Parameter Estimation for an Inverse Nonlinear Stochastic Problem: Reactivity Ratio Studies in Copolymerization
Parameter Estimation for an Inverse Nonlinear Stochastic Problem: Reactivity Ratio Studies in Copolymerization
复制标题
非线性逆随机问题的参数估计：共聚反应活性比研究
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
T. Duever
中科院分区：
文献类型：
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作者：
Yuncheng Du;H. Budman;T. Duever
提出了一种基于广义多项式混沌(GPC)的方法来估计共聚反应的竞聚率，其中竞聚率是随机未知的，通过比较模型预测和有限的实验数据来确定。将估计步骤表示为用极大似然函数求分布随机反应率参数的随机反问题。结果表明，基于GPC的竞聚率估计是有效和强大的，因为它同时提供了最优估计及其相应的方差。除了获得准确的估计结果外，还表明基于广义预测的方法的计算成本明显低于马尔可夫链蒙特卡罗模拟，从而显示了广义预测方法处理其他更复杂的非线性问题的潜力。
A generalized polynomial chaos (gPC)-based methodology is developed to estimate the reactivity ratio in copolymerization, where the reactivity ratio is assumed to be stochastic unknown and determined by comparing model predictions with limited experimental data. The estimation step is formulated as a stochastic inverse problem of finding the distributional stochastic reactivity ratio parameters with a maximum likelihood function. The results show that the gPC-based reactivity ratio estimation is efficient and powerful, since it simultaneously provides the best estimates and their corresponding variances. Beyond achieving accurate estimation results, it is shown that the computational cost of the gPC-based methodology is significantly lower than Markov chain Monte Carlo simulations, thus demonstrating the potential of the gPC method for dealing with other more complicated nonlinear problems.