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 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.

Quantification of the Impact of Uncertainties in Operating Conditions on the Flame Transfer Function With Nonintrusive Polynomial Chaos Expansion

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Alexander Avdonin ◽  
Wolfgang Polifke
Keyword(s):  
Transfer Function ◽  
Equivalence Ratio ◽  
Polynomial Chaos ◽  
Finite Impulse Response ◽  
Laminar Flame ◽  
Operating Parameter ◽  
Polynomial Chaos Expansion ◽  
Operating Conditions ◽  
Chaos Expansion ◽  
The Impact

Nonintrusive polynomial chaos expansion (NIPCE) is used to quantify the impact of uncertainties in operating conditions on the flame transfer function (FTF) of a premixed laminar flame. NIPCE requires only a small number of system evaluations, so it can be applied in cases where a Monte Carlo simulation is unfeasible. We consider three uncertain operating parameters: inlet velocity, burner plate temperature, and equivalence ratio. The FTF is identified in terms of the finite impulse response (FIR) from computational fluid dynamics (CFD) simulations with broadband velocity excitation. NIPCE yields uncertainties in the FTF due to the uncertain operating conditions. For the chosen uncertain operating bounds, a second-order expansion is found to be sufficient to represent the resulting uncertainties in the FTF with good accuracy. The effect of each operating parameter on the FTF is studied using Sobol indices, i.e., a variance-based measure of sensitivity, which are computed from the NIPCE. It is observed that in the present case, uncertainties in the FIR as well as in the phase of the FTF are dominated by the equivalence-ratio uncertainty. For frequencies below 150 Hz, the uncertainty in the gain of the FTF is also attributable to the uncertainty in equivalence-ratio, but for higher frequencies, the uncertainties in velocity and temperature dominate. At last, we adopt the polynomial approximation of the output quantity, provided by the NIPCE method, for further uncertainty quantification (UQ) studies with modified input uncertainties.

scholarly journals Optimized Sparse Polynomial Chaos Expansion With Entropy Regularization

2021 ◽  
Author(s):  
SiJie Zeng ◽  
XiaoJun Duan ◽  
JiangTao Chen ◽  
Liang Yan
Keyword(s):  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Entropy Change ◽  
Optimization Method ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Sparse Polynomial ◽  
Output Uncertainty ◽  
Sparse Polynomial Chaos Expansion ◽  
Fitting In

Abstract Sparse Polynomial Chaos Expansion(PCE) is widely used in various engineering fields to quantitatively analyse the influence of uncertainty, while alleviate the problem of dimensionality curse. However, current sparse PCE techniques focus on choosing features with the largest coefficients, which may ignore uncertainties propagated with high order features. Hence, this paper proposes the idea of selecting polynomial chaos basis based on information entropy, which aims to retain the advantages of existing sparse techniques while considering entropy change as output uncertainty. A novel entropy-based optimization method is proposed to update the state-of-the-art sparse PCE models. This work further develops an entropy-based synthetic sparse model, which has higher computational efficiency. Two benchmark functions and a CFD experiment are used to compare the accuracy and efficiency between the proposed method and classical methods. The results show that entropy-based methods can better capture the features of uncertainty propagation, and the problem of over-fitting in existing sparse PCE methods can be avoided.

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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