Calibration of the contact parameters for soybean-bonded particle model based on DEM

Calibration of the contact parameters for soybean-bonded particle model based on DEM | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Calibration of the contact parameters for soybean-bonded particle model based on DEM Dandan Han, Qing Wang, Chao Tang, Wei Li, You Xu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3985360/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract To retrieve the simulation contact parameters of the soybean-bonded particle for an effective gas-solid two-phase flow coupling simulation analysis of the working procedure of the pneumatic seed-metering device, the angle of repose (AoR) and angle of stacking (AoS) from the physical seed-piling test were captured as the evaluation indexes. The Plackett-Burman test and the steepest ascent test were ratified to simplify the simulation analysis of the soybean-bonded particles, screening out the crucial influenced factors and centroids. The Box-Behnken response surface test was then implemented to identify the desired saliency factor values, and the universality of the calibrated contact parameters for soybean-bonded particles synthesized with varying fraction particle sizes was eventually confirmed. The results revealed that the effect of the static friction coefficient of soybean-plexiglass ( µ p−g ) on AoR was exceedingly significant, and that of the static and rolling friction coefficients of soybean-soybean ( µ p−p & C p−p ) was generally prominent. While it was abundantly clear that both µ p−p and C p−p supremely affected AoS. The optimal values determined by the Box-Behnken response surface test yielded ideal values of 0.0678 for µ p−p , 0.2453 for µ p−g , and 0.0079 for C p−p , culminating in an AoR of 28.32° and AoS of 28.76°, respectively. Based on the derived optimal simulation contact parameters, the maximal error between the simulated and measured values of AoR and AoS of soybean-bonded particles constructed with various fraction particle sizes was estimated to be 1.59%, implying that the calibrated contact parameters have a superior generality. The insights of this investigation can be effectively applied to the coupled simulation analysis of the pneumatic soybean seed-metering device’s operations, as well as a reference for other researchers to erect particle models for DEM simulation using the bonded particle method. soybean kernel discrete element method contact properties parameter calibration response surface methodology Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1 Introduction The computational fluid dynamics and discrete element method (CFD-DEM) coupling approach is frequently employed in engineering investigations as a numerical analytical tool for simulating multiphase flow [ 1 – 3 ]. The working process of the pneumatic seed-metering device typically involves a gas-solid two-phase flow motion [ 4 ], and the volume fraction of the mesh occupied by the particle model is required to be no more than 70% even if the Eulerian coupling model is utilized while performing the CFD-DEM coupling simulation on it [ 5 ]. Since the holes in the seed-metering device are required to be finely meshed and smaller in size than the seeds, it is challenging to satisfy the stipulation that the volume of the particle model is not over 70% of the minimized mesh volume of the chamber delineation [ 6 ]. The multi-sphere (MS) method has been extensively employed in agricultural engineering studies as an ordinary approach for designing particle models [ 7 – 9 ]. However, the particle model built with MS is regarded as a separate entity that participates in the subsequent simulation computations, and the volume of the MS particle is much larger than the divided mesh volume of the seed-metering device chamber, making it unsuitable for coupling simulation and analysis of the pneumatic seed-metering device’s service [ 10 ]. In contrast, the coupling simulation analysis of the pneumatic seed-metering device is better suited for the bonded particle model (BPM), which is comprised of several distinct fraction particles cemented by adhesive bonds [ 11 – 12 ]. It is stipulated that the fraction particles constituting the BPM can irrespectively organize the dimensions and then participate in the ensuing simulation computations. Moreover, it is relatively convenient to realize the maximal scale limitation of the Eulerian coupling model on the volume fraction of the mesh by dividing the mesh logically in the CFD domain [ 13 ]. However, there are certain discrepancies in the morphologies of BPM, MS particles, and authentic seeds, triggering an error between the contact parameters and the reality values. Hence, it is imperative to calibrate the contact parameters exploited in the CFD-DEM coupling simulation with the seed particle model created via the BPM method [ 14 ]. In terms of research on the calibration of particle contact parameters, Zhang et al. [ 15 ] synchronized the contact parameters of the maize-bonded particle created by BPM, and the results of the parameters calibrated (the static and rolling friction coefficients of maize-maize were 0.031 and 0.0039) differed significantly from the results of Wang et al. [ 16 ] on the calibrated contact parameters of maize particles created by MS (which were 0.182 and 0.051). Therefore, it is extremely essential to calibrate the contact parameters of the soybean-bonded particle. Currently, the soybean particle model derived from MS has been applied in numerous studies on the calibration of soybean contact parameters [ 17 – 23 ]. Despite the results of the proceeding investigations are incompatible with the contact properties of the soybean-bonded particle model, the calibration process and experimental setup are highly beneficial and instructive for this study. The soybean seeds used for sowing were examined, and the BPM method was adopted to construct a soybean-bonded particle model. The angle of repose (AoR) and angle of stacking (AoS) were evaluated as indicators leveraging the seed-piling test. The prominent parameters and their centroids were sieved by the Plackett-Burman and steepest ascent tests. The multi-objective optimization was computed through the Box-Behnken response surface test to derive the mathematical model between the saliency parameters and each evaluation index. The preferred calibration parameter values were discovered and empirically confirmed. The purpose of this publication is intended to serve as a reference for other researchers attempting to construct particle models for DEM simulations using the BPM method. 2 Materials and methods 2.1 Test materials The soybean variety used in this experiment was “Zhonghuang 39”, which was measured in the early stages of the basic parameters, as displayed in Table 1 . The sizes of soybean seeds are unpredictable but tend to comply with a normal distribution. Soybean seeds have dimensions of 8.53 mm in length, 6.55 mm in width, and 7.31 mm in thickness, with an approximate globe shape and a sphericity of roughly 0.87. Table 1 Basic characteristic parameters of soybean seed Parameters Ranges Averaged values Moisture content (%) 11.21 ~ 13.47 12.66 ± 0.08 Density (g·cm − 3 ) 1.10 ~ 1.33 1.22 ± 0.08 100-grain weight (g) 24.33 ~ 25.98 25.13 ± 0.45 Length (mm) 6.91 ~ 10.7 8.53 ± 0.61 Width (mm) 5.13 ~ 7.37 6.55 ± 0.41 Thickness (mm) 5.85 ~ 8.13 7.31 ± 0.37 Sphericity 0.70 ~ 0.99 0.87 ± 0.03 2.2 Physical seed-piling test AoR and AoS are two macroscopic features describing the flow and frictional properties of granular materials, which pertain to the physical properties of the contacting apparatus and the particles [ 24 ]. Accordingly, they can be applied in the contact parameter calibration tests of discrete element models. The AoR and AoS were estimated by physical seed-piling tests. The testing apparatus was a rectangular container made of plexiglass plate with specifications of 300 mm long, 60 mm broad, and 300 mm high. The width of the discharging port was 40 mm. The baffle was initially canceled before the test, and soybean seeds of about 3/4 volume were distributed fairly into the upper container. The upper surface of the seeds pedestal was then flattened with a scraper. The seeds began to tumble and pile up under gravity as the baffle was swiftly eliminated, and until it stabilized. Two triangular seed heaps attended to be assembled symmetrically on both sides of the upper container, as represented in Fig. 1 . To alleviate the distortion caused by personal inspection, after the physical seed-piling test had culminated, Matlab (version R2021b) was programmed to denoise, grayscale, and binarize the captured images to obtain the boundary points, which were then linked together to construct the boundary curve of the seeds pile. Upon integrating the least squares approach to fit the curve, the tangent value of the actual AoR or AoS of the soybean seeds was estimated to be the slope of the straight line. Figure 2 depicts how angles are calculated. 2.3 Simulated piling test The technique of the simulated seed-piling test was supposed to be identical to the physical. According to the basic specifications of soybean seeds listed in Table 1 , the 3D model was rendered using Solidworks (version 2022) and imported as a .step file into EDEM (version 2018, DEM Solution Ltd., Edinburgh, Scotland). BPM was introduced in this paper to establish the soybean-bonded particle model. The radius of fraction particles adopted was 0.5 mm ( R f =0.5 mm) proportional to the volume of soybean seeds, and the total quantity was 236 ( N f =236), as stated in Fig. 3 . The geometric model of the seed-piling test apparatus and the DEM model of soybean seeds were loaded into EDEM. The adequate amount of soybean particles was adjusted such that 3/4 of the upper container was filled. The images were captured once each simulation test was done, and manipulated as well as deploying Matlab to yield the simulated AoR ( β ) and AoS ( γ ). 2.4 Calibration method for the contact parameters of soybean seeds 2.4.1 Plackett-Burman test Design-Expert (version 13.0, Stat-Ease Ltd., Godward St NE, Minneapolis, USA) was instructed to design the Plackett-Burman (PB) test with the AoR, and AoS as response values, and the simulated factors with noteworthy effects were screened out. To identify the major variables modifying the AoR and AoS, eight input parameters for the DEM simulation were selected, accounting for the dynamics between seeds and seeds as well as seeds and the seed-metering device during the working process. Three dummy variables were set to facilitate error analysis. Each parameter was assigned two levels, namely high and low, denoted by codes + 1 and − 1, respectively. The limits of each parameter were configured after a thorough examination of the literature and numerous pre-tests, and the findings are listed in Table 2 . Table 2 Factors and levels of the Plackett-Burman test Notation Parameter Low level (-1) High level (-1) References ν p Poisson’s ratio of soybean seeds 0.08 0.41 [ 25 – 26 ] G p Shear modulus of soybean (MPa) 13.3 137.0 [ 25 , 27 ] e p−p Restitution coefficient of soybean-soybean 0.10 0.70 [ 28 , 29 ] e p−g Restitution coefficient of soybean- plexiglass 0.30 0.735 [ 30 – 32 ] µ p−p Static friction coefficient of soybean-soybean 0.001 0.50 [ 25 , 31 ] µ p−g Static friction coefficient of soybean-plexiglass 0.05 0.65 [ 27 , 31 ] C p−p Rolling friction coefficient of soybean-soybean 0.0001 0.08 [ 31 , 33 ] C p−g Rolling friction coefficient of soybean-plexiglass 0.005 0.09 [ 27 , 34 – 35 ] I、J、K Null 2.4.2 Steepest ascent test The elements that substantially alter the AoR and AoS were derived based on the results of the PB test and the steepest ascent test was then executed. The optimal range interval of the simulation test’s significance parameters was determined by integrating the relative error results, which were evaluated as an index between the simulation and practical test results. The equations for calculating the errors in AoR ( e AoR ) and AoS ( e AoS ) are steadily as follows: $${e_{AoR}}=\frac{{\beta - \theta }}{\theta } \times 100\%$$ 1 $${e_{AoS}}=\frac{{\gamma - \varphi }}{\varphi } \times 100\%$$ 2 Where θ and φ are the physical test’s AoR and AoS in (°), β and γ are the simulation test’s AoR and AoS in (°), e AoR and e AoS are the errors of AoR and AoS in %. 