Abstract To address the inefficiency of centrifugal compressor fault warning caused by sample data scarcity, this paper proposes a compressor early-warning method based on Transformer-KAN and transfer learning. First, a time series prediction model that integrates Transformer and KAN is constructed and pre-trained using large-scale source domain data. Transfer learning is then performed, where the CORAL algorithm is used to align the feature distributions of the small sample target domain data with the source domain. The aligned target domain data is used to fine-tune the pre-trained model, resulting in a fault warning model suitable for the target scenario. Finally, the monitoring data from the target domain is input into the model for testing. Experimental results show that, when sample data is insufficient, the proposed method reduces the MAE and RMSE errors by 86.1% and 85.7%, respectively, compared to non-transfer learning models. Additionally, the constructed prediction model achieves an R 2 of 99.04%. Compared to the actual fault occurrence time, the model is able to detect early signs of failure and provide an effective warning three days in advance.

Turbomachinery fault diagnosis faces two major challenges: the scarcity of fault data and the distribution discrepancies among samples of the same fault type. Existing diagnostic methods often fail to adequately exploit the complementary information embedded in different data modalities. This study proposes a hierarchical multimodal transfer fusion framework enhanced with a fine-tuning mechanism to overcome these limitations. The proposed architecture integrates three modality-specific sub-models that extract complementary diagnostic features from waveform, spectrum, and shaft orbit data. The outputs of the three sub-models are then fused by summation, which involves fewer parameters to achieve high model accuracy on small datasets. A two-stage learning process, consisting of pre-training and fine-tuning, enables robust adaptation to limited and heterogeneous data conditions. To further enhance model generalization, phase-shifted waveform generation (PSWG) and shaft orbit transformation (SOT) are introduced to enrich data diversity and mitigate intra-class distribution discrepancies. The proposed method is validated on real-world turbomachinery datasets containing five representative fault types, namely unbalance, misalignment, oil whirl, rubbing, and surge. Experimental results demonstrate that PSWG and SOT enhance the diagnostic accuracy of the waveform- and shaft orbit-based models by 9.20% and 11.63%, respectively. The ablation result indicates that the proposed fusion model achieves a 1.65% higher diagnostic accuracy than the individual sub-models. Comparative analyses further confirm that the proposed fusion framework achieves higher diagnostic accuracy and robustness than state-of-the-art methods. These findings demonstrate that the proposed framework provides an effective and robust solution for intelligent fault diagnosis of turbomachinery.

Abstract Time-varying structural elements (TVSEs) have emerged as a promising approach for designing structural elements (SEs) in morphological filtering used for extracting impulsive features from signals. However, there is still a notable lack of comprehensive research on the performance of various combined morphological operators (CMOs) under TVSEs. To mitigate the impact of uncertainty in selecting SE shape and length on the performance of CMOs, this study presents a unified evaluation of the performance of CMOs under diverse interference conditions using a TVSE. To improve resistance to interference noise, an enhanced morphological gradient product operator (EMGPO) is constructed based on two high-performance CMOs. Additionally, to mitigate the impact of noise on the construction of TVSEs, a construction framework of denoised TVSE (DTVSE) is proposed, enabling the design of TVSEs with high sensitivity to transient features, and a designated DTVSE is constructed by incorporating advanced denoising techniques into its design. Furthermore, the power spectrum (PS) (representing the autocorrelation’s frequency domain) is utilized on the processed signal to suppress broadband noise disturbances. Finally, an early fault diagnosis method for rotating machinery is introduced, integrating the EMGPO, DTVSE, and PS analysis. The proposed approach is validated using simulated data, experimental data and real-world fault datasets from two wind turbines and is compared against state-of-the-art methods. The findings indicate that this approach accurately identifies transient features triggered by rotating machinery faults under multi-source noise interference. Moreover, it outperforms existing methods in terms of accuracy, noise immunity, and feature extraction, establishing its effectiveness for early fault diagnosis in practical engineering applications.

