Modeling and Comparing Vertical Density Profiles
Keywords:Vertical density profile, nonparametric regression, cubic spline, oriented strandboard, furnish moisture content, press closure rate
The vertical density profile of pressed wood panels is influenced by the manufacturing process and is important to panel end-users. Modeling the vertical density profile and making statistical comparisons among profiles resulting from different manufacturing treatments are critical to understanding and improving panel properties. Nonparametric regression analysis was used to model the vertical density profile of aspen (Populus tremuloides) oriented strandboard panels. A methodology is presented to compare vertical density profile curves. Twenty-seven laboratory panels were manufactured at 608 kg/m3 incorporating three levels of furnish moisture content (4%, 8%, 12%) and three levels of press closure rate (20 s, 60 s, 100 s) in a replicated, experimental design.
The nonparametric regression technique called cubic splines was used to fit the data, R2 ranged from 0.985 to 0.998. Detailed discussion is presented that describes the method and interpretation of the nonparametric regression analysis. Statistical comparison of vertical density profile curves among treatment levels revealed that the 4% furnish moisture content level was significantly different (P = 0.015) from the 8% and 12% levels; the 8% level was not significantly different (P > 0.99) from the 12% level. Vertical density profile curves for all press closure rate treatments were significantly different (P < 0.003).
Altman, N. S. 1992. An introduction to kernel and nearest-neighbor nonparametric regression. Am. Statist. 46(3): 175-185.nBolton, A. J., P. E. Humphrey, and P. K. Kavvouras. 1989. The hot pressing of dry-formed wood-based composites. Part VI. The importance of stresses in the pressed mattress and their relevance to the minimization of pressing time, and the variability of board properties. Holzforschung 43(6):406-410.nDraper, N. R., and H. Smith. 1988. Applied regression analysis, 2nd ed. John Wiley and Sons, Inc., New York, NY.nHardle, W. 1990. Applied nonparametric regression. Cambridge University Press, New York, NY. 333 pp.nHarless, T. E. G., F. G. Wagner, P. H. Short, R. D. Seale, P. H. Mitchell, and D. S. Ladd. 1987. A model to predict the density profile of particleboard. Wood Fiber Sci. 19(1):81-92.nKamke, F. A., and L. J. Casey. 1988. Fundamentals of flakeboard manufacture: internal mat conditions. Forest Prod. J. 38(6):38-44.nKamke, F. A., and M. P. Wolcott. 1991. Fundamentals of flakeboard manufacture: wood-moisture relationships. Wood Sci. Technol. 25:57-71.nKing, E., J. D. Hart, and T. E. Wehrly. 1991. Testing the equality of two regression curves using linear smoothers. Statist. Prob. Lett. 12:239-247.nLemaster, R., and A. Green. 1992. The use of air-coupled AE sensors to measure density profiles in wood-based products. NPA Pressline Technology Seminars. National Particleboard Association, Charlotte, NC. Pp. 65-69.nLaufenberg, T. L. 1986. Using gamma radiation to measure density gradients in reconstituted wood products. Forest Prod. J. 36(2):59-62.nMcfarland, D. L. 1992. Internal density variation of hot-pressed wood panels in response to changes in flake moisture content and press closure rate. M.S. thesis, Department of Forestry, Wildlife and Fisheries, The University of Tennessee, Knoxville, TN. 518 pp.nMilton, J. S., and J. C. Arnold. 1990. Introduction to probability and statistics: principles and applications for engineering and the computing sciences. McGraw-Hill Publishing Company, New York, NY. 700 pp.nSas Institute Inc. 1989. JMP User's guide, Version 2 of JMP. SAS Institute Inc., Cary, NC. 584 pp.nSas Institute Inc. 1993. User's guide for SAS/INSIGHT. SAS Institute Inc., Cary, NC. 368 pp.nSilverman, B. W. 1984. Spline smoothing: The equivalent variable kernel method. Annals Statist. 12(3):898-916.nSuchsland, O. 1962. The density distribution of flake-boards. Michigan Agric. Exp. Station, Michigan State University. Quart. Bull. 45(1):104-121.nWahba, G. 1979. How to smooth curves and surfaces with splines and cross-validation. Proc. 24th Conference on Design of Experiments. U.S. Army Research Office, Research Triangle Park, NC. No. 79(2):167-192.nWahba, G. 1985. A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem. Annals Statist. 13:1378-1402.nWahba, G. 1990. Spline models for observational data. Society for Industrial and Applied Mathematics, Philadelphia, PA. 169 pp.nWhittaker, E. T. 1923. On a new method of graduation. Proc. Edinburgh Math. Soc. 41:63-75.nWinistorfer, P. M. 1992. Pressing strategies. NPA Pressline Technology Seminars. National Particleboard Association, Charlotte, NC. Pp. 19-25.nWinistorfer, P. M., and W. W. Moschler, Jr. 1992. Monitoring changes in density of a wood particle mat during pressing. USDA National Research Initiative Competitive Grant No. 92-37103-8082.nWinistorfer, P. M., and W. W. Moschler, Jr. 1994. Measuring the vertical density profile in situ during pressing. In P. Steiner, ed. Proc. Second Pacific Rim Bio-Based Composites Symposium. University of British Columbia, Vancouver, Canada November, 1994.nWinistorfer, P. M., W. C. Davis, and W. W. Moschler, Jr. 1986. A direct scanning densitometer to measure density profiles in wood composite products. Forest Prod. J. 36(11/12):82-86.nWolcott, M. P., F. A. Kamke, and D. A. Dillard. 1990. Fundamentals of flakeboard manufacture: Viscoelastic behavior of the wood component. Wood Fiber Sci. 22(4): 345-360.nWright, S. P. 1992. Adjusted P-values for simultaneous inference. Biometrics 48(4):1005-1015.n
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