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.
