Optimization of gas turbine fault identification based on time-frequency analysis of acoustic and vibration signals and transformer

Abstract

Introduction:

Gas turbines are core equipment in industrial development, and their safe operation is of paramount importance. Fault identification in gas turbines can prevent significant economic losses and safety accidents; however, traditional approaches are time-consuming and inefficient.

Methods:

Therefore, this research introduces an optimized fault identification method based on time-frequency analysis of acoustic and vibration signals and a two-branch Transformer model. First, variational mode decomposition is performed on the acquired signals. Key intrinsic mode function components are selected based on correlation coefficients to reconstruct the signal, and their time-frequency domain features are extracted. Second, an autoencoder is used to reduce the dimensionality of high-dimensional features to retain key fault information. Finally, a two-branch Transformer model is constructed from the time step dimension and channel feature dimension to achieve accurate classification of fault states. Among them, the time step branch captures the temporal dependencies between vibration and acoustic signals through a masked multi head attention mechanism, which is consistent with the continuity of the fault evolution process. Channel branches utilize global attention to fuse the correlation features between multiple sensors, reflecting the collaborative changes of different measurement points in fault states.

Results:

Tests on three states show that, through variational mode decomposition and feature reduction to extract essential signal features, the introduced model obtains an overall classification accuracy of 92.5%. In cross-load condition tests, the constructed model achieves an average identification accuracy of 94.7%, with a maximum of 98.2%. Compared to the standard Transformer, the constructed model obtains a 5.9% improvement in identification accuracy under strong disturbance conditions with an 11.6% reduction in parameters.

Discussion:

This method demonstrates higher identification accuracy and stronger stability, further contributing to the reliability of gas turbine fault identification. This provides a reliable technical solution for the accurate fault identification and health management of gas turbines and other mechanical equipment.

1 Background

Gas turbines (GTs) play a crucial role in improving the energy structure and promoting sustainable environmental progress. They have advantages such as environmental protection and energy saving, and fast start-up. GTs are broadly applied in many crucial domains like power, ships, and oil and gas. Components such as GT blades and rotors are more prone to cracks, rubbing, imbalance and other faults [1]. Therefore, it is necessary to seek an intelligent fault identification technology to better ensure the dependable functioning of GTs. Traditional diagnostic methods rely more on the manual construction and selection of time-frequency domain (TFD) features based on expert experience. Their generalization ability and recognition accuracy are often constrained by changes in working conditions [2]. In recent times, deep learning (DL) tools like convolutional neural networks (CNN) and recurrent neural networks (RNNs) have shown high efficiency and accuracy in automatic feature extraction and pattern recognition. However, CNN has limited ability to model long-term dependencies of time-series signals, while RNNs have problems such as low training efficiency [3]. Self-attention mechanism models represented by Transformer have emerged as a prominent technology in the realm of time series data processing, but their effective fusion of heterogeneous features and processing of local and global dependencies in signals have become limitations in the development of complex mechanical multi-source signal recognition [4].

Many scholars have adopted various intelligent methods in the work of GT fault detection and have achieved some good results. Nadir F et al. used a five-layer neural network (NN) nonlinear principal component analysis technique to detect GT faults and used the filtered squared prediction error index for fault identification. The findings demonstrated that the fault detection accuracy of this approach was improved by 15% [5]. Yan W et al. designed a multi-arm spiral microphone array and a multi-channel audio acquisition system for GT fault detection, and combined it with an audio data imaging analysis method constructed by feature extraction and autoencoder (AE) network. The findings demonstrated that the accuracy of this method exceeded 98% [6]. Akhtar M et al. first built a three-dimensional model of the rotor and combined it with modal analysis and harmonic response analysis methods to achieve early identification of GT rotor faults. The findings demonstrated that the critical speed and vibration value of the model were 99.7% and 99.1% respectively [7]. Raghavan S M accurately evaluated the fault location of different systems based on the operating data and artificial NN for the identification of performance degradation of GT components. The findings demonstrated that the goodness of fit was greater than 0.95 [8].

In recent years, the application results of intelligent recognition technology based on Transformer in the field of industrial parts have shown that each method has the advantages of high precision, strong robustness or high efficiency. For example, in order to detect the loose state of multi-bolt connection, Li X X et al. built a new framework that combines Transformer model and recursive feature elimination. The findings demonstrated that the technology had high precision and strong robustness, and the recognition accuracy rate was 99.6% [9]. Rahmati M et al. designed a multi-modal DL framework for accurate identification of defects in industrial parts. It integrates CNN, RNN and signal Transformer to extract cross-modal features and time dependence. The findings demonstrated that the classification accuracy reached 94.7% [10]. Zhang W et al. used Swin-Transformer and U-Net as generative surrogate models to analyze the efficiency problem of multi-physics distribution prediction of air film cooling of turbine blades. The findings demonstrated that the model had less computation time [11]. To solve the problem of recognition of signals under complex channels and strong noise interference, Li J et al. introduced a network grounded in dual-stream Transformer to extract the time-frequency map features of the signal and combined it with a multi-head attention (MHA) module with adaptive soft threshold for noise suppression. The findings demonstrated that the recognition rate was improved by up to 5.9% [12].

