Output-only identification methods have been developed on a stochastic framework, but for the first time, a subspace-based approach is proposed without using geometric and statistical tools. This aids the computational efforts to be significantly reduced and the range of input sources to be extended in a much realistic manner for future output-only analyses. The approach encompasses any input type and can properly work for systems excited by inputs with finite periods. It is demonstrated that the row space of the output sequences spanned by column vectors of the decomposed orthonormal matrix is sufficient to reconstruct the observations. The transient and steady-state portions of the output row space, afterward, can be captured to reconstruct an integrated innovation model. The advantages of the algorithm are highlighted through several numerical and experimental examples comparing with the traditional subspace identification algorithms.

References

1.
Ho
,
Β.
, and
Kálmán
,
R. E.
,
1966
, “
Effective Construction of Linear State-Variable Models From Input/Output Functions
,”
Automatisierungstechnik
,
14
(
1–12
), pp.
545
548
.
2.
Silverman
,
L.
,
1971
, “
Realization of Linear Dynamical Systems
,”
IEEE Trans. Autom. Control
,
16
(
6
), pp.
554
567
.
3.
Dickinson
,
B.
,
Morf
,
M.
, and
Kailath
,
T.
,
1974
, “
A Minimal Realization Algorithm for Matrix Sequences
,”
IEEE Trans. Autom. Control
,
19
(
1
), pp.
31
38
.
4.
Akaike
,
H.
,
1974
, “
Stochastic Theory of Minimal Realization
,”
IEEE Trans. Autom. Control
,
19
(
6
), pp.
667
674
.
5.
Moore
,
B. C.
,
1979
, “
Singular Value Analysis of Linear Systems
,”
IEEE
Conference on Decision and Control Including the 17th Symposium on Adaptive Processes
, San Diego, CA, Jan. 10–12, pp.
66
73
.
6.
Kung
,
S.-Y.
,
1978
, “
A New Identification and Model Reduction Algorithm Via Singular Value Decomposition
,”
12th Asilomar Conference on Circuits, Systems, and Computers
, Pacific Grove, CA, Nov. 6–8, pp.
705
714
.
7.
Giannakis
,
G. B.
, and
Serpedin
,
E.
,
1998
, “
Blind Identification of ARMA Channels With Periodically Modulated Inputs
,”
IEEE Trans. Signal Process.
,
46
(
11
), pp.
3099
3104
.
8.
Jafari
,
K.
,
2017
, “
A Parameter Estimation Approach Based on Binary Measurements Using Maximum Likelihood Analysis-Application to MEMS
,”
Int. J. Control, Autom. Syst.
,
15
(
2
), pp.
716
721
.
9.
Tong
,
L.
, and
Perreau
,
S.
,
1998
, “
Multichannel Blind Identification: From Subspace to Maximum Likelihood Methods
,”
Proc. IEEE
,
86
(
10
), pp.
1951
1968
.
10.
Tsoi
,
A. C.
, and
Ma
,
L.
,
2003
, “
Blind Deconvolution of Dynamical Systems Using a Balanced Parameterized State Space Approach
,”
IEEE International Conference on Acoustics, Speech, and Signal Processing
(
ICASSP
'03), Hong Kong, China, Apr. 6–10, p.
IV–309
.
11.
Van Overschee
,
P.
, and
De Moor
,
B.
,
1993
, “
Subspace Algorithms for the Stochastic Identification Problem
,”
Automatica
,
29
(
3
), pp.
649
660
.
12.
Wang
,
D.-Q.
,
Zhang
,
Z.
, and
Yuan
,
J.-Y.
,
2017
, “
Maximum Likelihood Estimation Method for Dual-Rate Hammerstein Systems
,”
Int. J. Control, Autom. Syst.
,
15
(
2
), pp.
698
705
.
13.
Wang
,
L.
,
Cheng
,
P.
, and
Wang
,
Y.
,
2011
, “
Frequency Domain Subspace Identification of Commensurate Fractional Order Input Time Delay Systems
,”
Int. J. Control, Autom. Syst.
,
9
(
2
), pp.
310
316
.
14.
Yu
,
C.
, and
Verhaegen
,
M.
,
2016
, “
Blind Multivariable ARMA Subspace Identification
,”
Automatica
,
66
, pp.
3
14
.
15.
Zhang
,
L.-Q.
