Ramie Field Distribution Model and Miss Cutting Rate Prediction Based on the Statistical Analysis

Abstract

Ramie is an important cash crop in China, and ramie fiber is an important raw material for the textile industry. As a shrub plant, the spatial distribution of the ramie plant is different from that of herbaceous crops, and its plant spacing and row spacing are not fixed, which affects the cutting operation during harvest. In order to solve the above problems, this study constructed a ramie spatial distribution model with statistical methods, and built a prediction model of ramie harvesting feeding quantity on this basis. Based on the analysis of the absolute motion trail of the ramie harvester cutting knife, the calculation equation of the missing cutting area was established, and then the prediction model of the mis-cutting rate was obtained. The results of the ramie field harvest showed that the prediction model of the feed quantity and mis-cutting rate was effective. These methods can provide references to the control and optimization of ramie harvester parameters.

1. Introduction

Ramie (Boehmeria nivea L. Gaud.), also known as Chinese grass, is a species native to China which produces the oldest textile fiber and has been cultivated in the Yangtze River Basin for 4700 years. Today, China is still the world’s largest ramie producer, with the largest planting area and output in the world, accounting for more than 90% of the world’s total planting area and output. Ramie can be used in many fields. Ramie fiber has good application prospects in the composite material and textile fields. Ramie fiber, with the advantages of long length, high crystallinity and large modulus of elasticity, is one of the natural fibers which have been developed to strengthen composite materials in recent years [1,2,3]. The high protein content of ramie leaves has led researchers to investigate its feed capacity and consider it a plant with high breeding potential because of its high feed yield and quality [4]. In different experiences of cattle, sheep, pigs, horses and poultry, ramie has been shown to be viable as a green feed [5]. The Green Forage combine harvester and ramie stripping machine is the research focus of ramie production mechanization [6,7,8]. However, mechanized ramie harvesting technology, which can improve harvesting efficiency, is less studied. In the early 1990s, Japan tried to use sensor technology to develop a ramie harvester, but failed to make in-depth research, although a prototype structure was reported. Anna Dilfi K F et al. [9] presented a review of the existing mechanical harvesting systems for bast fiber crops in Europe and China, with special reference to hemp, flax, and kenaf, but there is no data query on ramie harvesters. Jicheng Huang et al. [10] analyzed the effects of interaction of various factors on cutting efficiency, failure rate and transport rate by response surface method. They also conducted multi-objective optimization on a regression model according to the importance of optimization objectives, and obtained the optimal combination of operating parameters for cutting and conveying parts of the ramie combined harvester. Zhengwei Chen et al. [11] proposed a navigation line extraction algorithm of the ramie combine harvester based on the U-NET neural network to solve the problem whereby ramie tilt interferes with ramie boundary extraction and thus affects navigation line extraction accuracy. However, these studies often focus on mechanical mechanism design and local optimization, ignoring the biological characteristics of ramie, which are very important for ramie harvest. Shen Cheng et al. [12] assumed the geometric shape of ramie stem and established the mechanical model of ramie stem with the theory of composite material mechanics.

As a shrub plant, ramie is not evenly distributed in the field. Ramie field plant distribution can affect the performance indexes of the harvester at the time of harvesting. This research used a field investigation to determine the ramie field plant distribution type and distribution parameters. The absolute movement trajectory of the cutter was analyzed, and the missing rate could be calculated with the ramie field plants distribution. The ramie field plant distribution model can provide data support for the simulation study of ramie field harvest, which can be used to optimize the design parameters of the ramie combine harvester.

2. Materials and Methods

2.1. Statistical Analysis of Ramie Field Plant Distribution

In order to study the distribution of ramie plants in the field, quantity information of ramie plants in a certain area was collected in Xiangyang Lake Ramie Experimental Base in Xianning City, Hubei Province. The ramie variety is “Huazhu No. 4”. Ramie cultivation plots were square plots of 80 m × 80 m. A double diagonal sampling method was appropriate for sampling larger square plots, i.e., the sampling points were evenly distributed on the two diagonals of the four corners of the standard plot for survey sampling. The sample plot size was set to 1.6 m × 1.6 m because the cutting width of the ramie harvester is 1.6 m. The square plot of 80 m × 80 m was divided into 2500 small plots of 1.6 m × 1.6 m, and 100 small plots on the two diagonal lines were taken as the quadrats to count the number of ramie field plants. Ramie can be harvested three times a year and is named first crop ramie, second crop ramie and third crop ramie, respectively, in this paper in chronological order. The sampling method was the diagonal sampling method, and the quantity information of first crop ramie, second crop ramie and third crop ramie were collected, respectively. The ramie planting map is shown in Figure 1.