In summary, existing intelligent fault identification methods largely employ various novel DL technologies and have achieved good results. However, from the perspective of signal processing and physical mechanisms, the vibration and acoustic signals of GTs exhibit non-stationary and strongly modulated characteristics when faults such as rotor imbalance, blade cracks, collision friction, etc., occur. Standard CNN extracts features through local convolution, making it difficult to model global temporal dependencies. Although the standard Transformer has a global attention mechanism, it does have shortcomings in modeling the physical structure of signals by directly treating time steps as lexical elements to process mechanical signals. Specifically, the sound and vibration signals collected by multiple sensors exhibit both physical coupling between different measurement points in the spatial dimension and continuity of fault evolution in the temporal dimension. A single structured CNN or standard Transformer is difficult to effectively model these two heterogeneous relationships simultaneously, which has become a common bottleneck in current methods. This lack of targeted theoretical design limits the feature expression ability and robustness of the model under variable load conditions and strong aerodynamic noise interference. Therefore, this study delves into the time-frequency analysis and feature learning of multi-source signals such as sound and vibration from GTs, and designs an innovative fault identification optimization method. First, the acquired multi-source signals are decomposed using Variational Mode Decomposition (VMD) to obtain their intrinsic time-frequency structure. Then, feature dimensionality reduction is performed using an AE. Finally, a two-branch Transformer is designed to improve fault identification accuracy. This research aims to improve the fault identification rate of GTs and provide safe and efficient detection technologies for power generation, transportation, and other fields.

2 Fault identification method based on VMD and two-branch Transformer model

2.1 Time-frequency analysis and feature dimensionality reduction of multi-source signals

The study extracts features of GT fault modes from multi-source signals of GTs. Unlike traditional methods, the study first preprocesses the multi-source signals and selects the reconstructed signal as the Intrinsic Mode Function (IMF) component based on the largest correlation coefficient. The video and features of the reconstructed signal are extracted and feature reduction is performed using AE to generate a dimensionality-reduced feature set [13]. The processing flow from multi-source signals to dimensionality-reduced features and the AE structure are shown in Figure 1. Figure 1a is the feature processing flow chart for equipment fault diagnosis. First, the original signal is input and decomposed into multiple IMF components by VMD to achieve frequency band splitting of the signal. Then, 16 TFD features are extracted from the IMF components after VMD decomposition, and the signal is converted into a feature vector that can be used for classification.

FIGURE 1

The collected data is preprocessed by VMD. In VMD, a variational problem is constructed first. The original input signal is decomposed into components [14]. This study used Pearson correlation coefficient as the screening criterion for IMF, mainly because this index can quantify the strength of information correlation between various modal components and the original signal. High correlation IMF usually contains effective modulation components directly related to faults, while low correlation components are mostly noise or redundant information. By filtering through correlation coefficients, signal purification can be achieved while maximizing the preservation of fault features, thereby improving the reliability of subsequent feature extraction and fault recognition. The expression of the corresponding constraint variation is shown in Equation 1.

In Equation 1, is the time derivative. is the Dirac delta function. is the set of IMF components, and is the th modal component. is the set of center frequencies. is the L2 norm. is the frequency phase shift factor. After the th iteration, the frequency domain (FD) update value of the th modal component is given by Equation 2 [15].

In Equation 2, is the FD of the original signal. is the FD of the th modal component. is the FD of the Lagrange multiplier. is the iteration number. is the penalty parameter, used to control the minimization of bandwidth and the weights between the signal and constraints. Through grid search, was used throughout the entire work. represents the normalization term, i.e., the weights balancing the bandwidth constraints and the remaining signal. From the perspective of signal processing, VMD can be regarded as a set of adaptive Wiener filters at the physical level, which can effectively avoid mode aliasing problems. It decouples the overlapping modulation frequency caused by mechanical faults into a relatively pure IMF, laying a theoretical foundation for subsequent feature extraction.

Figure 1b is a schematic diagram of the AE structure. The autoencoder consists of symmetric encoder and decoder. The encoder contains three fully connected layers with 288, 128, and 18 neurons; the first two use ReLU activation, while the last layer uses linear activation to output an 18-dimensional latent representation. The decoder mirrors the encoder with layers of 128 and 288 neurons, and a Sigmoid output layer to constrain reconstructions to [0,1]. The 288-dimensional input is compressed to 18 dimensions at a ratio of 16:1. Dropout (rate = 0.2) is added after each encoder layer to mitigate overfitting. The model is trained with MSE loss using the Adam optimizer (learning rate = 1 × 10⁻³) for 100 epochs. Its function is to optimize the connection weights between each layer through training, so as to ensure that the output is infinitely close to the input, thereby ensuring that the model can obtain the same effective features as the input data [16]. Let the input sample data be , and the expression of the encoder is shown in Equation 3.

