Nonlinear stochastic modeling to improve state estimation in process monitoring and control

Abstract

in Wiley Online Library (wileyonlinelibrary.com).State estimation from plant measurements plays an important role in advanced monitoring and control technologies, especially for chemical processes with nonlinear dynamics and significant levels of process and sensor noise. Several types of state estimators have been shown to provide high-quality estimates that are robust to significant process disturbances and model errors. These estimators require a dynamic model of the process, including the statistics of the stochastic disturbances affecting the states and measurements. The goal of this article is to introduce a design method for nonlinear state estimation including the following steps: (i) nonlinear process model selection, (ii) stochastic disturbance model selection, (iii) covariance identification from operating data, and (iv) estimator selection and implementation. Results on the implementation of this design method in nonlinear examples (CSTR and large dimensional polymerization process) show that the linear time-varying autocovariance least-squares technique accurately estimates the noise covariances for the examples analyzed, providing a good set of such covariances for the state estimators implemented. On the estimation implementation, a case study of a chemical reactor demonstrates the better capabilities of MHE when compared with the extended Kalman filter.

Observability analysis and model formulation for nonlinear state estimation

“…This can lead to poor performance or even filter divergence. On the other hand, if the matrix Q is guessed higher than the actual value, the state estimates will be noisy and uncertain, as this would lead to increased values of the state covariance matrix, P. In a few words, choosing the right value of the tuning parameters is very important for successful application of EKF [19,22,23].…”

An Approximate Expectation Maximization Algorithm for Estimating Parameters, Noise Variances, and Stochastic Disturbance Intensities in Nonlinear Dynamic Models

“…3,7 Parameter estimates obtained using SDE models are suitable for online process monitoring applications because SDE models account for measurement errors and stochastic process disturbance, the two types of random errors that are accounted for by extended Kalman filters (EKFs) and related state estimators. 8,9 In this article, we consider a multi-input multi-output (MIMO) nonlinear SDE model of the following form: where x ∈ R X is the vector of state variables, t is time, f: R X × R U × R P → R X is a vector of nonlinear functions, u ∈ R U is the vector of input variables, and θ ∈ R P is the vector of unknown model parameters, η(t) ∈ R X is a continuous zero-mean stationary white-noise process with covariance matrix E{η(t 1 )η T (t 2 )}= Qδ(t 2 − t 1 ), where Q is a diagonal power spectral density matrix with dimension X × X:…”

Constrained dual ensemble Kalman filter for state and parameter estimation

“…Thus, the performance of the state estimation algorithm is dependant on the accuracy of the mechanistic model and accurate characterisation of the unmeasured disturbances and noise. Recently, there have been approaches proposed in literature to obtain the covariance matrices of the process and measurement noise ( [1] and [2]). …”