## 3 Results and Discussion
### Optimization of UHRE Conditions  
The BBD was used for optimizing the experimental conditions for extracting the four flavonoids. The experimental runs were randomized for minimizing the effects of uncontrollable factors. The test results of 17 runs are shown in Table 2.  
Using multiple regression analysis based on the experimental data, the response variables and independent variables were expressed by second-order polynomial equations:  
\[ \begin{array}{c}Y_{1}=0.105-6.76\times 10^{-4}X_{1}+8.68\times 10^{-4}X_{2}-1.4 3\times 10^{-2}X_{3}+4.06\times 10^{-3}X_{1}X_{2}-5.34\times 10^{-3}X_{1}X_{3}-\\ 3.35\times 10^{-3}X_{2}X_{3}-7.25\times 10^{-3}X_{1}^{2}-1.25\times 10^{-2}X_{2} ^{2}-1.34\times 10^{-2}X_{3}^{2},\end{array}  \tag{2}\]  
\[ \begin{array}{c}Y_{2}=0.400-5.00\times 10^{-3}X_{1}+3.84\times 10^{-3}X_{2}-3.39 \times 10^{-2}X_{3}+1.61\times 10^{-2}X_{1}X_{2}-1.49\times 10^{-2}X_{1}X_{3}-\\ 3.12\times 10^{-2}X_{2}X_{3}-2.09\times 10^{-2}X_{1}^{2}-5.01\times 10^{-2}X_{2} ^{2}-5.02\times 10^{-2}X_{3}^{2},\end{array}  \tag{3}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Independent Variables**} & \multicolumn{4}{c}{**Yield (mg/g)**} \\ \cline{2-9}
**Runs** & \begin{tabular}{c} **Extraction Time** \\ **(X\({}_{1}\), min)** \\ \end{tabular} & \begin{tabular}{c} **Ultrasonic** \\ **Power (X\({}_{2}\), W)** \\ \end{tabular} & \begin{tabular}{c} **Liquid–Solid** \\ **Ratio (X\({}_{3}\), mL/g)** \\ \end{tabular} & \begin{tabular}{c} **QU** \\ \end{tabular} & \begin{tabular}{c} **KA** \\ \end{tabular} & \
\begin{tabular}{c} **GI** \\ \end{tabular} &
\begin{tabular}{c} **SC** \\ \end{tabular} \\ \hline
1 & 30 (1) & \(150\) (\(-1\)) & 30 (0) & 0.083 & 0.326 & 0.023 & 0.278 \\
2 & 10 (\(-1\)) & 250 (1) & 30 (0) & 0.080 & 0.299 & 0.020 & 0.240 \\
3 & 20 (0) & 200 (0) & 30 (0) & 0.105 & 0.400 & 0.030 & 0.355 \\
4 & 20 (0) & 250 (1) & 20 (\(-1\)) & 0.063 & 0.244 & 0.017 & 0.211 \\
5 & 30 (1) & 250 (1) & 30 (0) & 0.093 & 0.351 & 0.024 & 0.317 \\
6 & 30 (1) & 200 (0) & 20 (\(-1\)) & 0.060 & 0.262 & 0.017 & 0.207 \\
7 & 20 (0) & 200 (0) & 30 (0) & 0.105 & 0.400 & 0.030 & 0.355 \\
8 & 20 (0) & 150 (\(-1\)) & 40 (1) & 0.089 & 0.293 & 0.028 & 0.309 \\
9 & 10 (\(-1\)) & 150 (\(-1\)) & 30 (0) & 0.086 & 0.339 & 0.023 & 0.277 \\
10 & 30 (1) & 200 (0) & 40 (1) & 0.101 & 0.356 & 0.025 & 0.319 \\
11 & 20 (0) & 200 (0) & 30 (0) & 0.105 & 0.400 & 0.030 & 0.355 \\
12 & 20 (0) & 150 (\(-1\)) & 20 (\(-1\)) & 0.068 & 0.283 & 0.020 & 0.239 \\
13 & 10 (\(-1\)) & 200 (0) & 20 (\(-1\)) & 0.079 & 0.331 & 0.025 & 0.280 \\
14 & 10 (\(-1\)) & 200 (0) & 40 (1) & 0.098 & 0.365 & 0.025 & 0.324 \\
15 & 20 (0) & 200 (0) & 30 (0) & 0.105 & 0.400 & 0.030 & 0.355 \\
16 & 20 (0) & 250 (1) & 40 (1) & 0.097 & 0.378 & 0.025 & 0.341 \\
17 & 20 (0) & 200 (0) & 30 (0) & 0.105 & 0.400 & 0.030 & 0.355 \\ \hline \hline \end{tabular}  
* QU, KA, GI and SC are quercetin, kaempfer, ginkgetin and sciadipitysin, respectively.  
\end{table} 
Table 2: The Box–Behnken design of independent variables for process optimization. \[ \begin{split} Y_{3}=3.01\times 10^{-2}-5.46\times 10^{-4}X_{1}-9.03 \times 10^{-4}X_{2}-3.07\times 10^{-3}X_{3}+9.38\times 10^{-4}X_{1}X_{2}-1.81\times 1 0^{-3}\\ X_{1}X_{3}+3.29\times 10^{-5}X_{2}X_{3}-3.67\times 10^{-3}X_{1} ^{2}-3.95\times 10^{-3}X_{2}{}^{2}-3.58\times 10^{-3}X_{3}{}^{2},\end{split}  \tag{4}\]  
\[ \begin{split} Y_{4}=0.355+3.18\times 10^{-5}X_{1}+6.56\times 10^{-4}X _{2}-4.46\times 10^{-2}X_{3}+1.90\times 10^{-2}X_{1}X_{2}-1.72\times 10^{-2}X_{ 1}X_{3}-\\ 1.49\times 10^{-2}X_{2}X_{3}-3.48\times 10^{-2}X_{1}{}^{2}-4.26 \times 10^{-2}X_{2}{}^{2}-3.79\times 10^{-2}X_{3}{}^{2},\end{split}  \tag{5}\]  
where \(Y_{1}\), \(Y_{2}\), \(Y_{3}\) and \(Y_{4}\) represent yields of quercetin, kaempfer, ginkgetin and sciadopitysin (mg/g), respectively; \(X_{1}\), \(X_{2}\) and \(X_{3}\) respectively represent extraction time (min), ultrasonic power (W) and liquid-solid ratio (mL/g).