考虑稳态和动态数据的S-型生化系统参数估计方法  

Parameter estimation method of S-type biochemical systems by steady-state and dynamic data

作　　者：邱玲 徐恭贤[1] QIU Ling;XU Gongxian(College of Mathematical Science,Bohai University,Jinzhou 121013,China)

机构地区：[1]渤海大学数学科学学院,辽宁锦州121013

出　　处：《沈阳师范大学学报（自然科学版）》2023年第1期45-48,共4页Journal of Shenyang Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11101051);辽宁省科技厅自然科学基金资助项目(20180550839);辽宁省教育厅科学研究经费项目(LJ2020015)。

摘　　要：针对具有稳态实验数据和动态实验数据的一类S-型生化系统的参数估计问题,以浓度误差、斜率误差与稳态误差之和为极小化目标,构建了一种参数估计优化模型。为了求解参数估计问题,利用四阶龙格库塔离散化格式,将优化问题中的微分方程转化为代数方程,同时将所构建的优化模型转化为稳态约束条件下的非线性规划问题。为了求解上述非线性规划问题,应用样条插值估计实验值的速率。为了说明算法的有效性可行性,将建立的优化模型与求解方法应用到已有的S-型生化系统中,并绘制了仿真结果的图像。与已有方法比较,数值结果表明,加入稳态误差优化与稳态约束后,可获得更为精确的参数估计结果。Aiming at the parameter estimation problem of a class of S-type biochemical systems with steady-state experimental data and dynamic experimental data,an optimization model of parameter estimation has been established with the sum of concentration error,slope error and steady-state error as the minimization target.In order to solve the parameter estimation problem,the fourth-order Runge-Kutta discretization scheme is used to convert the differential equations in the optimization problem into algebraic equations,and the constructed optimization model is transformed into a nonlinear programming problem under steady-state constraints.In order to solve the above nonlinear programming problem,spline interpolation is used to estimate the rate of the experimental values.In order to demonstrate the effectiveness and feasibility of the algorithm,the established optimization model and solution method are applied to the existing S-type biochemical system,and the simulation results are drawn.Compared with existing methods,the numerical results show that more accurate parameter estimation results can be obtained by adding steady-state error optimization and steady-state constraint.

关 键 词：S-型生化系统 稳态数据 动态数据 参数估计 稳态约束 

分 类 号：O29[理学—应用数学]