Despite the advances in hardware and software techniques, standard numerical methods fail in providing real-time simulations, especially for complex processes such as additive manufacturing applications. A real-time simulation enables process control through the combination of process monitoring and automated feedback, which increases the flexibility and quality of a process. Typically, before producing a whole additive manufacturing structure, a simplified experiment in the form of a bead-on-plate experiment is performed to get a first insight into the process and to set parameters suitably. In this work, a reduced order model for the transient thermal problem of the bead-on-plate weld simulation is developed, allowing an efficient model calibration and control of the process. The proposed approach applies the proper generalized decomposition (PGD) method, a popular model order reduction technique, to decrease the computational effort of each model evaluation required multiple times in parameter estimation, control, and optimization. The welding torch is modeled by a moving heat source, which leads to difficulties separating space and time, a key ingredient in PGD simulations. A novel approach for separating space and time is applied and extended to 3D problems allowing the derivation of an efficient separated representation of the temperature. The results are verified against a standard finite element model showing excellent agreement. The reduced order model is also leveraged in a Bayesian model parameter estimation setup, speeding up calibrations and ultimately leading to an optimized real-time simulation approach for welding experiment using synthetic as well as real measurement data.

尽管硬件和软件技术取得了进步，但标准数值方法无法提供实时模拟，尤其是对于增材制造应用等复杂过程。实时仿真通过过程监控和自动反馈的结合实现过程控制，从而提高过程的灵活性和质量。通常，在生产整个增材制造结构之前，会进行板上珠实验形式的简化实验，以初步了解该过程并适当设置参数。在这项工作中，开发了用于板焊道仿真瞬态热问题的降阶模型，从而可以进行有效的模型校准和过程控制。所提出的方法应用适当的广义分解（PGD）方法（一种流行的模型降阶技术）来减少参数估计、控制和优化中多次评估每个模型所需的计算量。焊枪是通过移动热源建模的，这导致很难分离空间和时间，而空间和时间是 PGD 模拟的关键因素。应用一种分离空间和时间的新颖方法并将其扩展到 3D 问题，从而可以导出温度的有效分离表示。结果与标准有限元模型进行了验证，显示出极好的一致性。降阶模型还用于贝叶斯模型参数估计设置，加快校准速度，并最终使用合成数据和真实测量数据为焊接实验提供优化的实时模拟方法。