Application of Grey Relational Analysis and Multiple Linear Regression to Establish the Cutting Force Model of Oil Peony Stalk

Du, Zhe; Zhang, Liyuan; Xie, Xiaolin; Li, Denghui; Li, Xinping; Zhang, Zhihong; Pang, Jing

doi:https://doi.org/10.1155/2022/2341766

Mathematical Problems in Engineering

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Abstract Introduction Materials and Methods Results and Discussion Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2022 | Article ID 2341766 | https://doi.org/10.1155/2022/2341766

Application of Grey Relational Analysis and Multiple Linear Regression to Establish the Cutting Force Model of Oil Peony Stalk

Zhe Du,^1,2Liyuan Zhang,¹Xiaolin Xie,¹Denghui Li,¹Xinping Li,¹Zhihong Zhang,¹and Jing Pang¹

Academic Editor: Georgios I. Giannopoulos

Received10 Jan 2022

Accepted15 Mar 2022

Published28 Apr 2022

Abstract

Oil peony is an important oil crop, which has high quality and oil content. In order to improve the cutting quality and harvest efficiency of oil peony, the cutting equipment of the pruning machine and harvester is a key component. Also, the accurate prediction of cutting force of oil peony stalk is one of the essential processes for the design of the cutting equipment. In this article, to accurately predicted the cutting force of the stalk, the physical property parameters and chemical components were considered as influencing factors, which were used to establish the model of mechanical property parameter of oil peony stalk. The physical property parameters of oil peony stalk included the stalk diameter, internode distance, fresh weight, dry weight, relative moisture content, volume, fresh density, and dry density. The chemical components of the stalk were cellulose, hemicellulose, and lignin. Besides, the modeling methods, which were the partial least squares regression (PLSR), principal component analysis (PCA) couple with multiple linear regression (MLR), and grey relational analysis (GRA) couple with MLR, were used to optimize the multiple parameters (physical property parameters and chemical components). The results showed that the internode distance and relative moisture content had significant effects on the cutting force of oil peony stalk. The and values of the GRA (0.5) + MLR method were 0.801 and 0.820, and RMSEC and RMSEP values were 2.862N and 4.715N, respectively. Consequently, the GRA + MLR method could be used to predict the cutting force of oil peony stalk, which was an important basis for the design of precision cutting equipment.

1. Introduction

Peony (Paeonia suffruticosa Andr.) is an unique perennial deciduous shrub plant in China. It is not only a significant economic crop but also a new woody oil crop [1, 2]. As a new oil economic crop, the characteristics of oil peony seeds are high oil content of 24.12%–37.83% and high quality of unsaturated fatty acid content of 92.26% [3]. In particularly, the contents of α-linolenic acid, oleic acid, and linoleic acid of peony seed oil are 43.18%, 21.93%, and 27.15%, respectively. The α-linolenic acid is praised as “blood nutrient and plant brain gold” by the World Health Organization (WHO), Food and Agriculture Organization of the United Nations (FAO) [4, 5]. Based on the advantages of the rich nutrition and high yield of peony seed oil, the vigorous development of oil peony could alleviate the daily supply of edible oil. In recent years, although the peony seed oil industry has developed well and the planting area is increasing, there are some problems such as the low harvest efficiency and short harvest time in the development of oil peony [6]. In order to solve the above problems, the major challenge of oil peony industry development is to research and develop the high-efficiency cutting equipment of the pruning machine and harvester [7]. Also, the cutting quality and harvest efficiency of the cutting equipment is significantly affected by the mechanical properties of oil peony stalk. Due to different woody structure and biomass values of oil peony stalk, the existing cutting equipment has no high-quality and high-effect cutting effect [8, 9]. Therefore, the study of the mechanical property of oil peony stalk is the prerequisite to design the effective and efficient cutting equipment of pruning machine and harvester of oil peony.

