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Keywords = frequency-limited Gramians

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19 pages, 6060 KB  
Article
Gramian Angular Field–Gramian Adversial Network–ResNet34: High-Accuracy Fault Diagnosis for Transformer Windings with Limited Samples
by Hongwen Liu, Kun Yang, Guochao Qian, Jin Hu, Weiju Dai, Liang Zhu, Tao Guo, Jun Shi and Dongyang Wang
Energies 2025, 18(16), 4329; https://doi.org/10.3390/en18164329 - 14 Aug 2025
Viewed by 282
Abstract
Transformers are critical equipment in power transmission and distribution systems, and the condition of their windings significantly impacts their reliable operation. Therefore, the fault diagnosis of transformer windings is of great importance. Addressing the challenge of limited fault samples in traditional diagnostic methods, [...] Read more.
Transformers are critical equipment in power transmission and distribution systems, and the condition of their windings significantly impacts their reliable operation. Therefore, the fault diagnosis of transformer windings is of great importance. Addressing the challenge of limited fault samples in traditional diagnostic methods, this study proposes a small-sample fault diagnosis method for transformer windings. This method combines data augmentation using the Gramian angular field (GAF) and generative adversarial networks (GAN) with a deep residual network (ResNet). First, by establishing a transformer winding fault simulation experiment platform, frequency response curves for three types of faults—axial displacement, bulging and warping, and cake-to-cake short circuits—and different fault regions were obtained using the frequency response analysis method (FRA). Second, a frequency response curve image conversion technique based on the Gramian angular field was proposed, converting the frequency response curves into Gramian angular summation field (GASF) and Gramian angular difference field (GADF) images using the Gramian angular field. Next, we introduce several improved GANs to augment the frequency response data and evaluate the quality of the generated samples. We compared and analysed the diagnostic accuracy of ResNet34 networks trained using different GAF–GAN combination datasets for winding fault types, and we proposed a transformer winding small-sample fault diagnosis method based on GAF-GAN-ResNet34, which can achieve a fault identification accuracy rate of 96.88% even when using only 28 real samples. Finally, we applied the proposed fault diagnosis method to on-site transformers to verify its classification performance under small-sample conditions. The results show that, even with insufficient fault samples, the proposed method can achieve high diagnostic accuracy. Full article
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16 pages, 3892 KB  
Article
Fault Diagnosis Method for Shearer Arm Gear Based on Improved S-Transform and Depthwise Separable Convolution
by Haiyang Wu, Hui Zhou, Chang Liu, Gang Cheng and Yusong Pang
Sensors 2025, 25(13), 4067; https://doi.org/10.3390/s25134067 - 30 Jun 2025
Viewed by 343
Abstract
To address the limitations in time–frequency feature representation of shearer arm gear faults and the issues of parameter redundancy and low training efficiency in standard convolutional neural networks (CNNs), this study proposes a diagnostic method based on an improved S-transform and a Depthwise [...] Read more.
To address the limitations in time–frequency feature representation of shearer arm gear faults and the issues of parameter redundancy and low training efficiency in standard convolutional neural networks (CNNs), this study proposes a diagnostic method based on an improved S-transform and a Depthwise Separable Convolutional Neural Network (DSCNN). First, the improved S-transform is employed to perform time–frequency analysis on the vibration signals, converting the original one-dimensional signals into two-dimensional time–frequency images to fully preserve the fault characteristics of the gear. Then, a neural network model combining standard convolution and depthwise separable convolution is constructed for fault identification. The experimental dataset includes five gear conditions: tooth deficiency, tooth breakage, tooth wear, tooth crack, and normal. The performance of various frequency-domain and time-frequency methods—Wavelet Transform, Fourier Transform, S-transform, and Gramian Angular Field (GAF)—is compared using the same network model. Furthermore, Grad-CAM is applied to visualize the responses of key convolutional layers, highlighting the regions of interest related to gear fault features. Finally, four typical CNN architectures are analyzed and compared: Deep Convolutional Neural Network (DCNN), InceptionV3, Residual Network (ResNet), and Pyramid Convolutional Neural Network (PCNN). Experimental results demonstrate that frequency–domain representations consistently outperform raw time-domain signals in fault diagnosis tasks. Grad-CAM effectively verifies the model’s accurate focus on critical fault features. Moreover, the proposed method achieves high classification accuracy while reducing both training time and the number of model parameters. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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19 pages, 5298 KB  
Article
A Health Status Identification Method for Rotating Machinery Based on Multimodal Joint Representation Learning and a Residual Neural Network
by Xiangang Cao and Kexin Shi
Appl. Sci. 2025, 15(7), 4049; https://doi.org/10.3390/app15074049 - 7 Apr 2025
Viewed by 506
Abstract
Given that rotating machinery is one of the most commonly used types of mechanical equipment in industrial applications, the identification of its health status is crucial for the safe operation of the entire system. Traditional equipment health status identification mainly relies on conventional [...] Read more.
