Wind Turbine Gearbox Fault Detection Based on Sparse Filtering and Graph
  Neural Networks
The wind energy industry has been experiencing tremendous growth and
confronting the failures of wind turbine components. Wind turbine gearbox
malfunctions are particularly prevalent and lead to the most prolonged downtime
and highest cost. This paper presents a data-driven gearbox fault detection
algorithm base on high frequency vibration data using graph neural network
(GNN) models and sparse filtering (SF). The approach can take advantage of the
comprehensive data sources and the complicated sensing networks. The GNN
models, including basic graph neural networks, gated graph neural networks, and
gated graph sequential neural networks, are used to detect gearbox condition
from knowledge-based graphs formed using wind turbine information. Sparse
filtering is used as an unsupervised feature learning method to accelerate the
training of the GNN models. The effectiveness of the proposed method was
verified on practical experimental data.
Jinsong Wang, Kenneth A. Loparo
# Wind Turbine Gearbox Fault Detection Based on Sparse Filtering and Graph Neural Networks

###### Abstract

The wind energy industry has been experiencing tremendous growth and confronting the failures of wind turbine components. Wind turbine gearbox malfunctions are particularly prevalent and lead to the most prolonged downtime and highest cost. This paper presents a data-driven gearbox fault detection algorithm base on high frequency vibration data using graph neural network (GNN) models and sparse filtering (SF). The approach can take advantage of the comprehensive data sources and the complicated sensing networks. The GNN models, including basic graph neural networks, gated graph neural networks, and gated graph sequential neural networks, are used to detect gearbox condition from knowledge-based graphs formed using wind turbine information. Sparse filtering is used as an unsupervised feature learning method to accelerate the training of the GNN models. The effectiveness of the proposed method was verified on practical experimental data.

Keywords:Wind energy, fault detection, graph neural network, sparse filtering 

## 0 Introduction

The wind market of 2021 trend data shows that the global market has an installed base of 590-GW that delivers clean energy to the consumers representing a 10% increase compared with 2020 [1]. China and the United States have the largest wind energy capacities at 211,392 MW and 96,433 MW, respectively [1]. Average turbine size (rotor diameter, and hub height) and capacity (nameplate) are continuing a long-term growth trend. Comparing utility-scale wind turbines in 2010 and 2018, in 2018 the average diameter is 116 (m) and the average hub height is 88 (m) (a 35% increase) while the average nameplate capacity is 2.4 MW (a 60% increase) [1]. If current trends continue, wind energy can save consumers $280 billion, reduce 12.3 gigatons of greenhouse gases emission, preserve 260 million gallons of water, increase tax revenue by $3.2 billion, and support 600,000 jobs by 2050 [2].

Wind energy reliability issues are a result of the rapidly growing market and wind turbine technology development. Higher wind energy reliability can improve operation and maintenance (O&M) costs, capacity factors, levelized cost, and grid interconnection [3]. The failure of wind turbine components is a critical reliability issue; downtime caused by component failures has harmful effects economic and operational aspects [4]. Gerbox malfunctions have the most prolonged downtime, the most expensive O&M costs, and the most substantial impact on grid operations [5]. Gerbox vibration is monitored to assist with wind turbine health management and avoid malfunctions [6].

Internet of Things (IoT) has been an attracting technology for real-time monitoring of valuable devices. IoT-based wind turbine Prognostics and Health Management (PHM) is defined as a lifecycle support system, in which, (1) wind turbine data is collected for mission-critical and cost-sensitive components, for example, the gearbox; (2) fault detection, diagnosis, and prognosis are implemented by processing and modeling these data; (3) decision support system is able to interpret these outcomes to accomplishable required operational and maintenance strategies [7]. By 2030, IoT-based wind turbine technologies such as PHM [7] have the potential to increase wind turbine production by 25% and reduce cost by 50% [8]. However, IoT-based PHM systems can be challenging, they require sensing and vibration condition monitoring, analysis of oil debris, and accurate and reliable fault detection, diagnosis, and prediction algorithms to improve decision-making [7].

