Multiple parameter determination in textile material design:A Bayesian inference approach based on simulation

A mathematical model of heat-moisture transfer within textiles and a corresponding inverse problem of textile material design (IPTMD) are reformulated. A stability theorem for the forward problem is given to show wellposedness of the heat-moisture transfer model. A Bayesian inference approach is presented to solve the IPTMD based on thermal comfort of clothing. The triple parameters (thickness, thermal conductivity, porosity of textiles) are simultaneously determined in the sense of the statistical point estimation by the likelihood function. The Bayesian techniques based on Markov chain Monte Carlo (MCMC) methods are employed to simultaneously determine three parameters in IPTMD, where the Metropolis-Hastings algorithm is applied in the inversion process. The interpolated likelihood function reduces significantly the computational cost associated with the implementation of MCMC method without loss of accuracy in the parameters estimation. Numerical experiments confirm that Bayesian inference method can provide more accurate solutions to the IPTMD.