A Bayesian Conjugate Model for the Estimation of Friction Intensity

Abstract

This paper addresses the Coulomb dry friction force as a technical indicator for fast and efficient condition-based maintenance. To estimate the value of friction force, the Bayesian analysis is used. Instead of the complex Markov Chain Monte Carlo numerical method, a closed-form analytical solution is applied. Thus, a simple and efficient procedure for friction estimation is described. Such a solution in the Bayesian context is known as the conjugate prior. The procedure presented here is verified numerically and experimentally by directly comparing the estimated value with the measured one. Two families of conjugate priors, the gamma-exponential and the normal-gamma, are compared. It is shown that the latter is suitable for friction estimation. An additional parameter, the precision parameter, was proposed as a criterion for the acceptance of estimation.