On the other hand, there are some data-driven approaches that using the sensing data collected from IoT system for fault detection of wind turbines. Neural-network-based approaches have been widely used for fault detection, resulting is high performance in some applications. Samanta presented a genetic algorithm-based artificial neural network for fault detection and diagnosis [9]. In Samanta's work, time-domain statistical features are extracted from the raw vibration data obtained under different loading and operating conditions. This data was then used as input to a multilayer perceptron neural network, and a genetic algorithm is used for feature selection to optimize the classification accuracy. The GA-based ANN achieved 100% classification accuracy, which was better than without the GA and like a GA-based support vector machine (SVM). Amar et al. proposed an ANN-based detection and diagnosis system using frequency-domain features extracted by the Fast Fourier Transform (FFT) [10]. Feature selection from the FFT spectral images was based on a 2D averaging filter and binary image. Saravanan et al. proposed an ANN-based fault detection system
using the discrete wavelet transformation (DWT) [11]. Gaussian Process (GP) is used for wind turbine condition monitoring to identify operational anomalies [12]. An artificial neural network (ANN)-based condition monitoring approach using data from supervisory control and data acquisition system is proposed [13]. Random Forests and XGboost are combined to establish a data-driven wind turbine fault detection framework [14]. Denoising auto encoder (DAE) is also used to develop a multivariate data-driven fault detection framework [15]. Ensemble empirical mode decomposition (EEMD) and independent component analysis (ICA) are proposed to integrate to conduct wind turbine gearbox diagnosis [16]. In order to select the optimal variables, a PCA-based approach is proposed [17]. Compressed sensing is proposed to identify the impulsive feature [18]. These previous works used a typical fault detection and diagnosis process: signal preprocessing, feature extraction and selection, and classification. Lei et al. propose an intelligent fault diagnosis method for mechanical vibration data with unsupervised feature learning [19]. This method contained two stages: unsupervised feature extraction and classification. Sparse filtering [20] was implemented by an unsupervised two-layer neural network based on optimized sparsity distribution from the raw data for feature extraction. The features were then classified using SoftMax regression [21]. As compared to traditional ANN-based models, Lei's work reduced the prior knowledge and related feature extraction expertise that is required. The model had similar efficiency to CNN-based models using comprehensive vibration data but reduced computational cost. Zhang et al. proposed an innovative approach for wind turbine fault detection based on Gaussian Processes (GP) [22] and bootstrap-based ensemble neural networks (BENN) [23] to produce early prediction of the health conditions, with high level accuracy when applied to gearbox oil temperature and the generator winding voltage datasets [24]. However, the hidden domain knowledge of wind turbine such as the structural information of the sensing data, and the features (or the number of features) are still manual selected. A comprehensive review of vibration-based fault diagnosis of wind turbine gearbox is given by Wang et al [25].

To address the issues and opportunities discussed above, this paper presents a hybrid approach of sparse filtering and GNN (SF-GNN) for wind turbine fault detection. In general, SF-GNN identifies the gearbox health condition from a knowledge-based input graph that efficiently conducts high frequency sensor data via the acceleration of sparsening filtering and ontologically describes the wind turbine and gearbox, and generates either a single output of the condition of an individual component and sequential outputs with additional semantical information to the conditions. Three GNN models are deployed in this paper: basic graph neural networks [26][27], Gated Graph Neural Networks (GG-NNs) [28] and Gated Graph Sequence Neural Networks (GGS-NNs) [28]. All three GNN-based models are trained in a supervised manner for node classification. The input graph is modeled by a knowledge-based structure that explicitly incorporates wind turbine terminologies, sensors, and operating conditions.

The motivation to use GNN-based models is to classify the target node by considering complete wind turbine information, that is the composition of wind turbine, and the structure of sensors are utilized to provide robust and reasonable results. In a general sense of sensor network, a large number of sensors are mounted and organized as a complex network. For example, each component of a wind turbine gearbox is monitored by one or more sensor(s) for comprehensive operation state tracking. To detect the fault and malfunctional events based on an induvial or partial sensor(s) is time-consuming and suffering low accuracy outcomes, due to massive data sources. Therefore, this paper claims that deep neural nets with graph input, containing a group of sensors structured by relation types (such as hierarchical and causal), outperforms the methods only considering individual sensors.

Additionally, the literatures reviewed in this paper present highlights of prediction models with input of individual sensor data source or a group of sources but without relations, which causes that the detection outcomes are adapted to a fixed operation situation. However, the fault events are caused by one or more impacts. For example, a data source of the mid shaft is applied for the fault detection, that is, the fault is assumed to occur in such situation of the defect of the shaft instead of considering the comprehensive causes as a real world problem.

