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Multilevel Monte Carlo simulations of composite structures with uncertain manufacturing defects
Probabilistic Engineering Mechanics ( IF 2.6 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.probengmech.2020.103116
T.J. Dodwell , S. Kynaston , R. Butler , R.T. Haftka , Nam H. Kim , R. Scheichl

By adopting a Multilevel Monte Carlo (MLMC) framework, we show that only a handful of costly fine scale computations are needed to accurately estimate statistics of the failure of a composite structure, as opposed to the thousands typically needed in classical Monte Carlo analyses. We introduce the MLMC method, compare its theoretical complexity with classical Monte Carlo, and give a simple-to-implement algorithm which includes a simple extension called MLMC with selective refinement to efficiently calculated structural failure probabilities. To demonstrate the huge computational gains we present two benchmark problems in composites: (1) the effects of fibre waviness on the compressive strength of a composite material, (2) uncertain buckling performance of a composite panel with uncertain ply orientations. For our most challenging test case, estimating a rare ($\sim 1/150$) probability of buckling failure of a composite panel, we see a speed-up factor $> 1000$. Our approach distributed over $1024$ processors reduces the computation time from $218$ days to just $4.5$ hours. This level of speed up makes stochastic simulations that would otherwise be unthinkable now possible.?

中文翻译:

具有不确定制造缺陷的复合材料结构的多级蒙特卡罗模拟

通过采用多级蒙特卡罗 (MLMC) 框架,我们表明,与经典蒙特卡罗分析中通常需要的数千次相比,只需进行少量成本高昂的精细规模计算即可准确估计复合结构失效的统计数据。我们介绍了 MLMC 方法,将其理论复杂性与经典蒙特卡罗方法进行了比较,并给出了一种易于实现的算法,其中包括一个称为 MLMC 的简单扩展,具有选择性细化以有效计算结构故障概率。为了证明巨大的计算收益,我们提出了复合材料中的两个基准问题:(1)纤维波纹度对复合材料抗压强度的影响,(2)具有不确定层板取向的复合板的屈曲性能不确定。对于我们最具挑战性的测试用例,估计复合板屈曲失效的罕见($\sim 1/150$)概率,我们看到加速因子 $> 1000$。我们的方法分布在 1024 美元的处理器上,将计算时间从 218 美元天减少到 4.5 美元小时。这种水平的加速使得现在无法想象的随机模拟成为可能。?
更新日期:2021-01-01
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