Fig. 1. Comparison of signal before and after adding noise. (a) Pure second harmonic signal; (b) second harmonic signal with noise

Fig. 2. VMD mode with K=3

Fig. 3. VMD mode with K=4

Fig. 4. Chart of S-G filtering effect comparison. (a) Before S-G filtering; (b) after S-G filtering

Fig. 5. Six modes after EMD

Fig. 6. Chart of EMD and filtering algorithm based on VMD effect comparison. (a) Reconstruction result of EMD; (b) result of filtering algorithm based on VMD

Fig. 7. Diagram of system structure

Fig. 8. Instrument picture

Fig. 9. Chart of noise reduction experiment comparison. (a) Second harmonic before noise reduction; (b) second harmonic after noise reduction

Fig. 10. Relationship between second harmonic signal and gas volume fraction under VMD filtering algorithm

Fig. 11. Relationship between second harmonic signal and gas volume fraction under EMD algorithm