Test Data,” AIAA J.,
29(7), pp. 1174–1179.

[CrossRef]
Sanayei,
M.
,
Onipede,
O.
, and
Babu,
S. R.
, 1992, “
Selection of Noisy Measurement Locations for Error Reduction in Static Parameter Identification,” AIAA J.,
30(9), pp. 2299–2309.

[CrossRef]
Liu,
P.-L.
, 1995, “
Identification and Damage Detection of Trusses Using Modal Data,” J. Struct. Eng.,
121(4), pp. 599–608.

[CrossRef]
Lim,
T. W.
, 1990, “
A Submatrix Approach to Stiffness Using Modal Test Data,” AIAA J.,
28(6), pp. 1123–1130.

[CrossRef]
Lim,
T. W.
, 1991, “
Structural Damage Detection Using Modal Test Data,” AIAA J.,
29(12), pp. 2271–2274.

[CrossRef]
Lim,
T. W.
, 1994, “
Structural Damage Detection of a Planar Truss Structure Using a Constrained Eigenstructure Assignment,” 35th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Paper No. AIAA-94-1715-CP, pp. 336–346.

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.

[CrossRef]
Zimmerman,
D. C.
,
Simmermacher,
T.
, and
Kaouk,
M.
, 1995, “
Structural Damage Detection Using Frequency Response Functions,” 13th International Modal Analysis Conference, Vol.
2460, pp. 375–381.

Zimmerman,
D. C.
,
Kaouk,
M.
, and
Simmermacher,
T.
, 1995, “
On the Role of Engineering Insight and Judgement Structural Damage Detection,” 13th International Modal Analysis Conference, Vol.
2460, pp. 414–420.

Chang,
J.-D.
, and
Guo,
B.-Z.
, 2007, “
Identification of Variable Spacial Coefficients for a Beam Equation From Boundary Measurements,” Automatica,
43(4), pp. 732–737.

[CrossRef]
Ju,
F. D.
,
Akgun,
M.
,
Paez,
T. L.
, and
Wong,
E. T.
, 1982, “
Diagnosis of Fracture Damage in Simple Structures: A Modal Method,” New Mexico University, Albuquerque Bureau of Engineering Research, Paper No. CE-62 (82) AFOSR-993-1.

Nguyen,
V. V.
, and
Wood,
E. F.
, 1982, “
Review and Unification of Linear Identifiability Concepts,” SIAM Rev.,
24(1), pp. 34–51.

[CrossRef]
Franco,
G.
,
Betti,
R.
, and
Longman,
R. W.
, 2006, “
On the Uniqueness of Solutions for the Identification of Linear Structural Systems,” ASME J. Appl. Mech.,
73(1), pp. 153–162.

[CrossRef]
De Angelis,
M.
,
Lus,
H.
,
Betti,
R.
, and
Longman,
R. W.
, 2002, “
Extracting Physical Parameters of Mechanical Models From Identified State-Space Representations,” ASME J. Appl. Mech.,
69(5), pp. 617–625.

[CrossRef]
Sun,
H.
,
Luş,
H.
, and
Betti,
R.
, 2013, “
Identification of Structural Models Using a Modified Artificial Bee Colony Algorithm,” Comput. Struct.,
116, pp. 59–74.

[CrossRef]
Reynders,
E.
, 2012, “
System Identification Methods for (Operational) Modal Analysis: Review and Comparison,” Arch. Comput. Methods Eng.,
19(1), pp. 51–124.

[CrossRef]
Simani,
S.
,
Fantuzzi,
C.
, and
Patton,
R. J.
, 2013, Model-Based Fault Diagnosis in Dynamic Systems Using Identification Techniques,
Springer Science & Business Media,
Berlin.

Rugh,
W. J.
, 1996, Linear System Theory, Vol.
2,
Prentice Hall,
Upper Saddle River, NJ.

Segerlind,
L. J.
, and
Saunders,
H.
, 1987, Applied Finite Element Analysis,
Wiley,
New York.

Meurant,
G.
, 1992, “
A Review on the Inverse of Symmetric Tridiagonal and Block Tridiagonal Matrices,” SIAM J. Matrix Anal. Appl.,
13(3), pp. 707–728.

[CrossRef]
Nabben,
R.
, 1999, “
Decay Rates of the Inverse of Nonsymmetric Tridiagonal and Band Matrices,” SIAM J. Matrix Anal. Appl.,
20(3), pp. 820–837.

[CrossRef]
Demko,
S.
,
Moss,
W. F.
, and
Smith,
P. W.
, 1984, “
Decay Rates for Inverses of Band Matrices,” Math. Comput.,
43(168), pp. 491–499.

[CrossRef]
Eijkhout,
V.
, and
Polman,
B.
, 1988, “
Decay Rates of Inverses of Banded M-Matrices That are Near to Toeplitz Matrices,” Linear Algebra Appl.,
109, pp. 247–277.

[CrossRef]
Yamamoto,
T.
, and
Ikebe,
Y.
, 1979, “
Inversion of Band Matrices,” Linear Algebra Appl.,
24, pp. 105–111.

[CrossRef]
Balageas,
D.
,
Fritzen,
C.-P.
, and
Güemes,
A.
, eds., 2006, Structural Health Monitoring, Vol.
493,
ISTE,
London, UK.

