Uncertainty associated to regression models used for assessing the stiffness of structural timber elements

Abstract

The evaluation of the mechanical behaviour of timber beams or glued laminated timber lamellas in-service are generally a difficult task due to the different sources of uncertainty involved (small knowledge about the initial quality of timber, small samples, models uncertainty, human errors). The use of statistical methods that can incorporate part of the uncertainty are probably a suitable way to ensure that the predictions made could provide a reliable prediction of the desired property. In most situations while performing in situ assessment of timber structures, the application of non or semi-destructive testing (NDT or SDT) methods relies on regression linear models showing no-ticeable different coefficients of determination. Another source of uncertainty happens when mak-ing in-situ testing relying on the application of existing regression models to timber members with-out being sure about the wood species or the origin of the wood species. Can these models be used when it is commonly accepted that knowledge on timber’s origin and species have a major impact on the capability to predict strength and stiffness? To comply with uncertainty several studies have been trying to use statistical methods that can incorporate prior information (e.g. Bayesian meth-ods) or uncertainty (e.g. Markov chain Monte Carlo - MCMC). In the present paper uncertainty associated to the use of linear regression models are discussed using as example the prediction of static modulus of elasticity from dynamic modulus of elasticity. For that purpose, data taken from literature and from studies conducted at LNEC are compared, analysed and discussed having in mind to verify the utility of the application of Bayesian linear re-gression approach and Monte Carlo Markov Chains (MCMC) estimation.