Real-time Bayesian data assimilation with data selection, correction of model bias, and on-the-fly uncertainty propagation

Rubio, Paul-Baptiste; Chamoin, Ludovic; Louf, François

doi:10.1016/j.crme.2019.11.004

Cited by 11 publications

(11 citation statements)

References 18 publications

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“…For each realization we compute several performance metrics, which are averaged over all time steps t = 1, ..., T. We compute the state estimation error for each component, i = 1, 2, as given by the absolute difference between the digital twin estimate,Q i t , and the ground-truth value. We also compute the observation error, t , as given in (14). Finally, we report the accuracy of the UAV's decision making, given by the percentage of time steps in which the action taken by the UAV (informed by the state estimate), matches the optimal action (informed by the ground truth).…”

Section: Digital Twin Model Adaptation Resultsmentioning

confidence: 99%

“…), our inference procedure does not automatically correct for model bias. Future work could involve extending our approach in this direction (see for example [14,15,36]). Our methods have been demonstrated using a case study in which a fixed-wing UAV uses structural sensors to detect damage or degradation on one of its wings.…”

Section: Discussionmentioning

confidence: 99%

“…A limitation of our approach is that although we can detect model inadequacy or model bias (via the error measure defined in Section 3.3), our inference procedure does not automatically correct for model bias. Future work could involve extending our approach in this direction 14,15,36 . Our methods have been demonstrated using a case study in which a fixed‐wing UAV uses structural sensors to detect damage or degradation on one of its wings.…”

Section: Discussionmentioning

confidence: 99%

“…Motivated by the proliferation of low‐cost sensors and increasing connectivity between physical assets, we adopt a data‐driven approach in which sensor data gathered by an asset guide adaptation of the digital twin. We show how the prespecified model library allows us to frame the digital twin adaptation problem as a tractable, yet mathematically rigorous Bayesian state‐estimation problem 13,14 . This state‐estimation procedure combines observed sensor data with a state transition probability model (typically derived from historical data or computed via physics‐based simulations), to yield a probabilistic classification of the current state of an asset into the model library.…”

Section: Introductionmentioning

confidence: 99%

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Data‐driven physics‐based digital twins via a library of component‐based reduced‐order models

Kapteyn

Knezevic²,

Huynh³

et al. 2020

Numerical Meth Engineering

131

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This work proposes an approach that combines a library of component-based reduced-order models with Bayesian state estimation in order to create data-driven physics-based digital twins. Reduced-order modeling produces physics-based computational models that are reliable enough for predictive digital twins, while still being fast to evaluate. In contrast with traditional monolithic techniques for model reduction, the component-based approach scales efficiently to large complex systems, and provides a flexible and expressive framework for rapid model adaptation-both critical features in the digital twin context. Data-driven model adaptation and uncertainty quantification is formulated as a Bayesian state estimation problem, in which sensor data is used to infer which models in the model library are the best candidates for the digital twin. This approach is demonstrated through the development of a digital twin for a 12ft wingspan unmanned aerial vehicle. Offline, we construct a library of pristine and damaged aircraft components. Online, we use structural sensor data to rapidly adapt a physics-based digital twin of the aircraft structure. The data-driven digital twin enables the aircraft to dynamically replan a safe mission in response to structural damage or degradation.

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Section: Digital Twin Model Adaptation Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Data‐driven physics‐based digital twins via a library of component‐based reduced‐order models

Kapteyn

Knezevic²,

Huynh³

et al. 2020

Numerical Meth Engineering

131

View full text Add to dashboard Cite

show abstract

“…This representation is computed in an offline phase with controlled accuracy [8] before being evaluated at low cost in the online phase. It is shown in the paper that the PGD technique (i) facilitates the computation of the likelihood function involved in the Bayesian inference framework [3,26]; (ii) can be effectively coupled with Transport Map sampling for the calculation of the maps, as it directly provides information on solution derivatives [27,28]; (iii) is a particularly effective tool for performing uncertainty propagation through the forward model as well as command law synthesis. A particular focus is made here on the latter point dealing with effective command in a stochastic framework; this has been investigated in very few works of the literature, even though it is a major aspect of the DDDAS procedure.…”

Section: Introductionmentioning

confidence: 99%

Real-time data assimilation and control on mechanical systems under uncertainties

Rubio

Chamoin

Louf

2021

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

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This research work deals with the implementation of so-called Dynamic Data-Driven Application Systems (DDDAS) in structural mechanics activities. It aims at designing a real-time numerical feedback loop between a physical system of interest and its numerical simulator, so that (i) the simulation model is dynamically updated from sequential and in situ observations on the system; (ii) the system is appropriately driven and controlled in service using predictions given by the simulator. In order to build such a feedback loop and take various uncertainties into account, a suitable stochastic framework is considered for both data assimilation and control, with the propagation of these uncertainties from model updating up to command synthesis by using a specific and attractive sampling technique. Furthermore, reduced order modeling based on the Proper Generalized Decomposition (PGD) technique is used all along the process in order to reach the real-time constraint. This permits fast multi-query evaluations and predictions, by means of the parametrized physics-based model, in the online phase of the feedback loop. The control of a fusion welding process under various scenarios is considered to illustrate the proposed methodology and to assess the performance of the associated numerical architecture.

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Transport map Bayesian parameter estimation for dynamical systems

Grashorn,

Urrea-Quintero,

Broggi

et al. 2023

Proc Appl Math and Mech

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Accurate online state and parameter estimation of uncertain non-linear dynamical systems is a demanding task that has been traditionally handled by adopting non-linear Kalman Filters or particle filters. However, in case of Kalman filters the system needs to be linearised and for particle filters the computational demand can be high. Recent advances in optimal transport theory and the application to Bayesian model updating pave the way for other approaches to system and parameter identification. They also provide a way of formulating the problem in such a way that efficient online estimation for complex systems is possible. In this work, we investigate the properties of the transport map approach when compared to standard Markov Chain Monte Carlo in an off-line setting as a first step towards on-line parameter estimation. We apply both approaches to an analytical exponential model and a dynamical system with seven unknown parameters subjected to ground displacement. Details on the theory of transport maps and on the used MCMC algorithm are also given.

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Real-time Bayesian data assimilation with data selection, correction of model bias, and on-the-fly uncertainty propagation

Cited by 11 publications

References 18 publications

Data‐driven physics‐based digital twins via a library of component‐based reduced‐order models

Data‐driven physics‐based digital twins via a library of component‐based reduced‐order models

Real-time data assimilation and control on mechanical systems under uncertainties

Transport map Bayesian parameter estimation for dynamical systems

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