Comparing the adaptive Gaussian mixture filter with the ensemble Kalman filter on synthetic reservoir models

Stordal, Andreas S.; Valestrand, Randi; Karlsen, Hans Arnfinn; Nævdal, Gunnar; Skaug, Hans J.

doi:10.1007/s10596-011-9262-2

Cited by 15 publications

(6 citation statements)

References 20 publications

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“…Indeed, for the cases considered here, the number of intermediate tempering distributions (not reported) computed at each observation time, is invariant with respect to our choices of J. This is somewhat an expected outcome since our choice of J tresh in (45) is always a fraction of J. It is also worth mentioning that the effect of J is less noticeable when we look at the error with respect to the truth.…”

Section: Reducing the Cost Of Smc By Adjusting Tunable Parametersmentioning

confidence: 59%

“…It is clear that tempering can be understood as a regularization to the Bayesian inverse problem; the effect of α n,r is to flatten out the posterior and allow for a more controlled/regularized transition between the sequence of measures. Other works highlighting the connection between ensemble Kalman methods and SMC approaches include [43,44,39]. In addition, by noticing from (3.15) that, for each n = 1, .…”

Section: 2mentioning

confidence: 99%

“…The amount of tempering is controlled by the number of parameters obtained via (45). The greater the number of tempering parameters, the larger the α n,r 's which in turn indicates that more regularization is needed to ensure a stable transition between those measures.…”

Section: A Note On Temperingmentioning

confidence: 99%

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Bayesian inversion in resin transfer molding

2018

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We study the Bayesian inverse problem of inferring the permeability of a porous medium within the context of a moving boundary framework motivated by Resin Transfer Molding (RTM), one of the most commonly used processes for manufacturing fiber-reinforced composite materials. During the injection of resin in RTM, our aim is to update our probabilistic knowledge of the permeability of the material by inverting pressure measurements as well as observations of the resin moving domain. We consider both one-dimensional and two-dimensional forward models for RTM. Based on the analytical solution for the one-dimensional case, we prove existence of the sequence of posteriors that arise from a sequential Bayesian formulation within the infinite-dimensional framework. For the numerical characterisation of the Bayesian posteriors in the one-dimensional case, we investigate the application of a fully-Bayesian Sequential Monte Carlo method (SMC) for high-dimensional inverse problems. By means of SMC we construct a benchmark against which we compare performance of a novel regularizing ensemble Kalman algorithm (REnKA) that we propose to approximate the posteriors in a computationally efficient manner under practical scenarios. We investigate the robustness of the proposed REnKA with respect to tuneable parameters and computational cost. We demonstrate advantages of REnKA compared with SMC with a small number of particles. We further investigate, in both the one-dimensional and two-dimensional settings, practical aspects of REnKA relevant to RTM, which include the effect of pressure sensors configuration and the observational noise level in the uncertainty in the log-permeability quantified via the sequence of Bayesian posteriors.It has been extensively recognized [11,12,28,27,34,38] that imperfections in 73 during its fabrication and packing in the molding cavity can lead to variability in fib 74 results in a heterogenous highly-uncertain preform permeability. In turn, these unkn 75 in permeability of the preform give rise to inhomogeneous resin flow patterns which 76 detrimental e↵ect on the quality of the produced part, reducing its mechanical prope 77 leading to scrap. To limit these undesirable e↵ects arising due to uncertainties, 78 are used which lead to heavier, thicker and, consequently, more expensive material 79 performance being compromised. Clearly, the uncertainty quantification of material p 80 µ J n−1 (u) ≡ 1 J J j=1

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Section: Reducing the Cost Of Smc By Adjusting Tunable Parametersmentioning

confidence: 59%

Section: 2mentioning

confidence: 99%

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Bayesian inversion in resin transfer molding

2018

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“…The weights are then used to resample the ensemble to better represent non-Gaussian behavior. For more details, see [6], [14].…”

