Research on the Condition Assessment Method of Mechanical Seal Based on Fusing Multi-Graph Neural Networks From Decision Layer

Abstract

Mechanical seals play a crucial role in mechanical equipment by effectively preventing liquid or gas leakage, ensuring the normal operation of the equipment, and avoiding energy waste and environmental pollution. Especially in pumps, compressors, and other devices, mechanical seals ensure sealing performance while extending the equipment’s lifespan and improving work efficiency. Therefore, research on the condition assessment of mechanical seals is both necessary and important. In order to achieve high accuracy in the assessment model, a comprehensive evaluation model that fuses multilevel information is proposed. Firstly, several types of sensors are used to monitor the operational status of the mechanical seal comprehensively and accurately, capturing different signal features to provide richer multidimensional data. Secondly, multiple methods are used to process and convert the collected data into graph data, ensuring the diversity of the training data through different channels and graph construction techniques. Thirdly, in order to future improve the assessment performance, multi-GNNs models are fused by using different combined methods. Finally, the effectiveness of the assessment method is validated by using the test data of mechanical seal.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

1. Introduction

In the context of Industry 4.0, reliable production and high-quality products depend on the effective operation and maintenance of mechanical equipment [1, 2]. A mechanical seal, which is a mechanism that uses the relative sliding of two sealing surfaces to maintain sealing effect and prevent fluid leakage, is a fundamental part of many rotating machines. Their effectiveness has a direct impact on the equipment’s dependability, safety, and energy efficiency. They are frequently found in fluid machinery that rotates, such as gearboxes, compressors, and pumps [3, 4]. The integrity of the sealing surface, which is the fundamental component of mechanical seals, directly affects the caliber of sealing performance. New insights and solutions have emerged as a result of the artificial intelligence technology’s rapid progress, particularly with the introduction of graph neural networks (GNNs) [5].

GNNs have garnered significant interest in the mechanical state assessment domain because of their superiority in handling intricate relational data. By translating the temporal signals that sensors record into graph data, GNNs is able to analyze sensor data efficiently and effectively, expressing and capturing the dynamic properties seen in mechanical systems. A novel GNN model was presented by Hu et al. [6] to accomplish accurate and comprehensible time series event prediction by encoding state graphs. A variety of techniques can enhance the precision of state evaluation when it comes to decision level fusion tactics [7]. If multi-GNN models could be fused, the accuracy of assessment performance could be improved. Therefore, how to fuse multi-GNN models would be researched.

This article puts forth a multi-GNN methodology based on decision layer fusion for the assessment of mechanical seals. The method initially employs multichannel sensor data to characterize the overall operation of the mechanical seal. Subsequently, the original signal is converted into graph data through the utilization of diverse graph data construction techniques, thereby enhancing the diversity of the dataset. Following training, the evaluation results are obtained by integrating the outputs of multiple GNN models at the decision layer. The experimental verification demonstrated that the proposed evaluation method is capable of effectively identifying the various operating conditions of mechanical seals, including the normal state, stationary ring (SR) damage, and rotating ring (RR) damage, and is able to distinguish between different levels of damage. Furthermore, through a comparison and analysis of different model structures and classification accuracy, the optimal evaluation model structure was determined. In conclusion, the GNN model based on decision layer fusion proposed in this study has the potential to significantly enhance the accuracy and comprehensiveness of mechanical seal state evaluation.

2. Graph Data, GNNs, and Fusion Strategy

2.1. Graph Data

The construction of graph data involves transforming multisource heterogeneous data of mechanical seal systems into a form that can be processed by GNNs. The definition of graph is as follows.

A graph can be represented as a set of vertices and edges, denoted as $G=V,E$, where $V=v_1,v_2,\dots ,v_n$ is a set with $n$ vertices and $E\subseteq V\times V$ is a set of edges.

Usually, the adjacency matrix $A\in {\mathbb{R}}^{n\times n}$ is used to represent the connection relationship between vertices. If each vertex contains H-dimensional features, use the feature matrix $F\in {\mathbb{R}}^{n\times m}$ for representation.

