Advancing the Diagnosis of Aero-Engine Bearing Faults with Rotational Spectrum and Scale-Aware Robust Network

Abstract

The precise monitoring of bearings is crucial for the timely detection of issues in rotating mechanical systems. However, the high complexity of the structures makes the paths of vibration signal transmission exceedingly intricate, posing significant challenges in diagnosing aero-engine bearing faults. Therefore, a Rotational-Spectrum-informed Scale-aware Robustness (RSSR) neural network is proposed in this study to address intricate fault characteristics and significant noise interference. The RSSR algorithm amalgamates a scale-aware feature extraction block, a non-activation convolutional network, and an innovative channel attention block, striking a balance between simplicity and efficacy. We provide a comprehensive analysis by comparing traditional CNNs, transformers, and their respective variants. Our strategy not only elevates diagnostic precision but also judiciously moderates the network’s parameter count and computational intensity, mitigating the propensity for overfitting. To assess the efficacy of our proposed network, we performed rigorous testing using two complex, publicly available datasets, with additional artificial noise introductions to simulate challenging operational environments. On the noise-free dataset, our technique increased the accuracy by 5.11% on the aero-engine dataset compared with the current mainstream methods. Even under maximal noise conditions, it enhances the average accuracy by 4.49% compared with other contemporary approaches. The results demonstrate that our approach outperforms other techniques in terms of diagnostic performance and generalization ability.

1. Introduction

Bearings are crucial components of rotating mechanical systems, including those used in aircraft, metallurgical processes, and chemical engineering. Particularly in aviation engines, they operate at high speeds under heavy loads, with various intricately coupled physical conditions and extremely harsh operating conditions. A failure to surpass critical thresholds can have catastrophic repercussions for engines, underscoring the need for precise and timely monitoring and fault diagnosis [1]. However, the path to effective monitoring is fraught with several challenges. Warning signals indicative of bearing anomalies, such as surface spalling, rolling element degradation, and fissures within bearing structures, must traverse convoluted transmission routes to reach the external vibration sensors [2]. Consequently, it is difficult to discern these weak signals because they are often obscured by wide-band and high-amplitude background noise. Stronger noise immunity and increased accuracy in weak feature extraction are long-term requirements of this industry.

Model-based and signal-based methods are the conventional approaches used for fault diagnosis and system status monitoring. Model-based fault diagnosis research has entered a golden age of development with the maturation of state space modeling and system identification technologies in the 1970s. Methods for parameter identification [3], observer-based approaches [4], and odd–even space methods [5] are examples of representative studies. Concurrently, signal-based fault diagnosis approaches have been successfully implemented owing to notable advancements in digital signal processing technology [6]. Various methods are available for identifying bearing defects in aero-engines during steady-state operation. These methods include matched pursuit [7], the wavelet transform [8], signal deconvolution [9], and others. However, the application of assessment techniques that rely on the model technique to extract direct fault representation becomes difficult, as complex aero-engines see an increase in semi-structural and unstructured faults [10]. Model-based approaches offer benefits when applied to airborne scenarios. However, the dependability of these methods tends to diminish as the level of nonlinear complexity and modeling uncertainty rises [11,12].

Deep learning (DL) offers distinct benefits for efficiently leveraging data and has demonstrated exceptional outcomes in domains such as computer vision, speech recognition, and image segmentation. In the industrial sector, the advent of intelligent instrumentation, digital communication networks, and advanced computing infrastructure has facilitated the collection and storage of vast volumes of process data. This data-rich environment represents an ideal setting for the deployment of DL techniques, propelling intelligent fault diagnosis into a new era of innovation. In recent years, numerous sophisticated neural network-based models have been introduced, each with the aim of continually enhancing diagnostic accuracy. These models capitalize on DL’s prowess in autonomously performing feature extraction, tailoring distinct feature collection strategies to the specificities of each diagnostic task. For instance, Zhang et al. [13] developed a multi-scale attention (MSA) mechanism and multi-objective contrastive learning approach to improve the generalization capability of semi-supervised learning methods on unlabeled data. To decrease the parameter count of the deep convolutional neural network, Zhao et al. [14] developed a CNN model called mixed information (MIXCNN). The accuracy and generalization ability of the model were enhanced by incorporating additional spatial information into the convolution kernel. The use of DL to automatically extract useful features from original vibration data for bearing fault diagnosis has advanced significantly after a while of study. Apart from the neural network backbone concept, several topologies have been widely applied. Various models have demonstrated efficacy in different contexts, such as autoencoders (AEs) and their variations, deep convolutional networks, transformers and their variations, and deep belief networks (DBNs). To enhance the performance, the literature [15,16] combines the AE model with data preparation techniques such as nonlinear spectrum and singular value decomposition. Researchers have proposed other versions of the AE model, with denoising autoencoders (DAEs) [17], which are typical representatives. ResNet [18] is one of the most famous CNN models. Researchers are actively searching for advancements in network design and input types to improve models. The transformer [19] has proven to perform better in a variety of domains and was first created for natural language processing. In recent years, it has been used in the field of sequence signal processing. Weng et al. introduced MCF [20], which is a neural network that integrates Vision Transformer with multi-scale convolution for diagnosing bearing faults. ConvET [21] introduced an advanced self-attention module that utilizes depthwise separable convolution to mitigate the influence of varying conditions on the accuracy of fault identification.