The calculation and prediction of the mechanical property of the stalk is one of the essential processes to accurate harvest. At present, there are much literature on the calculation and prediction of the mechanical properties of crops, such as rice, maize, and wheat. Zhou et al. calculated the anisotropic elastic properties of rice stalk with the multiscale simulation [10]. The effect of moisture content of maize grains on the physical and mechanical properties was studied by Mousaviraad and Tekeste [11]. However, compared with these crops, the study of mechanical properties on oil peony stalk needs to be increased [12, 13]. Liu et al. reported the effect of geometric parameters and cutting speed of cutter on cutting force of oil peony. They found that the cutting speed was directly proportional to the cutting force under the condition of the 10° sliding-cutting angle and 20° blade angle [13]. Similarly, Liu et al. established the constitutive model of oil peony stalk and simulated the cutting process of the stalk with ANSYS/LS-DYNA software [14]. Ji et al. found that the loading rate of the cutter, moisture content, size and shape had a significant effect on the breaking force of oil peony seed. The relationship between the breaking force of oil peony seed and related factor was established [15]. In addition to the parameters of the cutting equipment, the mechanical properties of the stalk were varied with the change of the stalk diameter, internode distance, weight, and moisture content [16, 17]. Other engineering property parameters of oil peony stalk, for example, the chemical components of hemicellulose, cellulose, and lignin, were different with other crops, which was worth discussing. The relationship model among the mechanical property, chemical components of hemicellulose, cellulose, and lignin could be established with the multiple linear regression (MLR) method [18–20].

There are many methods to establish the model of the mechanical property parameters. Fiaz et al. used a fuzzy algorithm to evaluate the effect of the loading rates and moisture contents on the mechanical property parameters of wheat stalk [21]. To investigate the temporal dynamics of the cutting force of rice stalk, Zhou et al. studied the correlation model between the cutting force and stalk diameter, between the cutting force and moisture content, and between the cutting force and chemical compositions by MLR method [22]. Hirai et al. established the mechanical model of crop to analyze the mechanical interaction between a combine harvester reel and the stalk [23]. Besides, the common modeling methods included the nonlinear regression (NR), grey relational analysis (GRA), stepwise regression (SR), principal component analysis (PCA), and partial least squares regression (PLSR). In particularly, the GRA method was an analytical method, which had been used in the agronomic traits, mechanical property parameters, harvest index, and physiological and biochemical traits [24, 25]. Based on the GRA method, Jin et al. assessed the leaf moisture content and water vegetation indexes of winter wheat. They found that the estimation accuracy of leaf moisture content could be improved with the GRA method [26]. The constitutive modeling of chemomechanical properties of soybean seed could be obtained through the GRA method [27].

The clear understanding of the mechanical property of oil peony stalk would be beneficial for the accuracy design of cutting equipment of pruning machine and harvester on oil peony. However, there were little literature on the mechanical property of oil peony stalk. The specific objective of this study was to analyze and evaluate the effect of physical property parameters (stalk diameter, internode distance, fresh weight, dry weight, relative moisture content, volume, fresh density, dry density) and chemical components (cellulose, hemicellulose, lignin) on the mechanical property parameter (cutting force) of oil peony stalk. Besides, the PLSR, PCA + MLR, and GRA + MLR methods were used to establish the cutting force model of oil peony stalk. This study could provide a theoretical basis for calculating and predicting the cutting force of woody crops similar to oil peony.

2. Materials and Methods

2.1. Material Preparation

Fengbai variety of oil peony with high oil content, good quality, and high yield was selected as test sample. The samples were obtained from the peony garden of Henan University of Science and Technology at Luoyang, China (longitude 112.42°E, latitude 34.60°N). The oil peony stalks were selected randomly from oil peony tree, which had good growth and no mechanical damages. The stalk samples are manually picked in August 2021, the picking and cutting position of the stalk are shown in Figure 1. The picking position should be lower than the cutting position. Also, the cutting position of oil peony stalk was between the peony pod and first leaf; the leaf blades and peony pod were removed prior to measure.