The turbine, as a critical component of gas turbines, has been widely used in marine propulsion. However, performance prediction based on small samples remains challenging. While data-driven methods easily overfit turbine characteristics, traditional loss models are difficult to calibrate due to their high-dimensional parameters. To address these issues, a rapid performance prediction method based on loss model theory and small-sample data-driven adaptive calibration was proposed. Various energy loss models were integrated, and the optimal model was identified through systematic multicriteria evaluation. Key parameters were determined using Self-Organizing Map analysis for intelligent dimensionality reduction. This process identified the most sensitive coefficients, reducing the number of parameters from 29 to 8 and cutting calibration time by 50%. For the single-stage turbine, the maximum prediction error was reduced from 3.84% to 0.83%. High accuracy was maintained in multistage turbines, where the inherent overestimation of losses was effectively corrected, as validated by 3D flow details. The model was further validated via 0D dynamic simulation, maintaining an average relative prediction error of less than 1.0% during a 25% load step-change. This research supports the construction and optimization of digital models for gas turbines.

Fault early warning based on gas turbine sensor networks is critical for intelligent predictive maintenance and operational safety in modern power systems. While data-driven techniques are prevalent, balancing computational efficiency with long-term modeling of measurement transients remains challenging under complex temporal drifts. This paper proposes a novel Multi-Scale Temporal Convolutional Network (MS-TCN) specifically designed for the long-term time series forecasting (LTSF) task in industrial environments. The proposed architecture introduces a mathematical decomposition framework featuring: 1) an autocorrelation-guided detrending module to mitigate non-stationary distribution shifts by extracting inherent periodic trends directly from multi-sensor streams; and 2) a dual-pooling mechanism that decomposes measurement sequences for highly efficient cross-scale dependency learning. Additionally, a full-history convolution layer provides the architectural capacity to integrate broader historical context. Rigorous evaluations on Long-Term Time Series Forecasting (LTSF) benchmarks demonstrate that the MS-TCN architecture reduces estimation errors by up to 43.2% (with improvements ranging from 18.5% to 43.2% depending on the specific dataset and forecasting horizon) compared to state-of-the-art computational models. Furthermore, to translate these LTSF predictions into practical industrial applications, a adaptive residual-weighted multi-level warning framework is established using adaptive weights to quantify decaying prediction confidence. A robust four-level alert system based on $3\sigma $ thresholds is introduced to explicitly account for sensing uncertainties and helps reduce false positives. Validation on real-world gas turbine operational data confirms that the proposed computing framework triggers warnings 4-6 hours earlier than conventional baselines, offering a practical and effective tool for industrial predictive maintenance.

As the supporting structure for the nacelle and rotor of a wind turbine, the tower plays a crucial role in ensuring safe and stable operation of the entire system. Accurate monitoring of tower structural deformation is essential for maintaining structural integrity and extending its operational lifespan. This paper proposes a digital twin-based data-physics fusion monitoring method for wind turbine towers under varying operating conditions. A 3D virtual model of the prototype wind turbine is developed to represent its physical counterparts, while a high-fidelity finite element model (FEM) is constructed to stimulate the structural behavior of the tower under wind loading. To enable efficient real-time analysis, a support vector regression (SVR) model is trained from FEM simulation data, allowing for a rapid representation of tower deformation. Additionally, a LSTM deformation prediction model is developed using sensor data to enhance monitoring accuracy. A digital twin framework and platform is established for real-time condition monitoring of wind turbine, integrating operating data from the wind turbine with tower deformation mechanism. Finally, experiments conducted on a small-scale prototype wind turbine demonstrate the effectiveness of the proposed methodology. This study provides a promising approach to integrating data, physics, and machine learning within a digital twin framework to enhance the accuracy of real-time condition monitoring for wind turbines.

