Inverse Problems in Population Balances. Determination of Aggregation Kernel by Weighted Residuals
Inverse Problems in Population Balances. Determination of Aggregation Kernel by Weighted Residuals
复制标题
人口平衡中的反问题。
DOI：
10.1021/acs.iecr.5b01368
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发表时间：
2015
影响因子：
4.2
通讯作者：
D. Ramkrishna
中科院分区：
文献类型：
--
作者：
Jayanta Chakraborty;Jitendra Kumar;Mehakpreet Singh;A. W. Mahoney;D. Ramkrishna
微粒系统的现象学通过破碎、聚集或生长核嵌入到种群平衡模型中。由于聚集核的非线性性质，它是一种难以从第一性原理预测的核。在这项工作中，我们展示了一种通过反问题方法获得聚合核的新方法。该方法基于加权残差法，不依赖于系统的自相似性等特定特征。残差法将反问题简化为一组线性方程的解。然而，方程组的条件很差，因此需要正则化才能得到准确的解。在这项工作中使用了吉洪诺夫正则化技术。新方法已经成功地证明了常数核、和核和积核。
The phenomenology of particulate systems are embedded into the population balance model through breakage, aggregation, or growth kernels. Aggregation kernel is a difficult kernel to predict from first principle because of its nonlinear nature. In this work we demonstrate a new methodology to obtain the aggregation kernel through inverse problem approach. This new approach is based on the method of weighted residuals and does not rely on specific traits of the system like self-similarity. The residual approach reduces the inverse problem into solution of a set of linear equations. However, the system of equations is badly conditioned and therefore requires regularization for accurate solution. In this work Tikhonov regularization technique has been used. The new method has been demonstrated successfully for constant, sum, and product kernel.