Planetary gearboxes, with their advantages of high transmission ratio and strong bearing capacity, are widely used in transmission systems of equipment in the energy, aerospace, and other fields. However, their maintenance and fault detection issues have also received considerable attention. This paper proposes a fault diagnosis method for planetary gearboxes based on visual spectral feature fusion. Initially, Welch’s transformation is applied to obtain the power spectrum of the planetary gearbox signals. The visual graph algorithm is then used to construct a graph spectrum, and the centrality indices of the graph nodes are calculated and fused into a feature matrix. Finally, an improved CNN-Inception model is employed to obtain the fault diagnosis results of the planetary gearbox. Experimental results demonstrate that this method can accurately identify faults in planetary gearboxes, achieving an accuracy rate of 98.57% on experimental datasets from two operational conditions, and the model exhibits generalization. Compared with other methods, this method enables efficient and accurate fault diagnosis.
1. Introduction
Planetary gearboxes, composed of key components such as the sun gear, planetary gears, ring gear, and planet carrier, have complex gear distributions and operational forms. When the ring gear is fixed and the sun gear rotates, the planetary gears rotate on their own axes while simultaneously revolving around the sun gear with the planet carrier. Due to their exposure to variable environmental excitations, the vibration signals of planetary gearboxes exhibit complex frequency information, strong time-varying characteristics, and obvious modulation features, which increase the difficulty of signal analysis and fault diagnosis.
Over the years, scholars have devoted considerable effort to developing effective fault diagnosis techniques for planetary gearboxes. Various methods, such as empirical mode decomposition (EMD) combined with deep convolutional neural networks (DCNN), optimized support vector machines (SVM), and multidimensional ensemble empirical mode decomposition (MEEMD) combined with variational mode decomposition (VMD) and deep residual networks (ResNet), have been proposed. However, due to the complexity of vibration signals in planetary gearboxes, effective feature extraction and fault diagnosis based on signal characteristics remain hot research directions.
Recently, the development of graph signal processing has provided new ideas for fault diagnosis techniques. Compared with traditional time, frequency, and time-frequency domains, analyzing and processing mechanical vibration signals in the vertex, graph spectrum, and vertex-graph spectrum domains can effectively extract more fault information hidden in the graph topology.
In response to the aforementioned issues, this paper proposes a fault diagnosis method combining visual graph spectral feature fusion and deep learning from the perspective of graph signal processing. The main contributions are as follows:
- Planetary gearbox vibration signals are divided, and power spectral values are extracted. The visual graph algorithm transforms the power spectral signals into graph structures, and the graph node feature matrix is calculated as signal features to fully extract signal spatial features.
- A CNN-Inception model is constructed. This model has multi-scale feature extraction capabilities and effectively performs planetary gearbox signal classification and diagnosis through learning and training of fused features.
2. Literature Review
Scholars have conducted extensive research on fault diagnosis methods for planetary gearboxes. The following is a brief overview of related research:
- Traditional Signal Processing Methods
Traditional fault diagnosis methods for planetary gearboxes primarily rely on signal processing techniques such as time-domain analysis, frequency-domain analysis, and time-frequency analysis. These methods are used to extract fault features from vibration signals and then diagnose faults through pattern recognition or machine learning algorithms. However, due to the complexity and time-varying nature of vibration signals in planetary gearboxes, traditional methods often face challenges in accurately extracting fault features.
- Modern Signal Processing and Machine Learning Methods
To overcome the limitations of traditional methods, scholars have proposed a series of modern signal processing and machine learning methods for fault diagnosis of planetary gearboxes. For example, empirical mode decomposition (EMD) is used to decompose vibration signals into intrinsic mode functions (IMFs), and then deep convolutional neural networks (DCNN) are used to extract features and classify them, thereby achieving automated diagnosis. Other methods include optimized support vector machines (SVM), deep residual networks (ResNet), and convolutional neural networks (CNN) combined with various signal processing techniques. These methods have achieved good results in fault diagnosis, but there is still room for improvement in feature extraction and diagnosis accuracy.
