This article introduces and evaluates adaptive polynomial Kolmogorov–Arnold network (AdaptPolyKAN) architectures for intelligent fault diagnosis, addressing limitations of classical KANs in dynamic and nonlinear industrial systems. While classical KANs offer interpretability, their fixed univariate mappings lack the flexibility needed for evolving operating conditions. The proposed AdaptPolyKAN uses adaptive polynomial expansions that adjust the degree of each basis according to local reconstruction errors, enabling real-time adaptation, improved accuracy, and efficient handling of complex nonstationary fault patterns. Three variants are examined-Standard PolyKAN, SplineKAN, and Online PolyKAN-alongside the proposed AdaptPolyKAN. Their performance is benchmarked against classical KAN, artificial neural networks, support vector machines, and random forest models in both real and simulated fault scenarios. The evaluation uses datasets from a cement rotary kiln at the Ain El Kebira plant, consisting of 768 normal samples, multiple simulated sensor faults, and one real fault. Monitored variables include temperatures, pressures, motor currents, and rotational speeds from 44 sensors recorded at 20-s intervals. The dataset contains noise, class imbalance, and limited duration, reflecting realistic industrial conditions. Comprehensive metrics—including accuracy, precision, recall, F1- score, false alarm rate (FAR), and missed detection rate (MDR)—demonstrate the superiority of the proposed approach. AdaptPolyKAN achieves 98.4% accuracy, balanced precision and recall (98.3% and 98.4%), and the lowest FAR (0.0060), while maintaining competitive MDR (0.178). Online PolyKAN adapts effectively to changing fault patterns, whereas classical KAN suffers from elevated false alarms. Overall, AdaptPolyKAN provides reliable detection in nonlinear and time-varying processes, offering a practical and interpretable solution for safety-critical industrial environments.

The accurate detection and diagnosis of faults are critical for maintaining optimal operation and ensuring the reliability of industrial processes. Notably, the topic of online fault detection and diagnosis has recently presented a significant challenge. This work mainly deploys a neural network technique for the comprehensive detection and diagnosis of faults within the Tennessee Eastman Process (TEP) on a low-computational power system, the Raspberry Pi board. The devolved methodology showcases a remarkable level of accuracy (94.50%) in diagnosing the various TEP faults, affirming its robustness and effectiveness. To elevate the practical applicability of the proposed approach, a meticulous investigation into the implementation of the suggested approach on a Raspberry Pi 4 card was undertaken. The successful realization of this implementation not only highlights the adaptability of the approach but also paves the way for its seamless integration into practical industrial applications.

The key idea behind this study is to integrate a moving window dynamic PCA (MW-DPCA) methodology for fault detection within the Tennessee Eastman process (TEP) into a low-computational power system, the Raspberry Pi 4 card, for real-time application. Indeed, the paramount importance of real-time fault detection (FD) in intricate industrial processes presents a critical challenge. Various data-driven techniques have been developed to ensure safety, maintain operational stability, and optimize productivity in such processes. Principal Component Analysis (PCA) is a fundamental data-driven technique that utilizes dimensionality reduction to extract the most informative features from high-dimensional data, simplifying analysis and potentially revealing underlying fault patterns. However, PCA primarily focuses on static relationships and may miss crucial temporal dynamics for fault identification. This is where dynamic PCA (DPCA) excels. By incorporating lagged values of variables, DPCA captures the temporal evolution of features, enabling a more comprehensive understanding of process behavior and improving the detection of faults involving dynamic changes. In order to address the stochastic measurements, a moving average filter tool is also employed. The results obtained and the successful realization of this implementation demonstrate the adaptability of the approach and pave the way for its seamless integration into practical industrial applications.

The interval-valued kernel PCA (UQ-KPCA) is a variation of the kernel PCA (KPCA) designed for interval-valued data, designed to handle data uncertainty by defining specific similarity measures and kernel functions for interval data. This paper introduces Uncertainty Quantification KPCA (UQ-KPCA) as a novel method to address uncertainties in data. UQ-KPCA converts the traditional KPCA model from single-valued to interval-valued representations, allowing for accurate error and uncertainty quantification. The process modeling using KPCA is then performed on data based on the interval model, followed by the computation of fault detection statistics such as T2, Q, and Φ. The method’s effectiveness is evaluated in the context of the cement rotary kiln process, and compared with the KPCA demonstrating superior performance in accurately identifying faults within a stochastic setting with unknown uncertainties.

This study introduces three novel dynamic interval-valued principal component analysis (DIPCA) methods: dynamic centers PCA (D-CPCA), dynamic vertices PCA (D-VPCA), and dynamic complete information PCA (D-CIPCA). These methods advance traditional interval-valued PCA (IPCA) by integrating dynamic aspects of industrial processes, thus addressing both data uncertainties and temporal correlations. The DIPCA methods were validated using real-world data from the Ain El Kebira cement plant. Results indicate significant improvements in fault detection accuracy, achieving lower false alarm rates and higher reliability compared to classical IPCA methods. Furthermore, an enhanced combined index for interval-valued data was developed, providing a single, comprehensive statistical measure for streamlined process monitoring.