## 3 Methodology
### Formulation of Measurement
#### 3.3.4 Computing Number of Maintenance  
To identify the maintenance events within each bridge's time-series data of deck condition ratings, each bridge deck condition rating is described in the NBI recording guide [17] in Table 4, we adopted a Bridge Intervention Matrix (BIM) to map improvement in condition ratings to its appropriate intervention. The implemented BIM in this study is based on the matrix first implemented by [PERSON] et al. [13] and was customized for the maintenance patterns in Nebraska. Under the guidance and discussion with a subject matter expert from the Nebraska Department of Transportation (DOT), the intervention criteria described in Table 5 were implemented in the new BIM. Table 6 describes the entire BIM used for this study.  
Considering the Bridge Intervention Matrix (BIM), we encounter three potential categories of bridge intervention. However, in our modeling approach, we simplify the prediction task by transforming it into a binary classification problem. Bridges that exhibit any form of observed maintenance are encoded as \"intervened\" or \"yes\". In contrast, bridges that show no indications of intervention or maintenance are encoded as \"non-intervened\" or \"no\".  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & & \multicolumn{8}{c}{**To Condition**} \\ \hline  & & **9** & **8** & **7** & **6** & **5** & **4** & **3** & **2** & **1** \\  & **9** & N & & & & & & & & \\  & **8** & Var & N & & & & & & & \\  & **7** & Rep & Var & N & & & & & & \\  & **6** & Rep & Rep & Var & N & & & & & \\  & **5** & Rab & Rep & Rep & Var & N & & & & \\  & **4** & Rec & Rec & Rab & Rep & Var & N & & & \\  & **3** & Rec & Rec & Rab & Rep & Par & N & & & \\  & **2** & Rec & Rec & Rab & Rep & Rep & Rep & N & \\  & **1** & NA & NA & NA & NA & NA & NA & NA & NA & NA & N \\ \hline \hline \end{tabular}
\end{table}
Table 6: Bridge Intervention Matrix (BIM) maps the improvement in bridge condition ratings to the possible bridge intervention. The abbreviations used in this table are explained in Table 5 above.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Rating** & **Description** \\ \hline N & Not Applicable \\ 9 & Excellent Condition \\ 8 & Very Good Condition \\ 7 & Good Condition \\ 6 & Satisfactory Condition \\ 5 & Fair Condition \\ 4 & Poor Condition \\ 3 & Serious Condition \\ 2 & Critical Condition \\ 1 & Imminent Failure Condition \\ 0 & Failed Condition \\ \hline \hline \end{tabular}
\end{table}
Table 4: Bridge deck condition ratings as described in NBI Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation’s Bridges [17].  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Type** & **Abbreviation** & **Criteria** \\ \hline Repair & Rep & If deck transition within 4 condition ratings \\ Rehab & Rab & If deck goes from 4 or 5 (or less) to 8 or 9 \\ Replace & Rec & If deck all goes from 4, 5, or 6 to 8 or 9 \\ Not applicable & NA & These bridges do not exist \\ Inspection variance & Var & Allowable inspection tolerance is 1 NBI condition code \\ None & N & No change in deck condition ratings \\ \hline \hline \end{tabular}
\end{table}
Table 5: Description of maintenance intervention and abbreviation.