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.

Efficient fault diagnosis in ship-to-shore cranes (STSC) is vital for reliable cargo transport. However, deep neural networks (DNNs) lack transparency, hindering their explainability and interaction with experts during diagnostic decision-making. Currently, neural-symbolic systems increasingly focus on knowledge translation and embedding to enhance DNNs applicability for real-world fault diagnosis. Hence, this article introduces a deep knowledge-augmented belief network (DKABN), where knowledge translation and embedding are conducted to visualize the behavior of deep belief networks and integrate domain knowledge. Specifically, for stacked restricted Boltzmann machines (RBMs) layers, a novel activation-weighted logic RBM (AWL-RBM) is designed to fairly consider the contribution of each literal and reduce the inconsistencies between symbolic logic and RBMs. In the AWL-RBM, we formally prove that multiple literal groups can still be mapped into a violation rank function be capable of equalizing RBM energy minimization. Besides, translation and embedding of symbolic literals are conducted to interpret how RBMs work and fuse domain knowledge. For fully connected layers, a rule format like IF-THENs is translated and embedded to provide a semantic representation for diagnosis decision-making, and integrate domain knowledge. Finally, verified using an STSC testbed, DKABN demonstrates exceptional diagnostic performance and significant application potential.

The fault diagnosis of hoist mechanisms in ship-to-shore cranes (STSCs) is paramount for maintaining shipping schedules and ensuring personnel safety at ports. Although deep networks have achieved some success in diagnosing faults in hoist mechanisms, their opaque nature often precludes them from providing trustworthy explanations for their decisions. To address this problem, this article introduces a deep logic convolutional neural network (DLCNN), which incorporates two symbolic languages (confidence and classification rules) to visualize how convolutional neural networks (CNNs) work. Confidence rules are extracted from logic convolutions (LCs). In the LC, confidence rules are designed from three perspectives-information loss, the tradeoff between soundness and interpretability, and quantitative reasoning-to provide a comprehensive understanding of the feature learning and reasoning of stacked convolutions. Besides, classification rules are extracted from CNN's full-connected layers to elucidate implicit relationships between fault features and labels. Our experimental investigations on an STSC testbed demonstrate that DLCNNs have powerful performance in fault recognition, interpretability, and potential engineering value.

During the age of the Industrial Internet of Things (IIoT), extensive sensors are deployed on steel production lines to construct intelligent monitoring systems. A fan is a crucial piece of machinery in steel production lines, making its fault diagnosis imperative to prevent air pollution and casualties. DNN (Deep Neural Network) with powerful real-time IIoT data analysis has achieved outstanding performance in recognizing faults. Due to the black-box nature of DNNs, these models cannot provide reasonable explanations for their diagnostic decisions. It is still challenging for experts to make reliable and trustworthy conclusions. To address the issue, this paper introduces a new neural-symbolic model, termed Confidence and Classification DBN (CC-DBN), where confidence and classification rules are extracted from a Deep Belief Network (DBN) to provide an explainable representation of DBN feature learning and reasoning. In order to extract confidence rules, this paper develops a new clustering logic Restricted Boltzmann Machine (C-LRBM). Confidence rules can generate latent features of the raw vibration data of the fan and simultaneously explain the hierarchical reasoning of stacked RBM. Besides, to make trustworthy fan diagnosis decisions, classification rules are extracted to provide an explainable symbolic representation between input and output feature spaces. The experiment is performed on an industrial fan dataset from a leading steel production line in Shanghai. The results demonstrate that the proposed CC-DBN can effectively discover knowledge for fan diagnostic decisions and simultaneously achieve superior fault discrimination over typical classifiers and DBNs.