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

Abstract

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.

1. Introduction

With the complexity of industrial manufacturing equipment and production processes increasing dramatically, a correspondingly extensive array of fault diagnosis methods has been proposed and discussed. These include the application of Petri nets (PNs) (Liu et al., 2017), deep learning techniques (Lei et al., 2020; Chen XH et al., 2021), and swarm intelligence algorithms (Ziani et al., 2017; Chen RH et al., 2020; Ye et al., 2023). As a distinctive tool within the knowledge-driven approach, the fuzzy Petri net (FPN) has been widely utilized for modeling, simulating, and executing diagnostic tasks within complex manufacturing systems, leading to fruitful results. This is primarily attributable to two key characteristics of FPNs (Zhou and Zain, 2016; Seatzu, 2019; Liu et al., 2022; Wang et al., 2022). First, the FPN maintains the PN’s ability to describe asynchronous concurrency and provides a graphical representation. Second, it offers a formal modeling approach for managing fuzzy and uncertain information within knowledge-based systems. This sets FPN apart from the opacity and black-box nature of deep learning, as FPNs can explicitly describe the states, events, and transitions within the system, thereby enhancing the interpretability and explainability of the inference process (Rudin, 2019).

Recently, more high-level PNs with fuzzy factors have been introduced to represent knowledge effectively and accommodate the diverse constraints inherent in real engineering issues. Notable examples include probabilistic linguistic PNs (Shi et al., 2024), Z-number PNs (Shi et al., 2022), spherical linguistic PNs (Mou et al., 2022), and linguistic PNs (Liu et al., 2022). As knowledge-based systems increase in size, their corresponding FPNs grow in scale (Zhou et al., 2019). This scaling phenomenon, known as the state explosion problem, poses a substantial challenge to the construction and application of FPNs (Valmari, 1998; Grobelna and Karatkevich, 2021). To address the state explosion problem, researchers have developed a suite of decomposition algorithms and reasoning techniques. These methods ensure that the resulting sub-PNs preserve the consistency of the original PN, thereby reducing the model’s scale. Chen SM (2000) ...