The motivation to use sparse filtering is to improve the efficiency of the GNN-based models, specifically to reduce the computational cost of feature learning. the data source used in this work is high frequency vibration data; that is, it presents extra sensitive noise impact than usual data source. Therefore, it is a challenge to use such as raw data input of a deep network, let alone organize such multiple sources in a relational graph. Therefore, sparse filtering is applied to control this issue. It is an unsupervised learning method and drives sparsity the feature matrix of the ultra-high frequency sensor signals, standardize the features to receive equal activation, and qualify the signals data validity to GNNs.

The contributions of this paper are considered that (1) a data-driven approach SF-GNN (based on sparse filtering and graph neural networks) is proposed for vibration-based wind turbine gearbox fault detection; (2) a knowledge-based graph of the ontological wind turbine gearbox and sensor data is developed; (3) sequential outputs provide semantical detection results for single or multiple defect occurrence; (4) SF-GNN outperforms accuracy and the computing time; (5) to the best of our knowledge, this is the first paper to use GNN-based for wind turbine fault detection.

The reminder of the paper is organized as follows: Section II introduces the SF-GNN models, the main GNN-based methods are reviewed, and their significance is explained. Section III introduces the experimental setup and the performance of the SF-GNN models are investigated with comparisons to neural-network-based models. The effect of sparse filtering for performance improvement and the impact of GNN-based fault detection are also discussed. Section IV provides a summary and conclusions.
## 1 Methods

### General Graph Neural Networks

The graph neural network (GNN) is a neural network-based approach for representation learning and classifying nodes in a graph [27]. Representation learning is an approach to simplify a complex graph structure. The graph of complex system, for example a biological network or group of social media users, can be very large and complicated. Features with structural information are extracted and interpreted from the graph and then used for the intended application, such as prediction and classification [29]. Traditionally, structural information is extracted using hand-engineered approaches. On the contrast, representation learning maps the original graph network to a low-dimensional space that can be used to infer and present the graph. This process is called node embedding or node labeling [29]. Representation learning accelerates graph-based applications to learn and encode structural information in a simplified approach.

Concisely, GNNs provide node embedding and node classification. In this work, a GNN is used as a supervised node classification method. The input graph is the knowledge-based graph structure of the wind turbine and the target node is one of the health condition nodes.

In the embedding stage, given the graph \(G=(V,E)\), each node in \(V\) is mapped to a low dimensional space. Each node representation \(x_{v}^{(t)}\) at timestep \(t\) is defined by \(f_{w}^{t}\), which is implemented as a recurrent neural network. The embedding of \(x_{v}^{(t=0)}\) is randomly initialized and in the absence of node attribute labels, each iteration updates the representation as [26][28] :

\[x_{v}^{(t)}=f_{w}^{t}(l_{w},l_{conv},l_{v^{\prime}},x_{v^{\prime}}^{(t-1)}). \tag{1}\]

GNN is based on a recursive approach where information (labels) from neighbor nodes and edges are aggregated and the network \(f_{w}^{t}\) is decomposed as the sum of per-edge aggregation functions \(f_{agt}\):

\[f_{Embed}\Big{(}l_{w},l_{conv},l_{v^{\prime}},x_{v^{\prime}}^{( t)}\Big{)}=\] \[\sum_{v^{\prime}_{in}}f_{agt}\Big{(}l_{w},l_{v^{\prime}\to v },l_{v^{\prime}},x_{v^{\prime}}^{(t-1)}\Big{)}+\] \[\sum_{v^{\prime}_{out}}f_{agt}(l_{w},l_{v\to v^{\prime}},l_{v^{ \prime}},x_{v^{\prime}}^{(t-1)}). \tag{2}\]

The \(f_{agt}\) are defined by a neural network [21] with configuration of labels and non-linear activation function, and a recursion for updating the trainable parameters \(w\) and \(b\) as follows:

\[x_{v}^{(t)}=\sum_{v^{\prime}\in V(v)}f_{agt}[W^{(l_{w}l_{v^{\prime}}-v^{\prime }l_{v^{\prime}})}x_{v^{\prime}}^{(t-1)}+b^{(l_{w}l_{v^{\prime}}-v^{\prime}l_{v^ {\prime}})}]. \tag{3}\]

