基于变步长果蝇优化算法的Richards模型参数估计
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摘要
为解决Richards模型参数估计困难的实际问题,在最小线性二乘的意义下,通过变步长果蝇优化算法(VS-FOA)对非线性函数进行优化,完成Richards模型的参数估计,将该模型应用于谷氨酸菌体生长浓度的预测,建立菌体拟合生长曲线和最优值的变化曲线。利用均方根误差、决定系数和平均绝对误差验证了该算法的有效性和可行性,实验结果表明,该算法对Richards模型的参数估计有着较好的适用性。
To solve practical problem that it is difficult to estimate parameters of Richards model,the variable step size fruit fly optimization algorithm(VS-FOA)was used to optimize the fitness function from the perspective of the least square method,to complete the parameter estimation of Richards model.This model was applied to predict the growth concentration of glutamic acid bacteria,and the growth curve and the optimum curve were established.The effectiveness and feasibility of algorithm were verified by root-mean-square error,coefficient of determination,and mean absolute errors.Experimental results show that the VS-FOA algorithm has fairly good applicability for the parameter estimation of Richards model.
To solve practical problem that it is difficult to estimate parameters of Richards model,the variable step size fruit fly optimization algorithm(VS-FOA)was used to optimize the fitness function from the perspective of the least square method,to complete the parameter estimation of Richards model.This model was applied to predict the growth concentration of glutamic acid bacteria,and the growth curve and the optimum curve were established.The effectiveness and feasibility of algorithm were verified by root-mean-square error,coefficient of determination,and mean absolute errors.Experimental results show that the VS-FOA algorithm has fairly good applicability for the parameter estimation of Richards model.
引文
[1]Purnachandra Rao Koya,Ayele Taye Goshu.Generalized mathematical model for biological growth[J].Open Journal of Modeling and Simulation,2013,1(4):42-53.
[2]ZHAO Fan.Research on growth variations of maize by whole film double furrow sowing based on Richards model from traditional cultivation mode[J].Agricultural Research in the Arid Areas,2016,34(4):211-216(in Chinese).[赵凡.基于Richards模型的全膜双垄沟播与传统栽培模式玉米生长势差异研究[J].干旱地区农业研究,2016,34(4):211-216.]
[3]Lv J,Wang K,Jiao J.Stability of stochastic Richards growth model[J].Journal of Biomathematics,2015,39(16):4821-4827.
[4]YAN Zhengang,HU Henian,LI Guang.Parameter estimation of Richards model and algorithm effectiveness based on particle swarm optimization algorithm[J].Journal of Applications,2014,34(10):2827-2830(in Chinese).[燕振刚,胡贺年,李广.基于粒子群优化算法的Richards模型参数估计和算法有效性[J].计算机应用,2014,34(10):2827-2830.]
[5]Zhan Zhihui,Zhang Jun,Li Yun,et al.Orthogonal learning particle swarm optimization[J].IEEE Transactions on Evolutionary Computation,2011,15(6):832-847.
[6]XIE Tao.The research on fault diagnosis for analog circuits based on(Multi)wavelet(packet)analysis neural networks and optimization[D].Changsha:Hunan University,2011:25-30(in Chinese).[谢涛.基于(多)小波(包)、神经网络及优化的模拟电路故障诊断研究[D].长沙:湖南大学,2011:25-30.]
[7]HAN Junying,LIU Chengzhong.Fruit fly optimization algorithm based on bacterial chemotaxis[J].Journal of Applications,2013,33(4):964-966(in Chinese).[韩俊英,刘成忠.基于细菌趋化的果蝇优化算法[J].计算机应用,2013,33(4):964-966.]
[8]WU Qiong,CHEN Zhijun.Runoff forecasting based on fruit fly optimization algorithm and SVM algorithm[J].Yellow River,2015,37(9):28-31(in Chinese).[吴琼,陈志军.基于果蝇优化算法的支持向量机径流预测[J].人民黄河,2015,37(9):28-31.]
