Fault Diagnosis Method for Rotating Machinery Based on Multi-scale Features

Rotating machinery is one of the most common and essential equipment in modern industry. It is used in many important machines, like gearboxes, steam turbines, gas turbines, fans, and generators. Rotating machines usually work under tough conditions and are prone to faults, so their predictive maintenance is significant for guaranteeing safe operations and reducing economic costs. Faults in the vital components, like gears and rolling-element bearings, are the main causes of rotating machine failures [1], including damages and fractures in bearings, as well as scratches, wear, and fractures in gears.

A typical fault diagnosis is carried out in three steps: data collection, feature extraction, and fault classification. Measured data should be processed before the extraction of features of potential faults. In terms of feature extraction, several methods have been proposed, such as fast Fourier transform (FFT) [2], empirical mode decomposition (EMD) [3], wavelets multiresolution analysis (WMRA) [4], and wavelet packet analysis (WPA) [5]. Strömbergsson et al. [6] found that, in the vibration analysis of bearing faults of fan gearbox, the wavelet packet transform (WPT) could detect faults earlier and more clearly than FFT and the discrete wavelet transform (DWT). Meanwhile, many machine learning algorithms have been utilized to implement fault diagnosis, such as the K-nearest neighbor (KNN) method [7], fuzzy neural networks (FNN) [8], multi-layer perceptron (MLP) [9], and support vector machine (SVM) [10]. Gong et al. [11] used SVM at the end of the LSTM network to diagnose small faults in a multi-sensor monitoring environment. Yang et al. [12] proposed to combine the energy entropy of set empirical mode decomposition (EEMD) with an artificial neural network (ANN) for fault diagnosis of asynchronous motor. Despite the superiorities of these methods, their diagnostic accuracy is limited. They usually extract shallow features and need human intervention, like expert experiences or prior knowledge, and the process is time-consuming. Moreover, since the feature extraction and fault classification are conducted separately, the suboptimal combination of the two steps may not provide promising fault diagnosis performance.

Deep learning can integrate feature extraction and classification, and it has become an effective method for intelligent diagnosis. The convolutional neural network (CNN), one of the typical deep learning algorithms, can automatically extract local features and integrate them. Its feature extraction and generalization capability is improved with an increasing number of layers. CNN has been widely used in the fields of computer vision [13] and natural language processing. Meanwhile, some attempts using 2D-CNNs have also been conducted in fault diagnosis. For instance, Chen et al. [14] estimated the 2D cyclic spectral coherence maps of vibration signals and employed 2D-CNNs to process and classify maps to diagnose bearing faults. Pham et al. [15] utilized 2D-CNN to diagnose multi-output bearing faults, which achieved higher accuracy and efficiency than traditional CNNs. Although 2D-CNN can learn complex objects and modes and process various 2D signals (such as images and video frames), it is difficult to adapt to 1D signals. 1D-CNN performs only 1D convolutions with a simple and compact configuration, making it feasible to achieve real-time performance and low-cost hardware implementation [16]. Yan et al. [17] extended the method based on 1D-CNN to fault diagnosis of chillers. Ince et al. [18] developed an integrated fault diagnosis system that uses 1D-CNN to monitor the conditions of a motor. Wang et al. [19] proposed a one-dimensional memory-augmented convolutional neural network (1D-MACNN) and a one-dimensional memory-augmented convolutional long short-term memory (1D-MACLSTM) network, which have been successfully used in the field of structural health monitoring. These methods utilized the 1D-CNN and extracted high-level features from raw signals without involving other processing for hand-crafted feature transformation.

Though CNNs have demonstrated their capacity, current studies only focused on a fixed time scale rather than multiple scales, thus limiting their further applications. When operated at changing speeds or heavy loads, rotating machinery is vulnerable to many tiny variations, and fluctuation of instantaneous loads, faults of a component, and noise from the environment can lead to the superposition of non-stationary signals. Thus, the vibration signals of rotating machinery are complex and have multi-scale features. The features extracted from an extended time span can reflect the overall trend of the signals, while those from a shorter time span can indicate subtle local changes.

The principle of multi-scale learning is to learn features on both long-term and short-term time scales that complement each other. The multi-scale CNN (MSCNN) is developed adopting this idea. Huang et al. [20] designed a multi-scale fusion layer in an original convolutional neural network, and enhanced the ability to distinguish different fault states by fusing multi-scale information of raw signals. Jiang et al. [21] provided a multi-scale coarse-grained operation, which reduced the complexity and computation and was easier to implement than the method in Ref. [22].