2.4.3 Response surface test The distinctive factors and their centroids were acquired by the PB and steepest ascent tests, and then the Box-Behnken response surface test was conducted. The test results were subjected to multiple regression analyses performed on the test data to establish the regression models of the saliency contact parameters with AoR and AoS, respectively. Based on the regression model and the measured AoR and AoS values, the optimal simulation parameters combination was ascertained by using the Optimization module in Design Expert software. 2.5 Generalized validation methods for simulation parameters The soybean particle constructed by the BPM method was composed of multiple isolated fraction particles wholly joined together by adhesive bonds, and the fraction particle can be uniquely sized and engaged in the subsequent simulation computations. On account of aspects like actual demand and computational speed, the soybean BPM model may need to be built with varying percent particle sizes in practical applications. Consequently, the radius of fraction particles was set to 0.4, 0.45, 0.55, and 0.60 mm under the realistic simulation prerequisite, and the BPM models of soybean seeds were established, correspondingly. The simulated seed-piling tests were executed with the calibrated contact parameters, and the results were compared to the measured values of AoR and AoS. 3 Results and discussion 3.1 Results of the physical piling test Ten iterations of the physical seed-piling test went through to mitigate the disparities in the data statistical results. The results of the physical seed-piling test were evaluated by calculating the average values of AoR and AoS obtained from ten repetitions, as shown in Table 3 . The average AoR of soybean seeds was finally derived to be 29.87°, with an average AoS of 28.80°. Table 3 Measured results of the physical seed-dropping test No. AoR (°) AoS (°) 1 29.76 28.46 2 27.69 28.94 3 28.62 29.33 4 28.04 28.71 5 27.62 28.25 6 29.64 28.38 7 29.25 28.73 8 27.57 28.11 9 27.88 29.43 10 27.70 29.68 Average 28.38 ± 0.872 28.80 ± 0.533 3.2 Plackett-Burman test results A total of twelve sets of tests were conducted with eight parameter variables selected for the PB test and three dummy variables assigned to aid in the error analysis. The design scheme and simulation results of the PB test are listed in Table 4 . Table 4 Design and results of Plackett-Burman test scheme No. Test factors AoR (°) AoS (°) ν p G p e p−p e p−g µ p−p µ p−g C p−p C p−g I J K 1 1 1 -1 1 1 1 -1 -1 -1 1 -1 38.76 35.23 2 -1 1 1 -1 1 1 1 -1 -1 -1 1 50.91 38.46 3 1 -1 1 1 -1 1 1 1 -1 -1 -1 33.76 29.47 4 -1 1 -1 1 1 -1 1 1 1 -1 -1 15.45 42.25 5 -1 -1 1 -1 1 1 -1 1 1 1 -1 39.00 33.79 6 -1 -1 -1 1 -1 1 1 -1 1 1 1 35.24 33.42 7 1 -1 -1 -1 1 -1 1 1 -1 1 1 15.70 42.79 8 1 1 -1 -1 -1 1 -1 1 1 -1 1 24.57 21.86 9 1 1 1 -1 -1 -1 1 -1 1 1 -1 10.36 32.43 10 -1 1 1 1 -1 -1 -1 1 -1 1 1 6.20 20.41 11 1 -1 1 1 1 -1 -1 -1 1 -1 1 10.14 34.22 12 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 5.67 21.05 The PB simulation test results were variance analyzed within Design-Expert, revealing the effect of each parameter as presented in Table 5 . Concerning AoR specifically, the effects of µ p−p ( P = 0.0116) and C p−p ( P = 0.0321) were generally exceptional, and µ p−g ( P = 0.0005) had a critically important effect. While extremely sizable effects of both µ p−p ( P = 0.0046) and C p−p ( P = 0.0098) were observed for AoS. The influence of other factors on AoR and AoS was not discernible ( P > 0.05). Accordingly, the three influential variables were quantified and optimized in the following steepest ascent test and response surface test. In case of other non-significant factors, the values were taken at the intermediate level of the PB test protocol, i.e., Poisson’s ratio ( ν p ) of soybean seeds was 0.245, shear modulus ( G p ) was 7.515×10 7 Pa, restitution coefficient of soybean-soybean ( e p−p ) was 0.4, restitution coefficient of soybean-plexiglas ( e p−g ) was 0.5175, and rolling coefficient of soybean-plexiglas ( C p−g ) was 0.0475. Table 5 Significance analysis of Plackett-Burman test parameters Sources AoR AoS Sum of squares df F value P value Significance Sum of squares df F value P value Significance Model 2537.61 8 39.86 0.0058 ** 627.56 8 11.93 0.0330 * ν p 30.66 1 3.85 0.1445 - 3.65 1 0.5555 0.5101 - G p 3.79 1 0.4758 0.5399 - 1.40 1 0.2131 0.6758 - e p−p 18.70 1 2.35 0.2228 - 5.10 1 0.7752 0.4434 - e p−g 3.70 1 0.4645 0.5444 - 1.78 1 0.2706 0.6389 - µ p−p 244.44 1 30.72 0.0116 * 386.47 1 58.79 0.0046 ** µ p−g 2099.34 1 263.83 0.0005 ** 0.0705 1 0.0107 0.9240 - C p−p 114.58 1 14.40 0.0321 * 227.59 1 34.62 0.0098 ** C p−g 22.41 1 2.82 0.1919 - 1.50 1 0.2279 0.6657 - Note: ** indicates that the impact is extremely significant ( P < 0.01), and * indicates that the impact is significant ( P < 0.05). An intuitive understanding of the significance ranking of all variables was provided in the Pareto chart, as well as the positive and negative effects on the evaluation indexes. It is evident from Fig. 4 that µ p−g , µ p−p , and C p−p have conspicuous positive effects on both AoR and AoS. Based on everything that preceded, the values of all three variables were oriented toward the ascending path during the steepest ascent test. 3.3 Steepest ascent test results To restrict the value ranges of the soybean seeds’ contact parameters, the steepest ascent test was conducted for the three genetically relevant factors. The results of the first steepest ascent test are listed in Table 6 . The AoR and AoS were progressively increasing along the climbing direction, while e AoR and e AoS were decimating before escalating. The e AoR was estimated to be the smallest at test number 3, whereas the e AoS was the least at test number 2, in which case the simulated values of both AoR and AoS were higher than the actual measured values. Table 6 Scheme and results of the first steepest ascent test No. µ p−p µ p−g C p−p AoR (°) e AoR (%) AoS (°) e AoS (%) 1 0.001 0.050 0.0001 5.99 -78.89 20.66 -28.26 2 0.084 0.148 0.0134 24.52 -13.60 30.19 4.83 3 0.167 0.246 0.0267 36.30 27.91 34.15 18.58 4 0.250 0.345 0.0400 42.95 51.34 35.34 22.71 5 0.333 0.443 0.0534 45.16 59.13 36.25 25.87 6 0.416 0.541 0.0667 47.27 66.56 37.69 30.87 7 0.500 0.640 0.0800 51.76 82.38 38.37 33.23 To further narrow down the range of optimal parameters, the second steepest ascent test was executed for µ p−g leveraging the simulation parameters of No. 2 (0.148) and No. 3 (0.246), µ p−p and C p−p with No.1 (0.001 and 0.0001) and No. 3 (0.167 and 0.0267), the results of which are provided in Table 7 . Table 7 exhibits that both e AoR and e AoS are noticeably miniaturized. Besides, e AoR was minimized at No. 5, while e AoS was ranked No. 3. Table 7 Scheme and results of the second steepest ascent test No. µ p−p µ p−g C p−p AoR e AoR AoS e AoS 1 0.0010 0.1480 0.0001 17.12 -39.68 20.66 -28.26 2 0.0342 0.1676 0.0054 20.84 -26.56 25.81 -10.37 3 0.0674 0.1872 0.0107 23.16 -18.39 29.73 3.23 4 0.1006 0.2068 0.0161 26.02 -8.32 31.72 10.14 5 0.1338 0.2264 0.0214 30.47 7.36 32.83 13.99 6 0.1670 0.2460 0.0267 36.30 27.91 34.15 18.58 Considering that the exceedingly prominent effect of µ p−g on AoR, and the generally discernible effect of µ p−p and C p−p on AoR but an incredibly impressive effect on AoS, it can be identified that the optimal interval for µ p−g was around No. 5, and µ p−p and C p−p were aligned near No. 3. Thus, to solicit the optimal parameter combinations, µ p−g , µ p−p , and C p−p were subjected to the following response surface test with centroids of 0.2264, 0.0674, and 0.0107, respectively. 3.4 Response surface test results 3.4.1 Box-Behnken Design Towards further investigating the relationship between AoR and AoS and µ p−g , µ p−p , and C p−p as well as identifying the optimal parameter combinations, the response surface test was carried out using Box-Behnken Design (BBD) based on the results of the PB and two steepest ascent tests. The codes and values of each simulation parameter are indicated in Table 8 . Table 8 Factors and codes of the BBD test Code Factors µ p−p µ p−g C p−p -1 0.0342 0.2068 0.0054 0 0.0674 0.2264 0.0107 + 1 0.1006 0.2460 0.0161 3.4.2 BBD test results The test protocol and results for the BBD test are listed in Table 9 , which was done in 5 replications totaling 17 simulations. Table 9 Factors and codes of the BBD test No. x 1 x 2 x 3 AoR (°) AoS (°) 1 -1.000 -1.000 0.000 24.54 27.13 2 1.000 -1.000 0.000 29.68 31.85 3 -1.000 1.000 0.000 27.40 28.57 4 1.000 1.000 0.000 30.66 29.52 5 -1.000 0.000 -1.000 24.46 26.53 6 1.000 0.000 -1.000 26.02 29.61 7 -1.000 0.000 1.000 26.10 27.43 8 1.000 0.000 1.000 30.46 30.71 9 0.000 -1.000 -1.000 25.22 27.56 10 0.000 1.000 -1.000 26.75 27.99 11 0.000 -1.000 1.000 28.55 30.29 12 0.000 1.000 1.000 31.87 29.64 13 0.000 0.000 0.000 27.39 29.91 14 0.000 0.000 0.000 27.90 30.10 15 0.000 0.000 0.000 27.45 29.73 16 0.000 0.000 0.000 28.16 29.30 17 0.000 0.000 0.000 27.83 29.76 Note: x 1 , x 2 , x 3 are the levels of µ p−p , µ p−g , C p−p , respectively. The variance analysis of the BBD test shown in Table 9 was performed using the software Design-Expert, and the results are given in Table 10 . Table 10 Variance analysis of the BBD test results Sources y AoR y AoS Sum of squares df F -value P -value Significance Sum of squares df F -value P -value Significance Model 69.82 9 26.95 0.0001 ** 30.76 9 20.37 0.0003 ** x 1 25.63 1 89.05 < 0.0001 ** 18.09 1 107.84 < 0.0001 ** x 2 9.44 1 32.79 0.0007 ** 0.1540 1 0.9181 0.3699 - x 3 26.39 1 91.68 < 0.0001 ** 5.09 1 30.33 0.0009 ** x 1 x 2 0.8836 1 3.07 0.1232 - 3.55 1 21.18 0.0025 ** x 1 x 3 1.96 1 6.81 0.0349 * 0.0100 1 0.0596 0.8141 - x 2 x 3 0.8010 1 2.78 0.1392 - 0.2916 1 1.74 0.2289 - x 1 2 1.08 1 3.76 0.0938 - 0.6611 1 3.94 0.0875 - x 2 2 2.91 1 10.10 0.0155 * 0.0390 1 0.2325 0.6444 - x 3 2 0.9671 1 3.36 0.1095 - 2.65 1 15.81 0.0053 ** Residual 2.01 7 1.17 7 Lack of Fit 1.60 3 5.12 0.0744 - 0.8237 3 3.13 0.1494 - Error 0.4165 4 0.3506 4 Cor Total 71.83 16 31.94 16 The regression fitting analysis of the BBD test results was performed to establish the regularity equations between y AoR , y AoS , and the respective factors: $$\left\{ \begin{gathered} {y_{AoR}}=27.75+1.79{x_1}+1.09{x_2}+1.82{x_3} - 0.47{x_1}{x_2}+0.7{x_1}{x_3}+0.4475{x_2}{x_3} - 0.5068{x_1}^{2}+0.8307{x_2}^{2} - 0.4792{x_3}^{2} \hfill \\ {y_{AoS}}=29.76+1.5{x_1} - 0.1387{x_2}+0.7975{x_3} - 0.9425{x_1}{x_2}+0.05{x_1}{x_3} - 0.27{x_2}{x_3} - 0.3963{x_1}^{2} - 0.0963{x_2}^{2} - 0.7937{x_3}^{2} \hfill \\ \end{gathered} \right.$$ 3 Where y AoR is the angle of repose in (°), and y AoS is the angle of stacking in (°). The variance analysis results of the BBD test reveal that the P values of the models examined in the regression Eq. ( 3 ) are all extremely significant, demonstrating that the test protocol is well-designed. Since the P values for the lack of fit terms are more than 0.05, i.e. not signed, which demonstrates that the regression equations are well-fitted to the practical scenario, and can be used for test predictions and analyses. The impacts of µ p−p ( x 1 ), µ p−g ( x 2 ), and C p−p ( x 3 ) were extremely significant for AoR, µ p−p ( x 1 ), and C p−p ( x 3 ) interactions ( x 1 x 3 ), as well as x 2 2 were moderately prominent, while the effects of other factors were not notable. For AoS, the influence of µ p−p ( x 1 ), C p−p ( x 3 ), µ p−p ( x 1 ) and µ p−g ( x 2 ) interaction ( x 1 x 2 ), and x 3 2 was supremely noteworthy, while the influence of other factors was not particularly noticeable. 