Real-time monitoring of additive manufacturing processes using a variational data assimilation method with model reduction and bias correction

Real-time monitoring of a system may be difficult when associated phenomena are multiphysics and multiscale. Difficulties mainly come from the numerical complexity which requires large computing resources that are hardly compatible with real-time.To overcome this issue, the initial high-fidelity parameterized physical model can be simplified, which leads to additional model bias. Moreover, parameter values can be inaccurate and erroneous. All those errors affect the effectiveness of numerical diagnosis and prognosis, and thus have to be corrected with assimilation techniques on observation data. Therefore, the monitoring of the process is made of two stages: (1) state estimation at the acquisition time, which may be associated with the identification of a set of unknown parameters of the parameterized model and the data-based enrichment of the model; (2) state prediction for future time steps from the updated model. The present study aims at implementing this framework with an extension, for time-dependent problems, of the Parameterized Background Data-Weak (PBDW) method introduced in [1]. Classical PBDW is a non-intrusive, reduced basis, real-time and in-situ data assimilation method that applies to physical systems modeled by parametrized pdes (initially for steady-state problems). The key idea of the formulation is to seek an approximation to the true state employing projection-by-data