The safety evaluation of engineering systems whose performance evaluation requires finite element analysis is a challenge in reliability theory. Recently, Adjusted Control Variates Technique (ACVAT) has proposed by the authors to solve this issue. ACVAT uses the results of a finite element method (FEM) model with coarse mesh density as the control variates of the model with fine mesh and efficiently solves FEM-based reliability problems. ACVAT however does not provide any results about the reliability-based mesh convergence of the problem, which is an important tool in FEM. Mesh-refinement analysis allows checking whether the numerical solution is sufficiently accurate, even though the exact solution is unknown. In this study, by introducing expanded control variates (ECV) formulation, ACVAT is improved and the capabilities of the method are also extended for efficient reliability mesh convergence analysis of FEM-based reliability problems. In the present study, the FEM-based reliability analyses of four practical engineering problems are investigated by this method and the corresponding results are compared with accurate results obtained by analytical solutions for two problems. The results confirm that the proposed approach not only handles the mesh refinement progress with the required accuracy, but it also reduces considerably the computational cost of FEM-based reliability problems.

中文翻译：

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通过引入扩展控制变量进行可靠性网格收敛分析

工程系统的安全性评估，其性能评估需要有限元分析，这是可靠性理论中的一个挑战。最近，作者提出了可调整控制变量技术（ACVAT）来解决此问题。ACVAT使用具有粗网格密度的有限元方法（FEM）模型的结果作为具有细网格的模型的控制变量，并有效解决了基于FEM的可靠性问题。但是，ACVAT没有提供有关基于可靠性的网格收敛问题的任何结果，这是FEM中的重要工具。网格细化分析允许检查数值解是否足够准确，即使确切解是未知的也是如此。在这项研究中，通过引入扩展控制变量（ECV）公式，改进了ACVAT，并扩展了该方法的功能，可对基于FEM的可靠性问题进行有效的可靠性网格收敛分析。在本研究中，通过这种方法研究了基于FEM的四个实际工程问题的可靠性分析，并将相应的结果与两个问题的解析解所得到的准确结果进行了比较。结果证实，所提出的方法不仅以所需的精度处理网格细化进度，而且还大大降低了基于FEM的可靠性问题的计算成本。该方法对基于FEM的四个实际工程问题进行了可靠性分析，并将相应结果与两个问题的解析解所得到的准确结果进行了比较。结果证实，所提出的方法不仅以所需的精度处理网格细化进度，而且还大大降低了基于FEM的可靠性问题的计算成本。该方法对基于FEM的四个实际工程问题进行了可靠性分析，并将相应结果与两个问题的解析解所得到的准确结果进行了比较。结果证实，所提出的方法不仅以所需的精度处理网格细化进度，而且还大大降低了基于FEM的可靠性问题的计算成本。