2.1.1. Graph Data With Cycled Sampling (GDCS)

Sun et al. [8] proposed a graph construction method, GDCS. This method divides the data into segments according to their periods, treating the data points as nodes and connecting them accordingly. The weight between two nodes is defined as the corresponding Euclidean sequence:$$\begin{array}{}\text{(1)}& dP,Q=\sqrt{{x_2-x_1}^2{+y_2-y_1}^2.}\end{array}$$

2.1.2. Visibility Graph (VG)

Lacasa [9] proposed a graph construction method named the VG. The brief description is as follows. Firstly, the data should be divided. Secondly, for arbitrary data values, (t_a, y_a) and (t_b, y_b) would be connected if any other data (tc, yc) between them could satisfy the following condition:$$\begin{array}{}\text{(2)}& y_c<y_b+y_a-y_b\frac{t_b-t_c}{t_b-t_a}.\end{array}$$

2.1.3. Horizontal Visibility Graph (HVG)

Based on the VG construction method, a HVG [10] construction method is proposed, with improvements made to the visibility criteria. The definitions of network nodes and edges are the same as in the VG construction method, but there are changes to the visibility criteria. The new visibility criterion is that for any two points $t_a,y_a$ and $t_b{,y}_b$, and any $t_c,y_c$ between them, they are connected if the following condition is satisfied:$$\begin{array}{}\text{(3)}& y_b,y_a>y_c\text{\hspace{0.17em}for\hspace{0.17em}all\hspace{0.17em}}c\text{\hspace{0.17em}such\hspace{0.17em}that\hspace{0.17em}}a<c<b.\end{array}$$

2.1.4. Limited Penetrable Visibility Graph (LPVG)

Zhou et al. [11] developed methods based on both HVGs and standard VGs in the context of complex network analysis. Then, a new method of constructing graph, LPVG, was proposed. The brief description is as follows. The definitions of network nodes and edges are the same as in the VG construction method, but there have been further changes to the visibility criteria. Using the same visibility calculation formula as in the VG construction method, but defining a finite visibility range $N$, these two nodes can still be connected if the interval n between them is less than $N$.

2.1.5. Graph Based on Short-Time Fourier Transform (STFT) (GS)

Goyal and Pabla [12] proposed a new graph construction method. The brief description is as follows. This method first performs a STFT on the data. Then it divides the data into $N$ segments. For each segment, compute the short-time spectrum and treat the computed values as individual graph nodes:$$\begin{array}{}\text{(4)}& \widehat{P}k,m=\frac{1}{T}{Yk,m}^2.\end{array}$$

Then connect each pair of nodes to form weighted edges, with the weights calculated using the Euclidean distance formula:$$\begin{array}{}\text{(5)}& e_{ij}^2=DisPi,t_f,Pj,t_f.\end{array}$$

2.1.6. Graph Based on Wavelet (GW)

Lu et al. [13] proposed a new graph construction method. First, the time series is divided into multiple sequential segments using a nonoverlapping sliding window, denoted as $X_1,X_2,\dots ,X_h,\dots$. Then, for each segment $X_h$, we decompose it using the WPD method. The resulting set of WPCs can be represented as a set of graphs by performing graph construction on each set of WPCs, denoted as $g^h=G_{l,0}^h,\dots ,G_{l,k}^h,\dots ,G_{l,K}^h$.

2.2. GNNs

GNNs are a class of neural networks designed to work with graph-structured data. Popular architectures include graph convolutional networks (GCNs) [14] and graph attention networks (GATs) [15]. It performs tasks such as node classification, graph classification, and link prediction by learning the relationships between nodes and the topology of the graph. The underlying principle is based on the ideas of message passing and node updating, where each node aggregates and passes on the information from its surrounding nodes to update its own representation vector.

