Parallel fault diagnosis using hierarchical fuzzy Petri net by reversible and dynamic decomposition mechanism

The state space explosion, a challenge analogous to that encountered in a Petri net (PN), has constrained the extensive study of fuzzy Petri nets (FPNs). Current reasoning algorithms employing FPNs, which operate through forward, backward, and bidirectional mechanisms, are examined. These algorithms streamline the inference process by eliminating irrelevant components of the FPN. However, as the scale of the FPN grows, the complexity of these algorithms escalates sharply, posing a significant challenge for practical applications. To address the state explosion issue, this work introduces a parallel bidirectional reasoning algorithm for an FPN that utilizes reverse and decomposition strategies to optimize the implementation process. The algorithm involves hierarchically dividing a large-scale FPN into two sub-FPNs, followed by a converse operation to generate the reversal sub-FPN for the right-sub-FPN. The detailed mapping between the original and reversed FPNs is thoroughly discussed. Parallel reasoning operations are then conducted on the left-sub-FPN and the resulting reversal right-sub-FPN, with the final result derived by computing the Euclidean distance between the outcomes from the output places of the two sub-FPNs. A case study is presented to illustrate the implementation process, demonstrating the algorithm’s significant enhancement of inference efficiency and substantial reduction in execution time.