## 4 Conclusions and Future Work  
In this study, a method to predict the vertical displacement (output) of bridges was proposed from the longitudinal strain (input) generated when vehicles pass across bridges by using an ANN. Pearson Type III distribution theory was used to express the actual vehicle distribution, and the training and test data were acquired using the verified FEM as an alternative to the difficulty of obtaining actual data. The proposed method showed the predictability of a bridge's dynamic displacement, which is relatively difficult to measure. ANN, which has a strong ability to define correlations between data, and a verified FEM for training data were used to predict displacement from strain, which is relatively easy to measure. Displacement is one of the most important types of physical data in the SHM of bridges. In addition, ANN can continuously predict displacement in real time. By using the proposed method, it is expected that the prediction of displacement of bridges and other structures, whether in use or newly constructed, can become easier and economically feasible.  
It is also examined the prediction accuracy by ANN structure, which has the greatest influence on the general prediction accuracy of an ANN. The comparison of the prediction accuracy for various numbers of hidden layers and of nodes suggested by [PERSON] et al. [55] showed a fairly high accuracy for all structures. Although the structure of the ANN does not have a major influence on the prediction accuracy in this study and it is costly and time consuming to find an ANN structure that has high accuracy, it is considered to be one of the processes that the researcher must perform to achieve better prediction.  
In the present study, the feasibility of displacement prediction by ANN is confirmed using an FE bridge model, not the real bridge. In future work, an experiment to apply the proposed method to actual bridge will be conducted. Especially, with actual bridges, natural conditions such as temperature and wind load may cause noise to the measured strains and displacements. Future study is intended to quantify the relation between the prediction accuracy and noise by predicting the displacements using measured data with noise. Also, study on determining the minimum number of strain-measurement points required for predicting displacements will be conducted using optimization techniques such as genetic algorithm.  
**Author Contributions:** conceptualization, H.S.M. and Y.M.L.; methodology, P.-j.C. and S.O.; validation, H.S.M.; formal analysis, P.-j.C. and S.O.; writing--original draft preparation, H.S.M. and S.O.; writing--review and editing, H.S.M. and Y.M.L.; supervision, Y.M.L.; project administration, H.S.M. and Y.M.L.  
**Acknowledgments:** This research was supported by a grant (19 CTAP-C152286-01) from Technology Advancement Research Program (TARP) funded by Ministry of Land, Infrastructure and Transport of Korean government; and also supported by the EDucation-research Integration through Simulation On the Net (EDISON) Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2014M3C1A6038855).  
**Conflicts of Interest:** The authors declare no conflict of interest.