2.2. Ramie Field Harvest Test

A model 4LMZ-160A ramie harvester, designed and manufactured by Nanjing Institute of Agricultural Mechanization, Ministry of Agriculture and Rural Affairs, was used in ramie harvesting experiments.

2.2.1. Overview of Ramie Harvester

The ramie combine harvester is composed of a chassis, a crawler track, a reciprocating knife cutter, a drag-link conveyor, an upper pick-up reel, a lower divider and grain lifter, etc. The overall structure is shown in Figure 2.

The main technical parameters of this ramie harvester are shown in

Table 1. Main technical parameters of this ramie harvester.

Parameter Items	Engine Parameter	Swath	Productivity	Stubble Height
Numerical value	25.7 kW	1600 mm	0.1–0.2 hm2/h	≤10 cm

.

The operation process of the ramie harvester is as follows: The height of the cutting table and the upper pick-up reel are adjusted by hydraulic cylinders to control the stubble height. The height of the upper pick-up reel is basically the same as the height of the middle and upper part of the ramie stalk. When the harvester moves forward, the ramie stalks are guided into the cutter by the lower divider and grain lifter, and the upper pick-up reel. Then, the cutter cuts the ramie stalks. Finally, the drag-link conveyer transports the cut ramie stalks to the tying machine for baling, thus completing the mechanical harvesting of ramie.

The stalks are plucked up and guided into the cutting device by the combined action of the lower divider and grain lifter, and the upper pick-up reel, and the cut stalks are transported to the baling device for baling by the double-layer chain conveyor, thus completing the mechanical harvesting of ramie.

2.2.2. Field Test Method

In the field test, the forward speed of the ramie harvester $v_m$ was preliminarily selected as 0.8–1.0 m/s, the cutting velocity of the ramie harvester $v_f$ was selected as 1.4 m/s. The feeding amount and miss cutting rate of the ramie harvester were measured and compared with the calculated values.

3. Results

According to the method mentioned in Section 2.1, the relevant data of the ramie plant number in the field were obtained. The original data are shown in Appendix A. SPSS 22.0 software was used for statistical analysis of the collected data.

3.1. Distribution Pattern of Ramie Plant Number

The Kolmogorov–Smirnov test was used to determine the distribution pattern of the ramie plant number, the test results are shown in

Table 2. Significance result of Kolmogorov–Smirnov test.

Distribution Pattern	Progressive Significance (Bilateral)
	First Crop Ramie	Second Crop Ramie	Third Crop Ramie
Normal distribution	0.125	0.105	0.194
Uniform distribution	0.016	0.003	0.000
Poisson distribution	0.000	0.000	0.000
Exponential distribution	0.000	0.000	0.000

.

As shown in the table above, the progressive significance (bilateral) values of uniform distribution, Poisson distribution and exponential distribution are all less than 0.05, rejecting the null hypothesis. Statistical analysis of ramie field plant distribution follows normal distribution.

Where normal distribution is an arrangement of data in which most values are near the center of the range and gradually become fewer towards each end, shown in a graph as the shape of a bell:

The resulting variable has a nearly normal distribution.

Normal distributions consistently occur only when they involve random events and a large sample.

3.2. Normality Test

The normality test mainly includes the following test methods.

3.2.1. Normality Test: Graphic Qualitative Judgment

The shape of the histogram and the corresponding normal probability density curve roughly determines whether the data follow the normal distribution.

In Figure 3, the abscissa is the ramie number and the ordinate is the ramie frequency. It can be seen that the shape of the histogram drawn is roughly the same as that of the corresponding normal distribution curve, and basically it can be judged that the data follows the normal distribution.