2.3. Fusion Strategy

2.3.1. Voting Method

Voting methods are collective decision-making techniques that rely on the choices made by voters to determine one or more optimal options. Mainly, methods include the majority voting method, absolute majority voting method, preferential voting method, and cumulative voting method.

2.3.2. Weighted Average Method

The weighted average method [16] is a statistical approach for calculating the mean of a set of values, where each value is assigned a different weight that reflects its importance or influence. The formula to calculate the weighted average is as follows:$$\begin{array}{}\text{(6)}& \text{Weighted\hspace{0.17em}Average}=\frac{{{\displaystyle \sum }}_{i=1}^n{w}_i{x}_i}{{{\displaystyle \sum }}_{i=1}^n{w}_i},\end{array}$$where $x_i$ indicates the value of the $i$th item; $w_i$ indicates the weight of the $i$th item; and $n$ represents the total number of items.

3. Assessment Method Based on Fusing Multi-GNNs

In order to achieve a more accurate and comprehensive evaluation of the status of the mechanical seal, we have developed an innovative comprehensive evaluation method. The key of this method lies in the integration of sensor data from disparate sources and types, each of which reflects distinct aspects and operating states of the mechanical seal system. Due to the constraints of a single sensor, they frequently only capture a subset of the system’s operating characteristics. However, by integrating multiple sources of information, a more comprehensive and accurate representation of the system’s health status can be constructed.

In the first instance, the accumulated raw data are typically presented in Euclidean form, that is to say, as numerical data points, which is not directly applicable to the processing of GNNs. It is therefore necessary to transform the data into a graph structure prior to conducting GNN training. This involves mapping the data points to nodes in the graph and establishing edges based on their correlations. In this process of transformation, the adoption of diverse construction strategies can serve to further enrich the dataset and increase the learning dimension of the model.

Figure 1 illustrates a decision layer structure that integrates multiple GNNs, thereby enabling each GNN to analyze and interpret input data from its own perspective. The specific focus of each GNN may vary, with some concentrating on time series patterns and others on spatial distribution characteristics, for example. The features extracted by each GNNs are aggregated in the decision layer through parallel processing, forming a comprehensive evaluation result that reflects a multiangle understanding of the complex state of the mechanical seal system. This approach significantly improves the accuracy and reliability of the evaluation.

[figure(s) omitted; refer to PDF]

In this research, six graph data construction methods are used, and the details are shown in Table 1. Two fusion strategies are used, and the details are shown in Table 2. The GNNs contain two Conv layers, two graph pooling layers, two readout layers, and two FC layers, and the detailed information could be found in Li et al. [17].

Table 1

Six graph data construction methods.

Method	Description
GDCS	Constructing the graph data by using cycle features
VG	Using the visibility criteria to construct the graph data
HVG	Using the horizontal visibility criteria to construct the graph data
LPVG	Using the limited penetrable visibility criteria to construct the graph data
GS	Constructing the graph based on STFT
GW	Constructing the graph based on wavelet

Table 2

Two fusion strategies for decision layer of GNNs.

Method	Description
Cumulative voting	Each voter has multiple votes that they can allocate to one or more options
Weighted average	Calculating the mean of a set of values which is assigned a different weight

Therefore, an assessment process for mechanical seal is proposed, as shown in Figure 2. The process can be divided into two parts, one is training part, and the other is testing part. For training part, firstly, the original data, which are collected by using several sensors, should be processed, liking removing outliers and so on. Secondly, the original wave is converted into the graph data, and then the test datasets are constructed for training. Finally, the assessment model could be gotten by fusing multi-GNNs from decision layer. For testing part, the specific channel sensors, which are determined based on the training results, are monitored online firstly. Secondly, the monitored data are converted into the graph data by using specific methods based on the assessment model. Finally, the assessment result could be gotten. Moreover, the damage degree of mechanical seal could be gotten too if the running condition is abnormal.

