Efficient sensor placement for ocean measurements using low-dimensional concepts

Yildirim, Battalgazi; Chryssostomidis, Chryssostomos; Karniadakis, George

doi:10.1016/j.ocemod.2009.01.001

Cited by 139 publications

(119 citation statements)

References 29 publications

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“…More recently, the low-rank POD approximations were combined with sparse representation to enable ROM computations with very limited sensors [5,8]. Significant effort has been applied to develop principled, rather than random, sensor placement for ROMs [59,63,15,51]. Although none of the above methods solve the typically NP-hard sensor placement optimization problem, they have been demonstrated to be quite effective in many applications.…”

Section: Related Workmentioning

confidence: 99%

Sparse Sensor Placement Optimization for Classification

Brunton¹,

Brunton²,

Proctor³

et al. 2016

SIAM J. Appl. Math.

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Abstract. Choosing a limited set of sensor locations to characterize or classify a high-dimensional system is an important challenge in engineering design. Traditionally, optimizing the sensor locations involves a brute-force, combinatorial search, which is NP-hard and is computationally intractable for even moderately large problems. Using recent advances in sparsity-promoting techniques, we present a novel algorithm to solve this sparse sensor placement optimization for classification (SSPOC) that exploits low-dimensional structure exhibited by many high-dimensional systems. Our approach is inspired by compressed sensing, a framework that reconstructs data from few measurements. If only classification is required, reconstruction can be circumvented and the measurements needed are orders-of-magnitude fewer still. Our algorithm solves an 1 minimization to find the fewest nonzero entries of the full measurement vector that exactly reconstruct the discriminant vector in feature space; these entries represent sensor locations that best inform the decision task. We demonstrate the SSPOC algorithm on five classification tasks, using datasets from a diverse set of examples, including physical dynamical systems, image recognition, and microarray cancer identification. Once training identifies sensor locations, data taken at these locations forms a low-dimensional measurement space, and we perform computationally efficient classification with accuracy approaching that of classification using full-state data. The algorithm also works when trained on heavily subsampled data, eliminating the need for unrealistic full-state training data.

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Section: Related Workmentioning

confidence: 99%

Sparse Sensor Placement Optimization for Classification

Brunton¹,

Brunton²,

Proctor³

et al. 2016

SIAM J. Appl. Math.

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“…(8) In [18,19], the authors demonstrate numerically the convergence of the reconstruction error of the Gappy-POD method: g becomes closer to c as the number of sensors increases. More specifically, ∑ K k=1 (a k − b k ) 2 → 0 as number of sensors increases.…”

Section: Remarkmentioning

confidence: 99%

“…As in [19], we will also impose "declustering" constraints on the sensors as we have observed to avoid redundant measurements at near-by points. Because we use the extrema of the first few modes, empirically, the condition number of the matrix in the linear system of gappy pod method is reduced as shown in [18,19]. We find that this strategy also helps to reduce the reconstruction error.…”

Section: Introductionmentioning

confidence: 99%

“…In [18], the authors showed that only a few spatio-temporal POD modes are sufficient to describe the most energetic ocean dynamics. In particular, they demonstrated that the extrema of the POD spatial modes are very good locations for sensor placement and accurate field reconstruction given a limited number of observing stations and assuming perfect measurements.…”

Section: Introductionmentioning

confidence: 99%

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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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“…Furthermore, taking advantage of the well known property of HOSVD-based methods in identifying patterns and consequently constructing lower dimensional models, the methods developed in this Thesis can be further improved developing a new method able to efficiently determine critical positions in a multidimensional database which are best candidates to be tested in order to improve the fidelity of the reconstructed database. This concept has been already addressed in literature, mainly based on POD methods [43,44].…”

Section: Introductionmentioning

confidence: 99%

Aerodynamic database reconstruction via gappy high order singular value decomposition

López¹

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Aerodynamic database reconstruction via gappy high order singular value decompositionby Ana Isabel MORENO LÓPEZ A method based on an iterative application of high order singular value decomposition is derived for the reconstruction of missing data in multidimensional databases. The method is inspired by a seminal gappy reconstruction method for two-dimensional databases invented by Everson and Sirovich (1995) and improved by Beckers and Rixen (2003) and Venturi and Karniadakis (2004). In addition, the method is adapted to treat both noisy and structured-but-nonrectangular databases.The method is calibrated and illustrated using a three-dimensional toy model database that is obtained by discretizing a transcendental function. The performance of the method is tested on three aerodynamic databases for the flow past a wing, one obtained by a semi-analytical method, and two resulting from computational fluid dynamics. The method is finally applied to an experimental database consisting in a non-exhaustive parameter space measurement of forces for a box-wing configuration.iii ResumenReconstrucción de bases de datos aerodinámicas a través de la descomposición en valores sigulares para tensores de alto orden por Ana Isabel MORENO LÓPEZ Esta Tesis se centra en el desarrollo de un método para la reconstrucción de bases de datos experimentales incompletas de más de dos dimensiones. Como idea general, consiste en la aplicación iterativa de la descomposición en valores singulares de alto orden sobre la base de datos incompleta. Este nuevo método se inspira en el que ha servido de base para la reconstrucción de huecos en bases de datos bidimensionales inventado por Everson y Sirovich (1995) que a su vez, ha sido mejorado por Beckers y Rixen (2003) y simultáneamente por Venturi y Karniadakis (2004). Además, se ha previsto la adaptación de este nuevo método para tratar el posible ruido característico de bases de datos experimentales y a su vez, bases de datos estructuradas cuya información no forma un hiperrectángulo perfecto.Se usará una base de datos tridimensional de muestra como modelo, obtenida a través de una función transcendental, para calibrar e ilustrar el método. A continuación se detalla un exhaustivo estudio del funcionamiento del método y sus variantes para distintas bases de datos aerodinámicas. En concreto, se usarán tres bases de datos tridimensionales que contienen la distribución de presiones sobre un ala. Una se ha generado a través de un método semi-analítico con la intención de estudiar distintos tipos de discretizaciones espaciales. El resto resultan de dos modelos numéricos calculados en CFD. Porúltimo, el método se aplica a una base de datos experimental de más de tres dimensiones que contiene la medida de fuerzas de una configuración ala de Prandtl obtenida de una campaña de ensayos en túnel de viento, donde se estudiaba un amplio espacio de parámetros geométricos de la configuración que como resultado ha generado una base de datos donde la información está dispersa.v

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Efficient sensor placement for ocean measurements using low-dimensional concepts

Cited by 139 publications

References 29 publications

Sparse Sensor Placement Optimization for Classification

Sparse Sensor Placement Optimization for Classification

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

Aerodynamic database reconstruction via gappy high order singular value decomposition

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