• Acta Optica Sinica
  • Vol. 40, Issue 19, 1901001 (2020)
Wei Chong1、2、*, Wenhua Lü1、2, Jian Zhang1、3、4, Jing Liang1, Xiaotong Yang1, and Guoyu Zhang1、3、4
Author Affiliations
  • 1School of Opto-Electronic Engineering, Changchun University of Science and Technology, Changchun, Jilin 130022, China
  • 2Meteorological Observation Center of CMA, Beijing 100081, China
  • 3Key Laboratory of Opto-Electronic Measurement and Optical Information Transmission Technology, Ministry of Education, Changchun, Jilin 130022, China
  • 4Opto-Electronic Measurement and Control Instrumentation, Jilin Province Engineering Research Center, Changchun, Jilin 130022, China
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    DOI: 10.3788/AOS202040.1901001 Cite this Article Set citation alerts
    Wei Chong, Wenhua Lü, Jian Zhang, Jing Liang, Xiaotong Yang, Guoyu Zhang. Modeling and Validation Analysis of Sigmoid Function for Solar Radiation Diffuse Fraction[J]. Acta Optica Sinica, 2020, 40(19): 1901001 Copy Citation Text show less
    Fitting curves and surfaces of diffuse fraction Sigmoid model. (a) S0 model fitting curve based on 1 h training data; (b) S0 model fitting curve based on 10 min training data; (c) S0 model fitting curve based on 1 min training data; (d) S1 model fitting surface based on 1 h training data; (e) S1 model fitting surface based on 10 min training data; (f) S1 model fitting surface based on 1 min training data
    Fig. 1. Fitting curves and surfaces of diffuse fraction Sigmoid model. (a) S0 model fitting curve based on 1 h training data; (b) S0 model fitting curve based on 10 min training data; (c) S0 model fitting curve based on 1 min training data; (d) S1 model fitting surface based on 1 h training data; (e) S1 model fitting surface based on 10 min training data; (f) S1 model fitting surface based on 1 min training data
    Validation comparison diagrams for S0 models with different parameters. (a) Validation comparison diagram for S0 model using 1 h radiation data collected in May, 2012 at Lijiang station; (b) validation comparison diagram for S0 model using 10-min radiation data collected in May, 2012 at Lijiang station; (c) validation comparison diagram for S0 model using 1 h radiation data collected in July, 2012 at Kazuo station; (d) validation comparison diagram for S0 model using 10-min radiation data collec
    Fig. 2. Validation comparison diagrams for S0 models with different parameters. (a) Validation comparison diagram for S0 model using 1 h radiation data collected in May, 2012 at Lijiang station; (b) validation comparison diagram for S0 model using 10-min radiation data collected in May, 2012 at Lijiang station; (c) validation comparison diagram for S0 model using 1 h radiation data collected in July, 2012 at Kazuo station; (d) validation comparison diagram for S0 model using 10-min radiation data collec
    Validation comparison diagrams for S1 models with different parameters. (a)--(c) Validation comparison diagrams for S1 model using 1-h data collected in May, 2012 at Lijiang station; (d)--(f) validation comparison diagrams for S1 model using 10-min data collected in May, 2012 at Lijiang station; (g)--(i) validation comparison diagrams for S1 model using 1-h data collected in July, 2012 at Kazuo station; (j)--(l) validation comparison diagrams for S1 model using 10-min data collected in December,
    Fig. 3. Validation comparison diagrams for S1 models with different parameters. (a)--(c) Validation comparison diagrams for S1 model using 1-h data collected in May, 2012 at Lijiang station; (d)--(f) validation comparison diagrams for S1 model using 10-min data collected in May, 2012 at Lijiang station; (g)--(i) validation comparison diagrams for S1 model using 1-h data collected in July, 2012 at Kazuo station; (j)--(l) validation comparison diagrams for S1 model using 10-min data collected in December,
    ModelTraining dataa1a2a3a4a5
    S01-h data0.2258 (0.2057, 0.2458)(with 95% confidence bounds)-0.7401 (-0.7886, -0.6916)(with 95% confidence bounds)-5.141 (-5.955, -4.327)(with 95% confidence bounds)8.406 (7.116, 9.696)(with 95% confidence bounds)
    10-min data0.1949(0.1698, 0.2201)(with 95% confidence bounds)-0.8155(-0.8903, -0.7407)(with 95% confidence bounds)-3.121(-3.639, -2.604)(with 95% confidence bounds)5.446(4.609, 6.283)(with 95% confidence bounds)
    1-min data0.2146(0.2089, 0.2203)(with 95% confidence bounds)-0.7548(-0.7749, -0.7346)(with 95% confidence bounds)-3.604(-3.803, -3.405)(with 95% confidence bounds)6.202(5.889, 6.515)(with 95% confidence bounds)
