Multiscale Uncertainty Quantification with Arbitrary Polynomial Chaos
Multiscale Uncertainty Quantification with Arbitrary Polynomial Chaos
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DOI：
10.1016/j.cma.2019.112571
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发表时间：
2019-12
影响因子：
7.2
通讯作者：
Nick Pepper;F. Montomoli;Sanjiv Sharma
中科院分区：
文献类型：
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作者：
Nick Pepper;F. Montomoli;Sanjiv Sharma
这项工作提出了一个框架，在多尺度模型的不确定性。这个问题与航空航天应用有关，在航空航天应用中，有必要从试样上的实验数据来估计完整部件（例如飞机机翼）的可靠性。与航空航天相关的一个特殊方面是可用数据的稀缺性。该框架需要两个主要方面：概率意义上的升级等价性和能够处理稀缺数据的有效（稀疏）非侵入多项式混沌公式。通过概率密度函数（PDF）匹配方法定义了上尺度等价性。通过用广义多项式混沌扩展（gPCE）表示粗尺度模型的输入，随机尺度放大问题可以被重新转换为优化问题。为了定义一个数据驱动的框架，能够处理稀缺的数据，稀疏近似矩基于任意多项式混沌。稀疏性允许这个优化问题的解决方案，以减少计算密集型比升级方法依赖于蒙特卡罗采样。此外，这使得PDF匹配方法对于单独的模拟运行可能在计算上昂贵的工业应用更可行。使用任意多项式混沌允许框架直接使用实验数据。最后，在多目标优化的情况下，使用Kolmogorov-Smirnov（KS）距离和矩量法来量化分布之间的差异。结果表明，过滤的动力学信息包含在细尺度的粗模型可以避免通过一个低保真度，高阶模型的建设。
This work presents a framework for upscaling uncertainty in multiscale models. The problem is relevant to aerospace applications where it is necessary to estimate the reliability of a complete part such as an aeroplane wing from experimental data on coupons. A particular aspect relevant to aerospace is the scarcity of data available.The framework needs two main aspects: an upscaling equivalence in a probabilistic sense and an efficient (sparse) Non-Intrusive Polynomial Chaos formulation able to deal with scarce data. The upscaling equivalence is defined by a Probability Density Function (PDF) matching approach. By representing the inputs of a coarse-scale model with a generalised Polynomial Chaos Expansion (gPCE) the stochastic upscaling problem can be recast as an optimisation problem. In order to define a data driven framework able to deal with scarce data a Sparse Approximation for Moment Based Arbitrary Polynomial Chaos is used. Sparsity allows the solution of this optimisation problem to be made less computationally intensive than upscaling methods relying on Monte Carlo sampling. Moreover this makes the PDF matching method more viable for industrial applications where individual simulation runs may be computationally expensive. Arbitrary Polynomial Chaos is used to allow the framework to use directly experimental data. Finally, the difference between the distributions is quantified using the Kolmogorov–Smirnov (KS) distance and the method of moments in the case of a multi-objective optimisation. It is shown that filtering of dynamical information contained in the fine-scale by the coarse model may be avoided through the construction of a low-fidelity, high-order model.