Once the final embedding space is computed, the second stage of node classification is defined by the neural network \(g_{w}^{t}\)[21]:

\[y_{v}^{(t)}=g_{w}^{t}(x_{v}^{(t)},l_{v}). \tag{4}\]

### The gated Graph Neural Networks

The gated graph sequential neural network (GGS-NN) is a GNN-based approach using a modified gated graph neural network (GG-NN) [28]. In the GNN, neighbor node information is aggregated by one shared neural network across layers. When the complexity of the input graph increases, over fitting the GNN parameters and the computational cost of training by backpropagation with vanishing gradient problem is a problem [29]. The GG-NN addresses these issues by performing a recurrent update with similar gating mechanisms. The GG-NN includes "information aggregation \(+\) RNN" [29] with fixed-steps of representation learning and unrolling recurrence using backpropagation optimization methods through time and specific node information as the initialized input. GGS-NN is an extension of GG-NN where multiple GGS-NNs are used to perform predictions of: (1) the output of the current step, and (2) initialization for the next step [28].

In the initialization step, each node \(v\in V\) is annotated with a real-valued feature \(F^{(v)}\in\mathbb{R}^{D}\), and then the state vector is initialized from the features. In this work, features are optimized using sparse filtering. In the propagation step, the graph is unrolled to the fixed step while the nodes aggregate information from neighbors. The aggregation function is the same as with the GNN, but the general propagation model is replaced by the Gated Recurrent Unit (GRU) [30] that is used for hidden state updating that depends on aggregation and the previous state. In the output step, node-level output is computed like the GNN; the GGS-NN is used to produce an output sequence of the wind turbine's operating condition, including component type and name, sensor, and final health state.

### Sparsity Optimization

Sparse filtering is an unsupervised learning method with the objective to make the feature matrix sparse [20]. Each feature in column (\(d\)) and row (\(i\)) in the feature matrix is defined as:

\[F_{i}^{d}=W^{T}x^{d} \tag{5}\]

where \(W\) denotes the weight matrix; \(x^{d}\) denotes the \(d\)-\(th\) input data from the training set of \(\{x^{d}\}_{d=1}^{D}\), \(x^{d}\in\mathbb{R}^{N\times 1}\). The sparse filtering iteration begins with normalization of each input data using the \(L_{2}\) norm:

\[L_{2}(F_{i})=F_{i}/\|F_{i}\|_{2}. \tag{6}\]

Each feature from the normalized input data is then normalized using the \(L_{2}\) norm,

\[L_{2}(F^{d})=F^{d}/\|F^{d}\|_{2}. \tag{7}\]
Each normalized feature is then minimized using the \(L_{1}\) norm:

\[min\ \sum_{l=1}^{D}\left\|L_{2}(F^{d})\right\|_{1}. \tag{8}\]

The learning performance is measured according to three properties of the features: population sparsity, lifetime sparsity, and high dispersal [20].

Population sparsity describes the quantity of non-zero active element should be minimal, which requires high sparseness from the input data. The sparsity of the input \(x^{d}\) is defined as the \(L_{1}\) norm of \(F^{d}\). During the \(L_{2}\) normalization process, the feature is projected onto the surface of the unit ball. Then by the \(L_{1}\) minimization, the sparseness of the feature is improved.

Lifetime sparsity describes the quality of the sparsity of the feature that is expected to be discriminative with a high potential of selectivity [31]. The sparsity of feature \(F_{i}\) is defined as the \(L_{1}\) norm of \(F_{i}\). A significantly high level of sparseness can achieve lifetime sparsity.

High dispersal describes the statistical properties of features that are expected to have similar activation. The activation similarity is measured by the variance over all features. Lower values of variance indicate higher dispersal. The \(L_{2}\) norm, based on Euclidian distance, measures the variance [31] and normalized features share equal activation.

Sparse filtering can deal with high-dimensional inputs gracefully, and is very easy to use, for it has only one hyperparameter, the number of features to learn.

