Bayesian Rectification of Nonlinear Dynamic Chemical Process Systems

非线性动态化学过程系统的贝叶斯校正

• 批准号: 0321911
• 负责人: Bhavik Bakshi
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-11-15 至 2008-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0321911&HistoricalAwards=false
• 关键词: Bayesian; Rectification; Nonlinear; Dynamic; Chemical

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.

研究：数据纠正或估计是清理测量数据并估计未知变量和参数的任务。 准确而快速的纠正对于化学过程的有效运行至关重要，因为许多任务在内，包括模型预测性控制，故障检测和诊断以及过程优化，都利用了整流或估计的数量。 所有方法都依赖于简化假设来获得可计算上的问题。 但是，现有的非线性动态数据整流（NDDR）方法（例如固定形状的分布）的大多数假设通常是不正确的。 这会恶化纠正的准确性和效率。由于强大的计算挑战，确定没有这种假设的最佳解决方案实际上是不可行的。统计物理学和贝叶斯统计的界面的最新进展，加上增加的计算能力，正在推动贝叶斯方法的开发和使用来解决复杂的随机问题。 这项研究旨在利用这些新工具来开发一种针对化学过程系统的NDDR的新颖且统计上严格的方法。与现有的方法相同，这种方法不会对概率分布施加预定的形状，但可以根据系统动力学，约束和测量来适应它们。 通过使用顺序的蒙特卡洛采样（SMC）方法获得这种灵活性。 最终的方法是递归的，不需要非线性编程。 因此，该方法应比现有NDDR方法提供更好的准确性和计算速度。 预计化学工程和统计之间的合作将通过解决各种实际情况来推动贝叶斯NDDR的理论和实践。 这些包括完全或部分指定模型的纠正，同时进行动态建模和整流，施加约束，处理非高斯错误以及估计诸如偏差，噪声和模型参数之类的未知数量。 还将研究理论特性，例如收敛性，样品数量对准确性的影响以及所选重要性函数的影响。最终的方法将应用于文献和工业合作者不同复杂性的案例研究。广泛的影响：为了鼓励在化学过程操作和控制中使用贝叶斯方法，将开发并广泛传播适当的教学教程和软件。 这项工作的结果将纳入统计和化学工程课程中。 还将开发针对行业的简短课程。 预计这些活动的成功完成将产生最初的贡献，这些贡献解决了在美国化学工业的2020年愿景报告中确定的关键需求，以及有关过程控制的NSF研讨会。预计这项工作还通过提高其效率和全球竞争力对美国制造过程产生更大的影响。