[figure(s) omitted; refer to PDF]

4. Test, Results, and Discussion

4.1. Test Rig and Simulated Faults

The test rig of mechanical seal is shown in Figure 3. The test mechanical seal is mounted in the chamber. In order to measure the preload force of mechanical seal, a sensor ring, which consists of four force sensors (F1, F2, F3, and F4), is mounted on back of the SR. One acoustic emission (AE) sensor (GM150) directly measures the running data of seal interface, and the other AE sensor (G150) measures the overall running data of mechanical seal. The sampling rate of AE sensors is 1 MHz, and the sampling point is 1 M points. The sampling rate of force sensors is 3.2 KHz, and the sampling point is 3.2 K points.

[figure(s) omitted; refer to PDF]

In order to simulate the fault of mechanical seal, the grooves are processed for RR and SR by using laser. The width of grooves includes two types, 0.1 and 0.3 mm, as shown in Figure 4. Then, the test datasets are generated, as shown in Table 3.

[figure(s) omitted; refer to PDF]

Table 3

Description of the test datasets.

Condition	Fault location	Fault dimension (mm)	Rotating speed (r/min)	Data size	Label
Normal			3000	3000	0
[email protected]	Stationary ring	0.1	3000	3000	1
[email protected]	Rotating ring	0.1	3000	3000	2
[email protected]	Stationary ring	0.3	3000	3000	3
[email protected]	Rotating ring	0.3	3000	3000	4

4.2. Signal Processing Results and Graph Data

Taking GM150 and F1 as example, five data are extracted from five different running conditions, and the signal processing results and graph data of five data are shown as follows.

  Normal condition

  [email protected] condition

  [email protected] condition

  [email protected] condition

  [email protected] condition

4.3. Assessment Results

Because the number of combinations for multi-sensors, graph construction methods, and fusion strategy is very large, partial assessment models are shown in Table 4, and the assessment of partial assessment models is shown in Table 5.

Table 4

The description of structures for partial assessment models.

Model	Sensor channels	Graph data construction methods	Fusion strategy
Model 1	GM150	VG	Weighted average
	F2	LPVG
	G150	GS
	F4	HVG
Model 2	GM150	VG	Cumulative voting
	F2	LPVG
	G150	GS
	F4	HVG
Model 3	GM150	VG	Weighted average
	F2	LPVG
	GM150	HVG
	G150	HVG
Model 4	GM150	VG	Weighted average
	F2	LPVG
	G150	VG
	F4	HVG
Model 5	GM150	VG	Weighted average
	F2	LPVG
	G150	VG
	GM150	HVG
Model 6	GM150	VG	Cumulative voting
	G150	LPVG
	F1	VG
	F2	HVG
	F3	VG
	F4	GDCS

Table 5

The accuracies of partial assessment models for test datasets.

Model	Condition	Accuracy	Mean accuracy
Model 1	Normal	1.0	1.0
	[email protected]	1.0
	[email protected]	1.0
	[email protected]	1.0
	[email protected]	1.0
Model 2	Normal	0.99	0.988
	[email protected]	0.99
	[email protected]	1.0
	[email protected]	0.98
	[email protected]	0.98
Model 3	Normal	1.0	0.92
	[email protected]	0.88
	[email protected]	0.83
	[email protected]	0.95
	[email protected]	0.94
Model 4	Normal	1.0	0.978
	[email protected]	0.94
	[email protected]	1.0
	[email protected]	0.95
	[email protected]	1.0
Model 5	Normal	0.95	0.908
	[email protected]	0.85
	[email protected]	0.83
	[email protected]	0.97
	[email protected]	0.94
Model 6	Normal	1.0	0.986
	[email protected]	0.96
	[email protected]	0.98
	[email protected]	0.99
	[email protected]	1.0

4.4. Discussion

4.4.1. Comparison of Signal Processing Results

In Section 4.2, as shown in Figures 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14, a comparison was made between the differences in the raw waveforms obtained by the GM150 sensor, the FFT, and the STFT under different states. For instance, under typical circumstances, there are notable discrepancies between the [email protected] and [email protected], as well as the [email protected] and [email protected], when comparing GM150 and F1 sensor data. These alterations are indicative of modifications in the vibration characteristics of mechanical seals in response to varying degrees of damage (which correspond to different state outcomes). In particular, damage to the RR or SR, whether minor damage (@0.1) or severe damage (@0.3), results in distinctive changes in the amplitude, frequency components, and time-frequency distribution of the signal, which can provide valuable insights for assessing the mechanical seal state.

