• Chinese Physics B
  • Vol. 29, Issue 8, (2020)
Jie Shi1、2、3、†, Yulin Liu3, Shengguo Shi1、2、3, Anding Deng3, and Hongdao Li3
Author Affiliations
  • 1Acoustic Science and Technology Laboratory, Harbin Engineering University, Harbin 5000, China
  • 2Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China
  • 3College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China
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    DOI: 10.1088/1674-1056/ab9285 Cite this Article
    Jie Shi, Yulin Liu, Shengguo Shi, Anding Deng, Hongdao Li. Inversion method of bubble size distribution based on acoustic nonlinear coefficient measurement[J]. Chinese Physics B, 2020, 29(8): Copy Citation Text show less
    Nonlinear coefficients under assumed distribution.
    Fig. 1. Nonlinear coefficients under assumed distribution.
    Inversion results of nonlinear coefficient method.
    Fig. 2. Inversion results of nonlinear coefficient method.
    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. 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.
    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. 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.
    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. 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.
    Experimental settings of measuring nonlinear coefficients of bubble medium.
    Fig. 6. Experimental settings of measuring nonlinear coefficients of bubble medium.
    Experimental system block diagram.
    Fig. 7. Experimental system block diagram.
    Nonlinear coefficients measured in experiment.
    Fig. 8. Nonlinear coefficients measured in experiment.
    Results of bubble size distribution retrieved by NC inversion method.
    Fig. 9. Results of bubble size distribution retrieved by NC inversion method.
    Results of bubble size distribution retrieved by SH inversion method.
    Fig. 10. Results of bubble size distribution retrieved by SH inversion method.
    Expected inversion effect under experimental conditions.
    Fig. 11. Expected inversion effect under experimental conditions.
    Inversion effects of β data in different frequency ranges.
    Fig. 12. Inversion effects of β data in different frequency ranges.
    DF inversionSH inversionNC inversion
    Case I3.9602 ×10294.7111 × 10336.2547 × 1024
    Case II1.3283 × 10258.7555 × 10291.3440 × 1021
    Table 1. Comparison of condition number among three inversion methods.
    1%3%5%10%
    Assumed as G distribution0.98020.96750.94200.9376
    Assumed as PL distribution0.81740.79420.79620.7794
    Table 2. Comparison of correlation coefficient between inversion and assumed distribution after adding errors under NC inversion.
    Inversion methodsErrors\Assumed1%3%5%10%
    DF inversionG distribution0.61530.57200.59970.6077
    PL distribution0.71890.77440.79170.6093
    SH inversionG distribution0.32450.20210.20810.3530
    PL distribution0.10480.03550.06420.0892
    Table 3. Comparison of correlation coefficient between inversion and assumed distribution after adding errors under DF and SH inversion.
    Jie Shi, Yulin Liu, Shengguo Shi, Anding Deng, Hongdao Li. Inversion method of bubble size distribution based on acoustic nonlinear coefficient measurement[J]. Chinese Physics B, 2020, 29(8):
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