Typically, the intermediate representations generated by neural network methodologies are perceived as the automatic extraction of data features, lacking straightforward interpretability. This characteristic confines the tangible value of such algorithms to their final output, diverging from traditional algorithms, which offer flexibility to fine-tune parameters in alignment with the target object. In the field of aeroengineering, where the margin for error is exceptionally narrow, neural networks must attain exceptional levels of accuracy in order to be of practical use. To address these challenges, Yan et al. [22] utilized unlabeled vibration signals to address the challenging issues of variable working conditions, strong noise, and limited data in rotating machinery fault diagnosis. Wang et al. [23] proposed a novel digital twin framework for aero-engines that achieves the digitalization of physical systems. They used quadratic complex domain equations along with a high-power feature extraction module to identify rolling bearing faults. An et al. [24] proposed a new approach for fault diagnosis in transformers that utilized Gaussian mixture variation. Li et al. [25] proposed a novel clustering federated learning (CFL) method with a self-attention mechanism for bearing fault diagnosis. This methodology has the capability to effectively identify faults in various working situations.

From an engineering perspective, the essence of fault monitoring in rotating machinery, particularly aviation engines, is to ensure continuous operation of the rotating shaft. The rotational excitation of the spinning shaft produces a valuable signal only after bearing failure. Therefore, speed signals play a crucial role as an invaluable source of information that should not be disregarded. Although classic digital signal methods provide a high level of interpretability and can convert signals from the time domain to many domains, they lack effective modeling strategies for unknown entities. Similarly, the restricted accuracy of deep learning techniques hinders their applicability in certain fields, and engineering applications persistently encounter substantial obstacles [26]. Merely stacking various layers of the neural network would not only fail to enhance accuracy but also lead to significant degradation.

The demand for lightweight, high-speed, and high-temperature components in aircraft engines, coupled with exposure to corrosive exhaust, pollution, and extreme mechanical stresses from vibration and cycling, presents significant challenges in diagnosing bearing faults [27]. These harsh conditions lead to unique distortions in fault information, characterized by overlapping distortions and harmonic forms, diverging from typical exponential decay waveforms [28]. This results in a distinctive noise-fault signal coupling. As engine operations increase in speed and stress, the temperatures of the oil and bearing metals increase, introducing additional thermal noise that further obscures fault signals [29]. Bearing-related information in vibration signals is notably scant, exacerbated by limited sensor placement options, intricate engine architecture, and severe operational conditions. These factors intensify the coupling between noise components and bearing health indicators. Despite the widespread application of deep learning in fault diagnosis, the use of raw velocity signals to identify subtle defect features in high-noise environments remains under-explored.

The main contributions of this work can be summarized as follows.

• The rotation spectrum was fused with deep neural networks to guide the learning of the key features of the bearing faults. Furthermore, a diagnostic network RSSR was proposed for rotating machinery bearing health state recognition.
• The application of a composite feature extraction block captures intricate signal characteristics, thereby markedly improving the diagnostic performance. The anti-noise block is established by scale-aware feature extraction, non-activation convolutional networks, and channel attention modules.
• Comprehensive validation of our proposed method using two distinct public datasets: one representing a broad spectrum of bearing failure scenarios across rotating machinery and the other specifically focused on aircraft engine data. The inclusion of a comparative noise level analysis further underscores the robustness and superiority of the proposed algorithm.

The remainder of this article is organized as follows. Section 2 provides an in-depth elucidation of the developed fault diagnostic system, detailing its architecture and functional capabilities. Section 3 presents an exhaustive overview of two distinct rolling bearing datasets, accompanied by a discussion of the empirical results derived from these datasets. In Section 4, we undertake a series of ablation studies, rigorously evaluating the robustness and effectiveness of various components of our proposed model. Finally, Section 5 concludes the paper, summarizing key findings and reflecting on the implications and potential future directions of this research.

2. Proposed Approach

In this study, we developed a neural network called Rotational-Spectrum-informed Scale-aware Robustness (RSSR), which is capable of effectively capturing and classifying fault features from vibration signals in high-noise environments, as depicted in Figure 1. The network primarily addresses the signal heterogeneity caused by varying rotational speeds through precise resampling and feature extraction techniques, thus achieving high-accuracy fault diagnosis. A detailed description of the network workflow is provided below.