Based on the literature and previous research, there were many significant factors affecting the mechanical property of the stalk. The influencing factors were the stalk diameter, internode distance, fresh weight, dry weight, relative moisture content, volume, fresh density, dry density, cellulose content, hemicellulose content, and lignin content [28, 29]. Firstly, the mechanical property of the stalk was measured in this article, and then, the chemical composition was analyzed after drying. In the test of chemical composition, the main chemical medicines included HCI, Ca(NO₃)₂, CH₃COOH, and H₂SO₄.

2.2. Testing Apparatus

The mechanical property of oil peony stalk was the cutting force of first internode at the time of harvest. The cutting force was measured by a texture tester TA-XT plus (Stable Mycro System, UK). This device had a wide moving range of 0.1∼295 mm with 0.025% force measurement accuracy. The cutting mode of oil peony stalk in the texture tester is shown in Figure 2. The loading rate of 1.5 mm/s was set in the cutting test.

For the physical property of oil peony stalk, the required test apparatus included the LE204E scale (Mettler, Switzerland), drying case, and vernier caliper. The test apparatus of the chemical composition included the full-wavelength microplate spectrum (Spectra Max190, USA), HWS-series electric thermostatic water bath, and digital bottle mouth titrator.

2.3. Analysis of Physical and Chemical Property Parameters

2.3.1. Physical Property Parameters

The physical property of the stalk diameter, internode distance, fresh weight, dry weight, relative moisture content, volume, fresh density, and dry density had important influence on the mechanical property of oil peony stalk. In the physical property parameters, the stalk diameter and internode distance were measured by the vernier caliper. The fresh weight and dry weight of the stalk could be obtained with the drying case and scale. The relative moisture content, W, was calculated by the below equation:where, G_f is the fresh weight in ; G_d is the dry weight in .

The stalk volume, V, was calculated using the following equation:where, l is the stalk internode distance in mm; D is the stalk diameter in mm.

The fresh density and dry density, ρ_f and ρ_d, were calculated from the following expression [30]:

2.3.2. Chemical Components

Hemicellulose, cellulose, and lignin were the main components of the stalk cell wall, which affected the mechanical property of oil peony stalk. To analyze the chemical components of oil peony stalk, the hydrochloric acid hydrolysis, concentrated sulfuric acid, and anthrone sulfate colorimetry methods were used to determine the content of hemicellulose, cellulose, and lignin [31]. In the test of chemical composition, the following formulas were used.where, y_h is the hemicellulose content in %; y_r is the reduction of sugar content in %; 0.9 is the conversion coefficient of reducing sugar to hemicellulose; y_c is the cellulose content in %; A is the cellulose content value in the colorimetric tube checked on the standard curve in mg; D_c is the extraction multiple number; m_c is the sample weight in mg; y_l is the lignin content in %; K is the sodium thiosulfate concentration in mol/L; a is the volume of sodium thiosulfate consumed in blank titration in ml; b is the volume of sodium thiosulfate consumed by titration solution in ml; and n_c is the sample mass in .

2.4. Model Establishment Method

2.4.1. Model Analysis

The modeling purpose was to describe the relationship between the physical quantities and their related variables through the mathematical methods. There were many common modeling methods such as PLSR, PCA, GRA, and MLR used in this article. In particularly, PLSR method is a mathematical optimization technique, which finds the best function matching of data by minimizing the sum of squares of errors. When a small amount of data have multicollinearity, PLSR method could provide a better functional relationship. PCA method is a multivariate statistical analysis method that selects some important variables by the linear transformation of multiple variables. GRA method is an optimized and simplified technique for the model parameters based on the grey system theory originally, which solves the complex relationship among multiple factors [32]. PCA and GRA method could be used to simplify the model parameters. Based on the model parameters, MLR method could be applied to build a mathematical model, which describes the relationship among multiple variables.

