Author Affiliations
1Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 5000, China2Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China3College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, Chinashow less
Fig. 1. Nonlinear coefficients under assumed distribution.
Fig. 2. Inversion results of nonlinear coefficient method.
Fig. 3. Error analysis of inversion results from nonlinear coefficient method: [(a)–(d)] 1%-G, 3%-G, 5%-G, and 10%-G distributions, respectively; [(e)–(h)] 1%-PL, 3%-PL, 5%-PL, and 10%-PL distributions, respectively.
Fig. 4. Error analyses of inversion results of DF inversion method: [(a)–(d)] 1%-G, 3%-G, 5%-G, and 10%-G distributions, respectively; [(e)–(h)] 1%-PL, 3%-PL, 5%-PL, and 10%-PL distributions, respectively.
Fig. 5. Error analyses of inversion results of SH inversion method: [(a)–(d)] 1%-G, 3%-G, 5%-G, and 10%-G distributions, respectively; [(e)–(h)] 1%-PL, 3%-PL, 5%-PL, and 10%-PL distributions, respectively.
Fig. 6. Experimental settings of measuring nonlinear coefficients of bubble medium.
Fig. 7. Experimental system block diagram.
Fig. 8. Nonlinear coefficients measured in experiment.
Fig. 9. Results of bubble size distribution retrieved by NC inversion method.
Fig. 10. Results of bubble size distribution retrieved by SH inversion method.
Fig. 11. Expected inversion effect under experimental conditions.
Fig. 12. Inversion effects of β data in different frequency ranges.
| DF inversion | SH inversion | NC inversion |
---|
Case I | 3.9602 ×1029 | 4.7111 × 1033 | 6.2547 × 1024 | Case II | 1.3283 × 1025 | 8.7555 × 1029 | 1.3440 × 1021 |
|
Table 1. Comparison of condition number among three inversion methods.
| 1% | 3% | 5% | 10% |
---|
Assumed as G distribution | 0.9802 | 0.9675 | 0.9420 | 0.9376 | Assumed as PL distribution | 0.8174 | 0.7942 | 0.7962 | 0.7794 |
|
Table 2. Comparison of correlation coefficient between inversion and assumed distribution after adding errors under NC inversion.
Inversion methods | Errors\Assumed | 1% | 3% | 5% | 10% |
---|
DF inversion | G distribution | 0.6153 | 0.5720 | 0.5997 | 0.6077 | PL distribution | 0.7189 | 0.7744 | 0.7917 | 0.6093 | SH inversion | G distribution | 0.3245 | 0.2021 | 0.2081 | 0.3530 | PL distribution | 0.1048 | 0.0355 | 0.0642 | 0.0892 |
|
Table 3. Comparison of correlation coefficient between inversion and assumed distribution after adding errors under DF and SH inversion.