Angular Domain Resampling: The received raw vibrational signals are transformed into signals with uniform sampling rates by dynamically adjusting the sampling points according to the actual rotational speed. This crucial step was achieved by reading the rotational speed signals to adjust the sampling intervals dynamically, ensuring a consistent number of data points per rotation. Consequently, the time-domain signals are converted into angular-domain signals. This conversion provides a uniform data format that is essential for subsequent feature extraction and eliminates inconsistencies in data sampling at different speeds, which is a key prerequisite for the accurate analysis of vibration signals. During the angular domain resampling process, the original vibration signal s(t) is resampled based on the rotational speed $\omega \left(t\right)$. This process is represented by the partial differential equation:

$${\displaystyle \frac{\partial s^{\prime }(t,\theta )}{\partial \theta }}=s\left(t\right)·\omega \left(t\right)$$

(1)

where $\theta$ represents the angle per rotation, t is the time, and s′(t, θ) is the signal transformed into the angular domain. This equation demonstrates that the rate of change in the signal in the angular domain is directly proportional to the product of the time-domain signal and the rotational speed.

Scale-Aware Robust Block (SAR Block): These blocks are designed to effectively extract features from the angular-domain vibrational signals. They employ large convolutional kernels to delve into spatial features while maintaining the linear attributes of the features through non-activating convolution layers, aiding in the capture of more subtle fault signals. Additionally, by incorporating channel attention modules, SAR blocks can automatically adjust the weights of each channel, enhance the sensitivity of the model to useful features, and suppress irrelevant noise, thereby improving the accuracy of fault diagnosis. The backbone of the network is built by stacking multiple SAR blocks, facilitating feature learning from simple to complex levels, and providing a rich and discriminative feature representation for fault classification. The feature-extraction process is described by a set of equations involving convolution and nonlinear transformations.

$${\displaystyle \frac{\partial F_k}{\partial x}}=\sigma \left(W_k\ast F_{k-1}+b_k\right)$$

(2)

where $F_k$ represents the feature map of the k-th layer; $W_k$ and $b_k$ are the convolutional kernel and bias of that layer, respectively; ‘*’ denotes the convolution operation; and $\sigma$ is an activation function such as ReLU. This equation shows that the spatial derivative of the feature map (rate of feature change) is obtained through convolution of the feature map of the previous layer and nonlinear activation.

Classification and Decision Layer: Finally, the network employs an adaptive average pooling layer (Adaptive AvgPool) to summarize the features globally, which helps reduce the computational load while retaining essential information. Subsequently, a linear classifier layer performs the final fault-category decisions. This linear layer simplifies the final output of the model, providing a direct decision basis for the fault categories.

Through meticulous processing and intelligent feature extraction strategies, it can accurately diagnose faults in rotating equipment, such as bearings, in complex and variable industrial environments, providing a scientific basis for maintaining system reliability.

2.1. Rotational Spectrum

The vibration signal during the acceleration and deceleration phases of rotating machinery include abundant status information. Throughout its operation, the machine experiences constant fluctuations in its speed, power, load, and other variables, resulting in notable non-stationary characteristics. In this scenario, the conventional Fourier transform, which relies on sampling signals at equal time intervals, exhibits deficiencies and limitations. When the rotational speed of rotating machinery changes, using equal time intervals for sampling can lead to undersampling during high-speed rotation, causing the loss of certain feature points. Conversely, oversampling can occur at low rotational speeds, resulting in spectrum aliasing and energy leakage. This results in issues such as signal aliasing, significant leakage resulting in spectrum tailing, and high-order ambiguities.

The order tracking method is an excellent approach for enhancing the stationarity of vibration signals. The link between frequency and order can be described as follows:

$$Order={\displaystyle \frac{F}{\omega /60}}$$

(3)

where F represents the frequency; $\omega$ represents rotational speed.

The measured signal consists of several components, including several orders and vibration noise. A composite signal consisting of numerous orders can be mathematically represented as the summation of time-varying vectors, which can be stated as

$$X\left(t\right)=\sum _{-\infty }^{+\infty }A(k,t)sin[2\pi (k/T)t+{\phi }_k]$$

(4)

where A(k,t) represents the replica of the k order, which is also a time-dependent function denoted by t. Variable ${\phi }_k$ represents the initial phase angle of the k order, and k represents the tracked order. T denotes the period.

The order tracking method converts vibration signals sampled over a period of time into the angular domain, using the rotational speed of the shaft and the sampling frequency as references. It aims to sample signals at a consistent angle between rotating shafts. The angle domain signal is a highly effective method for monitoring and diagnosing defects in rotating shafts that operate under varying conditions.

Figure 2 depicts the process by which the vibration sensor acquires the vibration signal from the surface of the equipment and converts it into a digital signal using analog-to-digital (AD) conversion. The rotational speed sensor acquires the pulse signal representing the rotational speed and determines the speed of the shaft by measuring the time gap between pulses. Subsequently, we compute the quantity of resampling points in neighboring time intervals by utilizing the sampling rate, and employ the interpolation algorithm and downsampling technique to carry out angle domain resampling in various scenarios.

