## 4 Discussion  
This paper extended the dynamic relational network involving spatiotemporal interpolation of the missing data of the sensors. In the earlier study [3], the dynamic relational network includes real and virtual sensors. The virtual sensors in the previous models are defined for prediction. In this paper, however, the virtual sensors are defined for prediction and interpolation of the missing data. The proposed model [12] of this work handles the sensor faults and compensates the missing data using the sensors associated. The simulations of this paper demonstrated that the missing data of the faulted sensors are interpolated by averaging observed values of the neighbor sensors. The sensor value estimated by the single sensor is not plausible. However the averaged sensor values are interpolated from the several sensors. This paper examined two scenarios as the case studies: The fault of the single sensor (Section 3.2) and faults of the multiple sensors (Section 3.3). In Case Study 1, the single sensor fails, however, the faulted sensor was replaced with the virtual sensor by information processing. In the simulation, finally, the virtual sensor compensates the real one that outputs the interpolated values estimated by the neighbor sensors. In Case Study 2, further, neighbor sensors were simultaneously unsuccessful to create virtual ones in the demonstration. Finally, however, the both sensors were also replaced with virtual ones. This paper also showed the significance of the proposed model in Table 1 because the credibilities with the spatiotemporal interpolation are larger than without one. The spatiotemporal interpolation by neighbor nodes for the virtual sensors support the resilience of the network. However, the period until replacing with virtual sensors depends on the observed data. The plots on the credibility of the time development showed that the credibilities of the sensors oscillated between small and intermediate values in Figure 12. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**(a)**} \\ \hline  & \(E\) & \(V_{1}\) & \(V_{2}\) & \(V_{3}\) & \(E_{24}\) \\ \hline
**Interpolation (Used)** & 0.795 & 0.803 & 0.884 & 0.981 & 0.8501 \\ \hline
**Interpolaton (Unused)** & 0.793 & 0.022 & 0.821 & 0.826 & 0.8081 \\ \hline  & \multicolumn{3}{c}{**(b)**} \\ \hline  & \(E\) & \(V_{1}\) & \(V_{2}\) & \(V_{3}\) & \(E_{24}\) \\ \hline
**Interpolation (Used)** & 0.739 & 0.631 & 0.627 & 0.775 & 0.8181 \\ \hline
**Interpolation (Unused)** & 0.630 & 0.048 & 0.048 & 0.637 & 0.7691 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of the credibility for each sensor. Each cell indicates the credibility. The sensors \(V_{1}\), \(V_{2}\), and \(V_{3}\) respectively correspond to the solar wind speed of ACE, STEREO-A, and STEREO-B. The sensors \(E\) and \(E_{24}\) respectively correspond to the high-energy electron flux and its flux 24 h ahead. Case study 1 (Fault of a single sensor). The sensor of ACE for the solar wind speed is faulted. (**a**) Case study 1 (Fault of a single sensor). The sensor of ACE for the solar wind speed is faulted; (**b**) Case study 2 (Faults of two sensors). The sensors of ACE and STEREO-A for the solar wind speed failed. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Single Sensor Failed** & **Two Sensors Failed** \\ \hline
**Interpolation (Used)** & 0.849 & 0.833 \\
**Interpolation (Unused)** & 0.850 & 0.834 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of forecasting for high-energy electron flux 24 h ahead. Each cell in the table shows a prediction success rate where the credibility threshold is 0.5. The sensor \(E_{24}\) alarms if its credibility is less than or equal the threshold. Constructing the resilient sensor networks is an important issue in computer science. Various kinds of studies have attempted to build the resilient computer networks and sensor networks [7; 8; 9; 10; 11].