Spectral likelihood expansions for Bayesian inference

Nagel, Joseph B.; Sudret, Bruno

doi:10.1016/j.jcp.2015.12.047

Cited by 36 publications

(32 citation statements)

References 104 publications

(119 reference statements)

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“…Model calibration is a cornerstone of engineering science provided with a mathematically sound framework rooted in Bayesian inference [6,7]. In principle, a forward model, some experimental observation, and a measure of their likelihood are used to infer some quantity of interest not directly observable (i.e., calibration parameters).…”

Section: R a F Tmentioning

confidence: 99%

Bayesian Experimental Design of Cyber-Physical Tests for Hydrodynamic Model Calibration

Abbiati¹,

Sauder²

2021

Preprint

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An application of cyber-physical testing to the empirical estimation of difference-frequency quadratic transfer functions is presented. As an alternative to today's procedure based on hydrodynamic tests with broad-banded or realistic (e.g., JONSWAP) wave spectra, tests in bichromatic waves are considered. The laboratory setup is the one developed by Sauder \& Tahchiev (2020) that enables magnifying the sensitivity of the floater response to the low-frequency wave loading by adjusting the stiffness and damping parameters of a virtual soft mooring system. Bayesian experimental design is proposed to optimize the selection of the control variables (frequencies in the bichromatic wave and properties of the virtual mooring system) for a batch of cyber-physical tests. The experimental design algorithm is based on the recent work of Huan \& Marzouk (2013). In a virtual yet realistic case study using an uncertain parametric quadratic transfer function, we demonstrate how the uncertainty of its describing parameters and other calibration parameters (low-frequency added mass and hydrodynamic damping) can be reduced. Results indicate that the proposed procedure has the potential for reducing experimental cost for calibration of hydrodynamic models.

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Section: R a F Tmentioning

confidence: 99%

Bayesian Experimental Design of Cyber-Physical Tests for Hydrodynamic Model Calibration

Abbiati¹,

Sauder²

2021

Preprint

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“…Several papers have leveraged these analyses to consider the impact of discretisation error in the forward problem on the inferences that are made for the inverse problem (Schwab and Stuart, 2012;Schwab, 2013, 2014;Nouy and Soize, 2014;Bui-Thanh and Ghattas, 2014;Schwab, 2015, 2016c,a;Nagel and Sudret, 2016). These analyses all focus on static inverse problems (i.e.…”

Section: Numerical Error and Its Analysismentioning

confidence: 99%

Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment

Oates

Cockayne

Aykroyd

et al. 2019

Journal of the American Statistical Association

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The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of state-estimation for the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods. In this paper, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimised implementation is provided in Python.

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“…It should be noted that calibration methods that do not rely on MCMC have been developed, in order to avoid the numerous difficulties associated with the implementation of MCMC algorithms. Other approaches for constructing surrogate models consist in using polynomial chaos expansions [1,2,3,4].…”

Section: Mathematically P Postmentioning

confidence: 99%

Statistical inverse identification for nonlinear train dynamics using a surrogate model in a Bayesian framework

Lebel

Soize

Funfschilling

et al. 2019

Journal of Sound and Vibration

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This paper presents a Bayesian calibration method for a simulation-based model with stochastic functional input and output. The originality of the method lies in an adaptation involving the representation of the likelihood function by a Gaussian process surrogate model, to cope with the high computational cost of the simulation, while avoiding the surrogate modeling of the functional output. The adaptation focuses on taking into account the uncertainty introduced by the use of a surrogate model when estimating the parameters posterior probability distribution by MCMC. To this end, trajectories of the random surrogate model of the likelihood function are drawn and injected in the MCMC algorithm. An application on a train suspension monitoring case is presented.

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Spectral likelihood expansions for Bayesian inference

Cited by 36 publications

References 104 publications

Bayesian Experimental Design of Cyber-Physical Tests for Hydrodynamic Model Calibration

Bayesian Experimental Design of Cyber-Physical Tests for Hydrodynamic Model Calibration

Bayesian Probabilistic Numerical Methods in Time-Dependent State Estimation for Industrial Hydrocyclone Equipment

Statistical inverse identification for nonlinear train dynamics using a surrogate model in a Bayesian framework

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