Data from the UHV projects mainly contains three parts: structural, simi-structural, and non-structural data. Project investment table, equipment list are typical structural data. Equipment inventory is simi-structural data because the properties can be put into the same cell and break the structural feature of the data. Preliminary design instructions, feasibility study reports are some of the non-structural data, which account for a large proportion. The knowledge graph is a structured semantic knowledge base used to describe concepts in the physical world and their relationships in symbolic form. In this section, a two-stage method is proposed to construct a UHV knowledge graph.

1) Knowledge graph ontology construction

Ontology is a model and a pattern constraint on the data that constitutes the knowledge graph. Building an ontology in a specific domain requires cooperation with multiple experts in vertical fields. The inputs for constructing ontology include domain knowledge, terminology dictionary, experience of experts, etc. The output includes the entity categories that constitute the knowledge graph, as well as the relationships between categories, the set of attributes that entities of a specific category, and so on. There are generally three methods for constructing knowledge graph ontology: top-down, bottom-up, and a combination of the two. Among them, the top-down approach is to define the most common top-level concepts in the field and then expand downwards in sequence. It requires a thorough understanding of a specific domain both in the business aspect and the data aspect as well. The bottom-up method is just the opposite. It starts with entities, summarizes and organizes entities to form low-level concepts, and then gradually abstracts upward to form upper-level concepts.

In the UHV projects knowledge domain, heterogeneous data comes from different sources. On the one hand, existing data models such as traditional power system engineering systems and expert knowledge bases can provide equipment information and other constraints. On the other hand, rich knowledge is buried in various types of data such as unstructured, semi-structured, and structured data, which needs to be added to the knowledge base using data mining methods. To ensure the integrity of UHV knowledge graph ontology, a combination of top-down and bottom-up is used. Expert experiences are regarded as the guidelines of the construction, while knowledge extracted from data is a supplement to the ontology. These two aspects together form the conceptual part of the knowledge graph.

2) Knowledge graph construction for UHV projects

Knowledge construction for UHV projects constitutes the data layer of the knowledge graph. It mainly contains 2 components: knowledge extraction and knowledge fusion.

Knowledge extraction is a technology that automatically extracts structured information such as entities, relationships, and entity attributes from heterogeneous data. Conventional named entity recognition(NER) algorithm includes BiBERT-LSTM-CRF (Huang et al., 2015), RoBerta-CRF (Liu et al., 2019), and other deep neural network models. To solve the nested entity problem, methods based on entity matrix such as GlobalPointer are proposed. Other methods such as TPLinker, Tencent Muti-head, and Deep Biaffine are also suitable for solving nested NER problems. As for relation extraction, recent research mainly focuses on joint extraction methods, which can be divided into two categories: sequence annotation-based methods which converts joint extraction problem into sequence annotation problem when decoding, and sequence-to-sequence based methods (Zeng et al., 2018; Takanobu et al., 2019). For constructing a UHV knowledge graph, due to the fact that there exists a nested NER phenomenon, a combination of manual annotation and GlobalPointer is recommended. For example, given a sentence “The Beijing 1000 kV substation project requires four new main transformers”, which describes the quantity of transformers in the project. To recognize the nested entity “Beijing 1000 kV substation project”, GlobalPointer first lists all the entity candidates and then Pick out the real entities with entity labels. It can be concluded that a sentence with n words could generate n n + 1 2 candidates. With m labels, the NER problem is then converted to a multi-label classification problem. Although the time complexity is σ n 2 , with the use of Transformer and the design of parallel computing, it can be reduced to σ 1 .

Knowledge fusion refers to the fusion of description information about the same entity or concept from multiple data sources and the integration and disambiguation of heterogeneous data under unified standards for knowledge graphs. It requires two processes such as implement entity linking and knowledge merging. The process of entity linking is to use a given entity referent to perform entity disambiguation and coreference resolution through similarity calculation. After confirming the correct entity object, the entity referent is linked to the corresponding entity in the knowledge graph. Among them, entity disambiguation solves the problem of ambiguity of entities with the same name, and coreference resolution solves the problem of multiple references corresponding to the same entity object.

Based on the data extracted from a UHV project, Figure 3 shows the constructed knowledge graph. As can be seen, a UHV project mainly contains six parts: electrical primary part, electrical secondary part, hydraulic part, HVAC part, remote control part and protection part, which is represented as orange nodes in the figure. Each part contains multiple equipment, with components followed.

After obtaining the knowledge graph of UHV projects, we use attributed network model to analyze the knowledge reasoning problem. To transform knowledge graphs to attributed networks, we take entities as nodes and edges between entities become edges between nodes. And attributes of each node are embedded before concatenated as a vector. For a specific UHV graph, we divide it into multi-view graphs considering the difference of multiple attributes of a node. Taking the accuracy and effectiveness of the multi-view divide into account, there are two principles: 1) attributes with different units need to be divided into different views in order to avoid confusion of attribute information due to excessive numerical differences; 2) pure numeric properties and mixed text and numeric properties should be separated into separate views.

