A Two-Phase Monte Carlo Simulation/Non-Intrusive Polynomial Chaos (MSC/NIPC) Method for Quantification of Margins and Mixed Uncertainties (QMMU) in Flutter Analysis

Abstract

A two-phase Monte Carlo Simulation/Non-intrusive Polynomial Chaos (MCS/NIPC) method for quantification of margins and mixed uncertainties (aleatory and epistemic uncertainties) is proposed in this paper for the flutter speed boundary analysis. Compared with the traditional MCS/MCS method which needs lots of numerical simulations, the MCS/NIPC method can reduce the computational cost without losing accuracy due to the use of point collocation non-intrusive polynomial chaos in the inner loop. Based on the results of uncertainty quantification, a novel practical quantification of margins and mixed uncertainties (QMMU) framework is proposed considering both aleatory and epistemic uncertainties such as the parametric uncertainties in complicated models. A two-dimensional airfoil and a three-dimensional benchmark wing, the AGARD 445.6 wing, are both employed to illustrate the practical application of the proposed methods for flutter speed computation in the presence of mixed uncertainties arising from the material properties and flight conditions. Within the analysis, aleatory and mixed uncertainty quantification are conducted to prove the effectiveness and efficiency of the MCS/NIPC method. Then the QMMU metrics are accomplished for the flutter speed boundary analysis of the two airfoil models. The results demonstrate the potential of the proposed QMMU framework to analyze the stability of engineering systems. INDEX TERMS Flutter, non-intrusive polynomial chaos, probability bounds, quantification of margins and mixed uncertainties, uncertainty quantification

Reliability analysis of mechanisms with mixed uncertainties using polynomial chaos expansion

“…[16][17][18] In order to efficiently compute probability bounds for the system response function, a series of new uncertainty propagation methods have emerged for the parametric probability box problem, represented by double-layer circular sampling. [19][20][21] Most current methods of mechanism reliability analysis are only applicable to random variables. 22 However, in many engineering applications, some uncertain parameters can only be modelled by interval variables 23 due to the difficulty of determining the random distribution of the parameters.…”

“…Besides, to exploit the advantages of both probability and interval theory, the effect of random and interval uncertainty is represented using a cumulative distribution function (CDF) bound on the system response quantities, called the probability box (P‐box) 16–18 . In order to efficiently compute probability bounds for the system response function, a series of new uncertainty propagation methods have emerged for the parametric probability box problem, represented by double‐layer circular sampling 19–21 …”

Computation of parametric uncertainty margin using stability boundary locus: An application to load frequency control

“…In Akkaya et al (2016), a parametric method of modeling the middle ware service architecture for smart grid applications is presented using the Monte Carlo simulations followed by the regression analysis. In Hu et al (2020), the mixed uncertainty margins are quantified by utilizing a dual-phase Monte Carlo Simulation (MCS)/Non-intrusive Polynomial Chaos (NIPC) approach for the computation of flutter speed boundary. In Hu et al (2019), a generalized polynomial chaos expansion (PCE) technique is implemented for the assessment of parametric uncertainty in hydrological modeling.…”