1Department of Electronic Engineering and Intelligent Building Research Center, National Taiwan University of Science and Technology, 43 Keelung Road, Section 4, Taipei, Taiwan
Neng-Chung Hu and Chin-Chuan Wu, "Optimal selection of commercial sensors for linear model representation of daylight spectra," Appl. Opt. 47, 3114-3123 (2008)
The average spectral power distribution of a set of measured daylight spectra, , is used for preliminary screening to select optimal sensor sets for daylight recovery. Spectra quite different from are applied to the screened sets to obtain minimum total spectral error, which is closely related to recovery metrics but not to the coefficient of error. All basis functions should be utilized to make these two errors equal, to predict precisely the best sensor set, and to extend a set of few sensors to a set of many sensors. These are not acquirable by an exhaustive full search method.
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Averaged GFC, of Spectra Not in Training Set (S.D)
25
0.036513
0.99927 (0.00048586)
0.036513 (0.011065357)
0.430733 (0.288045)
0.041322 (0.01254234)
0.99901 (0.0006123)
40
0.036823
0.99928 (0.00041771)
0.036823 (0.009660086)
0.440445 (0.228941)
0.041632 (0.012103535)
0.999 (0.0006215)
2
0.036973
0.99928 (0.00037038)
0.036973 (0.008564635)
0.447471 (0.30467)
0.041781 (0.011245231)
0.99899 (0.0005924)
4
0.037296
0.99926 (0.00041765)
0.037296 (0.009427938)
0.452398 (0.185165)
0.042103 (0.0118234455)
0.99897 (0.0006125)
45
0.037459
0.99924 (0.00051636)
0.037459 (0.010860239)
0.453989 (0.310414)
0.042265 (0.0125694211)
0.99896 (0.0006429)
80
0.03759
0.99924 (0.00044203)
0.03759 (0.009840196)
0.493536 (0.346251)
0.042419 (0.012386542)
0.99894 (0.0006543)
11
0.037811
0.99924 (0.00039581)
0.037811 (0.008956544)
0.499538 (0.220432)
0.04263 (0.0113445901)
0.99893 (0.0006312)
5
0.037851
0.99924 (0.00042266)
0.037851 (0.009441143)
0.500057 (0.519831)
0.042657 (0.0124021897)
0.99891 (0.0007164)
35
0.037904
0.99924 (0.00041559)
0.037904 (0.009359716)
0.968214 (0.857549)
0.042613 (0.0111422145)
0.99891 (0.0005928)
13
0.038031
0.99923 (0.00043012)
0.038031 (0.009644981)
0.971252 (0.573222)
0.042834 (0.0124428891)
0.9989 (0.0007321)
S.D., standard deviation. The rightmost two columns are the recovery metrics for the spectra not in the training sets.
Error of the difference between original and reconstructed waveforms.
Table 4
Top Ten Sensor Sets Obtained by a Full Search Method and by the Proposed Method Are the Samea
Sensor Set No.
Sensor No.
Sensor No.
Sensor No.
Sensor No.
Sensor No.
Sensor No.
GFC
Spectral Error
Full search method
103217
1
10
24
25
26
27
0.99927
0.036513
473415
7
10
11
24
25
27
0.99928
0.036823
554960
10
23
24
25
26
27
0.99928
0.036973
543319
10
11
23
24
25
27
0.99926
0.037296
477221
7
10
22
24
25
27
0.99924
0.037459
543264
10
11
22
23
24
27
0.99924
0.03759
554729
10
20
24
25
26
27
0.99924
0.037811
554891
10
22
23
24
25
27
0.99924
0.037851
543284
10
11
22
24
25
27
0.99924
0.037904
543144
10
11
20
24
25
27
0.99923
0.038031
Proposed method
25
10
24
27
25
26
1
0.99927
0.036513
40
10
24
27
25
11
7
0.99928
0.036823
2
10
24
27
25
23
26
0.99928
0.036973
4
10
24
27
25
23
11
0.99926
0.037296
45
10
24
27
25
22
7
0.99924
0.037459
80
10
24
27
23
11
22
0.99924
0.03759
11
10
24
25
25
20
26
0.99924
0.037811
5
10
24
27
25
23
22
0.99924
0.037851
35
10
24
27
25
11
22
0.99924
0.037904
13
10
24
27
25
20
11
0.99923
0.038031
The sensors obtained by the proposed method are arranged in a certain order according to their importance. For example, sensor 10 is the most important, while sensor 1 is the least important in set 25. This ranking does not exist in a full search method.
