Predicting mechanical properties of timber elements by regression analysis considering multicollinearity of non-destructive test results


Sousa, Hélder S.; Branco, Jorge M.; Machado, José S.; Lourenço, Paulo B.

Timber elements; Non-destructive tests; Regression analysis; Multicollinearity

Introduction: Information retrieved from different sources, which are necessarily uncertain to some extent, must be compiled to have a reliable assessment of a timber element. Means to obtain information are often limited to non or semi destructive tests. Therefore, the available information is an indi-rect measurement of the element’s mechanical properties, and are incomplete predictors if not complemented with more data. In that scope, data is commonly added using different predictors in a regression analysis. If the predictors themselves are uncorrelated, the determination coeffi-cient, R2, is directly related to the measure being explained. However, predictors are usually cor-related and thus multicollinearity exists. In extreme cases, multicollinearity results in imprecise and unstable R2, thus the relative importance among predictors is not accurately measured.Developments: Inclusion of all predictors in a regression model, is typically impeded by high multicollinearity. Estimation of a predicted variable, using all combinations of explanatory predictors, may be un-feasible when the number of predictors is large, thus it is important to assess which are the most influent. This paper discusses the application of multiple regression analysis for prediction of properties of timber elements, using adjusted R2 depending on the number of predictors and the contribution of each predictor measured by Shapley value regression procedure. Data of a multi-scale experimental campaign on chestnut timber elements was used accounting correlations of non-destructive tests with mechanical properties and differentiation by visual grading.Conclusion: By measuring the relative importance of a predictor, it was showed which can be used for the as-sessment of existing timber elements, thus allowing for a more reliable assessment within a safety analysis of a timber structure.