We extend the model-free Data-Driven computing paradigm to solids and structures that are stochastic due to intrinsic randomness in the material behavior. The behavior of such materials is characterized by a likelihood measure instead of a constitutive relation. We specifically assume that the material likelihood measure is known only through an empirical point-data set in material or phase space. The state of the solid or structure is additionally subject to compatibility and equilibrium constraints. The problem is then to infer the likelihood of a given structural outcome of interest. In this work, we present a Data-Driven method of inference that determines likelihoods of outcomes from the empirical material data and that requires no material or prior modeling. In particular, the computation of expectations is reduced to explicit sums over local material data sets and to quadratures over admissible states, i. e., states satisfying compatibility and equilibrium. The complexity of the material data-set sums is linear in the number of data points and in the number of members in the structure. Efficient population annealing procedures and fast search algorithms for accelerating the calculations are presented. The scope, cost and convergence properties of the method are assessed with the aid selected applications and benchmark tests.
翻译:我们将无模型数据驱动计算模式扩大到因物质行为本身随机性而具有随机性的固态和结构。这些材料的行为具有一种可能性衡量的特征,而不是构成关系。我们特别假定,物质概率计量仅通过材料或阶段空间的经验点数据集而为人所知。固态或结构的状况还受兼容性和平衡性的限制。然后的问题是推导产生某种感兴趣的结构结果的可能性。在这项工作中,我们提出了一个数据生成推论方法,确定实验材料数据的结果的可能性,而不需要材料或先前的模型。特别是,对预期的计算将降低到对当地材料数据集的明确数字,并对可接受状态进行等量的等量,即符合兼容性和平衡性。材料数据集的复杂程度是数据点数量和结构中成员数量的线性。为加速计算,我们介绍了高效的人口内嵌程序和快速搜索算法。方法的范围、成本和趋同性与选择的应用基准和测试进行了评估。该方法的范围、成本和趋同性都与选定的援助基准进行了评估。