Fig. 1. Diagram of POD implementation process

Fig. 2. Data processing flow diagram (square cavity temperature field)

Fig. 3. Schematic diagram of square cavity test device

Fig. 4. (a) Diagram of square cavity with background temperature；(b) Diagram of square cavity removed background temperature

Fig. 5. Air temperature variation curve from July 7th to 9th

Fig. 6. (a) Energy contribution rate of the first 20 POD modes of square cavity；(b) Cumulative energy contribution rate of the first 20 POD modes of square cavity

Fig. 7. (a) Original temperature field of square cavity at all times；(b) Temperature field of square cavity predicted by 16 POD modes；(c) Temperature field of square cavity predicted by 30 POD modes

Fig. 8. Comparison of temperature field prediction errors with different sensors

Fig. 9. (a) Square cavity sensor distribution at 12:00 on July 7th; (b) Temperature field of square cavity predicted by POD mode; (c) Temperature field of square cavity predicted by sensors

Fig. 10. (a) Square cavity sensor distribution at 12:00 on July 8th; (b) Temperature field of square cavity predicted by POD mode; (c) Temperature field of square cavity predicted by sensors

Fig. 11. (a) Schematic diagram of typical positions on the surface of square cavity；(b) Typical position 1；(c) Typical position 2；(d) Typical position 3

Fig. 12. (a) Diagram of the tank geometry model with heat producer; (b) Schematic diagram of the tank grid with heat producer

Fig. 13. Air temperature variation curve from April 8th to 10th

Fig. 14. (a) Energy contribution rate of the first 20 POD modes of 24 trains of tank model；(b) Cumulative energy contribution rate of the first 20 POD modes of 24 trains of tank model；(c) Energy contribution rate of the first 20 POD modes of 48 trains of tank model；(d) Cumulative energy contribution rate of the first 20 POD modes of 48 trains of tank model

Fig. 15. (a) Original temperature field of tank at all times；(b) Temperature field of 24 trains of tank predicted by 20 POD modes；(c) Temperature field of 48 trains of tank predicted by 20 POD modes

Fig. 16. (a) Sensor temperature field distribution of 24 trains of tank at 13:00 on April 10th；(b) Temperature field predicted result by 24 trains of tank；(c) Sensor temperature field distribution of 48 trains of tank at 13:00 on April 10th；(d) Temperature field predicted result by 48 trains of tank

Fig. 17. (a) Sensor temperature field distribution of 24 trains of tank at 20:00 on April 10th；(b) Temperature field predicted result by 24 trains of tank；(c) Sensor temperature field distribution of 48 trains of tank at 20:00 on April 10th；(d) Temperature field predicted result by 48 trains of tank

Fig. 18. (a) Schematic diagram of typical positions on the surface of tank；(b) Typical position 1；(c) Typical position 2

Table 1. Temperature field prediction error with different POD modes

Table 2. Temperature field prediction error with different sensors

Table 3. Temperature field prediction error with 20 POD modes of two reduced order models

Table 4. Temperature field prediction error with 30 sensors of two reduced order models

Table 5. Running time of different algorithms