Propagation of Parametric Uncertainties in a Nonlinear Aeroelastic System Using an Improved Adaptive Sparse Grid Quadrature Routine

A novel uncertainty quantification routine in the genre of adaptive sparse grid stochastic collocation (SC) has been proposed in this study to investigate the propagation of parametric uncertainties in a stall flutter aeroelastic system. In a hypercube stochastic domain, presence of strong nonlinearities can give way to steep solution gradients that can adversely affect the convergence of nonadaptive sparse grid collocation schemes. A new adaptive scheme is proposed here that allows for accelerated convergence by clustering more discretization points in regimes characterized by steep fronts, using hat-like basis functions with nonequidistant nodes. The proposed technique has been applied on a nonlinear stall flutter aeroelastic system to quantify the propagation of multiparametric uncertainty from both structural and aerodynamic parameters. Their relative importance on the stochastic response is presented through a sensitivity analysis.

Affordable Uncertainty Quantification for Industrial Problems: Application to Aero-Engine Fans

Uncertainty quantification (UQ) is an increasingly important area of research. As components and systems become more efficient and optimized, the impact of uncertain parameters is likely to become critical. It is fundamental to consider the impact of these uncertainties as early as possible during the design process, with the aim of producing more robust designs (less sensitive to the presence of uncertainties). The cost of UQ with high-fidelity simulations becomes therefore of fundamental importance. This work makes use of least-squares approximations in the context of appropriately selected polynomial chaos (PC) bases. An efficient technique based on QR column pivoting has been employed to reduce the number of evaluations required to construct the approximation, demonstrating the superiority of the method with respect to full-tensor quadrature (FTQ) and sparse-grid quadrature (SGQ). Orthonormal polynomials used for the PC expansion are calculated numerically based on the given uncertainty distribution, making the approach optimal for any type of input uncertainty. The approach is used to quantify the variability in the performance of two large bypass-ratio jet engine fans in the presence of shape uncertainty due to possible manufacturing processes. The impacts of shape uncertainty on the two geometries are compared, and sensitivities to the location of the blade shape variability are extracted. The mechanisms at the origin of the change in performance are analyzed in detail, as well as the differences between the two configurations.

A Novel Robust Sparse-Grid Quadrature Kalman Filter Design for HCV Transfer Alignment Against Model Parameter Uncertainty

A novel robust scheme for Transfer Alignment (TA) is proposed for improving the accuracy of the navigation of a Hypersonic Cruise Vehicle (HCV). The main goal is to instil robustness in the safety and accuracy of the attitude determination, despite mode uncertainties. This article focuses on Robust Sparse-Grid Quadrature Filtering (R-SGQF) using two given robust factors for norm-bounded model uncertainties in non-linear systems. Missile dynamic and measurement model uncertainties are established to validate TA technologies. The nominal stability of the R-SGQF is defined by estimating error dynamics. The technique gives sufficient conditions for the R-SGQF in terms of two parameterised Riccati equations. Robust stability is analysed using Lyapunov theory and the accuracy level of the Sparse-Grid Quadrature (SGQ) algorithm. Embedding the SGQ technique into the robust filter structure, R-SGQF is not only of robust stability against uncertainty but also of higher accuracy. The simulation results of the TA algorithm demonstrate that attitude determinations validate the effectiveness of the R-SGQF algorithm.