A variational method for the extraction of intermittently unstable time-dependent modes directly from system observables
Abstract
The objective of this proposal is to develop an inexpensive methodology that will allow for the adaptive selection of time-dependent modes associated with finite-time instabilities directly through system observables. The PI will approach the objective by formulating a variational principle that will generate a time-dependent set of orthonormal modes which will move towards directions associated with the most intense finite-time instabilities. The modes will be driven by observable functions similarly with the Koopman modes setting, allowing the PI to define a basis that captures finite time instabilities using deterministic data generated from an independent solving procedure. Second, the PI will use this time-dependent basis to perform a modified Galerkin projection that will respect available information about the systemÕs statistical steady state spectrum. In particular, the statistical steady state information for the system in hand will be used to rigorously diagnose the persistent (in contrary to the transient) energy fluxes from the modes that the PI does not include in the order-reduction scheme to those that constitute the subspace of interest. Using these energy fluxes will complement the reduced-order equations with information that comes from statistically steady state statistics (obtained through a few accurate numerical simulations) resulting in a more accurate and energetically consistent reduced order model. The PI will test his approach against two problems: transient growth in a turbulent system (jet in a cross flow) and low-energy predictors of slowly growing instabilities in very high dimensions (power-grid network failures).
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jan 12, 2017
- Source ID
- W911NF1510164
Entities
People
- Themistoklis Sapsis
Organizations
- Army Contracting Command
- Massachusetts Institute of Technology
- United States Army