Fault detection and diagnosis in a closed-loop nonlinear distillation process: application of extended Kalman filters

Abstract

A strategy for fault detection and diagnosis in a closed-loop nonlinear system is described. An extended Kalman filter (EKF) is applied inside the control loop. The EKF recovers information from noisy measurement signals, providing estimates of state variables and unknown parameters of the process. The state estimates produced by the EKF are the inputs to the controller. Since the noise in the measurements is reduced significantly, the control quality is much better than that achieved with application of exponential filters. The estimates of unknown process parameters, where the deviations from normal values are considered faults, are the basis to make alarm decisions. The EKF successfully tracks and distinguishes faults occurring simultaneously. The influences of correlated noises, a special issue of estimation in closed-loop systems, model errors, and number of measurements have been studied. The proposed strategy is applied to a 30-stage binary distillation column with a partial condenser and a reboiler. The simulation results are presented to show the effectiveness of the approach.

A Survey of Fault Diagnosis and Fault-Tolerant Techniques—Part I: Fault Diagnosis With Model-Based and Signal-Based Approaches

“…A general fault detection and diagnosis procedure was first proposed in [92] by using residuals (or innovations) generated by Kalman filters with similar structure to observers, where the faults were diagnosed by statistic testing on whiteness, mean and covariance of the residuals. A variety of statistical tools, such as generalized likelihoods [93], χ 2 testing [94], cumulative sum algorithms [95] and multiple hypothesis test [96] [97]. The unscented Kalman filter (UKF), depending on a more accurate stochastic approximation, i.e., unscented transform, can better capture the true mean and covariance leading to better diagnosis performance [98,99].…”

Robust model‐based fault detection and isolation for nonlinear processes using sliding modes

“…Step 3: The nonlinear state equation and output functions are linearized around the current estimated state, b e x k 1 , as in Equations (19) and (20):…”

Dynamic fault detection and diagnosis using neural networks

“…A binary distillation column used by Li and 01-son [5] and Benallou et al [6] was chosen in this work as a test problem. The distillation column consisted of 30 trays, a condenser and a reboiler.…”

“…The standard deviation of the noise was five percent of the measurements. The reason for using composition on the middle trays instead of those on the top and bottom is that the middle trays are more sensitive to faults [5]. In addition, after the faults are overcome by regulators, the top and bottom compositions remain unchanged while the compositions of the two middle trays transit to new steady states.…”

“…In the following simulations a zero output-window length was used. [5]. When L f is larger than 4, too much information is packed in the window so that the neural network, trained by sixteen fault patterns, is not able to distinguish faults in the test data set and the prediction errors increase.…”