scholarly journals Analysis of a Nonlinear Aeroelastic System with Parametric Uncertainties Using Polynomial Chaos Expansion

2011 ◽  
pp. 697-716
Author(s):  
A Desai ◽  
S Sarkar
Keyword(s):  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Parametric Uncertainties ◽  
Chaos Expansion ◽  
Aeroelastic System

scholarly journals Analysis of a Nonlinear Aeroelastic System with Parametric Uncertainties Using Polynomial Chaos Expansion

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Ajit Desai ◽  
Sunetra Sarkar
Keyword(s):  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Stochastic Bifurcation ◽  
Parametric Uncertainties ◽  
Chaos Expansion ◽  
Aeroelastic Stability ◽  
Aeroelastic System ◽  
Important Concern ◽  
Stochastic Framework ◽  
Flutter Boundary

Aeroelastic stability remains an important concern for the design of modern structures such as wind turbine rotors, more so with the use of increasingly flexible blades. A nonlinear aeroelastic system has been considered in the present study with parametric uncertainties. Uncertainties can occur due to any inherent randomness in the system or modeling limitations, and so forth. Uncertainties can play a significant role in the aeroelastic stability predictions in a nonlinear system. The analysis has been put in a stochastic framework, and the propagation of system uncertainties has been quantified in the aeroelastic response. A spectral uncertainty quantification tool called Polynomial Chaos Expansion has been used. A projection-based nonintrusive Polynomial Chaos approach is shown to be much faster than its classical Galerkin method based counterpart. Traditional Monte Carlo Simulation is used as a reference solution. Effect of system randomness on the bifurcation behavior and the flutter boundary has been presented. Stochastic bifurcation results and bifurcation of probability density functions are also discussed.

scholarly journals An Efficient Polynomial Chaos Expansion Method for Uncertainty Quantification in Dynamic Systems

2021 ◽  
Vol 2 (3) ◽  
pp. 460-481
Author(s):  
Jeongeun Son ◽  
Yuncheng Du
Keyword(s):  
Uncertainty Quantification ◽  
Chemical Engineering ◽  
Polynomial Chaos ◽  
Expansion Method ◽  
Polynomial Chaos Expansion ◽  
Parametric Uncertainties ◽  
Chaos Expansion ◽  
Generalized Dimension ◽  
Model Predictions ◽  
Engineering Problems

Uncertainty is a common feature in first-principles models that are widely used in various engineering problems. Uncertainty quantification (UQ) has become an essential procedure to improve the accuracy and reliability of model predictions. Polynomial chaos expansion (PCE) has been used as an efficient approach for UQ by approximating uncertainty with orthogonal polynomial basis functions of standard distributions (e.g., normal) chosen from the Askey scheme. However, uncertainty in practice may not be represented well by standard distributions. In this case, the convergence rate and accuracy of the PCE-based UQ cannot be guaranteed. Further, when models involve non-polynomial forms, the PCE-based UQ can be computationally impractical in the presence of many parametric uncertainties. To address these issues, the Gram–Schmidt (GS) orthogonalization and generalized dimension reduction method (gDRM) are integrated with the PCE in this work to deal with many parametric uncertainties that follow arbitrary distributions. The performance of the proposed method is demonstrated with three benchmark cases including two chemical engineering problems in terms of UQ accuracy and computational efficiency by comparison with available algorithms (e.g., non-intrusive PCE).

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 Uncertainty Quantification of a Nonlinear Aeroelastic System Using Polynomial Chaos Expansion With Constant Phase Interpolation

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Ajit Desai ◽  
Jeroen A. S. Witteveen ◽  
Sunetra Sarkar
Keyword(s):  
Dynamical System ◽  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Turbine Blades ◽  
Flexible Structures ◽  
Period Doubling ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Aeroelastic System ◽  
Phase Interpolation

The present study focuses on the uncertainty quantification of an aeroelastic instability system. This is a classical dynamical system often used to model the flow induced oscillation of flexible structures such as turbine blades. It is relevant as a preliminary fluid-structure interaction model, successfully demonstrating the oscillation modes in blade rotor structures in attached flow conditions. The potential flow model used here is also significant because the modern turbine rotors are, in general, regulated in stall and pitch in order to avoid dynamic stall induced vibrations. Geometric nonlinearities are added to this model in order to consider the possibilities of large twisting of the blades. The resulting system shows Hopf and period-doubling bifurcations. Parametric uncertainties have been taken into account in order to consider modeling and measurement inaccuracies. A quadrature based spectral uncertainty tool called polynomial chaos expansion is used to quantify the propagation of uncertainty through the dynamical system of concern. The method is able to capture the bifurcations in the stochastic system with multiple uncertainties quite successfully. However, the periodic response realizations are prone to time degeneracy due to an increasing phase shifting between the realizations. In order to tackle the issue of degeneracy, a corrective algorithm using constant phase interpolation, which was developed earlier by one of the authors, is applied to the present aeroelastic problem. An interpolation of the oscillatory response is done at constant phases instead of constant time and that results in time independent accuracy levels.

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