基于改进随机梯度下降的反应动力学参数估计方法  

Estimation of reaction kinetic parameters based on modified stochastic gradient descent

作　　者：唐立森 陈伟锋[1] TANG Li-sen;CHEN Wei-feng(School of Information Engineering,Zhejiang University of Technology,Hangzhou 310023,China)

机构地区：[1]浙江工业大学信息工程学院,浙江杭州310023

出　　处：《高校化学工程学报》2022年第3期426-436,共11页Journal of Chemical Engineering of Chinese Universities

基　　金：国家重点研发计划(2017YFE0106700);国家自然科学基金(61873242)。

摘　　要：针对传统优化方法利用所有采样数据进行参数估计存在的求解困难问题,在联立求解的框架下,通过引入随机优化和扩展目标函数,提出基于改进随机梯度下降的反应动力学参数估计方法。该方法对多数据集的大规模系统进行机理建模,基于灵敏度微分方程法获得灵敏度矩阵,同时利用模型标度化技术处理多状态变量对多参数估计的同步收敛性问题。为了减小迭代过程中噪声方差的影响,在现有的随机平均梯度下降方法的基础上,利用随机扩展目标函数增加目标函数中计算梯度的信息量,并给出该方法收敛的理论性分析。数值仿真结果验证了该方法的有效性和可行性。Considering the solution difficulty of conventional optimization algorithm in parameter estimation using all sampled data, a reaction kinetic parameter estimation method based on modified stochastic gradient descent was proposed by introducing stochastic optimization and extended objective function in the framework of simultaneous solution. Firstly, the mechanism of large-scale system with multiple data sets was modeled, and the sensitivity matrix was obtained based on the sensitivity differential equation method, and the model scaling technique was used to deal with the simultaneous convergence problem of multi-state variables to multi-parameter estimation. In order to reduce the influence of noise variance in the iterative process, based on the existing stochastic average gradient descent method, the stochastic extended objective function was applied to increase the amount of information for calculating the gradient in the objective function, and the theoretical convergence of the method was given. Relevant numerical simulation results have verified the effectiveness and feasibility of the proposed method.

关 键 词：参数估计 随机优化 扩展目标 灵敏度矩阵 

分 类 号：TQ03[化学工程]