The bracing components in steel I-girder bridge systems are essential structural components for the bridges to restrain their rotation due to lateral torsional buckling (LTB). Current design specifications require bracing components to be installed to prevent I-girder sections from unexpectedly twisting due to instability. To estimate the bracing internal forces acting on the bracing elements, we can use approximate design equations that provide considerably conservative design values. Otherwise, it is necessary to conduct a thorough finite element analysis considering initial imperfections to obtain accurate bracing internal forces in the steel I-girder bracing systems. This study aims to provide estimation models based on deep neural network (DNN) algorithms to more accurately estimate the internal forces acting on the bracing element compared with the current design methodology when LTB occurs. This is conducted by constructing structural response data based on the geometrically nonlinear analysis with imperfections to provide accurate bracing internal forces, namely bracing moments ($M_{br}$) and bracing forces ($F_{br}$). To propose prediction models, 16 input and three output variables were selected for training the structural response data. Furthermore, a parametric study on the hyperparameters used in DNN models was analyzed for the number of hidden layers, neurons, and epochs. Based on statistical performance indices (i.e., RMSE, MSE, MAE, and R²), the estimated values using DNN models were evaluated to determine the best prediction models. Finally, DNN models that more accurately estimate internal forces ($M_{br}$, $F_{br}$) in bracing elements, and that provide the best prediction results depending on hyperparameters (numbers of hidden layers, neurons, and epochs), are proposed.

Horizontally curved I-girder bridges are known to be complex. Bending and torsion forces are imposed on the bridges owing to their shapes with initial curvatures. This torsion is a combination of pure and warping forces. The horizontally curved I-girder is significantly affected by warping behavior, which decreases the bending rigidity of its member. To investigate the warping behavior of the horizontally curved I-girder bridges a finite element analysis (FEA) must be performed. In this study, an FEA was performed to investigate the warping torsional behavior of a horizontally curved I-girder bridge, and a structural response database was obtained. Based on the database, the least absolute shrinkage and selection operator was employed to select features affecting the warping behavior. Subsequently, deep neural network models were trained with selected features for an input layer and maximum lateral flange moment data for an output layer. Several models were constructed and compared according to the number of hidden layers and neurons, and the model with the highest performance was proposed. Finally, it was confirmed that the estimated lateral flange moments computed by the proposed model showed a good correlation with the FEA results.

Finite element analysis requires the construction of a model that accurately reflects the structural characteristics of a target structure. Such models must incorporate precise material and geometric properties. However, discrepancies often arise between the properties assumed during the design phase and those observed in the actual structure. To address this, the models are iteratively updated using real measurement data, minimizing the errors between measured and analytical results. This process, however, can be time-consuming, particularly for complex structures. In this study, we propose a novel approach to directly estimate the parameters of a finite element model by utilizing the modal information from the structure, including natural frequencies and mode shapes. Our algorithm integrates a deep neural network that effectively solves complex problems using a convolutional neural network that captures the relationships between the nodal data and modes. Verification using a beam model demonstrated that the proposed methodology successfully updated the finite element analysis model to accurately match the target modal information.