In this article, the PLSR, PCA + MLR, and GRA + MLR methods were used to establish the cutting force model of oil peony stalk. PCA + MLR method was employed with the threshold value of 4%. When the GRA + MLR method was taken, the threshold values were the grey relational grade (GRG) of 0.5 and 0.7, respectively. To compare the fit goodness of different methods, the determination coefficient of , , and root-mean-square error of RMSEC and RMSEP were applied. The and RMSEC were represented the determination coefficient and root-mean-square error of calibration. Besides, the and RMSEP were represented the determination coefficient and root-mean-square error of prediction; 15 and 5 group data were chosen as the calibration and prediction data-set to establish the model. And 5 group data were used to compare the correlation between the predicted and actual values of optimal model.

2.4.2. Grey Relational Analysis Method

In the GRA method, the cutting force and the influencing factors were selected to be a grey system. The cutting force (x₀) of oil peony stalk was the reference sequence, the stalk diameter (x₁), internode distance (x₂), fresh weight (x₃), dry weight (x₄), relative moisture content (x₅), volume (x₆), fresh density (x₇), dry density (x₈), cellulose content (x₉), hemicellulose content (x₁₀), and lignin content (x₁₁) were the comparison sequences. The calculation process of GRA method was as follow [33, 34].

The first step was the data preprocessing. Because the units of the influencing factors were different, the normalization process, defined as the following equation, was necessary.where, X_t(k) is the normalized value; x_t(k) is the initial measurement value; t is the trial number, from 1 to 15; k is from 0 to 11.

The second step was the determination of deviation sequence, △x_t(i) (i = 1 − 11).

The third step was the determination of the grey relational coefficient (GRC), which was calculated by the following equation.where, Y_t(i) is the GRC value; μ is the distinguishing coefficient, 0.5.

The fourth step was to calculate the average sum of GRC values. The GRG value was the average sum of GRC value, which was calculated with the following equation.where, r_i is the GRG value; n is the number of GRC value.

The GRC values and corresponding GRG values were obtained by the equations. The influence degree of comparison sequences on reference sequence could be determined with the comparison of the GRG value. The correlation degree was higher with GRG value.

3. Results and Discussion

3.1. Mechanical Property Parameters of Oil Peony Stalk

The mechanical and physical property parameters of oil peony stalk included cutting force, stalk diameter, internode distance, fresh weight, dry weight, relative moisture content, volume, fresh density, and dry density. The average values of mechanical and physical property parameters are shown in Table 1. The range of cutting force on oil peony stalk was from 52.331 to 97.316N with a mean value of 73.227N. The stalk diameter, internode distance, fresh weight, and dry weight ranged from 3.530 to 5.030 mm, from 74.100 to 141.690 mm, from 0.530 to 1.810 g, from 0.280 to 0.850 g, respectively. Also, the mean values of these parameters were 4.474 mm, 98.198 mm, 1.067 g, and 0.542 g, respectively. Based on equations (1)–(4), the values of relative moisture content, volume, fresh density, and dry density were calculated. The range of relative moisture content, volume, fresh density, and dry density were from 42.188% to 53.261%, from 0.768 to 2.661 cm³, from 0.507 to 0.819 g/cm³, from 0.274 to 0.611 g/cm³, respectively. Also, their mean values were 48.572%, 1.587 cm³, 0.683 g/cm³, and 0.358 g/cm³, respectively. Figure 3 shows the value variation of mechanical and physical property parameters with different numbers. Compared with the values of the cutting force, internode distance, and relative moisture content, the variation ranges of the parameters, such as diameter, fresh weight, dry weight, volume, fresh density, and dry density, were small. Figure 3(a) and Table 1 show that the numerical change of internode distance and relative moisture content has an important influence on the variation trend of cutting force. The numerical variation law of diameter, fresh weight, dry weight, and volume is basically the same, which is similar to that of cutting force, as shown in Figure 3(b) and Table 1.