## 2 The Proposed Method

A SF-GNN is developed for wind turbine fault detection based on graph neural networks accelerated by sparse filtering. The core concept of the approach is to use the GNNs to classify the vibration data labeled as normal or fault within a graph structure, and the aim is to produce single and sequential detection outcomes. The approach includes three modules: graph identification, feature learning, and fault detection.

### Graph Identification

A graph is a type of data structure that describes relationships and interactions between individual entities. The edges and nodes of a graph define the directed graph structure, \(G=(V,E)\), where \(V\) denotes the nodes \(v\in V\), and \(E\) denotes the edges with direction from node \(v\) to \(v^{\prime}\), \(e=(v,v^{\prime})\in V\times V\)[29].

In this paper, the graph structure includes the following configurations to each node and edge: Labels and Neighbors. Labels are assigned to the nodes and edges. Node label \(l_{v}\) describes the features of each entity, for example, the health conditions of the wind turbine components. Edge label \(l_{CON}\) describes the connection level between two entities. The edge label contains \(l_{v\to v^{\prime}}\) indicates an outgoing connection (\(v\to v^{\prime}\)) and \(l_{v^{\prime}\to v}\) for an incoming connection (\(v^{\prime}\to v\)). Neighbors are nodes that connect with node \(v\) with labels \(l_{v^{\prime}}\). \(v^{\prime}_{in}\) and \(v^{\prime}_{out}\) are incoming and outgoing nodes, respectively. The label and neighbor configurations above are used in the GNN [28].

The graph is formed as a knowledge-based structure that is adapted and modified from the wind energy ontology developed Dilek Kucuk et al [32]. In the knowledge-based graph, the labels and neighbors includes the following specifications of the three hierarchical levels: the wind turbine structural components, the sensors and data, and the conditions that include the four relationships: "is-a", "has", "measures", and "causes". Level 1 is modeled as the terminology node that is associated with the wind turbine components including the gearbox elements and the bearing arrangements. These nodes are connected by "has". Level 2 is modeled as the data node that defines the sensors mounted on the gearbox components and the corresponding measured data. They are connected to sensor type nodes by "is-a" and the data type nodes by "measures". Level 3 is modeled as the state nodes that define the health conditions of the wind turbine components that are connected by "causes". The meta nodes, for example, the data type and the component type, are used to define the attributes of the nodes.

### Sr-Gnn

The SF-GNN is a two-stage fault detection model. The input of the model is defined by a knowledge-based structure of the wind turbine, including the components, the sensor network, the health conditions, and the connection relationships (_Graph Identification_). The first stage is feature learning by sparse filtering where high frequency raw vibration data corresponding to the sensor nodes (_Feature Learning_) is preprocessed. The second stage is wind turbine using GNN-based models. The SF-GNN includes two of the models: the basic graph neural network and gated graph neural network. The basic GNN generates a single detection output that reflects

Figure 1: The knowledge-based structure. This figure presents a general sense of the graph identification. The actual input graph is explained in the experiment section.
the general health condition of the wind turbine gearbox. GGS-NN generate either single or sequential detection output(s). The sequential outputs reflect detailed health conditions of the components with type and name, sensor, and final health state. The general framework of the SF-GNN is presented in Fig. 2.

## 3 Experiments

### Experiment Setup

Experiments are conducted to demonstrate the node classification efficiency of the GNN-based approaches and the effect of the SF-based feature learning. In the first part of the experiment, the single output accuracy of GNN and GG-NN are investigated with the comparisons to a multilayer perceptron [21] and the SF-based Softmax regression [19]. In the second part, the sequence output accuracy of GGS-NN is investigated via using raw vibration data, SF-based features, time- and frequency-domain features [9], and graph inputs.

For the implementation, sparse filtering and other GNN-based approaches are adapted and modified from available models [33][34][35][36]. The activation function is log-sigmoid [37] and the loss function is cross entropy [37]. The hyperparameters are selected as: hidden layer size = 16; learning rate fixed at 0.001; \(\text{dropout}=0.2\), and length of \(L_{2}\) regularization = 0.05.

For the training procedure, the optimization uses Kingma et al's method [38]. The parameter (weight and bias) initialization uses Glorot et al.'s method [39]. The maximum epoch number is 1,000. An early stopping criterion is used to terminate computations if there is no improvement in the loss function for the first 20 epochs. The datasets are divided according to: 60% training, 20% testing, and 20% development. Both normal and defected datasets of 8 sensors are used for training. That is, the ground-truth data of the healthy or normal condition datasets are used for the method evaluations including generalization check of SF-GNN.

