# Causation Correlation Analysis of Aviation Accidents: A Knowledge Graph-Based Approach
## 2 Methods
### Modeling the ACAKG
Based on the defined scope of concepts in the ACAKG ontology, the relationships between entities include the relationships among accident causation, causation, and flight phases, and those between causation and accident types and causation and accident consequences. The corresponding entity relationships are \"result in\", \"phase is\", \"type is\", \"fatality consequence is\", and \"aircraft damage consequence is\". The \"result in\" relationship can exist among accident causal factors, among accident types, and between causal factors and accident types. In addition to primary causation relationships, accident causal factors can also have parallel relationships, but this paper only discusses causal relationships. After establishing the ontology and extracting concepts and relationships, the generated knowledge graph and triple relationships serve as the foundational data to build matrices from four dimensions: aviation accident causation, flight phases, accident types, and accident consequences. This process enables the construction of the ACAKG model. The model is represented by seven matrices, each with the following fundamental meanings:  
The first matrix is the Causal Adjacency Matrix (CAM), as shown in Equation (1). It determines whether there exists a unidirectional causal relationship between the head entity and the tail entity in the triple relationship. The adjacency matrix is determined by the triples containing the keyword \"Causation\". Here, both i and j can represent accident causation or accident types, and KTs represent the set of all triples identified. \[CAM_{ij}= \begin{cases}1\langle i,cause,j\rangle\in KTs\\ 0\langle i,cause,j\rangle\
otin KTs\end{cases}  \tag{1}\]  
The second matrix is the Accident Phase Matrix (APM), as shown in Equation (2). It describes the relationship between accident causation or accident types in the triple relationship and the flight phase in which the accident occurs. Specifically, it indicates whether accident causation or type i occurs in flight phase j. The adjacency matrix is determined by the knowledge triples containing the keyword \"Phase\". \[APM_{ij}= \begin{cases}1\langle i,phase,j\rangle\in KTs\\ 0\langle i,phase,j\rangle\
otin KTs\end{cases}  \tag{2}\]  
The third matrix is the Causal Relationship Strength Adjacency Matrix (CRSAM), as shown in Equation (3). Building upon Equation (1), this matrix assigns weights to the directed edges, representing the strength of the causal relationship between the head entity and the tail entity. Typically, this weight is related to the frequency of occurrence of a particular causal event in all triples. The higher the frequency, the greater the weight. \[CRSAM_{ij}= \begin{cases}\omega\langle i,cause-\omega,j\rangle\in KTs\\ 0\langle i,cause-\omega,j\rangle\
otin KTs\end{cases}  \tag{3}\]  
The fourth matrix is the Causation Types Matrix (TM), as shown in Equation (4). It describes the relationship between accident causation and consequences in the triple relationship. Specifically, it indicates whether accident causation i belongs to type j. The adjacency matrix is determined by the knowledge triples containing the keyword \"Type\". \[TM_{ij}= \begin{cases}1\langle i,type,j\rangle\in KTs\\ 0\langle i,type,j\rangle\
otin KTs\end{cases}  \tag{4}\]  
The fifth matrix is the Accident Consequence Matrix (ACM), as shown in Equation (5). It is defined in the knowledge triples, indicating whether accident causation i leads to accident consequence j. The weight of the directed edge \(\delta\) represents the severity of the accident consequence. The adjacency matrix is determined by the knowledge triples containing the keyword \"Consequence\". \[ACM_{ij}=\left\{ \begin{aligned} &\delta\langle i,\text{ consequence},j\rangle\in KTs\\ & 0\langle i,\text{ consequence},j\rangle\
otin KTs\end{aligned} \right. \tag{5}\]  
The sixth matrix is the Shortest Path Matrix (SPM), as shown in Equation (6). The causal relationship adjacency matrix forms a complex network structure mapping all accident causation and accident types.