Intelligent rolling bearing compound fault diagnosis based on frequency-domain Gramian angular field and convolutional neural networks with imbalanced data

Abstract

The effective fault feature extraction is the core of rolling bearing fault diagnosis. However, rolling bearings usually operate in normal state and fault duration is very short, which will cause imbalance in fault diagnosis data, thus leading to difficulty in fault feature extraction and low diagnosis accuracy. Meanwhile, mutual interference between multiple fault responses will also lead to poor diagnosis performance. To solve these issues, a novel compound fault diagnosis method with imbalanced data based on frequency-domain Gramian angular field (FGAF) and convolutional neural networks optimized by instance normalization and efficient channel attention (IECNN) is proposed. Firstly, FGAF is adopted to map frequency-domain features of fault signals to the polar coordinate to obtain 2D FGAF feature spectrum. Secondly, an instance normalization module is established to reduce internal covariant shift caused by data distribution discrepancy and improve generalization ability. An efficient channel attention module is constructed to further excavate fault features and improve anti-interference ability. Finally, experiments are conducted under imbalanced dataset and imbalance intensified dataset, and the average accuracy of 99.91% and 99.92% were obtained, respectively, which shows the proposed method has better resistance to data imbalance.

Keywords

bearing compound fault diagnosis frequency-domain Gramian angular field convolutional neural networks instance normalization efficient channel attention

1. Introduction

As the power source and transmission mechanism for the fundamental and critical facilities, rotating machinery is widely applied in petrochemical, rail transit, transportation, and other industries. As key components of rotating machinery, the health condition of bearings is of important engineering significance for ensuring the safe operation of basic equipment (Zhang et al., 2018). However, due to complex working conditions, structural damage to bearings often occurs, which may cause equipment collapse or even casualties if not detected and maintained in time. Therefore, bearing fault diagnosis is one of the research hotspots in recent years, which has attracted the attention of domestic and foreign scholars (Wang et al., 2022; Xiong et al., 2021).

The intelligent diagnosis method based on machine learning and deep learning does not rely on expert diagnosis knowledge, and is widely used in bearing fault diagnosis. The intelligent diagnosis method contains two parts: feature extraction and fault classification. Time-domain analysis (Wen et al., 2019), frequency-domain analysis (Jia et al., 2016), and time-frequency analysis (Liu et al., 2023) are commonly employed for feature extraction. Traditional machine learning diagnosis models include support vector machine (SVM), K nearest neighbors (KNN), etc. have been adopted as fault diagnosis models. However, the structure of these models is too simple and cannot fully exploit the high-dimensional features in the data.

Deep learning diagnosis models, such as stacked autoencoder (SAE), deep belief network (DBN), and convolutional neural networks (CNN), are widely used in bearing fault diagnosis field due to their powerful automatic feature extraction capabilities. For example, Plakias and Boutalis (2020) improved CNN to DCNN and combined with attention mechanism to propose a novel fault diagnosis model ADCNN. Jin et al. (2022) proposed an anti-noise multiscale convolutional neural network AM-CNN with better diagnosis accuracy and cross-domain performance. Dibaj et al. (2021) proposed an end-to-end bearing fault diagnosis method based on optimized variational mode decomposition (VMD) with CNN, which can accurately diagnose minor faults without masking them when two faults of different severity occur simultaneously. Xue et al. (2021) proposed TSFFCNN, which uses 1D convolution and 2D convolution to form two channels for feature extraction, respectively.

These methods focus on fault diagnosis under a single fault type and balanced dataset. However, bearings often fail at multiple locations at the same time besides the single fault, that is, compound fault (Huang et al., 2020; Ma et al., 2023; Wang and Du, 2020). Compound fault is easy to be classified as a single fault, which is mainly caused by the coupling of multiple single fault signals and single fault components with different strength. In addition, rolling bearings usually operate in normal state and fault duration is very short, there is usually data imbalance (Chen et al., 2020; Jeong and Lee, 2017; Tang et al., 2021) in actual fault diagnosis tasks, which is also a difficulty need to be solved.

