A deep mixed-effects modeling approach for real-time monitoring of metal additive manufacturing process

In-situ process monitoring of additive manufacturing (AM) is critically important and has been attracting significant efforts to achieve desirable process reliability and quality consistency. Despite enormous progress in embedding various sensors into the AM system, effectively fusing these sensor data for anomaly detection is very challenging, due to complex relationship among sensing signals, process condition and environment. In this article we propose a deep mixed-effects modeling approach to monitor the melt pool temperature for anomaly detection. It consists of a deep neural network (DNN) capturing the relationship between the temperature and other sensing data, a random-effect term accounting for the random variation of mean temperature, and a residual term modeling potential autocorrelations. To train the model (Phase I), an efficient hard expectation-maximization (EM) algorithm is developed, which iteratively optimizes the DNN parameters and the ones for the random-effect and residual terms. In online monitoring (Phase II), a T2-based and a generalized likelihood ratio (GLR) test-based control charts are developed to timely detect the process anomalies. The asymptotic behaviors of both the T2 and GLR statistics are further established. The effectiveness of the proposed approach is demonstrated through thorough simulation study and real case study of an AM process.