A sparsity-promoting resolvent analysis for the identification of spatiotemporally-localized amplification mechanisms

Lopez-Doriga, Barbara; Ballouz, Eric; Bae, H. Jane; Dawson, Scott T. M.

doi:10.2514/6.2023-0677

Cited by 6 publications

(2 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, Skene et al [44] developed an optimization framework to find sparse resolvent forcing modes, with small spatial footprints, that can be targeted by more realistic localized actuators. Similarly, Lopez-Doriga et al [45] introduced a sparsity-promoting resolvent analysis that allows identification of responsive forcings that are localized in space and time. Another important advancement for this framework is the structured input-output analysis, developed by Liu and Gayme [46], that preserves certain properties of the nonlinear forcing and is able to recover transitional flow features that were previously available only through nonlinear input-output analysis [47].…”

Section: Introductionmentioning

confidence: 99%

From resolvent to Gramians: extracting forcing and response modes for control

Herrmann¹,

Baddoo²,

Dawson³

et al. 2023

Preprint

View full text Add to dashboard Cite

During the last decade, forcing and response modes produced by resolvent analysis have demonstrated great potential to guide sensor and actuator placement and design in flow control applications. However, resolvent modes are frequency-dependent, which, although responsible for their success in identifying scale interactions in turbulence, complicates their use for control purposes. In this work, we seek orthogonal bases of forcing and response modes that are the most responsive and receptive, respectively, across all frequencies. We show that these frequency-independent bases of representative resolvent modes are given by the eigenvectors of the observability and controllability Gramians of the system considering full state inputs and outputs. We present several numerical examples where we leverage these bases by building orthogonal or interpolatory projectors onto the dominant forcing and response subspaces. Gramian-based forcing modes are used to identify dynamically relevant disturbances, to place point sensors to measure disturbances, and to design actuators for feedforward control in the subcritical linearized Ginzburg-Landau equation. Gramianbased response modes are used to identify coherent structures and for point sensor placement aiming at state reconstruction in the turbulent flow in a minimal channel at Reτ = 185. The approach does not require data snapshots and relies only on knowledge of the steady or mean flow.

show abstract

Section: Introductionmentioning

confidence: 99%

From resolvent to Gramians: extracting forcing and response modes for control

Herrmann¹,

Baddoo²,

Dawson³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently, Skene et al (2022) developed an optimization framework to find sparse resolvent forcing modes, with small spatial footprints, that can be targeted by more realistic localized actuators. Similarly, Lopez-Doriga et al (2023) introduced a sparsity-promoting resolvent analysis that allows identification of responsive forcings that are localized in space and time. Another important advancement for this framework is the structured input-output analysis, developed by Liu & Gayme (2021), that preserves certain properties of the nonlinear forcing and is able to recover transitional flow features that were available previously only through nonlinear input-output analysis (Rigas, Sipp & Colonius 2021).…”

mentioning

confidence: 99%

Interpolatory input and output projections for flow control

Herrmann,

Baddoo,

Dawson

et al. 2023

J. Fluid Mech.

View full text Add to dashboard Cite

Eigenvectors of the observability and controllability Gramians represent responsive and receptive flow structures that enjoy a well-established connection to resolvent forcing and response modes. However, whereas resolvent modes have demonstrated great potential to guide sensor and actuator placement, observability and controllability modes have been leveraged exclusively in the context of model reduction via input and output projections. In this work, we introduce interpolatory, rather than orthogonal, input and output projections, that can be leveraged for sensor and actuator placement and open-loop control design. An interpolatory projector is an oblique projector with the property of preserving certain entries in the vector being projected. We review the connection between the resolvent operator and the Gramians, and present several numerical examples where we perform both orthogonal and interpolatory input and output projections onto the dominant forcing and response subspaces. Input projections are used to identify dynamically relevant disturbances, place sensors to measure disturbances, and place actuators for feedforward control in the linearized Ginzburg–Landau equation. Output projections are used to identify coherent structures and place sensors aiming at state reconstruction in the turbulent flow in a minimal channel at $Re_{\tau }=185$ . The framework does not require data snapshots and relies only on knowledge of the steady or mean flow.

show abstract

An invitation to resolvent analysis

Rolandi,

Ribeiro,

Yeh

et al. 2024

Theor. Comput. Fluid Dyn.

View full text Add to dashboard Cite

Resolvent analysis is a powerful tool that can reveal the linear amplification mechanisms between the forcing inputs and the response outputs about a base flow. These mechanisms can be revealed in terms of a pair of forcing and response modes and the associated energy gains (amplification magnitude) at a given frequency. The linear relationship that ties the forcing and the response is represented through the resolvent operator (transfer function), which is constructed through spatially discretizing the linearized Navier–Stokes operator. One of the unique strengths of resolvent analysis is its ability to analyze statistically stationary turbulent flows. In light of the increasing interest in using resolvent analysis to study a variety of flows, we offer this guide in hopes of removing the hurdle for students and researchers to initiate the development of a resolvent analysis code and its applications to their problems of interest. To achieve this goal, we discuss various aspects of resolvent analysis and its role in identifying dominant flow structures about the base flow. The discussion in this paper revolves around the compressible Navier–Stokes equations in the most general manner. We cover essential considerations ranging from selecting the base flow and appropriate energy norms to the intricacies of constructing the linear operator and performing eigenvalue and singular value decompositions. Throughout the paper, we offer details and know-how that may not be available to readers in a collective manner elsewhere. Towards the end of this paper, examples are offered to demonstrate the practical applicability of resolvent analysis, aiming to guide readers through its implementation and inspire further extensions. We invite readers to consider resolvent analysis as a companion for their research endeavors.

show abstract

A sparsity-promoting resolvent analysis for the identification of spatiotemporally-localized amplification mechanisms

Cited by 6 publications

References 44 publications

From resolvent to Gramians: extracting forcing and response modes for control

From resolvent to Gramians: extracting forcing and response modes for control

Interpolatory input and output projections for flow control

An invitation to resolvent analysis

Contact Info

Product

Resources

About