Table 5
Deviations in the Response Value of for Sensor Set 25 under Different Noise Levelsa
Averaged GFC, of Spectra Not in Training Set (S.D)
25
0.036513
0.99927 (0.00048586)
0.036513 (0.011065357)
0.430733 (0.288045)
0.041322 (0.01254234)
0.99901 (0.0006123)
40
0.036823
0.99928 (0.00041771)
0.036823 (0.009660086)
0.440445 (0.228941)
0.041632 (0.012103535)
0.999 (0.0006215)
2
0.036973
0.99928 (0.00037038)
0.036973 (0.008564635)
0.447471 (0.30467)
0.041781 (0.011245231)
0.99899 (0.0005924)
4
0.037296
0.99926 (0.00041765)
0.037296 (0.009427938)
0.452398 (0.185165)
0.042103 (0.0118234455)
0.99897 (0.0006125)
45
0.037459
0.99924 (0.00051636)
0.037459 (0.010860239)
0.453989 (0.310414)
0.042265 (0.0125694211)
0.99896 (0.0006429)
80
0.03759
0.99924 (0.00044203)
0.03759 (0.009840196)
0.493536 (0.346251)
0.042419 (0.012386542)
0.99894 (0.0006543)
11
0.037811
0.99924 (0.00039581)
0.037811 (0.008956544)
0.499538 (0.220432)
0.04263 (0.0113445901)
0.99893 (0.0006312)
5
0.037851
0.99924 (0.00042266)
0.037851 (0.009441143)
0.500057 (0.519831)
0.042657 (0.0124021897)
0.99891 (0.0007164)
35
0.037904
0.99924 (0.00041559)
0.037904 (0.009359716)
0.968214 (0.857549)
0.042613 (0.0111422145)
0.99891 (0.0005928)
13
0.038031
0.99923 (0.00043012)
0.038031 (0.009644981)
0.971252 (0.573222)
0.042834 (0.0124428891)
0.9989 (0.0007321)
S.D., standard deviation. The rightmost two columns are the recovery metrics for the spectra not in the training sets.
Error of the difference between original and reconstructed waveforms.
Table 4
Top Ten Sensor Sets Obtained by a Full Search Method and by the Proposed Method Are the Samea
Sensor Set No.
Sensor No.
Sensor No.
Sensor No.
Sensor No.
Sensor No.
Sensor No.
GFC
Spectral Error
Full search method
103217
1
10
24
25
26
27
0.99927
0.036513
473415
7
10
11
24
25
27
0.99928
0.036823
554960
10
23
24
25
26
27
0.99928
0.036973
543319
10
11
23
24
25
27
0.99926
0.037296
477221
7
10
22
24
25
27
0.99924
0.037459
543264
10
11
22
23
24
27
0.99924
0.03759
554729
10
20
24
25
26
27
0.99924
0.037811
554891
10
22
23
24
25
27
0.99924
0.037851
543284
10
11
22
24
25
27
0.99924
0.037904
543144
10
11
20
24
25
27
0.99923
0.038031
Proposed method
25
10
24
27
25
26
1
0.99927
0.036513
40
10
24
27
25
11
7
0.99928
0.036823
2
10
24
27
25
23
26
0.99928
0.036973
4
10
24
27
25
23
11
0.99926
0.037296
45
10
24
27
25
22
7
0.99924
0.037459
80
10
24
27
23
11
22
0.99924
0.03759
11
10
24
25
25
20
26
0.99924
0.037811
5
10
24
27
25
23
22
0.99924
0.037851
35
10
24
27
25
11
22
0.99924
0.037904
13
10
24
27
25
20
11
0.99923
0.038031
The sensors obtained by the proposed method are arranged in a certain order according to their importance. For example, sensor 10 is the most important, while sensor 1 is the least important in set 25. This ranking does not exist in a full search method.
Table 5
Deviations in the Response Value of for Sensor Set 25 under Different Noise Levelsa