Many excellent diagnosis methods based on fault feature analysis have been proposed to deal with these issues currently. Li et al. (2019) proposed a signal processing method based on multiple enhanced sparse decomposition, which can separate the fault features of gears and bearings at the same time to realize the compound fault diagnosis of gearboxes. Zhao et al. (2019) proposed a generalized Vold-Kalman algorithm based on nonstationary multi-faults features for bearing compound fault diagnosis. Zhang et al. (2020) proposed a deep generative adversarial network to address the imbalanced data problem by explicitly creating additional training data. Qian and Li (2020) proposed a class imbalance-robust network for bearing fault diagnosis, which tackles class imbalance both in the feature extraction and classification stages. To accurately and automatically identify the conditions of rolling bearings, a normalized convolutional neural network is proposed in Zhao et al. (2020) for the diagnosis of different fault severities and orientations considering data imbalance and variable working conditions. Among them, some fault diagnosis methods separate the fault characteristics of every single fault from the compound fault signal, and then perform fault analysis. However, it requires the analysts to have specialized fault diagnosis knowledge, and therefore does not enable automatic diagnosis. Meanwhile, some methods only consider fault diagnosis under imbalanced data, missing the importance of diagnosis of compound faults.

Although many feature extraction methods and intelligent fault diagnosis models have been applied to bearing fault diagnosis tasks successfully, the following problems still need to be addressed. (1) Single and compound faults need to be diagnosed together. Compound faults are combined by multiple single fault components with different intensities, so they are easier to be misclassified as single faults. And most of the current compound fault diagnosis methods still rely on researchers with specialized diagnosis knowledge, so intelligent automatic diagnosis needs to be realized. (2) Diagnosis under data imbalance conditions. Most of the industrial site monitoring data are collected under normal operation conditions, which lead to few fault data samples under fault conditions. In addition, the number of data samples with known fault status and manual labeling is even small. Therefore, the number of fault samples is small, and the positive and negative samples are seriously imbalanced.

In order to overcome the above problems, a novel bearing fault diagnosis method based on frequency-domain Gramian angular field (FGAF) and CNN is proposed. Firstly, the FGAF features are extracted from the frequency-domain features of different vibration signals by Gramian angular field. FGAF is a very efficient signal processing method, which not only has excellent feature extraction capability, but also has less time consuming. Next, the proposed CNN optimized by instance normalization and efficient channel attention (IECNN) is applied to construct feature extraction and fault classification models. The instance normalization module is established to improve fault diagnosis accuracy and generalization ability, the efficient channel attention module is constructed to enhance features along the channel dimension and further improve the resistance to data imbalance.

2. The proposed FGAF-CNN model

The FGAF-CNN bearing fault diagnosis method proposed in this paper is shown in Figure 1. Firstly, the vibration signals of single faults, compound faults, and normal state are collected to form the preliminary dataset. Subsequently, the fault features are extracted from the different faults by the proposed FGAF, which converts the 1D time-domain vibration signals into 1D frequency-domain features, and then calculates the 2D feature map FGAF. Then, the imbalanced datasets with different imbalance degrees are constructed according to the imbalance ratio, which are adopted for fault diagnosis experiments under the condition of data imbalance. FGAF is able to extract differentiated features for different faults, which reducing the feature learning difficulty of CNN. In IECNN diagnosis model, instance normalization (IN) is introduced to normalize the feature maps and improve the feature learning ability of CNN. Efficient channel attention (ECA) weights the features to be classified extracted from the convolutional layers along the channel dimension, so that the model focuses more on the important information related to the classification. Finally, the proposed diagnosis model is trained under imbalanced datasets, and obtains the fault diagnosis results on testing dataset, and the diagnosis results are visualized at last.

2.1. Frequency-domain Gramian angular field

Gramian Angle Field (Wang and Oates, 2015) is a signal processing method that converts time series signal, or more generally 1D data sequence, into 2D matrix. In order to fully preserve the complete information of the signal and maintain its dependence on time, GAF is applied to the spectrum feature analysis of bearing vibration signals and fault features called fequency-domain Gramian angle field (FGAF) are obtained. FGAF is able to extract differentiated features for different faults especially the compound faults, which reduces the feature learning difficulty of CNN. The FGAF extraction process is detailed as follows.

2.1.1. Discrete Fourier transform

Let the collected time-domain sample be x(n), and each sample contains N sampling points. First, discrete Fourier transform (DFT) is performed to convert the 1D time-domain vibration feature x (n) of the bearing into 1D frequency-domain feature y (k). The DFT is as follows:

y (k) = \sum_{n = 0}^{N - 1} x (n) e^{\frac{- j 2 π n k}{L}}, 0 \leq k \leq L - 1

(1)

when the fault intensifies or the operating environment changes, the time-domain vibration signal changes irregularly, which makes it difficult to extract features. The advantage of converting time-domain fault features to frequency-domain representation is that the fault feature form is more stable for the same type of fault and different from other types of fault features.