3.4.3 Effects of interactions on evaluation indicators The results of the BBD test were processed to extract the response surface contours of the interactive effects of µ p−p ( x 1 ), µ p−g ( x 2 ) and C p−p ( x 3 ) on AoR and AoS, as depicted in Fig. 5 . It is evident that AoR is rather close to the target value (28.38°) when µ p−p is 0.0674 ~ 0.084, µ p−g is 0.2264 ~ 0.246, and C p−p is 0.00754 ~ 0.01396. As the effect of µ p−g on AoS is not notable, AoS is found to be comparable to the target value (28.80°) at µ p−p of 0.0508 to 0.0674 and C p−p of 0.00754 to 0.00968. 3.4.4 Optimization of the soybean contact parameters To pinpoint the optimal combination of soybean seed contact parameters, a mathematical model for parameter optimization was established using the target values of comprehensive evaluation indexes. The objective function and restrictions are as follows: The optimal combinations of soybean seed prominence contact parameters were derived as 0.0678 for µ p−p , 0.2453 for µ p−g , and 0.0079 for C p−p upon deploying the Optimization module of the Design-Expert software. 3.5 Validation test The generality verification test was run on the calibrated simulation contact settings, as presented in Fig. 6 . It is discernible from the summarized results in Table 11 that the particle filling quantity gradually reduced as the fraction particle radius soared, as did the AoR and AoS. The BPM models of soybean seeds generated with varying fraction particle radii had less influence on the simulation results, with a maximal inaccuracy of 1.59%, indicating that the calibrated simulation contact parameters are versatile. Table 11 Verification test results Target R f =0.40 mm, N f =446 R f =0.45 mm, N f =324 R f =0.50 mm, N f =236 R f =0.55 mm, N f =182 R f =0.60 mm, N f =146 AoR AoS AoR AoS AoR AoS AoR AoS AoR AoS Actual value (°) 28.38 28.80 28.38 28.80 28.38 28.80 28.38 28.80 28.38 28.80 simulated value (°) 28.83 29.11 28.67 28.92 28.32 28.76 28.20 28.63 27.96 28.45 Error (%) 1.59 1.08 1.02 0.42 -0.21 -0.14 -0.63 -0.59 -1.48 -1.22 4 Conclusions (1) The soybean seeds during sowing were focused for the study, and the actual seed-piling test revealed an AoR of 28.38° and an AoS of 28.80°. (2) The soybean-bonded particle model was established, and the AoR and AoS were assessed as the evaluation indexes. The three contributory factors with significant effects on population mobility were filtered out as µ p−p , µ p−g , and C p−p through the PB simulation seed-piling test. The steepest ascent test and Box-Behnken response surface test were conducted for the three salience factors. The results indicated that the AoR was 28.32° and AoS was 28.76° when µ p−p , µ p−g , and C p−p were 0.0678, 0.2453, and 0.0079, respectively. (3) The generality validation tests on the optimized simulation contact parameters were performed, and the results revealed that the soybean BPM models constructed by various fraction particles with differing radii had less effect on the simulation results, with an aggregate error of 1.59%, which indicated that the calibrated contact parameters had good applicability. Declarations Acknowledgments The authors acknowledge the support from the Natural Science Foundation of Sichuan Province (2022NSFSC0138), Technological Innovation R&D Projects of Chengdu Science and Technology Bureau (2022YF0501141SN), and the Listing Project of Rural Revitalization Research Institute of Sichuan Tianfu District (XZY1-11). Compliance with ethical standards Conflict of interest The authors declare that they have no conflict of interest. References Hu, H., Zhou, Z., Wu, W., Yang, W., Li, T., Chang, C., et al.: Distribution characteristics and parameter optimisation of an air-assisted centralized seed-metering device for rapeseed using a CFD-DEM coupled simulation. Biosyst. Eng. 208 , 246-259 (2021) Hoorijani, H., Esgandari, B., Zarghami, R., Sotudeh-Gharebagh, R., Mostoufi, N.: Comparative CFD-DEM study of flow regimes in spout-fluid beds. Particuology. 85 , 323-334 (2024) Li, J., Kuang, S., Huang, F., Liu, P., Yu, A.: CFD–DEM modeling and analysis of proppant transportation inside tortuous hydraulic fractures. Powder. Technol. 432 , 119115 (2024) Gao, X., Xie, G., Li, J., Shi, G., Lai, Q., Huang, Y.: Design and validation of a centrifugal variable-diameter pneumatic high-speed precision seed-metering device for maize. Biosyst. Eng. 227 , 161-181 (2023) Han, D., Zhang, D., Jing, H., Yang, L., Cui, T., Ding, Y., et al.: DEM-CFD coupling simulation and optimization of an inside-filling air blowing maize precision seed-metering device. Comput. Electron. Agric. 150 , 426-438 (2018) Xu, J., Sun, S., He, Z., Wang, X., Zeng, Z., Li, J., et al.: Design and optimisation of seed-metering plate of air-suction vegetable seed-metering device based on DEM-CFD. Biosyst. Eng. 230 , 277-300 (2023) Yan, D., Yu, J., Wang, Y., Zhou, L., Yu, Y.: A general modelling method for soybean seeds based on the discrete element method. Powder Technol. 372 , 212-226 (2020) Wang, Z., Cui, T., Zhang, D., Yang, L., He, X., Zhang, Z.: Design and experiment of rasp bar threshing element of corn combine harvester. Trans. Chin. Soc. Agric. Mach. 52 (9), 115-123 (2021) Han,·D., Xu,·Y., Huang,·Y., He,·B., Dai,·J., Lv,·X., et al.: DEM parameters calibration and verification for coated maize particles. Comput. Part. Mech. 10 , 1931-1941 (2023) Favier, J., Abbaspour-Fard, M., Kremmer, M., Raji, A.: Shape representation of axi-symmetrical, non-spherical particles in discrete element simulation using multi-element model particles. Eng. Computation, 16 (4), 467-480 (1999) Han D., Zhang, D., Yang, L., Cui, T., Ding, Y., Bian, X.: Optimization and Experiment of Inside-filling Air-blowing Seed Metering Device Based on EDEM-CFD. Trans. Chin. Soc. Agric. Mach. 48 (11), 43-51 (2017) Shi, S., Liu, H., Wei, G., Zhou, J., Jian, S., Zhang, R.: Optimization and experiment of pneumatic seed metering device with guided assistant filling based on EDEM-CFD. Trans. Chin. Soc. Agric. Mach. 51 (5), 54-66 (2020) Potyondy, D., Cundall, P.: A bonded-particle model for rock. Int. J. Rock. Mech. Min. 41 , 1329-1364 (2004) Wang, Y., Liang, Z., Zhang, D., Cui, T., Shi, S., Li, K., et al.: Calibration method of contact characteristic parameters for corn seeds based on EDEM. Trans. Chin. Soc. Agric. Eng. 32 (22), 36-42 (2016) Zhang, R., Zhou, J., Liu, H., Shi, S., Wei, G., He, T.: Determination of interspecific contact parameters of corn and simulation calibration of discrete element. Trans. Chin. Soc. Agric. Mach. 53 (S1), 69-77 (2022) Wang, M., Wang, W., Yang, L., Zhang, K., Zhang, Hongme.: Calibration of discrete element model parameters for maize kernel based on response surface methodology. J. Huanan. Agric. Univ. 39 (3), 111-117 (2018) Zhang, T., Liu, F., Zhao, M., Liu, Y., Li, F., Ma, Q., et al.: Measurement of physical parameters of contact between soybean seed and seed metering device and discrete element simulation calibration. J. Chin. Agric. Univ. 22 (9), 86-92 (2017) Xu, J., Wang, X., Zhang, Z., Wu, W.: Discrete element modeling and simulation of soybean seed using multi-spheres and super-ellipsoids, IEEE Access. 8 , 222672-222683 (2020) Yan, D., Yu, J., Liang, L., Wang, Y., Yu, Y., Zhou, L., et al.: A comparative study on the modeling of soybean particles based on the discrete element method. Processes. 9 , 286 (2021) Yan, D., Yu, J., Wang, Y., Sun, K., Zhou, L., Tian, Y., et al.: Measurement and calibration of DEM parameters of soybean seed particles. Agriculture. 12 , 1825 (2022) Yan, D., Yu, J., Wang, Y., Zhou, L., Sun, K., Tian, Y.: A review of the application of discrete element method in agricultural engineering: a case study of soybean. Processes. 10 , 1305 (2022) Jung, H., Yoon, W.: Determination and validation of discrete element model parameters of soybeans with various moisture content for the discharge simulation from a cylindrical model silo. Processes. 10 , 2622 (2022) Xu, T., Fu, H., Liu, M., Feng, W., Zhang, R., Wang, Y., et al.: Ellipsoidal seed modeling and simulation parameter selection based on the discrete element method. Mater. Today. Commun. 37 , 106923 (2023) Ileleji, K., Zhou, B.: The angle of repose of bulk corn stover particles. Powder. Technol. 187 (2), 110-118 (2008) Boac, J., Casada, M., Maghirang, R., Harner, J.: Material and interaction properties of selected grains and oil-seeds for modeling discrete particles. T. ASABE. 53 (4), 1201-1216 (2010) Zhang, X., Vu-Quoc, L.: Simulation of chute flow of soybeans using an improved tangential force-displacement model. Mech. Mater. 32 , 115-129 (2000) Xu, T., Yu, J., Yu, Y., Wang, Y.: A modelling and verification approach for soybean seed particles using the discrete element method. Adv. Powder. Technol. 29 (12), 3274-90 (2018) Vu-Quoc, L., Zhang, X., Walton, O.: A 3-D discrete element method for dry granular flows of ellipsoidal particles. Comput. Method. Appl. M. 187 (3-4), 483-528 (2000) Ghodki, B., Patel, M., Namdeo, R., Carpenter, G.: Calibration of discrete element model parameters: Soybeans. Comput. Part. Mech. 6 (1), 3-10 (2019) Horabik, J., Beczek, M., Mazur, R., Parafiniuk, P., Ryzak, M., Molenda, M.: Determination of the restitution coefficient of seeds and coefficients of visco-elastic Hertz contact models for DEM simulations. Biosyst. Eng. 161 , 106-119 (2017) Nguyen, T., Le, L., Nguyen, T., Nguyen, N., Le, T., Pham, B., et al.: Characterization of soybeans and calibration of their DEM input parameters. Particul. Sci. Technol. 39 (5), 5304548 (2021) Le, T.: Investigation of force transmission, critical breakage force and relationship between micro-macroscopic behaviors of agricultural granular material in a uniaxial compaction test using discrete element method. Particul. Sci. Technol. 40 (5), 620-637 (2022) Gong, H., Zeng, Z., Qi, L.: A discrete element model of seed-soil dynamics in soybean emergence. Plant. Soil. 437 (1-2), 439-54 (2019) Ghodki, B., Patel,·M., Namdeo,·R., Carpenter, G.: Calibration of discrete element model parameters: soybeans. Comput. Part. Mech. 6 (1), 3-10 (2019) Liu, Y., Zhao, M., Liu, F., Yang, T., Zhang, T., Li, F.: Simulation and optimization of working parameters of air suction metering device based on discrete element. Trans. Chin. Soc. Agric. Mach. 47 (7), 65-72 (2016) Additional Declarations No competing interests reported. 