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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decades fulfilling requirements of old reference codes. To mitigate the risk deriving from this state of the built infrastructures, an extensive structural assessment is needed. Mostly, this structural assessment implies intensive inspection activities, material tests (to reduce the influence of uncertainties) and a consistent number of simulations to compute probabilistic seismic demand models and fragility curves. Many authors in the related literature are focusing their research efforts on integrating Machine Learning (ML) probabilistic seismic assessment (Xie et al., 2020). For example, several studies investigate ML to configure surrogate demand models when dealing with classes of structures considering variability in structural characteristics (Du and Padgett, 2020; Guo et al., 2020; Lin et al., 2017; Mangalathu et al., 2019, 2018b, 2018a; Mangalathu and Jeon, 2019; Soleimani and Liu, 2022; Wang et al., 2021). Other studies extend the application of ML-based surrogate demand models to achieve multi-parameter fragility curves of specific bridge classes (Mangalathu et al., 2018a). While most of the research studies integrate ML-based strategy with the probabilistic seismic assessment of bridge classes, this paper explores the implementation of ML in bridge-specific applications. The use of ML algorithms is tested to predict the probabilistic seismic demand models of bridge substructure components (i.e., the displacements of the top of the piers) considering the knowledge-based uncertainty. In the adopted procedure, we train a Random Forest (RF) algorithm on the results of nonlinear time history analyses (NLTHA) performed considering many different predictors. Since NLTHA is the most time-consuming part of the whole probabilistic seismic assessment task, the investigation carried out in this study is targeted to test the potential of ML tools in reducing the analysis effort by surrogating NLTHA results. Therefore, the adopted methodology aims to compare the conventional procedure outlined in sub-section 3.2 Errore. L'origine riferimento non è stata trovata. based on NLTHA data, with an alternative approach exploiting the ML tools’ capability to partially surrogate data from NLTHA. Both quantities representative of the seismic excitations and the knowledge-based uncertainties are considered predictors. Preliminarily, we investigate their informative content, check their importance and select representative sub-groups to train the RF. With this phase, the explainability of the model is improved and the so- called “black box” effect, responsible for discouraging practitioners from using ML (Lin et al., 2017), is reduced. In the presented study, we test the proposed procedure with RF for a multi-span simply supported girder case-study reinforced concrete (RC) bridge which is representative of the most widespread bridge class in Europe. 2. Theoretical background This section briefly introduces the theoretical methods applied to perform the investigation. In particular, the conventional strategy for computing probabilistic seismic demand models along with a concise presentation of Random Forest is reported. This section also presents the methodology used in this study to integrate ML in the computation of probabilistic seismic demand models. Risk assessment of bridges requires fragility functions relating the probability of exceeding a given damage state with respect to a given value of seismic intensity measure (IM). Fragility functions can be analytically derived from probabilistic seismic demand models (Nettis et al., 2021a) expressing the probabilistic relationship between a selected engineering demand parameter (EDP) and an IM value. The EDP should represent the seismic demand of a given bridge (or single bridge component) with respect to a given damage state reflecting loss consequences in terms of e.g. repair cost or serviceability downtime for repairing. In structure-specific applications, probabilistic seismic demand models reflect the probabilistic relationships relating the EDP with respect to a given IM parameter by considering the (aleatoric) uncertainty related to record-to-record variability. The classical methodology assuming a power-law function between the median estimate of the EDP and IM is detailed in (Cornell et al., 2002). In case of incomplete initial knowledge level, probabilistic demand models should necessarily consider additional sources of uncertainty related to modelling, material or geometric parameters. RF algorithm for regression tasks builds on Regression Trees (RTs), which mainly consist of a set of conditions, rules or restrictions hierarchically organized. RTs are organized in nodes to which these conditions are applied: the starting node of the tree is the root node, while the terminal nodes are the leaves of the tree (Breiman et al., 1984). The rules (nodes) are built by selecting the dataset’s optimal splitting criterion, which implies the selection of an evaluation measure ( , ̂) for each splitting candidate, such as mean squared error or sum of squared residuals. The splitting criterion acts both on the selection of a feature, but also on the selection of the slitting point of that feature. Representing overfitting the most common pitfall of RT algorithms, RF overcome it by featuring an enhanced version of the Bootstrap Aggregation (Bagging) algorithm (Breiman, 1996): it combines (i.e., ensemble) numerous