## 6 Conclusions  
Recently, with the emergence of technologies like attention mechanisms, the capabilities of natural language processing have improved. These methods dynamically adjust the emphasis on relationships between words in a sentence. Motivated by these developments, we propose a fault detection method that calculates the distance between the query vector and training data. The distance value is then readjusted once the shared neighbors are selected through SNN. AAKR is utilized as the fault detection method, with the rescaled distance employed to calculate the weights and estimation values before computing the estimation vector. The performance of the proposed method is validated using both simulation data from the TEP benchmark and a real CFBC boiler shutdown case. The TEP experiment results show that the proposed method calculates lower type I and type II errors. Additionally, in the real CFBC shutdown case, the proposed method detects anomalies more than 2 h earlier than conventional methods, prior to the unplanned shutdown caused by fault propagation from tube leakage. Thus, by readjusting the distance between the query vector and training data, the proposed method enhances fault detection performance and shows potential for application in real-world complex processes.  
In future research, we will consider the following three topics. First, since the performance of AAKR depends on the bandwidth parameter h, we used k-fold cross validation to determine an appropriate value. In the future, we aim to find a method for assigning the parameter dynamically. Second, when rescaling the distance in the proposed method, we divided the distance by k, the number of neighbors, to rescale. However, when k becomes large, the value becomes small even with a penalty. We will research how to assign weights to solve this problem. Third, noisy data in the training set can lead to unreliable neighbor selection in the SNN-based process and degrade fault detection performance. To mitigate this issue, future research will focus on applying adaptive filtering techniques or noise-robust similarity measures to improve the reliability of neighbor selection.  
S.J. and B.K. conceived and designed the simulations; J.K. analyzed the data; E.K. advised on the whole process of manuscript preparation; M.K. analyzed the data and wrote the paper. The analysis results and the paper were supervised by S.K. All authors have read and agreed to the published version of the manuscript.  
This work was supported by BK21 FOUR, Creative Human Resource Education and Research Programs for ICT Convergence in the 4 th Industrial Revolution.  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy concerns.  
The authors declare no conflicts of interest.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **PCA** & **kNN** & **LOF** & **AAKR** & **AASKR-NP** & **AASKR** \\ \hline Boiler shutdown & & & 2020, 09, 09, 1435 & & \\ Detection time & 14:53 & 13:36 & 14:36 & 12:32 & 12:32 & 12:13 \\ Early detection time & \(-\)18 m & 59 m & -26 s & 2 h 3 m & 2 h 3 m & 2 h 21 m \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of the detection time of the proposed and conventional methods (faster is better).