# Grading of Scots Pine Seeds by the Seed Coat Color: How to Optimize the Engineering Parameters of the Mobile Optoelectronic Device

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Seed Samples

_{r}

_{(VIS)}(x

_{1}) [31], the angle of inclination of the detecting beam incident on the seed α (x

_{2}) [26] and the height h

_{sp}(x

_{3}) of the transparent seed pipe [24]. The choice of factors is in good agreement with the results of a priori ranking [35]. For each run of the experiment, three samples of 300 seeds each were selected, including a mixture of randomly selected 100 seeds of each color fraction.

#### 2.2. Design of Experiment

_{cf}(formalized y

_{1}) described by the equation:

_{cf}is number of graded seeds in the desired seed-color fraction; n

_{cf}is number of seeds in the original sample.

_{r}

_{(VIS)}(x

_{1}) is the wavelength of reflected radiation [31]; α (x

_{2}) is the angle of inclination of the detecting beam incident on the seed [26]; h

_{sp}(x

_{3}) is the height of the transparent seed pipe [24].

- choose the type of experiment matrix;
- select levels of factor variation, encode input variables x
_{1}, x_{2}, x_{3}and build a planning matrix; - complete the planning matrix in coded variables, taking into account quadratic and paired interactions, and supplement it with columns of average response values for each flower-seed fraction;
- calculate the coefficients of the regression equation;
- check the calculated coefficients for significance, first determining the variance of reproducibility, and obtain the regression equation in the encoded variables;
- check the adequacy of the received model;
- interpretation of the resulting model was then performed;
- write out the regression equation in natural variables.

## 3. Results

#### 3.1. The Choice of the Tri-Factorial Design, Factors and Levels of Their Variation

_{r}

_{(VIS)}(x

_{1}), the angle of inclination of the detecting beam incident on the seed α (x

_{2}) and the height h

_{sp}(x

_{3}) of the transparent seed pipe [24].

_{r}

_{(VIS)}.

_{sp}(x

_{3}) of the transparent seed pipe.

#### 3.2. Implementation of a Tri-Factor Design

^{3}, six experiments in the center of the plan, and six experiments at the distance of the “stellar arm” from the center of the experiment. Thus, we consider it quite sufficient to conduct 20 experiments to adequately describe the results of the technological process of grading seeds.

_{κp}= 2.0211. Hence, t

_{κp}${S}_{\left\{y\right\}}^{2}$ = 2.0211 × 0.002248 = 0.004543. The obtained value was compared with the absolute values of the regression coefficients, as a result of which the significance of all coefficients greater than this value was determined. The exception was the coefficient b

_{3}, which is considered insignificant due to the fact that its value is less than the product of the t-test and the variance of reproducibility. In the final form, the regression equation in normalized variables was written as follows:

- ${\overline{y}}_{j}$ is the average value of the response from the experiment;${\widehat{y}}_{j}$ is the response value calculated from the regression equation;
- n is the number of repetitions of each experience from the planning matrix, n = 3;
- N is the number of experiments according to the planning matrix, N = 20;
- P is the number of regression coefficients of the analyzed mode, P = 8.

_{ad}= N − P = 20 − 8 = 12 and the smaller variance f

_{y}= N (n − 1) = 40, the value F

_{tab}= 2.00 was found, while the calculated F

_{calc}= 0.49. In view of the fact that the condition F

_{calc}< F

_{tab}is met, the regression equation adequately describes the response surface.

## 4. Discussion

_{1}, x

_{2}, and x

_{23}is positive, therefore, with the increase of the values of the factors, but not more than the plan—wavelength visible radiation and angle of incidence of the detecting optical beam, as well as the effect of pair interaction from a combination of the angle and height of the seed pipe—will increase the degree of separation in the visible range of wavelengths. The coefficients for x

_{12}, x

_{13}, x

_{11}, x

_{22}, x

_{33}have a negative sign, so the response value will increase as these effects decrease.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The response surface (

**left**) and Excel–nomogram (

**right**) determine the optimum when implementing a composite full–factor experiment when fixing the wavelength of the reflected radiation in the center of the plan at the level of 700 nm.

**Figure 2.**The response surface (

**left**) and Excel–nomogram (

**right**) determine the optimum when implementing a composite full–factor experiment when fixing the angle of incidence of the optical beam in the center of the plan at the level of 45°.