The current methods that inherit MSCNN have demonstrated the capability of learning features on different time scales, but they usually use simple down-sampling and cannot learn raw signals effectively, which easily results in the loss of feature information. In this study, a fault diagnosis model called multi-branch one-dimensional convolutional neural network model (MBCNN) is proposed. Multi-branch CNN has been used in some fault diagnosis studies [23, 24], but in these studies, multiple branches of the network have the same structure, or only the optimal branch is selected for diagnosis according to the value of loss. The MBCNN model proposed in this paper can effectively learn features on multiple time scales through multiple branches with different convolutional layers and can extract features ranging from multiple time scales.

When the gearbox works, the interaction between the components and the coupling with other subsystems such as the generator make the vibration signal have various natural oscillation modes, showing multi-scale features. 1D-CNN can achieve end-to-end fault diagnosis, but it lacks multi-scale feature extraction ability.

The MBCNN proposed in this paper improves 1D-CNN with multi-scale learning. In the MBCNN, different branches adopt convolution kernels of different sizes and different convolution strides, and the first convolutional layer in each branch adopts a large convolution kernel and a large stride, thereby effectively extracting multi-scale features in the vibration signal. Moreover, the branches containing different numbers of convolution-pooling blocks can also hierarchically extract high-level features and capture rich information for diagnosis.

The MBCNN works in three consecutive stages: multi-branch generation, local convolution of each branch and fully connected classification. Figure 1 illustrates the framework of MBCNN with two branches (2b-CNN). The input of the model is the raw vibration data, and the output is fault types.

This study constructed an MBCNN with four branches (4b-CNN) for fault diagnosis of a rotating machine. The convolution stride of the first layer in the last branch (\(S_{4}^{1}\)) was initially set to 2. So, according to Eq. (7), the convolution stride of the first layer in the first branch (\(S_{1}^{1}\)) was 16, and the width of the convolution kernel (\(W_{1}^{1}\)) was 64. Substituting the number of the measured signals in one cycle (\(L_{{\text{c}}}\)) and \(S_{1}^{1}\) into Eq. (6), it could be found that the number of layers of the first branch (\(l_{1}^{{}}\)) is 4 or 5. The length of an input signal sample was set to 2048. Through Eq. (1), the output length was calculated, and it is 1 until the fifth convolution and pooling. Therefore, \(l_{1}^{{}}\) was set to 5. The number of channels was determined with the goal of reducing the loss, and it was set to 32 in the first branch.

The architecture and parameters of the 4b-CNN are shown in Figure 3.

In the following experiments, the programs were run on a computer equipped with an Intel i7-11700F 6-Core 2.50 GHz processor with 16 GB of RAM and an NVIDIA GeForce 3060 GPU. According to general parameter selection, the learning rate, the batch size, and the dropout ratio in the training were set to 0.0001, 512, and 0.1 separately. Meanwhile, a dataset was adopted to validate the model and compared it with other models based on signal processing, deep learning, CNN and MSCNN.

The paper proposes a CNN with multiple branches to identify complex multi-scale features of vibration signals of rotating machinery.

In terms of the structure of the MBCNN:

(1) The convolution kernels used in different branches have different widths and are related to each other, so the MBCNN can extract features containing the time scale of both a long-term and a short-term and reduce the number of model parameters.

(2) The last pooling layer of each branch is replaced with the global average pooling layer to avoid slow training speed and overfitting caused by too many model parameters.

Through experiments, the following conclusions are obtained:

(1) Comparing the ensemble learning method with the MBCNN, the former has a close classification accuracy with the 2b-CNN, but a lower classification accuracy than that of 3b-CNN and 4b-CNN. Even in low SNRs (from −4 to 0 dB), the diagnostic accuracy of the MBCNN is 7% higher. This is because the MBCNN can adjust the parameters of each branch according to the loss function and thus make the features of branches complementary, while the ensemble learning method comprehensively judges from the learned features, and the features have no information interaction.

(2) The visualization of the classification results demonstrates that increasing the number of branches in the MBCNN can make the similar faults more concentrated and the distinct faults more separated, so the features are more linearly separable, but more time is needed for training and testing in this case. The 2b-CNN and the 3b-CNN have a higher diagnostic accuracy than the 1D-CNN but they take nearly equal time (the difference is just 0.8 ms).

(3) Compared to the MSCNN, the MBCNN can not only learn more sufficient multi-scale information but also extract the higher-level features of signals from each branch. Therefore, the MBCNN can perform better on polluted signals with low SNRs (from −4 to 2 dB), and it is suitable for fault diagnosis in industries.