Evaluation of Petty's nonlinear model in wood permeability measurement

To calculate the effective radii of two conductive elements in series in wo od specimens by using the gas permeability measurement, the four parameters from the curvilinear relationship of superficial specific permeability aga inst reciprocal mean pressure as illustrated in Perry's model must be evalu ated. This paper describes a detailed procedure for obtaining such paramete rs by using the least-squares fit calculated from a statistical analysis sy stem (SAS) program. Three different iterative optimization algorithms and s tarting points were used separately to fit the Petty's nonlinear model base d on the same experimental data from one specimen of birch. The estimate of the parameters: A = 35.38 darcy, B = 80.51 darcy, 1 = 0.19 darcy atm, m = 6.34 darcy atm was recommended for the fitted model. Compared to the result s on the estimate of parameters obtained in the previous papers, this estim ate for the parameters was a global minimum, thus it was a refinement and m ore accurate. Since the Gauss-Newton method resulted in almost the same con vergence results for all the three sets of starting values with the least i terations in the evaluation, it was the preferred optimization algorithm bo th for simplicity and accuracy in solving the Petty's model. Because the sa me solutions for all three iterative optimization algorithms were obtained by using two different sets of starting points produced from the grid searc h, a grid search seemed to be very helpful for finding reasonable starting values for various iterative optimization techniques.