## 3 Results
### Comparison of the Simulation Results with Similar Clustering Model Algorithms
This was virtualized in the results for the six features dataset, which was drawn from the failure modes in the non-intrusive continuous sensor in the heat exchanger system. For the three clusters, a reasonable grouping was found, and it is represented by the colors blue, green, and orange. These colors indicate the normal state (orange region) and the abnormal state (green and blue region) for the mini-batch K-means clustering (A); the normal state (blue region) and the abnormal state (orange and green region) for the spectral clustering (B); the normal state (blue region) and the abnormal state (orange and green region) for the Gaussian mixture clustering (C); and finally, the normal state (green region) and the abnormal state (orange and blue region) for the birch clustering (D). The simulated results generate scatter and dense plots of the dataset, which are separated and identified by the different colors in the cluster. The clusters are generated by the association of the different datasets (observations) using the nearest mean. In Table 3, the simulated results \begin{table}
\begin{tabular}{c c c c} \hline \hline
**S/N** & **Clustering Model Algorithms** & **Faults State** & **Non-Faults State** \\ \hline
1 & K-means clustering & Blue region & Orange region \\
2 & Mini-batch K-means clustering & Orange region & Blue region \\
3 & Spectral clustering & Blue region & Orange region \\
4 & Gaussian mixture clustering & Blue region & Orange region \\
5 & Birch clustering & Blue region & Orange region \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of the simulated results for the different clustering model algorithms when two clusters are considered. for the clustering model algorithms that were implemented for managing the reliability of the non-intrusive continuous sensor are compared. The results show consistency with the K-Means clustering model algorithm, the spectral clustering model algorithm, and the Gaussian mixture clustering model, respectively. The following conclusions can be drawn from the compared simulated results for the non-intrusive continuous sensor used in heat exchanger systems that were analyzed using the different clustering model algorithms presented above:  
Figure 6: Simulated results for three clusters showing states of the sensor for the algorithms: mini-batch K-means clustering (**A**), spectral clustering (**B**), Gaussian mixture clustering (**C**), and birch clustering (**D**). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**S/N** & **Clustering Model Algorithms** & **Normal State** & **Abnormal State** \\ \hline
1 & K-means clustering & Blue region & Orange and green region \\
2 & Mini-batch K-means clustering & Orange region & Blue and green region \\
3 & Spectral clustering & Blue region & Green and orange region \\
4 & Gaussian mixture clustering & Blue region & Green and orange region \\
5 & Birch clustering & Green region & Blue and orange region \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the simulated results for the different clustering model algorithms when three clusters are considered. When the distribution of the dataset is unknown or unclear, it cannot achieve a perfect clustering result, even when two or three clusters are used for the analysis. * A single clustering mean cannot yield a perfect clustering result. * In clustering applications, traversing the samples several times is unavoidable.