基于粒子群优化算法的Richards模型参数估计和算法有效性

针对Richards模型参数估计较为困难的实际问题，提出将Richards模型的参数估计问题转化为一个多维无约束函数优化问题。结合谷氨酸菌体的实际生长浓度数据，在Matlab 2012b环境中，利用粒子群优化（PSO）算法建立适应度函数，在最小线性二乘意义下估计Richards模型中的4个参数，并建立了拟合的生长曲线和最优值变化曲线。为进一步验证算法有效性，将PSO算法与该模型传统参数估计法中的四点法和遗传算法(GA)进行了比较，以相关指数和剩余标准差作为评价指标。结果表明，PSO算法对Richards模型的拟合效果良好，对模型的参数估计有着很好的适用性。

Parameter estimation of Richards model and algorithm effectiveness based on particle swarm optimization algorithm

Aiming to the practical problem that it is difficult to estimate the Richards model parameters, the parameter estimation problem of the Richards model was formulated as a multi-dimensional unconstrained function optimization problem. Combined with the actual growth concentration of glutamic acid, in Matlab 2012b environment, the fitness function was established by Particle Swarm Optimization (PSO) algorithm, four parameters of Richards model were estimated by the least square method, and the growth curve and the optimum curve were established. To further verify the effectiveness of the algorithm, the PSO algorithm was compared with traditional parameter estimation method, such as four point method and Genetic Algorithm (GA) method, the related index and the residual standard deviation were used as the evaluation index. The results show that, the PSO algorithm has better fitting effect for Richards model and good applicability for parameter estimation.