A Nonlinear Regression Technique For Calculating the Average Diffusion Coefficient of Wood During Drying


  • Perry N. Peralta
  • Audimar P. Bangi


Diffusion, drying, diffusion coefficient, Fick's law, nonlinear regression, least-squares method


A nonlinear regression technique for determining the optimum drying diffusion coefficient of wood is described. This technique uses the least squares principle to estimate the diffusion coefficient in the infinite Fourier series solution to the one-dimensional unsteady-state form of Fick's law. Five different nonlinear iteration methods for solving the normal equations were evaluated in terms of their ability to find a solution, the rate of convergence, and sensitivity to the parameter's starting value. Application of this technique to a series of experimental isothermal drying runs involving red oak (Quercus rubra) resulted in a better fit between the actual and predicted drying curves, as compared to the logarithmic, square-root, and half-E techniques. The technique yielded diffusion coefficients and residual sum of squares that were almost identical to those obtained from a Fortran-based optimization method reported by Chen et al. (1994). However, the technique described in this paper is more computationally efficient by converging to a solution in a fewer number of iterations than the optimization method.


Bates, D.M., and D.L. Watts. 1981. A relative offset orthogonality convergence criterion for nonlinear least squares. Technometrics123:179-183.nChen, Y., E.T. Choong, and D.M. Wetzel. 1994. Optimum average diffusion coefficient: An objective index in description of wood drying data. Wood Fiber Sci.26(3):412-420.nCrank, J. 1975. The mathematics of diffusion. 2nd ed. Oxford University Press, New York, NY.nFletcher, R. 1980. Practical methods of optimization. 2nd ed. John Wiley & Sons, New York, NY.nGallant, A.R. 1987. Nonlinear statistical models. John Wiley & Sons, New York, NY.nSAS. 1999. SAS/STAT User's Guide: version 8. SAS Institute Inc., Cary, NC.nSiau, J.F. 1995. Wood: Influence of moisture on physical properties. Department of Wood Science and Forest Products, Virginia Polytechnic Institute and State University, Blacksburg, VA.nStamm, A.J. 1964. Wood and cellulose science. The Ronald Press Company, New York, NY.n






Research Contributions