    S11-h data0.2338-0.7386-5.57878.65730.2926
    10-min data0.2074-0.8187-3.29865.57180.1356
    1-min data0.2251-0.7648-3.95096.43510.2379
    Table 1. Parameters of diffuse fraction sigmoid models S0 and S1
    ModelTraining dataValidating datarEMBDERMSDtSkewnessKurtosis
    S01-h data1-h data collected in May, 2012 from Lijiang station0.92980.04060.12795.88730.94933.7014
    10-min data0.93960.00590.11470.90970.42652.9275
    1-min data0.93860.09300.11681.41370.45432.8173
    S11-h data0.93250.04170.12616.16950.74833.6499
    10-min data0.94260.01050.11201.65070.28712.9649
    1-min data0.94260.01410.11282.21540.30393.0297
    S01-h data10-min data collected in May, 2012 from Lijiang station0.93470.02990.122110.98220.83273.7552
    10-min data0.9441-0.00450.11241.72820.27932.8329
    1-min data0.9434-7.9555×10-40.11410.30280.34382.7508
    S11-h data0.93640.03100.120911.52560.53233.6769
    10-min data0.94502.3221×10-40.11080.09100.08152.9916
    1-min data0.94470.00430.11151.65760.08013.1446
    ModelTraining dataValidating datarEMBDERMSDtSkewnessKurtosis
    S01-h data1-h data collected in July, 2012 from Kazuo station0.9088-0.01280.12601.76310.26803.0993
    10-min data0.9045-0.06900.14928.98950.20472.4575
    1-min data0.9065-0.06300.15498.25350.24402.4820
    S11-h data0.9255-0.03890.12105.8554-0.00423.0082
    10-min data0.9115-0.08330.153311.15260.15382.4256
    1-min data0.9136-0.08640.153711.70330.15152.4872
    S01-h data10-min data collected in December, 2012 from Kazuo station0.96240.01280.08385.6638-0.33983.4018
    10-min data0.9599-0.03970.105414.8894-063062.4770
    1-min data0.9623-0.03330.101312.7599-0.58612.4319
    S11-h data0.9560-0.06800.111328.2822-1.10484.6325
    10-1-min data0.9555-0.09290.137933.3518-0.62552.6717
    1-min data0.9424-0.09890.142135.5077-0.70603.0019
    S01-h data1-h data collected in July, 2012 from Guangzhou station0.8768-0.02900.12634.3277-0.25844.2410
    10-min data0.8326-0.07850.162410.1203-0.16413.1330
    1-min data0.8446-0.07850.156510.6224-0.14823.3136
    S11-h data0.8795-0.02400.12403.6184-0.26284.0508
    10-min data0.8326-0.06980.15908.9599-0.19493.1146
    1-min data0.8455-0.06620.15148.9060-0.21413.2803
    S01-h data10-min data collected in December, 2012 from Guangzhou station0.94190.01410.09995.3019-0.22183.2726
    10-min data0.9391-0.04070.117713.6514-0.44122.3907
    1-min data0.9420-0.03420.113811.6802-0.39922.4080
    S11-h data0.9448-0.07370.120928.4774-1.04394.4547
    10-1-min data0.9400-0.09640.147032.2035-0.55752.6305
    1-min data0.9283-0.11670.165836.7535-0.65462.9579
    S01-h data1-h data collected in July, 2012 from Wuhan station0.9302-0.04800.12037.3646-0.20674.6677
    10-min data0.9111-0.09720.156913.3550-0.15983.2799
    1-min data0.9166-0.09430.151713.4203-0.08183.5798
    S11-h data0.9304-0.04550.11946.9757-0.49884.7733
    10-min data0.9097-0.08980.153412.1976-0.31803.3477
    1-min data0.9146-0.08480.147511.8862-0.37893.7344
    S01-h data10-min data collected in December, 2012 from Wuhan station0.92960.03350.119610.77141.64488.0956
    10-min data0.9165-5.8784×10-50.12570.01721.17807.8858
    1-min data0.92170.00290.12300.85831.06767.1379
    S11-h data0.9177-0.02030.12556.04761.43709.5559
    10-min data0.9029-0.03540.13879.73381.18778.2914
    1-min data0.8941-0.04730.147512.48170.86407.1872
    S01-h data1-h data collected in July, 2012 from Urumqi station0.94830.00910.09993.1903-0.51192.9069
    10-min data0.9438-0.04520.128013.1603-0.68702.2919
    1-min data0.9467-0.03820.123011.3951-0.67022.2984
    S11-h data0.9479-0.08230.129428.8043-1.03694.0392
    10-min data0.9453-0.10220.158329.5406-0.67452.4640
    1-min data0.9316-0.12180.176133.4283-0.69582.7061
    S01-h data10-1-min data collected in December, 2012 from Urumqi station0.8482-0.08320.18345.6485-0.08802.4156
    10-min data0.8258-0.13760.22308.6948-0.01042.0106
    1-min data0.8318-0.12920.21608.2784-0.01512.0626
    S11-h data0.8569-0.07840.17735.4667-0.12582.2557
    10-min data0.8312-0.13150.21748.4246-0.04451.9770
    1-min data0.8394-0.12160.20847.9730-0.07312.0014
    Table 2. Statistical results of diffuse fraction calculated by S0 and S1 models
    Wei Chong, Wenhua Lü, Jian Zhang, Jing Liang, Xiaotong Yang, Guoyu Zhang. Modeling and Validation Analysis of Sigmoid Function for Solar Radiation Diffuse Fraction[J]. Acta Optica Sinica, 2020, 40(19): 1901001
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