Robust optimization of a 3D printed periodic frame structure using the inferred characterization of the additive manufacturing system

Statistical process control has been successfully used to monitor manufacturing processes for decades. Some key variables are usually monitored, and their values can give valuable indications if the process is out of control. Usually, engineering optimization is deterministic, which does not consider any type of randomness in model parameters. However, robust optimization assuming uncertainties has been recently developed for engineering applications. In this work, we propose an approach using the data usually obtained from the statistical process control to design a 3D periodic structure with a vibration attenuation band robust to manufacturing variability. A procedure using a statistical regression model is proposed, as well as a design of experiments approach, to correlate the random mechanical properties that are usually already measured for statistical process control purposes. Forty-five samples are produced with a 3D printer to characterize the process variability and used to design the metastructure optimally. The obtained statistical model is subsequently combined with a kernel smoother to generate spatially correlated mechanical proprieties. The resulting random field model is then used to predict the wave and vibration response of the designed periodic structure. Finally, a robust optimization approach is proposed to define a final shape for the metastructure that is robust against the inferred variability. The final design presents a robust full and complete attenuation band from 5.9 kHz to 7.5 kHz. The optimal design is then manufactured, and vibration response measurements are used to validate the proposed methodology. It is shown that the final structure presents a band gap from 5.7 kHz to 9.9 kHz, which is inside the simulated 95% confidence interval for the width of the band gap. Although the proposed approach is applied to the vibration response of a periodic 3D frame structure, it opens the way for further extended and generalized robust design approaches in different fields.