2.2. Scale-Aware Robust Block

The Scale-Aware Robust Block (SAR) consists of a scale-aware feature extraction block, an LN layer, a depth direction convolution layer, an activation function, and a channel attention module, as shown in Figure 3.

We meticulously devised the quantity and magnitude of scale-aware modules, primarily employing one-dimensional large convolution kernels to enlarge the receptive field and furnish more comprehensive information for later network comprehension. We removed the Batch Normalization (BN) layer and Rectified Linear Unit (ReLU) layer that come after the convolution layer in the typical construction of a convolutional neural network, which is called non-activation convolution. The input signal is denoted as $X\in {\mathbb{R}}^{W\times 1\times 1}$, where W indicates the length of each sample. It is calculated as follows:

$$\begin{array}{cc}\hfill X^{\prime }=stack[& f^{n_1\times 1}\left(X\right);f^{n_2\times 1}\left(X\right);f^{n_3\times 1}\left(X\right);\hfill \\ \hfill & f^{n_4\times 1}\left(X\right)]\in {\mathbb{R}}^{W\times 1\times 4C}\hfill \end{array}$$

(5)

where $f^{n_1\times 1}$ represents a one-dimensional convolution with a convolution kernel size of $n_1$.

Subsequently, Layer Normalization (LN) is employed to standardize the input features and preserve the relative magnitudes between different characteristics within a given sample. After thorough testing, we chose the large convolution kernel for its capacity to accurately detect global features. The utilization of depthwise convolution in the network offers the benefit of reduced parameter quantity, as illustrated in Equation (6).

$$X^{″}=DWC\left(LN\left(X^{\prime }\right)\right)$$

(6)

The choice of the activation function is crucial. CNNs commonly employ the ReLU activation function to introduce nonlinearity. Its primary purpose is to prevent issues, such as gradient disappearance and gradient explosion. If the ReLU function encounters a significant number of eigenvalues that are less than zero, the eigenvalues are assigned a value of zero. This action restricts the ability of the network to continue learning. Maas et al. [30] introduced the leaky ReLU activation function, which involves multiplying characteristics that are less than zero by a small coefficient. However, the specific coefficient used is not optimal. He K et al. [31] introduced the parametric ReLU activation function, which allows the coefficient to be adjusted and optimized through training. The process for calculating PReLU is as follows:

$$PReLU\left(x\right)=\left\{\begin{array}{c}x,ifx\ge 0\\ ax,\mathrm{otherwise}\end{array}\right.$$

(7)

A novel channel attention module was developed, inspired by channel attention in SE-Net [32]. The revised module is illustrated in Figure 4. Employing convolutional layers instead of linear layers can effectively decrease the number of network parameters and computational complexity. There are benefits derived from comprehending the activation functions and convolutional networks in the preceding testing phase. The model employs two convolutional layers, with a Layer Normalization in between to normalize the features. The activation function was omitted. The calculation method is as follows:

$$X^{‴}=X^{″}+X^{″}\times \left(f^{5\times 1,2}\left(LN\left(f^{3\times 1,2}\right)\right)\right)$$

(8)

3. Experimental Details

The implemented RSSR utilizes PyTorch 2.1. In the experiment, the angle domain resampled data were empirically resampled ten times according to the rotational speed, and the SAR block was set to four layers. The one-dimensional convolution kernel size of the multi-scale module in each layer was (101, 201, 301, 401), the depth-wise convolution kernel size was set to 5, the convolution kernel size of the Conv layer was set to 7, an adaptive pooling strategy was adopted, the learning rate was set to 0.0001, the cross-entropy function was used as the loss function, and GELU was selected as the activation function. The experiments were performed using a machine equipped with a 16-core i7-13700 central processor unit and an NVIDIA GeForce GTX 4070 graphics processing unit. The experimental results are presented in this section.

3.1. Chosen Models for Comparison

Based on the commonly used categorization approach [26], we chose some classic models and the most recent advanced networks for comparison, including the following: (1) AE was initially presented in 2006. The encoder and decoder comprise the conventional AE model. The classification method uses the encoder output. (2) The denoising autoencoder (DAE) [17] is a derivative of the AE that was created for the task of signal denoising. (3) Resnet [18], proposed in 2016, achieved a higher classification accuracy than the human baseline. It is among the standard CNN representatives. (4) Transformer [19] has been widely employed in numerous domains since it originally saw significant success in the NLP industry. The multi-head self-attention module (MSA) and multi-layer perceptron (MLP) make up the majority of its structure, which is achieved by stacking numerous encoder and decoder structures of the same architecture. (5) The 2021 proposal for MCF-1DVIT [20] is a neural network for diagnosing bearing faults that incorporates Vision Transformer and scale-aware convolution. To attain improved precision, this model captures fault features at different scales by referring to the time information of rolling bearings. (6) ConvET [21] is a 2022 proposal for an enhanced self-attention module based on depth-separable convolution. In the following, the selected datasets are introduced in a targeted manner, and the results of various models are compared.