Given that rotating machinery is one of the most commonly used types of mechanical equipment in industrial applications, the identification of its health status is crucial for the safe operation of the entire system. Traditional equipment health status identification mainly relies on conventional single-modal data, such as vibration or acoustic modalities, which often have limitations and false alarm issues when dealing with real-world operating conditions and complex environments. However, with the increasing automation of coal mining equipment, the monitoring of multimodal data related to equipment operation has become more prevalent. Existing multimodal health status identification methods are still imperfect in extracting features, with poor complementarity and consistency among modalities. To address these issues, this paper proposes a multimodal joint representation learning and residual neural network-based method for rotating machinery health status identification. First, vibration, acoustic, and image modal information is comprehensively utilized, which is extracted using a Gramian Angular Field (GAF), Mel-Frequency Cepstral Coefficients (MFCCs), and a Faster Region-based Convolutional Neural Network (RCNN), respectively, to construct a feature set. Second, an orthogonal projection combined with a Transformer is used to enhance the target modality, while a modality attention mechanism is introduced to take into consideration the interaction between different modalities, enabling multimodal fusion. Finally, the fused features are input into a residual neural network (ResNet) for health status identification. Experiments conducted on a gearbox test platform validate the proposed method, and the results demonstrate that it significantly improves the accuracy and reliability of rotating machinery health state identification. Full article
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17 pages, 5553 KB  
Article
AI-Enabled Compact and Efficient Dynamic Light Scattering System for Precise Microparticle Sizing
by Yongxin Zhang, Shijie Fu, Qian Zhang, Xinyi Chen, Jiyu Feng, Jin Cui and Bin Ai
Appl. Sci. 2025, 15(4), 1900; https://doi.org/10.3390/app15041900 - 12 Feb 2025
Cited by 1 | Viewed by 1516
Abstract
A cost-effective and efficient AI-DLS framework integrating dynamic light scattering (DLS) with artificial intelligence (AI) enables precise microparticle size characterization. A compact DLS system was developed using a helium–neon laser, high-frequency photodetectors, and optimized optical components, achieving significant miniaturization—4.5% volume, 16.7% weight, and [...] Read more.
A cost-effective and efficient AI-DLS framework integrating dynamic light scattering (DLS) with artificial intelligence (AI) enables precise microparticle size characterization. A compact DLS system was developed using a helium–neon laser, high-frequency photodetectors, and optimized optical components, achieving significant miniaturization—4.5% volume, 16.7% weight, and 25% cost of conventional systems. Advanced signal processing, such as Kalman filtering, improved data quality, while deep learning models (deep neural network (DNN), one-dimensional convolutional neural network (1D-CNN), and 2D-CNN with Gramian angular field transformations) enhanced prediction accuracy. The 2D-CNN model achieved exceptional results, with a mean absolute error of 10 nm and 99% accuracy. The AI-DLS system matched the stability and accuracy of traditional instruments, reducing test time by 80%. This scalable, low-cost solution overcomes traditional DLS limitations, offering broad accessibility for scientific and industrial microparticle characterization. Full article
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15 pages, 548 KB  
Article
Laguerre-Based Frequency-Limited Balanced Truncation of Discrete-Time Systems
by Zhou Song, Qiu-Yan Song and Umair Zulfiqar
Mathematics 2025, 13(3), 448; https://doi.org/10.3390/math13030448 - 28 Jan 2025
Viewed by 608
Abstract
This paper introduces a novel model order reduction (MOR) method for linear discrete-time systems, focusing on frequency-limited balanced truncation (BT) techniques. By leveraging Laguerre functions, we develop two efficient MOR algorithms that avoid the computationally expensive generalized Lyapunov equation solvers used in traditional [...] Read more.
