BAYESIAN UPDATING USING THE MARKOV CHAIN MONTE CARLO METHOD TO DETERMINE FORCE COEFFICIENTS IN END MILLING

摘要

Bayesian updating of the force coefficients using the Markov Chain Monte Carlo (MCMC) method was presented. The single component Metropolis Hastings algorithm of MCMC was used. Bayesian inference provides a formal way of belief updating when new experimental data is available. Bayesian updating gives a posterior distribution that incorporates the uncertainty in variables as compared to traditional methods like the linear regression which give a deterministic value. By combining prior knowledge and experimental results, Bayesian inference reduces the number of experiments required for uncertainty quantification. Using Bayesian updating, a single test can give a distribution for force coefficients. The posterior distribution samples provide the covariance of the joint distribution as well. Experimental milling results showed that the linear regression approach did not give consistent results at 50% RI due to a poor quality of fit in the x direction mean forces, whereas Bayesian updating yielded consistent results at both radial immersions tested. Also, since Bayesian updating does not rely on a least squares fit, mean force data at different feed per tooth values is not required.