*3.3. Analysis of Experimental Design Results*

According to the data samples in Table 5, the quadratic polynomial regression model of net fruit rate with three factors was obtained using the data processing software Design-Expert 8.0, and the regression equation was the following:

Y = 94.76 + 1.64A + 1.11B + 2.35C <sup>−</sup> 1.13AB <sup>−</sup> 1.16AC + 1.55BC <sup>−</sup> 3.69A<sup>2</sup> <sup>−</sup> 4.79B2 <sup>−</sup> 8.87C2


**Table 5.** Experiment design and result.

In the formula, Y is the net fruit rate of hazelnuts; A is the sieve plate angle; B is the distance of the sieve plate; and C is the air flow velocity.

The regression model ANOVA and significance test results are shown in Table 6. From Table 6, it is clear that the fit of the net fruit rate model is highly significant (*p* < 0.01). The regression equation misfit was not significant, and it was a good fit with the actual situation. The *p*-values of the sieve plate angle, distance of the sieve plate, and air flow velocity could determine the effects of the three test factors on the net fruit rate of hazelnuts. The *p*-value of regression term B was less than 0.05 and the effect was significant, the *p*-values of regression terms A and C were less than 0.01 and the effects were highly significant, and the effects of the other terms were significant or highly significant. The effects of the test factors on the net fruit rate were air flow velocity, sieve plate angle, and distance between sieve plates in descending order.


**Table 6.** Analysis of variance.

\* *p* < 0.01 means extremely significant, 0.01 < *p* < 0.05 means significant, *p* > 0.05 means not significant, SS means Sum of Squares, df means Degree of Freedom, F means F-value

Using Design-Expert 8.0 software to process the data and analyze the relationship between the test index and factors, the effect of sieve plate angle, air flow velocity, and distance of the sieve plate on the net fruit rate can be obtained, and the response surface is shown in Figure 12, fixing the factors of sieve plate angle, air flow velocity, and distance of the sieve plate as the 0 level, respectively, and analyzing the interaction between the remaining two factors on the net fruit rate according to the response surface plot. The effect of the interaction between the remaining two factors on the net fruit rate was analyzed according to the response surface.

The response surface of the interaction between air flow velocity and distance of the sieve plate on the net fruit rate is shown in Figure 12a. When the air flow rate is certain, the net fruit rises first and then falls with the increase in distance of the sieve plate; when the distance of the sieve plate is certain, the net fruit rises first and then falls with the increase in air flow velocity. The response surface of the interaction effect of sieve plate angle and distance of the sieve plate on the net fruit rate is shown in Figure 12b. When the sieve plate angle is certain, with the increase in distance of the sieve plate, the net fruit rises first and then falls; when the distance of the sieve plate is certain, with the increase in sieve plate angle, the net fruit rises first and then falls. The response surface of the interaction between air flow velocity and sieve plate angle on the net fruit rate is shown in Figure 12c. When the air flow velocity is certain, with the increase in sieve plate angle, the net fruit rises first and then decreases. When the sieve plate angle is certain, the net fruit rate also rises first and then decreases with the increase in air flow velocity. Based on the interaction effect analysis, it can be seen that when any of the factors of air flow velocity, sieve plate angle, and distance of the sieve plate are fixed, the interaction of the remaining two factors is first increased to a certain value so that the net fruit effect in the impurity sorting process is significant, and then the net fruit rate decreases as the two factors continue to increase.

**Figure 12.** Response surface curve of interaction factors for test indexes: (**a**) the effect of AB interaction on Y; (**b**) the effect of AC interaction on Y; (**c**) the effect of BC interaction on Y.
