## 3 Results and Discussion
### No Turbidity Interference  
#### 3.1.1 Fdpe_Pls  
(1) First derivative spectroscopy  
In the absence of turbidity interference, the first derivative of the original spectrum was first processed. The acceleration and deceleration information of the original spectrum is added, as shown in Figure 4. Combining with PE in Section 3.1.1, (2) can accurately determine the characteristic values under the condition of reducing noise interference. It can be seen from Figure 4 that there are four local maximum points \(\alpha_{1},\alpha_{3},\alpha_{4},\alpha_{5}\) and one local minimum point \(\alpha_{2}\) in the first derivative spectrum, which reflected four local maximum values of change rate and one local minimum value of change rate in the original spectrum. When the concentration of the solution changed, the amplitudes and wavelengths of \(\alpha_{i}(i=1,2,3,4,5)\) changed accordingly.  
(2) Feature wavelengths extraction by PE  
PE can accurately locate the time and position of the sequence change. PE algorithm needs to configure parameters _L,m,t_. In this paper, according to reference [22] and several attempts, set \(L=10\), \(m=5\), and \(t=1\). After calculating the entropy values of the first derivative spectrum in the concentration range of \(1\sim\) 32 mg/L, Table 2 shows the windows in which entropy change from zero to non-zero.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Concentrations (mg/L)**} & \multicolumn{3}{c}{**Window in Which Entropy Change from Zero to Non-Zero (W)**} \\ \cline{2-6}  & **1** & **2** & **3** & **4** & **5** \\ \hline
1 & 7 & 31 & 42 & 71 & 89 \\ \hline
2 & 8 & 30 & 43 & 72 & 88 \\ \hline
3 &  
In Table 2, it can be found that the entropy changes five times from zero to non-zero, which means that the first derivative spectrum has five extreme points. The conclusion is consistent with the actual situation in Figure 4. By determining the window where entropy changes from zero to non-zero, \(\lambda_{i}(i=1,2,3,4,5)\) can be accurately found. According to the calculation of PE in reference [22], \(\lambda_{i}(i=1,2,3,4,5)\) can be calculated by Equation (16).  
\[\lambda_{i}=\lambda_{0}+W+L-3\;(i=1,2,3,4,5) \tag{16}\]  
where \(\lambda_{0}\) is starting wavelength, \(W\) is the window in which the entropy changes from zero to non-zero. The \(\lambda_{i}(i=1,2,3,4,5)\) COD solutions with different concentrations are shown in Figure 8.  
It can be seen from Figure 8 that \(\lambda_{i}(i=1,2,3,4,5)\), which are corresponded to \(\alpha_{i}(i=1,2,3,4,5)\), changes in a small range when the COD concentration changes. The variation range of \(\lambda_{i}(i=1,2,3,4,5)\) is shown in Table 3.  
In order to verify that \(\frac{dA}{d\lambda}\) and \(C\) are linear when \(\lambda\) changes in a small range. We established the fitting relationship between COD concentrations and \(\alpha_{i}(i=1,2,3,4,5)\). The results are shown in Figure 9 and Table 4. It can be seen from Table 4 that there are good linear relationships between COD concentrations and \(\alpha_{i}(i=1,2,3,4,5)\) when \(\lambda_{i}(i=1,2,3,4,5)\) changes in a small range. The selection of \(\lambda_{i}(i=1,2,3,4,5)\) and \(\alpha_{i}(i=1,2,3,4,5)\) are effective.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Wavelength** & **Variation Range** \\ \hline \(\lambda_{1}\) & 204 \(nm\leq\lambda_{1}\leq 206\;nm\) \\ \hline \(\lambda_{2}\) & 227 \(nm\leq\lambda_{2}\leq 228\;nm\) \\ \hline \(\lambda_{3}\) & 239 \(nm\leq\lambda_{3}\leq 243\;nm\) \\ \hline \(\lambda_{4}\) & 268 \(nm\leq\lambda_{4}\leq 271\;nm\) \\ \hline \(\lambda_{5}\) & 284 \(nm\leq\lambda_{5}\leq 290\;nm\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The variation range of \(\lambda_{i}(i=1,2,3,4,5)\).  
Figure 8: Found by PE in the concentration range of 1\(\sim\)32 mg/L.