• Acta Optica Sinica
  • Vol. 42, Issue 2, 0229001 (2022)
Liang Shan1, Tingting Zha1, Ming Kong2、*, and Bo Hong1
Author Affiliations
  • 1Key Laboratory of Electromagnetic Wave Information Technology and Metrology of Zhejiang Province, College of Information Engineering, China Jiliang University, Hangzhou, Zhejiang 310018, China
  • 2College of Metrology & Measurement Engineering, China Jiliang University, Hangzhou, Zhejiang 310018, China;
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    DOI: 10.3788/AOS202242.0229001 Cite this Article Set citation alerts
    Liang Shan, Tingting Zha, Ming Kong, Bo Hong. Particle Size Distribution Inversion of Cuckoo Search Algorithm Using Weber Distribution[J]. Acta Optica Sinica, 2022, 42(2): 0229001 Copy Citation Text show less
    Search process of WCS algorithm
    Fig. 1. Search process of WCS algorithm
    Relative root mean square error curves of unimodal particle size distribution inversion by different algorithms
    Fig. 2. Relative root mean square error curves of unimodal particle size distribution inversion by different algorithms
    Relative root mean square error curves of bimodal particle size distribution inversion by different algorithms
    Fig. 3. Relative root mean square error curves of bimodal particle size distribution inversion by different algorithms
    Experimental setup for small angle forward scattering
    Fig. 4. Experimental setup for small angle forward scattering
    Scattering image of particle. (a) Particle background; (b) unimodal particle; (c) bimodal particle
    Fig. 5. Scattering image of particle. (a) Particle background; (b) unimodal particle; (c) bimodal particle
    Experimental results of unimodal particle on Rosin-Rammlar distribution function inversion by WCS algorithm
    Fig. 6. Experimental results of unimodal particle on Rosin-Rammlar distribution function inversion by WCS algorithm
    Experimental results of bimodal particle on Rosin-Rammlar distribution function inversion by WCS algorithm
    Fig. 7. Experimental results of bimodal particle on Rosin-Rammlar distribution function inversion by WCS algorithm
    Particle size range /μmIncident light wavelength /nmLens focal length /mmRelative refractive index
    3.85--101.85632.8025.00(1.596-0.1i)/1.33
    Table 1. Parameter setting of small angle forward scattering system
    AlgorithmEvaluation criteriaParameterJohnson’s SBRosin-RammlerNormal
    Mean valuedM /μm10.00045.00010.00045.00010.00045.000
    AFSAStandard deviationd /10-4M /(10-4 μm)4.5500.5303.7202.4803.1004.440
    RRMSE /(10-4 μm)0.42015.0009.180
    Mean valuedM /μm10.00045.00010.00045.00010.00045.000
    ABCStandard deviationd /10-6M /(10-6 μm)2000.0001000.0000.0940.0666.6306.280
    RRMSE /(10-6 μm)20000.0000.0352.260
    Mean valuedM /μm10.00045.00010.00045.00010.00045.000
    CSStandard deviationd /10-11M /(10-12 μm)1.6002.4101.2408.1700.5205.880
    RRMSE /(10-11 μm)3.3903.3901.010
    Mean valuedM /μm10.00045.00010.00045.00010.00045.000
    CCSStandard deviationd /10-13M /(10-13 μm)0.9000.1009.8803.2906.5205.860
    RRMSE /(10-13 μm)3.0908.3708.460
    Mean valuedM /μm10.00045.00010.00045.00010.00045.000
    PCSStandard deviationd /10-13M /(10-12 μm)1.6800.0104.2100.3309.0201.620
    RRMSE /(10-13 μm)3.8708.9508.740
    Mean valuedM /μm10.00045.00010.00045.00010.00045.000
    MCSStandard deviationd /10-12M /(10-12 μm)0.1600.0301.1100.5401.9302.040