- Graph Signal Processing Methods
Recently, the development of graph signal processing has provided new ideas for fault diagnosis of planetary gearboxes. By analyzing and processing mechanical vibration signals in the vertex, graph spectrum, and vertex-graph spectrum domains, more fault information hidden in the graph topology can be effectively extracted. For example, the rolling bearing signal is converted into a visual graph, and then graph Fourier transform is used to calculate the graph spectral amplitude entropy as a fault feature parameter. Another method adopts the visual graph algorithm to convert time-domain signals into complex network graphs and extracts five statistical features of the graph, which are then input into a gradient boosting decision tree algorithm (CatBoost) for classification.
3. Proposed Method
This paper proposes a fault diagnosis method for planetary gearboxes based on visual graph spectral feature fusion and deep learning. The method mainly includes the following steps: data preprocessing, visual graph spectral feature matrix construction, model training, and fault classification and identification.
3.1 Data Preprocessing
The vibration data of the planetary gearbox is first divided into segments of 1024 data points each. Welch’s transformation is then applied to convert the data into a 513-length power spectrum. Welch’s transformation can extract effective features of the signal and reduce its length.
3.2 Visual Graph Spectral Feature Matrix Construction
The power spectral signals are processed using the visual graph algorithm to construct a graph structure. The degree centrality, betweenness centrality, and closeness centrality of the graph signal nodes are calculated to construct a 513×3 feature matrix. This feature matrix is divided into training, testing, and validation sets.
3.2.1 Visual Graph Algorithm
The horizontal visual graph algorithm, proposed by Luque et al., can accurately map the dynamic characteristics of random time series to the topological characteristics of the horizontal visual graph. For a time series, each data point can be regarded as a node in the network, and the edges in the network are formed by connecting each data point according to the visibility criterion. The visibility criterion states that if points (t_a, y_a) and (t_b, y_b) in a discrete time series can be connected, then for any point (t_c, y_c) in the data, where t_a < t_c < t_b, the following condition must be satisfied: y_a / (t_b – t_a) * (t_c – t_a) > y_c – y_a and y_b / (t_b – t_a) * (t_b – t_c) > y_b – y_c.
3.2.2 Graph Centrality Indices
Graph centrality indices are used to measure the importance and influence of nodes in a graph. The vertices represent signal points, and the edges represent the relationships between signal points. Let G = (V, E) be an undirected graph without weights, consisting of N nodes and M edges, where V = {v_1, v_2, …, v_n}. The degree centrality, betweenness centrality, and closeness centrality of each node are calculated as follows:
- Degree Centrality: Measures the number of edges connected to a node. It reflects the direct influence of a node on other nodes.
- Betweenness Centrality: Measures the number of shortest paths passing through a node. It reflects the importance of a node in controlling the flow of information or resources in the graph.
- Closeness Centrality: Measures the inverse of the average shortest path length from a node to all other nodes. It reflects the ease of access to other nodes from a given node.
3.2.3 Feature Fusion
To improve the robustness of features and achieve higher accuracy, the three indices are fused into a feature matrix in a parallel form. The fusion formula is as follows:
X_fusion = [X_CC, X_BC, X_DC]
where X_CC, X_BC, and X_DC represent the degree centrality, betweenness centrality, and closeness centrality feature matrices, respectively. The obtained feature samples need to be standardized to have values in the range (0, 1) for subsequent input into the neural network. The standardization formula is as follows:
X̂ = (X – X_min) / (X_max – X_min)
where X_min and X_max are the minimum and maximum values of the elements in the feature matrix X, respectively.
3.3 Model Training
The feature matrix is input into the improved CNN-Inception model for training to obtain the fault diagnosis model.
3.3.1 CNN-Inception Model
The Inception structure, first proposed in GoogLeNet, has the core idea of using different convolutional kernels to process input data in parallel and then concatenating the obtained feature maps along the depth dimension to obtain a deeper feature map. The Inception module applies 1×1 convolutional kernels before 3×3 and 5×5 convolutions to reduce dimensionality, thereby reducing the number of parameters and computations, increasing model depth, and improving nonlinear。
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