## 5 Conclusions  
In this study, a data-driven paradigm based on real-time monitoring data is proposed to identify the thermal insulation integrity of LNG storage tanks. Using the proposed approach, the perlite settlement, which is significant for thermal insulation but infeasible to monitor directly, can be predicted with promising accuracy. By integrating low- and high-fidelity data, the multi-fidelity machine learning framework addresses the limitations of each data type, achieving both improved predictive performance and generalisability. Compared to the data-driven approaches relying on individual data sources, the proposed approach utilises massive low-fidelity data to capture the basic mapping between the input and output and then incorporates scarce high-fidelity data to improve prediction accuracy. The data experimental results confirm the efficacy of the proposed framework, with the MLP-based multi-fidelity model achieving the highest accuracy (an \(R^{2}\) of 0.980 and an \(RMSE\) of 0.078 m). Additionally, the multi-fidelity machine learning framework demonstrates adaptability, as it allows for algorithm customisation based on specific engineering tasks.  
Due to the limitations in acquiring real-world data, the proposed data-driven approach is to be further validated using more reliable data, although its generalisability to scarce data was demonstrated. This study emphasises the importance of developing more accessible high-fidelity data sources to enhance model accuracy further.  
The proposed data-driven approach provides a feasible and practical solution for real-time thermal insulation monitoring and has been integrated into a digital twin system for asset management. The findings highlight the potential of multi-fidelity learning in complex engineering applications and pave the way for future research to further refine prediction paradigms.  
Conceptualization, W.L., M.Z. ([PERSON]) and M.Z. ([PERSON]); methodology, W.L. and M.Z. ([PERSON]); software, [PERSON], [PERSON] ([PERSON]) and [PERSON]; validation, [PERSON], [PERSON] ([PERSON]) and [PERSON] ([PERSON]); formal analysis, [PERSON], [PERSON] ([PERSON]) and [PERSON]; investigation, [PERSON], [PERSON] ([PERSON]) and [PERSON] ([PERSON]); resources, [PERSON] ([PERSON]) and X.X.; data curation, [PERSON], [PERSON] ([PERSON]) and J.C.; writing--original draft preparation, W.L.; writing--review and editing, [PERSON] ([PERSON]) and X.X.; visualization, [PERSON] and M.Z. ([PERSON]); supervision, X.X.; project administration, [PERSON] ([PERSON]) and X.X.; funding acquisition, X.X. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Key R&D Program of China [grant number 2023 YFC3806705], the National Natural Science Foundation of China [grant numbers 52038008 and 52378408], the China Scholarship Council [grant number 202206260174], the Science and Technology Commission of Shanghai Municipality [grant number 22 DZ1203004], and the State Grid Shanghai Municipal Electric Power Company [grant number 52090W23000B].  
Not applicable.  
The data presented in this study are available on request from the corresponding author due to legal issues.  
Author [PERSON] is employed by CNOOC Gas & Power Group 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.