In Equation 3, and are the outputs of the encoder and decoder, and and are the corresponding activation functions. and are the weight matrix (WM) and bias value (BV) of the encoder. and are the WM and BV of the decoder. The loss function of the encoder is . The study extracts multiple TFD features from the IMF components and constructs a feature set for the input of the subsequent recognition model, ( represents the th TFD feature of the third IMF component). The total number of TFD features of is determined by factors including the number of TFD features extracted from each component, the number of channels of the original signal, and the number of IMF components selected after VMD decomposition. Based on the actual situation, and are determined, and .

2.2 Construction of the two-branch Transformer recognition model

After VMD processes the original GT signal, the TFD features that can reflect the fault state are extracted. Then, the high-dimensional fault features extracted are reduced in dimensionality by AE to simplify the input complexity of the subsequent model. Finally, the processed fault features are input into the two-branch Transformer model to complete the fault identification task of the GT. Given that the original signal of the GT has rich fault information, and the TFD features of its vibration signal can reflect the fault state. To this end, a two-branch Transformer model was designed, which specifically includes a channel encoder and a time step encoder. The theoretical basis of this two-branch structure is derived from the physical nature of the acoustic vibration signal of GT faults. The physical significance of a channel encoder is that the acoustic vibration signals collected by multi-channel sensors inherently contain spatial structural information. When a fault occurs, the excitation force propagates through the rotor and casing to various sensors, forming spatial physical coupling. The MHA mechanism in channel branching is theoretically designed to model this cross channel interaction and extract the spatial distribution characteristics of fault sources [17]. The signal processing mechanism of the time step encoder is that mechanical faults usually manifest as periodic transient impacts or continuous energy changes in time. Introducing position encoding and masked MHA forces the network to follow the temporal causal relationship of signal processing, capturing the dynamic evolution and long-term degradation trend of faults [18]. The feature fusion of the two branches enables the model to map abstract one-dimensional time-domain signals into spatiotemporal physical representations that balance spatial distribution and temporal evolution. Compared to the standard single stream Transformer, which treats each time step as an independent semantic unit, this structure achieves effective decoupling and recombination of spatial coupling and temporal causality, fundamentally explaining its superior performance under complex working conditions and strong noise conditions.

The structure is presented in Figure 2. In Figure 2, the input time step data and spatial feature data are shown. An MHA mechanism is used for channel features to capture the global correlation of the input data. For the time step data, a position embedding module is added after the linear layer processing. This module adds temporal position information to the input features. This layer utilizes a masked MHA mechanism to avoid subsequent information leakage and to focus more on current or past information [19]. Then, it passes through a Residual (Res) + Normalization (Norm) layer, a Feedforward Fully Connected (FFC) layer, and a Res + Norm layer in sequence. The final outputs of the channel encoder and the time step encoder are fused together in the fusion layer, transformed by a linear layer, and finally output by Softmax to obtain the classification result.

FIGURE 2

It should be noted that the input of the dual branch Transformer is not a 16 dimensional static feature vector, but a multi-channel, multi time step temporal feature matrix. The core advantage of this model lies in its ability to synchronously capture temporal dependencies and spatial coupling characteristics between multiple sensors, which is difficult for simple classifiers such as Support Vector Machine (SVM) and Random Forest (RF) to achieve. Through AE dimensionality reduction and lightweight attention design, the model complexity has been effectively controlled without significant overfitting. In the low dimensional time-frequency feature space, Transformer can still achieve better diagnostic accuracy and generalization performance through its spatiotemporal joint modeling ability. In the MHA mechanism, the computational formula involved is Equation 4 [20].

In Equation 4, , , and are the query, key, and value vectors for attention calculation, respectively. , , and are the matrices composed of , , and . is the vector dimension of the model. , , and are the linear transformation matrices corresponding to the th head. is the output of the th single-head attention. The Res + Norm layer refers to avoiding the degradation of the attention mechanism output data during network training and normalizing the output data before entering the FFC layer. The FFC layer is essentially a two-layer NN. The first layer is used for linear transformation, and after passing through the ReLU activation function, it passes through another layer of NN [21]. An additional position embedding module is introduced in the time-step encoder. The calculation for position encoding is presented in Equation 5 [22].

In Equation 5, and are elements of the position encoding vector. is the position number of the current time step, and is the dimension index of the encoding vector. is the feature dimension of the model, . The function of the masked MHA mechanism is to set a mask for the future word position so that its attention weight is zero. The calculation formula is shown in Equation 6 [23].

In Equation 6, is a mask matrix that masks all word positions after the current word position, making the attention weights of these positions negative infinity, so that the weights are zero after the Softmax operation. In the fusion layer, the outputs of the two encoders are concatenated into a vector and output through a linear layer. The calculation formula for this process is shown in Equation 7 [24].

