Low-dimensional models of coherent structures in turbulence

Holmes, Philip; Lumley, John L.; Berkooz, Gal; Mattingly, Jonathan C.; Wittenberg, Ralf W.

doi:10.1016/s0370-1573(97)00017-3

Cited by 154 publications

(92 citation statements)

References 44 publications

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“…It must be pointed out that alternative functions could be employed in the approximation. In this context, the Proper Orthogonal Decomposition (POD) method (Sirovich, 1987;Holmes et al, 1997) provides a set of empirical basis functions which are optimal with respect to other possible expansions. This set is optimal in the sense that, for a given number of basis functions, it captures most of the relevant dynamic behavior of the original distributed system in the range of initial conditions, parameters, inputs, and/or perturbations of the experimental data (Balsa-Canto et al, 2004).…”

Section: The Kirchhoff Transform (3) Applied To This System Results Imentioning

confidence: 99%

Robust feed-back control of distributed chemical reaction systems

Vilas¹,

García²,

Banga³

et al. 2007

Chemical Engineering Science

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There are many distributed processes in the chemical industry as it is the case of tubular reactors in which the parameters or the structure of the reaction terms are only a rough approximation of reality. In order to efficiently control this kind of systems, it is important to take into account this lack of detailed information (robustness). In this work, we make use of the classical theory on the robust nonlinear control for finite dimensional systems and extend it to distributed process systems by taking advantage of the special nature of dissipative systems. In this way, theoretical issues related to the nonlinearity of the diffusion terms and inhomogeneous boundary conditions are handled by means of the Kirchhoff and state transformations, respectively. In addition, and for practical reasons, the problem of controller saturation is considered. The different aspects of the methodology will be illustrated through a number of computational experiments concerning non-isothermal tubular reactors with convection and/or diffusion terms.

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Section: The Kirchhoff Transform (3) Applied To This System Results Imentioning

confidence: 99%

Robust feed-back control of distributed chemical reaction systems

Vilas¹,

García²,

Banga³

et al. 2007

Chemical Engineering Science

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“…Projection-based model order reduction The second step computes reduced-order models for each measurement (q m ) and capability (s c ) through parametric Proper Orthogonal Decomposition (POD). [33][34][35][36][37][38][39][40][41][42] For each quantity we assemble the n e × n s matrix of complete snapshots and compute the POD basis vectors via singular value decomposition:…”

Section: A Multistep-rom Proceduresmentioning

confidence: 99%

Sensor placement strategy to inform decisions

Mainini

Willcox

2017

18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

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This paper introduces a computational strategy to determine optimal sets of sensor locations to support real-time operational decisions. We exploit unsupervised learning strategies (specifically self-organizing maps) to identify the most informative locations to place sensors. The sensor placement procedure is then combined with a Multi-Step-Reduced Order Modeling approach that exploits the low-dimensional map between the sparse sensed data and the decisions at hand. The approach is demonstrated for the real-time assessment of an unmanned aircraft wing panel undergoing structural degradation. For this application, we compare the optimal sets of sensor locations with random placements for a variety of sensor availabilities. By adopting our placement strategy, we achieve improvements in accuracy and robustness of capability predictions, even when measured data are sparse and cover less than 10% of the reference data.

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“…It was firstly proposed by Sirovich [38] and exploited by the group of Holmes and Lumley [39,40,41] in the context of fluid dynamics as a way to explore the routes to turbulence phenomena, and was rapidly extended to other fields such as chemical reaction and biological systems. In this technique, measurements of the spatio-temporal evolution of the field are employed to derive the ROM (Reduced Order Model).…”

Section: Introductionmentioning

confidence: 99%