Dynamic Mode Decomposition and Robust Estimation: Case Study of a 2D Turbulent Boussinesq Flow

Vijayshankar, Sanjana; Nabi, Saleh; Chakrabarty, Ankush; Grover, Piyush; Benosman, Mouhacine

doi:10.23919/acc45564.2020.9147823

Cited by 8 publications

(6 citation statements)

References 18 publications

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“…For comparison purposes, the state estimation by using the Kalman Filter [21,22] is considered. The combination of DMDc models with Kalman Filters has recently been shown to yield quite convincing results [3,[17][18][19][20]. One big potential of the Kalman Filter relies on the fact that it provides a minimum estimation error covariance based on a priori statistics of the model and measurement uncertainties, which are considered as white noise processes with covariances Q ∈ R r 2 ×r 2 and r ∈ R in the present context, i.e.,…”

Section: Kalman Filtermentioning

confidence: 96%

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Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems

Schaum¹

2021

Algorithms

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The application of autoencoders in combination with Dynamic Mode Decomposition for control (DMDc) and reduced order observer design as well as Kalman Filter design is discussed for low order state reconstruction of a class of scalar linear diffusion-convection-reaction systems. The general idea and conceptual approaches are developed following recent results on machine-learning based identification of the Koopman operator using autoencoders and DMDc for finite-dimensional discrete-time system identification. The resulting linear reduced order model is combined with a classical Kalman Filter for state reconstruction with minimum error covariance as well as a reduced order observer with very low computational and memory demands. The performance of the two schemes is evaluated and compared in terms of the approximated L2 error norm in a numerical simulation study. It turns out, that for the evaluated case study the reduced-order scheme achieves comparable performance with significantly less computational load.

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Section: Kalman Filtermentioning

confidence: 96%

“…Early lumping based on the combination of DMDc with state estimation has already been shown in several application scenarios to yield satisfactory performance [3,[17][18][19][20]. In these studies the Kalman Filter [21,22] has been used on the basis of the obtained finite-dimensional linear discrete-time model equations.…”

Section: Introductionmentioning

confidence: 99%

Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems

Schaum¹

2021

Algorithms

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“…The characteristic mode associated with the transition to time-dependent flow is of special interest and has also been reported by Xin & Le Quéré (2006) wherein the modes are obtained from the linear stability analysis. From our direct numerical simulation results, extraction of the relevant modes is possible via modal decomposition techniques (Taira et al 2017;Ramos et al 2019;Vijayshankar et al 2020). The well-known dynamic mode decomposition (DMD) pioneered by Schmid (2010) is used here to gain insight into the characteristic modes of the flow.…”

Section: Time Dependency and Instability Modesmentioning

confidence: 99%

Natural convection in vertical enclosures with conjugate boundary conditions

2022

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A numerical investigation and reduced-order modelling of natural convection in a cavity with differentially heated sidewalls is discussed. The effect of conjugate boundary conditions on the cavity's heat transfer and natural flow circulation with varying aspect ratios and Rayleigh numbers is examined. Validation of the canonical differentially heated cavity reveals that a modification to the definition of the Rayleigh number (Ra) is required to reconcile the $Nu\sim Ra^{1/4}$ scaling (where Nu is the Nusselt number) and validity of previously proposed correlations for the heat transfer in vertical enclosures. Dynamic mode decomposition is used to uncover the underlying time-dependent flow structures and the results are compared with stability bifurcation studies in the literature. A flow mode previously associated with smaller aspect ratio cavities is identified as the unstable mode for a larger aspect ratio of 4. The effect of conjugate boundary conditions is scaled based on the ratio of the internal and external boundary layers, wherein higher external Reynolds numbers aid in the heat transfer as the Nusselt number approaches the isothermal limit. A reduced-order theoretical model is proposed to predict the Nusselt number for the conjugate boundary conditions. The performance of conjugate boundary conditions is connected to the flow stability, with the parallel-flow configuration acting in a destabilizing manner while the counterflow configuration has a stabilizing effect and results in the highest heat transfer. We also found that relatively large heat transfer can be achieved with substantially lower external actuation with intermediate aspect ratios, translating to less power in practice.

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“…Besides these classical Kalman Filter approaches, e.g., particle filters (PF) and Adaptative Extended Kalman filter (AEKF) have also been used to predict the SOC in data-driven models but considering only the experimental and measurable outputs obtained from physical set-ups, leaving aside the underlying electrochemical behaviour (see, e.g., [45][46][47]). The combination of DMDc with Kalman filtering techniques has also been discussed in several studies (see, e.g., [48][49][50][51][52][53]), given that both are very systematic and easily implementable methods providing a high degree of precission and efficiency.…”

Section: Introductionmentioning

confidence: 99%

Low-Order Electrochemical State Estimation for Li-Ion Batteries

Moreno

Schaum

2023

Algorithms

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Batteries are complex systems involving spatially distributed microscopic mechanisms on different time scales whose adequate interplay is essential to ensure a desired functioning. Describing these phenomena yields nonlinearly coupled partial differential equations whose numerical solution requires considerable effort and computation time, making it an infeasible solution for real-time applications. Anyway, having information about the internal electrochemical states of the battery can pave the way for many different advanced monitoring and control strategies with a big potential for improving efficiency and longevity. For such purposes, in the present paper, a combination of a low-order representation of the essential dynamics associated to the internal electrochemical mechanisms based on Dynamic Mode Decomposition for control (DMDc) is proposed to obtain an improved equivalent circuit model (ECM) representation with continuously updated parameters and combined with an extended Kalman Filter (EKF). The model-order reduction step extensively exploits the model structure, yielding a well structured low-order representation without artificial numerical correlations. The performance of the proposed method is illustrated with numerical simulations based on a well-established reference model, showing its potential usefulness in real-time applications requiring knowledge of the internal electrochemical states besides the state-of-charge.

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Dynamic Mode Decomposition and Robust Estimation: Case Study of a 2D Turbulent Boussinesq Flow

Cited by 8 publications

References 18 publications

Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems

Autoencoder-Based Reduced Order Observer Design for a Class of Diffusion-Convection-Reaction Systems

Natural convection in vertical enclosures with conjugate boundary conditions

Low-Order Electrochemical State Estimation for Li-Ion Batteries

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