The Q–Q plot (quantile–quantile plot) reflects the extent to which the quantile of the actual observed value (abscissa) agrees with the theoretical quantile of the normal distribution (ordinate). The P–P plot (frequency–frequency plot) reflects the degree to which the cumulative frequency (abscissa) of the actual observed values agrees with the theoretical cumulative probability (ordinate) of the normal distribution.

Q–Q plot and P–P plot are similar in meaning, both can be used to examine whether the data obey a certain distribution type. If the distribution type of the test is normal distribution and the data point basically coincides with the theoretical line (i.e., the diagonal line), the data are basically considered to follow normal distribution. If it deviates from the straight line, it is considered that the data may not follow the normal distribution.

In the Q–Q(Figure 4)/P–P(Figure 5) plot above, the points approximately revolve around a straight line, and it can be roughly judged that the data presents an approximate normal distribution.

3.2.2. Normality Test: Shapiro–Wilk Test

The Shapiro–Wilk test is one of the most effective methods of normality testing. It is a method to test normality in frequency statistics. The Shapiro–Wilk test is suitable for small sample size, with the recommended sample size being 7~2000, and as this study sample size is 100, it is applicable to the Shapiro–Wilk test.

Table 3. Result of Shapiro–Wilk test.

Ramie Season	Statistic	Df	Sig.
First crop ramie	0.973	100	0.036
Second crop ramie	0.971	100	0.028
Third crop ramie	0.977	100	0.072

shows result of the Shapiro–Wilk test.

In the result of the Shapiro–Wilk test, the p value of third crop ramie is 0.072. At the test level of α = 0.05, p > 0.05, the null hypothesis is not rejected, and it can be considered that the third crop ramie obeys normal distribution.

However, the p value of first crop ramie is 0.036, and the p value of the second crop ramie is 0.028, both are less than 0.05, and do not obey normal distribution. The reason is that the test effect of the Shapiro–Wilk test is best when every sample value is unique, but it is not good when several values are repeated in the sample. Due to the small data interval of the sample, there are many duplicate data in the original data (attached table at the end of the paper). So, we can assume that the Shapiro–Wilk test results are not of reference value, and the data cannot be considered to be disobedient to a normal distribution.

3.2.3. Normality Test: Skewness and Kurtosis Quantitative Judgment Method

To prove whether the data conform to the normal distribution, the normal distribution index test should be used to judge, with the kurtosis and skewness Z-score test being a commonly used test method.

When skewness and kurtosis are used for a normality test, the corresponding Z-score (Z-score) can be calculated simultaneously, that is, skewness Z-score = skewness value/standard error, kurtosis Z-score = kurtosis value/standard error. At the test level of α = 0.05, if the Z-score is between ±1.96, it can be considered to obey the normal distribution, and if one does not meet the normal distribution, it is considered not to obey the normal distribution.

Under the test level of α = 0.05, the z-score of skewness and kurtosis of the three crops of ramie met the range of variables limited by the hypothesis (Z-score was between ±1.96), as shown in

Table 4. Normal distribution test results of three crops of ramie.

Parameters		First Crop Ramie	Second Crop Ramie	Third Crop Ramie
Skewness	statistics	−0.075	−0.184	−0.302
	standard error	0.241	0.241	0.241
	Z-score	−0.311	−0.763	−1.253
Kurtosis	statistics	−0.128	−0.249	0.023
	standard error	0.478	0.478	0.478
	Z-score	−0.268	−0.521	0.048

Note: Skewness Z-score = skewness value/standard error, kurtosis Z-score = kurtosis value/standard error.

, and the distribution of the three crops of ramie was normal.

The results of the normality test showed that the field distribution of ramie satisfied normal distribution.

3.3. Normal Distribution Parameters

According to the calculation results using SPSS software, the mean and standard deviation data of three crops of ramie were obtained as shown in

Table 5. Normal distribution parameters of three crops of ramie.

Parameters	First Crop Ramie	Second Crop Ramie	Third Crop Ramie
Mean value	72.34	72.74	72.42
standard deviation	2.026	2.043	2.257

.

