Bayesian Rectification of Nonlinear Dynamic Chemical Process Systems

研究：数据校正或估计是清理测量数据和估计未知变量和参数的任务。准确和快速的整流对于化学过程的有效运行至关重要，因为许多任务包括模型预测控制，故障检测和诊断以及过程优化，都使用整流或估计数量。所有方法都依赖于简化假设来获得计算上可处理的问题。然而，现有的非线性动态数据整流（NDDR）方法的大多数假设，如分布是固定形状的，通常是不正确的。这降低了整改的准确性和效率。由于巨大的计算挑战，在没有这些假设的情况下确定最优解实际上是不可行的。统计物理和贝叶斯统计的最新进展，加上不断增强的计算能力，正在推动贝叶斯方法在解决复杂随机问题中的发展和使用的复苏。本研究旨在利用这些新工具为化学过程系统的NDDR开发一种新颖且统计严谨的方法。与现有的方法不同，这种方法不会对概率分布施加预先确定的形状，而是允许它们根据系统动力学、约束和测量进行调整。这种灵活性是通过顺序蒙特卡罗采样（SMCS）方法获得的。得到的方法是递归的，不需要非线性规划。因此，该方法有望提供比现有NDDR方法更好的精度和计算速度。化学工程与统计学之间的合作有望通过解决各种实际情况来推进贝叶斯NDDR的理论和实践。这些包括完全或部分指定模型的校正，同时动态建模和校正，施加约束，处理非高斯误差，以及估计未知量，如偏差，噪声和模型参数。理论性质，如收敛性，样本数量对准确性的影响，以及所选择的重要函数的影响也将进行研究。由此产生的方法将应用于从文献和工业合作者的不同复杂性的案例研究。广泛影响：为了鼓励在化学过程操作和控制中使用贝叶斯方法，将编写和广泛传播适当的教育教程和软件。这项工作的结果将纳入统计学和化学工程课程。还将为工业开发短期课程。这些活动的成功完成预计将导致解决美国化学工业2020年愿景报告和美国国家科学基金会过程控制研讨会中确定的关键需求的原始贡献。预计这项工作还将通过提高美国制造业的效率和全球竞争力，对其产生更广泛的影响。

Research: Data rectification or estimation is the task of cleaning measured data and estimating unknown variables and parameters. Accurate and fast rectification is essential for efficient operation of chemical processes since many tasks including model predictive control, fault detection and diagnosis, and process optimization, utilize rectified or estimated quantities. All methods rely on simplifying assumptions to obtain a computationally tractable problem. However, most assumptions of existing Nonlinear Dynamic Data Rectification (NDDR) methods such as the distributions being of a fixed shape, are usually incorrect. This deteriorates the accuracy and efficiency of rectification. Determining the optimal solution without such assumptions has not been practically feasible due to formidable computational challenges. Recent advances at the interface of statistical physics and Bayesian statistics, combined with increasing computational power are driving a resurgence in the development and use of Bayesian methods for solving complex stochastic problems. This research aims to utilize these new tools to develop a novel and statistically rigorous approach for NDDR of chemical process systems.Unlike existing methods, this approach does not impose a pre-determined shape on the probability distributions, but allows them to adapt according to the system dynamics, constraints, and measurements. Such flexibility is obtained by using Sequential Monte Carlo Sampling (SMCS) methods. The resulting approach is recursive, and does not require nonlinear programming. Consequently, the method is expected to provide better accuracy and computation speed than existing NDDR methods. The collaboration between chemical engineering and statistics is expected to advance the theory and practice of Bayesian NDDR by addressing a variety of practical situations. These include rectification with fully or partially-specified models, simultaneous dynamic modeling and rectification, imposing constraints, handling non-Gaussian errors, and estimating unknown quantities such as bias, noise, and model parameters. Theoretical properties such as convergence, effect of number of samples on accuracy, and effect of the selected importance function will also be studied. The resulting methods will be applied to case studies of varying complexity from the literature and from industrial collaborators. Broad Impact:To encourage the use of Bayesian methods in chemical process operation and control, appropriate educational tutorials and software will be developed and widely disseminated. The results of this work will be incorporated in courses in statistics and chemical engineering. Short courses for industry will also be developed. Successful completion of these activities is expected to result in original contributions that address critical needs identified in the Vision 2020 report for the U.S. chemical industry and an NSF workshop on process control. The work is also expected to have a broader impact on U.S. manufacturing processes by improving their efficiency and global competitiveness.