# Data-Driven Modeling Algorithms for Cable-Stayed Bridges Considering Mechanical Behavior
## 3 Algorithm of Digital Model Generation
### Concept Design Stage  
During the design of a bridge, design activities occur at various levels across different disciplines. Data-driven design tools support the early design by rapid development of the design variants. This new approach will replace the various one-to-many and many-to-one data exchanges in a design project [22]. The integration of design intention and efficient data sharing is achieved through a digital master model as a series of related and interconnected digital objects. Figure 6 presents a modeling process for the conceptual design of a cable-stayed bridge. Various alternatives can be chosen by the designer through the modeling algorithm including the expert's experience of the conceptual design process. Figure 5: Modeling algorithms and datasets for different phases. In a conceptual design stage of a cable-stayed bridge, various design alternatives, including the bridge alignment, are created and discussed in terms of the different aspects to satisfy the client's requirements. Bridge alignment is defined as an alignment model with reference coordinates at both ends of the bridge and surfaces with slope definition to ensure roadway alignment. These data are the main master information for the modeling algorithms with parent-child relations. The arrangement of span lengths is decided by a designer and the positioning coordinates for bridge substructures are derived from the algorithm. From the coordinates and the 3D alignment curve, the normal and tangential vectors are derived to define the reference points for the modeling of a pylon and piers, as shown in Figure 4a. Further, the algorithm also enables a designer to add constraints on the digital models for strict design requirements, such as bridge clearance. Considering the thickness of the pavement, in addition to the height of the stiffening girder and bearing, the reference coordinates for the pylon and piers are defined. Thereafter, the position lines are defined to generate the substructures with different section profiles. Each location with the section change is defined as the position coordinates. The algorithm for each object uses a relative coordinate system (RCS), while the entire bridge has an absolute coordinate system (ACS). The reference position of a bridge will change the RCS of each object into an ACS for a roadway. The angles between the alignment of the superstructure and the substructures are considered in the algorithm to rotate the section of the substructure along the reference lines, as shown in Figure 4b. Through this process, the basic conceptual design model is generated. The main parameters of a stiffening girder in the conceptual design stage are the type, depth, width, and slopes. The stiffening girder has typically different sections at the supports, pier table, and anchorages. The algorithm includes parameters to define the sectional changes along the length of the bridge. For the local coordinates for the generation of the stiffening girder, the Y axis is along the bridge, the X axis is along the transverse direction of the deck, and the Z axis is along the elevation. The planes for the definition of the girder are defined by the local coordinates. Each dimension of the girder is considered as the parameters to generate the digital model in the algorithm. When the digital objects  
Figure 6: Modeling algorithms for concept design process. are combined to build a total bridge model, the section in the local coordinates will rotate, considering the relative angles with respect to the global coordinates of the bridge. In the stiffening girder, there are cable anchorages that are determined by the number of cable planes and cables. Some parts, such as in the pier table, are the key segments that do not have the anchorage details. The spacings of the cable are determined by the main parameters in the algorithm. For the case of the requirement of additional cables, such as for the back-stay cables and in the case of an uneven arrangement, the algorithm also functions to add more cables.