Inversion of micromechanical powder consolidation and sintering models using Bayesian inference and genetic algorithms

Abstract

It is shown that a genetic algorithm (GA) is in fact a Bayesian inference engine and as such the tools of Bayesian analysis can be applied to the output of a GA to rectify a number of deficiencies in the overall GA technique. In this work, the Bayesian enhanced GA addresses the inverse and ill-posed problem of optimizing the parameters of the micromechanical powder densification models for beryllium and copper powder using limited and uncertain data sets that leave the optimization problem underdetermined. The advantages of using the Bayesian approach to analyse GA output are described in detail. Firstly, the stochasticity of the GA is suppressed and thus a realistic assessment of model parameter sensitivity and covariance becomes available. Secondly, a suitable stopping criterion for the GA is defined by when the sum of the eigenvalues obtained from the principal component analysis of the a posteriori covariance matrix reaches a limiting value. Lastly, the generation of the posterior probability density allows a distribution of optimal model parameter vectors to be applied to the physics of the forward problem. The distribution of the resulting outcomes is then used as a guide in experimental design.