3.2. Dataset

(1) XJ-SQV dataset [33]: The origin of this dataset is Xi’an Jiaotong University. Figure 5 shows the experimental bench. The device consists of a servo motor, a rotor, an acceleration sensor, a CoCo80 data collector, and a load exerted by a tension band. The defective bearing is situated at the drive end of the motor, whereas the acceleration sensor is mounted on the motor end cover. This dataset covers the variable-speed state and applied load and better restores the real working conditions.

The dataset had a sample frequency of 12 kHz, and the rotation speed ranged from 0 to 2500 rpm. Six separate failure modes were built and paired with the bearings under normal circumstances to create seven different health states. This classification encompassed both inner-ring failure (IF) and outer-ring failure (OF) across three distinct levels of damage. To mimic the damage, single-point flaws of varying diameters and depths were introduced.

Table 1. Fault damage quantification of XJ-SQV datasets.

Fault Position	Degree of Fault	Label of Fault	Area of Fault (mm2)	Depth of Fault (mm)
Inner ring (IF)	minor	C1	4	0.5
Inner ring (IF)	moderate	C2	8	4
Inner ring (IF)	severe	C3	12	2
NC		C4
Outer ring (OF)	minor	C5	4	0.5
Outer ring (OF)	moderate	C6	8	4
Outer ring (OF)	severe	C7	12	2

provides a concise overview of the dimensions and extent of various flaws. Assign numbers 1, 2, and 3 to represent minor, moderate, and severe defects, respectively. To augment the sample count, the data were segmented using the overlap segmentation method with an overlap rate of 30%.

(2) HIT-dataset [34]: This study utilized an alternative collection of datasets derived from the vibration signals of the rotor and casing of an aero-engine. These datasets were used to construct a testing platform based on an aircraft engine from the Aerospace School of Harbin Institute of Technology. The experimental setup employed high-speed and low-speed motors to operate the high-voltage and low-voltage rotors, respectively. Furthermore, a lubrication system that accurately replicates real-world conditions was incorporated, as shown in Figure 6. The experiment was conducted using 28 sets of high- and low-pressure velocities. The displacement vibration signal of the low-pressure rotor was tested using two displacement sensors, while the acceleration vibration signal of the casing was tested using four acceleration sensors. The sampling frequency was 25 kHz. The baseline model had greater difficulty when applied to this dataset as compared to the CWRU and XJTU-SY datasets. Refer to

Table 2. Fault modes in HIT-dataset.

Fault Position	Label of Fault	Depth of Fault (mm)	Length of Fault (mm)
NC	C1
Outer ring	C2	0.5	0.5
Inner ring	C3	0.5	0.5
Inner ring	C4	0.5	1.0

for precise information.

Furthermore, to replicate intense noise interference situations more accurately, we introduced Gaussian white noise to the initial signal, with the signal-to-noise ratio (SNR) indicated by Equation (9). We selected seven signal-to-noise ratios (SNRs), −4, −2, 0, 2, 4, 6, and 8, to thoroughly assess the performance of every model in situations with severe, moderate, and mild noise interference.

$$SNR=10 \lg (P_s/P_n)$$

(9)

where $P_s$ is the power of the signal, $P_n$ is the power of the noise, and lg represents the logarithm of base 10.

3.3. Evaluation Indexes

To evaluate the performance of each model, we employed the accuracy ratio (acc), recall ratio (r), and F1 score as rating metrics. It is defined as follows:

$$acc={\displaystyle \frac{TP}{TP+FP}}$$

(10)

$$r={\displaystyle \frac{TP}{TP+FN}}$$

(11)

$$F1={\displaystyle \frac{2\times acc\times r}{acc+r}}$$

(12)

where TP represents a true positive sample, that is, a positive sample that is correctly classified as positive; FP denotes a false positive sample, meaning a negative sample that is incorrectly classified as a positive sample; and FN signifies a false negative sample, indicating a positive sample that is incorrectly classified as a negative sample. Positive samples refer to samples that belong to the current fault type, whereas negative samples refer to samples that do not belong to the current fault type.

3.4. Results and Discussion

This section presents a comparative analysis comparing RSSR with other fault diagnosis models introduced in Section 3.1. We evaluated the results under both non-noisy and noisy conditions to comprehensively assess the effectiveness and stability of all models. All experiments were independently conducted ten times using the same number of sampling conditions to mitigate the impact of randomness on the evaluation results.

Table 3. Classification result ± standard deviations based on XJ-SQV dataset.

