A non‐Gaussian Bayesian filter for sequential data assimilation with non‐intrusive polynomial chaos expansion

2021 ◽  
Author(s):  
Srikanth Avasarala ◽  
Deepak Subramani
Keyword(s):  
Data Assimilation ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Sequential Data ◽  
Chaos Expansion ◽  
Bayesian Filter ◽  
Non Gaussian ◽  
Sequential Data Assimilation

Propagation of Modeling Uncertainty by Polynomial Chaos Expansion in Multidisciplinary Analysis

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
S. Dubreuil ◽  
N. Bartoli ◽  
C. Gogu ◽  
T. Lefebvre
Keyword(s):  
Polynomial Chaos ◽  
Computational Cost ◽  
Polynomial Chaos Expansion ◽  
Feedback Loops ◽  
Nonlinear Stochastic System ◽  
Chaos Expansion ◽  
Multidisciplinary Analysis ◽  
Modeling Uncertainties ◽  
Coupling Variables ◽  
Non Gaussian

Multidisciplinary analysis (MDA) is nowadays a powerful tool for analysis and optimization of complex systems. The present study is interested in the case where MDA involves feedback loops between disciplines (i.e., the output of a discipline is the input of another and vice versa). When the models for each discipline involve non-negligible modeling uncertainties, it is important to be able to efficiently propagate these uncertainties to the outputs of the MDA. The present study introduces a polynomial chaos expansion (PCE)-based approach to propagate modeling uncertainties in MDA. It is assumed that the response of each disciplinary solver is affected by an uncertainty modeled by a random field over the design and coupling variables space. A semi-intrusive PCE formulation of the problem is proposed to solve the corresponding nonlinear stochastic system. Application of the proposed method emphasizes an important particular case in which each disciplinary solver is replaced by a surrogate model (e.g., kriging). Three application problems are treated, which show that the proposed approach can approximate arbitrary (non-Gaussian) distributions very well at significantly reduced computational cost.

scholarly journals Generalized Polynomial Chaos Expansion for Fast and Accurate Uncertainty Quantification in Geomechanical Modelling

Algorithms ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 156
Author(s):  
Claudia Zoccarato ◽  
Laura Gazzola ◽  
Massimiliano Ferronato ◽  
Pietro Teatini
Keyword(s):  
Sensitivity Analysis ◽  
Data Assimilation ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Fe Model ◽  
Chaos Expansion ◽  
Generalized Polynomial Chaos ◽  
Hydrocarbon Reservoir ◽  
Generalized Polynomial ◽  
Major Interest

Geomechanical modelling of the processes associated to the exploitation of subsurface resources, such as land subsidence or triggered/induced seismicity, is a common practice of major interest. The prediction reliability depends on different sources of uncertainty, such as the parameterization of the constitutive model characterizing the deep rock behaviour. In this study, we focus on a Sobol’-based sensitivity analysis and uncertainty reduction via assimilation of land deformations. A synthetic test case application on a deep hydrocarbon reservoir is considered, where land settlements are predicted with the aid of a 3-D Finite Element (FE) model. Data assimilation is performed via the Ensemble Smoother (ES) technique and its variation in the form of Multiple Data Assimilation (ES-MDA). However, the ES convergence is guaranteed with a large number of Monte Carlo (MC) simulations, that may be computationally infeasible in large scale and complex systems. For this reason, a surrogate model based on the generalized Polynomial Chaos Expansion (gPCE) is proposed as an approximation of the forward problem. This approach allows to efficiently compute the Sobol’ indices for the sensitivity analysis and greatly reduce the computational cost of the original ES and MDA formulations, also enhancing the accuracy of the overall prediction process.

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