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Reduced-order models (ROMs) can effectively balance the accuracy and efficiency of computational fluid dynamics (CFD). The nonlinear flow field characteristics cannot be captured accurately by traditional ROMs, such as proper orthogonal decomposition (POD). Combining isometric mapping (ISOMAP) and local linear embedding (LLE), a novel manifold learning method (ISOMAP-Local LLE) is proposed, performing global and accurate reconstruction of the nonlinear flow field. First, the nonlinear dimensionality reduction is derived by considering the global isometric characteristic and the local reconstruction relationship simultaneously. Then, the local interpolation model is constructed to improve the interpolation accuracy introduced by the global interpolation model. Finally, the flow field reconstruction is accomplished based on the inverse mapping. Furthermore, the criteria of hyperparameters have been established to achieve high-precision prediction. Several examples covering full speed flow field are carried out to demonstrate the accuracy and efficiency of ISOMAP-Local LLE. The proposed manifold learning-based ROM achieves prediction accuracy that surpasses that of other ROMs (such as POD, ISOMAP, LLE, etc.), resulting in significant time cost savings for CFD simulations. [ABSTRACT FROM AUTHOR]

Both the critical importance index of fault tree analysis(FTA) in probability safety assessment and global sensitivity index in reliability estimation can be employed to determine the important input variables. What are the differences and connections between the two kinds of importance degree? Firstly, the qualitative and quantitative analysis of fault tree in probabilistic safety assessment are introduced, and then the failure probability and global sensitivity analysis of fault tree in reliability estimation are presented. Finally, several FTAs of aircraft systems are analyzed and compared. It is found that the failure probabilities are basically consistent, but the important rank of basic events will be different for the randomness of the basic events' probabilities. And the influence of the distribution types and parameters on the global sensitivity index should be not negligible.

Optimization techniques combined with uncertainty quantification are computationally expensive for robust aerodynamic optimization due to expensive CFD costs. Surrogate model technology can be used to improve the efficiency of robust optimization. In this paper, non-intrusive polynomial chaos method and Kriging model are used to construct a surrogate model that associate stochastic aerodynamic statistics with airfoil shapes. Then, global search algorithm is used to optimize the model to obtain optimal airfoil fast. However, optimization results always depend on the approximation accuracy of the surrogate model. Actually, it is difficult to achieve a high accuracy of the model in the whole design space. Therefore, we introduce the idea of adaptive strategy to robust aerodynamic optimization and propose an adaptive stochastic optimization framework. The surrogate model is updated adaptively by increasing training airfoils according to historical optimization results to guarantee the accuracy near the optimal design point, which can greatly reduce the number of training airfoils. The proposed method is applied to a robust aerodynamic shape optimization for drag minimization considering uncertainty of Mach number in transonic region. It can be concluded that the proposed method can obtain better optimal results more efficiently than the traditional robust optimization method and global surrogate model method. [ABSTRACT FROM AUTHOR]