**Figure 3.**The response surface (

**left**) and Excel–nomogram (

**right**) determine the optimum when implementing a composite full–factor experiment when fixing the height of the seed pipe in the center of the plan at the level of 0.2 m.

**Table 1.**Some physical and physiological features of Scots pine seedlot’s color fraction used in this study.

Parameter | Seed-Color Fraction | ||
---|---|---|---|

Light (L) | Light-Dark (LD) | Dark (D) | |

Munsell’s [32] color system ^{1} | 4.9 YR 7.5/4.2 | 9.8 YR 6.0/4.1 | 7.3 YR 2.6/1.7 |

CMYKOG’s color system ^{1} | C0, M0, Y35, K26, Or10, G0 | C0, M0, Y14, K40, Or36, G6 | C63, M70, Y85, K54, Or0, G0 |

Fraction weight, g (% of the seedlot’s initial mass) | 361 (24.07) | 1006 (67.07) | 133 (8.86) |

1000 seeds weight ^{2}, g at humidity ^{3} (W, %) | 6.434 (8.36) | 7.869 (7.84) | 7.427 (10.66) |

Germination ^{4}, % | 96.5 | 96.0 | 94.5 |

^{1}These seed classes were classified in the color systems using the digital camera Canon Digital IXUS 100 IS 12.1 MPix (Canon Inc., Tokyo, Japan) for obtaining images and for image processing Digital Color Guide android-software (DIC Corp., Tokyo, Japan).

^{2}1000 seeds weight was determined using digital mini scale MTC-series readability 0.001 g (EasyTime Store, Shenzhen, China).

^{3}Seed moisture content was determined according to the GOvernment STandard of the Russian Federation (GOST RF) number 13056.3-86 [33].

^{4}Seed germination was determined according to GOST RF number 13056.6-97 [34].

**Table 2.**Values of factors and levels of their variation in the implementation of a uniform rotatable plan.

Designation | Levels of Factor Variation | Interval | |||||
---|---|---|---|---|---|---|---|

Natural. | Coded. | −α | −1 | 0 | +1 | +α | |

λ_{r}_{(VIS)}, HM | x_{1} | 600 | 640 | 700 | 760 | 800 | 60 |

α, degree | x_{2} | 35 | 39 | 45 | 51 | 55 | 6 |

h_{sp}, m | x_{3} | 0.10 | 0.14 | 0.20 | 0.26 | 0.30 | 0.06 |

${x}_{1}=\frac{{\lambda}_{r\left(\mathrm{VIS}\right)}-700}{60}$; ${x}_{2}=\frac{\mathsf{\alpha}-45}{6}$; ${x}_{3}=\frac{{h}_{sp}-0.2}{0.06}$ |

**Table 3.**Planning matrix for testing the efficiency of grading Scots pine seeds using a mobile optoelectronic separator in the visible wavelength range.

Experience Number | Design Matrix | Results of Experience | |||||
---|---|---|---|---|---|---|---|

Factors | |||||||

x_{1} (λ_{r}_{(VIS)}) | x_{2} (α) | x_{3} (h_{sp}) | y_{1} (D) | y_{1} (L) | y_{1} (LD) | $\overline{{\mathit{y}}_{1}}$ | |

