基于RVM的配比变量排肥掺混均匀度离散元仿真及验证
|
摘要
采用试验测量或现有的间接标定方法很难实现配比变量排肥离散元仿真的参数标定,针对此标定难题,该文提出一种基于肥料掺混均匀度-仿真参数相关向量机模型主动寻优的标定方法。将配比变量离散元排肥过程看作特定的非线性系统,采用相关向量机机器学习方法揭示模型参数与肥料掺混均匀度之间的映射关系,建立回归元模型;基于最优模型参数值对应的肥料掺混均匀度值应与试验值一致,采用建立的元模型结合试验统计结果构建适应度函数;基于约束最优的数学思想建立数学模型,通过最优参数值遗传算法迭代计算,得到最优值。5种排肥转速下(30、40、50、60、70 r/min),排肥器采用碰撞边缘为外凸曲线形的A型掺混腔时,标定模型排肥后肥料掺混均匀度与试验值的相对误差均值:氮肥为6.4%,磷肥为4.1%,钾肥为5.9%;标定前氮肥为26.8%,磷肥为28.9%,钾肥为36.1%。采用碰撞边缘为直线形的B型掺混腔时,标定模型排肥后肥料掺混均匀度与试验值的相对误差均值:氮肥为5.8%,磷肥为5.6%,钾肥为4.9%;标定前氮肥为21.9%,磷肥为32.5%,钾肥为28.9%;采用碰撞边缘为内凹曲线形的C型掺混腔时,标定模型排肥后肥料掺混均匀度与试验值的相对误差均值:氮肥为5.0%,磷肥为3.7%,钾肥为8.7%;标定前氮肥为36.2%,磷肥为31.6%,钾肥为24.4%,该方法能够实现配比变量排肥离散元仿真参数准确有效的标定。
With the development of computer simulation technology, the model establishment of variable rate fertilization with EDEM, demonstrates effectively the microcosmic dynamics behavior of fertilizer particles which can't be analyzed by experiments. The calibration of discrete element model parameters mainly includes experimental determination and indirect calibration. When method of particle board is used to measure the static friction coefficient between particles, particle bounce and collision are inevitable and accuracy is difficult to pursue. The method of indirect calibration, using try-and-error method or quadratic polynomial regression, isn't appropriate for the discrete element model of variable rate fertilization with nonlinear as well as multiple parameter values to be calibrated. Aiming at the problem above, a calibration method based on relevance vector machine is proposed. The discrete element simulation process of variable rate fertilization is a nonlinear system regarding model parameters as input and uniformity of fertilizer blending as output(when a group of parameters are given, certain uniformity value of fertilizer blending can be gotten by fertilization simulation). Firstly, the model parameter influencing the fertilization outcome of the discrete element simulation most can be defined as the main parameters by sensitivity analysis. The value domain of each main parameters are found and then the sample of parameters are got. The sample of parameters and the corresponding uniformity of fertilizer blending are regarded as training and test sample. The relevance vector machine is used to reveal mapping relationship between model parameters and the uniformity, and the regression model is established. The uniformity based on the optimal model parameters should be consistent with the that in experiment, the model parameters fitness function is constructed combined the established models with experimental statistical results. Based on the mathematical thought of the constraint optimization, the mathematical model of optimal parameters calculating is established, and the optimal parameters are generated by the genetic algorithm. For A-type mixing cavity whose the collision edge is the outer convex curve, the mean relative error of uniformity between test values and simulation values from model calibrated: for nitrogen fertilizer is 6.4%, phosphate fertilizer of 4.1%, and potash fertilizer of 5.9%. While nitrogen fertilizer is 26.8%, phosphate fertilizer is 28.9% and potash fertilizer is 36.1% for the model before calibration. For B-type mixing cavity whose the collision edge is the straight-line, the mean relative error of uniformity from model calibrated: nitrogen fertilizer is 5.8%, phosphate fertilizer of 5.6% and potash fertilizer of 4.9%. While nitrogen fertilizer is 21.9%, phosphate fertilizer is 32.5% and potash fertilizer is 28.9% for the model before calibration. For C-type mixing cavity whose the collision edge is the concave curve, the mean relative error of uniformity from model calibrated: for nitrogen fertilizer is 5.0%, phosphate fertilizer of 3.7%, potash fertilizer of 8.7%. While nitrogen fertilizer is 36.2%, phosphate fertilizer is 31.6% and potash fertilizer is 24.4% for the model before calibration. The above results show that the method can be used to realize accurate calibration of discrete element model parameters of variable rate fertilization.
