# A Canopy Density Model for Planar Orchard Target Detection Based on Ultrasonic Sensors

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Target Canopy Density Detection Method

#### 2.2. Target Density Detection System

^{3}. The leaves of the Chinese glossy privet (Ligustrum lucidum) were chosen for the experiment. The weight of each leaf was between 1.0 and 2.0 g, while the size of the leaf was about 10 cm × 6 cm. Under such conditions, the maximum weight of leaves that could be arranged in each layer was 212 g, while the maximum density of each layer was 1127.66 g/m

^{3}. The minimum density was set as 112.77 g/m

^{3}, which was 10% of the maximum density. In the test bench several layers of leaves could be combined to simulate canopies with different thicknesses. The density of each layer was the same. The leaves were evenly fixed in each row with interspersed arrangements in adjacent rows. In the adjacent layers, the arrangements were interspersed as well.

#### 2.3. Experiment for the Relationship between the Ultrasonic Energy and the Power Supply Voltage

#### 2.4. Experiment for Beam Width of Ultrasonic Sensor

_{R}is the distance between the center line and the right test plate; and W

_{L}is the distance between the center line and the left test plate. The value of S was calculated in the orthogonal regression central composite experiment (will be mentioned in Section 2.5).

_{R}or W

_{L}was manually measured between the test plate and the center line. Each measurement was conducted 3 times. The final value of W

_{R}or W

_{L}was the average of the 3 repetitions. The beam width was the sum of W

_{R}and W

_{L}which must be measured at the same detecting distance S.

#### 2.5. Orthogonal Regression Central Composite Experimental Design

_{c}is the number of orthogonal tests; m

_{0}is the number of the zero level repeat tests; n is the number of the total tests; γ is star test point parameter; and m

_{0}is the number of zero level repeat tests. In these orthogonal regression experiments, parameter m

_{0}was set as: m

_{0}= 3. The values of the other parameters were: p = 2, m

_{c}= 4, n = 11, γ = 1.15:

_{lj}, Z

_{uj}and Z

_{0j}are the lower level, upper level and zero level of the factor j respectively; Δ

_{j}is the range radius; Z

_{j}is the value of factor j; and x

_{j}is the factor level code. The factor levels coding is shown in Table 1.

_{j}are the sums of partial regression squares; f

_{j}is the degree of freedom of S

_{j}; S

_{e}was the sum of error squares within repeat test group; f

_{e}was the degree of freedom of S

_{e}; S

_{T}was the sum of regression squares; f

_{T}was the degree of freedom of S

_{T}; S

_{R}was the sum of residual squares; f

_{R}was the degree of freedom of S

_{R}; F

_{j}was the F distribution statistic of parameter j; and F was the F distribution statistic of the regression equation. The significant coefficients will be selected to build the regression equations based on the F-test.

_{lf}is the sum of lack of fit squares; f

_{lf}is the degrees of freedom of S

_{lf}; and F

_{lf}is the F distribution statistic used in the test for lack of fit.

#### 2.6. Verification Test Design

## 3. Results and Discussion

#### 3.1. Relationship between the Ultrasonic Energy and the Power Supply Voltage

^{2}was 0.9984:

_{N}is the normalized energy, c is the correction coefficient, and E is the calculation energy.

#### 3.2. Beam Width of the Ultrasonic Sensor

#### 3.3. Canopy Density Model

_{Lf}< 1, and F > F

_{0.90}(5,5) = 3.45, the flowing model was acceptable. The value of F

_{12}was less than F

_{0.90}(1,2) = 8.53, so the term x

_{1}x

_{2}could be ignored. The canopy density model equation with four layers was obtained as follows:

_{1}is the canopy density in g/m

^{3}, z

_{2}is the distance in m, and y is the echo energy. Similar experiments were conducted to establish canopy density models with three layers (Table 5). The equation coefficients and statistical parameters were calculated (Table 6).

