A Monte Carlo methods for identification and sensitivity analysis of coagulation processes
A Monte Carlo methods for identification and sensitivity analysis of coagulation processes
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DOI：
10.1016/j.jcp.2004.03.006
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发表时间：
2004-10
影响因子：
4.1
通讯作者：
A. Vikhansky;M. Kraft
中科院分区：
文献类型：
--
作者：
A. Vikhansky;M. Kraft
提出了一种计算种群平衡方程解的参数导数的随机模拟算法。离散系统近似为N粒子随机加权系综。通过在每次凝固时重新计算的统计权重的无穷小偏差来解释导数。因此，假定N足够大，所有参数导数可以沿过程的一个轨迹沿着计算。我们使用一个运营商分裂技术占表面生长的颗粒。所得解与已有的解析解吻合良好。只要已知参数导数，基于梯度的方法就可以应用于混凝过程的控制和辨识。所提出的技术的多维情况下的扩展是简单的。
A stochastic simulation algorithm is presented to calculate parametric derivatives of solutions of a population balance equation. The dispersed system is approximated by an N-particle stochastic weighted ensemble. The derivatives are accounted for through infinitesimal deviation of the statistical weights that are recalculated at each coagulation. Thus, all the parametric derivatives can be calculated along one trajectory of the process, given N sufficiently large. We use an operator-splitting technique to account for surface growth of the particles. The obtained solution is in good agreement with the available analytical solutions. As soon as the parametric derivatives are known the gradient-based methods can be applied to the control and identification of the coagulation process. The extension of the proposed technique to a multi-dimensional case is straightforward.