Combining Fundamental Models with Data

将开发将基本模型和数据相结合的新方法，以降低实验成本和缩短开发时间，从而实现准确的化学过程模型。从长远来看，这项研究将有助于开发数字双胞胎作为工业运营的先进工具。学生将接受建模和数据分析方面的宝贵培训，为有助于流程数字化和开发更绿色流程的职业做好准备。拟议的研究集中在两个持续存在的空白上，这两个空白使开发有效的化学和生化过程基本模型变得困难。首先，很难利用先验知识来选择最佳的实验条件，从而得到可靠的参数估计和准确的模型预测。虽然常规的过程数据可以免费获得，但基础模型构建所需的信息量很大的新实验可能会很昂贵。企业需要更好的工具来计划实验，这样才能在更短的时间内以更少的成本建立准确的模型。第二是难以调整动态模型以用于在线监测和控制。当新数据可用时，状态估计器可用于更新模型中的状态和参数。然而，状态估值器的调整(基于测量和模型不确定性)仍然是一个困难的问题。我们将通过开发改进的基于模型的实验设计(MBDOE)的顺序方法来解决第一个差距。新方法将允许MBDOE计算，即使有限的数据(或大量的模型参数)导致不可逆的Fisher信息矩阵。不可逆性问题将使用MBDOE目标函数中的贝叶斯项来解决。建议的方法将与目前的方法进行比较，这些方法使用的案例研究包括：i)生产生物来源聚醚；ii)二氧化碳加氢生产可再生燃料；iii)用于低溶剂汽车涂料的丙烯酸酯/甲基丙烯酸酯共聚。我们将使用新的同步方法来估计模型参数并获得用于状态估计器调整的不确定性信息，以解决第二个缺口。基本模型将增加新的经验随机项和状态方程，以考虑干扰和模型缺陷。基本模型参数、模型不确定性和测量噪声方差将使用有效的最大似然和贝叶斯算法从旧批动态数据中估计出来。建议的同时方法将与现有的调整扩展卡尔曼滤波器(EKF)和相关估计器的技术进行测试，在这些技术中，模型参数和噪声协方差是在单独的步骤中估计的。我们假设，拟议的同时方法将产生更可靠的参数和状态估计，从而导致改进的在线模型预测。一个典型的工业聚乙烯反应器模型将被用作案例研究。

New methods will be developed for combining fundamental models and data, leading to accurate chemical-process models with reduced experimental costs and shorter development times. In the longer-term, the research will contribute to development of digital twins as advanced tools for industrial operation. Students will receive valuable training in modeling and data analysis, preparing them for careers that contribute to process digitalization and development of greener processes. The proposed research focuses on two persistent gaps that make it difficult to develop effective fundamental models of chemical and biochemical processes. The first is that it is difficult to use prior knowledge to select optimal experimental conditions that result in reliable parameter estimates and accurate model predictions. Although routine process data may be freely available, informative new experiments required for fundamental-model building can be expensive. Companies need better tools to plan experiments so that accurate models can be built in a shorter time with less cost. The second is is that it is difficult to tune dynamic models for use in on-line monitoring and control. State estimators are available for updating states and parameters in models as new data become available. However, tuning of state estimators (based on measurement and model uncertainties) remains a difficult problem. We will address the first gap by developing improved sequential methods for Model-Based Design of Experiments (MBDOE). The new methods will permit MBDOE calculations even when limited data (or a large number of model parameters) results in a non-invertible Fisher information matrix. The non-invertibility problem will be addressed using Bayesian terms in the MBDOE objective functions. The proposed approach will be compared with current methods using case studies on i) production of bio-sourced polyethers, ii) CO2 hydrogenation for renewable fuels production and iii) acrylate/methacrylate copolymerization for low-solvent automotive coatings. We will address the second gap using new simultaneous methods to estimate model parameters and obtain uncertainty information for state-estimator tuning. Fundamental models will be augmented with new empirical stochastic terms and state equations to account for disturbances and model imperfections. Fundamental model parameters, model uncertainties and measurement-noise variances will be estimated from old batches of dynamic data using efficient maximum-likelihood and Bayesian algorithms. The proposed simultaneous method will be tested against existing techniques for tuning extended Kalman filters (EKFs) and related estimators wherein model parameters and noise covariances are estimated in separate steps. We hypothesize that more-reliable parameter and state estimates will result from the proposed simultaneous approach, leading to improved on-line model predictions. An industrial polyethylene reactor model will be used as a case study.