For evaluation, the confusion matrix [40] is used to quantify the classification accuracy, and the accuracy is defined as the ratio of the true positives and true negatives over the total set of classifications.

### Data Description

Wind turbine vibration data from the National Renewable Energy Laboratory (NREL) is used for the experiments [41]. The test turbine has three-blades, is stall-controlled and upwind, with rated power of 750kW; generator operates at 1200 rpm or 1800 rpm nominal. Two gearboxes (one "healthy" and one "damaged") are tested under the operating conditions: main shaft speed at 22.09 rpm, nominal high-speed shaft at 1800 rpm, 50% of rated power. The descriptions of the accelerometers are shown in Table I. The vibration data (m/s\({}^{2}\)) is collected at 40 kHz for 10 minutes by the accelerometers mounted on the gearboxes. The data are labeled as "healthy" and "damaged" according to the conditions of two gearboxes. Each 40-kHz dataset is divided into segments where each data segment is 0.1-second in length with 4,000 samples in each segment. There are 50,000 segments in total and these segments are considered as raw (vibration) data. In this dataset, the defects of the wind turbine are caused by oil-loss events. The fault type are summarized and labeled for the targeted node classification task. Vibratory acceleration data at high frequency is used in this paper. Disturbance of the acceleration indicates defect occurrence on the wind turbine gearbox. Accordingly, the faults of the wind turbine are detectable through vibration-based methods.

The input knowledge-based graph is formed based on the description provided previously. The graph includes 21 terminology nodes, 8 data nodes, 2 state nodes, and 4 meta nodes, with three different edge types. 8 sensor signals are considered in the experiment and correspond to the data nodes.

### Results and Discussions

\begin{table}
\begin{tabular}{c c} \hline Sensor Name & Description \\ \hline AN3 & Ring gear radial 6 o’clock \\ AN4 & Ring gear radial 12 o’clock \\ AN5 & LS-SH radial \\ AN6 & IMS-SH radial \\ AN7 & HS-SH radial \\ AN8 & HS-SH upwind bearing radial \\ AN9 & HS-SH downwind bearing radial \\ AN10 & Carrier downwind radial \\ \hline \end{tabular}
\end{table}
Table 1: The sensor description

Figure 2: The framework of SF-GNN. Module 1 identifies the input graph with wind turbine knowledge and raw sensor data. Module 2 learns processes feature learning on the raw sensor data within the input graph, which is the stage 1 of SF-GNN. Module 3 initiates GNN models and generates the single detection output by basic GNN and GG-NN and the sequential output by GGS-NN, which is the stage 2 of SF-GNN.
\(\bullet\) The Effect of Sparse Filtering: The only hyperparameter in sparse filtering is the input dimension. Four different input dimensions are tested as shown in Table II: 50, 100, 300 and 500. For the dimensions 100, 300 and 500, the models do not have significantly different accuracy; however, the running time does increase as the dimension increases. The 300-dimension test provides more detailed features than the 100-dimension test. The detailed features include redundant active entities, which incurs extra running time and overfitting. The 100-dimension test results can distinguish one active entity (the highest peak) and a few others with moderate running time. Therefore, the 100-dimension inputs are used for the experiments.

* Single Output Results: As presented in Table III, the combined approach of sparse filtering and GNN-based models achieves higher accuracy with increased computational cost. From the detection results, the SF-learned features with the GNN-based models efficiently outperform the raw and manual features (Feature-GNN and Feature-GG-NN), but still have greater computational cost than MLP and SF-SoftMax, which are baseline models with feature inputs without graph structure inputs. Therefore, they perform detection with less computing time.

