Uncertainty Quantification and Robust Modeling of Selective Laser Melting Process Using Stochastic Multi-Objective Approach


Selective laser melting (SLM) is a popular additive manufacturing process that creates 3D metal parts by fusing fine metal powders together. Modeling and optimization of SLM prototypes has been extensively studied deterministically in the literature considering different properties such as bead width, compressive strength, and tensile strength. However, due to existence of uncertainty sources in input parameters, material properties, and measurement instruments, it is very desirable to develop robust methods to deal with such uncertainties. In this paper, a multi-objective genetic programming algorithm integrating Monte Carlo simulations (MCSs) has been used for modeling and prediction of the bead width of prototypes in SLM process by taking into account probabilistic uncertainty in experimental data. The necessity of such probabilistic robust approach is shown by stochastic analysis and uncertainty quantification (UQ) of existing deterministic mathematical models in the literature. The objective functions that have been considered for multi-objective modeling process are the mean and standard deviation of the training errors, prediction errors, and the number of nodes which the latter is employed to use as a complexity index of the evolved GP-type models. The robustness of both deterministic and probabilistic models are compared and shown based on the cumulative distribution function (CDF) and probability density function (PDF) of statistical performance of objective functions. The results reveal that the suggested deterministic models in the literature are not trustworthy for practical usages due to large variations in objective functions while the model proposed by this study shows an acceptable robustness performance.