In this paper, we demonstrate the combination of machine learning and three dimensional numerical simulations for multi-objective optimization of low pressure die casting. The cooling of molten metal inside the mold is achieved typically by passing water through the cooling lines in the die. Depending on the cooling line location, coolant flow rate and die geometry, nonuniform temperatures are imposed on the molten metal at the mold wall. This boundary condition along with the initial molten metal temperature affect the product quality quantified in terms of micro-structure parameters and yield strength. A finite volume based numerical solver is used to determine the temperature-time history and correlate the inputs to outputs. The objective of this research is to develop and demonstrate a procedure to obtain the initial and wall temperatures so as to optimize the product quality. The non-dominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization in this work. The number of function evaluations required for NSGA-II can be of the order of millions and hence, the finite volume solver cannot be used directly for optimization. Therefore, a multilayer perceptron feed-forward neural network is first trained using the results from the numerical solution of the fluid flow and energy equations and is subsequently used as a surrogate model. As an assessment, simplified versions of the actual problem are designed to first verify results of the genetic algorithm. An innovative local sensitivity based approach is then used to rank the final Pareto optimal solutions and select a single best design.

中文翻译：

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使用数值模拟和机器学习优化压铸凝固

在本文中，我们展示了机器学习和三维数值模拟的结合，用于低压压铸的多目标优化。模具内熔融金属的冷却通常是通过使水通过模具中的冷却管线来实现的。根据冷却管线位置、冷却剂流速和模具几何形状，模具壁处的熔融金属会产生不均匀的温度。这种边界条件与初始熔融金属温度一起影响以微观结构参数和屈服强度量化的产品质量。基于有限体积的数值求解器用于确定温度-时间历史并将输入与输出相关联。本研究的目的是开发和演示获取初始温度和壁温以优化产品质量的程序。在这项工作中，非支配排序遗传算法（NSGA-II）用于多目标优化。NSGA-II 所需的函数评估数量可能达到数百万，因此，有限体积求解器不能直接用于优化。因此，多层感知器前馈神经网络首先使用流体流动和能量方程的数值解的结果进行训练，然后用作替代模型。作为评估，实际问题的简化版本旨在首先验证遗传算法的结果。