After the construction of multi-view graphs, a GCN-based encoder is adopted to get the latent representation of each graph. GCN is a convolutional neural network that can directly act on graphs and utilize their attribute and structural information. To get the most precious embedding of the graph, several layers of GCN are usually used. Given a graph G(V, A, X) with k views, each of the multi-view graph can be denoted as G i m g V , A , X i m g , where X = X 1 m g , X 2 m g , … , X k m g . The embedding of each layer can be denoted as: H l + 1 = f H l , A , W l (2) where H ^l is the input of the layer l, and W ^l is the trainable parameters.

More specifically, the function f H l , A , W l can be expressed as follows: f H l , A , W l = σ D ∼ − 1 2 A ∼ D ∼ − 1 2 H l W l (3) where A ∼ = A + I , D ∼ is the degree matrix of the nodes with D ∼ i , i = ∑ j A ∼ i , j , σ is an activation function such as Relu. To simplify the calculation, W l is shared for all the nodes. It is worth noticing that GCN can only capture the information of the neighborhood for a specific node. In order to take long-range information into consideration, a deep GCN network with k convolutional layers is required. However due to an over-smoothing problem, the number of layers is no more than three. In this paper, a UHV knowledge graph is built with a depth of three, thus a three-layer GCN network is used. The final feature representation can be expressed as: Z i mg = R e l u R e l u R e l u X mg , A , W 0 , A , W 1 A , W 2 (4)

For every low-dimensional feature representation, it is important to understand that each view only contains part of the attribute information of the nodes. To be more specific, in the UHV knowledge graph, Z 1 mg , Z 2 mg and Z 3 mg represent he embedding of rated voltage, quantity and device model respectively. To get the full description of the nodes, an aggregator gathering all information from every view seems sensible. There are usually two methods when it comes to representation aggregation, concatenation and weighted addition. As each attribute is equally important to a specific node, we apply concatenation to polymerize each representation. The unified representation of the original knowledge graph can be denoted as follows: Z = c o n c a t Z 1 mg , Z 2 mg , Z 3 mg (5)

After obtaining the unified representation of the UHV knowledge graph, traditional algorithms take it as an input to a multilayer perceptron(MLP) and output a possibility score of each category. Because the electric power grid infrastructure domain has a strong hierarchical relationship, especially in the equipment selection area, we can use a clustering method to get the node aggregation features in the knowledge graph. Further analysis of the knowledge graph shows a sparse characteristic which means the number of edges is far less than the number of nodes. Traditional algorithms such as the k-nearest neighbors algorithm(KNN) use the distance between nodes as the basis for classification, which is not suitable for graph data because it ignores the topology information. Therefore, considering the clear hierarchy relationship in components, parts, and equipment in the electric power equipment knowledge graph, we can obtain a chain of subgraphs based on the facts of the business situation without adopting a clustering algorithm. In this context, getting a series of representation of subgraphs effectively becomes the focus of this problem. In this paper, a Haar convolution-based pooling mechanism is leveraged to the graph unified representation.

Given a chain of the subgraphs (G ₀, G ₁, …, G _m ), each node in G _i is a set of nodes in G _i+1. As shown in Figure 4, G ₀ represents the original knowledge graph, while G ₃ can be a single node that represent the whole knowledge graph. The Haar convolutional-based pooling mechanism should be used in every layer of the chain, getting a smaller graph from G _i to G _i+1. Since a readout module is used afterward to integrate every representation of subgraphs, it is important to guarantee each matrix has the same output dimension. The output of a specific subgraph G _i (V ⁱ , E ⁱ ) is defined as: X i output = Φ i T X i input (6) where Φ i T is the transpose of Harr basis matrix of the ith subgraph, V ⁱ , E ⁱ represents the nodes and edges of G _i respectively.

Then the Haar basis could be obtained using the following steps: 1) order V ⁱ by their degrees of nodes as v 1 i , v 2 i , … , v N i , where N denotes the number of nodes in G _i ; 2) the N vectors can be calculated by the following equations: Φ 1 i = 1 N   l = 1 , Φ l i = N − l + 1 N − l + 2 x l − 1 i − ∑ j = l N x j i N − l + 1 (7) where x j i is a function for jth node, which could be expressed as: x j i v = 1 , v = v j i 0 , v ∈ V i \ v j i (8)

