# Bridge Health Monitoring Using Proper Orthogonal Decomposition and Transfer Learning
## 5 Results and Discussion
### Scenario 3: DL and DI Unknown  
The effectiveness of JDA-kernel was examined using the entire dataset by simultaneously varying loads, DL, and intensity. Categorization was performed for various DIs, and results are shown in Figure 8 for all models. When compared to the previous two scenarios, prediction error associated with each model increased due to an increase in the number of unknown variables. It was observed that JDA-kernel performance with respect to damage label prediction improved in higher DIs. It was of interest to compare using JDA-kernel for TL against using KNN without TL for each target model, because this comparison demonstrates the successful effect of JDA-kernel caused by mapping the transfer components from source to target domain on TL performance. Results of the comparisons are shown in Table 6, and significant improvement in prediction accuracy was observed in the JDA-kernel TL method. The runtimes are also reported in Table 6. It is noted that JDA-kernel requires several iterations to improve the performance.  
Figure 7: Confusion matrix for model \(M_{1}\) as target at DLs (**a**) 3, (**b**) 8, (**c**) 13, and (**d**) 18 (see Figure 1b).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**DL** & **Accuracy, Test Data (\%)** & **Accuracy, Entire Data (\%)** \\ \hline
3 & 82 & 81 \\
8 & 81 & 88 \\
13 & 88 & 93 \\
18 & 85 & 89 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Accuracy results for coupled POD JDA–kernel, Target: \(M_{1}\).  
The JDA-kernel TL method utilized a set of simulated experiments from a modeled bridge developed from a tested steel railway truss bridge, with experiments including different levels of uncertainty, to develop a TL-coupled POD framework for damage identification. A previously published POD-based approach for damage identification was used to extract POMs as damage features from each model [22]. The accuracy of the proposed approach was assessed using confusion matrices for predicted labels in each target model.  
Findings indicated that:  
* TL successfully identified DL labels for each target model. Label identification was less accurate at locations with similar POMs.
* TL was shown to be an effective method for identifying the DIs for the bridge and MUs that were studied. As expected, TL method accuracy improved at larger DIs.
* Live load position influenced TL method effectiveness, with more effective DI identification occurring in close proximity to loaded tracks.
* The JDA-kernel TL significantly improved damage identification when compared against KNN.  
Conceptualization, S.A. and S.E.A.; methodology, S.A. and S.E.A.; validation, S.A., S.E.A. and D.G.L.; formal analysis, S.A.; investigation, S.A.; data curation, S.A.; writing--original draft preparation, S.A.; writing--review and editing, S.A., S.E.A. and D.G.L.; visualization, S.A.; supervision, D.G.L.; funding acquisition, D.G.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Science Foundation, grant number 1762034, Spokes: MEDIUM: MIDWEST: Smart Big Data Pipeline for Aging Rural Bridge Transportation Infrastructure (SMARTI).  
Not applicable.  
The authors gratefully acknowledge assistance, access, computing resources, data, and expertise provided by the University of Nebraska Lincoln's Holland Computing Center, Union Pacific, and Bridge Diagnostics Inc. in association with this project. The authors would also like to thank all anonymous reviewers for their constructive suggestions.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.