scholarly journals Analysis of the Stochastic Quarter-Five Spot Problem Using Polynomial Chaos

Molecules ◽  
2020 ◽  
Vol 25 (15) ◽  
pp. 3370
Author(s):  
Hesham AbdelFattah ◽  
Amnah Al-Johani ◽  
Mohamed El-Beltagy
Keyword(s):  
Porous Media ◽  
Correlation Function ◽  
Polynomial Chaos ◽  
Monte Carlo Sampling ◽  
Model Parameters ◽  
Chaos Expansion ◽  
Stochastic Problem ◽  
First Order ◽  
Stochastic Problems ◽  
Exponential Correlation Function

Analysis of fluids in porous media is of great importance in many applications. There are many mathematical models that can be used in the analysis. More realistic models should account for the stochastic variations of the model parameters due to the nature of the porous material and/or the properties of the fluid. In this paper, the standard porous media problem with random permeability is considered. Both the deterministic and stochastic problems are analyzed using the finite volume technique. The solution statistics of the stochastic problem are computed using both Polynomial Chaos Expansion (PCE) and the Karhunen-Loeve (KL) decomposition with an exponential correlation function. The results of both techniques are compared with the Monte Carlo sampling to verify the efficiency. Results have shown that PCE with first order polynomials provides higher accuracy for lower (less than 20%) permeability variance. For higher permeability variance, using higher-order PCE considerably improves the accuracy of the solution. The PCE is also combined with KL decomposition and faster convergence is achieved. The KL-PCE combination should carefully choose the number of KL decomposition terms based on the correlation length of the random permeability. The suggested techniques are successfully applied to the quarter-five spot problem.

scholarly journals An Updating Method for Structural Dynamics Models with Uncertainties

2008 ◽  
Vol 15 (3-4) ◽  
pp. 245-256 ◽  
Author(s):  
B. Faverjon ◽  
P. Ladevèze ◽  
F. Louf
Keyword(s):  
Structural Dynamics ◽  
Polynomial Chaos ◽  
Error Estimator ◽  
Chaos Expansion ◽  
Finite Element Analyses ◽  
Industrial Structures ◽  
Stochastic Problems ◽  
Constitutive Relation Error ◽  
Dynamics Models

One challenge in the numerical simulation of industrial structures is model validation based on experimental data. Among the indirect or parametric methods available, one is based on the “mechanical” concept of constitutive relation error estimator introduced in order to quantify the quality of finite element analyses. In the case of uncertain measurements obtained from a family of quasi-identical structures, parameters need to be modeled randomly. In this paper, we consider the case of a damped structure modeled with stochastic variables. Polynomial chaos expansion and reduced bases are used to solve the stochastic problems involved in the calculation of the error.

scholarly journals Drag Parameter Estimation Using Gradients and Hessian from a Polynomial Chaos Model Surrogate

2014 ◽  
Vol 142 (2) ◽  
pp. 933-941 ◽  
Author(s):  
Ihab Sraj ◽  
Mohamed Iskandarani ◽  
W. Carlisle Thacker ◽  
Ashwanth Srinivasan ◽  
Omar M. Knio
Keyword(s):  
Inverse Problem ◽  
Posterior Distribution ◽  
Polynomial Chaos ◽  
Monte Carlo Sampling ◽  
Chaos Expansion ◽  
Optimal Parameters ◽  
Computational Burden ◽  
Similarities And Differences ◽  
Polynomial Chaos Expansions ◽  
The Cost

Abstract A variational inverse problem is solved using polynomial chaos expansions to infer several critical variables in the Hybrid Coordinate Ocean Model’s (HYCOM’s) wind drag parameterization. This alternative to the Bayesian inference approach in Sraj et al. avoids the complications of constructing the full posterior with Markov chain Monte Carlo sampling. It focuses instead on identifying the center and spread of the posterior distribution. The present approach leverages the polynomial chaos series to estimate, at very little extra cost, the gradients and Hessian of the cost function during minimization. The Hessian’s inverse yields an estimate of the uncertainty in the solution when the latter’s probability density is approximately Gaussian. The main computational burden is an ensemble of realizations to build the polynomial chaos expansion; no adjoint code or additional forward model runs are needed once the series is available. The ensuing optimal parameters are compared to those obtained in Sraj et al. where the full posterior distribution was constructed. The similarities and differences between the new methodology and a traditional adjoint-based calculation are discussed.

scholarly journals Performance of non-intrusive uncertainty quantification in the aeroservoelastic simulation of wind turbines

2019 ◽  
Vol 4 (3) ◽  
pp. 397-406 ◽  
Author(s):  
Pietro Bortolotti ◽  
Helena Canet ◽  
Carlo L. Bottasso ◽  
Jaikumar Loganathan
Keyword(s):  
Monte Carlo ◽  
Wind Turbine ◽  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Solution Space ◽  
Monte Carlo Sampling ◽  
Polynomial Chaos Expansion ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Chaos Expansion

Abstract. The present paper characterizes the performance of non-intrusive uncertainty quantification methods for aeroservoelastic wind turbine analysis. Two different methods are considered, namely non-intrusive polynomial chaos expansion and Kriging. Aleatory uncertainties are associated with the wind inflow characteristics and the blade surface state, on account of soiling and/or erosion, and propagated throughout the aeroservoelastic model of a large conceptual offshore wind turbine. Results are compared with a brute-force extensive Monte Carlo sampling, which is used as benchmark. Both methods require at least 1 order of magnitude less simulations than Monte Carlo, with a slight advantage of Kriging over polynomial chaos expansion. The analysis of the solution space clearly indicates the effects of uncertainties and their couplings, and highlights some possible shortcomings of current mostly deterministic approaches based on safety factors.

scholarly journals Performance of non-intrusive uncertainty quantification in the aeroservoelastic simulation of wind turbines

2019 ◽  
Author(s):  
Pietro Bortolotti ◽  
Helena Canet ◽  
Carlo L. Bottasso ◽  
Jaikumar Loganathan
Keyword(s):  
Monte Carlo ◽  
Wind Turbine ◽  
Uncertainty Quantification ◽  
Surface State ◽  
Polynomial Chaos ◽  
Solution Space ◽  
Monte Carlo Sampling ◽  
Chaos Expansion ◽  
Brute Force ◽  
Blade Surface

Abstract. The paper studies the effects of uncertainties on aeroservoelastic wind turbine models. Two non-intrusive uncertainty quantification methods are considered, namely non-intrusive polynomial chaos expansion and Kriging. Uncertainties are associated with the wind inflow characteristics and the blade surface state, on account of soiling and/or erosion, and propagated throughout the aeroservoelastic model of a large conceptual off-shore wind turbine. Results are compared with a brute-force extensive Monte Carlo sampling. Both methods appear to yield similar results, with a somewhat faster convergence for Kriging. The analysis of the solution space clearly indicates the effects of uncertainties and their couplings, and highlights some possible shortcomings of current mostly deterministic approaches.

scholarly journals Measurement Uncertainty Propagation in Transistor Model Parameters via Polynomial Chaos Expansion

2017 ◽  
Vol 27 (6) ◽  
pp. 572-574 ◽  
Author(s):  
Alessandra Petrocchi ◽  
Arun Kaintura ◽  
Gustavo Avolio ◽  
Domenico Spina ◽  
Tom Dhaene ◽  
...  
Keyword(s):  
Measurement Uncertainty ◽  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Polynomial Chaos Expansion ◽  
Model Parameters ◽  
Chaos Expansion ◽  
Transistor Model
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