Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls

Iglesias, Marco A.; Sawlan, Zaid A; Scavino, Marco; Tempone, Raúl; Wood, Christopher J.

doi:10.1088/1361-6420/aac224

Cited by 9 publications

(2 citation statements)

References 35 publications

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“…The UQLab Matlab toolbox [29] could be utilized to generalize Algorithm 2 to estimate temperature-dependent thermal parameters without assuming a specific functional form for them. In addition, our UQ framework could be extended to sequential filtering following the approach discussed in [30].…”

Section: Uncertainty Quantificationmentioning

confidence: 99%

Estimation of Temperature-Dependent Thermal Conductivity and Heat Capacity Given Boundary Data

Sharahy,

Sawlan

2023

Computation

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This work aims to estimate temperature-dependent thermal conductivity and heat capacity given measurements of temperature and heat flux at the boundaries. This estimation problem has many engineering and industrial applications, such as those for the building sector and chemical reactors. Two approaches are proposed to address this problem. The first method uses an integral approach and a polynomial approximation of the temperature profile. The second method uses a numerical solver for the nonlinear heat equation and an optimization algorithm. The performance of the two methods is compared using synthetic data generated with different boundary conditions and configurations. The results demonstrate that the integral approach works in limited scenarios, whereas the numerical approach is effective in estimating temperature-dependent thermal properties. The second method is also extended to account for noisy measurements and a comprehensive uncertainty quantification framework is developed.

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Section: Uncertainty Quantificationmentioning

confidence: 99%

Estimation of Temperature-Dependent Thermal Conductivity and Heat Capacity Given Boundary Data

Sharahy,

Sawlan

2023

Computation

Self Cite

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“…Compared to the adjoint-based variational methods or sampling-based Bayesian approaches, the salient advantages of IEnKM are that (i) it is derivative-free and code non-intrusive; (ii) it can provide reliable estimations with a small size ensemble (e.g., O(10) of ensemble members). Many successful applications of IEnKM have been witnessed in recent years for various inverse problems of computational mechanics, including field inversion in complex fluid flows [31][32][33][34], calibration of turbulence models [35][36][37][38], and state-parameter estimation in physiological systems [39][40][41], and others [42][43][44][45].…”

Section: Introductionmentioning

confidence: 99%

A Bi-fidelity Ensemble Kalman Method for PDE-Constrained Inverse Problems

Gao,

Wang

2020

Preprint

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Mathematical modeling and simulation of complex physical systems based on partial differential equations (PDEs) have been widely used in engineering and industrial applications.To enable reliable predictions, it is crucial yet challenging to calibrate the model by inferring unknown parameters/fields (e.g., boundary conditions, mechanical properties, and operating parameters) from sparse and noisy measurements, which is known as a PDE-constrained inverse problem. In this work, we develop a novel bi-fidelity (BF) ensemble Kalman inversion method to tackle this challenge, leveraging the accuracy of high-fidelity models and the efficiency of low-fidelity models. The core concept is to build a BF model with a limited number of high-fidelity samples for efficient forward propagations in the iterative ensemble Kalman inversion. Compared to existing inversion techniques, salient features of the proposed methods can be summarized as follow: (1) achieving the accuracy of high-fidelity models but at the cost of low-fidelity models, (2) being robust and derivative-free, and (3) being code nonintrusive, enabling ease of deployment for different applications. The proposed method has been assessed by three inverse problems that are relevant to fluid dynamics, including both parameter estimation and field inversion. The numerical results demonstrate the excellent performance of the proposed BF ensemble Kalman inversion approach, which drastically outperforms the standard Kalman inversion in terms of efficiency and accuracy.

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A Bi-fidelity ensemble kalman method for PDE-constrained inverse problems in computational mechanics

Gao

Wang

2021

Comput Mech

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Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls

Cited by 9 publications

References 35 publications

Estimation of Temperature-Dependent Thermal Conductivity and Heat Capacity Given Boundary Data

Estimation of Temperature-Dependent Thermal Conductivity and Heat Capacity Given Boundary Data

A Bi-fidelity Ensemble Kalman Method for PDE-Constrained Inverse Problems

A Bi-fidelity ensemble kalman method for PDE-constrained inverse problems in computational mechanics

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