_{Lf}< 1, and F > F

_{0.90}(5,5) = 3.45, the model was acceptable. The value of F

_{12}was less than F

_{0.90}(1,2) = 8.53, so the term x

_{1}x

_{2}could be ignored. The canopy density model equation with three layers was obtained as follows:

_{1}is the canopy density in g/m

^{3}, z

_{2}is the distance in m, and y is the echo energy.

#### 3.4. Model Equation Selection

#### 3.5. Model Equation Verification

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 6.**(

**a**) Relationship between ultrasonic energy and supply voltage; and (

**b**) fitting equation of correction coefficient and supply voltage.

Factor | Z_{l}_{j} | Z_{u}_{j} | Z_{0}_{j} | ∆_{j} | −γ | −1 | 0 | 1 | γ |
---|---|---|---|---|---|---|---|---|---|

Density (Z_{1}) [g/m^{3}] | 112.77 | 1127.66 | 620.21 | 440.91 | 112.77 | 179.31 | 620.21 | 1061.12 | 1127.66 |

Distance (Z_{2}) [m] | 0.5 | 1.5 | 1.0 | 0.43 | 0.5 | 0.57 | 1.0 | 1.43 | 1.5 |

Tests | S [m] | W_{L} [cm] | W_{R} [cm] | Average of W_{L} [cm] | Average of W_{R} [cm] |
---|---|---|---|---|---|

1 | 0.5 | 6 | 7 | 6.3 | 6.8 |

2 | 6.5 | 6.5 | |||

3 | 6.5 | 7 | |||

4 | 0.57 | 8 | 7 | 7.7 | 7.0 |

5 | 7.5 | 7 | |||

6 | 7.5 | 7 | |||

7 | 1.0 | 11 | 12 | 10.5 | 11.2 |

8 | 10.5 | 11 | |||

9 | 10 | 10.5 | |||

10 | 1.43 | 12 | 13 | 12.0 | 12.3 |

11 | 11 | 12 | |||

12 | 13 | 12 | |||

13 | 1.5 | 16 | 14 | 15.0 | 14.2 |

14 | 15 | 14.5 | |||

15 | 14 | 14 |

Z_{1} [g/m^{3}] (x_{1}) | Z_{1} [m] (x_{2}) | x_{1}x_{2} | x_{1}^{’} | x_{2}^{’} | Transmitted Energy [J] | Echo Energy [J] | Normalized Echo Energy [J] | Decuple Normalized Echo Energy [J] |
---|---|---|---|---|---|---|---|---|

1061.12(1) | 1.43(1) | 1 | 0.396 | 0.396 | 1.2738 | 0.1815 | 0.1586 | 1.586 |

1061.12(1) | 0.57(−1) | −1 | 0.396 | 0.396 | 1.2601 | 0.4878 | 0.4309 | 4.309 |

179.31(−1) | 1.43(1) | −1 | 0.396 | 0.396 | 1.2601 | 0.1528 | 0.1350 | 1.350 |

179.31)(−1) | 0.57(−1) | 1 | 0.396 | 0.396 | 1.3354 | 0.4230 | 0.3526 | 3.526 |

1127.66(r) | 1.0(0) | 0 | 0.716 | −0.604 | 1.3347 | 0.3338 | 0.2784 | 2.784 |

112.77(−r) | 1.0(0) | 0 | 0.716 | −0.604 | 1.3524 | 0.1818 | 0.1496 | 1.496 |

620.21(0) | 1.5(r) | 0 | −0.604 | 0.716 | 1.3291 | 0.2265 | 0.1897 | 1.897 |

620.21(0) | 0.5(−r) | 0 | −0.604 | 0.716 | 1.3036 | 0.5774 | 0.4930 | 4.930 |

620.21(0) | 1.0(0) | 0 | −0.604 | −0.604 | 1.3211 | 0.3670 | 0.3092 | 3.092 |

620.21(0) | 1.0(0) | 0 | −0.604 | −0.604 | 1.3249 | 0.3189 | 0.2679 | 2.679 |

620.21(0) | 1.0(0) | 0 | −0.604 | −0.604 | 1.3363 | 0.3126 | 0.2603 | 2.603 |

Regression Equation Parameters | Test for Lack of Fit of Density Model | Equation Parameter Hypothesis Test | |||
---|---|---|---|---|---|