Accurate three-dimensional flow field reconstruction in planar cascades is crucial for the aerodynamic design of turbomachinery. Existing methods for obtaining flow field data, including experimental measurements and numerical simulations, have limitations such as long cycles and high computational resource consumption. Driven by the development of artificial intelligence, data-driven modeling has emerged as a new paradigm for cascade flow field prediction. However, single models rely on large amounts of high-fidelity (HF) data, significantly increasing the modeling costs. Although multi-fidelity learning can improve the prediction accuracy by fusing multi-fidelity data, purely data-driven knowledge transfer however exhibits insufficient accuracy in predicting complex flows and is prone to overfitting. To address these issues, this study proposes a Physics-Informed Multi-Fidelity Neural Network with Fourier features (fPIMFNN) that integrates physics constrained multi-fidelity learning. The framework implements a multi-fidelity collaboration network for cross-fidelity knowledge transfer, embeds the Reynolds-Averaged Navier-Stokes (RANS) equations as physical constraints to ensure prediction consistency, and conducts Fourier feature embedding to strengthen the capture of multi-scale flow features. Experimental results on a transonic cascade demonstrate that the proposed fPIMFNN outperforms various competitors, thus providing a data-efficient solution for complex three-dimensional flow field modeling.

This study proposes a data-physics fusion intelligent methodology for multi-variable auto-calibration of transient performance model for gas turbines. A thermodynamics-based performance model is developed to accurately simulate the transient behavior of a heavy-duty gas turbine through automatic fitting of compressor characteristic curves, intelligent tuning of the combustion chamber under variable operating conditions, and optimal calibration of gas-specific heat properties. This physics-based model provides theoretical support for model-based calibration methods. A generalized implementation framework is established to seamlessly integrate actual operational data with the physics-based performance model using a genetic algorithm-based calibration methodology. A comparison study, conducted using data from two real-world gas turbines across various operational phases-including startup, load ramping and steady-state transitions-demonstrates the effectiveness of the proposed approach. Numerical results show that the proposed calibration methodology achieves an average error reduction of 86.3% compared to the original transient-surpassing Cuckoo Search Algorithm (50.7%) and Kalman Filter (64.4%)-significantly enhancing model accuracy. These findings confirm the framework's ability to balance computational efficiency with physical interpretability, ensuring robust performance across different gas turbine configurations.

Accurate performance prediction and preventive maintenance of heavy-duty gas turbines are critical for enhancing operational efficiency and reducing downtime. This study proposes an enhanced Deep Operator Network (DeepONet) framework for predicting key performance indicators of gas turbines, including efficiency, heat rate, and power output, to enable condition-based maintenance. The method replaces the conventional trunk network of DeepONet with Transformer, which architecture is capable of dynamically capturing complex temporal dependencies and long-range dependencies in historical data relevant to the prediction target through its self-attention mechanism. Additionally, causal convolutional units are embedded into the branch network to ensure temporal causality. The proposed framework is validated using real-world gas turbine operational data, demonstrating superior prediction accuracy compared to traditional DeepONet models, with the reduction of mean square error and mean absolute error values. The integration of multi-scale temporal modeling and causal constraints effectively addresses challenges posed by nonlinear dynamics, variable coupling in gas turbines. Predictive results are further utilized to quantify performance degradation trends, enabling early fault detection and optimized maintenance scheduling.

Wind speed forecasting is crucial for wind power prediction, wind farm operations, and power optimization scheduling. However, the inherent randomness and uncontrollability of wind resources make accurate forecasting a significant challenge. Traditional methods often struggle to effectively handle noise and uncertainty, limiting their practical applicability. This paper introduces a hybrid wind speed forecasting model that integrates self-adaptive Bayesian Wavelet Packet Thresholding (BDWPT) and a Deep Gaussian Process (DGP) to enhance prediction accuracy. BDWPT is utilized to adaptively reduce noise while preserving essential time series trends, thereby minimizing input uncertainties. The DGP model is then employed to capture the stochastic nature of wind speed fluctuations and generate probabilistic forecasts. Additionally, Monte Carlo simulation is applied to quantify output uncertainties. The proposed model was validated through a comparison study using real-world data from four wind farms operating under various conditions. Results demonstrate that the hybrid approach significantly outperforms traditional methods, achieving over 90% improvement in forecast accuracy. This method offers a reliable tool for wind power applications, enabling more informed decision-making and enhancing wind farm efficiency.

