This paper develops a dynamic Knowledge Graph (KG)-augmented Large Language Model (LLM) framework integrated with a Bidirectional Encoder Representations from Transformers-Cascade Relation Extraction (BERT-CasRel) architecture to address key challenges in aviation equipment fault diagnosis, including unstructured maintenance text processing, ambiguous domain semantics, static knowledge constraints, and limited explainable reasoning capabilities. The study first constructs a domain-specific aviation ontology and adopts a context-enhanced BERT-CasRel model to extract high-quality entity–relation triples from maintenance logs and technical documentation. These structured triples populate a dynamic aviation fault KG that supports hierarchical causal inference, subgraph refinement, and in-context learning for adaptive knowledge updating. Structured domain prompting enables bidirectional interaction between LLMs and the KG, facilitating traceable fault chain analysis and accurate root-cause diagnosis. Evaluated on CFM56-5 aero-engine turbine blade fault cases, the BERT-CasRel model achieves a triple extraction F1-score of 0.968, while the integrated LLM–KG framework attains fault diagnosis accuracy exceeding 95%. Benchmarking against conventional and state-of-the-art methods confirms the framework's superiority in extraction accuracy, diagnostic precision, interpretability, and scalability. It delivers strong cross-domain generalization and computational efficiency, mitigates LLM hallucinations, complies with aviation regulations, and provides an interpretable, scalable diagnostic solution while acknowledging limitations in large-scale knowledge iteration and full industrial deployment.

Fault identification plays a pivotal role in condition-based maintenance of rotating machinery, with identification accuracy highly dependent on the quality of extracted features. Multiscale permutation entropy (PE) methods have emerged as promising feature extraction tools due to the fast computation of PE and informative scalability of multiscale procedures. However, PE is unresponsive to amplitude variation due to the binary orbit similarity state, and the multiscale procedure suffers from scale information loss or even scale absence, all of which decrease the identification accuracy. To address these issues, this article proposes a novel approach termed the scale-compensation community distance entropy (SCDE) method for fault identification. On one hand, the community distance-based orbit similarity value is put forward to diversify orbit similarity states, achieving a dual-characteristic perception of both frequency and amplitude changes. On the other hand, the scale-compensation procedure is proposed to enrich overall and detailed information on continuous scales. The efficiency and superiority of SCDE are rigorously demonstrated using simulation data and experimental datasets.

Wheeled robot fault diagnosis is indispensable for ensuring its reliable and safe operations. However, two challenges impede the application of prevalent intelligent diagnosis methods. 1) Multisensor fusion: The complexity of robot movements necessitates multisensor for comprehensive monitoring, generating strong-coupled, and high-dimensional data that complicate both intrinsic relationship mining and effective fusion; 2) Heterogeneous data silos: Dispersibility, heterogeneity and privacy constraints across different robots lead to non-independent and identically distributed (Non-IID) data silos, severely limiting the development of universal diagnostic models. To overcome these two problems, this article proposes a tailored federated physics-informed graph framework (FedMA-PIG). On the client side, the kinematics mathematical model is constructed for each robot, which explores the inter-sensor correlations and forms a physics-informed graph. It enables multisensor data fusion and assists the client in training a local graph neural network. On the federated framework side, a Non-IID federated framework based on a multianchor contrastive mechanism is devised. It employs multiple anchors to capture common knowledge from heterogeneous robot data, guiding feature representations toward corresponding anchors and away from others, thereby promoting consistency and mitigating inter-client data heterogeneity. Comprehensive experiments were conducted on three representative wheeled robots- Mecanum-wheeled, 4WD-wheeled, and Omni-wheeled- distributed across four federated clients. The results demonstrate that FedMA-PIG achieves generalized and superior diagnostic performance compared to state-of-the-art methods.

Accurate and reliable bearing fault diagnosis is critical for ensuring the operational reliability of industrial machinery, yet it remains a challenge due to scarce labeled fault data and prevalent unknown health conditions. To enhance diagnostic reliability under such uncertainties, this paper proposes a digital twin (DT) augmented framework that integrates entropy-embedded partial domain adaptation. The approach constructs a high-fidelity virtual bearing model to reliably simulate fault dynamics and generate comprehensive fault signatures. By systematically applying entropy-based criteria to evaluate the uncertainty and complexity of features, the framework extracts and purifies the most informative and reliable characteristics between the physical and virtual domains. These purified features are aligned through a weighted block-diagonal structure, effectively mitigating domain shift caused by unknown health states and improving the reliability of knowledge transfer. This process ensures robust cross-domain diagnostics while minimizing negative interference from outlier conditions. Experimental validation across multiple bearing datasets confirms that the proposed framework reliably transfers diagnostic knowledge from virtual to physical systems, maintaining high fault identification accuracy even with completely unlabeled measurements. By leveraging entropy-based domain adaptation within a digital twin environment, this work achieves reliable fault diagnosis. Notably, the proposed approach maintains high efficacy despite the lack of annotated data and the presence of unexpected faults.

