Brittle porous materials are used in many applications, such as molten metal filter, battery, fuel cell, catalyst, membrane, and insulator. The porous structure of these materials causes variations in their fracture strength that is known as the mechanical reliability problem. Despite the importance of brittle porous materials, the origin of the strength variations is still unclear. The current study presents a machine learning approach to characterize the stochastic fracture of porous ceramics and glasses. A combined finite element modeling and fracture mechanics approach was used to generate a unique empirical data set consisting of normalized stress intensity factors (nSIFs, K I / σ ∞ = Y $$ \sqrt {\pi a} $$ π a ) that define fracture strength of brittle systems under uniaxial tensile loading and biaxial tensile loading. These empirical data sets were used to generate prediction functions and validate their accuracy. Monte Carlo simulations with two machine learning algorithms, random forests (RF) and artificial neural networks (ANN), were used to simultaneously determine the optimum percentages for the training and test data set split and the prediction function validation. The constraint was taken to be the mean absolute percentage error (MAPE) during the process. In the implementation step, new porous media with uniformly distributed pores were created and the prediction functions were used to obtain nSIFs and characterize the media. As a novelty of this approach, which ensures the predictive characterization of the generated media, a geometric matching method by means of the Euclidean bipartite matching between the empirical and the generated media was presented and the nSIFs were compared by means of MAPE. As a result of the study, MAPE ranges are 3.4–17.93% (uniaxial load) and 2.83–19.42% (biaxial load) for RF, 3.79–17.43% and 3.39–21.43 for ANN at the validation step; 3.54–18.20% (uniaxial load) and 3.06–21.60% (biaxial load) for RF, 3.57–18.26% and 3.43–21.76% for ANN at the implementation step. The proposed approach can be thus used as a predictive characterization tool, especially for the analysis and Weibull statistics of porous media subjected to brittle failure.

中文翻译：

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通过机器学习和几何匹配方法的脆性多孔材料预测失效框架

脆性多孔材料用于许多应用，例如熔融金属过滤器、电池、燃料电池、催化剂、膜和绝缘体。这些材料的多孔结构会导致其断裂强度发生变化，这被称为机械可靠性问题。尽管脆性多孔材料很重要，但强度变化的起源仍不清楚。目前的研究提出了一种机器学习方法来表征多孔陶瓷和玻璃的随机断裂。结合有限元建模和断裂力学方法来生成一个独特的经验数据集，该数据集由归一化应力强度因子 (nSIFs, KI / σ ∞ = Y $$ \sqrt {\pi a} $$ π a ) 组成，用于定义断裂脆性体系在单轴拉伸载荷和双轴拉伸载荷下的强度。这些经验数据集用于生成预测函数并验证其准确性。使用两种机器学习算法、随机森林 (RF) 和人工神经网络 (ANN) 进行蒙特卡罗模拟，同时确定训练和测试数据集拆分以及预测函数验证的最佳百分比。约束被认为是过程中的平均绝对百分比误差 (MAPE)。在实施步骤中，创建了具有均匀分布的孔隙的新多孔介质，并使用预测函数获得 nSIF 并表征介质。作为这种方法的新颖之处，它确保了生成的媒体的预测特征，提出了一种通过经验媒体和生成媒体之间的欧几里得二分匹配的几何匹配方法，并通过 MAPE 比较了 nSIF。作为研究的结果，在验证步骤中，RF 的 MAPE 范围为 3.4–17.93%（单轴负载）和 2.83–19.42%（双轴负载），ANN 的 MAPE 范围为 3.79–17.43% 和 3.39–21.43；在实施步骤中，RF 为 3.54–18.20%（单轴负载）和 3.06–21.60%（双轴负载），ANN 为 3.57–18.26% 和 3.43–21.76%。因此，所提出的方法可以用作预测表征工具，特别是用于易碎破坏多孔介质的分析和威布尔统计。43 用于 ANN 在验证步骤；在实施步骤中，RF 为 3.54–18.20%（单轴负载）和 3.06–21.60%（双轴负载），ANN 为 3.57–18.26% 和 3.43–21.76%。因此，所提出的方法可以用作预测表征工具，特别是用于易碎破坏多孔介质的分析和威布尔统计。43 用于 ANN 在验证步骤；在实施步骤中，RF 为 3.54–18.20%（单轴负载）和 3.06–21.60%（双轴负载），ANN 为 3.57–18.26% 和 3.43–21.76%。因此，所提出的方法可以用作预测表征工具，特别是用于易碎破坏多孔介质的分析和威布尔统计。