## 5 Conclusions  
Reliable HI curves construction and long-term dependencies learning of degradation data are important but challenging tasks for an accurate remaining useful life (RUL) estimation of concrete structures. In this study, we proposed an SAE-DNN model that automatically constructs HI curves from degradation raw signals. The HI curves constructed have better fitness metrics than statistical parameters-based HI curves. More specifically, these HI curves have the average monotonicity and trendability metrics of 0.67 and 0.68, respectively, which much higher than those of HI curves based on statistical parameters such as RMS, Kurtosis, or Sknewness, etc. Moreover, the curves' HI values are in the range of a [0, 1], therefore, threshold definition is no need for such HI employment.  
The HI curves constructed from training degradation data are then fed to train the LSTM-RNN for RUL prediction. The study validates the prediction performance of the LSTM-RNN by estimating RUL and calculating the average prediction error on testing experimental concrete beams at two times; at cycle 350 (minor crack initialization) and at cycle 450 (major crack initialization). Experimental results on concrete beams A, B, and C indicate that the LSTM-RNN generally estimates more accurate RULs of concrete beams than the GRU-RNN and the simple RNN. The average prediction error cycles of the LSTM-RNN on concrete beams A, B, C at cycle 350 are 32, 41, and 36, respectively; at cycle 450 are 21, 34, 24, respectively. These error values are lower than those of the GRU-RNN and much lower than those of the simple RNN. In other words, the proposed method outperformed a GRU-RNN and a simple RNN in predicting the RUL of concrete structures.  
Overfitting is an important issue that needs to be handled carefully during training deep neural networks, especially when the data training is limited as in this study. It makes the outcome of deep neural networks low and unstable. There are currently many  
Figure 16: LSTM-RNN-based RLU prediction results of concrete beam C: (**a**) at cycle 350; (**b**) at cycle 450.  
Figure 15: LSTM-RNN-based RLU prediction results of concrete beam B: (**a**) at cycle 350; (**b**) at cycle 450.  
techniques to help neural networks avoid overfitting such as L1 and L2 regularization, Monte Carlo dropout, etc. In the upcoming times, our focus is to dig deep into these techniques to find the best one for our model.  
Conceptualization, V.T., T.-K.N., C.-H.K. and J.-M.K.; methodology, V.T., T.-K.N., C.-H.K. and J.-M.K.; validation, V.T. and J.-M.K.; formal analysis, V.T., T.-K.N., C.-H.K. and [PERSON]-M.K.; resources, V.T. and [PERSON]-[PERSON]; writing--original draft preparation, V.T., T.-K.N.; writing--review and editing, C.-H.K. and [PERSON]-M.K.; visualization, V.T., T.-K.N. and [PERSON]-M.K.; supervision, J.-M.K.; project administration, J.-M.K.; funding acquisition, J.-M.K. All authors have read and agreed to the published version of the manuscript.  
This research was supported by a grant (2019-MOIS41-002) from the National Demand Customized Life Safety R&D Project funded by the Korean Ministry of Interior and Safety (MOIS). This work was also supported by the Technology development Program(S2860371) funded by the Ministry of SMEs and Startups (MSS, Korea).  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.