In Equation 7, is the output of the FFC layer, is the WM of the FFC layer, and is the BV of the FC layer. represents the output of the channel encoder, and represents the output of the time step encoder. represents the splicing operation. and are both weights, . is the final fused feature vector. This study uses 17 codes (S1∼S17) to represent different fault state codes of GT. S18 is used to refer to the comprehensive diagnostic accuracy of all 17 types of fault data. The detailed information of the number and its meaning is shown in Table 1.

2.3 Experimental platform and data collection

To simulate a real GT scenario, this study conducted multiple fault state simulation experiments on an industrial GT test bench. The test bench can simulate the operating state of GTs under various working conditions and reproduce typical faults by manually setting faulty components. The schematic diagram of the industrial GT test bench is shown in Figure 3. Figure 3 shows the compressor section, combustion chamber, turbine section, rotor shaft, and bearings. Data collection uses four acceleration sensors (V1-V4) to collect vibration signals, which are respectively arranged on the compressor housing (V1), front and rear bearing seats (V2, V3), and turbine housing (V4). At the same time, two microphones (M1 and M2) were used to collect acoustic signals and placed 30 cm away from the housing.

FIGURE 3

Before inputting the recognition model, this study adopts a sliding window slicing strategy to enhance the samples and reconstruct the structure of the original long-term time-domain signals. The specific processing flow is as follows. The experimental sampling frequency is 25,600 Hz, and the continuous sampling duration for a single operating condition is 120 s. Therefore, the total number of sampling points for the original signal is 120 s × 25,600 Hz = 3072000. Use a Hanning window with 2048 sampling points to slice the signal, with an overlap rate controlled below 10%. A single 120 s continuous collection can generate approximately 1500 independent sample fragments. This study collected a total of 18 operating states and three speed conditions, with each condition repeated 3 times. The total sample size was calculated as follows: 18 states × 3 speeds × 3 repetitions × 1500 samples/time ≈243,000 valid samples. All samples were randomly divided into training set, validation set, and testing set in a ratio of 7:2:1.

2.4 The overall process of work

To facilitate a clear understanding of the complete data processing flow of the proposed method, this study provides a unified explanation of the changes in feature dimensions from the original signal to the model input. Figure 4 shows the overall process of this study, which mainly includes four key stages. Phase one is VMD decomposition and signal reconstruction. Stage two is time-frequency domain feature extraction. Stage three is AE feature dimensionality reduction. Stage four is the input construction of a dual branch Transformer.

FIGURE 4

3 Results and analysis

3.1 Effectiveness of VMD and AE feature processing

To determine the Pearson correlation coefficient between the sum of all IMF components and the original signal under different values, the study analyzed the variation curves of the value and the Pearson correlation coefficient. Furthermore, to evaluate the effectiveness of the fault classification model, the accuracy of three states—healthy, compressor imbalance, and overdraft imbalance—was determined using a confusion matrix. These three types of states cover the normal operation of GT and typical fault modes of core rotating components, which can effectively reflect the model’s ability to distinguish basic fault modes. The outcomes of the two experiments are presented in Figure 5. In Figure 5a, when was 5, the correlation coefficient between the reconstructed signal and the original signal was 0.7895. As the value continued to increase, the improvement in reconstruction accuracy was minimal. Overall, a value of five was recommended. Components 3 (correlation coefficient 0.3162), 4 (correlation coefficient 0.6379), and five were selected as reconstructed signals based on their higher correlation, thus preserving key information from the original signal. In Figure 5b, the model demonstrated good classification performance for the three states, with significantly larger diagonal values and very few misclassified samples. The accuracy for turbine imbalance reached 100%, with no misclassified samples. The accuracy for compressor imbalance reached 91.4%. The healthy state had the largest number of samples, reaching 42. Overall, the classification accuracy of these three state models reached 92.5%.

FIGURE 5

The study examined the TFD features extracted from the IMF components. The definitions and mathematical formulas for 16 time-frequency domain features have been provided, as detailed in Appendix A. Figure 6 shows the TFD features of the vibration displacement signal under healthy conditions as a function of time. Figures 6a-f show the 12 time-domain features extracted from the components. The root mean square (RMS) represents the average level of vibration energy, and the standard deviation (SD) represents vibration stability. Figures 6g-i show the four frequency-domain features extracted from the components.

FIGURE 6

To verify the effectiveness of AE dimensionality reduction, different features obtained from the input AE were studied, illustrating three scenarios: healthy state, compressor imbalance, and turbine imbalance. The signal characteristics of different features after dimensionality reduction are presented in Figure 7. Figure 7a shows features one to three in the healthy state. Figure 7b indicates the signal variation trends of features one to three under the turbine imbalance condition. The fluctuation amplitude of feature three was significantly greater than that of features 1 and 2, indicating that this feature had a high sensitivity to turbine imbalance faults. The changes in vibration energy distribution or frequency structure caused by the fault were extracted and compressed by the AE and mapped onto the low-dimensional representation of feature 3, thus making it exhibit a more significant response under fault conditions. In Figure 7c, the fluctuation amplitude of compressor imbalance feature two was much greater than that of the other two conditions. Specifically, feature two had extremely high discriminative power for compressor imbalance faults. The dynamic response mode caused by this fault was effectively captured by the AE and reflected in this dimension. Therefore, the AE used had a good dimensionality reduction effect, which could retain information of different states while compressing the feature dimensions.