[9]ZHU Daqi,YUAN Yili,DENG Zhigang.Parameter identification of underwater vehicles based on the quantum-behaved particle swarm optimization algorithm[J].Control Engineering of China,2015,22(1):531-537(in Chinese).[朱大奇,袁义丽,邓志刚.水下机器人参数辨识的量子粒子群算法[J].控制工程,2015,22(1):531-537.]
[10]WANG Zhigang.Parameter estimation of nonlinear system model based on artificial bee colony algorithm[J].Mathematics in Practice and Theory,2013,43(16):142-147(in Chinese).[王志刚.基于人工蜂群算法的非线性系统模型参数估计[J].数学的实践与认识,2013,43(16):142-147.]
[11]LI Xingbao.Hybrid modeling of glutamic acid fermentation process based on prior knowledge and improved LS-SVM[D].Wuxi:Jiangnan University,2011(in Chinese).[黎兴宝.基于机理知识与改进LS-SVM的谷氨酸发酵混合建模[D].无锡:江南大学,2011.]
[2]ZHAO Fan.Research on growth variations of maize by whole film double furrow sowing based on Richards model from traditional cultivation mode[J].Agricultural Research in the Arid Areas,2016,34(4):211-216(in Chinese).[赵凡.基于Richards模型的全膜双垄沟播与传统栽培模式玉米生长势差异研究[J].干旱地区农业研究,2016,34(4):211-216.]
[3]Lv J,Wang K,Jiao J.Stability of stochastic Richards growth model[J].Journal of Biomathematics,2015,39(16):4821-4827.
[4]YAN Zhengang,HU Henian,LI Guang.Parameter estimation of Richards model and algorithm effectiveness based on particle swarm optimization algorithm[J].Journal of Applications,2014,34(10):2827-2830(in Chinese).[燕振刚,胡贺年,李广.基于粒子群优化算法的Richards模型参数估计和算法有效性[J].计算机应用,2014,34(10):2827-2830.]
[5]Zhan Zhihui,Zhang Jun,Li Yun,et al.Orthogonal learning particle swarm optimization[J].IEEE Transactions on Evolutionary Computation,2011,15(6):832-847.
[6]XIE Tao.The research on fault diagnosis for analog circuits based on(Multi)wavelet(packet)analysis neural networks and optimization[D].Changsha:Hunan University,2011:25-30(in Chinese).[谢涛.基于(多)小波(包)、神经网络及优化的模拟电路故障诊断研究[D].长沙:湖南大学,2011:25-30.]
[7]HAN Junying,LIU Chengzhong.Fruit fly optimization algorithm based on bacterial chemotaxis[J].Journal of Applications,2013,33(4):964-966(in Chinese).[韩俊英,刘成忠.基于细菌趋化的果蝇优化算法[J].计算机应用,2013,33(4):964-966.]
[8]WU Qiong,CHEN Zhijun.Runoff forecasting based on fruit fly optimization algorithm and SVM algorithm[J].Yellow River,2015,37(9):28-31(in Chinese).[吴琼,陈志军.基于果蝇优化算法的支持向量机径流预测[J].人民黄河,2015,37(9):28-31.]
[9]ZHU Daqi,YUAN Yili,DENG Zhigang.Parameter identification of underwater vehicles based on the quantum-behaved particle swarm optimization algorithm[J].Control Engineering of China,2015,22(1):531-537(in Chinese).[朱大奇,袁义丽,邓志刚.水下机器人参数辨识的量子粒子群算法[J].控制工程,2015,22(1):531-537.]
[10]WANG Zhigang.Parameter estimation of nonlinear system model based on artificial bee colony algorithm[J].Mathematics in Practice and Theory,2013,43(16):142-147(in Chinese).[王志刚.基于人工蜂群算法的非线性系统模型参数估计[J].数学的实践与认识,2013,43(16):142-147.]
[11]LI Xingbao.Hybrid modeling of glutamic acid fermentation process based on prior knowledge and improved LS-SVM[D].Wuxi:Jiangnan University,2011(in Chinese).[黎兴宝.基于机理知识与改进LS-SVM的谷氨酸发酵混合建模[D].无锡:江南大学,2011.]