Bayesian Estimation by Sequential Monte Carlo Sampling: Application to High-Dimensional Nonlinear Dynamic Systems

Abstract

Modern industrial enterprises have invested significant resources for collecting and distributing data, with the expectation that it will enhance profitability via better decision making. Due to the complexity of these problems, existing approaches tend to make convenient, but invalid assumptions so that tractable solution may be found. For example, for estimation in nonlinear dynamic systems, extended Kalman filtering (EKF) relies on Gaussian approximation and local linearization to find a closed-form solution. Moving horizon based least-squares estimation (MHE) also relies on Gaussian approximation, but the use of nonlinear models and constraints eliminates most of the computational benefits of this approximation, but can provide more accurate estimates than EKF. Unfortunately, in most practical nonlinear dynamic systems, the posterior distributions are often far from Gaussian, and continually change their shape.Our previous work has developed rigorous Bayesian methods for estimation in nonlinear dynamic systems with constraints. These methods rely on recent theoretical developments in Sequential Monte Carlo Sampling (SMC). It does not rely on assumptions about the shape of the distributions, or nature of the models. Furthermore, this approach is expected to be computationally more efficient due to its recursive formulation that does not rely on nonlinear programming. These claims have been supported via applications to relatively small scale CSTR case studies. However, there are no illustrations or theoretical proofs to indicate how SMC performs for high-dimensional systems.This paper applies our previous work on Bayesian rectification by SMC to large scale nonlinear dynamic systems and compares the computational efficiency and accuracy with MHE and EKF. The model of the selected polymerization reactor contains eight variables, exhibit significant linear and nonlinear dynamics under different operating conditions, and requires satisfaction of process constraints. Results indicate that the accuracy and computational benefits of SMC are significant even for such high-dimensional systems.