scholarly journals Bifurcation Analysis with Aerodynamic-Structure Uncertainties by the Nonintrusive PCE Method

2017 ◽  
Vol 2017 ◽  
pp. 1-17
Author(s):  
Linpeng Wang ◽  
Yuting Dai ◽  
Chao Yang
Keyword(s):  
Polynomial Chaos ◽  
Aerodynamic Force ◽  
Polynomial Chaos Expansion ◽  
Limit Cycle Oscillation ◽  
Structure Parameters ◽  
Chaos Expansion ◽  
Aeroelastic Model ◽  
Aerodynamic Parameters ◽  
Cycle Oscillation ◽  
The Time Domain

An aeroelastic model for airfoil with a third-order stiffness in both pitch and plunge degree of freedom (DOF) and the modified Leishman–Beddoes (LB) model were built and validated. The nonintrusive polynomial chaos expansion (PCE) based on tensor product is applied to quantify the uncertainty of aerodynamic and structure parameters on the aerodynamic force and aeroelastic behavior. The uncertain limit cycle oscillation (LCO) and bifurcation are simulated in the time domain with the stochastic PCE method. Bifurcation diagrams with uncertainties were quantified. The Monte Carlo simulation (MCS) is also applied for comparison. From the current work, it can be concluded that the nonintrusive polynomial chaos expansion can give an acceptable accuracy and have a much higher calculation efficiency than MCS. For aerodynamic model, uncertainties of aerodynamic parameters affect the aerodynamic force significantly at the stage from separation to stall at upstroke and at the stage from stall to reattach at return. For aeroelastic model, both uncertainties of aerodynamic parameters and structure parameters impact bifurcation position. Structure uncertainty of parameters is more sensitive for bifurcation. When the nonlinear stall flutter and bifurcation are concerned, more attention should be paid to the separation process of aerodynamics and parameters about pitch DOF in structure.

Analysis of Aeroelastic System Under Random Gust With Parametric Uncertainties Using Polynomial Chaos Expansion

2012 ◽  
Author(s):  
S. Venkatesh ◽  
Sunetra Sarkar ◽  
Ajit Desai
Keyword(s):  
Potential Flow ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Polynomial Chaos Expansion ◽  
The Body ◽  
Limit Cycle Oscillation ◽  
Chaos Expansion ◽  
Aeroelastic System ◽  
Flutter Speed ◽  
Wake Model

In the design of wind turbine structures, aeroelastic stability is of utmost importance. It becomes even more crucial when there are uncertainties involved in it. A symmetric airfoil with its pitch-plunge flexibility is considered under potential flow. The potential flow model is justified as the classical flutter model involves unseparated flow over the body so that inviscid assumptions are valid. In the present study of aeroelastic system, nonlinear parameters have been considered as it can stabilize the diverging growth of a flutter oscillation. Quantification of aleatoric uncertainties present in the system has been done by modeling them as a Gaussian parameters. The epistemic uncertainty present in the system has also been reduced by considering unsteady vortex lattice method (UVLM) instead of the rigid wake model of Wagner. In this model, the wake is free to evolve and also the shape of airfoil has been considered. The present study involves usage of UVLM code on a NACA 0012 airfoil. The values of the linear flutter speed predicted by using UVLM code is in close agreement with that of the fixed wake model of Lee et al. When the structural nonlinearities are present, the system exhibits a self sustained oscillation of constant amplitude called as Limit Cycle Oscillation (LCO) even beyond the linear flutter speed. In the present study, a horizontal gust is modeled with a given spectra by superposition of a set of sinusoidal components which is a standard practice. This gust has then been applied on the airfoil along with the structural uncertainties. A spectral uncertainty quantification tool called Polynomial Chaos Expansion is used to quantify the effect of uncertainty propagation and calculate the response statistics. A non-intrusive version of the method using stochastic projection approach is used to capture the time histories and plot the PDFs at various time instants of all the realizations with Monte Carlo Simulation as a reference solution. The evolution of PCE coefficients in the time domain along with its ensemble variations has also been looked into in the present study.

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.

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