Gaussian-process based modeling and optimal control of melt-pool geometry in laser powder bed fusion

Studies have shown that melt-pool characteristics such as melt-pool size and shape are highly correlated with the formation of porosity and defects in parts built with the laser powder bed fusion (L-PBF) additive manufacturing (AM) processes. Hence, optimizing process parameters to maintain a constant melt-pool size during the build process could potentially improve the build quality of the final part. This paper considers the optimal control of laser power, while keeping other process parameters fixed, to achieve a constant melt-pool size during the laser scanning of a multi-track build under L-PBF. First, Gaussian process regression (GPR) is applied to model the dynamic evolution of the melt-pool size as a function of laser power and thermal history, which are defined as the input features of the GPR model. Then a constrained finite-horizon optimal control problem is formulated, with a quadratic cost function defined to minimize the difference between the controlled melt-pool size and its reference value. A projected gradient descent algorithm is applied to compute the optimal sequence of laser power in the proposed control problem. The GPR modeling is demonstrated using simulated data sets, a mix of simulated and experimental data sets, or pure experimental data sets. Numerical verification of the control design of laser power is performed on a commercial AM software, Autodesk’s Netfabb Simulation. Simulation results demonstrate the effectiveness of the proposed GPR modeling and model-based optimal control in regulating the melt-pool size during the scanning of multi-tracks using L-PBF.