We present a minimally invasive method for forward propagation of material property uncertainty to full-field quantities of interest in solid dynamics. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known a priori . The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the evolution equations based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the driving term of the evolution equations. The implementation is model independent, storage and communication efficient, and straightforward. We demonstrate its efficiency, accuracy, scaling with dimension of the parameter space, and convergence in distribution with two problems: a quasi-one-dimensional bar impact, and a two material notched plate impact. For the bar impact problem, we provide an analytical solution to PDF of the solution fields for method validation. With the notched plate problem, we also demonstrate good parallel efficiency and scaling of the method.

中文翻译：

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一种在固体动力学中传播全场不确定性的微创有效方法

我们提出了一种微创方法，用于将材料特性不确定性向前传播到固体动力学中感兴趣的全场量。全场不确定性量化能够设计复杂系统，其中感兴趣的数量（例如故障点）不是先验已知的。该方法受湍流建模的众所周知的概率密度函数 (PDF) 传播方法的启发，使用解决方案的集合来提供域中每个点所需数量的联合 PDF。集合的一个小子集被精确计算，其余的样本是根据这些精确解通过近似演化方程计算的。尽管所提出的方法与直接应用于感兴趣量的传统插值随机搭配方法具有共性，它是独特的，并利用了演化方程驱动项的参数依赖性和平滑性。实现与模型无关，存储和通信高效且简单。我们证明了它的效率、准确性、参数空间维度的缩放以及分布收敛，有两个问题：准一维棒撞击和两种材料缺口板撞击。对于杆冲击问题，我们提供了用于方法验证的解域的 PDF 解析解。对于缺口板问题，我们还展示了该方法的良好并行效率和扩展性。和直截了当。我们证明了它的效率、准确性、参数空间维度的缩放以及分布收敛，有两个问题：准一维棒撞击和两种材料缺口板撞击。对于杆冲击问题，我们提供了用于方法验证的解域的 PDF 解析解。对于缺口板问题，我们还展示了该方法的良好并行效率和扩展性。和直截了当。我们证明了它的效率、准确性、参数空间维度的缩放以及分布收敛，有两个问题：准一维棒撞击和两种材料缺口板撞击。对于杆冲击问题，我们提供了用于方法验证的解域的 PDF 解析解。对于缺口板问题，我们还展示了该方法的良好并行效率和扩展性。