Analysing and quantifying parametric uncertainties numerically is a tedious task, even more so when the system exhibits subcritical bifurcations. Here a novel interpolation based approach is presented and applied to two simple models exhibiting subcritical Hopf bifurcation. It is seen that this integrated interpolation scheme is significantly faster than traditional Monte Carlo based simulations. The advantages of using this scheme and the reason for its success compared to other uncertainty quantification schemes like Polynomial Chaos Expansion (PCE) are highlighted. The paper also discusses advantages of using an equi-probable node distribution which is seen to improve the accuracy of the proposed scheme. The probabilities of failure (POF) are defined and plotted for various operating conditions. The possibilities of extending the above scheme to experiments are also discussed. © 2013 Elsevier Ltd.

Sunetra Sarkar

Department of Aerospace Engineering

R. I. Sujith

Interpolation schemes

Operating condition

Parametric uncertainties

Polynomial chaos expansion

Polynomial chaos expansion (PCE)

SUB-CRITICAL BIFURCATIONS

Subcritical Hopf bifurcation

Uncertainty quantifications

Hopf bifurcation

interpolation

Monte Carlo methods

Uncertainty analysis

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Probabilistic Engineering Mechanics

The present paper is about analyzing and quantifying parametric uncertainties in a nonlinear aeroelastic system. The response surface of a subcritical system has discontinuities which makes it difficult to analyze using spectral approaches. A quadrature based spectral parametric uncertainty tool called nonintrusive spectral projection (NISP) can capture discontinuities in the response surface only by infinite number of points. As the number of random variable increases, the order of expansion has to increase drastically in order to capture the response accurately. Hence an alternate approach using integrated interpolation scheme which was earlier applied for a thermoacoustic problem is being applied to a classical flutter problem. It is found to be accurate and computationally cheaper than traditional Monte Carlo simulations (MCS) in capturing the response surface. This paper intends to apply the interpolation scheme to the nonlinear aeroelastic model and compares it with quadrature based polynomial chaos expansion (PCE) approach and MCS. © 2016 The Authors.

Fulltext

Procedia Engineering

Uncertainty Quantification of Subcritical Nonlinear Aeroelastic System Using Integrated Interpolation Method and Polynomial Chaos Expansion

Stall induced oscillations are likely instabilities in modern wind engineering systems. For their robust design, it is crucial to take parametric and load uncertainties into consideration. Presently, study of a stall flutter system under the influence of random gust is undertaken using the probability density evolution method, and qualitative changes in the response output are presented. This probability based approach when compared with a spectral tool called polynomial chaos expansion, shows better accuracy for the same level of discretisation. © 2015 Elsevier Ltd.

Computers and Structures

Study of a stall induced dynamical system under gust using the probability density evolution technique

The role of non-normality and nonlinearity in thermoacoustic interaction in a Rijke tube is investigated in this paper. The heat release rate of the heating element is modeled by a modified form of King's law. This fluctuating heat release from the heating element is treated as a compact source in the one-dimensional linear model of the acoustic field. The temporal evolution of the acoustic perturbations is studied using the Galerkin technique. It is shown that any thermoacoustic system is non-normal. Non-normality can cause algebraic growth of oscillations for a short time even though the eigenvectors of the system could be decaying exponentially with time. This feature of non-normality combined with the effect of nonlinearity causes the occurrence of triggering, i.e., the thermoacoustic oscillations decay for some initial conditions whereas they grow for some other initial conditions. If a system is non-normal, then there can be large amplification of oscillations even if the excited frequency is far from the natural frequency of the system. The dependence of transient growth on time lag and heater positions is studied. Such amplifications (pseudoresonance) can be studied using pseudospectra, as eigenvalues alone are not sufficient to predict the behavior of the system. The geometry of pseudospectra can be used to obtain upper and lower bounds on the growth factor, which provide both necessary and sufficient conditions for the stability of a thermoacoustic system. © 2008 American Institute of Physics.

Physics of Fluids

Thermoacoustic instability in a Rijke tube: Non-normality and nonlinearity

Networks & Heterogeneous Media

Influence prediction for continuous-time information propagation on networks

Acta Acustica united with Acustica

The Rijke Tube: A Green's Function Approach in the Frequency Domain

Journal of Computational Physics

Effect of randomness on multi-frequency aeroelastic responses resolved by Unsteady Adaptive Stochastic Finite Elements

46th AIAA Aerospace Sciences Meeting and Exhibit

Efficient Uncertainty Quantification Applied to the Aeroelastic Analysis of a Transonic Wing

Uncertainty quantification of subcritical bifurcations

Journal	Probabilistic Engineering Mechanics
ISSN	02668920
Open Access	No