Adaptive Method for Non-Intrusive Spectral Projection—Application on a Stochastic Eddy Current NDT Problem
Adaptive Method for Non-Intrusive Spectral Projection—Application on a Stochastic Eddy Current NDT Problem
复制标题
非侵入式谱投影的自适应方法——在随机涡流无损检测问题上的应用
DOI：
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发表时间：
2012
影响因子：
2.1
通讯作者：
A. Benabou
中科院分区：
文献类型：
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作者：
K. Beddek;S. Clénet;O. Moreau;V. Costan;Y. L. Menach;A. Benabou
非侵入式光谱投影（NISP）方法广泛用于随机模型中的不确定性量化。确定多项式混沌解的展开式需要计算多维积分。已经开发出一种基于嵌套稀疏网格的自动自适应算法来评估这些积分。适应的算法考虑了每个随机变量相对于模型输出的权重。为了实现这一目标，它构建了均值的各向异性稀疏网格，从而减少了数值模拟的数量。此外，解的谱形式是从构造的正交方案中明确识别的。无损检测工业应用获得的数值结果证明了该方法的有效性。
The Non-Intrusive Spectral Projection (NISP) method is widely used for uncertainty quantification in stochastic models. The determination of the expansion of the solution on the polynomial chaos requires the computation of multidimensional integrals. An automatic adaptive algorithm based on nested sparse grids has been developed to evaluate those integrals. The adapted algorithm takes into account the weight of each random variable with respect to the output of the model. To achieve that it constructs anisotropic sparse grid of the mean, leading to a reduction of the number of numerical simulations. Furthermore, the spectral form of the solution is explicitly identified from the constructed quadrature scheme. Numerical results obtained on an industrial application in NDT demonstrate the efficiency of the proposed method.