关键词: 分位点, 高维, 极小目标失效概率, 重要抽样, 混合模型

Abstract: Evaluating the quantiles corresponding to target failure probabilities is central to efficiently decouple the reliability based design optimization of aircraft structure. However, efficient algorithms for quantile estimation are severely lacking for the extreme scenarios involving very low target failure probabilities random inputs required by airworthiness standards and high-dimensional. To address this, this paper proposes a circumferential-radial importance sampling based quantile evaluation (CRIS-QE) method. Leveraging the monotonic relationship between target failure probabilities and quantiles, the proposed CRIS-QE transforms the inverse problem of quantile evaluation into a forward problem of failure probability calibration at multiple thresholds. A parametric circumferential von-Mises-Fisher-radial Nakagami mixture model (vMFNM) is constructed to adaptively approach the optimal importance sampling density for failure probability calibration in a progressive and stratified manner. Concurrently, updating and information-sharing strategies for the vMFNM model are designed to guide the efficient search for quantiles in extreme scenarios. Numerical and engineering examples demonstrate that the proposed CRIS-QE significantly outperforms existing methods due to the substantial variance reduction provided by the vMFNM model and the efficient guidance offered by shared model information.

Key words: Quantile, Extremely low target failure probability, High-dimensional, Importance sampling, Mixture model