Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems: A New Approach Using Secants

Otto, Samuel E.; Rowley, Clarence W.

doi:10.1007/s00332-022-09806-9

Cited by 7 publications

(3 citation statements)

References 60 publications

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“…When dealing with nonlinear systems, standard techniques for feature selection and sensor placement that rely on linearity assumptions or simple statistical models can result in costly oversensing without guaranteeing the recovery of desired information from the measurements. To this end, Otto et al [ 38 ] discuss the importance of sensor placement and feature selection in solving inverse problems in nonlinear systems and highlight the limitations of existing techniques that rely on linearity or simple statistical models. To overcome these limitations, the authors propose a novel data-driven approach based on secant vectors between data points for a general type of nonlinear inverse problem.…”

Section: Placementmentioning

confidence: 99%

Understanding the Role of Sensor Optimisation in Complex Systems

Suslu,

Ali,

Jennions

2023

Sensors

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Complex systems involve monitoring, assessing, and predicting the health of various systems within an integrated vehicle health management (IVHM) system or a larger system. Health management applications rely on sensors that generate useful information about the health condition of the assets; thus, optimising the sensor network quality while considering specific constraints is the first step in assessing the condition of assets. The optimisation problem in sensor networks involves considering trade-offs between different performance metrics. This review paper provides a comprehensive guideline for practitioners in the field of sensor optimisation for complex systems. It introduces versatile multi-perspective cost functions for different aspects of sensor optimisation, including selection, placement, data processing and operation. A taxonomy and concept map of the field are defined as valuable navigation tools in this vast field. Optimisation techniques and quantification approaches of the cost functions are discussed, emphasising their adaptability to tailor to specific application requirements. As a pioneering contribution, all the relevant literature is gathered and classified here to further improve the understanding of optimal sensor networks from an information-gain perspective.

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Section: Placementmentioning

confidence: 99%

Understanding the Role of Sensor Optimisation in Complex Systems

Suslu,

Ali,

Jennions

2023

Sensors

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“…There are many ways in the literature to select the locations of the sensors: optimal sensor locations that improve the condition number of C [45,69], which are robust to sensor noise, the sample maximal variance positions [70], or using information contained in secant vectors between data points [71], for example. In this work, we are going to use the sparse sensor placement optimization for reconstruction described in details in [69] and implemented in PySensors [72].…”

Section: Gappy Pod For Sensors Datamentioning

confidence: 99%

A DeepONet multi-fidelity approach for residual learning in reduced order modeling

Demo

Tezzele

Rozza

2023

Adv. Model. and Simul. in Eng. Sci.

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In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the original model. The error introduced by the such operation is usually neglected and sacrificed in order to reach a fast computation. We propose to couple the model reduction to a machine learning residual learning, such that the above-mentioned error can be learned by a neural network and inferred for new predictions. We emphasize that the framework maximizes the exploitation of high-fidelity information, using it for building the reduced order model and for learning the residual. In this work, we explore the integration of proper orthogonal decomposition (POD), and gappy POD for sensors data, with the recent DeepONet architecture. Numerical investigations for a parametric benchmark function and a nonlinear parametric Navier-Stokes problem are presented.

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“…2014). Recently Otto & Rowley (2022) discussed the limitation of the linear methods in the case of selection and placement of sensors in a flow field.…”

Section: Introductionmentioning

confidence: 99%

From snapshots to manifolds – a tale of shear flows

et al. 2023

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We propose a novel nonlinear manifold learning from snapshot data and demonstrate its superiority over proper orthogonal decomposition (POD) for shedding-dominated shear flows. Key enablers are isometric feature mapping, Isomap, as encoder and, $K$ -nearest neighbours ( $K$ NN) algorithm as decoder. The proposed technique is applied to numerical and experimental datasets including the fluidic pinball, a swirling jet and the wake behind a couple of tandem cylinders. Analysing the fluidic pinball, the manifold is able to describe the pitchfork bifurcation and the chaotic regime with only three feature coordinates. These coordinates are linked to the vortex-shedding phases and the force coefficients. The manifold coordinates of the swirling jet are comparable to the POD mode amplitudes, yet allow for a more distinct and less noise-sensitive manifold identification. A similar observation is made for the wake of two tandem cylinders. The tandem cylinders are aligned and located at a streamwise distance which corresponds to the transition between the single bluff body and the reattachment regimes of vortex shedding. Isomap unveils these two shedding regimes while the Lissajous plot of the first two POD mode amplitudes features a single circle. The reconstruction error of the manifold model is small compared with the fluctuation level, indicating that the low embedding dimensions contain the coherent structure dynamics. The proposed Isomap– $K$ NN manifold learner is expected to be of great importance in estimation, dynamic modelling and control for a large range of configurations with dominant coherent structures.

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Inadequacy of Linear Methods for Minimal Sensor Placement and Feature Selection in Nonlinear Systems: A New Approach Using Secants

Cited by 7 publications

References 60 publications

Understanding the Role of Sensor Optimisation in Complex Systems

Understanding the Role of Sensor Optimisation in Complex Systems

A DeepONet multi-fidelity approach for residual learning in reduced order modeling

From snapshots to manifolds – a tale of shear flows

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