Kolmogorov Convolution Network: Knowledge Representation and Reasoning for Fault Diagnosis of Trolley Mechanism on Ship-to-Shore Cranes

Accurate fault diagnosis of trolley mechanisms in ship-to-shore cranes is essential for ensuring cargo transportation at ports. While deep neural networks (DNNs) have made some achievements in fault recognition, DNN’s inherent opacity often limits the ability to provide reliable explanations and interact with domain experts. In the field of neural-symbolic integration, researchers are increasingly focusing on methods to extract relational knowledge from DNNs to offer a semantic understanding of the DNN’s feature learning and reasoning processes, making their internal decision-making mechanisms more transparent and trustworthy for operators. This article introduces a Kolmogorov convolution network (KCN), which extracts relational knowledge that visualizes convolutional operations and simultaneously supports semantic reasoning similar to the IF-THEN form. For convolution visualization, based on the Kolmogorov representation theorem, we introduce a Kolmogorov convolution (KC) with trainable activation functions, which can represent the nonlinear relationships between input and feature maps based on several univariate functions. For the visualization of fully connected layers, a new rule format, classification rules, is designed to provide a semantic representation for fault diagnosis. Finally, experiments, conducted on a 1:4 STSC testbed, demonstrate that KCN achieves its outstanding diagnostic accuracy of 98.3% which outperforms conventional models, and demonstrates potential for optimizing prior knowledge use. The computational efficiency of KC increases by 37% using Levenberg–Marquardt optimization. The resemblance between relational knowledge from KCN and domain knowledge indicates that KCNs possess practical value in areas such as the optimization of prior diagnostic rules. These findings indicate that KCN is a promising approach for accurate and interpretable fault diagnosis in industrial scenarios.