# A Novel Decision Support System for Long-Term Management of Bridge Networks
## 2 Materials and Methods
### Adaptive Bridge Decision Ranking
The resultant score will give the sufficiency rating that could be used for ranking bridges for infrastructure management (priority ranking if the resultant score is subtracted from 100). First, the structural adequacy score is calculated by subtracting the score reductions from the overall condition rating and load capacity. The attained Rating Factor (RF) value from the load-rating test is input in Equation (2) to find the safety score S\({}_{1}\)[48]. \[\text{S}_{1}=55-(32.4-\text{RF})^{1.5}\times 0.3254-\text{CR}. \tag{2}\]  
Safety score S\({}_{1}\) cannot be less than zero and larger than 55. CR indicates the condition reduction for the lowest condition rating of the bridge components. The condition rating \(r\) in the scale of 0-9 is found, as discussed by [PERSON] (2008). The study proposes a translation from element condition ratings to NBI's component ratings [49]. Thus, the value of CR is determined for varied conditions as follows:  
* Critical condition and worse (r < 2) \(\rightarrow\) CR = 55;
* Serious condition (r = 3) \(\rightarrow\) CR = 40;
* Poor condition (r = 4) \(\rightarrow\) CR = 25;
* Fair condition (r = 5) \(\rightarrow\) CR = 10. Serviceability score S\({}_{2}\) in Equation (3) is calculated based on the geometry of the structure, deck condition, structural evaluation, average daily traffic, and structure type. \[\text{S}_{2}=30-[\text{SR}+\text{RS}+\text{VC}]. \tag{3}\]  
Serviceability score S\({}_{2}\) cannot be less than zero and larger than 30. SR indicates structural rating in which the rating scores from deck condition, structural evaluation, deck geometry, underclearances, waterway adequacy, and approach road alignment are summed. The total reductions in the structural rating cannot be greater than 13%. RS is determined based on the roadway sufficiency, which is calculated using average daily traffic (ADT) and road width. The per lane averages of ADT and road width are used as reference values to determine the score reduction. Finally, vertical clearance (VC) is another rating parameter for serviceability. For insufficient vertical clearance, a score reduction of 2% is applied. The detailed calculation steps of these reductions are explained in the FHWA's appraisal guide in Appendix D [48]. Bridge importance score S\({}_{3}\) is calculated based on the average daily traffic value (ADT), detour length (DL), and S\({}_{1}\) and S\({}_{2}\), as in Equation (4). \[\text{S}_{3}=15-\left\{15\left[\frac{\text{ADT}\times\text{DL}}{320,000\times \frac{\text{S}_{1}+\text{S}_{2}}{85}}\right]+2\right\}. \tag{4}\]  
Bridge importance score S\({}_{3}\) cannot be less than 0 and more than 15. In addition, there is also a special reduction score S\({}_{4}\), which is calculated based on detour length, structure type, and traffic safety features of the bridge, as shown in Equation (5). \[\text{S}_{4}=\left(\text{DL}^{4}\times 7.9\times 10^{-9}\right)+\text{STR}+ \text{TSR}. \tag{5}\]Special reduction score S\({}_{4}\) cannot be less than 0 and more than 13. The FHWA's bridge appraisals guide defines the structure type reduction STR as 5% for the structure types 10, 12, 13, 14, 15, 16, or 17; and the traffic safety reduction TSR as 1-3% based on the number of available traffic safety features (i.e., transitions, approach guardrail, and guardrail end) [48]. Decision ranking (DR) score extends the NBI's sufficiency rating in the way that it takes life cycle cost (LCC) into account and also offers flexibility to infrastructure owners' decision practice. The resultant score is calculated by summing individual scores that are adjusted by the weight factors w\({}_{1}\), w\({}_{2}\), w\({}_{3}\) and w\({}_{4}\), and multiplying it by the bridge value index (VI). VI considers the life cycle cost of the bridge in the decision ranking, as explained further in Equation (7). The default values of the weight factors are equal to 1.0. w\({}_{1}\) is calibrated based on the current and predicted future Health index.