Abstract

In this paper, the hidden variable damage tracking method developed in Part 1 is analyzed using a physics-based mathematical model of the experimental system: a mechanical oscillator with a nonstationary two-well potential. Numerical experiments conducted using the model are in good agreement with the experimental study presented in Part 1, and explicitly show how the tracking metric is related to the slow hidden variable evolution responsible for drift in the fast system parameters. Using the idea of averaging, the slow flow equation governing the hidden variable evolution is obtained. It is shown that the solution to the slow flow equation corresponds to the hidden variable trajectory obtained with the experimental tracking method. Thus we establish in principle the relationship of our algorithm to any underlying physical process. Based on this result, we discuss the application of the tracking method to systems with evolving material damage using the results of some preliminary experiments.

1.
Moon
,
F. C.
, and
Holmes
,
P.
,
1979
, “
A Magnetoelastic Strange Attractor
,”
J. Sound Vib.
,
65
(
2
), pp.
275
296
.
2.
Cusumano
,
J. P.
, and
Kimble
,
B.
,
1995
, “
A Stochastic Interrogation Method for Experimental Measurements of Global Dynamics and Basin Evolution: Application to a Two-Well Oscillator
,”
Nonlinear Dyn.
,
8
, pp.
213
235
.
3.
Takens, F., 1981, “Detecting Strange Attractor in Turbulence,” Rand, D. A., and Young, L. S., eds., Dynamical Systems and Turbulence, Warwick, Springer Lecture Notes in Mathematics, Springer-Verlag, Berlin, pp. 336–381.
4.
Sauer
,
T.
,
Yorke
,
J. A.
, and
Casdagli
,
M.
,
1991
, “
Embedology
,”
J. Stat. Phys.
,
65
(
3–4
), pp.
579
616
.
5.
Feeny
,
B. F.
,
Yuan
,
C. M.
, and
Cusumano
,
J. P.
,
2001
, “
Parametric Identification of an Experimental Magneto-Elastic Oscillator,” Accepted
,
J. Sound Vib.
,
247
(
5
), pp.
785
806
.
6.
Woodson, H. H., and Melcher, J. R., 1968, Electromechanical Dynamics, pt. 1: Discrete Systems, Wiley, New York.
7.
Strauss
,
E.
,
Golodnitsky
,
D.
, and
Peled
,
E.
,
1999
, “
Cathode Modification for Improved Performance of Rechargeable Lithium/Composite Polymer Electrolyte-Pyrite Battery
,”
Electrochem. Solid-State Lett.
,
2
(
3
), pp.
115
117
.
8.
Cusumano
,
J. P.
, and
Chatterjee
,
A.
,
2000
, “
Steps Towards a Qualitative Dynamics of Damage Evolution
,”
Int. J. Solids Struct.
,
37
(
44
), pp.
6397
6417
.
9.
Sanders, J. A., and Verhulst, F., 1985, Averaging Methods in Nonlinear Dynamical Systems, Springer-Verlag, New York.
You do not currently have access to this content.