This paper introduces a novel model order reduction (MOR) method for linear discrete-time systems, focusing on frequency-limited balanced truncation (BT) techniques. By leveraging Laguerre functions, we develop two efficient MOR algorithms that avoid the computationally expensive generalized Lyapunov equation solvers used in traditional methods. These algorithms employ recursive formulas to calculate Laguerre expansion coefficients, which are then used to derive low-rank decomposition factors for frequency-limited controllability and observability Gramians. Additionally, we enhance the Laguerre-based low-rank MOR algorithm by incorporating a modified frequency-limited BT method, further improving its computational efficiency. Numerical simulations validate the effectiveness of the proposed approach, demonstrating significant reductions in computational complexity while maintaining accuracy in system approximation. Full article
(This article belongs to the Section E: Applied Mathematics)
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21 pages, 6820 KB  
Article
Intelligent Fault Diagnosis of Variable-Condition Motors Using a Dual-Mode Fusion Attention Residual
by Fengyun Xie, Gang Li, Wang Hu, Qiuyang Fan and Shengtong Zhou
J. Mar. Sci. Eng. 2023, 11(7), 1385; https://doi.org/10.3390/jmse11071385 - 7 Jul 2023
Cited by 10 | Viewed by 1796
Abstract
Electric motors play a crucial role in ship systems. Detecting potential issues with electric motors is a critical aspect of ship fault diagnosis. Fault diagnosis in motors is often challenging due to limited and noisy vibration signals. Existing deep learning methods struggle to [...] Read more.
Electric motors play a crucial role in ship systems. Detecting potential issues with electric motors is a critical aspect of ship fault diagnosis. Fault diagnosis in motors is often challenging due to limited and noisy vibration signals. Existing deep learning methods struggle to extract the underlying correlation between samples while being susceptible to noise interference during the feature extraction process. To overcome these issues, this study proposes an intelligent bimodal fusion attention residual model. Firstly, the vibration signal to be encoded undergoes demodulation and is divided into high and low frequencies using the IEEMD (Improved Ensemble Empirical Mode Decomposition) composed of the EEMD (Ensemble Empirical Mode Decomposition) and the MASM (the Mean of the Standardized Accumulated Modes). Subsequently, the high-frequency component is effectively denoised using the wavelet packet threshold method. Secondly, current data and vibration signals are transformed into two-dimensional images using the Gramian Angular Summation Field (GASF) and aggregated into a bimodal Gramian Angle Field diagram. Finally, the proposed model incorporates the Self-Attention Squeeze-and-Excitation Networks (SE) mechanism with the Swish activation function and utilizes the ResNeXt architecture with a Dropout layer to identify and diagnose faults in the multi-mode fusion dataset of motors under various working conditions. Based on the experimental results, a comprehensive discussion and analysis were conducted to evaluate the performance of the proposed intelligent bimodal fusion attention residual model. The results demonstrated that, in comparison to traditional methods and other deep learning models, the proposed model effectively utilized multimodal data, thereby enhancing the accuracy and robustness of fault diagnosis. The introduction of attention mechanisms and residual learning enable the model to focus more effectively on crucial modal data and learn the correlations between modalities, thus improving the overall performance of fault diagnosis. Full article
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6 pages, 1430 KB  
Proceeding Paper
Model Reduction of Discrete-Time Index-3 Second-Order Form Systems for Limited Frequency Intervals
by Humaira Rauf Qazi, Shafiq Haider, Aamina Bintul Huda, Muhammad Saqlain and Ahmed Roohullah Arif
Eng. Proc. 2022, 20(1), 40; https://doi.org/10.3390/engproc2022020040 - 5 Aug 2022
Viewed by 1320
Abstract
A model order reduction framework for limited frequency interval response optimization of reduced order models (ROMs) for index-3 second-order form of systems (SOSs) is presented in this paper. Firstly, an index-3 SOS system is transformed into index-0 and the corresponding generalized first-order form. [...] Read more.
A model order reduction framework for limited frequency interval response optimization of reduced order models (ROMs) for index-3 second-order form of systems (SOSs) is presented in this paper. Firstly, an index-3 SOS system is transformed into index-0 and the corresponding generalized first-order form. In order to emphasize ROM response over the required frequency interval, frequency-limited gramians and corresponding generalized Lyapunov equations are presented and balancing of gramians is obtained by solving Lyapunov equations to obtain the required ROM exhibiting a good response in the intended frequency interval. The developments are tested on multiple systems and the superiority of the proposed extension over existing methods is certified. Propositions can be utilized for frequency-limited applications for index-3 SOSs. Full article
(This article belongs to the Proceedings of The 7th International Electrical Engineering Conference)
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6 pages, 1258 KB  
Proceeding Paper
Stable Reduced-Order Model for Index-3 Second-Order Systems
by Mubashir Rehan, Shafiq Haider, Aamina Bintul Huda, Muhammad Saqlain and Hussain Hadi
Eng. Proc. 2022, 20(1), 27; https://doi.org/10.3390/engproc2022020027 - 2 Aug 2022
Viewed by 1342
Abstract
A new technique for preserving the stability of a reduced-order model (ROM) for index-3 second-order systems (SOSs) in a limited frequency interval is discussed in this paper. This technique is implemented by making indefinite terms of algebraic Lyapunov equations definite, which can be [...] Read more.