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Han","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAxElEQVRIiWNgGAWjYBACAyCW4DGwkeNnb2x88IF4LQVpxpI9h5sNZxCv5cPhxA030tukOYjRYs5+9uCNNwaHjSVnPmyQZmCwk9NtIKDFsicv2XKOQbocv3Rig3EBQ7Kx2QFCDjuQYybNY2BtLDk7sSF5BsOBxG0EtZx/A9LCnLjh5sGGwzxEabkBtsUZ6H3GxmYitbwxBvoFFMiJzYwzDIjxy/kcwxtv/oCi8vjzHx8q7OQIakE3gTTlo2AUjIJRMApwAACTPEV9m+nDTwAAAABJRU5ErkJggg==","orcid":"","institution":"Sichuan Agricultural University","correspondingAuthor":true,"prefix":"","firstName":"Dandan","middleName":"","lastName":"Han","suffix":""},{"id":275141194,"identity":"4814dbd2-608f-40f5-9929-fd2c6981004d","order_by":1,"name":"Qing Wang","email":"","orcid":"","institution":"Sichuan Agricultural University","correspondingAuthor":false,"prefix":"","firstName":"Qing","middleName":"","lastName":"Wang","suffix":""},{"id":275141195,"identity":"e3435692-7153-4531-8d3c-650666dc8f65","order_by":2,"name":"Chao Tang","email":"","orcid":"","institution":"Sichuan Agricultural University","correspondingAuthor":false,"prefix":"","firstName":"Chao","middleName":"","lastName":"Tang","suffix":""},{"id":275141196,"identity":"8ce1e109-cfa4-4e6f-9b8d-bf824836af28","order_by":3,"name":"Wei Li","email":"","orcid":"","institution":"Sichuan Agricultural University","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Li","suffix":""},{"id":275141197,"identity":"dae92032-27cd-485d-8bf6-d1baef45b50a","order_by":4,"name":"You Xu","email":"","orcid":"","institution":"Sichuan Agricultural University","correspondingAuthor":false,"prefix":"","firstName":"You","middleName":"","lastName":"Xu","suffix":""}],"badges":[],"createdAt":"2024-02-24 15:19:34","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3985360/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3985360/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":51794288,"identity":"2c93cf1f-d7e0-4842-b4eb-c38700660aa3","added_by":"auto","created_at":"2024-02-29 06:56:43","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":212232,"visible":true,"origin":"","legend":"\u003cp\u003eApparatus of the practical seed-piling test\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3985360/v1/76788d67c4c5813990917bd4.png"},{"id":51794293,"identity":"c2aa9ce3-2bbe-49a2-a52a-34ff99364645","added_by":"auto","created_at":"2024-02-29 06:56:43","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":285232,"visible":true,"origin":"","legend":"\u003cp\u003eImages processing of the AoR and AoS\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-3985360/v1/d129a8618a8bbe712e3299c8.png"},{"id":51794289,"identity":"9c6bc551-f8a7-4230-b200-bcac3c79824d","added_by":"auto","created_at":"2024-02-29 06:56:43","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":62973,"visible":true,"origin":"","legend":"\u003cp\u003eDEM model of soybean seed\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-3985360/v1/8705cd56e7b95a33e9029262.png"},{"id":51794290,"identity":"62140a86-dce2-45fa-a95b-9a42b36d25a7","added_by":"auto","created_at":"2024-02-29 06:56:43","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":245861,"visible":true,"origin":"","legend":"\u003cp\u003ePareto charts of the PB test\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-3985360/v1/d0c17fe7e2e61e5e0b9eef2d.png"},{"id":51794291,"identity":"d94336fa-392f-4c4f-86c2-07c19f7bce6c","added_by":"auto","created_at":"2024-02-29 06:56:43","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":337564,"visible":true,"origin":"","legend":"\u003cp\u003eEffects of interactive factors on AoR and AoS\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-3985360/v1/3d236e325ae71fcbacbe244a.png"},{"id":51794631,"identity":"2887c955-8931-4173-a95b-cc6862caff3f","added_by":"auto","created_at":"2024-02-29 07:04:43","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":798803,"visible":true,"origin":"","legend":"\u003cp\u003eVerification tests\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-3985360/v1/28697d79e3ea11fa88c08cdf.png"},{"id":55412143,"identity":"47db06c7-00de-48ce-9dd3-935462c8fc45","added_by":"auto","created_at":"2024-04-27 01:51:17","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2016599,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3985360/v1/c9aa4235-e4aa-4d19-b65e-a1356e3adad3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Calibration of the contact parameters for soybean-bonded particle model based on DEM","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eThe computational fluid dynamics and discrete element method (CFD-DEM) coupling approach is frequently employed in engineering investigations as a numerical analytical tool for simulating multiphase flow [\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. The working process of the pneumatic seed-metering device typically involves a gas-solid two-phase flow motion [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e], and the volume fraction of the mesh occupied by the particle model is required to be no more than 70% even if the Eulerian coupling model is utilized while performing the CFD-DEM coupling simulation on it [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Since the holes in the seed-metering device are required to be finely meshed and smaller in size than the seeds, it is challenging to satisfy the stipulation that the volume of the particle model is not over 70% of the minimized mesh volume of the chamber delineation [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe multi-sphere (MS) method has been extensively employed in agricultural engineering studies as an ordinary approach for designing particle models [\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. However, the particle model built with MS is regarded as a separate entity that participates in the subsequent simulation computations, and the volume of the MS particle is much larger than the divided mesh volume of the seed-metering device chamber, making it unsuitable for coupling simulation and analysis of the pneumatic seed-metering device\u0026rsquo;s service [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. In contrast, the coupling simulation analysis of the pneumatic seed-metering device is better suited for the bonded particle model (BPM), which is comprised of several distinct fraction particles cemented by adhesive bonds [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. It is stipulated that the fraction particles constituting the BPM can irrespectively organize the dimensions and then participate in the ensuing simulation computations. Moreover, it is relatively convenient to realize the maximal scale limitation of the Eulerian coupling model on the volume fraction of the mesh by dividing the mesh logically in the CFD domain [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. However, there are certain discrepancies in the morphologies of BPM, MS particles, and authentic seeds, triggering an error between the contact parameters and the reality values. Hence, it is imperative to calibrate the contact parameters exploited in the CFD-DEM coupling simulation with the seed particle model created via the BPM method [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn terms of research on the calibration of particle contact parameters, Zhang et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] synchronized the contact parameters of the maize-bonded particle created by BPM, and the results of the parameters calibrated (the static and rolling friction coefficients of maize-maize were 0.031 and 0.0039) differed significantly from the results of Wang et al. [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] on the calibrated contact parameters of maize particles created by MS (which were 0.182 and 0.051). Therefore, it is extremely essential to calibrate the contact parameters of the soybean-bonded particle.\u003c/p\u003e \u003cp\u003eCurrently, the soybean particle model derived from MS has been applied in numerous studies on the calibration of soybean contact parameters [\u003cspan additionalcitationids=\"CR18 CR19 CR20 CR21 CR22\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. Despite the results of the proceeding investigations are incompatible with the contact properties of the soybean-bonded particle model, the calibration process and experimental setup are highly beneficial and instructive for this study.\u003c/p\u003e \u003cp\u003eThe soybean seeds used for sowing were examined, and the BPM method was adopted to construct a soybean-bonded particle model. The angle of repose (AoR) and angle of stacking (AoS) were evaluated as indicators leveraging the seed-piling test. The prominent parameters and their centroids were sieved by the Plackett-Burman and steepest ascent tests. The multi-objective optimization was computed through the Box-Behnken response surface test to derive the mathematical model between the saliency parameters and each evaluation index. The preferred calibration parameter values were discovered and empirically confirmed. The purpose of this publication is intended to serve as a reference for other researchers attempting to construct particle models for DEM simulations using the BPM method.\u003c/p\u003e"},{"header":"2 Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Test materials\u003c/h2\u003e \u003cp\u003eThe soybean variety used in this experiment was \u0026ldquo;Zhonghuang 39\u0026rdquo;, which was measured in the early stages of the basic parameters, as displayed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The sizes of soybean seeds are unpredictable but tend to comply with a normal distribution. Soybean seeds have dimensions of 8.53 mm in length, 6.55 mm in width, and 7.31 mm in thickness, with an approximate globe shape and a sphericity of roughly 0.87.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBasic characteristic parameters of soybean seed\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\"\u0026plusmn;\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRanges\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAveraged values\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMoisture content (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e11.21\u0026thinsp;~\u0026thinsp;13.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e12.66\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDensity (g\u0026middot;cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.10\u0026thinsp;~\u0026thinsp;1.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e1.22\u0026thinsp;\u0026plusmn;\u0026thinsp;0.08\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e100-grain weight (g)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e24.33\u0026thinsp;~\u0026thinsp;25.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e25.13\u0026thinsp;\u0026plusmn;\u0026thinsp;0.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLength (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.91\u0026thinsp;~\u0026thinsp;10.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e8.53\u0026thinsp;\u0026plusmn;\u0026thinsp;0.61\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.13\u0026thinsp;~\u0026thinsp;7.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e6.55\u0026thinsp;\u0026plusmn;\u0026thinsp;0.41\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThickness (mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.85\u0026thinsp;~\u0026thinsp;8.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e7.31\u0026thinsp;\u0026plusmn;\u0026thinsp;0.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSphericity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.70\u0026thinsp;~\u0026thinsp;0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\"\u0026plusmn;\" colname=\"c3\"\u003e \u003cp\u003e0.87\u0026thinsp;\u0026plusmn;\u0026thinsp;0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Physical seed-piling test\u003c/h2\u003e \u003cp\u003eAoR and AoS are two macroscopic features describing the flow and frictional properties of granular materials, which pertain to the physical properties of the contacting apparatus and the particles [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Accordingly, they can be applied in the contact parameter calibration tests of discrete element models. The AoR and AoS were estimated by physical seed-piling tests. The testing apparatus was a rectangular container made of plexiglass plate with specifications of 300 mm long, 60 mm broad, and 300 mm high. The width of the discharging port was 40 mm. The baffle was initially canceled before the test, and soybean seeds of about 3/4 volume were distributed fairly into the upper container. The upper surface of the seeds pedestal was then flattened with a scraper. The seeds began to tumble and pile up under gravity as the baffle was swiftly eliminated, and until it stabilized. Two triangular seed heaps attended to be assembled symmetrically on both sides of the upper container, as represented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo alleviate the distortion caused by personal inspection, after the physical seed-piling test had culminated, Matlab (version R2021b) was programmed to denoise, grayscale, and binarize the captured images to obtain the boundary points, which were then linked together to construct the boundary curve of the seeds pile. Upon integrating the least squares approach to fit the curve, the tangent value of the actual AoR or AoS of the soybean seeds was estimated to be the slope of the straight line. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e depicts how angles are calculated.