2.1.2. Piecewise aggregation approximation

The data size of frequency-domain feature after DFT is large and cannot be directly processed subsequently, so it needs to be reduced. We use piecewise aggregation approximation (PAA) to perform data dimensionality reduction and try best to minimize the feature loss in the process.

PAA uses a window of length M to decompose the frequency-domain feature sequence into adjacent, non-overlapping subsegments, and then takes the average of each subsegment as the approximate aggregation result. The formula of PAA is as follows, where t denotes the number of subsegments after decomposition, and y_scale(t) denotes the result after PAA.

y_{s c a l e} (t) = \frac{1}{M} \sum_{i = 0}^{M - 1} y_{t} (i) 0 \leq t \leq \frac{N}{M}

(2)

The aggregated results of each subsegment form a 1D feature vector, which is the output after PAA.

2.1.3. MinMaxScaler

The frequency-domain feature sequence after PAA has a high amplitude near the bearing fault frequency and very small amplitude at other frequencies. The difference between these data points is extremely large, and such a large difference is not conducive for model training. Therefore, the sequence is scaled using MinMaxScaler with the following equation:

{\tilde{y}}_{s} (t) = \frac{(y_{s} (t) - \max (y_{s})) + (y_{s} (t) - \min (y_{s}))}{\max (y_{s}) - \min (y_{s})}

(3)

where max(y_s) and min(y_s) represent the maximum and minimum of the sequence, respectively. After scaling, the amplitude of the frequency-domain features is limited to [−1, 1], where −1 corresponds to the minimum in the original sequence and 1 corresponds to the maximum.

2.1.4. Polar mapping

The frequency and amplitude information of the scaled sequence is mapped into the polar coordinate to obtain the corresponding radius and angle with the following mapping equations:

{\begin{cases} ϕ_{t} = \arccos ({\tilde{y}}_{s c a l e} (t)) \\ r_{t} = \frac{t}{T} T = \frac{N}{M} \end{cases}

(4)

where T is the number of data points of the sequence after scaling. ϕ is the angle of a point in the sequence mapped to the polar coordinate, and r is the corresponding radius. After the polar mapping, the larger the amplitude in the spectrum, the closer the angle is to 0, and vice, the closer it is to π. The radius corresponding to the low frequency part is smaller and closer to the center of the polar coordinate, while the high frequency part is farther from the center.

2.1.5. Gramian angular field

Based on the angular information obtained from the polar coordinate mapping, the FGAF is calculated with the following equation:

G = [\cos (ϕ_{i} + ϕ_{j})] = [\begin{array}{l} \cos (ϕ_{0} + ϕ_{0}) \dots \cos (ϕ_{0} + ϕ_{T}) \\ ⋮ ⋱ ⋮ \\ \cos (ϕ_{T} + ϕ_{0}) \dots \cos (ϕ_{T} + ϕ_{T}) \end{array}]

(5)

The FGAF feature map is symmetric about the main diagonal, and its diagonal elements are only related to each data point itself. The other elements are the operations between two different data points in the frequency-domain feature sequence, reflecting the correlation between different frequencies. From the FGAF formula, it can be seen that as the frequency increases, the frequency-domain features are sequentially mapped from the upper left corner to the lower right corner, and the 1D spectral features are converted to the 2D matrix by encoding while preserving the dependence and interaction between different frequencies.

The FGAF can convert time series data into image data, which can not only retain the complete information of the time series signal, but also maintain the dependence of the signal on time. After converting signal data into image data, differentiated features for different faults especially the compound faults can be efficiently extracted, and the advantages of CNN in classification and recognition can be fully utilized for modeling.

2.2. The architecture of the proposed IECNN

In order to improve the classification accuracy of different fault types, especially the recognition ability of compound faults under imbalanced data, a deep neural network CNN with ideal performance was adopted in the classification stage. Meanwhile, instance normalization (IN) is introduced to normalize the feature maps and improve the feature learning ability of CNN. ECA weights the features to be classified extracted from the convolutional layers along the channel dimension, so that the model focuses more on the important information related to the classification under imbalanced data.

2.2.1. Convolutional neural networks

CNN, with its powerful feature extraction ability and easy-to-modify structure, has become the most hotly researched deep learning model today.