FIGURE 7

3.2 Baseline validation on CWRU bearing dataset

3.2.1 Dataset description and experimental setup

To fully verify the universal effectiveness and algorithmic superiority of the proposed dual branch Transformer model in time series signal fault recognition, this study first used the Case Western Reserve University (CWRU) bearing dataset. Bearings are key rotating components in GTs, and the CWRU bearing dataset is a recognized standard benchmark in the field of rotating machinery fault diagnosis. Therefore, this study conducted baseline comparison experiments using this dataset. In the CWRU experiment, the acoustic branch of the model was temporarily deactivated, and the dual-branch framework processed only the multi-channel vibration signals through the vibration channel encoder to ensure compatibility with the unimodal dataset.

3.2.2 Network configuration

The test conditions are 0 horsepower load (HP0), 1 horsepower load (HP1), and 2 horsepower load (HP2) [25]. The network parameter configuration design for the two-branch Transformer and the traditional Transformer is shown in Table 2.

3.2.3 Comparative analysis under steady loads

The study was designed with HP0 conditions, and two-branch Transformer, Transformer, and CNN were all trained. The accuracy and loss values of different models under HP0 conditions are shown in Figure 8. In Figure 8a, the accuracy of the two-branch Transformer rapidly increased from 89.3% to 96.8% in the first five iterations. Subsequently, in the fifth to 100th iterations, its accuracy stabilized between 97.0% and 98.0%, with an average accuracy of approximately 97.5%. The accuracy of the CNN in 100 iterations was approximately between 88.4% and 90.5%, relatively more stable, but its accuracy was still low. The accuracy changes of the Transformer in the early stages were basically the same as those of the two-branch Transformer, but after 10 iterations, its fluctuations became more significant. In Figure 8b, the loss curve of the two-branch Transformer began to stabilize after 50 iterations, and ultimately its loss value was smaller than that of the CNN (0.31), at only 0.27. The Transformer’s loss curve stabilized after 10 iterations, with the lowest loss value of only 0.12. Overall, under HP0 conditions, the two-branch Transformer demonstrated higher fault identification accuracy.

FIGURE 8

Figure 9 shows the changes in accuracy and loss values of different models under HP1 conditions. In Figure 9a, the accuracy of the three models gradually increased and tended to stabilize with the increase of training iterations. The fault identification accuracy of the two-branch Transformer stabilized at 92.0% after five iterations. However, the accuracy curve of the Transformer fluctuated greatly during the iteration process, with its accuracy ranging from 82.5% to 98.0%. The CNN was relatively stable, but its accuracy stabilized at 74.0% after five iterations, which was lower than that of the two-branch Transformer. In Figure 9b, the loss curves of the three models decreased with the increase of iterations. After 20 iterations, the loss value of the two-branch Transformer was always smaller than that of the CNN. Meanwhile, with the increase of iterations, the loss value of the two-branch Transformer gradually approached that of the Transformer. Finally, the loss value of the Transformer was 0.29, while the loss value of the two-branch Transformer was 0.35. Considering both accuracy and loss value, the two-branch Transformer exhibited higher fault identification accuracy and greater stability under HP0 operating conditions.

FIGURE 9

Figure 10 shows the accuracy and loss values of different models under the HP2 test condition. In Figure 10a, the accuracy of CNN remained stable at 72.2% after 50 iterations. In contrast, the accuracy of Transformer fluctuated significantly, with a minimum accuracy of approximately 87.8% and a maximum accuracy of 99.0%. The accuracy of the two-branch Transformer remained relatively stable after 10 iterations, with an accuracy of approximately 93.8%. In Figure 10b, compared to the other two models, the loss curve of the two-branch Transformer showed significant fluctuations over 100 iterations, with the loss value dropping rapidly from 2.9 to 0.55 from the initial iteration. In contrast, the loss curves of CNN and Transformer dropped rapidly in the first 10 iterations, eventually stabilizing after 15 iterations, with loss values of 0.45 and 0.12, respectively. Under the HP2 test condition, the two-branch Transformer has a higher fault identification accuracy.

FIGURE 10

Figure 11 shows the fault identification accuracy of the introduced two-branch Transformer under various test conditions. In Figure 10, the average accuracy of the two-branch Transformer was low at only 88.5% under HP1 condition. For S12, the accuracy was only 74.2% under HP2 condition. Overall, the model achieved an accuracy of approximately 98.2% under HP0 condition. This was because it compensated for the shortcomings of the original Transformer model in handling strong noise interference and insufficient generalization ability under various conditions by uniformly modeling the global channel correlation and local time dependence in multi-source time-series signals.