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Simulated piling test\u003c/h2\u003e \u003cp\u003eThe technique of the simulated seed-piling test was supposed to be identical to the physical. According to the basic specifications of soybean seeds listed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the 3D model was rendered using Solidworks (version 2022) and imported as a .step file into EDEM (version 2018, DEM Solution Ltd., Edinburgh, Scotland). BPM was introduced in this paper to establish the soybean-bonded particle model. The radius of fraction particles adopted was 0.5 mm (\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=0.5 mm) proportional to the volume of soybean seeds, and the total quantity was 236 (\u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=236), as stated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The geometric model of the seed-piling test apparatus and the DEM model of soybean seeds were loaded into EDEM. The adequate amount of soybean particles was adjusted such that 3/4 of the upper container was filled. The images were captured once each simulation test was done, and manipulated as well as deploying Matlab to yield the simulated AoR (\u003cem\u003eβ\u003c/em\u003e) and AoS (\u003cem\u003eγ\u003c/em\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Calibration method for the contact parameters of soybean seeds\u003c/h2\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.4.1 Plackett-Burman test\u003c/h2\u003e \u003cp\u003eDesign-Expert (version 13.0, Stat-Ease Ltd., Godward St NE, Minneapolis, USA) was instructed to design the Plackett-Burman (PB) test with the AoR, and AoS as response values, and the simulated factors with noteworthy effects were screened out. To identify the major variables modifying the AoR and AoS, eight input parameters for the DEM simulation were selected, accounting for the dynamics between seeds and seeds as well as seeds and the seed-metering device during the working process. Three dummy variables were set to facilitate error analysis. Each parameter was assigned two levels, namely high and low, denoted by codes\u0026thinsp;+\u0026thinsp;1 and \u0026minus;\u0026thinsp;1, respectively. The limits of each parameter were configured after a thorough examination of the literature and numerous pre-tests, and the findings are listed in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFactors and levels of the Plackett-Burman test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNotation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLow level\u003c/p\u003e \u003cp\u003e(-1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eHigh level\u003c/p\u003e \u003cp\u003e(-1)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eReferences\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eν\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePoisson\u0026rsquo;s ratio of soybean seeds\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eShear modulus of soybean (MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e137.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRestitution coefficient of soybean-soybean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRestitution coefficient of soybean- plexiglass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.735\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan additionalcitationids=\"CR31\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStatic friction coefficient of soybean-soybean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStatic friction coefficient of soybean-plexiglass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRolling friction coefficient of soybean-soybean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRolling friction coefficient of soybean-plexiglass\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e[\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eI、J、K\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eNull\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.4.2 Steepest ascent test\u003c/h2\u003e \u003cp\u003eThe elements that substantially alter the AoR and AoS were derived based on the results of the PB test and the steepest ascent test was then executed. The optimal range interval of the simulation test\u0026rsquo;s significance parameters was determined by integrating the relative error results, which were evaluated as an index between the simulation and practical test results.\u003c/p\u003e \u003cp\u003eThe equations for calculating the errors in AoR (\u003cem\u003ee\u003c/em\u003e\u003csub\u003eAoR\u003c/sub\u003e) and AoS (\u003cem\u003ee\u003c/em\u003e\u003csub\u003eAoS\u003c/sub\u003e) are steadily as follows:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${e_{AoR}}=\\frac{{\\beta - \\theta }}{\\theta } \\times 100\\%$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${e_{AoS}}=\\frac{{\\gamma - \\varphi }}{\\varphi } \\times 100\\%$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eθ\u003c/em\u003e and \u003cem\u003eφ\u003c/em\u003e are the physical test\u0026rsquo;s AoR and AoS in (\u0026deg;), \u003cem\u003eβ\u003c/em\u003e and \u003cem\u003eγ\u003c/em\u003e are the simulation test\u0026rsquo;s AoR and AoS in (\u0026deg;), \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoR\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoS\u003c/em\u003e\u003c/sub\u003e are the errors of AoR and AoS in %.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.4.3 Response surface test\u003c/h2\u003e \u003cp\u003eThe distinctive factors and their centroids were acquired by the PB and steepest ascent tests, and then the Box-Behnken response surface test was conducted. The test results were subjected to multiple regression analyses performed on the test data to establish the regression models of the saliency contact parameters with AoR and AoS, respectively. Based on the regression model and the measured AoR and AoS values, the optimal simulation parameters combination was ascertained by using the Optimization module in Design Expert software.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.5 Generalized validation methods for simulation parameters\u003c/h2\u003e \u003cp\u003eThe soybean particle constructed by the BPM method was composed of multiple isolated fraction particles wholly joined together by adhesive bonds, and the fraction particle can be uniquely sized and engaged in the subsequent simulation computations. On account of aspects like actual demand and computational speed, the soybean BPM model may need to be built with varying percent particle sizes in practical applications. Consequently, the radius of fraction particles was set to 0.4, 0.45, 0.55, and 0.60 mm under the realistic simulation prerequisite, and the BPM models of soybean seeds were established, correspondingly. The simulated seed-piling tests were executed with the calibrated contact parameters, and the results were compared to the measured values of AoR and AoS.\u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results and discussion","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Results of the physical piling test\u003c/h2\u003e \u003cp\u003eTen iterations of the physical seed-piling test went through to mitigate the disparities in the data statistical results. The results of the physical seed-piling test were evaluated by calculating the average values of AoR and AoS obtained from ten repetitions, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The average AoR of soybean seeds was finally derived to be 29.87\u0026deg;, with an average AoS of 28.80\u0026deg;.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMeasured results of the physical seed-dropping test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAoR (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAoS (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e29.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.46\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e27.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e28.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.33\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e28.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e27.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e29.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.38\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e29.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e27.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.11\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e27.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.43\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e27.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e28.38\u0026thinsp;\u0026plusmn;\u0026thinsp;0.872\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.80\u0026thinsp;\u0026plusmn;\u0026thinsp;0.533\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Plackett-Burman test results\u003c/h2\u003e \u003cp\u003eA total of twelve sets of tests were conducted with eight parameter variables selected for the PB test and three dummy variables assigned to aid in the error analysis. The design scheme and simulation results of the PB test are listed in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDesign and results of Plackett-Burman test scheme\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"14\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eNo.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"11\" nameend=\"c12\" namest=\"c2\"\u003e \u003cp\u003eTest factors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eAoR (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c14\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eAoS (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eν\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cem\u003eI\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cem\u003eJ\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cem\u003eK\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e38.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e35.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e 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align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e35.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e33.42\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e 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align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e24.57\u003c/p\u003e \u003c/td\u003e 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align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e6.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e20.41\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e10.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e34.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e5.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e21.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe PB simulation test results were variance analyzed within Design-Expert, revealing the effect of each parameter as presented in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Concerning AoR specifically, the effects of \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0116) and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0321) were generally exceptional, and \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0005) had a critically important effect. While extremely sizable effects of both \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0046) and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.0098) were observed for AoS. The influence of other factors on AoR and AoS was not discernible (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026gt;\u0026thinsp;0.05). Accordingly, the three influential variables were quantified and optimized in the following steepest ascent test and response surface test.