Model	XJ-SQV
	Accuracy	F1	Recall
AE	0.6622 ± 0.0027	0.6580 ± 0.0012	0.6622 ± 0.0027
DAE	0.6471 ± 0.0037	0.6441 ± 0.0030	0.6471 ± 0.0037
Resnet	0.8307 ± 0.0162	0.8224 ± 0.0187	0.8307 ± 0.0162
Vit	0.8383 ± 0.0036	0.8298 ± 0.0052	0.8383 ± 0.0036
MCF	0.8832 ± 0.0072	0.8813 ± 0.0088	0.8832 ± 0.0072
Conv-ET	0.7543 ± 0.0105	0.7410 ± 0.0201	0.7543 ± 0.0105
RSSR	0.9343 ± 0.0064	0.9344 ± 0.0067	0.9345 ± 0.0067

presents the accuracy results of all the models on the XJ-SQV dataset with no noise, showing the average accuracy and variance after ten iterations.

Table 4. Classification result ± standard deviations based on HIT-datasets.

Model	HIT-Dataset
	Accuracy	F1	Recall
AE	0.9020 ± 0.0357	0.9016 ± 0.0364	0.9020 ± 0.0357
DAE	0.9564 ± 0.0044	0.9563 ± 0.0044	0.9564 ± 0.0044
Resnet	0.9998 ± 0.0003	0.9998 ± 0.0003	0.9998 ± 0.0003
Vit	0.9997 ± 0.0003	0.9997 ± 0.0003	0.9997 ± 0.0003
MCF	0.9995 ± 0.0005	0.9995 ± 0.0005	0.9995 ± 0.0005
Conv-ET	0.9984 ± 0.0010	0.9984 ± 0.0010	0.9984 ± 0.0010
RSSR	0.9989 ± 0.0017	0.9989 ± 0.0017	0.9989 ± 0.0017

presents the results of the HIT-dataset. Figure 7 illustrates the accuracy histograms for all models under noiseless conditions.

Table 5. Floating point operations and parameters in experiments.

Model	AE	DAE	Resnet	Vit	MCF	Conv-ET	RSSR
FLOPs	28.017 M	11.18 M	175.68 M	11.32 M	28.97 M	562.76 M	8.41 M
Params	280 K	111 K	3.84 M	128.50 K	1.27 M	225.04 K	78.11 K

lists the floating-point operations and parameters of each model used in the experiment. The table demonstrates that RSSR exhibits stable and reliable performance, possessing a better learning ability and generalization performance than the other evaluation models. The analysis conducted on the XJ-SQV dataset shows that the proposed framework achieves higher accuracy rates than the AE, DAE, Resnet, Vit, MCF, and Conv-ET techniques, with values of 27.20%, 28.71%, 10.35%, 9.60%, 5.11%, and 17.99%. On the HIT-dataset, Resnet, Vit, and MCF perform well, similar to RSSR. When examining the accuracy index, it is evident that standard AE methods have limitations in collecting particular features within a confined region and fail to consider the overall breadth of comprehensive information. Consequently, the accuracy of these approaches is quite low. Undoubtedly, the Transformer network significantly reduces the computational requirements compared to the Resnet network and has the ability to capture highly efficient characteristics. However, it is worth noting that the volatility of these indicators was higher. The MCF network integrates scale-aware modules with the transformer to enhance performance while incurring more computational complexity. Conversely, convolutional neural networks often employ a configuration of localized connections and shared weights, thereby mitigating the standard deviation of numerous computations. The convolution procedure in the CNN emphasizes local characteristics, hence enhancing the resilience of the model to input. The RSSR produces optimal outcomes with low processing complexity, maximum accuracy, and minimal volatility.

Table 6. Diagnosis accuracy on datasets with added noise.