3.4. Feeding Quantity Model of Ramie Harvester

As can be seen from the above table, the normal distribution parameters of the three crops of ramie are relatively close, and we assumed that the sample variance was equal to the population variance to verify whether there were differences among the three crops of ramie. At the test level of α = 0.05, according to the normal distribution table, the critical value U_0.025 = 1.96.

$$U_{1-2}=\frac{\left({\overline{X}}_2-{\overline{X}}_1\right)}{\sqrt{\frac{{\sigma }_1^2}{n_1}+\frac{{\sigma }_2^2}{n_2}}}=\frac{\left(72.74-72.34\right)}{\sqrt{\frac{{2.043}^2}{100}+\frac{{2.026}^2}{100}}}=1.39<U_{0.025}$$

(1)

$$U_{1-3}=\frac{\left({\overline{X}}_3-{\overline{X}}_1\right)}{\sqrt{\frac{{\sigma }_1^2}{n_1}+\frac{{\sigma }_3^2}{n_3}}}=\frac{\left(72.42-72.34\right)}{\sqrt{\frac{{2.257}^2}{100}+\frac{{2.026}^2}{100}}}=0.26<U_{0.025}$$

(2)

$$U_{2-3}=\frac{\left({\overline{X}}_2-{\overline{X}}_3\right)}{\sqrt{\frac{{\sigma }_2^2}{n_2}+\frac{{\sigma }_3^2}{n_3}}}=\frac{\left(72.74-72.42\right)}{\sqrt{\frac{{2.257}^2}{100}+\frac{{2.043}^2}{100}}}=1.05<U_{0.025}$$

(3)

After examination, it can be concluded that there are no significant differences among the three crops of ramie. The data of the three crops of ramie were collected to form an annual ramie date, and a normality test was conducted on the annual ramie date.

3.4.1. Normality Test

A normality test was carried out on the annual ramie date.

A graphic qualitative judgment of the annual ramie is shown in Figure 6.

In Figure 6a, the abscissa is the ramie number and the ordinate is the ramie frequency. It can be seen that the shape of the histogram drawn is roughly the same as that of the corresponding normal distribution curve, and it can be basically judged that the data follow the normal distribution. In the Q–Q/P–P plot above, the points approximately revolve around a straight line, and it can be roughly judged that the data present an approximate normal distribution.

The skewness and kurtosis normality test is a very practical normality test method.

Table 6. Normal distribution test results of annual ramie.

-	Skewness			Kurtosis
	Statistics	Standard Error	Z-Score	Statistics	Standard Error	Z-Score
Ramie	−0.203	0.141	−1.440	−0.106	0.281	−0.377

Note: Skewness Z-score = skewness value/standard error, kurtosis Z-score = kurtosis value/standard error.

. shows the normal distribution test results of the annual ramie.

Under the test level of α = 0.05, the skewness Z-score and kurtosis Z-score of three crops of ramie all met the range of variables limited by the hypothesis (Z-score was between ±1.96), and the ramie number followed the normal distribution.

3.4.2. Normal Distribution Parameters and Probability of Ramie Plant Range

According to the calculation results of SPSS software, the mean and standard deviation data of the annual ramie were obtained as shown in

Table 7. Normal distribution parameters of annual ramie.

-	Mean Value	Standard Deviation
Ramie	72.5	2.111

.

The number of ramie plants per unit area X obeys the normal distribution N (72.5, 4.456), and the distribution function of X has the following relationship with the standard normal distribution function:

$$\mathrm{F}\left(x\right)=\underset{-\infty }{\overset{x}{{\displaystyle \int }}}\frac{1}{\sqrt{2\pi }\sigma }{e}^{-\frac{\left(t-{\mu }^2\right)}{2{\sigma }^2}}dt=\mathsf{\Phi }\left(\frac{x-\mu }{\sigma }\right)=\mathsf{\Phi }\left(\frac{x-72.5}{2.111}\right)$$

(4)

The probability of ramie plant range was calculated according to the above formula, and is shown in

Table 8. Probability of ramie plant range.

Ramie Plant Range	(72, 73)	(71, 74)	(70, 75)	(69, 76)	(68, 77)	(67, 78)
Probability/%	18.96	52.22	76.2	90.3	96.68	99.1

.