With the development of computer simulation technology, the model establishment of variable rate fertilization with EDEM, demonstrates effectively the microcosmic dynamics behavior of fertilizer particles which can't be analyzed by experiments. The calibration of discrete element model parameters mainly includes experimental determination and indirect calibration. When method of particle board is used to measure the static friction coefficient between particles, particle bounce and collision are inevitable and accuracy is difficult to pursue. The method of indirect calibration, using try-and-error method or quadratic polynomial regression, isn't appropriate for the discrete element model of variable rate fertilization with nonlinear as well as multiple parameter values to be calibrated. Aiming at the problem above, a calibration method based on relevance vector machine is proposed. The discrete element simulation process of variable rate fertilization is a nonlinear system regarding model parameters as input and uniformity of fertilizer blending as output(when a group of parameters are given, certain uniformity value of fertilizer blending can be gotten by fertilization simulation). Firstly, the model parameter influencing the fertilization outcome of the discrete element simulation most can be defined as the main parameters by sensitivity analysis. The value domain of each main parameters are found and then the sample of parameters are got. The sample of parameters and the corresponding uniformity of fertilizer blending are regarded as training and test sample. The relevance vector machine is used to reveal mapping relationship between model parameters and the uniformity, and the regression model is established. The uniformity based on the optimal model parameters should be consistent with the that in experiment, the model parameters fitness function is constructed combined the established models with experimental statistical results. Based on the mathematical thought of the constraint optimization, the mathematical model of optimal parameters calculating is established, and the optimal parameters are generated by the genetic algorithm. For A-type mixing cavity whose the collision edge is the outer convex curve, the mean relative error of uniformity between test values and simulation values from model calibrated: for nitrogen fertilizer is 6.4%, phosphate fertilizer of 4.1%, and potash fertilizer of 5.9%. While nitrogen fertilizer is 26.8%, phosphate fertilizer is 28.9% and potash fertilizer is 36.1% for the model before calibration. For B-type mixing cavity whose the collision edge is the straight-line, the mean relative error of uniformity from model calibrated: nitrogen fertilizer is 5.8%, phosphate fertilizer of 5.6% and potash fertilizer of 4.9%. While nitrogen fertilizer is 21.9%, phosphate fertilizer is 32.5% and potash fertilizer is 28.9% for the model before calibration. For C-type mixing cavity whose the collision edge is the concave curve, the mean relative error of uniformity from model calibrated: for nitrogen fertilizer is 5.0%, phosphate fertilizer of 3.7%, potash fertilizer of 8.7%. While nitrogen fertilizer is 36.2%, phosphate fertilizer is 31.6% and potash fertilizer is 24.4% for the model before calibration. The above results show that the method can be used to realize accurate calibration of discrete element model parameters of variable rate fertilization.
引文
[1]Torbett J C,Roberts R K,Larson J A,et al.Perceived improvements in nitrogen fertilizer efficiency from cotton precision farming[J].Computers and Electronics in Agriculture,2008,64(2):140-148.
[2]陈贤友,吴良欢,韩科峰,等.包膜尿素和普通尿素不同掺混比例对水稻产量与氮肥利用率的影响[J].植物营养与肥料学报,2010,16(4):918-923.Chen Xianyou,Wu Lianghuan,Hang Kefeng,et al.Effects of different mixture rates of coated urea and prilled urea on rice grain yield and nitrogen use efficiency[J].Acta Metallurgica Sinica,2010,16(4):918-923.(in Chinese with English abstract)
[3]吴巍.科学施肥技术[M].北京:科学出版社,1998.
[4]何勇.精细农业[M].杭州:浙江大学出版社,2003.
[5]苑进,刘雪美.肥量配比全变量施肥装置及其控制方法中国:CN102487644A[P].2012-06-13.
