Abstract A machine learning aided reliability assessment framework is presented for functionally graded material (FGM) structures under plane strain/stress conditions with the consideration of elastoplasticity. The material nonlinearity of the FGM is modelled through the implementation of the Tamura-Tomota-Ozawa (TTO) model. For safety evaluation of FGM structures, the volume fraction of FGM has been modelled through spatially dependent uncertainty as random field for the concerned composite. In order to solve the complex stochastic elastoplastic problem, a further developed machine learning aided technique called the extended support vector regression (X-SVR) with a generalized Dirichlet feature mapping function has been introduced and then, the corresponding probabilistic features, including the statistical moments, probability density functions (PDFs), and cumulative distribution functions (CDFs), of the concerned structural responses can be effectively established for assessing the reliability of FGM structures. Moreover, the proposed approach is competent to deliver critical information regarding the uncertain system inputs which can be beneficial for subsequent safety assessment and structural designs for the FGM. Two test functions and two numerical examples have been adopted to visualise the accuracy, stability and capability of the proposed safety assessment framework for FGM structures.

中文翻译：

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具有材料非线性的功能梯度结构的安全评估

摘要 针对平面应变/应力条件下的功能梯度材料 (FGM) 结构，提出了一种机器学习辅助可靠性评估框架，并考虑了弹塑性。FGM 的材料非线性通过实施 Tamura-Tomota-Ozawa (TTO) 模型进行建模。对于 FGM 结构的安全评估，FGM 的体积分数已通过空间相关的不确定性建模为相关复合材料的随机场。为了解决复杂的随机弹塑性问题，引入了一种进一步发展的机器学习辅助技术，称为扩展支持向量回归 (X-SVR)，具有广义 Dirichlet 特征映射函数，然后，相应的概率特征，包括统计矩, 可以有效地建立相关结构响应的概率密度函数 (PDF) 和累积分布函数 (CDF)，以评估 FGM 结构的可靠性。此外，所提出的方法能够提供有关不确定系统输入的关键信息，这对 FGM 的后续安全评估和结构设计是有益的。采用两个测试函数和两个数值例子来可视化所提出的 FGM 结构安全评估框架的准确性、稳定性和能力。所提议的方法能够提供有关不确定系统输入的关键信息，这些信息可能有益于 FGM 的后续安全评估和结构设计。采用两个测试函数和两个数值例子来可视化所提出的 FGM 结构安全评估框架的准确性、稳定性和能力。所提议的方法能够提供有关不确定系统输入的关键信息，这些信息可能有益于 FGM 的后续安全评估和结构设计。采用两个测试函数和两个数值例子来可视化所提出的 FGM 结构安全评估框架的准确性、稳定性和能力。