## 5 Conclusions  
This paper proposes a reasoning model of a C2Q-KG based on a GAT and a two-branch reasoning network. Firstly, KGTBRN classifies the continuous casting triples according to the number distribution of the head entities and tail entities for each relation in the C2Q-KG. For the triples with a sparse entity distribution (1-side), KGTBRN uses the connection layer to ensure that the relevant entities can still be accurately reasoned on in the case of lacking information. For the triples with a dense entity distribution (N-side), the capsule layer is used for reasoning.  
In order to further improve the performance of KGTBRN, KGTBRN also introduces a GAT. By dynamically adjusting the attention distribution in different neighborhoods, the GAT enhances the ability of KGTBRN to capture the local neighborhood information of triples and enables it to better understand the implicit connections among entities, so that KGTBRN can still maintain high reasoning accuracy in the face of complex relations.  
In the experimental part, we compare KGTBRN with other cutting-edge models on the C2Q-KG. The experiment results show that KGTBRN shows higher accuracy and reliability, improving by 6.9% on HITS@1, by 6.2% on HITS@3 and by 5.6% on HITS@10. This shows that KGTBRN can not only adapt to reasoning tasks under different entity distributions but also perform effective root cause analysis of cast product defects in complex continuous casting process scenarios.  
We provide an effective knowledge graph reasoning model for the continuous casting domain. By combining the GAT and the two-branch reasoning network, the influence of  
Figure 6: Reasoning results for cause of “Crack” defect.  
the unbalanced distribution of entities on the reasoning accuracy is successfully solved. As KGTBRN is constructed based on the data characteristics of the C2Q-KG in the continuous casting domain, generalizing it to other industrial domains still presents challenges. Additionally, the two-branch reasoning network may increase model complexity and implementation difficulty. Future work will explore broader applications and introduce quality evaluation metrics to enhance the generalization capability of KGTBRN.  
The application of this method can help enterprises to more accurately identify the potential root causes of cast product defects in the production process, thereby advancing quality management technologies in intelligent manufacturing. With strong scalability and application potential, it is expected to promote process optimization and product quality improvement, thus facilitating the intelligent and digital transformation of the manufacturing industry.  
Conceptualization, [PERSON] ([PERSON]); methodology, [PERSON] ([PERSON]); software, [PERSON] ([PERSON]), M.S. and Y.S.; validation, [PERSON] ([PERSON]), [PERSON] ([PERSON]), Y.S. and M.S.; formal analysis, [PERSON] ([PERSON]); investigation, Q.G.; resources, Q.G.; data curation, [PERSON] ([PERSON]), [PERSON] ([PERSON]), Y.S. and Q.G.; writing--original draft preparation, [PERSON] ([PERSON]); writing--review and editing, [PERSON] ([PERSON]), Y.S. and M.S.; visualization, [PERSON] ([PERSON]); supervision, [PERSON] ([PERSON]); project administration, [PERSON] ([PERSON]); funding acquisition, Q.G. All authors have read and agreed to the published version of the manuscript.  
This research study was funded by Shaanxi Province Innovation Capacity Support Plan 2024 RS-CYTD-23.  
Not applicable.  
The data presented in this study are available upon request from the corresponding author.  
The authors would like to thank the anonymous reviewers for their valuable feedback.  
Author [PERSON] was employed by the company China National Heavy Machinery Research Institute Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.