Acta Optica Sinica, Volume. 42, Issue 2, 0229001(2022)
Particle Size Distribution Inversion of Cuckoo Search Algorithm Using Weber Distribution
Figures & Tables(12)
Fig. 2. Relative root mean square error curves of unimodal particle size distribution inversion by different algorithms
Fig. 3. Relative root mean square error curves of bimodal particle size distribution inversion by different algorithms
Fig. 5. Scattering image of particle. (a) Particle background; (b) unimodal particle; (c) bimodal particle
Fig. 6. Experimental results of unimodal 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
Table 1. Parameter setting of small angle forward scattering system
View tableTable 1. Parameter setting of small angle forward scattering system
Particle size range /μm Incident light wavelength /nm Lens focal length /mm Relative refractive index 3.85--101.85 632.80 25.00 (1.596-0.1i)/1.33
Table 2. Inversion results of different algorithms under unimodal distribution
View tableTable 2. Inversion results of different algorithms under unimodal distribution
Algorithm Evaluation criteria Parameter Johnson’s SB Rosin-Rammler Normal Mean value d M /μm 10.000 45.000 10.000 45.000 10.000 45.000 AFSA Standard deviation d /10-4 M /(10-4 μm) 4.550 0.530 3.720 2.480 3.100 4.440 RRMSE /(10-4 μm) 0.420 15.000 9.180 Mean value d M /μm 10.000 45.000 10.000 45.000 10.000 45.000 ABC Standard deviation d /10-6 M /(10-6 μm) 2000.000 1000.000 0.094 0.066 6.630 6.280 RRMSE /(10-6 μm) 20000.000 0.035 2.260 Mean value d M /μm 10.000 45.000 10.000 45.000 10.000 45.000 CS Standard deviation d /10-11 M /(10-12 μm) 1.600 2.410 1.240 8.170 0.520 5.880 RRMSE /(10-11 μm) 3.390 3.390 1.010 Mean value d M /μm 10.000 45.000 10.000 45.000 10.000 45.000 CCS Standard deviation d /10-13 M /(10-13 μm) 0.900 0.100 9.880 3.290 6.520 5.860 RRMSE /(10-13 μm) 3.090 8.370 8.460 Mean value d M /μm 10.000 45.000 10.000 45.000 10.000 45.000 PCS Standard deviation d /10-13 M /(10-12 μm) 1.680 0.010 4.210 0.330 9.020 1.620 RRMSE /(10-13 μm) 3.870 8.950 8.740 Mean value d M /μm 10.000 45.000 10.000 45.000 10.000 45.000 MCS Standard deviation d /10-12 M /(10-12 μm) 0.160 0.030 1.110 0.540 1.930 2.040 RRMSE /(10-13 μm) 5.170 25.100 19.400 Mean value d M /μm 10.000 45.000 10.000 45.000 10.000 45.000 WCS Standard deviation d /10-13 M /(10-14 μm) 1.080 0.630 0.210 0.990 0.310 2.360 RRMSE /(10-14 μm) 6.680 8.520 6.570
Table 3. Inversion results of different algorithms under bimodal distribution
View tableTable 3. Inversion results of different algorithms under bimodal distribution