    RRMSE /(10-13 μm)5.17025.10019.400
    Mean valuedM /μm10.00045.00010.00045.00010.00045.000
    WCSStandard deviationd /10-13M /(10-14 μm)1.0800.6300.2100.9900.3102.360
    RRMSE /(10-14 μm)6.6808.5206.570
    Table 2. Inversion results of different algorithms under unimodal distribution
    AlgorithmEvaluation criteriaParameterJohnson’s SBRosin-RammlerNormal
    Mean valued1d2M1 /μmM2 /μm6.00005.990030.000070.00005.99006.000030.000070.00005.99006.000030.000069.9900
    AFSAStandard deviationd1 /10-4d2 /10-4M1 /(10-4 μm)M2 /(10-4 μm)32.0000 5.20006.71001.14009.94002.410036.0000 3.390023.0000 2.080018.0000 2.4500
    RRMSE /μm0.00720.00220.0035
    Mean valued1d2M1 /μmM2 /μm5.99006.160030.010070.03005.99006.020030.010070.10006.00006.040030.000070.0300
    ABCStandard deviationd1d2M1 /μmM2 /μm0.0380 0.31200.02400.07600.03400.01900.0250 0.19700.00200.00100.0010 0.0020
    RRMSE /μm1.58000.33000.4800
    Mean valued1d2M1 /μmM2 /μm6.00006.000030.000070.00006.00006.000030.000070.00006.00006.000030.000070.0000
    CSStandard deviationd1 /10-4d2 /10-4M1 /(10-5 μm)M2 /(10-4 μm)5.7400 6.61004.2400 2.30002.7000 1.32008.5900 6.82003.1800 2.81007.55003.4800
    RRMSE /μm0.00210.00160.0011
    Mean valued1d2M1 /μmM2 /μm6.00006.000030.000070.00006.00006.000030.000070.00006.00006.000030.000070.0000
    CCSStandard deviationd1 /10-6d2 /10-6M1 /(10-6 μm)M2 /(10-6 μm)4.48001.47000.0980.61000.50000.97000.5100 2.68004.61003.21003.36008.1700
    RRMSE /(10-5 μm)0.40000.31002.0400
    Mean valued1d2M1 /μmM2 /μm6.00006.000030.000070.00006.00006.000030.000070.00006.00006.000030.000070.0000
    PCSStandard deviationd1 /10-6d2 /10-6M1 /(10-6 μm)M2 /(10-6 μm)0.28000.7000 0.21001.30003.38002.0000 6.290031.30001.06004.32000.57002.8300
    RRMSE /(10-5 μm)0.47002.88000.7800
    Mean valued1d2M1 /μmM2 /μm6.00006.000030.000070.00006.00006.000030.000070.00006.00006.000030.000070.0000
    MCSStandard deviationd1 /10-6d2 /10-6M1 /(10-6 μm)M2 /(10-6 μm)5.590015.60000.45004.38005.47007.39004.4300 44.40001.88001.76000.39001.3900
    RRMSE /(10-5 μm)0.84003.83000.6400
    Mean valued1d2M1 /μmM2 /μm6.00006.000030.000070.00006.00006.000030.000070.00006.00006.000030.000070.0000
    WCSStandard deviationd1 /10-7d2 /10-6M1 /(10-8 μm)M2 /(10-7 μm)3.64000.4800 6.76001.35001.49000.12006.27005.11005.13001.24007.87008.3100
    RRMSE /(10-6 μm)1.05000.82003.4900
    Table 3. Inversion results of different algorithms under bimodal distribution
    AlgorithmDistributionfunctionM /μmRelativeerror /%
    Johnson’s SB50.080.16
    CSRosin-Rammler48.163.67
    Normal50.100.21
    Johnson’s SB50.050.10
    WCSRosin-Rammler48.263.48
    Normal50.040.08
    Table 4. Results of unimodal particle swarm inversion by CS algorithm and WCS algorithm
    AlgorithmDistribution functionM1 /μmM2 /μmRelative errorof M1 /%Relative errorof M2 /%
    Johnson’s SB50.24101.720.481.72
    CSRosin-Rammler50.03100.070.060.07
    Normal50.11101.650.221.65
    Johnson’s SB50.13101.550.261.55
    WCSRosin-Rammler50.01100.010.020.01
    Normal50.05101.490.101.49
    Table 5. Results of bimodal particle swarm inversion by CS algorithm and WCS algorithm
    Liang Shan, Tingting Zha, Ming Kong, Bo Hong. Particle Size Distribution Inversion of Cuckoo Search Algorithm Using Weber Distribution[J]. Acta Optica Sinica, 2022, 42(2): 0229001
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