(a)

(b)

Based on previous studies, it could be found that the physical morphological characteristics of stalk were very important for its mechanical properties. In order to measure the mechanical property of the stalk, the relationship between the mechanical properties and physical properties should be studied [16, 17]. These viewpoints could also be verified from this article. The numerical values of mechanical properties were closely related to some physical numerical parameters. In this article, the numerical variation ranges of internode distance, relative moisture content, and cutting force were large, whereas the numerical variation ranges of diameter, fresh weight, dry weight, volume, fresh density, and dry density were small. In addition, due to the viscoelastic property of oil peony stalk, the plant variety and species had a great influence on the physical and mechanical properties of the stalk. Yisa et al. found the average cutting force of 68.99N on the cassava root [35]. The obtained values were different from those of Oyefeso et al. who reported the cutting force of cocoyam to be within the range of 63.99 to 114.09N [36]. Accordingly, the physical and mechanical property parameters of plant were varied with the change of plant variety [37]. However, this article only uses one oil peony variety to measure the physical and mechanical property parameters, which is not comprehensive. In the future, it is necessary to study the physical and mechanical property parameters of multiple varieties for the optimization of cutting equipment parameters.

3.2. Chemical Components of Oil Peony Stalk

In addition to the mechanical and physical properties, the inherent characteristics of oil peony stalk were also included the chemical property. The chemical components of oil peony stalk mainly included the cellulose, hemicellulose, and lignin. Based on the equations (5)–(7), the mass fraction of cellulose, hemicellulose, and lignin content of oil peony stalk are calculated, as shown in Table 2. The mass fraction of cellulose and hemicellulose content were ranged between 15.198% and 19.616%, between 15.736% and 18.097%, respectively. Their average values were 17.331% and 16.898%. This compared with the mean value of 24.079% for the mass fraction of the lignin content in the range of 21.047%–25.982%. As shown in Figure 4, the average mass fraction of lignin content is the highest, next the hemicellulose content, and the cellulose content is the lowest. Because oil peony was a woody oil crop, its mass fraction of the lignin content was more than that of the cellulose and hemicellulose content. In the mass fraction, the cellulose and hemicellulose content of the stalk were similar. Cellulose, hemicellulose, and lignin content were the main components of stalk cell wall, which had related to physical and mechanical properties of stalk. Similar studies were reported with Du et al. and Huang et al. [6, 38].

3.3. Grey Relational Analysis

In order to unify the units, the corresponding normalized values of cutting force and main influencing factors were obtained using equation (8). The results are shown in Table 3. To compare the experimental and ideal data, the normalized data was transformed into deviation sequence by equation (9). Table 4 displays the absolute difference values between the cutting force and indicators. Then, the GRC value was calculated by equation (10). Finally, the GRG value of the influencing factors on cutting force could be computed with equation (11). The GRG value was the average GRC value, which represented the correlation between the cutting force and influencing factors. The higher the GRG value, the stronger the correlation.

The GRG values of influencing factors on cutting force of oil peony stalk are summarized in Table 5. The range of 0.432–0.764 was the relational grade of influencing factors on cutting force. The order for GRG value was the relative moisture content, internode distance, lignin content, cellulose content, hemicellulose content, stalk diameter, volume, fresh weight, fresh density, dry weight, and dry density. When the selection of GRG value was greater than 0.5, the influencing factors were the relative moisture content, internode distance, lignin content, cellulose content, and hemicellulose content. When the GRG threshold was 0.7, the influencing factors were the relative moisture content and internode distance. In Table 5, the GRG value of the relative moisture content is 0.764, implying that the relative moisture content has a significant influence on cutting force. This reason might be the strong relevance between the relative moisture content and other physical properties, which was similar with the findings of Aydin and Arslan [37].

The mechanical property of oil peony stalk was affected by many factors, such as plant variety, sample location, stalk segment number, physical properties, chemical composite, and others [39]. But the variation trend of the mechanical property on oil peony stalk had no definite relationship with the physical property of weight, density, and chemical components. Thus, the influencing factors with little correlation were deleted to determine the model of cutting force based on this research. For different biological oil peony cultivars, there were some differences in plant characteristic (mechanical, physical, and chemical property parameters). The reason for the difference might be attributed to the individual characteristics, cultivation environment, regional difference, climate environment, and plant variety. In order to reduce the impact of individual characteristics, cultivation environment, regional difference, and climate environment on plant characteristics, numerous cutting experiments with multiple varieties should be carried out in the next research.

