Mathematical and statistical tools for chemical process modeling and performance improvement

化学工程师使用数学模型来满足各种需求-总结对化学过程如何工作的理解，预测如果发生变化，它们将如何表现，学习如何改进产品或制造过程的设计，设计控制器以确保安全，可靠和有利可图的操作，并监控过程的操作以观察设备的恶化和故障。在构建模型时，工程师必须决定使用哪种类型的数学方程，以及要建模多少物理细节。我们的目标是平衡对复杂模型的需求和使用它们的好处。数学模型还包含常数，这些常数必须通过运行实验和从运行的工厂收集实验信息来估计。这些常数是使用统计技术估计的，挑战在于决定要包括多少细节以及要估计哪些常数。该研究项目正在开发数学和统计工具，以帮助做出这些决定。该研究集中在两种类型的问题：优化工厂操作的模型构建（实时优化），以及当我们试图预测剖面（曲线）而不是单个数字时估计模型。曲线的一个示例是正在被再加热的钢锭中的温度曲线。一个相对较新的统计技术称为函数数据分析正在用于这个问题。我们还可以使用这种方法来估计描述化学过程如何随时间变化的模型。函数数据分析提供了一种特殊的方法来估计模型，这应该使构建有用的模型变得更容易。 该研究项目的最后一部分将开发一种新的方法来制造有价值的分子，使用细胞和一种特殊的方式为细胞提供底物（食物），并去除细胞制造的产物。通过这种方式，我们可以避免由于底物过多或产物过多而导致细胞生产率低下的情况。

Chemical engineers use mathematical models for a variety of needs -  to summarize understanding about how chemical processes work, for predicting how they will behave if changes are made, for learning how to improve the design of products or manufacturing processes, for designing controllers to ensure safe, reliable and profitable operation, and to monitor the operation of the processes to watch for deteriorating equipment and failures. When building models engineers have to decide what type of mathematical equations to use,  and how much physical detail to model. The goal is to balance the need for complicated models against the benefits from using them. Mathematical models also contain constants which have to be estimated by running experiments and collecting experimental information from operating plants. These constants are estimated using statistical techniques.The challenge is to decide how much detail to include and which constants to estimate. This research project is developing mathematical and statistical tools to help make these decisions. The research is focusing on two types of problems: model-building for optimizing plant operation (real-time optimization), and estimating models when we are trying to predict profiles (curves), instead of single numbers. An example of a profile is the temperature profile in a steel ingot that is being reheated. A relatively new statistical technique called Functional Data Analysis is being used for this problem. We can also use this approach to estimate models that describe how chemical processes change with time. Functional data analysis provides a special way of estimating the models that should make it easier to build useful models.  The last part of the research project is going to develop a new approach for making valuable molecules, using cells and a special way of providing substrate (food) to the cells, and removing the products that the cells make. In this way, we can avoid situations where the cell productivity is poor because there is too much substrate, or too much product.