The accurate estimation of sensitive parameters in a mathematical model predicting the outcome of a real experiment is of great importance in studying a complex physical phenomenon. A systematic methodology based on the uncertainty and sensitivity analysis framework is proposed for precise estimation of model parameters. The nonintrusive polynomial chaos expansion and the Sobol’-based sensitivity indices are used to quantify the uncertainties in the model prediction due to parameter uncertainties, and the Monte Carlo method is used for the validation of uncertainty quantification results. A population balance model for an unseeded batch cooling crystallization of l-asparagine monohydrate with two different sets of kinetic models for nucleation and crystal growth is selected to demonstrate the methodology. The results clearly demonstrate the effectiveness of the proposed strategy in improving the predictive ability of the population balance model. For models involving many uncertain parameters, the proposed strategy can be adopted to rank parameters by decreasing importance and then achieve precise estimation of the more significant parameters using a suitable optimization algorithm and experimental data set.

中文翻译：

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使用不确定性和敏感性分析的人口平衡模型中的参数识别

在预测真实实验结果的数学模型中准确估计敏感参数对于研究复杂的物理现象非常重要。提出了一种基于不确定性和敏感性分析框架的系统方法，用于精确估计模型参数。采用非侵入式多项式混沌展开和基于Sobol'的灵敏度指标量化模型预测中由于参数不确定性的不确定性，并采用蒙特卡罗方法对不确定性量化结果进行验证。l的无种子批次冷却结晶的种群平衡模型选择具有两组不同的成核和晶体生长动力学模型的-天冬酰胺一水合物来演示该方法。结果清楚地证明了所提出的策略在提高人口平衡模型的预测能力方面的有效性。对于包含许多不确定参数的模型，可以采用本文提出的策略，通过降低重要性对参数进行排序，然后使用合适的优化算法和实验数据集对更重要的参数进行精确估计。