# A Novel Decision Support System for Long-Term Management of Bridge Networks
## 2 Materials and Methods
### Adaptive Bridge Decision Ranking  
For optimal bridge management, it is very important to make network-level decisions that take into account all bridges in a transportation network. There is always limited capital to be spent in maintenance and repair. Therefore, the bridges have to be prioritized based on their importance and the capital needs for improvement. In the proposed decision support methodology, all bridges in a defined transportation network are ranked according to a wide range of criteria such as past inspection history, average daily traffic, number of alternative routes, condition growth rate, and life cycle cost. The ranking methodology also accounts for the available maintenance budget and allowed timeline as these external factors will also have a significant impact on the decision making. Due to the complexity of optimizing the decisions within a large number of ranking criteria, a deep learning-based model was used in this study to tackle the multivariate problem in the groupwise scoring. To develop and train the model, TF-Ranking, a scalable deep learning library recently published by the Google TensorFlow team was used [43; 44]. The same ranking model was already deployed in Google's major software platforms such as Google Drive and Gmail [45]. The proposed TF-Ranking model for bridge prioritization first inputs the multivariate data in Library for Support Vector Machines (LBSVM) format [46]), then extracts features from each decision ranking criteria (i.e., factors affecting the bridge prioritization such as structural condition, repair cost, importance of location, life cycle cost, etc.). From these extracted features, a scoring function is created in the hidden layer of the neural network. During training, the weights of the scoring function are optimized using Softmax Cross Entropy, a commonly used listwise loss metric. Finally, the model is served in the SageMaker to make predictions from the raw data entries. Figure 11 describes the TF-Ranking model used in the proposed decision support system. The major challenge in deep-learning-based ranking models for infrastructure decision making is the unavailability of supervised training data. These data would require example rankings prepared by a large number of inspectors from many different bridges. Therefore, a different strategy was followed in this study to generate the necessary training data. The TF-Ranking model was initialized by training with an artificial dataset. First, the bridges are scored based on the factors affecting the maintenance decision. The scoring method uses NBI's sufficiency rating as the basis but extends the ranking to include also bridge  
Figure 11: TF-Ranking model to prioritize bridges based on multi-criteria decision factors [44] (the prepared training data are fed into the model, deep features of ranking create a scoring function, and the model is evaluated using the defined loss metrics. Lastly, the trained model is served, and ranking scores are predicted from the input raw data). life cycle cost, current health index calculated from NDE, future predicted health index, and available maintenance/repair budget. The scored bridges are used as initial training data for the TF-Ranking model. However, the model will not learn the covariate features in the bridge prioritization since the scoring was made independently for bridges. Therefore, the model needs to be fine-tuned via incremental learning. As inspectors use the decision support system, the inspector's alterations in the prioritizations are used as finetuning data. The system will then gradually improve and adapt the infrastructure owner's practice. The sufficiency rating in NBI's bridge appraisals receives input from local and global assessments as well as some additional parameters [47]. Similarly, the appraisals of bridges in this study are carried out by scoring the bridges in three categories: safety, serviceability, and essentiality. After the scores in these categories are summed, special reductions are made.