3.4. Model Establishment

There were three modeling methods, PLSR method, PCA + MLR method, GRA + MLR method, which was applied to establish the cutting force model of oil peony stalk. In PCA + MLR method, the most information (above 98.23%) of the whole indicators could be replaced by six influencing factors (stalk diameter, internode distance, fresh weight, dry weight, relative moisture content, and volume). When the GRA + MLR method was employed, the threshold values of 0.5 and 0.7 GRG values were used to establish the cutting force model. The model results with different methods are shown in Table 6. In GRA (0.5) + MLR method, the value was 0.801, which was the greatest than the value of other methods. Meanwhile, the RMSEC value was 2.862N. In the calibration model, the order of value was GRA (0.5) + MLR method, PCA + MLR method, PLSR method, and GRA (0.7) + MLR method. All values in prediction model were larger than 0.701, which had a significant fitting effect. Besides, the and RMSEP values of GRA (0.5) + MLR method were 0.820 and 4.715N.

Figure 5 shows that the relevance between the actual and predicted value of cutting force. In the regression fitting, the determination coefficient R² and RMSE values were 0.956 and 3.669N. The predicted value was very close to the actual value. In conclusion, the GRA (0.5) + MLR method could be used for the cutting force model, which was suitable for the estimation of cutting force.

The knowledge of mechanical property of stalk and grain was very important in designing and optimizing the cutting equipment, which was also highly useful in improving the work efficiency and harvest effect of cutting machines. Many studies had investigated the geometric, physical, chemical, and mechanical properties, such as diameter, shape, volume, density, fiber, force, and energy required, to achieve the purpose of the high-quality and high-effect cutting and harvesting [40–42]. The geometric, physical, and mechanical properties of oleifera seeds, jatropha seeds, rice stalk, sunflower stalk, and alfalfa stalk had been widely reported. Besides, the influence of chemical components and microstructure on mechanical property had also been studied. The above information of mechanical property, physical property, chemical property, and microstructure was meaningful for the design of a suitable harvesting equipment. In this study, due to the small amount of sample data and the use of only one test variety, the GRA + MLR model of cutting force has some limitations. The GRG value between the influencing factors (stalk diameter, inter-node distance, fresh weight, dry weight, relative moisture content, volume, fresh density, dry density, cellulose content, hemicellulose content, lignin content) and mechanical property parameter (cutting force) may be varied with the change of oil peony cultivar and sample number. Based on different GRG values, the model of the mechanical property parameters with different oil peony materials could be established. Therefore, for the establishment of a general cutting force model for the high-efficiency cutting equipment of oil peony stalk, the physical, chemical, and mechanical properties of more plant varieties and types need to be considered.

4. Conclusions

The purpose of this article was to examine the model of mechanical property parameter (cutting force) of oil peony stalk, which was the important basis for the accuracy design of cutting equipment of pruning machine and harvester on oil peony. The experiment results showed that the internode distance and relative moisture content had an obvious effect on the cutting force of stalk. The variation trend of the diameter, fresh weight, dry weight, and volume was basically the same as that of cutting force. The average mass fraction of lignin content of oil peony stalk was higher than that of hemicellulose and cellulose content. The order on GRG value of cutting force was the relative moisture content, internode distance, lignin content, cellulose content, hemicellulose content, stalk diameter, volume, fresh weight, fresh density, dry weight, and dry density. Based on the modeling methods of PLSR, PCA + MLR, and GRA + MLR, the influencing factors were applied to establish the model of cutting force. The values of , , RMSEC, and RMSEP of GRA (0.5) + MLR method were 0.801, 0.820, 2.862N, and 4.715N, respectively. The values of cutting force were better than these of other models. The GRA (0.5) + MLR method was suitable for the estimation and prediction of cutting force. Future research needs to consider the effects of internal and climatic factors, such as stalk microstructure and wind speed, on cutting force.

Data Availability

The raw data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This study was supported by the Henan Provincial Department of Science and Technology Research Project (212102110034) and National Natural Science Foundation of China (52105251).

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