A new technique for preserving the stability of a reduced-order model (ROM) for index-3 second-order systems (SOSs) in a limited frequency interval is discussed in this paper. This technique is implemented by making indefinite terms of algebraic Lyapunov equations definite, which can be used in applications such as signal reconstruction controller design and filter design. The index-3 form is first converted into index-0 form, and then the Lyapunov equations are solved to compute the limited frequency Gramians. The terms that are indefinite can be made definite by assigning them the nearest possible positive eigenvalues. Gramians are balanced to obtain Hankel singular values, which are used later to obtain the ROM using balanced truncation. Full article
(This article belongs to the Proceedings of The 7th International Electrical Engineering Conference)
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29 pages, 1173 KB  
Article
Development of Frequency Weighted Model Reduction Algorithm with Error Bound: Application to Doubly Fed Induction Generator Based Wind Turbines for Power System
by Sajid Bashir, Sammana Batool, Muhammad Imran, Muhammad Imran, Mian Ilyas Ahmad, Fahad Mumtaz Malik and Usman Ali
Electronics 2021, 10(1), 44; https://doi.org/10.3390/electronics10010044 - 29 Dec 2020
Cited by 16 | Viewed by 3471
Abstract
The state-space representations grant a convenient, compact, and elegant way to examine the induction and synchronous generator-based wind turbines, with facts readily available for stability, controllability, and observability analysis. The state-space models are used to look into the functionality of different wind turbine [...] Read more.
The state-space representations grant a convenient, compact, and elegant way to examine the induction and synchronous generator-based wind turbines, with facts readily available for stability, controllability, and observability analysis. The state-space models are used to look into the functionality of different wind turbine technologies to fulfill grid code requirements. This paper deals with the model order reduction of the Variable-Speed Wind Turbines model with the aid of improved stability preserving a balanced realization algorithm based on frequency weighting. The algorithm, which is in view of balanced realization based on frequency weighting, can be utilized for reducing the order of the system. Balanced realization based model design uses a full frequency spectrum to perform the model reduction. However, it is not possible practically to use the full frequency spectrum. The Variable-Speed Wind Turbines model utilized in this paper is stable and includes various input-output states. This brings a complicated state of affairs for analysis, control, and design of the full-scale system. The proposed work produces steady and precise outcomes such as in contrast to conventional reduction methods which shows the efficacy of the proposed algorithm. Full article
(This article belongs to the Section Systems & Control Engineering)
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15 pages, 838 KB  
Article
Balanced Truncation Model Order Reduction in Limited Frequency and Time Intervals for Discrete-Time Commensurate Fractional-Order Systems
by Marek Rydel, Rafał Stanisławski and Krzysztof J. Latawiec
Symmetry 2019, 11(2), 258; https://doi.org/10.3390/sym11020258 - 19 Feb 2019
Cited by 8 | Viewed by 3030
Abstract
In this paper we investigate an implementation of new model order reduction techniques to linear time-invariant discrete-time commensurate fractional-order state space systems to obtain lower dimensional fractional-order models. Since the models of physical systems correctly approximate the physical phenomena of the modeled systems [...] Read more.
In this paper we investigate an implementation of new model order reduction techniques to linear time-invariant discrete-time commensurate fractional-order state space systems to obtain lower dimensional fractional-order models. Since the models of physical systems correctly approximate the physical phenomena of the modeled systems for restricted time and frequency ranges only, a special attention is given to time- and frequency-limited balanced truncation and frequency-weighted methods. Mathematical formulas for calculation of the time- and frequency-limited, as well as frequency-weighted controllability and observability Gramians, are extended to fractional-order systems. An instructive simulation experiment corroborates the potential of the introduced methodology. Full article
(This article belongs to the Special Issue Fractional Differential Equations: Theory, Methods and Applications)
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