FIGURE 11

3.2.4 Ablation experiment

To quantify the independent contributions of each key component in the proposed complete framework, this study conducted ablation experiments based on test data under HP0 operating conditions. Six model configurations were constructed by removing or replacing core modules layer by layer, and the recognition accuracy comparison of each variant model is shown in Table 3. In Table 3, comparing M0 and M1, the accuracy decreased by 4.7% after removing VMD. VMD decouples non-stationary acoustic signals into relatively pure IMF components, suppressing the interference of GT emphasis noise on subsequent feature learning. Compared to M0 and M2, the accuracy of manually extracted features decreased by 2.5%. The accuracy of M3 and M4 decreased by 2.1% and 2.2% respectively compared to M0, indicating that both the AE module and the two-branch structure can achieve performance improvement. M5, on the other hand, is an unprocessed raw signal and serves as a standard Transformer, resulting in a 9.0% decrease in accuracy compared to M0. The proposed model relies on key components to improve performance.

3.2.5 Comprehensive comparison with different methods

To analyze the overall performance of the introduced approach, it was compared with various fault identification methods. Table 4 indicates the performance comparison of different fault identification methods. Compared with modality decomposition + machine learning methods (methods one and 2), the average accuracy of the introduced approach was improved by 11.6% and 9.2%, respectively. The deep feature learning and deep model used in the proposed method had strong capabilities in complex fault mode recognition. Under HP2 conditions, the accuracy of the proposed method (93.8%) was significantly higher than that of 2D-CNN (86.5%), 1D-CNN (83.2%), and LSTM (82.0%), with improvements of 7.3%, 10.6%, and 11.8%, respectively. This was due to the fact that the two-branch Transformer in the proposed method could simultaneously model local and global dependencies and was unresponsive to shifts in operating circumstances. The proposed method achieved the best balance between accuracy, efficiency, and robustness. Specifically, the accuracy of the introduced approach was better than that of the standard Transformer and Informer because the two-branch structure was specifically designed for mechanical signals and solved the problem of semantic ambiguity in time steps. The proposed method had significantly fewer parameters (14.2M) than the CNN-Transformer hybrid model (25.7M) and faster inference speed (4.0 m vs. 10.2 m). The proposed method demonstrated the most stable performance across all three operating conditions and exhibited the strongest generalization ability.

3.3 Validation on GT test bench

3.3.1 Dataset description and experimental setup

After confirming the baseline performance of the algorithm on the CWRU dataset, the ultimate goal of this study is to address specific fault diagnosis challenges in GT. Therefore, the actual GT test bench dataset used in this study was used for core validation of the proposed framework. The detailed composition of the GT bench dataset is summarized in Table 5.

3.3.2 Robustness under variable speeds and noise

To verify the robustness of the proposed model under varying operating conditions and varying noise conditions, tests were conducted at three different speeds: 3000 rpm, 4500 rpm, and 6000 rpm. In addition, the study further added Gaussian white noise with different Signal to Noise Ratios (SNR) to the collected vibration and acoustic signals at a speed of 4500 rpm. The experimental results under the above two conditions are shown in Table 6. According to the speed test data in Table 6, the model performs the best under the condition of 4500 rpm, with an average accuracy of 93.8%. The recognition rate slightly decreased under high-speed conditions of 6000 rpm, mainly due to the increased aerodynamic noise during high-speed operation. In the anti noise performance test, when the SNR is 5 dB, the accuracy of the proposed model is 85.6%, which is 5.9% higher than the standard Transformer (79.7%), verifying the superiority of the proposed model under strong interference conditions.

3.3.3 Synergistic contribution of acoustic-vibration fusion

To quantitatively evaluate the actual contribution of acoustic signals in the proposed diagnostic framework, this study compared the fault recognition accuracy of three input modes under different operating conditions: using only 4-channel vibration signals, using only 2-channel acoustic signals, and fusing all 6-channel acoustic signals. The strong noise condition refers to the test results obtained by artificially adding Gaussian white noise with a signal-to-noise ratio of 5 dB to the HP0 operating signal. The comparison results are shown in Table 7. According to the results in Table 7, when only using acoustic signals, the accuracy under various operating conditions is about 88%–91%, which is lower than the 92%–96% when only using vibration signals. This is mainly due to the low signal-to-noise ratio of acoustic signals, which are more significantly affected by environmental background noise interference. Under all testing conditions, the fusion mode achieved improved accuracy compared to using only vibration signals. Specifically, it is reflected in a 2.4% increase in HP0 operating conditions, a 3.2% increase in HP1 operating conditions, a 4.1% increase in HP2 operating conditions, and an average increase of 3.2% across operating conditions. Under strong noise conditions, the accuracy brought by fusion increased from 87.2% to 94.5%, and the gain was further expanded to 7.3%. When vibration signals are severely contaminated by noise, acoustic signals can provide more robust complementary diagnostic information.