\u003c/p\u003e \u003cp\u003eIn case of other non-significant factors, the values were taken at the intermediate level of the PB test protocol, i.e., Poisson\u0026rsquo;s ratio (\u003cem\u003eν\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e) of soybean seeds was 0.245, shear modulus (\u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e) was 7.515\u0026times;10\u003csup\u003e7\u003c/sup\u003e Pa, restitution coefficient of soybean-soybean (\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e) was 0.4, restitution coefficient of soybean-plexiglas (\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e) was 0.5175, and rolling coefficient of soybean-plexiglas (\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e) was 0.0475.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSignificance analysis of Plackett-Burman test parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSources\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e \u003cp\u003eAoR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c11\" namest=\"c7\"\u003e \u003cp\u003eAoS\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSum of squares\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eF\u003c/em\u003e value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSignificance\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSum of squares\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cem\u003eF\u003c/em\u003e value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eSignificance\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2537.61\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e39.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0058\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e627.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e11.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0330\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eν\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1445\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.5555\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.5101\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4758\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5399\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.2131\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.6758\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.2228\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.7752\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.4434\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.4645\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.5444\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.2706\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.6389\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e244.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e30.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0116\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e386.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e58.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0046\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2099.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e263.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.0705\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.0107\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.9240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e114.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e14.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0321\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e227.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e34.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0098\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e22.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1919\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.2279\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.6657\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"11\"\u003eNote: ** indicates that the impact is extremely significant (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.01), and * indicates that the impact is significant (\u003cem\u003eP\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05).\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eAn intuitive understanding of the significance ranking of all variables was provided in the Pareto chart, as well as the positive and negative effects on the evaluation indexes. It is evident from Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e that \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e have conspicuous positive effects on both AoR and AoS. Based on everything that preceded, the values of all three variables were oriented toward the ascending path during the steepest ascent test.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Steepest ascent test results\u003c/h2\u003e \u003cp\u003eTo restrict the value ranges of the soybean seeds\u0026rsquo; contact parameters, the steepest ascent test was conducted for the three genetically relevant factors. The results of the first steepest ascent test are listed in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The AoR and AoS were progressively increasing along the climbing direction, while \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoR\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoS\u003c/em\u003e\u003c/sub\u003e were decimating before escalating. The \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoR\u003c/em\u003e\u003c/sub\u003e was estimated to be the smallest at test number 3, whereas the \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoS\u003c/em\u003e\u003c/sub\u003e was the least at test number 2, in which case the simulated values of both AoR and AoS were higher than the actual measured values.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eScheme and results of the first steepest ascent test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAoR (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoR\u003c/em\u003e\u003c/sub\u003e (%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAoS (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoS\u003c/em\u003e\u003c/sub\u003e (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.050\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-78.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e20.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-28.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.084\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0134\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e24.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-13.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e30.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4.83\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.167\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.246\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e36.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e27.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e34.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e18.58\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.345\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e42.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e51.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e35.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e22.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.333\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.443\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0534\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e45.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e59.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e36.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e25.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.541\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0667\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e47.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e66.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e37.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e30.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.640\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e51.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e82.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e38.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e33.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo further narrow down the range of optimal parameters, the second steepest ascent test was executed for \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e leveraging the simulation parameters of No. 2 (0.148) and No. 3 (0.246), \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e with No.1 (0.001 and 0.0001) and No. 3 (0.167 and 0.0267), the results of which are provided in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e exhibits that both \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoR\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoS\u003c/em\u003e\u003c/sub\u003e are noticeably miniaturized. Besides, \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoR\u003c/em\u003e\u003c/sub\u003e was minimized at No. 5, while \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoS\u003c/em\u003e\u003c/sub\u003e was ranked No. 3.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eScheme and results of the second steepest ascent test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAoR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoR\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAoS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoS\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1480\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e17.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-39.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e20.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-28.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0342\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1676\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0054\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e20.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-26.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e25.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-10.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0674\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1872\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0107\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e23.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-18.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e29.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3.23\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0161\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e26.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-8.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e31.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e10.14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1338\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2264\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0214\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e30.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e7.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e32.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e13.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1670\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0267\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e36.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e27.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e34.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e18.58\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eConsidering that the exceedingly prominent effect of \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e on AoR, and the generally discernible effect of \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e on AoR but an incredibly impressive effect on AoS, it can be identified that the optimal interval for \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e was around No. 5, and \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e were aligned near No. 3. Thus, to solicit the optimal parameter combinations, \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e were subjected to the following response surface test with centroids of 0.2264, 0.0674, and 0.0107, respectively.