Bayesian system identification based on probability logic

We present an inversion strategy capable of using real‐time high‐rate GPS data to simultaneously solve for a distributed slip model and fault geometry in real time as a rupture unfolds. We employ Bayesian inference to find the optimal fault geometry and the distribution of possible slip models for that geometry using a simple analytical solution. By adopting an analytical Bayesian approach, we can solve this complex inversion problem (including calculating the uncertainties on our results) in real time. Furthermore, since the joint inversion for distributed slip and fault geometry can be computed in real time, the time required to obtain a source model of the earthquake does not depend on the computational cost. Instead, the time required is controlled by the duration of the rupture and the time required for information to propagate from the source to the receivers. We apply our modeling approach, called Bayesian Evidence‐based Fault Orientation and Real‐time Earthquake Slip, to the 2011 Tohoku‐oki earthquake, 2003 Tokachi‐oki earthquake, and a simulated Hayward fault earthquake. In all three cases, the inversion recovers the magnitude, spatial distribution of slip, and fault geometry in real time. Since our inversion relies on static offsets estimated from real‐time high‐rate GPS data, we also present performance tests of various approaches to estimating quasi‐static offsets in real time. We find that the raw high‐rate time series are the best data to use for determining the moment magnitude of the event, but slightly smoothing the raw time series helps stabilize the inversion for fault geometry.

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“…of maximum entropy [see, e.g., Jaynes, 2003;Beck, 2010]. Similarly, Gaussian priors are commonly used for regression variables.…”

mentioning

confidence: 99%

Real‐time inversions for finite fault slip models and rupture geometry based on high‐rate GPS data

et al. 2014

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“…The Bayesian method then allows a posterior probability distribution to be constructed from the optimal prior probability distribution and the experimental data. Many works have been published in the literature (see for instance textbooks on the Bayesian method such as [59,60,61,62] and papers devoted to the use of the Bayesian method in the context of uncertain mechanical and dynamical systems such as [12,128,129,130,131,132,133]. We will use such a Bayesian approach in Sections 4.6 and 6.…”

Section: Identification Of the Stochastic Model Of Random Variables Imentioning

confidence: 99%

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Soize

2013

Journal of Sound and Vibration

140

106

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To cite this version:Christian Soize. Stochastic modeling of uncertainties in computational structural dynamics -Recent theoretical advances. Journal of Sound and Vibration, Elsevier, 2013, 332 (10) AbstractThis paper deals with a short overview on stochastic modeling of uncertainties. We introduce the types of uncertainties, the variability of real systems, the types of probabilistic approaches, the representations for the stochastic models of uncertainties, the construction of the stochastic models using the maximum entropy principle, the propagation of uncertainties, the methods to solve the stochastic dynamical equations, the identification of the prior and the posterior stochastic models, the robust updating of the computational models and the robust design with uncertain computational models. We present recent theoretical advances in this field concerning the parametric and the nonparametric probabilistic approaches of uncertainties in computational structural dynamics for the construction of the prior stochastic models of both the uncertainties on the computational model parameters and on the modeling uncertainties, and for their identification with experimental data. We also present the construction of the posterior stochastic model of uncertainties using the Bayesian method when experimental data are available.

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“…where p(D i | θ, M i ) is the likelihood function, p( θ|M i ) is the prior PDF and p(D i |M i ) is the evidence (marginal likelihood) that will be used for model selection [4] if multiple models are available. Note that the evidence is a normalizing constant for the posterior PDF calculated by:…”

Section: Hierarchical Bayesian Framework For Heterogeneous Datamentioning

confidence: 99%

“…The evidence of M HB , p(D|M HB ), will be used to perform model selection. In the Bayesian framework, one can evaluate the posterior probabilities of different models to pick the optimal model or to perform predictions weighted by the probability values [4].…”

Section: Hierarchical Bayesian Framework For Heterogeneous Datamentioning

confidence: 99%

Hierarchical Bayesian Modeling for Molecular Dynamics Simulations Using Heterogeneous Data

Wu¹,

Angelikopoulos²,

Tauriello³

et al. 2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

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Abstract. Heterogeneous data are often used to calibrate the parameters of Molecular Dynamics (MD) simulations. The inference of the MD model parameters from such data may lead however to significant inconsistencies. We propose a hierarchical Bayesian framework to systematically integrate heterogeneous data in MD simulations and demonstrate our approach in simulations of liquid water. The MD parameters are calibrated with a set of experimental data for diffusivity, radial distribution function and density of water. Furthermore, we tackle the high computational demands associated with hierarchical Bayesian models by combining a surrogate model based on the Empirical Interpolation Method with a parallelized sampling-based estimation scheme. We discuss extensions of this approach to the calibration of MD simulations of other systems using heterogeneous experimental data.

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Bayesian system identification based on probability logic

Cited by 543 publications

References 29 publications

Real‐time inversions for finite fault slip models and rupture geometry based on high‐rate GPS data

Real‐time inversions for finite fault slip models and rupture geometry based on high‐rate GPS data

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

Hierarchical Bayesian Modeling for Molecular Dynamics Simulations Using Heterogeneous Data

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