Bayesian parameter estimation for a jet-milling model using Metropolis-Hastings and Wang-Landau sampling
Bayesian parameter estimation for a jet-milling model using Metropolis-Hastings and Wang-Landau sampling
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DOI：
10.1016/j.ces.2012.11.027
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发表时间：
2013-02-15
影响因子：
4.7
通讯作者：
Himawan, Chrismono
中科院分区：
文献类型：
--
作者：
Kastner, Catharine A.;Braumann, Andreas;Himawan, Chrismono
贝叶斯参数估计的计算昂贵的多响应喷射铣削模型计算使用大都会黑斯廷斯和王朗道马尔可夫链蒙特卡罗抽样算法。该模型是伴随着从74个实验中获得的数据在不同的工艺设置，这是用来估计模型参数。实验测量的量是所得粒度分布的第10、第50和第90分位数。对由射流膨胀、研磨和分级三个子过程组成的总体平衡喷射研磨模型进行了参数估计。该模型包含八个需要估计的参数，并且可以计算实验中确定的相同数量。由于该模型求解起来在计算上是昂贵的，因此将采样算法应用于代理模型以建立算法特定参数并获得模型参数估计值。由此产生的参数估计与讨论其可靠性和观察到的行为的两个采样算法。比较两种算法生成的样本之间的自相关函数表明，Wang-Landau算法表现出更快的衰减。两种算法的参数样本的迹线图似乎是类似的，并鼓励假设马尔可夫链已收敛到感兴趣的分布。一维和二维密度图表明所有参数均呈单峰分布，这表明所获得的估计值是唯一的。二维密度图还表明至少两个模型参数之间的相关性。这两种算法产生的实现分布产生一致的结果，并表现出类似的行为。对于在这项工作中考虑的应用程序，王-朗道算法被发现表现出上级性能的相关性和等效性能在所有其他方面。(C)2012爱思唯尔有限公司保留所有权利。
Bayesian parameter estimates for a computationally expensive multi-response jet-milling model are computed using the Metropolis-Hastings and Wang-Landau Markov Chain Monte Carlo sampling algorithms. The model is accompanied by data obtained from 74 experiments at different process settings which is used to estimate the model parameters. The experimentally measured quantities are the 10th, 50th and 90th quantiles of the resulting particle size distributions. Parameter estimation is performed on a population balance jet-milling model composed of three subprocesses: jet expansion, milling and classification. The model contains eight parameters requiring estimation and can compute the same quantities that are determined in the experiments. As the model is computationally expensive to solve, the sampling algorithms are applied to a surrogate model to establish algorithm specific parameters and to obtain model parameter estimates. The resulting parameter estimates are given with a discussion of their reliability and the observed behaviour of the two sampling algorithms. Comparison of the autocorrelation function between samples generated by the two algorithms shows that the Wang-Landau algorithm exhibits more rapid decay. Trace plots of the parameter samples from the two algorithms appear to be analogous and encourage the supposition that the Markov Chains have converged to the distribution of interest. One- and two-dimensional density plots indicate a unimodal distribution for all parameters, which suggests that the obtained estimates are unique. The two-dimensional density plots also suggest correlation between at least two of the model parameters. The realised distribution generated by both algorithms produced consistent results and demonstrated similar behaviour. For the application considered in this work, the Wang-Landau algorithm is found to exhibit superior performance with respect to the correlation and equivalent performance in all other respects. (C) 2012 Elsevier Ltd. All rights reserved.