3.5. Kinematic Analysis of Reciprocating Cutter

Figure 7 shows the kinematic analysis of the crank-link mechanism and cutting knife. The mechanical diagram of the cutting knife is shown in Appendix B. This paper analyzes the trajectory of the cutter movement.

3.5.1. Cutting Knife Stroke

Cutting knife stroke is calculated by the following equation.

$$S=2r$$

(5)

where S is the cutting knife stroke, r is the crank radius.

3.5.2. Displacement of Cutting Knife

Displacement of cutting knife is calculated by the following equation.

$$x=\mathrm{L}+r-\left(\mathrm{lcos}\alpha +\mathrm{rcos}\omega t\right)$$

(6)

where L is the connecting rod length.

Because r is much less than l, and α is close to 0°, so

$$x=r\left(1-\cos \omega t\right)$$

(7)

Take the derivative with respect to time t, the speed of the cutter v can be obtained:

$$v_f=\frac{dx}{dt}=\omega r\sin \omega t$$

(8)

The derivative again gives the acceleration of the cutter a:

$$\mathrm{a}=\frac{dv}{dt}={\omega }^{2}r\cos \omega t$$

(9)

3.5.3. Absolute Motion Trail of Cutting Knife

The absolute motion of the reciprocating cutter is a compound motion, one is the linear motion of random constant speed forward, the other is the reciprocating motion of the blade relative to the frame. The equation for the machine’s constant linear motion is as follows.

$$\mathrm{y}=v_{m}t$$

(10)

where $v_m$ is the forward speed of the machine, t is time, y is the distance the machine travels in time t.

When the crank turns half a turn, the cutter moves horizontally for a stroke S, and the cutter moves with the harvester for a distance H, called the advance distance.

$$H=\frac{60v_m}{2n}=\frac{\pi }{\omega }{v}_m$$

(11)

where H is the advance distance, mm; v_m is the forward speed of the machine, m/s; ω is the angular speed of the crank, rad/s; n is the revolving speed of the crank, r/min.

So, let us substitute Formula (2) into Formula (1)

$$\mathrm{y}=\frac{H}{\pi }\omega ·t=\frac{H}{\pi }\Phi$$

(12)

$$\Phi =\arccos \frac{r-x}{r}$$

(13)

So,

$$\mathrm{y}=\frac{H}{\pi } \arccos \frac{r-x}{r}$$

(14)

The motion trajectory function of another set of cutters is as follows.

$$\mathrm{y}=\frac{H}{\pi } \arccos \frac{r+x}{r}$$

(15)

This is the equation of the absolute motion of the cutter, and its trajectory is an arc-cosine curve.

Through the integral operation, the area of the missing cutting area, the single cutting area and the repeat cutting area can be obtained.

$${{\displaystyle \int }}^{ }\frac{H}{\pi } \arccos \frac{r-x}{r}dx=-\frac{rH}{\pi }\left(\frac{r-x}{r}\arccos \frac{r-x}{r}-\sqrt{1-{\left(\frac{r-x}{r}\right)}^2}+\mathrm{C}\right)$$

(16)

$${{\displaystyle \int }}^{ }\frac{H}{\pi } \arccos \frac{r+x}{r}dx=\frac{rH}{\pi }\left(\frac{r+x}{r}\arccos \frac{r+x}{r}-\sqrt{1-{\left(\frac{r+x}{r}\right)}^2}+\mathrm{C}\right)$$

(17)

As can be seen from the above formula, when other conditions are the same, the absolute motion trajectory of the cutter and the distribution of the cutting area are directly related to the advance distance H. The cutting diagram of double-acting cutter at different advance distances is shown in Figure 8 below.

The relationship between the speed of the cutter and the forward speed of the machine can be expressed by the cutting speed ratio K:

$$K=\frac{v_f}{v_m}=\frac{Sn/30}{Hn/30}=\frac{S}{H}$$

(18)

where $v_f$ is the average speed of the cutter, m/s; S is the cutting stroke of the double movable blade cutter, mm.

