Characterizing uncertainty through Bayesian hierarchical models in structural engineering : new approaches for characterizing the tensile strength of lumber based on a spatial distribution of knots

Knots are common characteristics of sawn lumber that can adversely affect its strength properties. Clusters of knots and knots adjacent to each other are known to have combined lumber strength-reducing effects. However, grading rules that stipulate the allowable sizes and distances among distinct knots are somewhat qualitative and subjective, as the spatial interaction of knots and their resulting relationship to strength properties are not fully understood. This thesis’s objective is to investigate and quantify the strength-reducing effects of the spatial distribution of knots on Douglas Fir (DF) lumber, via high-resolution scans of its surfaces. A new approach for modelling lumber strength is proposed with an important extension that incorporates all relevant knot information, rather than a single strength-reducing knot. To complete the dataset needed for the new approach, we identify the spatial locations and sizes of the knot faces for individual lumber specimens using the knot detection and localization algorithms developed concurrently. The knot matching algorithm recently developed in our lab is used to reconstruct the knots’ internal three-dimensional structures. Non-destructive testing is conducted to obtain the transverse vibration measurement of Modulus of Elasticity (MOE). The destructive strength testing is then carried out to each specimen to obtain the strength measurement of its ultimate tensile strength (UTS) with the mode and location of failure recorded. We adopt the Bayesian approach to handle the model inference problem. The fitted model provides a predictive distribution for lumber tensile strength that accounts for the spatial distribution of knots and their strength-reducing characteristics. The efficacy of the approach is demonstrated via simulation studies and then applied to the data collected by testing a sample of 113 DF lumber specimens. The predictive performance of the model is investigated, and comparisons are made to the baseline regression models. The insights gained on the strength-reducing effects of knots and their spatial locations are described. We then discuss how the new approach could contribute to the improvement of lumber grading practices.Science, Faculty ofStatistics, Department ofGraduat