Section: Ensemble Based Methods For Data Assimilationmentioning

confidence: 99%

Data Assimilation Using Mri Data

Nævdal¹,

Sævareid²,

Lorentzen³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Contrast enhanced dynamic MRI data is important for classifying anomalies in tissue and blood circulation, e.g. tumors, stokes, kidney failure. The resulting sequence of images providing spatial-temporal representation of contrast agent concentration must be given meaningful clinical interpretation. Current processing typically relies on localized strategies, where the images are analyzed voxel by voxel. The consensus seems to be that taking direct advantage of the global structure of the images potentially will allow for more accurate and robust interpretations.Based on a workflow that has been extensively studied within both petroleum and ground water research, the current paper combines explicit porous media flow modelling and state of the art data assimilation. Starting from a multi-compartment global flow model, we explore MRI interpretation via synthetic cases where model generated images are used as input to a parameter identification algorithm based on ensemble based data assimilation like the ensemble Kalman filter (EnKF).From reasonable assumptions, the procedure demonstrates ability to identify relevant model parameters for two synthetic cases.This study indicates that flow based assimilation of MRI data is viable and that it might provide valuable supplementing insight compared to state of the art. Regularizations are made on a firm statistical basis, eliminating the need for ad hoc parameters, and leading to estimates that are rigorous in terms of error thresholds. A priori knowledge can easily be incorporated in the procedure. The flow model allows explicit representation of basic material properties, and adds regularization to the procedure by enforcing globally consistent flow fields.

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“…A performance comparison of the AGM with the EnKF is performed for reservoir models in [48]. The results show that the AGM estimates have higher correlation with the reference data compared to the EnKF.…”

Section: Enkf With Gaussian Mixture Modelsmentioning

confidence: 99%

Distributed ensemble Kalman filtering

Shahid

Üstebay

Coates

2014

2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM)

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Distributed estimation in a wireless sensor network has many advantages. It eliminates the need of the centralized knowledge of the measurement model parameters and does not have a single point of failure. Also, any sensor node can be queried to retrieve the state estimate. Furthermore, for high dimensional measurements, local processing of information also results in a significant reduction in the communication overhead.The existing distributed Kalman filtering schemes have good computational and communication efficiency, but do not work well for non-linear and non-Gaussian problems. On the other hand, the distributed particle filtering schemes handle the non-linearities well, but have a much higher computational and communication cost.In this thesis, we propose novel distributed filtering schemes based on the ensemble Kalman filter (EnKF). We consider three forms of the EnKF and express their update equations in an alternative information form. This allows us to use the randomized gossip algorithm to reach consensus on the sufficient statistics and perform local updates. The simulation results show that all three forms of the EnKF have a considerably lower computational cost compared to the particle filters. The results suggest that the proposed distributed schemes outperform the existing state-of-the-art distributed filtering schemes in two scenarios, a) linear measurement model with non-linear state dynamics, and b) high dimensional measurements (model parameters known everywhere in the network) with nonlinear measurement model and state dynamics. In both of these scenarios, the proposed schemes achieve an estimation accuracy comparable to the existing state-of-the-art schemes while significantly reducing the communication cost.ii Résumé L'estimation distribuée dans un réseau de capteurs sans fil possède plusieurs avantages. Ellé elimine le besoin d'une connaissance centralisée des paramtres du modèle de mesure et n'a pas un point de défaillance unique. Aussi, n'importe quel agent-capteur peut-être consulté pour obtenir une approximation de l'état général. De plus, pour des mesures de hautes dimensions, le calcul local d'informations résulte en une réduction significative des coûts de communication.Les implémentations courantes du filtre de Kalman sont efficaces sur les plans de la charge de calcul et de la communication mais ne le sont pas pour les problmes non-linéaires et non-gaussiens. D'un autre côté, les techniques distribuées de filtrage particulaire gèrent avec succès les cas non-linéaires mais sont coûteuses sur les plans de la charge de calcul et de la communication.Dans cette thèse, nous proposons des techniques de filtrage distribué basées sur le filtre de Kalman d'ensemble (FKEn). Nous considérons trois formes du FKEn et exprimons leurséquations de changement sous une forme alternative. Cela nous permet d'utiliser un algorithme de gossip aléatoire afin d'atteindre un consensus sur les statistiques suffisantes et calculer les changements locaux. Les résultats des simulations montrent que ...

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Comparing the adaptive Gaussian mixture filter with the ensemble Kalman filter on synthetic reservoir models

Cited by 15 publications

References 20 publications

Bayesian inversion in resin transfer molding

Bayesian inversion in resin transfer molding

Data Assimilation Using Mri Data

Distributed ensemble Kalman filtering

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