Browsing by Subject "Robust Stability"
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Item Imposing Physical Structure within Input-Output Analysis of Fluid Flows: Methods and Applications(2023-07) Mushtaq, TalhaInput-output (I/O) methods have recently been proposed as simulation-free methods for identifying and quantifying fluid flow instabilities. Recent developments in I/O methods have focused on imposing additional physical structure within the I/O framework by (i) accounting for the structure of the nonlinear terms (i.e., structured I/O), or (ii) promoting sparsity in the identified instability mechanisms (i.e., spatially-localized modal analysis). This dissertation contributes to the state of the art by formulating and applying I/O analysis algorithms that are both computationally efficient and impose this physical structure in a mathematically consistent manner. First, we propose algorithms for performing the structured I/O analysis, which involves computing structured singular value (SSV) bounds (worst-case gains) and mode shapes by exploiting the underlying mathematical structure of the convective nonlinearity in the incompressible Navier-Stokes equations (NSE). The analysis yields physical insights of the global flow mechanisms, which are useful for identifying flow instabilities. We demonstrate the analysis on a laminar channel flow, and a turbulent channel flow over riblets. For both models, we identify various relevant flow mechanisms that are consistent with the ones predicted in high-fidelity numerical simulations, e.g., Kelvin-Helmholtz (KH) vortices, lift-up effects and Near-Wall (NW) cycles. Second, we propose computationally efficient algorithms for spatially-localized modal analysis. Unlike state of the art methods that promote sparsity, the methods proposed here work to solve a cardinality-constrained optimization problem. The solution to the optimization are sparse modes that highlight most pertinent flow quantities for triggering instabilities. We demonstrate the analysis on a laminar channel flow, where the sparse modes identify various spatially-localized flow mechanisms that contribute to the kinetic energy growth of the flow, e.g., the lift-up effect and Tollmien-Schlichting instabilities.Item Non-Parametric Estimation of Uncertain Closed-Loop Multivariate Frequency Response for Stability Assurance(2022-03) Regan, ChristopherSystem identification of closed-loop, multivariate systems presents a complex challenge; the use case for this study is on estimation for the purpose of stability margin assurance. Assessing both the nominal, or "best", estimated stability margins and the uncertainty range of those estimates are critical. This challenge is addressed by subjecting the system to multisine excitations and evaluating the response at both the excited frequencies and a set of null frequencies that are interleaved with the excited frequencies. This unique form of frequency separation allows for isolation of the response due to disturbances; which provides a critical source of estimation uncertainty. Additional sources of uncertainty, arising from response variations with time and spectral leakage, are combined to form a total estimated uncertainty. The impact of nonlinearities in the response are addressed, along with a particular approach to identification of nonlinearities. System stability assessment is performed, that directly accounts for estimation uncertainty. The approach to system estimation and stability assessment requires minimal prior knowledge and relies on only in situ data; the result is an independent assurance of system stability.