Methods	Dataset	Metrics	SNR (dB)
			−4	−2	0	2	4	6	8
AE	XJ-SQV	Acc	0.6123	0.6214	0.6308	0.6401	0.6371	0.6365	0.6359
		F1	0.6085	0.6099	0.6231	0.6224	0.6161	0.6267	0.6273
		Recall	0.6123	0.6214	0.6308	0.6396	0.6392	0.6365	0.6359
	HIT-dataset	Acc	0.7078	0.8079	0.8671	0.9068	0.9251	0.9406	0.9503
		F1	0.7064	0.8089	0.8673	0.9062	0.9249	0.9405	0.9504
		Recall	0.7078	0.8079	0.8671	0.9068	0.9258	0.9406	0.9503
DAE	XJ-SQV	Acc	0.6158	0.6246	0.6312	0.6355	0.6502	0.6436	0.6397
		F1	0.6102	0.6230	0.6260	0.6359	0.6427	0.6412	0.6352
		Recall	0.6158	0.6246	0.6312	0.6333	0.6471	0.6436	0.6397
	HIT-dataset	Acc	0.7563	0.8513	0.9097	0.9523	0.9634	0.9728	0.9802
		F1	0.7577	0.8520	0.9099	0.9519	0.9623	0.9728	0.9802
		Recall	0.7563	0.8513	0.9097	0.9497	0.9611	0.9728	0.9802
Conv-ET	XJ-SQV	Acc	0.7438	0.7654	0.7488	0.7434	0.7317	0.7463	0.7526
		F1	0.7291	0.7551	0.7305	0.7249	0.7142	0.7294	0.7334
		Recall	0.7438	0.7654	0.7488	0.7434	0.7317	0.7463	0.7526
	HIT-dataset	Acc	0.5520	0.7931	0.8729	0.9247	0.9541	0.9726	0.9833
		F1	0.5750	0.7950	0.8746	0.9246	0.9541	0.9725	0.9832
		Recall	0.5520	0.7931	0.8729	0.9247	0.9541	0.9726	0.9833
Resnet	XJ-SQV	Acc	0.7947	0.7918	0.8058	0.7967	0.8038	0.8096	0.8122
		F1	0.7854	0.7819	0.7975	0.7875	0.7945	0.8045	0.8049
		Recall	0.7947	0.7918	0.8058	0.7967	0.8038	0.8096	0.8122
	HIT-dataset	Acc	0.6915	0.7994	0.8732	0.9275	0.9599	0.9786	0.9901
		F1	0.7084	0.8047	0.8738	0.9282	0.9600	0.9786	0.9901
		Recall	0.6915	0.7994	0.8732	0.9275	0.9599	0.9786	0.9901
Vit	XJ-SQV	Acc	0.7838	0.8054	0.8188	0.8454	0.8545	0.8366	0.8372
		F1	0.7691	0.7951	0.8121	0.8345	0.8484	0.8278	0.8298
		Recall	0.7838	0.8054	0.8188	0.8450	0.8565	0.8366	0.8372
	HIT-dataset	Acc	0.9263	0.9092	0.9264	0.9619	0.9798	0.9762	0.9984
		F1	0.9259	0.9073	0.9358	0.9707	0.9893	0.9761	0.9984
		Recall	0.9263	0.9092	0.9264	0.9686	0.9894	0.9762	0.9984
MCF	XJ-SQV	Acc	0.8736	0.8735	0.8874	0.8746	0.8910	0.8806	0.8879
		F1	0.8708	0.8710	0.8856	0.8848	0.8968	0.8772	0.8862
		Recall	0.8736	0.8735	0.8874	0.8882	0.8953	0.8806	0.8879
	HIT-dataset	Acc	0.8706	0.9239	0.9715	0.9576	0.9806	0.9901	0.9975
		F1	0.8708	0.9239	0.9715	0.9644	0.9857	0.9901	0.9975
		Recall	0.8706	0.9239	0.9715	0.9649	0.9876	0.9901	0.9975
RSSR	XJ-SQV	Acc	0.9022	0.9058	0.9183	0.9186	0.9246	0.9210	0.9267
		F1	0.9026	0.9056	0.9183	0.9185	0.9245	0.9206	0.9263
		Recall	0.9022	0.9058	0.9183	0.9186	0.9246	0.9210	0.9267
	HIT-dataset	Acc	0.9317	0.9661	0.9638	0.9793	0.9857	0.9945	0.9972
		F1	0.9326	0.9662	0.9638	0.9793	0.9857	0.9945	0.9972
		Recall	0.9317	0.9661	0.9638	0.9793	0.9857	0.9945	0.9972

displays the experimental findings obtained in the presence of noise. The noise levels are characterized by SNR values ranging from −4 to 8, with increments of 2. The RSSR method demonstrated superior performance compared with earlier strategies across several measures on both datasets. The performance of this product was exceptional, particularly in areas with high noise levels. It has more resilience than that in Table 3. The RSSR method was substantially less affected by noise than the comparison algorithm. Particularly on the HIT-dataset, there are clear disparities in robustness under varying SNR settings, and the precision of AE, DAE, Resnet, and Conv-ET is noticeably diminished. This indicates that these algorithms are inappropriate for diagnosing bearing faults in the aircraft engine industry. When comparing the MCF and RSSR algorithms, notable distinctions arise when subjected to high levels of noise with SNRs of −4 and −2.

Figure 8 shows the accuracy bar chart of the XJ-SQV dataset under noisy conditions. No significant differences were observed among the algorithms with different levels of noise. In comparing different algorithms, RSSR outperformed the others, achieving an accuracy rate of over 90% across all noise conditions. RSSR demonstrated excellent diagnostic performance under varying operating conditions affected by noise. Meanwhile, the results of Vit were marginally inferior to those of MCF. As an enhancement to Vit, the multi-scale feature enhancement in MCF showed a relatively limited improvement in diagnostic performance compared to the noise resistance performance, which was more significant. Figure 9 depicts the accuracy bar chart for the HIT-dataset under noisy conditions. In contrast to variable operating conditions, the high-speed rotation of aircraft engines considerably affected the diagnostic results owing to noise. The proposed method achieved an accuracy of over 93%, outperforming other comparable methods.