The reliability of the main bearings in wind turbines is crucial for their safe and stable operation. However, due to their structural complexity and exposure to harsh operating conditions, these bearings experience variable loads and frequent failures, which affect the overall reliability of wind turbines. Traditional finite element methods (FEM) struggle to meet the requirements of real-time condition monitoring and predictive maintenance. To address this, we propose a novel remaining usage life (RUL) prediction method that integrates finite element model (FEM), dimension reduction technique, and damage accumulation modeling (DAM) theory. First, a high-fidelity physics-based FEM is developed to simulate the behavior of double rolling element bearings under specific operating conditions. Then, Proper Orthogonal Decomposition (POD) is applied to extract dominant modal features from stress field simulations, enabling an efficient low-dimensional representation of the high-dimensional physical field. The method combines data-driven machine learning regression techniques for lightweight modeling. Numerical results demonstrate that the proposed method achieves a over 95

Remaining useful life (RUL) prediction is essential for the prognostic health management (PHM) of industrial equipment, such as aero engines, enabling predictive maintenance and reducing failure risks. Data-driven models have gained significant attention in RUL prediction due to their ability to capture complex nonlinear relationships. However, the variability in data distributions across multiple operating conditions makes it challenging for traditional models to capture temporal and spatial features of equipment operation, leading to unstable prediction performance. To address this issue, this paper proposes a novel LSTM-KAN-DANN transfer learning method for RUL prediction. First, we train a LSTM-Kolmogorov-Arnold Network (KAN) model using multiple source domain datasets, allowing it to extract nonlinear features and provides preliminary RUL estimates. Then, Domain-Adversarial Neural Networks (DANN) is integrated with LSTM-KAN by introducing a domain discriminator and gradient reversal layer. This enables the model to learn domain-invariant features, reducing discrepancies between the source and target domains and improving generalization across different operating conditions. A comparison study using the CMAPSS dataset demonstrates that LSTM-KAN effectively captures nonlinear features, particularly under complicated operating conditions, outperforming traditional methods in generalization. The DANN integration further enhances predictive accuracy in cross-domain scenarios, leading to notable reductions in RMSE and Score across most transfer tasks. The proposed LSTM-KAN-DANN transfer learning framework provides a robust and efficient solution for industrial equipment PHM, offering significant potential for real-world applications.

Existing turbomachinery fault diagnosis methods can identify coarse fault categories but fail to achieve fine-grained diagnosis, thereby preventing field engineers from performing targeted maintenance. This limitation mainly arises from their reliance on time-domain, frequency-domain, and shaft-orbit features while ignoring their temporal evolution. To address this limitation, we propose a fine-grained fault diagnosis method based on multivariate feature time series. First, a dual-branch neural network architecture is developed to integrate temporal evolution features from multivariate feature time series with complementary statistical features. Second, an efficient gated recurrent unit (EGRU) is designed to capture global dependencies in time series. Third, a data augmentation strategy is proposed, which combines segmentation-concatenation for time series and class distribution-based sampling for statistical features. Finally, an automated framework facilitates industrial fault diagnosis and deployment. A comparative study validates the method on a real-world dataset with seven fault types. By incorporating EGRU and data augmentation, the proposed method improves the average test accuracy by 1.22% and 2.4%, respectively, achieving a total improvement of 6.44% and surpassing comparable methods. Numerical results demonstrate that the proposed method provides a promising direction for fine-grained fault diagnosis of turbomachinery.

