Physics-informed Machine Learning for Digital Twins of Metal Additive Manufacturing

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Virginia Tech


Metal additive manufacturing (AM) is an emerging technology for producing parts with virtually no constraint on the geometry. AM builds a part by depositing materials in a layer-by-layer fashion. Despite the benefits in several critical applications, quality issues are one of the primary concerns for the widespread adoption of metal AM. Addressing these issues starts with a better understanding of the underlying physics and includes monitoring and controlling the process in a real-world manufacturing environment. Digital Twins (DTs) are virtual representations of physical systems that enable fast and accurate decision-making. DTs rely on Artificial Intelligence (AI) to process complex information from multiple sources in a manufacturing system at multiple levels. This information typically comes from partially known process physics, in-situ sensor data, and ex-situ quality measurements for a metal AM process. Most current AI models cannot handle ill-structured information from metal AM. Thus, this work proposes three novel machine-learning methods for improving the quality of metal AM processes. These methods enable DTs to control quality in several processes, including laser powder bed fusion (LPBF) and additive friction stir deposition (AFSD). The proposed three methods are as follows 1. Process improvement requires mapping the process parameters with ex-situ quality measurements. These mappings often tend to be non-stationary, with limited experimental data. This work utilizes a novel Deep Gaussian Process-based Bayesian optimization (DGP-SI-BO) method for sequential process design. DGP can model non-stationarity better than a traditional Gaussian Process (GP), but it is challenging for BO. The proposed DGP-SI-BO provides a bagging procedure for acquisition function with a DGP surrogate model inferred via Stochastic Imputation (SI). For a fixed time budget, the proposed method gives 10% better quality for the LPBF process than the widely used BO method while being three times faster than the state-of-the-art method.

  1. For metal AM, the process physics information is usually in the form of Partial Differential Equations (PDEs). Though the PDEs, along with in-situ data, can be handled through Physics-informed Neural Networks (PINNs), the activation function in NNs is traditionally not designed to handle multi-scale PDEs. This work proposes a novel activation function Self-scalable tanh (Stan) function for PINNs. The proposed activation function modifies the traditional tanh function. Stan function is smooth, non-saturating, and has a trainable parameter. It can allow an easy flow of gradients and enable systematic scaling of the input-output mapping during training. Apart from solving the heat transfer equations for LPBF and AFSD, this work provides applications in areas including quantum physics and solid and fluid mechanics. Stan function also accelerates notoriously hard and ill-posed inverse discovery of process physics.

  2. PDE-based simulations typically need to be much faster for in-situ process control. This work proposes to use a Fourier Neural Operator (FNO) for instantaneous predictions (1000 times speed up) of quality in metal AM. FNO is a data-driven method that maps the process parameters with a high dimensional quality tensor (like thermal distribution in LPBF). Training the FNO with simulated data from PINN ensures a quick response to alter the course of the manufacturing process. Once trained, a DT can readily deploy the model for real-time process monitoring.

The proposed methods combine complex information to provide reliable machine-learning models and improve understanding of metal AM processes. Though these models can be independent, they complement each other to build DTs and achieve quality assurance in metal AM.



Additive Manufacturing, Deep Gaussian Process, Bayesian Optimization, Physics-informed Neural Networks, Fourier Neural Operators