Gas storage facilities have long faced bottlenecks in the core control systems of high-power compressors, where operational safety, efficiency, and automation under complex conditions remain key challenges. Traditional single-sensor monitoring offers limited perception and low data utilization, falling short of ensuring reliable operation and intelligent decision-making. With AI engineering advancing toward multi modal and heterogeneous industrial applications, research has increasingly focused on multi-sensor fusion and intelligent diagnostics. Although multi-sensor networks provide complementary information and enhanced perception, issues like data heterogeneity, class imbalance, and cross-domain distribution differences continue to constrain diagnostic performance. To address these issues, a Dual-branch Heterogeneous Synergistic Network (DHSNet) is proposed to achieve cross-modal fusion of vibration signals and infrared thermal imaging signals. The framework incorporates a cross domain adaptation strategy to enhance domain-invariant feature learning and a dynamic focal loss function to adaptively adjust class weights based on real-time output indicators, mitigating the impact of sample imbalance. Experimental results demonstrate that the proposed method achieves an average diagnostic accuracy of 93.27% in cross-load transfer tasks, outperforming other methods used in imbalanced scenarios by over 4%. Besides, the proposed method maintains robust diagnostic performance exceeding 90% accuracy across most load transfer scenarios, even under moderately imbalanced data conditions. Feature contribution analysis further validates the effectiveness of multi modal synergy, and revealing the complementary mechanism of multi-source data. This study enhances Prognostics and Health Management (PHM) systems' engineering applicability and perception capabilities in multi-sensor industrial environments, providing reliable multi-modal diagnostics to advance intelligent maintenance.

Spectral entropy (SE) is a promising nonlinear measure for detecting dynamic variations in vibration signals acquired from rolling element bearings (REB). However, in real world scenarios, characteristic spectral features relating to REB fault gets concealed by unwanted frequency components due to the association of heavy environmental noise. Consequently, original SE not only fails to detect incipient REB fault but also fails to monitor the progression of the fault along with predicting the remaining useful life of the faulty REB. Aiming to address aforementioned problems, in this paper, firstly, characteristic spectral features of REB fault is revealed by calculating the spectrum of the adaptively demodulated weighted squared envelope of the corresponding vibration signal. Subsequently, instead of using classical Shannon entropy theory corresponding to original SE, comprehensive prognosis of the analyzed REB health is achieved through the information quantification of the calculated spectrum by incorporating dispersion entropy (DE) theory. In this context, the proposed measure is named as adaptively demodulated dispersive spectral entropy (ADDSE). Two different run to failure REB data have been utilized to verify the effectiveness of the proposed ADDSE. Results show that the proposed ADDSE not only can overcome the limitations of the original SE in comprehensive dynamic prognosis of REB health but also demonstrate superior performance in compare to other conventional measures such as original DE and root mean square (RMS); advanced version of spectral entropy namely cumulative spectrum distribution entropy (CSDE) and three dimensional holo hilbert spectral entropy (MHHSE3D); alternative sparsity based measure namely Gini index (GI).

Bearing health monitoring (BHM) is vital in preventing unforeseen machinery shutdowns caused by frequent bearing failures. Within the BHM process, constructing health indicators takes center stage, serving the dual purpose of detecting incipient faults and assessing the monotonous degradation trend for predicting residual useful life. In terms of detecting incipient faults, permutation entropy (PE) serves as a promising tool due to its simplicity and rapid computation. However, when it comes to assessing irreversible degradation, PE often exhibits notable fluctuations and nonmonotonicity even after signal denoising processes. This issue arises from PE's vulnerability to impulsive noise and its invariance to monotonic signal transformations. To tackle this challenge, the article introduces a novel approach termed condition-adaptive permutation entropy (CAPE) for BHM. CAPE begins with a condition-based signal processing method to mitigate the influence of impulsive noise, followed by an amplitude-aware algorithm to break PE's invariance to monotonic signal processing. Moreover, CAPE adaptively selects fault-relevant permutation patterns to enhance its monotonicity. The effectiveness, superiority, and applicability of CAPE are rigorously demonstrated using simulation data and two experimental datasets.