Algorithm Evaluation criteria Parameter Johnson’s SB Rosin-Rammler Normal Mean value d1 d2 M1 /μm M2 /μm 6.0000 5.9900 30.0000 70.0000 5.9900 6.0000 30.0000 70.0000 5.9900 6.0000 30.0000 69.9900 AFSA Standard deviation d1 /10-4 d2 /10-4 M1 /(10-4 μm) M2 /(10-4 μm) 32.0000 5.2000 6.7100 1.1400 9.9400 2.4100 36.0000 3.3900 23.0000 2.0800 18.0000 2.4500 RRMSE /μm 0.0072 0.0022 0.0035 Mean value d1 d2 M1 /μm M2 /μm 5.9900 6.1600 30.0100 70.0300 5.9900 6.0200 30.0100 70.1000 6.0000 6.0400 30.0000 70.0300 ABC Standard deviation d1 d2 M1 /μm M2 /μm 0.0380 0.3120 0.0240 0.0760 0.0340 0.0190 0.0250 0.1970 0.0020 0.0010 0.0010 0.0020 RRMSE /μm 1.5800 0.3300 0.4800 Mean value d1 d2 M1 /μm M2 /μm 6.0000 6.0000 30.0000 70.0000 6.0000 6.0000 30.0000 70.0000 6.0000 6.0000 30.0000 70.0000 CS Standard deviation d1 /10-4 d2 /10-4 M1 /(10-5 μm) M2 /(10-4 μm) 5.7400 6.6100 4.2400 2.3000 2.7000 1.3200 8.5900 6.8200 3.1800 2.8100 7.5500 3.4800 RRMSE /μm 0.0021 0.0016 0.0011 Mean value d1 d2 M1 /μm M2 /μm 6.0000 6.0000 30.0000 70.0000 6.0000 6.0000 30.0000 70.0000 6.0000 6.0000 30.0000 70.0000 CCS Standard deviation d1 /10-6 d2 /10-6 M1 /(10-6 μm) M2 /(10-6 μm) 4.4800 1.4700 0.098 0.6100 0.5000 0.9700 0.5100 2.6800 4.6100 3.2100 3.3600 8.1700 RRMSE /(10-5 μm) 0.4000 0.3100 2.0400 Mean value d1 d2 M1 /μm M2 /μm 6.0000 6.0000 30.0000 70.0000 6.0000 6.0000 30.0000 70.0000 6.0000 6.0000 30.0000 70.0000 PCS Standard deviation d1 /10-6 d2 /10-6 M1 /(10-6 μm) M2 /(10-6 μm) 0.2800 0.7000 0.2100 1.3000 3.3800 2.0000 6.2900 31.3000 1.0600 4.3200 0.5700 2.8300 RRMSE /(10-5 μm) 0.4700 2.8800 0.7800 Mean value d1 d2 M1 /μm M2 /μm 6.0000 6.0000 30.0000 70.0000 6.0000 6.0000 30.0000 70.0000 6.0000 6.0000 30.0000 70.0000 MCS Standard deviation d1 /10-6 d2 /10-6 M1 /(10-6 μm) M2 /(10-6 μm) 5.5900 15.6000 0.4500 4.3800 5.4700 7.3900 4.4300 44.4000 1.8800 1.7600 0.3900 1.3900 RRMSE /(10-5 μm) 0.8400 3.8300 0.6400 Mean value d1 d2 M1 /μm M2 /μm 6.0000 6.0000 30.0000 70.0000 6.0000 6.0000 30.0000 70.0000 6.0000 6.0000 30.0000 70.0000 WCS Standard deviation d1 /10-7 d2 /10-6 M1 /(10-8 μm) M2 /(10-7 μm) 3.6400 0.4800 6.7600 1.3500 1.4900 0.1200 6.2700 5.1100 5.1300 1.2400 7.8700 8.3100 RRMSE /(10-6 μm) 1.0500 0.8200 3.4900
Table 4. Results of unimodal particle swarm inversion by CS algorithm and WCS algorithm
View tableTable 4. Results of unimodal particle swarm inversion by CS algorithm and WCS algorithm
Algorithm Distribution function M /μm Relative error /% Johnson’s SB 50.08 0.16 CS Rosin-Rammler 48.16 3.67 Normal 50.10 0.21 Johnson’s SB 50.05 0.10 WCS Rosin-Rammler 48.26 3.48 Normal 50.04 0.08
Table 5. Results of bimodal particle swarm inversion by CS algorithm and WCS algorithm
View tableTable 5. Results of bimodal particle swarm inversion by CS algorithm and WCS algorithm
Algorithm Distribution function M1 /μm M2 /μm Relative error of M1 /% Relative error of M2 /% Johnson’s SB 50.24 101.72 0.48 1.72 CS Rosin-Rammler 50.03 100.07 0.06 0.07 Normal 50.11 101.65 0.22 1.65 Johnson’s SB 50.13 101.55 0.26 1.55 WCS Rosin-Rammler 50.01 100.01 0.02 0.01 Normal 50.05 101.49 0.10 1.49
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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
Paper Information
Category: Scattering
Received: Jul. 5, 2021
Accepted: Aug. 13, 2021
Published Online: Dec. 29, 2021
The Author Email: Kong Ming (mkong@cjlu.edu.cn)
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