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Response surface test results\u003c/h2\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e3.4.1 Box-Behnken Design\u003c/h2\u003e \u003cp\u003eTowards further investigating the relationship between AoR and AoS and \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e as well as identifying the optimal parameter combinations, the response surface test was carried out using Box-Behnken Design (BBD) based on the results of the PB and two steepest ascent tests. The codes and values of each simulation parameter are indicated in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFactors and codes of the BBD test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eCode\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c4\" namest=\"c2\"\u003e \u003cp\u003eFactors\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0342\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0054\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0674\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2264\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0107\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e+\u0026thinsp;1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1006\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.2460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0161\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e3.4.2 BBD test results\u003c/h2\u003e \u003cp\u003eThe test protocol and results for the BBD test are listed in Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, which was done in 5 replications totaling 17 simulations.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab9\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 9\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFactors and codes of the BBD test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNo.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAoR (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAoS (\u0026deg;)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e24.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e27.13\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e29.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e31.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e27.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e28.57\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e30.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e29.52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e24.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e26.53\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e26.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e29.61\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e26.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e27.43\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e30.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e30.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e25.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e27.56\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e26.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e27.99\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e-1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e28.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e30.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e31.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e29.64\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e27.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e29.91\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e27.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e30.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e27.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e29.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e28.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e29.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e27.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e29.76\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"6\"\u003eNote: \u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e, \u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e are the levels of \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e, respectively.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe variance analysis of the BBD test shown in Table\u0026nbsp;\u003cspan refid=\"Tab9\" class=\"InternalRef\"\u003e9\u003c/span\u003e was performed using the software Design-Expert, and the results are given in Table\u0026nbsp;\u003cspan refid=\"Tab10\" class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab10\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 10\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVariance analysis of the BBD test results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSources\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003ey\u003c/em\u003e\u003csub\u003eAoR\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"5\" nameend=\"c11\" namest=\"c7\"\u003e \u003cp\u003e\u003cem\u003ey\u003c/em\u003e\u003csub\u003eAoS\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSum of squares\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eF\u003c/em\u003e-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eSignificance\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eSum of squares\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003edf\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cem\u003eF\u003c/em\u003e-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cem\u003eP\u003c/em\u003e-value\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eSignificance\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e69.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e26.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e30.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e20.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0003\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e25.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e89.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e18.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e107.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e32.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.1540\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.9181\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.3699\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e26.39\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e91.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;0.0001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e30.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0009\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.8836\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1232\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e21.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0025\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0349\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.0100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.0596\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.8141\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.8010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1392\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.2916\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.2289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0938\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.6611\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0875\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0155\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e*\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.0390\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.2325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.6444\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9671\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.1095\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e15.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e**\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eResidual\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLack of Fit\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0744\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.8237\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e3.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.1494\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eError\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.4165\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.3506\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCor Total\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e71.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e31.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"11\"\u003eThe regression fitting analysis of the BBD test results was performed to establish the regularity equations between \u003cem\u003ey\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoR\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003ey\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoS\u003c/em\u003e\u003c/sub\u003e, and the respective factors:\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003cdiv id=\"Equ3\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\left\\{ \\begin{gathered} {y_{AoR}}=27.75+1.79{x_1}+1.09{x_2}+1.82{x_3} - 0.47{x_1}{x_2}+0.7{x_1}{x_3}+0.4475{x_2}{x_3} - 0.5068{x_1}^{2}+0.8307{x_2}^{2} - 0.4792{x_3}^{2} \\hfill \\\\ {y_{AoS}}=29.76+1.5{x_1} - 0.1387{x_2}+0.7975{x_3} - 0.9425{x_1}{x_2}+0.05{x_1}{x_3} - 0.27{x_2}{x_3} - 0.3963{x_1}^{2} - 0.0963{x_2}^{2} - 0.7937{x_3}^{2} \\hfill \\\\ \\end{gathered} \\right.$$\u003c/div\u003e \u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWhere \u003cem\u003ey\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoR\u003c/em\u003e\u003c/sub\u003e is the angle of repose in (\u0026deg;), and \u003cem\u003ey\u003c/em\u003e\u003csub\u003e\u003cem\u003eAoS\u003c/em\u003e\u003c/sub\u003e is the angle of stacking in (\u0026deg;). The variance analysis results of the BBD test reveal that the \u003cem\u003eP\u003c/em\u003e values of the models examined in the regression Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e) are all extremely significant, demonstrating that the test protocol is well-designed. Since the \u003cem\u003eP\u003c/em\u003e values for the lack of fit terms are more than 0.05, i.e. not signed, which demonstrates that the regression equations are well-fitted to the practical scenario, and can be used for test predictions and analyses.\u003c/p\u003e \u003cp\u003eThe impacts of \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e), and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e) were extremely significant for AoR, \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e) interactions (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e), as well as \u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e were moderately prominent, while the effects of other factors were not notable. For AoS, the influence of \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e), \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e) and \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e) interaction (\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e), and \u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003csup\u003e2\u003c/sup\u003e was supremely noteworthy, while the influence of other factors was not particularly noticeable.