## 2 Data and Sensor System
### Modeling: Identifying Relations among Sensors  
The proposed forecasting system is based on a _dynamic relational network_[22]. The dynamic relational network model is a self-recognition network in which sensor nodes evaluate each other to detect faulty sensors and events of interest. Each sensor node is capable of information processing for manipulating sensor data. The status of each sensor node is represented by credibility. The credibility of a sensor is indicated as a continuous value ranging from 0 (not credible) to 1 (fully credible). An important function of the dynamic relational network is to evaluate the sensor data based on consistency with other sensor data within the sensor system. As the data change dynamically, the consistency also changes, and hence the evaluations as well. Another role of the model is to define and generate _profiles_ in several ways. For example, the structure (of the network expressing relations among sensors) and model parameters (such as threshold to determine whether the sensor data are consistent with the relations) are used as profiles. Dynamic relational networks are used for detection of events in a combustion system of an automobile engine [23] and for home intrusion detection [15]. The dynamic relational network model is also applied to space weather prediction for high-energy electron flux 24 h ahead at GEO [13]. Figure 1 shows both the previous model (Figure 1a) [13] and the proposed model (Figure 1b). The network consists of nodes corresponding to real sensors and a node corresponding to an imaginary sensor. Real sensors are those monitoring solar wind speed, north-south component of interplanetary magnetic field, and high-energy electron flux at GEO. The imaginary sensor represents the high-energy electron flux 24 h ahead. The imaginary sensor is used for prediction of a flux alert level. The previous model (Figure 1a) involves sensors equipped with two satellites. The network contains three real sensors: a single north-south component of IMF, solar wind speed, and high-energy electron flux. The proposed model (Figure 1b), on the other hand, involves seven sensors in total, three north-south components of IMF, three solar wind speeds, and one high-energy electron flux. Both models include a single imaginary sensor of high-energy electron flux 24 h ahead. There are three kinds of computation model for a dynamic relational network [22]: _black and white_ model, _skeptical_ model, and _gray_ model. In the _black and white model_, a credibility of a sensor node converges either normal (credibility = 1) or fault (credibility = 0) as a diagnosis proceeds. In the _skeptical model_, a sensor node evaluates a target sensor as normal if only they evaluate normal each other. In the _skeptical model_, therefore, the diagnosis process is more careful than _black and white_ model. For the _skeptical_ model, however, the convergence tendency of the credibility is same in the _black and white_ model. The credibility of the _skeptical_ model also converges to the above condition. We use the gray model for prediction. In the _gray model_, the credibility can be an intermediate value between 0 and 1. The credibility of the _gray model_ can reflect ambiguous states in which the status of the sensor normal/abnormal is not determined exactly. The space weather forecasting of high-energy electron flux also involves ambiguous situations in which the change of the flux is unpredictable. Therefore, the gray model is suitable for forecasting of high-energy electron flux in this study. A warning to alarm is determined by comparing with the threshold and the credibility of the sensors in operation. The alarm thresholds for warning can be tunable parameters, because the threshold is controlled by a policy of spacecraft operational teams. For instance, the alarm threshold can be smaller value less than 0.5. For this case, this policy selects safety operation since the sensor sensitivity for anomaly detection becomes sensitive. The alarm threshold is 0.5 and fixed value in this paper.