Industrial control system intrusion detection method based on belief rule base with gradient descent

Intrusion detection is important for maintaining the smooth operation of industrial control systems (ICSs). The belief rule base (BRB), as a hybrid information-driven model, has been widely used in various fields because of its high accuracy and good interpretability. However, when facing intrusion detection problems in ICSs with highdimensional features, excessive rules often arise, leading to slow model inference and optimization due to the large number of rules. Therefore, this paper proposes an interval structure belief rule base with mini-batch gradient descent optimization (IBRB-MBGD) for ICS intrusion detection. First, to address the issue of rule explosion caused by high-dimensional features, a new modeling approach is proposed that uses reference intervals instead of single values, and the rule generation mode is changed from conjunction to disjunction, further improving the model inference method and effectively solving the combination rule explosion. Second, the large amount of historical data slows down the model optimization process; thus, an optimization method based on minibatch gradient descent is proposed to quickly optimize the parameters in the BRB. Finally, experiments were conducted on natural gas pipeline system and water storage tank system intrusion detection data, and the detection rate reached >90 %, verifying the effectiveness of the model.