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| Content Provider | Springer Nature Link |
|---|---|
| Author | ack, Bernd R. Protas, Bartosz MorzyĆski, Marek |
| Copyright Year | 2013 |
| Abstract | We propose a general framework for the parameter-free identification of a class of dynamical systems. Here, the propagator is approximated in terms of an arbitrary function of the state, in contrast to a polynomial or Galerkin expansion used in traditional approaches. The proposed formulation relies on variational data assimilation using measurement data combined with assumptions on the smoothness of the propagator. This approach is illustrated using a generalized dynamic model describing oscillatory transients from an unstable fixed point to a stable limit cycle and arising in nonlinear stability analysis as an example. This 3-state model comprises an evolution equation for the dominant oscillation and an algebraic manifold for the low- and high-frequency components in an autonomous descriptor system. The proposed optimal model identification technique employs mode amplitudes of the transient vortex shedding in a cylinder wake flow as example measurements. The reconstruction obtained with our technique features distinct and systematic improvements over the well-known mean-field (Landau) model of the Hopf bifurcation. The computational aspect of the identification method is thoroughly validated showing that good reconstructions can also be obtained in the absence of accurate initial approximations. |
| Ending Page | 275 |
| Page Count | 31 |
| Starting Page | 245 |
| File Format | |
| ISSN | 09388974 |
| e-ISSN | 14321467 |
| Journal | Journal of Nonlinear Science |
| Issue Number | 2 |
| Volume Number | 24 |
| Language | English |
| Publisher | Springer US |
| Publisher Date | 2013-10-30 |
| Publisher Place | Boston |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Mathematical modeling (models of systems, model-matching, etc.) ApplicationMathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics Mean-field models Wakes and jets Reduced-order models Optimization and variational techniques Analysis Hydrodynamic instabilities Adjoint-based optimization Mechanics Economic Theory Variational data assimilation |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Engineering Modeling and Simulation |
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