## 2 Challenges and Methodology
### Challenges and Our Methodology  
The state of the physical system may be gradually changed with uncertainty and nonlinearity and the cumulative impact of the undetected subtle changes during the operation might be considered negative to providing safe of CPS. In order to achieve a high level of the adaptability of the system and respond to the sensitivity of the generated residual, our first idea is to approximately identify and assess normality with residual derived from the normal operation. There are numerous methods which follow a heuristic process to support approximation derived from statistical analysis of incoming data [1; 2; 28; 29]. The normality of the system aims to differentiate between normal and anomalous data by analyzing the tendency of the residual generation patterns. At an abstract level, identifying the normality is to define a region representing the normal condition and pick out any residual which does not belong to the normal region. Only the anomalous data that are acceptable to the system are quantitatively identified through assessing normality of the physical system during the normal driving operation. However, the data with environment uncertainty affect the quality of the tendency analysis of the residual generation pattern since they seem to be similar to the actual normal data. Another issue disturbing the normality assessment is related to model uncertainty (modeling errors) and a critical challenge is to measure quantitatively the effects of modeling uncertainty. In addition, the current normal data might not be representative of the normal state after changing the operation of the system. Hence a model representing the normality of the physical system needs to be designed with some flexibility, considering a data pattern of fluctuations caused by outlier and noise related to environment uncertainty and modeling uncertainty. Note that the normality with flexibility for data cannot be obviously defined since the uncertainty distribution is unknown. We consider a number of  
Figure 1: An example of anomalies observed from a left encoder sensor while driving. The red circle indicates one of anomalies which occur during the normal operation (just driving) on the real road, and disappear soon without any damage to the Jackal behavior. cases for possible normality and perform statistical tendency analysis for only one input for the same physical variable (i.e., the velocity of Jackal UGV). The normality assessment should be performed for each operation of the system. In the tendency analysis, we assume that if noise and outlier have a small magnitude as well as being infrequent, then they are negligible. The noise and the outlier are considered the normal data even if there is big difference from normal data but it does not happen often. We, therefore, focus on an anomaly frequency of data within a given period for the data obtained during the normal operation. Although the existing statistical analysis mainly requires a large amount of data, we use only a small amount of data with a certain uncertainty limited by time intervals. Through the statistical tendency analysis, we offer a new way to allow the data itself to suggest a normality model fit for its purpose, which does not assume an underlying model. In other words, rather than trying to eliminate noise and outliers for accurate measurement, we adopt a strategy using a temporary identifier when defining the normality. Accordingly, the system is provided with an acceptable region including noisy data and outlier as well as normal data. It is reasonable that the system requires high sensitivity with respect to low modeling uncertainty and also requires high adaptability to accommodate environment uncertainty. It is, however, difficult to achieve high levels of adaptability and sensitivity simultaneously because two competitive variables are considered to determine the AT. Besides achieving high accuracy in the fault detection, a detector should raise properly an alarm for actual faults.