b_{0} | 2.750 | S_{R} | 0.301 | F_{1} | 13.601 |

b_{1} | 0.376 | S_{T} | 13.243 | F_{2} | 153.131 |

b_{2} | −1.262 | S_{Lf} | 0.163 | F_{12} | 0.037 |

b_{12} | −0.137 | S_{e} | 0.138 | F_{11} | 14.276 |

b_{11} | −0.533 | F_{Lf} | 0.786 | F_{22} | 9.481 |

b_{22} | 0.434 | f_{R} | 5 | F | 43.971 |

F_{T} | 5 | ||||

f_{Lf} | 3 | ||||

f_{e} | 2 |

Z_{1} [g/m^{3}] (x_{1}) | Z_{1} [m] (x_{2}) | x_{1}x_{2} | x_{1}^{’} | x_{2}^{’} | Transmitted Energy [J] | Echo Energy [J] | Normalized Echo Energy [J] | Decuple Normalized Echo Energy [J] |
---|---|---|---|---|---|---|---|---|

1061.12(1) | 1.43(1) | 1 | 0.396 | 0.396 | 1.3381 | 0.2098 | 0.1745 | 1.745 |

1061.12(1) | 0.57(−1) | −1 | 0.396 | 0.396 | 1.3362 | 0.5665 | 0.4718 | 4.718 |

179.31(−1) | 1.43(1) | −1 | 0.396 | 0.396 | 1.3506 | 0.1185 | 0.0977 | 0.977 |

179.31)(−1) | 0.57(−1) | 1 | 0.396 | 0.396 | 1.3301 | 0.3277 | 0.2742 | 2.742 |

1127.66(r) | 1.0(0) | 0 | 0.716 | −0.604 | 1.3468 | 0.3936 | 0.3253 | 3.253 |

112.77(−r) | 1.0(0) | 0 | 0.716 | −0.604 | 1.3531 | 0.1693 | 0.1393 | 1.393 |

620.21(0) | 1.5(r) | 0 | −0.604 | 0.716 | 1.3524 | 0.2002 | 0.1648 | 1.648 |

620.21(0) | 0.5(−r) | 0 | −0.604 | 0.716 | 1.3424 | 0.5427 | 0.4499 | 4.499 |

620.21(0) | 1.0(0) | 0 | −0.604 | −0.604 | 1.3512 | 0.3146 | 0.2591 | 2.591 |

620.21(0) | 1.0(0) | 0 | −0.604 | −0.604 | 1.3569 | 0.2879 | 0.2361 | 2.361 |

1061.12(1) | 1.43(1) | 0 | −0.604 | −0.604 | 1.3426 | 0.3253 | 0.2697 | 2.697 |

Regression Equation Parameters | Test for Lack of Fit of Density Model | Equation Parameter Hypothesis Test | |||
---|---|---|---|---|---|

b_{0} | 2.602 | S_{R} | 0.144 | F_{1} | 121.882 |

b_{1} | 0.735 | S_{T} | 14.193 | F_{2} | 328.565 |

b_{2} | −1.207 | S_{Lf} | 0.085 | F_{12} | 0.182 |

b_{12} | −0.302 | S_{e} | 0.059 | F_{11} | 9.270 |

b_{11} | −0.280 | F_{Lf} | 0.963 | F_{22} | 9.915 |

b_{22} | 0.290 | f_{R} | 5 | F | 95.589 |

f_{T} | 5 | ||||

f_{Lf} | 3 | ||||

f_{e} | 2 |

Density [g/m^{3}] | Distance [m] | Normalized Echo Energy [J] | Model Equation with Three Layers | Model Equation with Four Layers | ||
---|---|---|---|---|---|---|

Calculated Value [J] | Relative Error [%] | Calculated Value [J] | Relative Error [%] | |||

