## 5 Conclusions and Future Studies  
This study proposes a novel detection model, which uses machine learning approaches, for the detection of cyber-attacks on WDSs. To propose a novel cyber-attack detection model in WDSs, this study performed two types of analyses. First, the machine learning approach with the most suitable detection performance was identified and analyzed. For this analysis, the most commonly used and well-known machine learning algorithms (i.e., KNN, SVM, ANNs, and ELM) were compared to determine the one with the best detection performance. Second, by considering the improved  
Figure 4: Performance comparison between observed and prediction data for the improved versions of ELM: (**a**) OS-ELM, (**b**) B-ELM, (**c**) W-ELM. version of the outstanding algorithm among the compared algorithms, the characteristics of the improved algorithms, in terms of the cyber-attack detection problem, were analyzed. Moreover, various performance indices were used to compare the quantitative performance of each algorithm and correctly classify the state of the WDSs under cyber-attack situations. According to the performance analysis of the improved versions of ELM in this study, the three ELM algorithms have an outstanding performance compared with the other machine learning approaches (e.g., KNN, ANNs, and SVM) in the aspect of the score \(S\), which reflects overall performance. However, through the applied problem in this study and the characteristics of each ELM algorithm, this study can derive several limitations. The initial version of ELM was developed to increase process speed, accuracy and to solve large real-world problems. Therefore, according to the simulation results of this study, the performance of ELMs was outperformed, however, compared to the other algorithms applied in this study, the ratio of the false positive detection was relatively high. The trend of false positive detection differs depending on the algorithm's characteristics, such as when the false predictions occur before the attack (OS-ELM), or when most of the false predictions occur near the attack conditions (W-ELM). One practical solution for solving this problem may be using some heuristic pre-knowledge information from the urban water systems and hydraulic system to make the classifier more intelligent. This helps the classifier to use some of its pre-knowledge to accurately predict the right condition. In addition, utilizing fuzzy logic (fuzzy theory) along with the ELM makes decision making much easier. Similarly, the various ELMs proposed have several limitations in terms of algorithm improvement (e.g., reducing false detection and improving true detection probability) and application aspects (e.g., image training problems, abnormal condition detection problems, time series problems, and regression problems). Although this study has the above limitations, it analyzed the characteristics of various types of ELM algorithms and the application problems of the various ELMs; this research serves as a good case study of ELMs to extend their applications to different and various fields. Moreover, the generated prediction results and analyses are expected to benefit the development of new ELM approaches, considering the thorough evaluation of each algorithm. Future studies may refer to the conclusions of this study to develop highly accurate algorithms. In doing so, one must not only consider benchmark problems but various other types of problems as well, such as (_i_) training data configuration: binary, real number, integer, and mix-integer; (_ii_) data collection type: sequencing data, prepared whole data; and (_iii_) data characteristics: continuous data (i.e., time series) versus discrete data. Besides, other improved/hybrid versions of ELM, particularly convolutional neural networks used for feature learning along with ELM as a classifier, may enhance the accuracy of the obtained results. Conceptualization, A.S. and J.H.K. ; Data curation, Y.H.C. ; Methodology, Y.H.C. ; Supervision, J.H.K. ; Writing--original draft, Y.H.C.