* Sequential Outputs Results: The GGS-NN learns the nodes and their relationships from the entire input graph. The output sequence includes node predictions of components, data types, and the health state; and includes the relationship (edge) predictions of "has", "is-a", "measures", and "causes". Semantically, for example, the level 1 outputs are "the gearbox has a ring gear" and "the ring gear has AN3"; the level 2 outputs are "AN3 is a sensor" and "AN3 measures vibration"; and the level 3 output is "AN3 causes fault operations"-meaning the fault is located on the component where AN3 is mounted. This experiment includes two test cases: one fault signal and two fault signals. As presented in Table IV, the two cases achieve similar accuracy. Compared to the overall accuracy of the basic GGS-NN at 87.27%, which is like the work of Li et al., the sparse filtering has an accuracy of 90.73%. For the sequence results, we observe: (1) SF-learned features perform better than the GGS-N; (2) sequential outputs have lower accuracy than single outputs. Sparse filtering is a problem-specific feature learning method for the single output case in which the GG-NN concentrates on state node prediction depending on the vibration signal data; therefore, sparse filtering has direct impact on GG-NN performance. Node annotation for initialization can impact accuracy. During the procedure of GGS-NN, annotated nodes predicted by the GG-NN models has unstable performance compared to the pre-set and fixed annotations in the single-output case; therefore, lower accuracy occurs in the case of sequential outputs.

\(\bullet\) The Impact of the GNN-Based Approaches: According to the performance of wind turbine fault detection system using the graph models, the GNN-based approaches are the most effective and have the greatest promise. Specifically: (1) graph-based inputs can integrate related knowledge of the configuration and operations of the wind turbine, the sensor network, and the data sources. This integration of information helps to interpret and manage how data from different sensors and wind turbines can effectively be used in developing learning algorithms and systems for fault detection, diagnosis, and prognosis. The results of sequential detection indicate that GNN-based approaches can effectively use multiple factors for fault detection and produce comprehensive analytical results for IoT applications such as using "big" data from wind turbine experiments to develop a fault detection and diagnosis system that can improve wind turbine operational reliability and transmission grid reliability and resiliency.

## 4 Conclusion

A GNN-based wind turbine fault detection method is proposed in this paper using experimental data from NREL. This work deploys two methods: GNNs and sparse filtering. SF-GNN identifies the gearbox health condition from a knowledge-based input graph that ontologically describes the wind turbine and gearbox and generates a single output of the condition of an individual component and sequential outputs with additional semantical information to the conditions. Sparse filtering is deployed to sparsity the feature matrix of the high frequency sensor signals, standardize the features to receive equal activation, and qualify the signals data validity to GNNs. As compared to the original GNNs achievements, this work presents a complex input graph with multiple edge and node types and more sensitive and higher frequency signals, and outperforms in accuracy and efficiency by acceleration of sparse filtering.

As the experiment demonstrated, the GNN-based approaches can efficiently detect the component faults using both single and sequential output detection strategies. The GGS-NN can successfully produce a logical and reasonable fault detection sequence using data from a single sensor or from multiple sensors. Sparse filtering provides significant improvements in

\begin{table}
\begin{tabular}{c c c} \hline Preprocessing & 1 fault signal & 2 fault signals \\ \hline SF & 90.73 & 90.36 \\ Raw & 87.27 & 88.17 \\ Feature & 90.04 & 89.56 \\ \hline \end{tabular}
\end{table}
Table 4: The sequence outputs accuracies (%)

\begin{table}
\begin{tabular}{c c c c} \hline Input Dimension & GNN & GG-NN & GGS-NN & Running time (s) \\ \hline
50 & 74.24 & 88.25 & 82.57 & \(<\) 60 \\
100 & 92.33 & 93.74 & 90.73 & \(<\) 60 \\
300 & 91.72 & 94.14 & 90.12 & 62 \\
500 & 92.41 & 93.62 & 90.83 & 78 \\ \hline \end{tabular}
\end{table}
Table 2: The effect of Sf on GNN-based models

\begin{table}
\begin{tabular}{c c c} \hline Models & Accuracy (\%) & Running time (s) \\ \hline SF-GNN & 92.33 & 54 \\ SF-GG-NN & **93.74** & 47 \\ Feature-GNN & 83.54 & 58 \\ Feature-GG-NN & 89.28 & 52 \\ SF-SoftMax & 89.92 & **38** \\ \hline \end{tabular}
\end{table}
Table 3: The single output accuracies
the single output cases but only modest improvements in the sequential output cases.

Future work is necessary to improve accuracy, reduce the computational burden, and further explore the GGS-NN-based method. We have observed in our application that GNN-based methods can be improved by including representation learning using raw data instead of incorporating a separate feature learning stage.