The convolution layer extracts the spatial features of the input by sliding the convolution kernel to perform convolution operations. For the input x_i and the kernel k_j, the output of the convolution layer is:

\begin{array}{l} y_{i, j} = f (b_{j} + \sum_{i} k_{j} * x_{i}) \\ f (x) = \max (0, x), x > 0 \end{array}

(6)

where * is the convolution operation; k, b are the shared kernel and bias; f is the activation function, and Rectified Linear Unit (ReLU) is usually used.

In addition, the CNN uses a max-pooling layer for downsampling to reduce the volume of data and a fully connected layer to integrate the extracted local features into global features for fault classification.

2.2.2. Instance normalization

Normalization can accelerate the training process and improve the generalization ability of the model, making it more stable. The commonly used normalization method is Batch normalization, which normalizes the corresponding layers of feature maps of all types of samples at the same time. However, the different FGAF features proposed in this paper differ greatly from each other and are not suitable to use Batch normalization, so Instance normalization (Ulyanov et al., 2016), which normalizes each channel of each sample separately, is used, and its normalization process is as follows:

\begin{array}{l} μ = \frac{1}{H W} \sum_{l = 1}^{W} \sum_{m = 1}^{H} x_{l m} \\ σ^{2} = \frac{1}{H W} \sum_{l = 1}^{W} \sum_{m = 1}^{H} {(x_{l m} - μ)}^{2} \\ y = \frac{x - μ}{\sqrt{σ^{2} + ε}} \end{array}

(7)

where x is the feature map of a channel of a sample; H and W represent height and width, respectively; μ and σ² are the mean and variance of this feature map, respectively; y is the output of IN.

Fault features are mapped to the appropriate range by IN, which facilitates model training. At the same time, the operation of normalizing each feature map individually makes the feature maps of each class still retain the fault style of itself, which is convenient for model to identify and classify, improving the fault classification effect effectively.

2.2.3. Efficient channel attention

Efficient channel attention (Wang et al., 2020) is a network for weighting the feature maps of each channel, which has the advantages of less parameters, plug-and-play, and obvious feature enhancement effect, and its structure is shown in Figure 2.

The network takes the channel feature map as input, converts it into a 1D vector using global average pooling, and then obtains the attention weights of each channel through the 1D convolution kernel and softmax layer, and finally assigns each weight to the corresponding feature map to achieve feature enhancement, highlighting the important features and suppressing the interference of irrelevant features. The 1D convolutional kernel learns the optimal parameters following the training process of the diagnosis model to achieve better weighting effect. The feature weighting operation of ECA is as follows:

μ = g (x) = \frac{1}{W H} \sum_{i = 1, j = 1}^{W, H} x_{i j}

(8)

where x is the input with size [H, W]. g represents the global average pooling, and μ represents the 1D mean vector after global average pooling. The attention weights of channel i are as follows:

ω_{i} = σ (k e l * μ_{i k})

(9)

where kel denotes 1D convolution kernel of size k; μ_ik represents the area covered by the kernel and σ is the softmax function.

2.2.4. The proposed IECNN

The proposed diagnosis model IECNN adopts the structure of three convolutional layers with two fully connected layers, so the volume of model parameters is small, which is a lightweight diagnosis model.

The model starts with a feature extraction consisting of three convolutional layers with kernels of 8, 16, and 32, respectively, IN layer and 2*2 max-pooling layer are followed each layer. After the feature extraction stage, the feature maps are extracted and then weighted by ECA to highlight the important features and suppress the irrelevants. It helps to improve the classification effect, and can improve the stability and enhance the anti-interference ability. Two fully connected layers optimized by dropout layer are to integrate the local features of each channel into global features. The model finally applies Softmax layers for classification, and the number of outputs is set to 8, corresponding to eight types of bearing faults. The activation functions are all ReLU. The detailed structure and parameter settings of the model are shown in Table 1.

Table 1.

Parameters of the proposed IECNN.

