A Sparse Data-Driven Polynomial Chaos Expansion Method for Uncertainty Propagation

2016 ◽  
Author(s):  
F. Wang ◽  
F. Xiong ◽  
S. Yang ◽  
Y. Xiong
Keyword(s):  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Expansion Method ◽  
Polynomial Chaos Expansion ◽  
Data Driven ◽  
High Dimensional ◽  
Chaos Expansion ◽  
Least Angle Regression ◽  
Structure Problem

The data-driven polynomial chaos expansion (DD-PCE) method is claimed to be a more general approach of uncertainty propagation (UP). However, as a common problem of all the full PCE approaches, the size of polynomial terms in the full DD-PCE model is significantly increased with the dimension of random inputs and the order of PCE model, which would greatly increase the computational cost especially for high-dimensional and highly non-linear problems. Therefore, a sparse DD-PCE is developed by employing the least angle regression technique and a stepwise regression strategy to adaptively remove some insignificant terms. Through comparative studies between sparse DD-PCE and the full DD-PCE on three mathematical examples with random input of raw data, common and nontrivial distributions, and a ten-bar structure problem for UP, it is observed that generally both methods yield comparably accurate results, while the computational cost is significantly reduced by sDD-PCE especially for high-dimensional problems, which demonstrates the effectiveness and advantage of the proposed method.

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 Identification of Fractional Damping Parameters in Structural Dynamics Using Polynomial Chaos Expansion

2021 ◽  
Vol 2 (4) ◽  
pp. 956-975
Author(s):  
Marcel S. Prem ◽  
Michael Klanner ◽  
Katrin Ellermann
Keyword(s):  
Polynomial Chaos ◽  
Constitutive Relations ◽  
Computational Cost ◽  
Material Model ◽  
Polynomial Chaos Expansion ◽  
Computational Technique ◽  
Chaos Expansion ◽  
Material Damping ◽  
Fractional Damping ◽  
Assembly Technique

In order to analyze the dynamics of a structural problem accurately, a precise model of the structure, including an appropriate material description, is required. An important step within the modeling process is the correct determination of the model input parameters, e.g., loading conditions or material parameters. An accurate description of the damping characteristics is a complicated task, since many different effects have to be considered. An efficient approach to model the material damping is the introduction of fractional derivatives in the constitutive relations of the material, since only a small number of parameters is required to represent the real damping behavior. In this paper, a novel method to determine the damping parameters of viscoelastic materials described by the so-called fractional Zener material model is proposed. The damping parameters are estimated by matching the Frequency Response Functions (FRF) of a virtual model, describing a beam-like structure, with experimental vibration data. Since this process is generally time-consuming, a surrogate modeling technique, named Polynomial Chaos Expansion (PCE), is combined with a semi-analytical computational technique, called the Numerical Assembly Technique (NAT), to reduce the computational cost. The presented approach is applied to an artificial material with well defined parameters to show the accuracy and efficiency of the method. Additionally, vibration measurements are used to estimate the damping parameters of an aluminium rotor with low material damping, which can also be described by the fractional damping model.

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