PSI - Issue 84

Stefano Bozza et al. / Procedia Structural Integrity 84 (2026) 852–858

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Since carriageway narrower than 6m shown outlier values compared to the rest of the datasets, geometries with deck width equal to 8 m and sidewalks width equal to 1.5 m are discarded from further analyses, reducing the size of the dataset from 42480 to 39647 cases. 2.4. Fitting functions In order to provide a tool for preliminary assessment of existing bridges, different functions were fitted to the data obtained by the parametric analysis described. Since, according to Bozza et al. (2023), the bridge span seems to be one of the most influent parameters on the ratio between bending moments induced by outdated traffic load models and by D.M. 2018 traffic load model ( ρ hereafter), the span length L is assumed as the independent variable. To keep the fitting model as simple as possible, only four fitting functions were considered, with at most five parameters: a linear model (LI), a quadratic model (Q), a cubic model (C), and a bi-linear model (BL). The analytical expressions of the investigated models are: ( ) = 0 + 1 (LI) (2) ( ) = 0 + 1 + 2 2 (Q) (3) ( ) = 0 + 1 + 2 2 + 3 3 (C) (4) ( ) = 0 + 1 + 2 ∙ | − 3 | (BL) (5) Where is the deck span and 0 , 1 , 2 , 3 are model parameters that have to be calibrated on the data obtain by the parametric study previously described. Note that equation (5) is equivalent to: ( ) = {( 0 + 2 ∙ 3 )+( 1 − 2 ) ≤ 3 ( 0 − 2 ∙ 3 )+( 1 + 2 ) > 3 (6) The model parameters were fitted to the datasets minimizing the quadratic deviation, using the optimize.minimize function of the scipy Python package (Virtanen et al. (2020)). In order to choose the best fitting model, the Bayesian Information Criteria (BIC) (Schwartz (1978)) was used, and coefficients of determination R 2 and the mean absolute error ̅ were also compute to measure the goodness of fit of the calibrated models. 3. Results and discussion In Figure1 both datasets and best models are graphically represented, while Table 1 the fitted parameters of the best model the coefficient of determination R 2 and the mean absolute error ̅ are reported for each regulation and bridge class considered. The bi-linear model was indicated as the best model in all regulations and bridge classes, with the only exception of first class bridges of D.M. 2005, for which the cubic model performed a better BIC score. However, in most cases the quadratic, the cubic and the bi-linear model shown very close goodness of fit, while the linear model scored worse than the others in most of the case considered. The best fitting results were obtained for D.1933 and D.M.2005 first class bridges, with coefficient of determination R 2 about 0.97 and mean absolute error about 0.01 in both cases. Thus, the bridge span is the main parameter related to the ratio ρ and the fitted models can be used to perform a fast preliminary assessment with good reliability. Overall, high coefficients of determination were obtained for regulations issued before 1980 and for D.M. 2005, with R 2 values at least equal to 0.74, showing a good agreement between the whole datasets and the fitted models. The mean absolute error ranges between 0.006 and 0.025, with usually higher values for second class bridges (more scattered data) compared to first class ones (less scattered data), with the exception of C. 1945, which first class bridges are comparable with second class bridges of C. 1962.