1061.12 | 1.43 | 0.1586 | 0.2099 | 32.35 | 0.1896 | 19.57 |

1061.12 | 0.57 | 0.4309 | 0.4513 | 4.74 | 0.4420 | 2.59 |

179.31 | 1.43 | 0.1350 | 0.0628 | 53.47 | 0.1168 | 13.50 |

179.31 | 0.57 | 0.3526 | 0.3042 | 13.71 | 0.3692 | 4.71 |

1127.66 | 1.0 | 0.2784 | 0.3036 | 9.06 | 0.2606 | 6.38 |

112.77 | 1.0 | 0.1496 | 0.1343 | 10.23 | 0.1768 | 18.14 |

620.21 | 1.50 | 0.1897 | 0.1549 | 18.33 | 0.2012 | 6.08 |

620.21 | 0.50 | 0.4930 | 0.4356 | 11.64 | 0.4947 | 0.34 |

620.21 | 1.0 | 0.3092 | 0.2560 | 17.19 | 0.2892 | 6.45 |

620.21 | 1.0 | 0.2679 | 0.2560 | 4.43 | 0.2892 | 7.96 |

620.21 | 1.0 | 0.2603 | 0.2560 | 1.66 | 0.2892 | 11.10 |

Density [g/m^{3}] | Distance [m] | Normalized Echo Energy [J] | Model Equation with Three Layers | Model Equation with Four Layers | ||
---|---|---|---|---|---|---|

Calculated Value [J] | Relative Error [%] | Calculated Value [J] | Relative Error [%] | |||

1061.12 | 1.43 | 0.1745 | 0.2192 | 25.60 | 0.1608 | 7.87 |

1061.12 | 0.57 | 0.4718 | 0.4560 | 3.37 | 0.4304 | 8.78 |

179.31 | 1.43 | 0.0977 | 0.0721 | 26.14 | 0.0882 | 9.75 |

179.31 | 0.57 | 0.2742 | 0.3089 | 12.64 | 0.3478 | 26.83 |

1127.66 | 1.0 | 0.3253 | 0.3101 | 4.67 | 0.2504 | 23.02 |

112.77 | 1.0 | 0.1393 | 0.1408 | 1.09 | 0.1568 | 12.54 |

620.21 | 1.50 | 0.1648 | 0.1648 | 0.01 | 0.1711 | 3.85 |

620.21 | 0.50 | 0.4499 | 0.4401 | 2.19 | 0.4846 | 7.71 |

620.21 | 1.0 | 0.2591 | 0.2625 | 1.32 | 0.2692 | 3.88 |

620.21 | 1.0 | 0.2361 | 0.2625 | 11.18 | 0.2692 | 14.00 |

620.21 | 1.0 | 0.2697 | 0.2625 | 2.65 | 0.2692 | 0.19 |

Density [g/m^{3}] | Distance [m] | Transmitted Energy [J] | Echo Energy [J] | Normalized Echo Energy [J] | Model Value [J] | Relative Error [%] |
---|---|---|---|---|---|---|

319.15 | 0.8 | 1.3330 | 0.3631 | 0.3032 | 0.3076 | 1.46 |

319.15 | 1.2 | 1.3330 | 0.2002 | 0.1672 | 0.1902 | 13.78 |

478.72 | 0.8 | 1.3215 | 0.3886 | 0.3273 | 0.3402 | 3.92 |

478.72 | 1.2 | 1.3271 | 0.2540 | 0.2130 | 0.2228 | 4.59 |

744.68 | 0.8 | 1.3087 | 0.4354 | 0.3703 | 0.3634 | 1.88 |

744.68 | 1.2 | 1.3267 | 0.2500 | 0.2098 | 0.2460 | 17.26 |

904.26 | 0.8 | 1.3153 | 0.3995 | 0.3381 | 0.3587 | 6.10 |

904.26 | 1.2 | 1.3285 | 0.2448 | 0.2050 | 0.2413 | 17.68 |

Density [g/m^{3}] | Distance [m] | Transmitted Energy [J] | Echo Energy [J] | Normalized Echo Energy [J] | Model Value [J] | Relative Error [%] |
---|---|---|---|---|---|---|