Condition monitoring is critical for intelligent equipment maintenance, enabling early fault detection, improved safety, and reduced unplanned downtime. However, existing approaches are highly dependent on data quality and often lack generalization across diverse machine types and operating conditions, leading to inaccurate fault alarms. To address these limitations, this study proposes a generalized similarity-based method for fault identification in rotating machines. The method integrates wavelet packet Bayesian thresholding to suppress noise in multidimensional data and employs the Manhattan distance metric within the generalized Enhanced Auto-Associative Kernel Regression (EAKR) model to evaluate sample similarity. A practical procedure for implementing EAKR in automatic early fault detection is also developed. An ablation study demonstrates that the proposed EAKR model achieves higher fault identification accuracy and robustness compared to traditional approaches. Furthermore, validation on real-world datasets from gas turbines, wind turbines, and centrifugal compressors confirms its broad applicability. The proposed EAKR model exhibits strong generalization capability and feasibility, highlighting its potential as a fundamental approach for improving condition monitoring and enhancing the reliability of industrial rotating machinery.

Fatigue damage prediction research is critically vital to ensuring the structural integrity and operational reliability of mechanical systems. A transfer learning Transformer- Kolmogorov-Arnold Networks (TLT-KAN) framework integrating Transformer encoders and Kolmogorov-Arnold Networks (KAN) is proposed to predict residual fatigue damage under multi-level loading with limited samples. To address the dual limitations of physics-based models (inaccuracies caused by over simplification) and conventional data-driven methods (requiring sufficient data), TLT-KAN leverages simulation data from the validated Manson-Halford physics-based model as the source domain for pre-training, transferring knowledge by fine-tuning the model on scarce real experimental data (target domain). Validation results on a comprehensive dataset comprising 14 materials demonstrate that TLT-KAN achieves competitive prediction accuracy using only 8.3% of the training data required by conventional machine learning (ML) models. When the training data increases to 16.7% of that needed by conventional ML models, its accuracy surpasses all ML models. Ablation studies confirm the critical roles of the Transformer encoder’s feature interaction and KAN’s adaptive nonlinear mapping. The model exhibits exceptional data efficiency, enabling high-accuracy fatigue prediction under scenarios of limited experimental data.

Accurate wind speed forecasting is essential for the reliable and cost-effective integration of wind energy into modern power systems. This paper provides a comprehensive state-of-the-art review on data-driven artificial intelligence methods for wind speed forecasting from 2014 to early 2026 and evaluates their practical performance through a multi-site benchmark. The bibliometric trend analysis is conducted to identify the methodological evolution. These methods are categorized into four groups, i.e., statistical, machine learning, deep learning, and hybrid, with particular attention to decomposition enhanced forecasting frameworks. Ten representative forecasting methods combined with three data decomposition techniques are evaluated using four datasets from China, Norway, and a public benchmark. The results show that hybrid models with wavelet based decomposition generally improve the accuracy and robustness of short-term wind speed forecasting. Decomposition enhanced Transformer and Gaussian process models achieve relatively stable performance across different datasets and forecasting horizons. It is suggested that model selection relies on multiple factors including data characteristics, forecasting horizon, and computational constraints. Based on the review and benchmarking results, this study provides practical guidance on model selection for wind energy applications and identifies key research directions, including long-term forecasting, data-physics fusion learning, forecasting under extreme conditions, adaptive learning and explainable AI for broader climatic and operational scenarios. The findings offer actionable insights for improving forecasting reliability in large scale wind energy deployment.

Triply periodic minimal surface (TPMS) structures, characterized by high space utilization, low weight, and high stiffness, have been widely applied in the design of advanced heat exchangers. In this study, an IWP-type biomimetic cellular heat transfer structure is investigated. A numerical model is established and validated through additive manufacturing experiments to systematically examine the internal flow mechanisms and the effects of surface roughness on flow and heat transfer performance. The results indicate that the flow and heat transfer within the IWP-type TPMS structure exhibit pronounced spatial non-uniformity. Both pressure drop and temperature reduction are primarily concentrated in the inlet region. The flow and heat transfer processes are predominantly governed by the main flow channels that traverse the structure, while low-velocity stagnation zones and stable vortex structures tend to form in the intersections of adjacent main channels, thereby influencing the local heat transfer and flow resistance distribution. Further analysis reveals that surface roughness plays a critical role in regulating near-wall flow behavior and thus affects heat transfer performance. As roughness increases, near-wall disturbances and momentum dissipation are intensified, leading to higher pressure drop and fanning friction factor. Meanwhile, fluid mixing is enhanced, resulting in an increase in the Nusselt number. However, a clear trade-off exists between heat transfer enhancement and flow resistance. An appropriate level of roughness (e.g., Ra=50 µm) can achieve improved heat transfer while maintaining a controlled increase in flow resistance, thereby optimizing the overall performance. The findings of this study are expected to provide useful guidance for the optimal design and additive manufacturing of TPMS-based heat exchangers.