,
Cichocki
,
A.
, and
Amari
,
S.
,
2000
, “
Kalman Filter and State-Space Approach to Blind Deconvolution
,”
Neural Networks for Signal Processing X, IEEE Signal Processing Society Workshop
, Sydney, Australia, Dec. 11–13, pp.
425
434
.
16.
Phan
,
M. Q.
,
Vicario
,
F.
,
Longman
,
R. W.
, and
Betti
,
R.
,
2017
, “
State-Space Model and Kalman Filter Gain Identification by a Kalman Filter of a Kalman Filter
,”
ASME J. Dyn. Syst., Meas., Control
,
140
(
3
), p.
030902
.
17.
Peeters
,
B.
, and
De Roeck
,
G.
,
2001
, “
Stochastic System Identification for Operational Modal Analysis: A Review
,”
ASME J. Dyn. Syst., Meas., Control
,
123
(
4
), pp.
659
667
.
18.
Peeters
,
B.
, and
De Roeck
,
G.
,
1999
, “
Reference-Based Stochastic Subspace Identification for Output-Only Modal Analysis
,”
Mech. Syst. Signal Process.
,
13
(
6
), pp.
855
878
.
19.
Reynders
,
E.
,
Pintelon
,
R.
, and
De Roeck
,
G.
,
2008
, “
Uncertainty Bounds on Modal Parameters Obtained From Stochastic Subspace Identification
,”
Mech. Syst. Signal Process.
,
22
(
4
), pp.
948
969
.
20.
Batel
,
M.
,
2002
, “
Operational Modal Analysis—Another Way of Doing Modal Testing
,”
J. Sound Vib.
,
36
(
8
), pp.
22
27
.http://www.sandv.com/downloads/0208batl.pdf
21.
Basseville
,
M. L.
,
Benveniste
,
A.
,
Goursat
,
M.
,
Hermans
,
L.
,
Mevel
,
L.
, and
Van der Auweraer
,
H.
,
2001
, “
Output-Only Subspace-Based Structural Identification: From Theory to Industrial Testing Practice
,”
ASME J. Dyn. Syst., Meas., Control
,
123
(
4
), pp.
668
676
.
22.
Hautus
,
M. L.
,
1983
, “
Strong Detectability and Observers
,”
Linear Algebra Appl.
,
50
, pp.
353
368
.
23.
Kratz
,
W.
,
1995
, “
Characterization of Strong Observability and Construction of an Observer
,”
Linear Algebra Appl.
,
221
, pp.
31
40
.
24.
Kurek
,
J.
,
1988
, “
Strong Observability and Strong Reconstructibility of a System Described by the 2-D Roeser Model
,”
Int. J. Control
,
47
(
2
), pp.
633
641
.
25.
Moreno
,
J. A.
,
Rocha-Cózatl
,
E.
, and
Wouwer
,
A. V.
,
2014
, “
A Dynamical Interpretation of Strong Observability and Detectability Concepts for Nonlinear Systems With Unknown Inputs: Application to Biochemical Processes
,”
Bioprocess Biosyst. Eng.
,
37
(
1
), pp.
37
49
.
26.
Liu
,
C.
, and
Li
,
C.
,
2013
, “
Reachability and Observability of Switched Linear Systems With Continuous-Time and Discrete-Time Subsystems
,”
Int. J. Control, Autom. Syst.
,
11
(
1
), pp.
200
205
.
27.
Bauer
,
D.
,
2001
, “
Order Estimation for Subspace Methods
,”
Automatica
,
37
(
10
), pp.
1561
1573
.
28.
Chiuso
,
A.
, and
Picci
,
G.
,
2004
, “
On the Ill-Conditioning of Subspace Identification With Inputs
,”
Automatica
,
40
(
4
), pp.
575
589
.
29.
De Moor
,
B.
,
Vandewalle
,
J.
,
Moonen
,
M.
,
Vandenberghe
,
L.
, and
Van Mieghem
,
P.
,
1988
, “
A Geometrical Strategy for the Identification of State Space Models of Linear Multivariable Systems With Singular Value Decomposition
,”
IFAC Proc. Vol.
,
21
(
9
), pp.
493
497
.
30.
Gustafsson
,
T.
,
2001
, “
Subspace Identification Using Instrumental Variable Techniques
,”
Automatica
,
37
(
12
), pp.
2005
2010
.
