First, the EC-PLS models were sorted according to RMSEPM in an ascending order. Second, the evolution of their RMSEPM values was observed. The RMSEPM of the global optimal EC-PLS model was 2.67 g·L−1 (Table 3), which corresponded to the case of s = 1. The first 200 values of RMSEPM are given in Fig. 5 . When , the corresponding RMSEPM was less than or equal to 2.81 g·L−1. These 100 models almost had no difference with the optimal EC-PLS model in terms of prediction effect (Fig. 5) and were thus regarded as allowable. The number of allowable models (S) was set to within 100 in the experiments.
For the cases of S=10, 20,..., 100, the corresponding optimal combinations of discrete wavelengths were selected according to the method mentioned in Section 2.6. The number of adopted wavelengths (N) of the optimal model of discrete wavelengths corresponding to each number of allowable models (S) were further determined. The RMSEPM and N of the optimal model of discrete wavelengths for each S are shown in Fig. 6. The minimum RMSEPM (RMSEPM =2.55 g·L−1) was achieved when S=40, and the corresponding N was also close to the minimum (N=42). The corresponding parameters and modeling effects are also summarized in Table 3. The results indicated that the optimal discrete model was superior to the optimal EC-PLS model (RMSEPM =2.67 g·L−1, N=71) in terms of prediction performance and complexity of the wavelength model. The wavelength combination () of the optimal discrete model was the follows: 1242, 1254, 1266, 1278, 1290, 1302, 1314, 1326, 1338, 1350, 1362, 1374, 1386, 1398, 1410, 1434, 1458, 1482, 1506, 1530, 1554, 1578, 1602, 1626, 1650, 1674, 1698, 1722, 1746, 1770, 1794, 1818, 1842, 1866, 2108, 2132, 2156, 2180, 2204, 2228, 2252, 2276 nm. The model is a non-equidistant discrete combination model. For easy observation, these wavelengths are labeled in the average spectrum of the samples in Fig. 7. For comparison, the equidistant wavelength combinations of the optimal EC-PLS model are also labeled in Fig. 7. Notably, the wavelength combination (N=42) of the optimal discrete model was included in the equidistant wavelength combination (N=71) of the optimal EC-PLS model. This result indicated that these two models possessed good consistency. The results also shown that the optimal equidistant model indeed contained many redundant wavelengths.
We further investigated the case of S=40. A total of 260 wavelengths appeared in the 40 allowable models (K=260). For each number of adopted wavelengths , the corresponding predicted effect (RMSEPM) is shown in Fig. 8. The corresponding wavelength combination was as follows: 1242, 1266, 1290, 1314, 1338, 1362, 1386, 1410, 1434, 1458, 1482, 1506, 1530, 1554, 1578, 1602, 1626, 1650, 1674, 1698, 1722, 1746, 1770, 1794, 1818, 1842, 1866, 2108, 2132, 2156, 2180, 2204, 2228, 2252, 2276 nm. This model is also a non-equidistant discrete combination model. The wavelength combination was included in the wavelength combination . Among all the models that are superior to the optimal equidistant model, this model is the simplest. Therefore, it also has a reference value.