To comprehensively assess the effectiveness of the proposed RSSR model, we used t-SNE graphs to reduce the dimensionality and visualize the data. Figure 10 and Figure 11 show the 2D t-SNE representation of the test instance, which can be seen to be quite confusing. Figure 12 and Figure 13 represent the 2D t-SNE representation of the output results of different algorithms adding −4 dB noise to the data. Based on the XJ-SQV data, the CNN and Transformer networks demonstrate greater performance in feature aggregation when compared to the AE and DAE networks. The Vit and MCF networks demonstrated increased dispersion when faced with identical failure scenarios. RSSR exhibits superior discrimination for various faults compared with other networks. Additionally, it demonstrates greater aggregation levels for C1, C2, C3, and C4, with only a small occurrence of aliasing in a limited number of samples. Based on the HIT-dataset, the distinctions between various health states were evident, making the aforementioned conclusion more apparent. The RSSR technique demonstrates a higher performance than the other methods.

4. Effectiveness Verification

A set of ablation experiments is conducted to investigate the influence of the constructed scale-aware module, convolutional network, and channel attention approach on the RSSR model. (a) Scale-aware experiments are conducted to validate the efficacy of the scale-aware module. A Batch Normalization (BN) layer and Rectified Linear Unit (ReLU) layer following the convolutional layer are denoted as scale-aware#1. If these layers are not included, they correspond to scale-aware#0. (b) To ascertain the impact of the activation function in the convolutional network, PReLU is denoted as AF#0, LeakRelu is denoted as AF#1, and Relu is denoted as AF#2. (c) To assess the efficacy of the channel attention module, the suggested network is denoted as channel-attention#0. The channel-attention#1 means that the network contains the BN and ReLU layer.

A total of 4000 samples are allocated from the XJ-SQV dataset for training purposes, 2000 samples are reserved for testing, and the training process is conducted five times to obtain an average.

The TSNE representation of the features at the updated position of the network is depicted in Figure 14. Based on the analysis of scale-aware, it appears that the data have been excessively normalized, leading to increased complexity. Additionally, the activation function excessively over-crops negative features, causing a lack of obvious differentiation between C1, C2, and C3. AF#1 and AF#2 serve as substitutes for the activation functions in the original backbone network, without altering any other components. AF#1 exhibits substantial disparities in features, but AF#2 has a minor impact. The influence of AF#2 on the accuracy index is demonstrated in

Table 7. Ablation result of different methods.

Method	Acc (%)	F1 Score (%)	Recall (%)
scale-aware#0	93.43 ± 0.082	93.44 ± 0.084	93.45 ± 0.082
scale-aware#1	88.20 ± 1.04	87.86 ± 1.22	88.20 ± 1.04
AF#0	93.43 ± 0.082	93.44 ± 0.084	93.45 ± 0.082
AF#1	90.11 ± 0.49	90.03 ± 0.44	90.11 ± 0.49
AF#2	91.18 ± 0.37	90.98 ± 0.45	91.18 ± 0.37
channel-attention#0	93.43 ± 0.082	93.44 ± 0.084	93.45 ± 0.082
channel-attention#1	88.84 ± 1.13	88.65 ± 1.20	88.84 ± 1.13

to be minimal. The Channel-attention#1 module alters the channel attention element of the initial network. The aliasing artifacts observed on channels C1, C2, C3, C6, and C7 are more prominent in channel attention#1 when compared to the original network. Thus, it can be deduced that the cautious implementation of Batch Normalization (BN) layers and activation functions aid in diminishing the intricacy of features, thereby augmenting the dependability of the RSSR.

5. Conclusions

This paper presents a novel RSSR procedure for diagnosing faults in aero-engine bearings. Our approach leverages the rotation rate to convert the vibration signal from the time domain to the angle domain, and effectively utilizes the gathered signals. Within the RSSR network, the scale-aware fusion module enhances the extraction of more comprehensive information from the signal by using larger convolution kernels. Notably, it differs from the other networks by excluding the use of BN and ReLU layers. The backbone network employs depth-direction convolution as a layer, and the utilization of the PReLU activation function produces a slight boost compared to alternative activation functions. The back-end is outfitted with a channel attention module that incorporates a large kernel. To simplify the system and enhance its performance, the BN and activation functions are removed, resulting in the creation of an RSSR network that exhibits an improved accuracy, and greater resistance to noise. We conducted a thorough assessment of the efficacy of RSSR using statistical analysis and visualization, showing its ability to accurately capture crucial data in dynamic and noisy settings. It achieves the highest accuracy with the smallest number of parameters and the lowest algorithm complexity. We validated the efficacy of our approach for different components by using ablation tests. Future research will investigate the potential of RSSR in anomaly detection and semi-supervised fields to expand its applicability in this domain.