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e3.4.3 Effects of interactions on evaluation indicators\u003c/h2\u003e \u003cp\u003eThe results of the BBD test were processed to extract the response surface contours of the interactive effects of \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e), \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e) and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e(\u003cem\u003ex\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e) on AoR and AoS, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. It is evident that AoR is rather close to the target value (28.38\u0026deg;) when \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e is 0.0674\u0026thinsp;~\u0026thinsp;0.084, \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e is 0.2264\u0026thinsp;~\u0026thinsp;0.246, and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e is 0.00754\u0026thinsp;~\u0026thinsp;0.01396. As the effect of \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e on AoS is not notable, AoS is found to be comparable to the target value (28.80\u0026deg;) at \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e of 0.0508 to 0.0674 and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e of 0.00754 to 0.00968.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec19\" class=\"Section3\"\u003e \u003ch2\u003e3.4.4 Optimization of the soybean contact parameters\u003c/h2\u003e \u003cp\u003eTo pinpoint the optimal combination of soybean seed contact parameters, a mathematical model for parameter optimization was established using the target values of comprehensive evaluation indexes. The objective function and restrictions are as follows:\u003c/p\u003e\u003cp\u003e\u003cimg src=\"https://myfiles.space/user_files/122228_c8a1650c59388082/122228_custom_files/img1709189657.png\"\u003e\u003cbr\u003e\u003c/p\u003e \u003cp\u003eThe optimal combinations of soybean seed prominence contact parameters were derived as 0.0678 for \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e, 0.2453 for \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e, and 0.0079 for \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e upon deploying the Optimization module of the Design-Expert software.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec20\" class=\"Section2\"\u003e \u003ch2\u003e3.5 Validation test\u003c/h2\u003e \u003cp\u003eThe generality verification test was run on the calibrated simulation contact settings, as presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. It is discernible from the summarized results in Table\u0026nbsp;\u003cspan refid=\"Tab11\" class=\"InternalRef\"\u003e11\u003c/span\u003e that the particle filling quantity gradually reduced as the fraction particle radius soared, as did the AoR and AoS. The BPM models of soybean seeds generated with varying fraction particle radii had less influence on the simulation results, with a maximal inaccuracy of 1.59%, indicating that the calibrated simulation contact parameters are versatile.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab11\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 11\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVerification test results\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"11\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTarget\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=0.40 mm, \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=446\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=0.45 mm, \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=324\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=0.50 mm, \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=236\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=0.55 mm, \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=182\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c11\" namest=\"c10\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=0.60 mm, \u003cem\u003eN\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e=146\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAoR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAoS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAoR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAoS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAoR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAoS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eAoR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eAoS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eAoR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003eAoS\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eActual value (\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e28.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e28.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e28.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e28.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e28.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e28.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e28.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e28.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e28.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e28.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003esimulated value (\u0026deg;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e28.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e29.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e28.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e28.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e28.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e28.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e28.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e28.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e27.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e28.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eError (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e-0.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e-0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-0.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e-0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e-1.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e-1.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4 Conclusions","content":"\u003cp\u003e(1) The soybean seeds during sowing were focused for the study, and the actual seed-piling test revealed an AoR of 28.38\u0026deg; and an AoS of 28.80\u0026deg;.\u003c/p\u003e \u003cp\u003e(2) The soybean-bonded particle model was established, and the AoR and AoS were assessed as the evaluation indexes. The three contributory factors with significant effects on population mobility were filtered out as \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e through the PB simulation seed-piling test. The steepest ascent test and Box-Behnken response surface test were conducted for the three salience factors. The results indicated that the AoR was 28.32\u0026deg; and AoS was 28.76\u0026deg; when \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e,\u003c/sub\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e were 0.0678, 0.2453, and 0.0079, respectively.\u003c/p\u003e \u003cp\u003e(3) The generality validation tests on the optimized simulation contact parameters were performed, and the results revealed that the soybean BPM models constructed by various fraction particles with differing radii had less effect on the simulation results, with an aggregate error of 1.59%, which indicated that the calibrated contact parameters had good applicability.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe authors acknowledge the support from the Natural Science Foundation of Sichuan Province (2022NSFSC0138), Technological Innovation R\u0026amp;D Projects of Chengdu Science and Technology Bureau (2022YF0501141SN), and the Listing Project of Rural Revitalization Research Institute of Sichuan Tianfu District (XZY1-11).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompliance with ethical standards\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e The authors declare that they have no conflict of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eHu, H., Zhou, Z., Wu, W., Yang, W., Li, T., Chang, C., et al.: Distribution characteristics and parameter optimisation of an air-assisted centralized seed-metering device for rapeseed using a CFD-DEM coupled simulation. 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Mach. \u003cstrong\u003e47\u003c/strong\u003e(7), 65-72 (2016)\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"soybean kernel, discrete element method, contact properties, parameter calibration, response surface methodology","lastPublishedDoi":"10.21203/rs.3.rs-3985360/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3985360/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo retrieve the simulation contact parameters of the soybean-bonded particle for an effective gas-solid two-phase flow coupling simulation analysis of the working procedure of the pneumatic seed-metering device, the angle of repose (AoR) and angle of stacking (AoS) from the physical seed-piling test were captured as the evaluation indexes. The Plackett-Burman test and the steepest ascent test were ratified to simplify the simulation analysis of the soybean-bonded particles, screening out the crucial influenced factors and centroids. The Box-Behnken response surface test was then implemented to identify the desired saliency factor values, and the universality of the calibrated contact parameters for soybean-bonded particles synthesized with varying fraction particle sizes was eventually confirmed. The results revealed that the effect of the static friction coefficient of soybean-plexiglass (\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e) on AoR was exceedingly significant, and that of the static and rolling friction coefficients of soybean-soybean (\u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e \u0026amp; \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e) was generally prominent. While it was abundantly clear that both \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e supremely affected AoS. The optimal values determined by the Box-Behnken response surface test yielded ideal values of 0.0678 for \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e, 0.2453 for \u003cem\u003e\u0026micro;\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;g\u003c/em\u003e\u003c/sub\u003e, and 0.0079 for \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u0026minus;p\u003c/em\u003e\u003c/sub\u003e, culminating in an AoR of 28.32\u0026deg; and AoS of 28.76\u0026deg;, respectively. Based on the derived optimal simulation contact parameters, the maximal error between the simulated and measured values of AoR and AoS of soybean-bonded particles constructed with various fraction particle sizes was estimated to be 1.59%, implying that the calibrated contact parameters have a superior generality. The insights of this investigation can be effectively applied to the coupled simulation analysis of the pneumatic soybean seed-metering device\u0026rsquo;s operations, as well as a reference for other researchers to erect particle models for DEM simulation using the bonded particle method.\u003c/p\u003e","manuscriptTitle":"Calibration of the contact parameters for soybean-bonded particle model based on DEM","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-29 06:56:39","doi":"10.21203/rs.3.rs-3985360/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"3c43ec40-1f4d-4df4-a153-058c593a6d83","owner":[],"postedDate":"February 29th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-04-27T01:42:40+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-29 06:56:39","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3985360","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3985360","identity":"rs-3985360","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}