Koopman mode analysis on thermal data for building energy assessment

Boskic, Ljuboslav; Brown, Cory N.; Mezić, Igor

doi:10.1080/17512549.2020.1842802

Cited by 10 publications

(6 citation statements)

References 22 publications

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“…In [47] HDMDc was also applied for modeling intersection queue length dynamics. Another interesting application of DMD in random dynamical system identification is demonstrated in [8] where it was applied in infrastructure energy assessment. In this work, the authors used HDMD to extract insights into the thermal dynamics of an airport.…”

Section: Application Of Dmdc In System Identificationmentioning

confidence: 99%

A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility

Mustavee

Agarwal

Enyioha

et al. 2021

Preprint

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This paper investigates the impact of human activity and mobility (HAM) in the spreading dynamics of an epidemic. Specifically, it explores the interconnections between HAM and its effect on the early spread of the COVID-19 virus. During the early stages of the pandemic, effective reproduction numbers exhibited a high correlation with human mobility patterns, leading to a hypothesis that the HAM system can be studied as a coupled system with disease spread dynamics. This study applies the generalized Koopman framework with control inputs to determine the nonlinear disease spread dynamics and the input-output characteristics as a locally linear controlled dynamical system. The approach solely relies on the snapshots of spatiotemporal data and does not require any knowledge of the system’s physical laws. We exploit the Koopman operator framework by utilizing the Hankel Dynamic Mode Decomposition with Control (HDMDc) algorithm to obtain a linear disease spread model incorporating human mobility as a control input. The study demonstrated that the proposed methodology could capture the impact of local mobility on the early dynamics of the ongoing global pandemic. The obtained locally linear model can accurately forecast the number of new infections for various prediction windows ranging from two to four weeks. The study corroborates a leader-follower relationship between mobility and disease spread dynam-

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Section: Application Of Dmdc In System Identificationmentioning

confidence: 99%

A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility

Mustavee

Agarwal

Enyioha

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…Furthermore, they made predictions on traffic queue length and applied Koopman spectral analysis to determine queue length instability. Another interesting application of DMD in random dynamical system identification is demonstrated in [35] where it was applied in infrastructure energy assessment. In this work, the authors used HDMD to extract insights into the thermal dynamics of an airport.…”

Section: Application Of Dmdc In System Identificationmentioning

confidence: 99%

A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility

Mustavee¹,

Agarwal²,

Enyioha³

et al. 2021

Preprint

View full text Add to dashboard Cite

This paper investigates the impact of human activity and mobility (HAM) in the spreading dynamics of an epidemic. Specifically, it explores the interconnections between HAM and its effect on the early spread of the COVID-19 virus. During the early stages of the pandemic, effective reproduction numbers exhibited a high correlation with human mobility patterns, leading to a hypothesis that the HAM system can be studied as a coupled system with disease spread dynamics. This study applies the generalized Koopman framework with control inputs to determine the nonlinear disease spread dynamics and the inputoutput characteristics as a locally linear controlled dynamical system. The approach solely relies on the snapshots of spatiotemporal data and does not require any knowledge of the system's physical laws. We exploit the Koopman operator framework by utilizing the Hankel Dynamic Mode Decomposition with Control (HDMDc) algorithm to obtain a linear disease spread model incorporating human mobility as a control input. The study demonstrated that the proposed methodology could capture the impact of local mobility on the early dynamics of the ongoing global pandemic. The obtained locally linear model can accurately forecast the number of new infections for various prediction windows ranging from two to four weeks. The study corroborates a leader-follower relationship between mobility and disease spread dynamics. In addition, the effect of delay embedding in the HDMDc algorithm is also investigated and reported. A case study was performed using COVID infection data from Florida, US, and HAM data extracted from Google community mobility data report.

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“…To capture more information on ψh (x k ), we need to construct the time-delay embedded outputs as the lifting functions [111][112][113]. This is a typical approach used to construct KORs when outputs partially measure the states [90,94,[111][112][113][114]. In the case of pure output measurements, the time-delay embedded outputs capture the maximum dynamics that is observed by the outputs.…”

Section: Proof Case (1)mentioning

confidence: 99%

The Effect of Sensor Fusion on Data-Driven Learning of Koopman Operators

Balakrishnan,

Hasnain,

Egbert

et al. 2021

Preprint

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Dictionary methods for system identification typically rely on one set of measurements to learn governing dynamics of a system. In this paper, we investigate how fusion of output measurements with state measurements affects the dictionary selection process in Koopman operator learning problems. While prior methods use dynamical conjugacy to show a direct link between Koopman eigenfunctions in two distinct data spaces (measurement channels), we explore the specific case where output measurements are nonlinear, non-invertible functions of the system state. This setup reflects the measurement constraints of many classes of physical systems, e.g., biological measurement data, where one type of measurement does not directly transform to another. We propose output constrained Koopman operators (OC-KOs) as a new framework to fuse two measurement sets. We show that OC-KOs are effective for sensor fusion by proving that when learning a Koopman operator, output measurement functions serve to constrain the space of potential Koopman observables and their eigenfunctions. Further, low-dimensional output measurements can be embedded to inform selection of Koopman dictionary functions for high-dimensional models. We propose two algorithms to identify OC-KO representations directly from data: a direct optimization method that uses state and output data simultaneously and a sequential optimization method. We prove a theorem to show that the solution spaces of the two optimization problems are equivalent. We illustrate these findings with a theoretical example and two numerical simulations.

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Koopman mode analysis on thermal data for building energy assessment

Cited by 10 publications

References 22 publications

A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility

A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility

A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility

The Effect of Sensor Fusion on Data-Driven Learning of Koopman Operators

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