	Layer	Kernel	Number of filter	Filter size	Padding	Output size
1	Input	/	/	/	/	(56,56)
2	Conv	Kernels	8	3*3	Yes	(56,56,8)
3	IN	/	/	/	/	(56,56,8)
4	Max-pool	Pooling size	/	2*2	/	(28,28,8)
5	Conv	Kernels	16	3*3	Yes	(28,28,16)
6	IN	/	/	/	/	(28,28,16)
7	Max-pool	Pooling size	/	2*2	/	(14,14,16)
8	Conv	Kernels	32	3*3	Yes	(14,14,32)
9	IN	/	/	/	/	(14,14,32)
10	Max-pool	Pooling size	/	2*2	/	(7,7,32)
11	ECA	/	/	/	/	(7,7,32)
12	FC	/	256	/	/	(256,1)
13	Dropout	Dropout rate	/	0.2	/	(256,1)
14	FC	/	126	/	/	(126,1)
15	Dropout	Dropout rate	/	0.2	/	(126,1)
16	Softmax	/	/	/	/	(8,1)

3. Experimental validation

3.1. Data description

The experiment adopts our laboratory’s self-built bearing fault diagnosis dataset which is based on vibration signal. The dataset is obtained by the self-built rotating machinery fault diagnosis simulation platform HFZZ-II. The composition of the platform is shown in Figure 3, which contains asynchronous motor, motor control system, bearing housing (including bearing), acceleration sensor, data acquisition instrument, computer, and others. No radial force is added to the shaft under all situations in these experiments.

The tested bearings are N205. The IEPE piezoelectric accelerometer 1A111E is used for data acquisition, mounted on the vertical direction of the bearing housing. The dataset contains normal state, three single faults, and four compound faults, which will be directly called eight fault types later. These fault types are normal condition (NC), inner fault (IF), outer fault (OF), ball fault (BF), inner-outer compound fault (IOF), ball-inner compound fault (BIF), ball-outer compound fault (BOF), and ball-inner-outer compound fault (BIOF).

The bearings with different faults are shown in Figure 4. The faults of each part of the bearing are rectangular grooves with depth of 0.5 mm and width of 0.2 mm.

All samples are collected at 1750 r/min, 2000 r/min, and 2250 r/min, and there are 30 samples under each speed. The sampling frequency is set to 12.8 KHz, each sample contains 9600 sampling points. The details of the self-built dataset are shown in Table 2, where label is the defined label for different fault types.

Table 2.

The details of self-built bearing fault diagnosis dataset.

Speeds (rpm)	Fault types	Number of samples	Label
1750/2000/2250	NC	30/30/30	0
1750/2000/2250	OF	30/30/30	1
1750/2000/2250	IF	30/30/30	2
1750/2000/2250	BF	30/30/30	3
1750/2000/2250	OIF	30/30/30	4
1750/2000/2250	BIF	30/30/30	5
1750/2000/2250	OBF	30/30/30	6
1750/2000/2250	OBIF	30/30/30	7

3.2. Analysis of FGAF

The FGAF with unique and obvious fault forms are further extracted from the acquired self-built dataset. Due to the data dimensionality reduction of PAA, the size of final FGAF feature map is 56*56. The FGAF of different fault types are shown in Figure 5.

As can be seen, the FGAF feature map is symmetric along the main diagonal. The feature maps a, f, and g are similar and only have subtle discrepancy in some areas, so it’s impossible to accurately judge fault type just by observation, thus, CNN with strong feature learning capability is needed for fault diagnosis. CNN can achieve accurate identification of different faults by learning higher-order features that cannot be directly observed in the features.

3.3. Fault diagnosis under imbalanced dataset

3.3.1. Imbalanced dataset

The operation time of each state of bearings is not balanced, the majority of the time is in the normal state, the fault state is relatively less. In addition, single faults tend to occur more frequently than compound faults. It leads to more normal samples than fault samples, and more single fault samples than compound fault samples when the actual fault diagnosis is performed. The data imbalance can make the model tend to identify the fault types with large sample size, which reduces the diagnosis accuracy.

To verify the diagnosis effect of the proposed method for single and compound faults of bearings under data imbalance conditions, three imbalanced datasets are constructed, and one balanced dataset is constructed as comparison experiments (Jia et al., 2018). The detailed settings of the imbalanced datasets are shown in Table 3. Take dataset B as an example, there are 30*3 = 90 samples for each fault type (30 samples for each speed), firstly, 30% of them are randomly selected as the testing dataset to ensure that model trained by different imbalanced datasets can be tested by the testing dataset with the same data volume. Then the remaining 70% samples are used to construct the imbalanced training dataset, and the imbalanced ratio for different fault is set as normal condition: single-fault: double-compound-fault:triple-compound-fault = 7:5:3:1. The imbalanced training datasets C and D are constructed in a similar way as B. A is used as a balanced dataset for comparison, and the number of samples for each type is equal.