[figure(s) omitted; refer to PDF]

4.4.2. Comparison of Methods for Constructing Graph Data

Similarly, in Section 4.2, as shown in Figures 15, 16, 17, 18, 19, 20, 21, 22, 23, and 24, six distinct graph data construction methods (LPVG, GDCS, HVG, VG, GS, and GW) were employed for the generation of graph data for the GM150 and F1 sensors. The graph data also demonstrate notable discrepancies across different states. Each construction method employs a distinct processing approach, such as the LPVG, which emphasizes time-frequency relationships, and the GDCS, which emphasizes periodic patterns. It is evident that even under the same state, graph data obtained using different construction methods will exhibit disparate features, which is of paramount importance for comprehending the varying degrees of damage in mechanical seals.

[figure(s) omitted; refer to PDF]

4.4.3. Comparison of Model Structure and Classification Accuracy

In Section 4.3, we conducted an evaluation of the performance of various model structures in classification tasks, including the combination of different sensor channels, the construction of graph data, and the implementation of fusion strategies. A comparison of the classification accuracy of Models 1 to 6 revealed that Model 1 achieved 100% accuracy under all conditions on all test datasets, thereby demonstrating its outstanding performance in state assessment. While other models may demonstrate higher accuracy under certain conditions, they have not been shown to surpass the performance of Model 1 in overall evaluation. Accordingly, Model 1 is identified as the optimal evaluation model structure, as illustrated in Figure 25. This model employs a weighted average fusion strategy, integrating the LPVG, VG, GS, and HVG map data from the GM150, G150, F2, and F4 sensor channels to achieve precise evaluation of the mechanical seal status.

[figure(s) omitted; refer to PDF]

In conclusion, a comprehensive analysis of signal processing outcomes, graph data construction techniques, and model architectures has not only substantiated the pronounced dissimilarities in signal characteristics across diverse states but also corroborated the efficacy and superiority of the proposed GNN fusion model in mechanical seal state assessment. Additionally, the most accurate mechanical seal detection model and sensor type were identified.

5. Conclusions

The new assessment model and assessment process for mechanical seal, which are based on fusing multi-GNNs, are proposed. The main conclusions include the following:

1. From the results of signal processing, it could be found that the phenomena of normal, damage for SR, and damage for RR are totally different.

2. It could be found that the phenomena of different damage degree for SR and RR are different too.

3. The different channels of sensors, including two AE (G150 and GM150) and four force (F1, F2, F3, F4), could represent partially running condition information of mechanical seal. Therefore, the data, which are collected by different sensors, are complementary and divergent.

4. Although diversity exists among the different sensors, it also could be found that the diversity could be generated by using different graph data construction methods.

5. Because of the diversity of different channels and graph data, the GNNs which are trained by using different training datasets could inherit the diversity and then embody the diversity in the network structures. Therefore, it could improve the accuracy after fusing multi-GNNs.

6. Two fusion strategies are discussed, including weighted average and voting. The fusion strategy of GNNs with the decision level should be researched in the future.

7. The assessment results show that the model of fusing multi-GNNs could accurately assess the running condition of the mechanical seal.

Author Contributions

Xiaoran Zhu: funding acquisition, supervision, conceptualization, methodology, writing – review and editing, and data curation. Binhui Wang: writing – original draft, software, and data curation. Junchao Chen: software and data curation. Zipeng Li: writing – review and editing.

Funding

This research was supported by the Henan Provincial Science and Technology Research Project (grant no. 222102220115).

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