scholarly journals Probabilistic surrogate models for uncertainty analysis: Dimension reduction‐based polynomial chaos expansion

2019 ◽  
Vol 121 (6) ◽  
pp. 1198-1217 ◽  
Author(s):  
Jeongeun Son ◽  
Yuncheng Du
Keyword(s):  
Uncertainty Analysis ◽  
Dimension Reduction ◽  
Polynomial Chaos ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion

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 Deep Neural Network and Polynomial Chaos Expansion-Based Surrogate Models for Sensitivity and Uncertainty Propagation: An Application to a Rockfill Dam

Water ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 1830
Author(s):  
Gullnaz Shahzadi ◽  
Azzeddine Soulaïmani
Keyword(s):  
Polynomial Chaos ◽  
Complex Structure ◽  
Uncertainty Propagation ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
Soil Parameters ◽  
Chaos Expansion ◽  
Rockfill Dam ◽  
Parametric Studies ◽  
The Impact

Computational modeling plays a significant role in the design of rockfill dams. Various constitutive soil parameters are used to design such models, which often involve high uncertainties due to the complex structure of rockfill dams comprising various zones of different soil parameters. This study performs an uncertainty analysis and a global sensitivity analysis to assess the effect of constitutive soil parameters on the behavior of a rockfill dam. A Finite Element code (Plaxis) is utilized for the structure analysis. A database of the computed displacements at inclinometers installed in the dam is generated and compared to in situ measurements. Surrogate models are significant tools for approximating the relationship between input soil parameters and displacements and thereby reducing the computational costs of parametric studies. Polynomial chaos expansion and deep neural networks are used to build surrogate models to compute the Sobol indices required to identify the impact of soil parameters on dam behavior.

scholarly journals From wind to loads: wind turbine site-specific load estimation with surrogate models trained on high-fidelity load databases

2018 ◽  
Vol 3 (2) ◽  
pp. 767-790 ◽  
Author(s):  
Nikolay Dimitrov ◽  
Mark C. Kelly ◽  
Andrea Vignaroli ◽  
Jacob Berg
Keyword(s):  
Wind Turbine ◽  
Nearest Neighbor ◽  
Polynomial Chaos ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
High Fidelity ◽  
Chaos Expansion ◽  
Site Specific ◽  
Sensitivity Indices ◽  
Fatigue Loads

Abstract. We define and demonstrate a procedure for quick assessment of site-specific lifetime fatigue loads using simplified load mapping functions (surrogate models), trained by means of a database with high-fidelity load simulations. The performance of five surrogate models is assessed by comparing site-specific lifetime fatigue load predictions at 10 sites using an aeroelastic model of the DTU 10 MW reference wind turbine. The surrogate methods are polynomial chaos expansion, quadratic response surface, universal Kriging, importance sampling, and nearest-neighbor interpolation. Practical bounds for the database and calibration are defined via nine environmental variables, and their relative effects on the fatigue loads are evaluated by means of Sobol sensitivity indices. Of the surrogate-model methods, polynomial chaos expansion provides an accurate and robust performance in prediction of the different site-specific loads. Although the Kriging approach showed slightly better accuracy, it also demanded more computational resources.

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