4 Summary and future work

GT faults are complex and diverse, and relying solely on manual diagnosis is insufficient to guarantee operational reliability. To enahnce the precision and robustness of fault identification, this research proposed an intelligent identification method integrating VMD, AE, and a two-branch Transformer. This method first used VMD combined with correlation coefficient filtering to reconstruct and denoise the original vibration signal, and then used AE to compress the extracted high-dimensional time-frequency features. Subsequently, a two-branch Transformer structure was designed to capture the correlation between channels and the dependencies in the time series in parallel. Experimental findings demonstrated that this method performed well under various operating conditions. When the VMD parameter was set to 5, the correlation coefficient between the reconstructed signal and the original signal reached 0.7895. Features extracted based on the selected IMF components, after dimensionality reduction using AE, could clearly distinguish different fault types. In tests on the CWRU bearing dataset with three load conditions, the average identification accuracy of this method was 94.7%, reaching a maximum of 98.2% under the HP0 condition, significantly outperforming other comparative methods. Under HP2 conditions, its recognition accuracy of 93.8% was 7.3%, 10.6%, and 11.8% higher than 2D-CNN, 1D-CNN, and LSTM, respectively. Compared with the standard Transformer model, the introduced approach achieved a better balance between parameter scale and inference efficiency while maintaining improved accuracy. The primary contribution of this study resides in the design of a dedicated two-branch Transformer architecture for multi-source time-series signals, which effectively alleviates the problems of time-step semantic loss and insufficient feature fusion in traditional Transformers for mechanical signal diagnosis, providing a feasible new approach for fault identification under complex working conditions. However, the performance of the designed model requires manual setting of hyperparameters such as the number of VMD decomposition layers and Transformer, lacking an adaptive adjustment mechanism, which affects the stability of the model under different data distributions. Future research can use the key parameters of the model as learnable variables and embed them into an end-to-end training framework. In addition, it can combine Bayesian optimization or meta-learning to achieve adaptive configuration of hyperparameters to further enhance its generalization performance.

References

• 1.

  BaguaHKhaldiBSIratniAIratniAHafaifaAColakI. Model-based faults diagnostics of single shaft gas turbine using fuzzy faults tolerant control. Automatic Control Computer Sci (2024) 58(2):117–30. 10.3103/S0146411624700020

  • CrossRef
  • Google Scholar
  • View reference in article

• 2.

  HadrougNIratniAHafaifaAAliliBColakI. Implementation of vibrations faults monitoring and detection on gas turbine system based on the support vector machine approach. J Vibration Eng and Tech (2024) 12(3):2877–902. 10.1007/s42417-023-01020-5

  • CrossRef
  • Google Scholar
  • View reference in article

• 3.

  BuJSunJGaoXSuCDuS. Wear failure analysis of ball bearings with artificial pits for gas turbines. J Fail Anal Prev (2024) 24(3):1365–75. 10.1007/s11668-024-01928-4

  • CrossRef
  • Google Scholar
  • View reference in article

• 4.

  HadrougNIratniAHafaifaAColakI. Intelligent faults diagnostics of turbine vibration’s via Fourier transform and neuro-fuzzy systems with wavelets exploitation. Smart Sci (2024) 12(1):155–84. 10.1080/23080477.2023.2281734

  • CrossRef
  • Google Scholar
  • View reference in article

• 5.

  NadirFMessaoudBEliasH. Utilizing principal component analysis for the identification of gas turbine defects. J Failure Analysis Prevention (2024) 24(1):97–107. 10.1007/s11668-023-01817-2

  • CrossRef
  • Google Scholar
  • View reference in article

• 6.

  YanWHuMWenFGuoPGuoZ. Research on fault diagnosis method and application of gas turbine based on acoustic imaging technology IET Conference Proceedings CP889. Stevenage, 2024. UK: The Institution of Engineering and Technology (2024). p. 141–6. 10.1049/icp.2024.2827

  • CrossRef
  • Google Scholar
  • View reference in article

• 7.

  AkhtarMAshrafWMHayatNHayatNUddinGMRiazF. Numerical and experimental investigation of gas turbine rotor for early fault detection. Energy Sci and Eng (2025) 13(5):2546–64. 10.1002/ese3.70054

  • CrossRef
  • Google Scholar
  • View reference in article

• 8.

  RaghavanSMPalatelASimonJ. Artificial neural networks based parametric curve generation for health assessment of industrial gas turbine systems. Process Integration and Optimization for Sustainability (2024) 8(2):577–90. 10.1007/s41660-023-00372-5

  • CrossRef
  • Google Scholar

• 9.

  LiXXLiDRenWXSunXT. An RFE-aided Transformer-SVM framework for multi-bolt connection loosening identification using wavelet entropy of vibro-acoustic modulation signals. Adv Struct Eng (2025) 28(1):89–103. 10.1177/13694332241269233

  • CrossRef
  • Google Scholar

• 10.

  RahmatiMRahmatiN. A multimodal deep learning framework for real-time defect recognition in industrial components using visual, acoustic and vibration signals. J Intell Manufacturing Spec Equipment (2025) 6(3):273–92. 10.1108/JIMSE-07-2025-0015

  • CrossRef
  • Google Scholar
  • View reference in article

• 11.

