Model Reduction and State Estimation for Nonlinear Complex Systems
Creators: Debnath, Sarupa
Publisher: name: University of Alberta Library
Year: 2024

<p>Modern industries are increasingly embracing complex, large-scale processes with interconnected units for their economic benefits. The increasing scale of industrial processes and the complexity of unit interactions substantially complicate the development of advanced process control systems. Model reduction has been recognized as a promising framework for managing large-scale complex systems. It involves deriving low-dimensional models of computationally efficient systems, yet accurately represent the behavior of the overall system. Hence, this is essential for simulating high-dimensional systems in real-time, such as for control decisions or process monitoring, where accurate yet rapidly-solvable models are necessary. However, industrial processes bring added complexities along with high dimensionality such as varying time scales, challenges in measuring real-time outputs, nonlinearities, unknown parameters, and dynamic system behaviors. Therefore, this thesis focuses on addressing the high dimensionality of large-scale systems in process monitoring and control to accommodate various aforementioned industrial complexities. </p>

<p>A class of nonlinear systems, expressed by ordinary differential equations (ODE) with implicit two-time-scale behavior, is taken into account. The system is decomposed into fast and slow subsystems based on the singular perturbation theory and a composite solution for the system is proposed. Local estimators are designed for each subsystem and a one-directional communication scheme is used. A benchmark chemical process example is used to illustrate the proposed method. Attention is then given to nonlinear systems with essential process variables that are not measured but need to be monitored accurately from an operational perspective. It is assumed that a mechanistic model is available but is too computationally complex for estimator design and that only a subset of the states needs to be estimated. The aim is to form a reduced state estimation that can estimate the desired variables. A dynamic sensitivity-based approach is obtained to determine the appropriate inputs and outputs for data collection and data-driven model training. The proposed method is applied to a chemical process, and its applicability is demonstrated.</p>

<p>We consider a type of nonlinear system defined by partial differential equations (PDE) for an agrohydrological system. The inherent large-scale nature of the models stems from the discretization of the underlying PDE. The numerical simulation of such large-scale dynamical systems imposes overwhelming demands on computational resources. A reduced framework for large-scale systems is devised, leveraging unsupervised machine learning. However, in dynamic environments, the properties and behavior of the system might undergo changes. We therefore rely on dynamic data-driven reduced models where different reduced models are computed based on the performance of the model. The proposed approach is implemented to estimate the soil moisture of a real agricultural field located in Lethbridge, Canada. We also explore the proposed dynamic model reduction in estimating the soil water content and soil hydraulic parameters in real-case analysis applied to the farm, using experimental data collected in the summer of 2022.</p>