1 | +1 | +1 | +1 | 0.82 | 0.86 | 0.85 | 0.8433 |

2 | −1 | +1 | −1 | 0.8 | 0.83 | 0.87 | 0.8333 |

3 | +1 | −1 | −1 | 0.85 | 0.89 | 0.88 | 0.8733 |

4 | −1 | −1 | +1 | 0.78 | 0.8 | 0.82 | 0.8000 |

5 | +1 | +1 | −1 | 0.81 | 0.85 | 0.83 | 0.8300 |

6 | −1 | +1 | +1 | 0.86 | 0.89 | 0.87 | 0.8733 |

7 | +1 | −1 | +1 | 0.8 | 0.81 | 0.78 | 0.7967 |

8 | −1 | −1 | −1 | 0.79 | 0.78 | 0.75 | 0.7733 |

9 | 0 | 0 | 0 | 1.00 | 1.00 | 0.98 | 0.9933 |

10 | 0 | 0 | 0 | 0.98 | 1.00 | 0.99 | 0.9900 |

11 | 0 | 0 | 0 | 0.99 | 0.99 | 0.99 | 0.9900 |

12 | 0 | 0 | 0 | 1.00 | 0.99 | 1.00 | 0.9967 |

13 | 0 | 0 | 0 | 1.00 | 1.00 | 1.00 | 1.0000 |

14 | 0 | 0 | 0 | 0.98 | 0.99 | 0.99 | 0.9867 |

15 | +1.682 | 0 | 0 | 0.95 | 0.98 | 0.97 | 0.9667 |

16 | −1.682 | 0 | 0 | 0.94 | 0.96 | 0.98 | 0.9600 |

17 | 0 | +1.682 | 0 | 0.89 | 0.87 | 0.88 | 0.8800 |

18 | 0 | −1.682 | 0 | 0.88 | 0.89 | 0.87 | 0.8800 |

19 | 0 | 0 | +1.682 | 0.93 | 0.97 | 0.92 | 0.9400 |

20 | 0 | 0 | −1.682 | 0.94 | 0.95 | 0.91 | 0.9333 |

**Table 4.**Planning matrix with interaction effects for determining the coefficients of the regression equation.

Experience Number | Factors | Interactions | Average | |||||||
---|---|---|---|---|---|---|---|---|---|---|

x_{1} | x_{2} | x_{3} | x_{1}x_{2} | x_{2}x_{3} | x_{1}x_{3} | (x_{1})^{2} | (x_{2})^{2} | (x_{3})^{2} | $\overline{{\mathit{y}}_{1}}$ | |

1 | +1 | +1 | +1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.8433 |

2 | −1 | +1 | −1 | −1 | −1 | 1 | 1 | 1 | 1 | 0.8333 |

3 | +1 | −1 | −1 | −1 | 1 | −1 | 1 | 1 | 1 | 0.8733 |

4 | −1 | −1 | +1 | 1 | −1 | −1 | 1 | 1 | 1 | 0.8000 |

5 | +1 | +1 | −1 | 1 | −1 | −1 | 1 | 1 | 1 | 0.8300 |

6 | −1 | +1 | +1 | −1 | 1 | −1 | 1 | 1 | 1 | 0.8733 |

7 | +1 | −1 | +1 | −1 | −1 | 1 | 1 | 1 | 1 | 0.7967 |

8 | −1 | −1 | −1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.7733 |

9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.9933 |

10 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.9900 |

11 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.9900 |

12 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.9967 |

13 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1.0000 |

14 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.9867 |

15 | +1.682 | 0 | 0 | 0 | 0 | 0 | 2.829 | 0 | 0 | 0.9667 |

16 | −1.682 | 0 | 0 | 0 | 0 | 0 | 2.829 | 0 | 0 | 0.9600 |

17 | 0 | +1.682 | 0 | 0 | 0 | 0 | 0 | 2.829 | 0 | 0.8800 |

18 | 0 | −1.682 | 0 | 0 | 0 | 0 | 0 | 2.829 | 0 | 0.8800 |

19 | 0 | 0 | +1.682 | 0 | 0 | 0 | 0 | 0 | 2.829 | 0.9400 |

20 | 0 | 0 | −1.682 | 0 | 0 | 0 | 0 | 0 | 2.829 | 0.9333 |

b_{0} | b_{1} | b_{2} | b_{3} | b_{12} | b_{23} | b_{13} | b_{11} | b_{22} | b_{33} | RE-coefs |

0.9958 | 0.005458 | 0.01001 | 0.001065 | −0.0163 | 0.0129 | −0.0163 | −0.03039 | −0.05985 | −0.03982 |

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**MDPI and ACS Style**

Novikov, A.I.; Zolnikov, V.K.; Novikova, T.P.
Grading of Scots Pine Seeds by the Seed Coat Color: How to Optimize the Engineering Parameters of the Mobile Optoelectronic Device. *Inventions* **2021**, *6*, 7.
https://doi.org/10.3390/inventions6010007

**AMA Style**

Novikov AI, Zolnikov VK, Novikova TP.
Grading of Scots Pine Seeds by the Seed Coat Color: How to Optimize the Engineering Parameters of the Mobile Optoelectronic Device. *Inventions*. 2021; 6(1):7.
https://doi.org/10.3390/inventions6010007

**Chicago/Turabian Style**

Novikov, Arthur I., Vladimir K. Zolnikov, and Tatyana P. Novikova.
2021. "Grading of Scots Pine Seeds by the Seed Coat Color: How to Optimize the Engineering Parameters of the Mobile Optoelectronic Device" *Inventions* 6, no. 1: 7.
https://doi.org/10.3390/inventions6010007