BRBcast: A new approach to belief rule-based system parameter learning via extended causal strength logic

The belief rule-based (BRB) system has demonstrated advantages in complex system modeling and evaluation, with strong nonlinear relationship approximation capabilities. BRB parameter learning processes have been proved to be effective in improving the approximation accuracy of BRB systems. However, the running time complexity is regarded as an important challenge in BRB parameter learning efficiency. In this paper, a new approach to BRB parameter learning via extended causal strength (CAST) logic (BRBcast) is proposed in order to reduce the complexity of BRB parameter learning and maintain the approximation accuracy of BRB systems. First, the parameter numbers of traditional BRB parameter learning are analyzed to show the necessity of complexity reduction. Furthermore, the binary CAST logic is extended to fulfill the requirements of multi-state modeling and evaluation. Thereafter, an optimization model for parameter learning with CAST logic is established based on the analysis conclusion, and further applied to reduce the BRB parameter learning complexity. In BRBcast, the CAST parameters, instead of BRB parameters, are trained and translated to construct belief rule bases in BRB parameter learning, which involves less parameters than those of traditional BRB parameter learning approaches. Following this, the detailed BRBcast procedure is presented with the differential evolutionary (DE) algorithm. Finally, a numerical case and practical example on pipeline leak detection are investigated in order to verify the efficiency of BRBcast. The experimental results indicate that the proposed BRBcast exhibits superior performance, in both reducing the BRB parameter learning complexity and ensuring the approximation accuracy of BRB systems, which provides a promising avenue for constructing accurate and robust disaster emergency and rapid response systems.