Quantification of Forecast Uncertainty and Data Assimilation Using Wiener’s Polynomial Chaos Expansion

2016 ◽  
pp. 141-176
Author(s):  
Junjun Hu ◽  
S. Lakshmivarahan ◽  
John M. Lewis
Keyword(s):  
Data Assimilation ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Forecast Uncertainty

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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