Sensor Placement Based on Proper Orthogonal Decomposition Modeling of a Cylinder Wake

Cohen, Kelly; Siegel, Stefan; McLaughlin, Thomas

doi:10.2514/6.2003-4259

Cited by 42 publications

(45 citation statements)

References 12 publications

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“…Authors in [18,30] demonstrate that the extrema of POD modes are very good locations, when examining reconstruction error in l 2 norm, see Equations (10) and (11), to place the sensors for regional ocean forecasting. Yang et al [19] further introduced the exclusion cylinder to further increase the accuracy of the reconstruction by reducing the redundancy as locations of extrema of different POD modes can be very close.…”

Section: Constrained Sensor Placementmentioning

confidence: 99%

POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study

2016

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Abstract:It is shown in literature that sensor placement at the extrema of Proper Orthogonal Decomposition (POD) modes is efficient and leads to accurate reconstruction of the field of quantity of interest (velocity, pressure, salinity, etc.) from a limited number of measurements in the oceanography study. In this paper, we extend this approach of sensor placement and take into account measurement errors and detect possible malfunctioning sensors. We use the 24 hourly spatial wind field simulation data sets simulated using the Weather Research and Forecasting (WRF) model applied to the Maine Bay to evaluate the performances of our methods. Specifically, we use an exclusion disk strategy to distribute sensors when the extrema of POD modes are close. We demonstrate that this strategy can improve the accuracy of the reconstruction of the velocity field. It is also capable of reducing the standard deviation of the reconstruction from noisy measurements. Moreover, by a cross-validation technique, we successfully locate the malfunctioning sensors.

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Section: Constrained Sensor Placementmentioning

confidence: 99%

POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study

2016

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“…This observation corresponds well to the heuristic sensor placement procedure suggested in [11]. In that work, sensors were placed at local spatial optima for each mode.…”

Section: ) Gappy Sensor Placementmentioning

confidence: 99%

“…As discussed in [11], it is desirable to place the sensors in location that experiences relatively large modal amplitudes. POD modal amplitude as a function of time for pulse plunge input.…”

Section: ) Gappy Sensor Placementmentioning

confidence: 99%

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Unsteady Flow Sensing and Estimation via the Gappy Proper Orthogonal Decomposition

Willcox

2004

2nd AIAA Flow Control Conference

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Abstract-The proper orthogonal decomposition (POD) has been widely used in fluid dynamic applications for extracting dominant flow features. The "gappy" POD is an extension to this method that allows the consideration of incomplete data sets. In this paper, the gappy POD is extended to handle unsteady flow reconstruction problems, such as those encountered when limited flow measurement data is available. In addition, a systematic approach for effective sensor placement is formulated within the gappy framework. Two applications are considered. The first aims to reconstruct the unsteady flow field using a small number of surface pressure measurements for a subsonic airfoil undergoing plunging motion. The second considers estimation of POD modal content of a cylinder wake flow for active control purposes. In both cases, using the dominant POD basis vectors and a small number of sensor signals, the gappy approach is found to yield accurate flow reconstruction results.

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“…(Throughout the paper, we shall use (21) to obtain the Hessian.) However, whenever the second partial derivatives ∇ 2 f q (s) are available with reasonable cost, the whole formula (19) should be used to render more rapid convergence to a global solution, especially for large residual problems.…”

Section: Solution Proceduresmentioning

confidence: 99%

A ‘best points’ interpolation method for efficient approximation of parametrized functions

Nguyen

Patera

Peraire

2007

Numerical Meth Engineering

171

166

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SUMMARYWe present an interpolation method for efficient approximation of parametrized functions. The method recognizes and exploits the low-dimensional manifold structure of the parametrized functions to provide good approximation. Basic ingredients include a specific problem-dependent basis set defining a lowdimensional representation of the parametrized functions, and a set of 'best interpolation points' capturing the spatial-parameter variation of the parametrized functions. The best interpolation points are defined as solution of a least-squares minimization problem which can be solved efficiently using standard optimization algorithms. The approximation is then determined from the basis set and the best interpolation points through an inexpensive and stable interpolation procedure. In addition, an a posteriori error estimator is introduced to quantify the approximation error and requires little additional cost. Numerical results are presented to demonstrate the accuracy and efficiency of the method.

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Sensor Placement Based on Proper Orthogonal Decomposition Modeling of a Cylinder Wake

Cited by 42 publications

References 12 publications

POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study

POD-Based Constrained Sensor Placement and Field Reconstruction from Noisy Wind Measurements: A Perturbation Study

Unsteady Flow Sensing and Estimation via the Gappy Proper Orthogonal Decomposition

A ‘best points’ interpolation method for efficient approximation of parametrized functions

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