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Chinese Physics B, Volume. 29, Issue 8, (2020)

Inversion method of bubble size distribution based on acoustic nonlinear coefficient measurement

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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    AbstractGet PDF
    Figures&Tables (15)
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    References (26)
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    Figures & Tables(15)
    Nonlinear coefficients under assumed distribution.

    Fig. 1. Nonlinear coefficients under assumed distribution.

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    Inversion results of nonlinear coefficient method.

    Fig. 2. Inversion results of nonlinear coefficient method.

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    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.

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    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.

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    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.

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    Experimental settings of measuring nonlinear coefficients of bubble medium.

    Fig. 6. Experimental settings of measuring nonlinear coefficients of bubble medium.

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    Experimental system block diagram.

    Fig. 7. Experimental system block diagram.

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    Nonlinear coefficients measured in experiment.

    Fig. 8. Nonlinear coefficients measured in experiment.

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    Results of bubble size distribution retrieved by NC inversion method.

    Fig. 9. Results of bubble size distribution retrieved by NC inversion method.

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    Results of bubble size distribution retrieved by SH inversion method.

    Fig. 10. Results of bubble size distribution retrieved by SH inversion method.

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    Expected inversion effect under experimental conditions.

    Fig. 11. Expected inversion effect under experimental conditions.

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    Inversion effects of β data in different frequency ranges.

    Fig. 12. Inversion effects of β data in different frequency ranges.

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    • Table 1. Comparison of condition number among three inversion methods.

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      Table 1. Comparison of condition number among three inversion methods.

      DF inversionSH inversionNC inversion
      Case I3.9602 ×10294.7111 × 10336.2547 × 1024
      Case II1.3283 × 10258.7555 × 10291.3440 × 1021

    • Table 2. Comparison of correlation coefficient between inversion and assumed distribution after adding errors under NC inversion.

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      Table 2. Comparison of correlation coefficient between inversion and assumed distribution after adding errors under NC inversion.

      1%3%5%10%
      Assumed as G distribution0.98020.96750.94200.9376
      Assumed as PL distribution0.81740.79420.79620.7794

    • Table 3. Comparison of correlation coefficient between inversion and assumed distribution after adding errors under DF and SH inversion.

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      Table 3. Comparison of correlation coefficient between inversion and assumed distribution after adding errors under DF and SH 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
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    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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    Paper Information

    Received: Jan. 11, 2020

    Accepted: --

    Published Online: Apr. 29, 2021

    The Author Email: Shi Jie (shijie@hrbeu.edu.cn)

    DOI:10.1088/1674-1056/ab9285

    Topics

    Nuclear physics
    Particles and fields
    Particle and nuclear astrophysics and cosmology