As a nonlinear measure, Lempel–Ziv complexity (LZC) can be considered as a suitable parameter for characterizing bearing health status by measuring the complexity of vibration signals. However, in continuous monitoring scenario under noisy condition, all components of a multicomponent bearing signal are not equally sensitive toward a change of LZC value. As a result, a direct application of LZC for bearing health monitoring not only suffers from its inefficient early fault warning but also fails to infer the fault progression. In this article, instead of direct utilization of a whole vibration signal, its fundamental component (FC) sensitive to LZC calculation is separated with the help of continuously adjustable parameterized tunable$Q$factor wavelet transform (TQWT). In this context, a study based on sparsity indices has been done for$Q$factor selection of TQWT. Since TQWT uses an oscillation-based bearing FC separation scheme for LZC calculation, the proposed measure is termed as oscillatory Lempel–Ziv complexity (OLZC). Two experimental cases are used for validation. Performance of OLZC is compared with original LZC, representative sparsity indices and recently proposed multiscale symbolic Lempel–Ziv complexity. Results demonstrate that the proposed OLZC can not only overcome the limitations of the original LZC but also performs better than other indices in comparison to continuous monitoring of bearing health.

The health condition monitoring of planetary gearboxes has drawn increasing attention due to the importance for safety operation and failure prevention. A novel diagnosis methodology based on multiscale symbolic diversity entropy (SDivEn) is proposed in this article. Herein, dynamical complexity of measured data is quantified by SDivEn. Compare to other entropy-based descriptors, SDivEn has advantages in its robustness and computation efficiency. To increase the feature representation capability of entropy descriptors, multiscale analysis is performed, where the measurement data in time series is decomposed into multiple scaled series by using the coarse graining process and then processed individually by using SDivEn method. The proposed multiscale SDivEn method is applied for fault recognition of planetary gearboxes. Experimental results indicate that the proposed method obtains the highest accuracy in recognizing seven health conditions of planetary gearboxes in comparison with three other existing entropy-based methods.

In this article, a novel intelligent fault diagnosis method based on multiscale symbolic Lempel-Ziv (MSLZ) is proposed to identify several faults of railway vehicle systems (RVSs). The proposed MSLZ is essentially for the purpose of estimating the irregularity of a given time series. In the proposed MSLZ method, the symbolization and multiscale techniques are combined with Lempel-Ziv (LZ) to enhance its feature extraction ability. First, the symbolization can facilitate LZ to remove the noises and reserve the fault information. Second, multiscale analysis can extend LZ to multiple time scales, which can further enhance the description ability of dynamic characteristics. Using numerical data and experimental signals collected from RVSs, the performance of the MSLZ method is demonstrated to be sensitive to periodical impulses and robust to environmental noise. Moreover, it has been demonstrated that MSLZ has superiority in extracting fault information of the RVS compared with LZ, symbolic LZ, and multiscale LZ methods.

In this article, a fault diagnosis scheme based on multiscale diversity entropy (MDE) and extreme learning machine (ELM) is presented. First, a novel entropy method called diversity entropy (DE) is proposed to quantify the dynamical complexity. DE utilizes the distribution of cosine similarity between adjacent orbits to track the inside pattern change, resulting in better performance in complexity estimation. Then, the proposed DE is extended to multiscale analysis called MDE for a comprehensive feature description by combining with the coarse gaining process. Third, the obtained features using MDE are fed into the ELM classifier for pattern identification of rotating machinery. The effectiveness of the proposed MDE method is verified using simulated signals and two experimental signals collected from the bearing test and the dual-rotator of the aeroengine test. The analysis results show that our proposed method has the highest classification accuracy compared with three existing approaches: sample entropy, fuzzy entropy, and permutation entropy.

Fault diagnosis of bearings using classification techniques plays an important role in industrial applications, and, hence, has received increasing attention. Recently, significant efforts have been made to develop various methods for bearing fault classification and the application of Case Western Reserve University (CWRU) data for validation has become a standard reference to test the fault classification algorithms. However, a systematic research for evaluating bearing fault classification performance using the CWRU data is still lacking. This paper aims to provide a comprehensive benchmark analysis of the CWRU data using various entropy and classification methods. The main contribution of this paper is applying entropy-based fault classification methods to establish a benchmark analysis of entire CWRU datasets, aiming to provide a proper assessment of any new classification methods. Recommendations are provided for the selection of the CWRU data to aid in testing new fault classification algorithms, which will enable the researches to develop and evaluate various diagnostic algorithms. In the end, the comparison results and discussion are reported as a useful baseline for future research.