[6]韩丹丹,张东兴,杨丽,等.基于EDEM-CFD耦合的内充气吹式排种器优化与试验[J].农业机械学报,2017,48(11):43-51.Han Dandan,Zhang Dongxing,Yang Li,et al.Optimization and experiment of inside-filling air-blowing seed metering device based on EDEM-CFD[J].Transactions of the Chinese Society for Agricultural Machinery,2017,48(11):43-51.(in Chinese with English abstract)
[7]韩丹丹,张东兴,杨丽,等.内充气吹式玉米排种器工作性能EDEM-CFD模拟与试验[J].农业工程学报,2017,33(13):23-31.Han Dandan,Zhang Dongxing,Yang Li,et al.EDEM-CFDsimulation and experiment of working performance of inside-filling air-blowing seed metering device in maize[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2017,33(13):23-31.(in Chinese with English abstract)
[8]朱德泉,李兰兰,文世昌,等.滑片型孔轮式水稻精量排种器排种性能数值模拟与试验[J].农业工程学报,2018,34(21):17-26.Zhu Dequan,Li Lanlan,Wen Shichang,et al.Numerical simulation and experiment on seeding performance of slide hole-wheel precision seed-metering device for rice[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2018,34(21):17-26.(in Chinese with English abstract)
[9]廖庆喜,张朋玲,廖宜涛,等.基于EDEM的离心式排种器排种性能数值模拟[J].农业机械学报,2014,45(2):109-114.Liao Qingxi,Zhang Pengling,Liao Yitao,et al.Numerical simulation on seeding performance of centrifugal rape-seed metering device based on EDEM[J].Transactions of the Chinese Society for Agricultural Machinery,2014,45(2):109-114.(in Chinese with English abstract)
[10]张涛,刘飞,赵满全,等.基于离散元的排种器排种室内玉米种群运动规律[J].农业工程学报,2016,32(22):27-35.Zhang Tao,Liu Fei,Zhao Manquan,et al.Movement law of maize population in seed room of seed metering device based on discrete element method[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2016,32(22):27-35.(in Chinese with English abstract)
[11]Elvis López Bravo,Engelbert Tijskens,Miguel Herrera Suárez,et al.Prediction model for non-inversion soil tillage implemented on discrete element method[J].Computers and Electronics in Agriculture,2014,106:120-127.
[12]Salar M R,Esehaghbeygi A,Hemmat A.Soil loosening characteristics of a dual bent blade subsurface tillage implement[J].Soil&Tillage Research,2013,134:17-24.
[13]Kornél Tamás,István J Jóri,Abdul M Mouazen.Modelling soil-sweep interaction with discrete element method[J].Soil&Tillage Research,2013,134:223-231.
[14]Franck Bourrier,Franc ois Kneib,Bruno Chareyre,et al.Discrete modeling of granular soils reinforcement by plant roots[J].Ecological Engineering,2013,61:646-657.
[15]Leblicq Tom,Smeets Bart,Ramon Herman,et al.A discrete element approach for modelling the compression of crop stems[J].Computers and Electronics in Agriculture,2016,123:80-88.
[16]苑进,刘勤华,刘雪美,等.多肥料变比变量施肥过程模拟与排落肥结构优化[J].农业机械学报,2014,45(11):81-87.Yuan Jin,Liu Qinhua,Liu Xuemei,et al.Simulation of multi-fertilizers blending process and optimization of blending cavity structure in nutrient proportion of variable rate fertilization[J].Transactions of the Chinese Society for Agricultural Machinery,2014,45(11):81-87.(in Chinese with English abstract)
[17]苑进,刘勤华,刘雪美,等.配比变量施肥中多肥料掺混模拟与掺混腔结构优化[J].农业机械学报,2014,45(6):125-132.Yuan Jin,Liu Qinhua,Liu Xuemei,et al.Granular multiflows fertilization process simulation and tube structure optimization in nutrient proportion of variable rate fertilization[J].Transactions of the Chinese Society for Agricultural Machinery,2014,45(6):125-132.(in Chinese with English abstract)
[18]黄小毛,查显涛,潘海兵,等.油菜籽粒点面接触碰撞中恢复系数的测定及分析[J].农业工程学报,2014,30(24):22-29.Huang Xiaomao,Zha Xiantao,Pan Haibing,et al.Measurement and analysis of rapeseeds’restitution coefficient in point-to-plate collision model[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2014,30(24):22-29.(in Chinese with English abstract)
[19]韩燕龙.碾米机内米粒运动特征及碾白特性[D].哈尔滨:东北农业大学,2017.Han Yanlong.Study on the Movement Characteristics and the Whitening Behavior of Rice Grains in a Friction Type Mill[D].Harbin:Northeast Agricultural University,2017.(in Chinese with English abstract)
[20]González-Montellano C,Fuentes J M,Ayuga-Téllez E,et al.Determination of the mechanical properties of maize grains and olives required for use in DEM simulations[J].Journal of Food Engineering,2012,111(4):553-562.