To speed up the calculation process, a compressed Haar basis matrix is used to replace the original Φ i . Considering the fact that the first N _i+1 represents the low frequency coefficients which contains the majority information of the graph, we adopt a tailor operation to reduce the size of Φ i . The Haar convolutional-based pooling mechanism requires less computational complexity than the traditional graph Fourier transform. The use of fast algorithms further improves calculation speed. The key to the fast algorithms is the Haar basis, which are sparse matrixes to which a compressive method can be adopted. Specifically, given a chain of subgraphs (G ₀, G ₁, …, G _m ), where G _m is the coarsest graph with only one node. Each subgraph could generate a set of n orthogonal vectors called Haar basis, where n is the number of nodes in the specific subgraph. They are the representations of the input in the Haar domain. Analysis shows that these matrixes are sparse and several low-frequency coefficients contains most of the information of the input. Therefore, we use first n _j+1 Haar basis vector in our pooling layer, while the other components are aborted.

In order to minimize errors caused by information loss, a hierarchical mechanism is adopted. As shown in Figure 5, every low-dimensional representation is aggregated together using a Readout module and then an MLP is used to get the probability of each label for subgraph G _i . Y = softmax MLP X Readout (9)

The construction of the UHV projects knowledge graph contains heterogeneous data from multiple data sources such as Preliminary Design Instructions, Equipment Inventory, Specialized Reports, and so on. It requires efforts from experts from both the power electrical domain and computer domain. Due to the complexity of different business needs, we only construct a dataset based on the requirements of power transmission and transformation project review with a focus on equipment. Therefore, the dataset mainly contains four levels: the first level is the name of the projects; the second level contains six professional fields based on construction guidelines, such as electrical primary part, electrical secondary part, protection part, telecontrol part, hydraulic part and fire-controlling part; the third level mainly refers to major equipment of each part of second level, such as main transformers, 1000 kV power distribution unit; the tertiary level contains parts of the major equipment, such as cable, voltage transformer, current transformer, breaker and so on.

Taking each project as a subgraph, a label is assigned to each graph indicating the type of the project, which are the new substation project, substation expansion project, and bay expansion project. The difference between the three kinds of projects mainly lies on the quantity and equipment models. For example, a new substation project usually has more main transformers than substation expansion projects and a bay expansion project may only have some in-bay equipment such as isolating switches and lightning protectors. Thus, we constructed 120 graphs, with an average of 130 nodes and 128 edges per graph. We first test our model and our model without multi-view mechanism on this dataset and the results are illustrated in Figure 6 and Table 1. It can be seen that the accuracy of our model with a multi-view mechanism is improved by 21.43% with a little more time consumption.

We also add an analysis regarding the number of Haar pooling layers. It describes the number of subgraphs which is an indicator of different clustering methods. It should be noted that 1 layer represents the model without the Haar pooling strategy, and 2 layers only consist of two subgraphs which are the original knowledge graph and the final knowledge graph with only one node. The results are shown in Figure 7. Due to the fact that the UHV knowledge graph could be divided into three levels which are professional domains, equipment, and parts, a three-level clustering is most proper and the result of the experience also proves the conclusion.

To test the performance of the Haar pool, we selected three traditional pooling methods as the control group such as SAGPoll (Lee et al., 2019), CGIPool (Pang et al., 2021), and GSAPool (Zhang et al., 2020). The results are illustrated in Table 2. According to test results of different pooling mechanisms, our proposed model shows excellent performance both in accuracy and loss. Although a multi-view mechanism with SAGPoll achieves the highest computational efficiency, the accuracy and the loss of our proposed model outperforms it by 4.88% and 63.5%. It shows that a little sacrifice of the time complexity returns good performance.

To test the generalizability of our proposed model, we use the NCI-1 dataset as our input. NCI-1 is a popular open-source benchmark dataset mainly focused on chemical and medical domain. It contains 4,100 compounds, each one of which could be seen as a graph sample. Among them, nodes represent atoms and edges represent chemical bonds. The task of the dataset is to determine whether the compound has properties that hinder the growth of cancer cells. As experiments in Section 4.1, we first test multi-view mechanism on this dataset. The results are shown in Figure 8 and Table 3. It shows an increase in test accuracy by 18.67% when comparing the model with a multi-view mechanism to the one without. As the number of samples increases, the running time is also extended. The difference between both algorithms is extended when compared to UHV datasets, which implies that traditional GCN has a non-linear computational complexity.

As for the number of Haar pooling layers, there is no obvious structure of the NCI-1 dataset. We make a test from layer 1 to layer 5. The results are shown in Figure 9. According to training accuracy, apart from the results for 1 layer, the rest of the results are almost the same.

To test the performance of the Haar pool, we also employ the traditional pooling mechanism as in Section 4.1. And the results are shown in Table 4. It demonstrates that our proposed method is best-considering test accuracy and test loss. Due to the multi-view mechanism, the running time is not the shortest of all experiments, but considering the increase in performance, it is completely acceptable.