Wang,
S. Q.
, and
Li,
H. J.
, 2012, “
Assessment of Structural Damage Using Natural Frequency Changes,” Acta Mech. Sinica,
28(1), pp. 118–127.

[CrossRef]
Salawu,
O. S.
, 1997, “
Detection of Structural Damage Through Changes in Frequency: A Review,” Eng. Struct.,
19(9), pp. 718–723.

[CrossRef]
Lo,
S. S.
,
Philippe,
B.
, and
Sameh,
A.
, 1987, “
A Multiprocessor Algorithm for the Symmetric Tridiagonal Eigenvalue Problem,” SIAM J. Sci. Stat. Comput.,
8(2), pp. s155–s165.

[CrossRef]
Trefftz,
C.
,
Huang,
C. C.
,
McKinley,
P. K.
,
Li,
T. Y.
, and
Zeng,
Z.
, 1995, “
A Scalable Eigenvalue Solver for Symmetric Tridiagonal Matrices,” Parallel Comput.,
21(8), pp. 1213–1240.

[CrossRef]
Fernandez,
F. A.
,
Davies,
J. B.
,
Zhu,
S.
, and
Lu,
Y.
, 1991, “
Sparse Matrix Eigenvalue Solver for Finite Element Solution of Dielectric Waveguides,” Electron. Lett.,
27(20), pp. 1824–1826.

[CrossRef]
Gruber,
R.
, 1980, “
HYMNISBLOCK—Eigenvalue Solver for Blocked Matrices,” Comput. Phys. Commun.,
20(3), pp. 421–428.

[CrossRef]
Demmel,
J. W.
,
Marques,
O. A.
,
Parlett,
B. N.
, and
Vömel,
C.
, 2008, “
Performance and Accuracy of LAPACK's Symmetric Tridiagonal Eigensolvers,” SIAM J. Sci. Comput.,
30(3), pp. 1508–1526.

[CrossRef]
Peng,
D.
,
Middendorf,
N.
,
Weigend,
F.
, and
Reiher,
M.
, 2013, “
An Efficient Implementation of Two-Component Relativistic Exact-Decoupling Methods for Large Molecules,” J. Chem. Phys.,
138(18), p. 184105.

[CrossRef] [PubMed]
Beyn,
W. J.
, 2012, “
An Integral Method for Solving Nonlinear Eigenvalue Problems,” Linear Algebra Appl.,
436(10), pp. 3839–3863.

[CrossRef]
Davidson,
G. G.
,
Evans,
T. M.
,
Jarrell,
J. J.
,
Hamilton,
S. P.
,
Pandy,
T. M.
, and
Slaybaugh,
R. N.
, 2014, “
Massively Parallel, Three-Dimensional Transport Solutions for the k-Eigenvalue Problem,” Nucl. Sci. Eng.,
177(2), pp. 111–125.

[CrossRef]
Barrett,
W. W.
, 1979, “
A Theorem on Inverse of Tridiagonal Matrices,” Linear Algebra Appl.,
27, pp. 211–217.

[CrossRef]
Engwerda,
J. C.
,
Ran,
A. M.
, and
Rijkeboer,
A. L.
, 1993, “
Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution of the Matrix Equation X + A * X − 1A = Q,” Linear Algebra Appl.,
186, pp. 255–275.

[CrossRef]
Adams,
R. D.
,
Cawley,
P.
,
Pye,
C. J.
, and
Stone,
B. J.
, 1978, “
A Vibration Technique for Non-Destructively Assessing the Integrity of Structures,” J. Mech. Eng. Sci.,
20(2), pp. 93–100.

[CrossRef]
Qian,
G.-L.
,
Gu,
S.-N.
, and
Jiang,
J.-S.
, 1990, “
The Dynamic Behaviour and Crack Detection of a Beam With a Crack,” J. Sound Vib.,
138(2), pp. 233–243.

[CrossRef]
Gillich,
G.-R.
,
Praisach,
Z.-I.
, and
Negru,
I.
, 2012, “
The Relationship Between Changes of Deflection and Natural Frequencies of Damaged Beams,” Advances in Remote Sensing, Finite Differences and Information Security: (F-And-B ′12),(REMOTE ′12), (ISP ′12),
E. Scutelnicu
,
L. Lazic
, and
P. F. de Arroyabe
, eds.,
Wseas LLC,
Stevens Point, WI, pp. 38–42.

Hearn,
G.
, and
Testa,
R. B.
, 1991, “
Modal Analysis for Damage Detection in Structures,” J. Struct. Eng.,
117(10), pp. 3042–3063.

[CrossRef]
Hassiotis,
S.
, 2000, “
Identification of Damage Using Natural Frequencies and Markov Parameters,” Comput. Struct.,
74(3), pp. 365–373.

[CrossRef]
Li,
R. C.
, 2013, “
Rayleigh Quotient Based Optimization Methods for Eigenvalue Problems,” Summary of Lectures Delivered at Gene Golub SIAM Summer School,
World Scientific Publishing Company,
Singapore.

Kato,
T.
, 2012, Perturbation Theory for Linear Operators,
Springer Science & Business Media,
Berlin.