  ZhangWLiuZSongYLuYFengZ. Prediction of multi-physics field distribution on gas turbine endwall using an optimized surrogate model with various deep learning frames. Int J Numer Methods Heat and Fluid Flow (2024) 34(8):2865–89. 10.1108/HFF-10-2023-0620

  • CrossRef
  • Google Scholar

• 12.

  LiJJiaQCuiXGulliverTAJiangBLiSet alAutomatic modulation recognition of underwater acoustic signals using a two-stream transformer. IEEE Internet Things J (2024) 11(10):18839–51. 10.1109/JIOT.2024.3367852

  • CrossRef
  • Google Scholar

• 13.

  LiYYangZGuoP. Optimal design of vibration and noise for medium-high frequency transformer core based on genetic Algorithm. J Electr Eng and Technology (2025) 20(1):377–87. 10.1007/s42835-024-01948-y

  • CrossRef
  • Google Scholar

• 14.

  AkbarpourSKhosrowjerdiMJ. A multiple model-based approach for gas turbine fault diagnosis. Iranian J Sci Technol Trans Electr Eng (2025) 49(1):265–78. 10.1007/s40998-024-00754-6

  • CrossRef
  • Google Scholar
  • View reference in article

• 15.

  LiJYingY. A novel machine learning based fault diagnosis method for all gas-path components of heavy duty gas turbines with the aid of thermodynamic model. IEEE Trans Reliability (2024) 73(4):1805–18. 10.1109/TR.2024.3383922

  • CrossRef
  • Google Scholar

• 16.

  PhamDAHanSH. Advanced machine learning model based on Bi-LSTM and attention mechanism for fault detection in wind turbine systems. J Electr Eng and Technology (2025) 20(8):5429–42. 10.1007/s42835-025-02373-5

  • CrossRef
  • Google Scholar
  • View reference in article

• 17.

  DhimanHSPatilSWagleSSoniNKotechaKSelvachandranGet alMulti-head attention transformer and Bayesian inference recommendation engine-based blade icing detection framework for wind turbines. Neural Comput Appl (2025) 37(31):26157–76. 10.1007/s00521-025-11619-2

  • CrossRef
  • Google Scholar
  • View reference in article

• 18.

  BelayMABernardinoLFBlaksethSSRasheedAMontañésRMRossiPS. Unsupervised leak detection for heat recovery steam generators in combined-cycle gas and steam turbine power plants. IEEE Sensors J (2025) 26(1):652–64. 10.1109/JSEN.2025.3630886

  • CrossRef
  • Google Scholar
  • View reference in article

• 19.

  WangJHuBLuLZhongWFangFLiuY. Event-triggered sliding mode control for networked control systems with actuator faults: application to gas turbine system. Trans Inst Meas Control (2024) 46(9):1791–802. 10.1177/01423312231204700

  • CrossRef
  • Google Scholar
  • View reference in article

• 20.

  AkbarpourSKhosrowjerdiMJ. Estimation of combustor and compressor faults in industrial gas turbines by using multiple model approach. Iranian Chem Eng J (2024) 23(134):54–68. 10.22034/ijche.2023.392185.1301

  • CrossRef
  • Google Scholar
  • View reference in article

• 21.

  FentayeADKyprianidisKG. Gas turbine prognostics via Temporal Fusion Transformer. The Aeronaut J (2024) 128(1325):1594–609. 10.1017/aer.2024.40

  • CrossRef
  • Google Scholar
  • View reference in article

• 22.

  AbinayARamDSAI. Boiler technologies and fault diagnosis in thermal power plants. Int J Sci Innovation Eng (2025) 2(6):790–7. 10.70849/IJSCI

  • CrossRef
  • Google Scholar
  • View reference in article

• 23.

  NayeeifAAAl-AmeenESJeburNAOgailiAAFHamdanZKNjimEK. Investigation of the effects of unbalance and bearing wear on shaft vibration in a natural gas turbine plant. Appl Sci Eng Prog (2025) 18(4):7863–73. 10.14416/j.asep.2025.07.012

  • CrossRef
  • Google Scholar
  • View reference in article

• 24.

  DunaiA. Definition of requirements and stepwise development of a diagnostic model algorithm for the TV3-117V gas turbine engine. Aerospace Technic Technology (2025) 4 (Suppl. 2): 166–70. 10.32620/aktt.2025.4sup2.19

  • CrossRef
  • Google Scholar
  • View reference in article

• 25.

  NemitallahMAEl-AdawyMAbdulrahmanGAQMansourSHabibMAKhalifaA. Hydrogen mobility toward affordable and clean energy production in gas turbines: State-of-the-Art and perspectives. Energy and Fuels (2025) 39(13):6045–77. 10.1021/acs.energyfuels.4c05875

  • CrossRef
  • Google Scholar
  • View reference in article