[21]贾富国,韩燕龙,刘扬,等.稻谷颗粒物料堆积角模拟预测方法[J].农业工程学报,2014,30(11):254-260.Jia Fuguo,Han Yanlong,Liu Yang,et al.Simulation prediction method of repose angle for rice particle materials[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2014,30(11):254-260.(in Chinese with English abstract)
[22]Coetzee C J,Els D N J.Calibration of discrete element parameters and the modelling of silo discharge and bucket filling[J].Computers&Electronics in Agriculture,2009,65(2):198-212.
[23]Ucgul M,Fielke J M,Sarnders C.Three-dimensional discrete element modeling of tillage:Determination of a suitable contact model and parameters for a cohesionless soil[J].Biosystems Engineering,2014,121(2):105-117.
[24]王云霞,梁志杰,张东兴,等.基于离散元的玉米种子颗粒模型种间接触参数标定[J].农业工程学报,2016,32(22):36-42.Wang Yunxia,Liang Zhijie,Zhang Dongxing,et al.Calibration method of contact characteristic parameters for corn seeds based on EDEM[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2016,32(22):36-42.(in Chinese with English abstract)
[25]刘凡一,张舰,李博,等.基于堆积试验的小麦离散元参数分析及标定[J].农业工程学报,2016,32(12):247-253.Liu Fanyi,Zhang Jian,Li Bo,et al.Calibration of parameters of wheat required in discrete element method simulation based on repose angle of particle heap[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2016,32(12):247-253.(in Chinese with English abstract)
[26]苑进,刘成良,古玉雪,等.基于相关向量机的双变量施肥控制序列优化[J].农业机械学报,2011,42(增刊1):184-189,171.Yuan Jin,Liu Chengliang,Gu Yuxue,et al.Bivariate fertilization control sequence optimization based on relevance vector machine[J].Transactions of the Chinese Society for Agricultural Machinery,2011,41(Supp.1):184-189,171.(in Chinese with English abstract)
[27]苑进.贝叶斯学习框架下非线性制造过程建模及多目标优化关键技术研究[D].上海:上海大学,2008.Yuan Jin.Research on Some Key Issues of Bayesian Learning Framework Based Nonlinear Manufacturing Process Modeling and Multiobjective Optimization[D].Shanghai:Shanghai University,2008.(in Chinese with English abstract)
[28]Liu Xuemei,Zhang Xiaohui,Yuan Jin.Relevance vector machine and fuzzy system based multi-objective dynamic design optimization:A case study[J].Expert Systems with Applications,2010,37:3598-3604.
[29]刘雪美,张晓辉,刘丰乐,等.喷杆喷雾机风助风筒相关向量机多目标优化设计[J].农业机械学报,2010,41(6):75-80.Liu Xuemei,Zhang Xiaohui,Liu Fengle,et al.Multiobjective dynamic design optimization for air duct of air-assisted boom sprayer based on RVM[J].Transactions of the Chinese Society for Agricultural Machinery,2010,41(6):75-80.(in Chinese with English abstract)
[30]Yuan J,Wang K S,Yu T,et al.Integrating relevance vector machines and genetic algorithms for optimization of seed-separating process[J].Engineering Applications of Artificial Intelligence,2007,20(7):970-979.
[31]Coetzee C J,Lombard S G.Discrete element method modelling of a centrifugal fertilizer spreader[J].Biosystems Engineering,2011,109(4):308-325.
[32]Ding Shangpeng,Bai Lu,Yao Yuxiang,et al.Discrete element modelling(DEM)of fertilizer dual-banding with adjustable rates[J].Computers and Electronics in Agriculture,2018,152:32-39.
[33]Holland J.Searching nonlinear functions for high values[J].Applied Mathematics and Computation,1989,32(23):255-274.
[2]陈贤友,吴良欢,韩科峰,等.包膜尿素和普通尿素不同掺混比例对水稻产量与氮肥利用率的影响[J].植物营养与肥料学报,2010,16(4):918-923.Chen Xianyou,Wu Lianghuan,Hang Kefeng,et al.Effects of different mixture rates of coated urea and prilled urea on rice grain yield and nitrogen use efficiency[J].Acta Metallurgica Sinica,2010,16(4):918-923.(in Chinese with English abstract)
[3]吴巍.科学施肥技术[M].北京:科学出版社,1998.
[4]何勇.精细农业[M].杭州:浙江大学出版社,2003.
