In modern manufacturing, Artificial Intelligence (AI) and several data analysis techniques are frequently used and developed in various fields. These quantitative approaches, however, are somewhat focused on the assumption that sensor data properly expresses the physical phenomenon. Another issue is that the data can be obtained through experiments, but due to the constraints of time and cost of experiments, obtaining a large amount of data that may be able to fully explain diverse natural occurrences is impossible. In the present study, we propose a hybrid method that combines scientific knowledge and machine learning methods via an optimization framework containing Lagrange multiplier concept. Experiments with real manufacturing data from the Friction Stir Welding (FSW) process demonstrate the scientific consistency and effectiveness of the proposed idea.
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