Accurate wind speed forecasting can mitigate wind power fluctuations, enhance grid dispatch efficiency, reduce operational and maintenance costs, improve system accommodation capacity, and ensure secure and stable power system operation. This study proposes a hybrid framework integrating Bayesian Discrete Wavelet Packet Transform denoising with Kolmogorov-Arnold Network for short-term wind speed forecasting. The framework initially employs BDWPT’s multiscale decomposition capability and integrates with Bayesian unbiased hypothesis testing to perform adaptive denoising on raw wind speed data, thereby enhancing the data representation capability. Subsequently, a KAN-based neural architecture is constructed, leveraging learnable spline-based activation functions to achieve high-precision modeling of complex nonlinear relationships, effectively capturing both temporal dynamic characteristics and abrupt variation patterns in wind speed sequences. The efficacy of the proposed hybrid model is substantiated through rigorous comparative experiments. Results from two distinct datasets demonstrate that the hybrid model surpasses the original baseline models across three key evaluation metrics in the context of short-term wind speed forecasting. Additionally, comparative analyses with alternative denoising techniques paired with KAN reveal that the BDWPT-KAN configuration outperforms other combinations, thereby validating the effectiveness of integrating BDWPT with KAN.

Wind speed forecasting has become an essential part of power forecasting, daily operation, and optimal scheduling of wind farms. However, due to the extreme randomness and unpredictability of wind resources, it’s still a very challenging task to accurately forecast wind speed considering data uncertainties. Most existing methods do not take into account the data uncertainty and randomness in wind speed forecasting, resulting in inaccurate results in practical applications. This paper proposes a hybrid intelligent model for wind speed forecasting under uncertainties by adeptly integrating Bayesian Discrete Wavelet Packet Transform (BDWPT) and Gaussian Process Regression (GPR). Firstly, the BDWPT method is applied to reduce the noise and randomness of raw data by taking advantage of its powerful adaptive denoising capability. Then, the GPR model is developed to model the randomness in wind speed forecasting. Finally, a comparison study with traditional methods by using the data collected from real-world wind farms is conducted to show the advantages of the proposed methodology in terms of one-step and multi-step cases. This study provides a promising approach to accurately forecast wind speed for turbine design and power management considering data uncertainties.

The accurate extraction of machine fault-related information is the premise for implementing condition-based maintenance. In vibration analysis, morphological filtering is an effective method to detect bearing fault signatures, wherein the design of structural element and the construction of morphological operator are crucial to its performance. In this paper, a generalized morphological diagonal slice operator (GMDSO) framework is established for constructing new morphological operators with strong immunity to multi-source noise. Then, by introducing high-performance morphological operators into the GMDSO framework, a specific morphological gradient diagonal slice operator (MGDSO), is designed for extracting transient signatures. To optimize the signature excavation of morphological operators and attenuate the influence of noise in selecting structural element shape and length, an enhanced adaptive time-varying structural element (EATVSE) is proposed for more exact matching fault signatures. Finally, to accurately diagnose the early faults of rolling bearings, an enhanced adaptive time-varying morphological filtering (EATVMF) is proposed in combination with MGDSO and EATVSE. The fault diagnosis capability of EATVMF is testified on simulated signals, experimental signals, and bearing accelerated degradation datasets, and compared with five existing methods. The results demonstrate that EATVMF has excellent transient signature excavation and noise elimination capabilities under strong interference noise, and outperforms comparison methods.