Adaptive Threshold Generation for Fault Detection with High Dependability for Cyber-Physical Systems

Cyber-physical systems (CPS) applied to safety-critical or mission-critical domains require high dependability including safety, security, and reliability. However, the safety of CPS can be significantly threatened by increased security vulnerabilities and the lack of flexibility in accepting various normal environments or conditions. To enhance safety and security in CPS, a common and cost-effective strategy is to employ the model-based detection technique; however, detecting faults in practice is challenging due to model and environment uncertainties. In this paper, we present a novel generation method of the adaptive threshold required for providing dependability for the model-based fault detection system. In particular, we focus on statistical and information theoretic analysis to consider the model and environment uncertainties, and non-linear programming to determine an adaptive threshold as an equilibrium point in terms of adaptability and sensitivity. To do this, we assess the normality of the data obtained from real sensors, define performance measures representing the system requirements, and formulate the optimal threshold problem. In addition, in order to efficiently exploit the adaptive thresholds, we design the storage so that it is added to the basic structure of the model-based detection system. By executing the performance evaluation with various fault scenarios by varying intensities, duration and types of faults injected, we prove that the proposed method is well designed to cope with uncertainties. In particular, against noise faults, the proposed method shows nearly 100% accuracy, recall, and precision at each of the operation, regardless of the intensity and duration of faults. Under the constant faults, it achieves the accuracy from 85.4% to 100%, the recall of 100% from the lowest 54.2%, and the precision of 100%. It also gives the accuracy of 100% from the lowest 83.2%, the recall of 100% from the lowest 43.8%, and the precision of 100% against random faults. These results indicate that the proposed method achieves a significantly better performance than existing dynamic threshold methods. Consequently, an extensive performance evaluation demonstrates that the proposed method is able to accurately and reliably detect the faults and achieve high levels of adaptability and sensitivity, compared with other dynamic thresholds.