Uncertainty quantification for polymer micromilling force models using Bayesian inference

摘要

In the current work, we describe and evaluate the application of Bayesian inference to estimate and/or refine the mechanistic model force coefficients, as well as to quantify the uncertainties associated with the force coefficients in force models for polymer micromilling. Proper modeling of forces is important to optimize process accuracy and productivity, including characterizing stability of micromachining process. Although the precision of mechanistic models depends on the uncertainty of the force coefficients, these models are deterministic and do not take into account the uncertainty in the model parameters. Bayesian inference provides a formal framework to incorporate uncertainty into the model formulation. In this study, the posterior probabilities in each Bayesian update are estimated using a numerical Markov Chain Monte Carlo (MCMC) scheme, known as Metropolis-Hastings (MH) algorithm. To determine the starting point of Markov Chain, two different calibration approaches are first used to obtain the deterministic coefficients of the mechanistic model: genetic algorithm (GA) and nonlinear regression. The uncertainties in these coefficients are then evaluated using the Bayesian inference approach. For both of the cases, a uniform prior distribution is used. Finally, the uncertainty in coefficients is propagated into predicted micromilling forces to obtain the uncertainties in predicted forces. It is concluded that the presented approach is successful in uncertainty quantification of the force model coefficients for polymer micromilling and assessing their effect on forces with different calibration approaches.