Table 3.

The details of different imbalanced datasets.

Fault type	Training samples				Testing samples
Fault type	A (%)	B (%)	C (%)	D (%)	A (%)/B (%)/C (%)/D (%)
NC	70	70	70	70	30/30/30/30
BF	70	50	30	10	30/30/30/30
IF	70	50	30	10	30/30/30/30
OF	70	50	30	10	30/30/30/30
IOF	70	30	50	30	30/30/30/30
BOF	70	30	50	30	30/30/30/30
BIF	70	30	50	30	30/30/30/30
BIOF	70	10	10	50	30/30/30/30

3.3.2. Experiment under imbalanced datasets

The fault diagnosis effect of the proposed method under the data imbalance condition is evaluated through four imbalanced datasets. To verify the improvement of IN and ECA on the model, three comparison experiments are set up: IN only (the model only uses IN), ECA only (the model only uses ECA), and NULL (without IN and ECA). The training period is set to 200 epochs, and the batch size is 32. The fault diagnosis results of the model are shown in Figure 6. Each experiment is performed 10 times to reduce the influence of random factors.

From the results above, it can be seen that the proposed model has the best diagnosis effect on all four imbalanced datasets, and the diagnosis accuracy is higher than the other three comparison tests under the same dataset. The comparison tests IN and ECA had lower accuracy compared to IN + ECA, and the standard deviation increased, indicating a decrease in the stability of the model. However, these two still have higher diagnosis accuracy and stability compared to the experiment NULL. It indicates that IN and ECA have a boosting effect for the model.

In addition, it can be seen in the four experiments that the diagnosis accuracy is the lowest on dataset D. The reason is that dataset D contains the least single fault samples, while the compound fault samples is most. However, compound faults contain multiple single fault feature components, for example, BOF will contain some of the features of OF and BF. Therefore, the diagnosis model trained with dataset D will be more inclined to identify the compound faults, making the single faults to be incorrectly identified as compound faults, which reduces the diagnosis accuracy.

3.3.3. Experiment under imbalance intensified datasets

The degree of data imbalance is stronger in real working conditions, that is, the sample size is usually not equal in single fault or compound fault. Therefore, to further simulate the real data imbalance, we modify the imbalanced dataset B to aggravate the imbalance, and construct four new imbalance intensified datasets E, F, G, and H. The reason to select dataset B is to ensure that the sample size of single fault is larger than that of compound fault while intensifying the imbalance. The imbalance ratio of the three faults in the single fault is BF:IF:OF = 1:0.75:0.5, which means that for OF, there are 90*0.5*0.5 = 22 samples in the training dataset. The details of the imbalance intensified datasets are shown in Table 4.

Table 4.

The details of different imbalanced intensified datasets.

Fault type	Training samples				Testing samples
Fault type	E	F	G	H	E (%)/F (%)/G (%)/H (%)
NC	70%	70%	70%	70%	30/30/30/30
BF	50%*1	50%*1	50%*0.75	50%*0.5	30/30/30/30
IF	50%*1	50%*0.75	50%*1	50%*0.75	30/30/30/30
OF	50%*1	50%*0.5	50%*0.5	50%*1	30/30/30/30
IOF	30%*1	30%*1	30%*0.75	30%*0.5	30/30/30/30
BOF	30%*1	30%*0.75	30%*1	30%*0.75	30/30/30/30
BIF	30%*1	30%*0.5	30%*0.5	30%*1	30/30/30/30
BIOF	10%	10%	10%	10%	30/30/30/30

Four imbalanced intensified datasets are adopted to further verifying the diagnosis effect of the proposed method, and the diagnosis results are shown in Figure 7.

As seen from the results above, the fault diagnosis model proposed still has the best diagnosis effect under the condition of data imbalance intensified, which further verifies the fault diagnosis capability of the proposed model.

3.3.4. Comparison with other diagnosis methods

In this section, we compare the diagnosis effects of other published methods in literatures to highlight the advantages of the proposed method, as shown in Table 5. Except for Xue et al. (2021), the diagnosis methods all use self-built compound fault datasets. Xue et al. (2021) used the CWRU dataset to simulate compound faults. Since the experiment settings of all methods are not exactly the same, the parts with differences are converted into a uniform format here and experiments are performed under HFZZ-II dataset, and the specific differences are not stated.

