This paper proposes a method to identify non-Gaussian random noise in an unknown system through the use of a modified system identification (ID) technique in the stochastic domain, which is based on a recently developed Gaussian system ID. The non-Gaussian random process is approximated via an equivalent Gaussian approach. A modified Fokker–Planck–Kolmogorov equation based on a non-Gaussian analysis technique is adopted to utilize an effective Gaussian random process that represents an implied non-Gaussian random process. When a system under non-Gaussian random noise reveals stationary moment output, the system parameters can be extracted via symbolic computation. Monte Carlo stochastic simulations are conducted to reveal some approximate results, which are close to the actual values of the system parameters.

References

References
1.
Basin
,
M.
, and
Calderon-Alvarez
,
D.
,
2008
, “
Optimal LQG Controller for Linear Stochastic Systems With Unknown Parameters
,”
J. Franklin Inst.
,
345
, pp.
293
302
.10.1016/j.jfranklin.2007.10.003
2.
Sun
,
Y.
, and
Cao
,
J.
,
2007
, “
Adaptive Synchronization Between Two Different Noise-Perturbed Chaotic Systems With Fully Unknown Parameters
,”
Physica A
,
376
, pp.
253
265
.10.1016/j.physa.2006.10.039
3.
Yelderman
,
M.
,
1990
, “
Continuous Measurement of Cardiac Output With the Use of Stochastic System Identification Techniques
.”
J. Clin. Monitoring
,
6
, pp.
322
332
.
4.
Peeters
,
B.
, and
Roeck
,
G. D.
,
2001
, “
Stochastic System Identification for Operational Modal Analysis: A Review
.”
ASME J. Dyn. Syst., Meas., Control
,
123
, pp.
659
667
.10.1115/1.1410370
5.
Capodaglio
,
A. G.
,
Zheng
,
S.
,
Novotny
,
V.
, and
Feng
,
X.
,
1990
, “
Stochastic System Identification of Sewer-Flow Models
.”
J. Environ. Eng.
,
116
, pp.
284
298
.10.1061/(ASCE)0733-9372(1990)116:2(284)
6.
Cordeiro
,
H. M.
,
2009
, “
Stochastic Dynamical System Identification Applied to Combustor Stability Margin Assessment
,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
7.
Hios
,
J. D.
, and
Fassois
,
S. D.
,
2008
, “
Stochastic Vector Identification and Uncertain Modal Parameter Estimation for a Smart Composite Beam
,”
3rd International Conference Smart Materials Structures Systems
.
8.
Li
,
J.
, and
Roberts
,
J. B.
,
1999
, “
Stochastic Structural System Identification, Part 2: Variance Parameter Estimation
,”
Comput. Mech.
,
24
, pp.
211
215
.10.1007/s004660050454
9.
Robert-Nicoud
,
Y. R.
,
Rapael
,
B.
, and
Smith
,
I. F. C.
,
2005
, “
System Identification Through Model Composition and Stochastic Search
,”
J. Comput. Civil Eng.
,
19
, pp.
239
247
.10.1061/(ASCE)0887-3801(2005)19:3(239)
10.
Heo
,
H.
,
Lee
,
J.
,
Park
,
S.
,
Lee
,
D.
, and
Chae
,
K.
,
2007
, “
Method Apparatus for Identifying System in Stochastic Domain Using Output Parameter and Record Medium Thereof
,” Patent No. 1010829190000, patent registered in Korea, 2011.
11.
Park
,
S.
,
Kwon
,
O.
,
Kim
,
J.
, and
Heo
,
H.
,
2009
, “
Stochastic System Identification of Unknown Flexible Cantilever Beam Under Turbulent Flow
,”
Int. J. Modell., Identif. Control
,
8
, pp.
68
72
.10.1504/IJMIC.2009.028877
12.
Lozinski
,
A.
,
Owens
,
R. G.
, and
Fang.
J.
,
2004
, “
A Fokker–Planck-Based Numerical Method for Modeling Non-Homogeneous Flows of Dilute Polymeric Solution
,”
J. Non-Newtonian Fluid Mech.
,
122
, pp.
273
286
.10.1016/j.jnnfm.2004.01.025
13.
Heo
,
H.
,
Cho
,
Y.
, and
Kim
,
D.
,
2003
, “
Stochastic Control of Flexible Beam in Random Flutter
,”
J. Sound Vib.
,
267
, pp.
335
354
.10.1016/S0022-460X(03)00184-6
14.
Ibrahim
,
R. A.
,
2006
, “
Excitation-Induced Stability and Phase Transition: A Review
,”
J. Vib. Control
,
12
, pp.
1093
1170
.10.1177/1077546306069912
15.
Lee
,
J.
,
Cho
,
Y.
,
Yang
,
I.
,
Ko
,
I.
,
Kwon
,
D.
, and
Heo
,
H.
,
2009
, “
A Stochastic Controller Design Using Approximate Solution of FPK Equation
,”
J. Vib. Control
,
15
, pp.
567
581
.10.1177/1077546308094248
16.
Heo
,
H.
,
Yang
,
I.
,
Kim
,
J.
,
Kwon
,
O.
,
Park
,
S.
,
Na
,
S.
, and
Kim
,
G.
,
2008
, “
Apparatus of System Identification in Electrical Circuit System and Method Thereof
,” Patent No. 1010471130000, patent registered in Korea, 2011.
17.
Yang
,
I.
, and
Heo
,
H.
,
2011
, “
An Identification Method for Stochastic System Under Unknown Random Noise
,” The 2nd Korea-Japan Joint Symposium on Dynamics and Control.
18.
Wu
,
D.
,
Luo
,
X.
, and
Zhu
,
S.
,
2007
, “
Stochastic System With Coupling Between Non-Gaussian and Gaussian Noise Terms
,”
Physica A
,
373
, pp.
203
214
.10.1016/j.physa.2006.02.049
19.
Fuentes
,
M. A.
,
Toral
,
R.
, and
Wio
,
H. S.
,
2001
, “
Enhancement of Stochastic Resonance (the Role of Non Gaussian Noises)
,”
Physica A
,
295
, pp.
114
122
.10.1016/S0378-4371(01)00062-0
You do not currently have access to this content.