319.15 | 0.8 | 1.2742 | 0.3378 | 0.2951 | 0.3076 | 4.26 |

319.15 | 1.2 | 1.3317 | 0.1985 | 0.1659 | 0.1902 | 14.63 |

478.72 | 0.8 | 1.3245 | 0.4098 | 0.3444 | 0.3402 | 1.23 |

478.72 | 1.2 | 1.3256 | 0.2112 | 0.1773 | 0.2228 | 25.64 |

744.68 | 0.8 | 1.3112 | 0.3698 | 0.3139 | 0.3634 | 15.78 |

744.68 | 1.2 | 1.3274 | 0.2372 | 0.1989 | 0.2460 | 23.68 |

904.26 | 0.8 | 1.3192 | 0.3754 | 0.3168 | 0.3587 | 13.24 |

904.26 | 1.2 | 1.3211 | 0.2936 | 0.2474 | 0.2413 | 2.46 |

Density [g/m^{3}] | Distance [m] | Transmitted Energy [J] | Echo Energy [J] | Normalized Echo Energy [J] | Model Value [J] | Relative Error [%] |
---|---|---|---|---|---|---|

319.15 | 0.8 | 1.3285 | 0.3267 | 0.2737 | 0.3076 | 12.41 |

319.15 | 1.2 | 1.3235 | 0.2340 | 0.1967 | 0.1902 | 3.31 |

478.72 | 0.8 | 1.3184 | 0.3805 | 0.3213 | 0.3402 | 5.88 |

478.72 | 1.2 | 1.3272 | 0.2189 | 0.1836 | 0.2228 | 21.33 |

744.68 | 0.8 | 1.3155 | 0.3546 | 0.3000 | 0.3634 | 21.13 |

744.68 | 1.2 | 1.3260 | 0.2416 | 0.2028 | 0.2460 | 21.31 |

904.26 | 0.8 | 1.3077 | 0.3939 | 0.3352 | 0.3587 | 6.99 |

904.26 | 1.2 | 1.3221 | 0.2365 | 0.1991 | 0.2413 | 21.17 |

Density [g/m^{3}] | Distance [m] | Transmitted Energy [J] | Echo Energy [J] | Normalized Echo Energy [J] | Model Value [J] | Relative Error [%] |
---|---|---|---|---|---|---|

319.15 | 0.8 | 1.3148 | 0.3293 | 0.2788 | 0.3076 | 10.35 |

319.15 | 1.2 | 1.3806 | 0.2306 | 0.1859 | 0.1902 | 2.32 |

478.72 | 0.8 | 1.3110 | 0.3378 | 0.2867 | 0.3402 | 18.63 |

478.72 | 1.2 | 1.3852 | 0.2232 | 0.1793 | 0.2228 | 24.21 |

744.68 | 0.8 | 1.3248 | 0.3541 | 0.2975 | 0.3634 | 22.15 |

744.68 | 1.2 | 1.3363 | 0.2343 | 0.1951 | 0.2460 | 26.04 |

904.26 | 0.8 | 1.3202 | 0.3275 | 0.2761 | 0.3587 | 29.92 |

904.26 | 1.2 | 1.3277 | 0.2611 | 0.2188 | 0.2413 | 10.26 |

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**MDPI and ACS Style**

Li, H.; Zhai, C.; Weckler, P.; Wang, N.; Yang, S.; Zhang, B.
A Canopy Density Model for Planar Orchard Target Detection Based on Ultrasonic Sensors. *Sensors* **2017**, *17*, 31.
https://doi.org/10.3390/s17010031

**AMA Style**

Li H, Zhai C, Weckler P, Wang N, Yang S, Zhang B.
A Canopy Density Model for Planar Orchard Target Detection Based on Ultrasonic Sensors. *Sensors*. 2017; 17(1):31.
https://doi.org/10.3390/s17010031

**Chicago/Turabian Style**

Li, Hanzhe, Changyuan Zhai, Paul Weckler, Ning Wang, Shuo Yang, and Bo Zhang.
2017. "A Canopy Density Model for Planar Orchard Target Detection Based on Ultrasonic Sensors" *Sensors* 17, no. 1: 31.
https://doi.org/10.3390/s17010031