Sparse Sensor Placement Optimization for Classification

Brunton, Bingni W.; Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

doi:10.1137/15m1036713

Cited by 93 publications

(68 citation statements)

References 59 publications

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“…However, in the context of modeling physical systems, classification relies on additional design choices, such as sensor placement. Classification methods that explicitly take into account the placement of sensors have been recently shown to successfully classify states of dynamical systems into regimes of characteristic behaviors [12,39,11,23,10], and further improvements are ongoing. The suitability of a given classification approach also depends on the problem character.…”

Section: 2mentioning

confidence: 99%

Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models

Krämer¹,

Peherstorfer²,

Willcox³

2017

SIAM J. Appl. Dyn. Syst.

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Abstract. We consider control and stabilization for large-scale dynamical systems with uncertain, time-varying parameters. The time-critical task of controlling a dynamical system poses major challenges: using large-scale models is prohibitive, and accurately inferring parameters can be expensive, too. We address both problems by proposing an offline-online strategy for controlling systems with timevarying parameters. During the offline phase, we use a high-fidelity model to compute a library of optimal feedback controller gains over a sampled set of parameter values. Then, during the online phase, in which the uncertain parameter changes over time, we learn a reduced-order model from system data. The learned reduced-order model is employed within an optimization routine to update the feedback control throughout the online phase. Since the system data naturally reflects the uncertain parameter, the data-driven updating of the controller gains is achieved without an explicit parameter estimation step. We consider two numerical test problems in the form of partial differential equations: a convection-diffusion system, and a model for flow through a porous medium. We demonstrate on those models that the proposed method successfully stabilizes the system model in the presence of process noise.

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Section: 2mentioning

confidence: 99%

Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models

Krämer¹,

Peherstorfer²,

Willcox³

2017

SIAM J. Appl. Dyn. Syst.

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“…Next, based on the robust principal components obtained from historical data, we design a small subset of key spatial measurement locations that best inform the shim gap distribution of a new aircraft. Our procedure, called PIXel Identification Despite Uncertainty in Sensor Technology (PIXI-DUST), is based on recent advances in convex optimization for sensor placement (Brunton et al, 2016;Manohar et al, 2017a,b). We demonstrate the success of PIXI-DUST on historical production data from 54 Boeing aircraft, predicting 99% of the shim gaps within the desired measurement tolerance using approximately 3% of the available laser scan data.…”

Section: Introductionmentioning

confidence: 99%

Predicting shim gaps in aircraft assembly with machine learning and sparse sensing

Manohar

Hogan

Buttrick

et al. 2018

Journal of Manufacturing Systems

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A modern aircraft may require on the order of thousands of custom shims to fill gaps between structural components in the airframe that arise due to manufacturing tolerances adding up across large structures. These shims, whether liquid or solid, are necessary to eliminate gaps, maintain structural performance, and minimize pull-down forces required to bring the aircraft into engineering nominal configuration for peak aerodynamic efficiency. Currently, gap filling is a time-consuming process, involving either expensive by-hand inspection or computations on vast quantities of measurement data from increasingly sophisticated metrology equipment. In either case, this amounts to significant delays in production, with much of the time being spent in the critical path of the aircraft assembly.In this work, we present an alternative strategy for predictive shimming, based on machine learning and sparse sensing to first learn gap distributions from historical data, and then design optimized sparse sensing strategies to streamline the collection and processing of data. This new approach is based on the assumption that patterns exist in shim distributions across aircraft, and that these patterns may be mined and used to reduce the burden of data collection and processing in future aircraft. Specifically, robust principal component analysis is used to extract low-dimensional patterns in the gap measurements while rejecting outliers. Next, optimized sparse sensors are obtained that are most informative about the dimensions of a new aircraft in these low-dimensional principal components. We demonstrate the success of the proposed approach, called PIXel Identification Despite Uncertainty in Sensor Technology (PIXI-DUST), on historical production data from 54 representative Boeing commercial aircraft. Our algorithm successfully predicts 99% of the shim gaps within the desired measurement tolerance using around 3% of the laser scan points that are typically required; all results are rigorously cross-validated.

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“…Clusterbased reduced-order modeling (CROM) [3] was recently introduced to approximate the Perron-Frobenius operator in an unsupervised manner from high-dimensional data yielding a low-dimensional, linear model in probability space. The present work combines CROM with sparsity-promoting techniques, particularly the sparse sensor placement optimization for classification (SSPOC) architecture [4], as a critical enabler for real-time prediction and control. The sparsity enabled CROM identifies the probabilistic dynamics from few optimized measurements or compressed data facilitating its application for online prediction, estimation, and control and faster computations for high-dimensional systems.…”

Section: Introductionmentioning

confidence: 99%

Sparsity enabled cluster reduced-order models for control

Kaiser

Morzyński

Daviller

et al. 2018

Journal of Computational Physics

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International audienceCharacterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron–Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible

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Sparse Sensor Placement Optimization for Classification

Cited by 93 publications

References 59 publications

Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models

Feedback Control for Systems with Uncertain Parameters Using Online-Adaptive Reduced Models

Predicting shim gaps in aircraft assembly with machine learning and sparse sensing

Sparsity enabled cluster reduced-order models for control

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