Bayesian Error Propagation for a Kinetic Model of n -Propylbenzene Oxidation in a Shock Tube
Bayesian Error Propagation for a Kinetic Model of n -Propylbenzene Oxidation in a Shock Tube
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激波管中正丙基苯氧化动力学模型的贝叶斯误差传播
DOI：
10.1002/kin.20855
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发表时间：
2014
影响因子：
1.5
通讯作者：
Mosbach S
中科院分区：
文献类型：
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作者：
Mosbach S
我们将贝叶斯参数估计技术应用于正丙基苯在激波管中氧化的化学动力学机理，以将实验数据中的误差传播到Arrhenius参数和预测的物种浓度的误差中。我们发现，为了成功地应用该方法，需要将常规优化作为初步步骤。这分两个阶段进行：首先，使用Sobol低偏差序列进行准随机全局搜索，然后利用混合梯度下降/牛顿迭代法进行局部优化。在不同的温度、压力和当量比下对37种物质的浓度进行了优化，总共有2378次实验观察。然后，我们应用贝叶斯方法研究了实验测量中的不确定性对模型中的一些Arrhenius参数以及一些预测的物种浓度的影响。用马尔可夫链蒙特卡罗算法对后验概率密度进行抽样，用高阶多项式拟合出模型响应。我们的结论是，该方法为分析模型参数和响应的分布，特别是它们的不确定性和相关性提供了一个有用的工具。讨论了该方法的局限性。例如，我们发现，使用二阶响应面和假设传播误差的正态分布在很大程度上是足够的，但并不总是如此。
We apply a Bayesian parameter estimation technique to a chemical kinetic mechanism forn‐propylbenzene oxidation in a shock tube to propagate errors in experimental data to errors in Arrhenius parameters and predicted species concentrations. We find that, to apply the methodology successfully, conventional optimization is required as a preliminary step. This is carried out in two stages: First, a quasi‐random global search using a Sobol low‐discrepancy sequence is conducted, followed by a local optimization by means of a hybrid gradient‐descent/Newton iteration method. The concentrations of 37 species at a variety of temperatures, pressures, and equivalence ratios are optimized against a total of 2378 experimental observations. We then apply the Bayesian methodology to study the influence of uncertainties in the experimental measurements on some of the Arrhenius parameters in the model as well as some of the predicted species concentrations. Markov chain Monte Carlo algorithms are employed to sample from the posterior probability densities, making use of polynomial surrogates of higher order fitted to the model responses. We conclude that the methodology provides a useful tool for the analysis of distributions of model parameters and responses, in particular their uncertainties and correlations. Limitations of the method are discussed. For example, we find that using second‐order response surfaces and assuming normal distributions for propagated errors is largely adequate, but not always.