[5]苑进,刘雪美.肥量配比全变量施肥装置及其控制方法中国:CN102487644A[P].2012-06-13.
[6]韩丹丹,张东兴,杨丽,等.基于EDEM-CFD耦合的内充气吹式排种器优化与试验[J].农业机械学报,2017,48(11):43-51.Han Dandan,Zhang Dongxing,Yang Li,et al.Optimization and experiment of inside-filling air-blowing seed metering device based on EDEM-CFD[J].Transactions of the Chinese Society for Agricultural Machinery,2017,48(11):43-51.(in Chinese with English abstract)
[7]韩丹丹,张东兴,杨丽,等.内充气吹式玉米排种器工作性能EDEM-CFD模拟与试验[J].农业工程学报,2017,33(13):23-31.Han Dandan,Zhang Dongxing,Yang Li,et al.EDEM-CFDsimulation and experiment of working performance of inside-filling air-blowing seed metering device in maize[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2017,33(13):23-31.(in Chinese with English abstract)
[8]朱德泉,李兰兰,文世昌,等.滑片型孔轮式水稻精量排种器排种性能数值模拟与试验[J].农业工程学报,2018,34(21):17-26.Zhu Dequan,Li Lanlan,Wen Shichang,et al.Numerical simulation and experiment on seeding performance of slide hole-wheel precision seed-metering device for rice[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2018,34(21):17-26.(in Chinese with English abstract)
[9]廖庆喜,张朋玲,廖宜涛,等.基于EDEM的离心式排种器排种性能数值模拟[J].农业机械学报,2014,45(2):109-114.Liao Qingxi,Zhang Pengling,Liao Yitao,et al.Numerical simulation on seeding performance of centrifugal rape-seed metering device based on EDEM[J].Transactions of the Chinese Society for Agricultural Machinery,2014,45(2):109-114.(in Chinese with English abstract)
[10]张涛,刘飞,赵满全,等.基于离散元的排种器排种室内玉米种群运动规律[J].农业工程学报,2016,32(22):27-35.Zhang Tao,Liu Fei,Zhao Manquan,et al.Movement law of maize population in seed room of seed metering device based on discrete element method[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2016,32(22):27-35.(in Chinese with English abstract)
[11]Elvis López Bravo,Engelbert Tijskens,Miguel Herrera Suárez,et al.Prediction model for non-inversion soil tillage implemented on discrete element method[J].Computers and Electronics in Agriculture,2014,106:120-127.
[12]Salar M R,Esehaghbeygi A,Hemmat A.Soil loosening characteristics of a dual bent blade subsurface tillage implement[J].Soil&Tillage Research,2013,134:17-24.
[13]Kornél Tamás,István J Jóri,Abdul M Mouazen.Modelling soil-sweep interaction with discrete element method[J].Soil&Tillage Research,2013,134:223-231.
[14]Franck Bourrier,Franc ois Kneib,Bruno Chareyre,et al.Discrete modeling of granular soils reinforcement by plant roots[J].Ecological Engineering,2013,61:646-657.
[15]Leblicq Tom,Smeets Bart,Ramon Herman,et al.A discrete element approach for modelling the compression of crop stems[J].Computers and Electronics in Agriculture,2016,123:80-88.
[16]苑进,刘勤华,刘雪美,等.多肥料变比变量施肥过程模拟与排落肥结构优化[J].农业机械学报,2014,45(11):81-87.Yuan Jin,Liu Qinhua,Liu Xuemei,et al.Simulation of multi-fertilizers blending process and optimization of blending cavity structure in nutrient proportion of variable rate fertilization[J].Transactions of the Chinese Society for Agricultural Machinery,2014,45(11):81-87.(in Chinese with English abstract)
[17]苑进,刘勤华,刘雪美,等.配比变量施肥中多肥料掺混模拟与掺混腔结构优化[J].农业机械学报,2014,45(6):125-132.Yuan Jin,Liu Qinhua,Liu Xuemei,et al.Granular multiflows fertilization process simulation and tube structure optimization in nutrient proportion of variable rate fertilization[J].Transactions of the Chinese Society for Agricultural Machinery,2014,45(6):125-132.(in Chinese with English abstract)
[18]黄小毛,查显涛,潘海兵,等.油菜籽粒点面接触碰撞中恢复系数的测定及分析[J].农业工程学报,2014,30(24):22-29.Huang Xiaomao,Zha Xiantao,Pan Haibing,et al.Measurement and analysis of rapeseeds’restitution coefficient in point-to-plate collision model[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2014,30(24):22-29.(in Chinese with English abstract)
[19]韩燕龙.碾米机内米粒运动特征及碾白特性[D].哈尔滨:东北农业大学,2017.Han Yanlong.Study on the Movement Characteristics and the Whitening Behavior of Rice Grains in a Friction Type Mill[D].Harbin:Northeast Agricultural University,2017.(in Chinese with English abstract)
[20]González-Montellano C,Fuentes J M,Ayuga-Téllez E,et al.Determination of the mechanical properties of maize grains and olives required for use in DEM simulations[J].Journal of Food Engineering,2012,111(4):553-562.
