Simulation of the Localized Modulus of Elasticity of Hardwood Boards by Means of an Autoregressive Model

Abstract

An autoregressive (AR) model for the simulation of modulus of elasticity (MOE) fluctuations along hardwood boards without pronounced knot periodicity is presented. The model is calibrated based on contiguous, localized (100 mm gauge length) empirical MOEs from European white oak boards. The calibration involves the computation of the sample autocorrelation function (SACF). For this computation, the stationary data resulting from a two-step transformation method are used: (1) first, board-internal MOE normalization suppresses the interboard bias; and (2) the rather left-skewed normalized data are described by a log-gamma distribution, which is then mapped to N(0,1) to obtain the needed stationary data. A first-order AR process suffices to accurately describe the data and is thus used as a basis to simulate MOE profiles, followed by the sketched transformation procedure in reverse order. The quality of the simulated MOE profiles and of the methodological approach is shown by comparison with the experimental MOE profiles. It was found that the simulation model correctly reproduces the statistical information of the MOE variations while also producing very plausible profiles, with similar characteristics as the empirical MOE profiles. This model can be used to better study the size effect of glued-laminated timber by means of numerical simulations.