BAYESIAN-ESTIMATION APPLIED TO EFFECTIVE HEAT-TRANSFER COEFFICIENTS IN A PACKED-BED

We present a Bayesian estimation framework for the analysis of data fr om ill-controlled experiments and apply it to the determination of mod el parameters for heat transfer in a packed bed. The Bayesian method i s a statistical procedure that allows the systematic incorporation and proper weighting of experimental data, prior knowledge of model and p arameters, and probabilistic models of sources of experimental error. The interplay of these elements determines the best model parameter es timates. Furthermore, because of its probabilistic structure, the meth od also characterizes uncertainty of the estimates in a natural way. F or our heat transfer problem, standard estimation techniques-were not adequate because they did not account for several important error sour ces. Our analysis explicitly accounts for three major experimental dif ficulties: (i) standard measurement error of thermocouples, (ii) uncer tainty in thermocouple (probe) positions, an error which is sensitive to temperature gradients, and (iii) an uncontrolled inlet temperature profile. This third error source introduces correlations between error s at different probes, and is modeled by solving a partial differentia l equation with a stochastic boundary condition. The results of this s tudy show the benefits of the Bayesian method in obtaining best parame ter estimates with narrow confidence regions. The methodology is quite general and can be applied to the systematic solution of difficult es timation problems in many fields, when sources of uncertainty can be i dentified and modeled.