The cutting performance is strongly influenced by the cutting speed ratio. When the cutting speed ratio K is too small, it will lead to high miss cutting rate and unstable stubble height; when the cutting speed ratio K is too large, there is a high probability of repeated cutting, resulting in power waste.

3.6. Analysis on the Results of Ramie Field Harvesting Experiment

A ramie field harvesting experiment was carried out as described in Section 2.2 above, and the results of the ramie field harvest are shown in the following

Table 9. Results of ramie field harvest.

Forward Speed vm (m/s)	Cutting Speed Ratio K	Experimental Value		Calculated Value
		Feed Quantity (Plant/s)	Miss Cutting Rate/%	Feed Quantity (Plant/s)	Miss Cutting Rate/%
0.8	1.75	36.7 ± 1.059	2.183 ± 0.1172	(33.5,39)	(1.9,2.4)
0.85	1.65	38.8 ± 1.135	2.481 ± 0.0999	(35.6,41.4)	(2.1,2.7)
0.9	1.56	41.3 ± 1.252	2.748 ± 0.0629	(37.7,43.8)	(2.2,2.9)
0.95	1.47	40.7 ± 1.059	3.049 ± 0.0950	(39.8,46.3)	(2.4,3.3)
1	1.4	45.7 ± 1.160	3.318 ± 0.1311	(41.9,48.7)	(2.7,3.8)

.

The experimental value of feed quantity and mis-cutting rate were in the range of the calculated value, showing that the prediction model has a good prediction effect. These methods can provide references to the control of feed quantity and mis-cutting rate.

4. Discussion

The target of ramie harvesting is the ramie stalks. Since ramie is a shrub plant, although the row spacing of ramie roots is fixed at the time of transplanting, the distribution of ramie stalks is not uniform at the time of harvesting, which makes it difficult to cut and transport ramie stalks, and the variation in feeding volume leads to under-powering or over-powering of the cutting and transporting parts. The main cultivation area of ramie is the hilly mountainous area in southern China. The mechanized harvesting technology of ramie is not mature, and there is no research related to the field of the distribution of ramie stalks.

In this paper, the type of ramie stalk field distribution was determined as normal distribution by statistical methods such as normality testing and hypothesis testing, combined with the analysis of cutter motion to determine the prediction model of mis-cutting rate and feed quantity, and with the conduction of a ramie mechanized harvesting test to verify the reliability of the model. This study can better distribute the harvester power, reduce harvesting losses, and provide a basis for intelligent decision making for ramie harvesters.

This study mainly discusses the spatial distribution of stalks under the current common ramie cropping patterns, but other cropping patterns or other shrub crops can be studied along the lines of this paper to construct a prediction model for feed quantity and mis-cutting rate, so as to improve the efficiency of harvester power utilization and reduce harvesting losses.

5. Conclusions

In this study, the ramie plant field distribution model based on statistical analysis was established. Based on analysis of the absolute motion trail of the ramie harvester cutting knife, the calculation equation of the missing cutting area was established. Verified by ramie field harvesting, it showed that the prediction model of feed quantity and mis-cutting rate has good prediction effect.

(1)

The number of ramie stalks per unit area (1.6 m × 1.6 m) X obeys the normal distribution N (72.5, 4.456), when the ramie plant number range is in (67, 78), the probability is 99.1%. At this probability level, according to the ramie harvester forward speed, the feed quantity of the ramie harvester in different forward speeds (0.8–1 m/s) was determined.

(2)

The absolute motion trail of the ramie harvester cutting knife is analyzed and the motion equation is obtained. The calculation equation of the area of the missing cutting area is obtained by integral operation, as shown in Formula (15), and then the prediction model of the mis-cutting rate is obtained, as shown in Formulas (16) and (17).

(3)

The results of the ramie field harvest were all within the predicted range, showing that the prediction model of the feed quantity and mis-cutting rate was effective. These methods can provide references to the control and optimization of ramie harvester parameters, improve the efficiency of harvester power utilization, and reduce harvesting losses.

(4)

In this study, only the spatial distribution model of ramie stems under common ramie cropping patterns was investigated. However, other cropping patterns and mechanized harvesting studies of bush crops can also refer to the research ideas in this paper.