PSI - Issue 62

Fabio Parisi et al. / Procedia Structural Integrity 62 (2024) 701–709 F. Parisi et al. / Structural Integrity Procedia -- (2024) _ – _

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absolute errors ( ae = max( ) ) are reported.

Table 5. Metrics of performance of prediction for the EPDs of P3 and P4. Metric P3 P4 R 2 0.984 0.976 mae [m] 0.0076 0.0063 sae [m] 0.764 0.628 ae max [m] 0.052 0.053

Figure 5. Performance of RF in predicting the EDPs 3 of the pier P3: predicted values 3̂ over real values 3 .

Figure 6. Performance of RF in predicting the EDPs 4 of the pier P4: predicted values 4̂ over real values 4 .

5.2. Probabilistic seismic demand models Probabilistic seismic demand models can be derived by using and ′ dataset mentioned in Section Errore. L'origine riferimento non è stata trovata. . The use of a partially generated datasets implies benefits in terms of computational effort with respect to dataset entirely generated by means of NLTHA. In addition, ML can be also efficiently used to assess variations in probabilistic seismic demand related to the uncertain structural parameters. This can be exploited by analysts in case of incomplete knowledge to investigate the impact of given uncertain structural parameters of seismic performance/fragility and to address inspection plans. For example, Errore. L'origine riferimento non è stata trovata. illustrates the variation of the power-law models by varying : the power-law models predicted by using NLTHA and the RF-based partially surrogated datasets. The value of PGV is used as IM. Errore. L'origine riferimento non è stata trovata. a and Errore. L'origine riferimento non è stata trovata. b show that the RF can be used to achieve accurate power-law models and, therefore, can accurately estimate the median seismic demand with respect to NLTHA. Those results offer preliminary observations on the accuracy of partially surrogated probabilistic seismic demand models. However, it is worth mentioning that further comparisons should aim to assess the accuracy of ML and RF based probabilistic seismic demand models considering the errors in fragility and risk estimations. 6. Conclusion In this study, a procedure integrating ML algorithms in the field of fragility and risk assessment of bridges was introduced. It was tested to predict the probabilistic seismic demand of substructure components considering the knowledge-based uncertainty. The procedure presented consists of subsequent steps. First, a seismic demand dataset was developed by performing 5000 nonlinear time history analyses. The dataset was then properly partialized, and a small portion was used to study the feature importance and train a Random Forest algorithm as regressors to predict the seismic demand (i.e., the transverse displacements of the top of the piers). The RF was used to generate data configuring a new dataset. To conclude, both the original and the generated ones were used to fit the power-law relationships that were compared. The approach proposed is applied to a case-study reinforced concrete multi-span simply supported girder bridge. The feature importance and selection phase highlighted the poor performance of the permutation importance strategy and the need for further investigation for feature selection, such as hierarchical clustering. Preliminary results in terms of probabilistic seismic demand models discuss the accuracy of the ML tools in predicting the power-law models. In conclusion, in this study, RF showed its potential in surrogating the proper portion of the original dataset. Those results offer preliminary observations on the potential of the procedure proposed in diminishing considerably the non-linear time history analyses required for the risk assessment of such a class of bridges. Further investigations should be aimed at evaluating the accuracy of the approach in fragility estimates considering other bridge structural