Polynomial-Chaos-Expansion Based Integrated Dynamic Modelling Workflow for Computationally Efficient Reservoir Characterization: A Field Case Study

2017 ◽  
Author(s):  
Rajan G. Patel ◽  
Tarang Jain ◽  
Japan J. Trivedi
Keyword(s):  
Reservoir Characterization ◽  
Polynomial Chaos ◽  
Dynamic Modelling ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Computationally Efficient ◽  
Field Case

scholarly journals Modified Dimension Reduction-Based Polynomial Chaos Expansion for Nonstandard Uncertainty Propagation and Its Application in Reliability Analysis

Processes ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1856
Author(s):  
Jeongeun Son ◽  
Yuncheng Du
Keyword(s):  
Dimension Reduction ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Computationally Efficient ◽  
Standard Distribution

This paper presents an algorithm for efficient uncertainty quantification (UQ) in the presence of many uncertainties that follow a nonstandard distribution (e.g., lognormal). Using the polynomial chaos expansion (PCE), the algorithm builds surrogate models of uncertainty as functions of a standard distribution (e.g., Gaussian variables). The key to build these surrogate models is to calculate PCE coefficients of model outputs, which is computationally challenging, especially when dealing with models defined by complex functions (e.g., nonpolynomial terms) under many uncertainties. To address this issue, an algorithm that integrates the PCE with the generalized dimension reduction method (gDRM) is utilized to convert the high-dimensional integrals, required to calculate the PCE coefficients of model predictions, into several lower-dimensional ones that can be rapidly solved with quadrature rules. The accuracy of the algorithm is validated with four examples in structural reliability analysis and compared to other existing techniques, such as Monte Carlo simulations and the least angle regression-based PCE. Our results show our algorithm provides accurate UQ results and is computationally efficient when dealing with many uncertainties, thus laying the foundation to address UQ in complex control systems.

scholarly journals Advanced computational technique based on kriging and Polynomial Chaos Expansion for structural stability of mechanical systems with uncertainties

2021 ◽  
Vol 130 (1) ◽  
Author(s):  
E. Denimal ◽  
J.-J. Sinou
Keyword(s):  
Material Properties ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Computational Time ◽  
Computational Technique ◽  
Chaos Expansion ◽  
Computationally Efficient ◽  
Buckling Loads ◽  
Compression Load ◽  
Rigid Supports

AbstractIn this paper, a numerical strategy based on the combination of the kriging approach and the Polynomial Chaos Expansion (PCE) is proposed for the prediction of buckling loads due to random geometric imperfections and fluctuations in material properties of a mechanical system. The original computational approach is applied on a beam simply supported at both ends by rigid supports and by one punctual spring whose location and stiffness vary. The beam is subjected to a deterministic axial compression load. The PCE-kriging meta-modelling approach is employed to efficiently perform a parametric analysis with random geometrical and material properties. The approach proved to be computationally efficient in terms of number of model evaluations and in terms of computational time to predict accurately the buckling loads of a beam system. It is demonstrated that the buckling loads are substantially impacted not only by both the location and the stiffness of the spring, but also by the random parameters.

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