[21]贾富国,韩燕龙,刘扬,等.稻谷颗粒物料堆积角模拟预测方法[J].农业工程学报,2014,30(11):254-260.Jia Fuguo,Han Yanlong,Liu Yang,et al.Simulation prediction method of repose angle for rice particle materials[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2014,30(11):254-260.(in Chinese with English abstract)
[22]Coetzee C J,Els D N J.Calibration of discrete element parameters and the modelling of silo discharge and bucket filling[J].Computers&Electronics in Agriculture,2009,65(2):198-212.
[23]Ucgul M,Fielke J M,Sarnders C.Three-dimensional discrete element modeling of tillage:Determination of a suitable contact model and parameters for a cohesionless soil[J].Biosystems Engineering,2014,121(2):105-117.
[24]王云霞,梁志杰,张东兴,等.基于离散元的玉米种子颗粒模型种间接触参数标定[J].农业工程学报,2016,32(22):36-42.Wang Yunxia,Liang Zhijie,Zhang Dongxing,et al.Calibration method of contact characteristic parameters for corn seeds based on EDEM[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2016,32(22):36-42.(in Chinese with English abstract)
[25]刘凡一,张舰,李博,等.基于堆积试验的小麦离散元参数分析及标定[J].农业工程学报,2016,32(12):247-253.Liu Fanyi,Zhang Jian,Li Bo,et al.Calibration of parameters of wheat required in discrete element method simulation based on repose angle of particle heap[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2016,32(12):247-253.(in Chinese with English abstract)
[26]苑进,刘成良,古玉雪,等.基于相关向量机的双变量施肥控制序列优化[J].农业机械学报,2011,42(增刊1):184-189,171.Yuan Jin,Liu Chengliang,Gu Yuxue,et al.Bivariate fertilization control sequence optimization based on relevance vector machine[J].Transactions of the Chinese Society for Agricultural Machinery,2011,41(Supp.1):184-189,171.(in Chinese with English abstract)
[27]苑进.贝叶斯学习框架下非线性制造过程建模及多目标优化关键技术研究[D].上海:上海大学,2008.Yuan Jin.Research on Some Key Issues of Bayesian Learning Framework Based Nonlinear Manufacturing Process Modeling and Multiobjective Optimization[D].Shanghai:Shanghai University,2008.(in Chinese with English abstract)
[28]Liu Xuemei,Zhang Xiaohui,Yuan Jin.Relevance vector machine and fuzzy system based multi-objective dynamic design optimization:A case study[J].Expert Systems with Applications,2010,37:3598-3604.
[29]刘雪美,张晓辉,刘丰乐,等.喷杆喷雾机风助风筒相关向量机多目标优化设计[J].农业机械学报,2010,41(6):75-80.Liu Xuemei,Zhang Xiaohui,Liu Fengle,et al.Multiobjective dynamic design optimization for air duct of air-assisted boom sprayer based on RVM[J].Transactions of the Chinese Society for Agricultural Machinery,2010,41(6):75-80.(in Chinese with English abstract)
[30]Yuan J,Wang K S,Yu T,et al.Integrating relevance vector machines and genetic algorithms for optimization of seed-separating process[J].Engineering Applications of Artificial Intelligence,2007,20(7):970-979.
[31]Coetzee C J,Lombard S G.Discrete element method modelling of a centrifugal fertilizer spreader[J].Biosystems Engineering,2011,109(4):308-325.
[32]Ding Shangpeng,Bai Lu,Yao Yuxiang,et al.Discrete element modelling(DEM)of fertilizer dual-banding with adjustable rates[J].Computers and Electronics in Agriculture,2018,152:32-39.
[33]Holland J.Searching nonlinear functions for high values[J].Applied Mathematics and Computation,1989,32(23):255-274.