31.
Katayama
,
T.
, and
Tanaka
,
H.
,
2007
, “
An Approach to Closed-Loop Subspace Identification by Orthogonal Decomposition
,”
Automatica
,
43
(
9
), pp.
1623
1630
.
32.
Ljung
,
L.
, and
McKelvey
,
T.
,
1996
, “
Subspace Identification From Closed Loop Data
,”
Signal Process.
,
52
(
2
), pp.
209
215
.
33.
Miller
,
D. N.
, and
De Callafon
,
R. A.
,
2013
, “
Subspace Identification With Eigenvalue Constraints
,”
Automatica
,
49
(
8
), pp.
2468
2473
.
34.
Moonen
,
M.
, and
Ramos
,
J.
,
1993
, “
A Subspace Algorithm for Balanced State Space System Identification
,”
IEEE Trans. Autom. Control
,
38
(
11
), pp.
1727
1729
.
35.
Peternell
,
K.
,
Scherrer
,
W.
, and
Deistler
,
M.
,
1996
, “
Statistical Analysis of Novel Subspace Identification Methods
,”
Signal Process.
,
52
(
2
), pp.
161
177
.
36.
Swindlehurst
,
A.
,
Roy
,
R.
,
Ottersten
,
B.
, and
Kailath
,
T.
,
1992
, “
System Identification Via Weighted Subspace Fitting
,”
American Control Conference
(
ACC
), Chicago, IL, June 24–26, pp.
2158
2163
.
37.
Verhaegen
,
M.
, and
Dewilde
,
P.
,
1992
, “
Subspace Model Identification Part 1. The Output-Error State-Space Model Identification Class of Algorithms
,”
Int. J. Control
,
56
(
5
), pp.
1187
1210
.
38.
Viberg
,
M.
,
1995
, “
Subspace-Based Methods for the Identification of Linear Time-Invariant Systems
,”
Automatica
,
31
(
12
), pp.
1835
1851
.
39.
Zhang
,
S.
,
Liu
,
T.
,
Hou
,
J.
, and
Ni
,
X.
,
2017
, “
LQ Decomposition Based Subspace Identification Under Deterministic Type Disturbance
,”
Syst. Sci. Control Eng.
,
5
(
1
), pp.
243
251
.
40.
Arun
,
K.
, and
Kung
,
S.
,
1990
, “
Balanced Approximation of Stochastic Systems
,”
SIAM J. Matrix Anal. Appl.
,
11
(
1
), pp.
42
68
.
41.
Tanaka
,
H.
,
ALMutawa
,
J.
, and
Katayama
,
T.
,
2005
, “
Stochastic Subspace Identification of Linear Systems With Observation Outliers
,”
44th IEEE Conference on Decision and Control European Control Conference
(
CDC-ECC
'05), Seville, Spain, June 25–28, pp.
7090
7095
.
42.
Van Overschee
,
P.
, and
De Moor
,
B.
,
1996
,
Subspace Identification for Linear Systems: Theory—Implementation—Applications
, Kluwer Academic Publishers, Dordrecht, The Netherlands.
43.
Van Overschee
,
P.
, and
De Moor
,
B.
,
1994
, “
N4SID: Subspace Algorithms for the Identification of Combined Deterministic-Stochastic Systems
,”
Automatica
,
30
(
1
), pp.
75
93
.
44.
Lipschutz
,
S.
, and
Lipson
,
M.
,
2008
,
Schaum's Outline of Linear Algebra
, 4th ed.,
McGraw-Hill Professional
, New York.
45.
Piziak
,
R.
, and
Odell
,
P. L.
,
2007
,
Matrix Theory: From Generalized Inverses to Jordan Form
,
CRC Press
, Boca Raton, FL.
46.
Puntanen
,
S.
,
Styan
,
G. P.
, and
Isotalo
,
J.
,
2011
,
Matrix Tricks for Linear Statistical Models: Our Personal Top Twenty
,
Springer, Berlin
.
47.
Ljung
,
L.
,
1999
,
System Identification. Theory for the User
, 2nd ed.,
Prentice Hall
, Upper Saddle River, NJ.
48.
Verhaegen
,
M.
,
1994
, “
Identification of the Deterministic Part of MIMO State Space Models Given in Innovations Form From Input-Output Data
,”
Automatica
,
30
(
1
), pp.
61
74
.
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