Table 5.

Comparison of the proposed method with other diagnosis methods.

Ref.	Key technology	Imbalance ratio	Accuracy(%)
Gao et al. (2022)	MSACS; MCKD; CNN	Balaced	99.52
Xue et al. (2021)	TSFFCNN; PSO; SVM	Balanced	95.49
Jin et al. (2021)	STFT; DARN	Balanced	99.87
Shao et al. (2017)	DBN; DTCWPT	Balanced	95.68
Proposed	FGAF; IN; ECA; CNN	1:1:1:1	100
		7:5:3:1	100
		7:3:5:1	99.95
		7:1:3:5	99.69

It can be seen that the proposed method has the best diagnosis effect. First of all, the proposed diagnosis method performs compound fault diagnosis under data imbalance condition, which is closer to the real industrial environment. Compared with other diagnosis methods based on balanced datasets, the proposed method achieves higher diagnosis accuracy with less data volume under more severe diagnosis conditions, much higher than 95.49% and 95.68% of Xue et al. (2021) and Shao et al. (2017), and slightly higher than 99.52% of Gao et al. (2022). Although Jin et al. (2021) have 99.87% diagnosis accuracy, it is based on the balanced dataset and need more training samples.

3.3.5. Comparison with other feature extraction methods

To verify the extraction capability of FGAF for bearing fault features, this section selects FGAF, WT, STFT, CSCoh (Chen et al., 2020) and MFCC (Jiang et al., 2019) as feature extraction methods, compares their diagnosis effect under imbalanced datasets. WT and STFT are time-frequency analysis methods widely used in signal processing. CSCoh is a method for processing cyclic stationary signals, converting the signal to 2D feature map with both dimensions as frequencies. The MFCC is a feature extraction method in acoustic signal feature extraction, which converts 1D signals into 2D feature maps through Mel-filtering. The fault diagnosis results of the five methods under imbalanced datasets A, B, C, and D are shown in Figure 8.

As seen from the results above, the average accuracy of FGAF is the highest, and it is much higher than the other four methods. In addition, the accuracy of FGAF is also the highest, and the standard deviation is the smallest in four datasets. Therefore, using the FGAF proposed in this paper as the feature extraction method can obtain the best fault diagnosis performance.

3.3.6. Feature visualization analysis

The t-SNE (Van der Maaten and Hinton, 2008) is adopted to visualize the diagnosis effects of the proposed methods under each imbalanced dataset which will have a more intuitive understanding of the diagnosis effects, as shown in Figure 9. Eight different colors represent eight types of faults.

It can be seen that the proposed diagnosis method has good effect under each imbalanced dataset, and can realize the diagnosis of single and compound faults of bearings accurately.

4. Conclusion

A novel bearing fault diagnosis method based on FGAF and CNN is proposed to improve the diagnosis accuracy of single and compound faults of bearings under data imbalance conditions. Firstly, the FGAF based on frequency-domain features of bearing vibration signals is proposed. Since the frequency-domain features change less and are more stable compared with the time-domain features when the external conditions change, the FGAF extracted from the frequency-domain features can better characterize the bearing faults. Second, a CNN fault diagnosis model optimized by IN and ECA is proposed. IN is used to accelerate the training process of the model and normalize the data to improve the fault diagnosis effect. In addition, IN normalizes each feature map individually, so it is insensitive to the batch size and more practical. ECA is used for feature enhancement to generate better channel weights by the local cross-channel features of 1D convolution which focuses more on important features, so that the model can still obtain significant fault features from samples with small data size, and the model’s resistance to data imbalance is enhanced. The results of fault diagnosis experiments under various imbalanced datasets show that the proposed method has better accuracy and resistance to data imbalance.

Data imbalance is inevitable in real industrial environments, which leads to the existing diagnosis methods usually failing to achieve the desired effect. The proposed diagnosis method based on FGAF and CNN in this paper can achieve accurate diagnosis of single and compound faults of bearings under data imbalance conditions.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Key Research and Development Project [grant number 2023YFB3709601], the National Natural Science Foundation of China [grant number 62373215, 62373219, 62073193], the Key Research and Development Plan of Shandong Province [grant number 2021CXGC010204, 2022CXGC020902], the Fundamental Research Funds of Shandong University [grant number 2021JCG008].

ORCID iD

Faye Zhang

Data availability statement

The data that support the findings of this study are available upon reasonable request from the authors.

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