Raghunathan Rengasamy

Kalman filter and its variants have been used for state estimation of systems described by ordinary differential equation (ODE) models. Moving Horizon Estimation (MHE) has been a popular approach in chemical engineering community for the estimation of both ODE and differential algebraic equation (DAE) systems but is computationally demanding. There has been some work on applying Extended Kalman filter for state estimation of DAE systems with measurements as functions of only the differential states. This work describes the estimation of nonlinear DAE systems with measurements being a function of both the differential and algebraic states. An Unscented Kalman filter (UKF) formulation is also derived for semi-explicit index 1 DAE systems. The utility of these formulations are demonstrated through a case study.

The quality of process data in a chemical plant significantly affects the performance and benefits gained from activities like performance monitoring, online optimization and control. Since many chemical processes often exhibit nonlinear dynamics, techniques like Extended Kalman Filter (EKF) and Nonlinear Dynamic Data Reconciliation (NDDR) have been developed to improve the data quality. There are various issues that arise with the use of either of these techniques: EKF cannot handle inequality or equality constraints, while the NDDR has high computational cost. Recently a recursive estimation technique for nonlinear dynamic processes has been proposed which combines the merits of EKF and NDDR techniques. This technique, named as Recursive Nonlinear Dynamic Data Reconciliation (RNDDR), provides state and parameter estimates that satisfy bounds and other constraints imposed on them. However, the estimate error covariance matrix in RNDDR is computed in the same manner as in EKF, that is, the effects of both nonlinearity and constraints are neglected in the computation of the estimate error covariance matrix. A relatively new method known as the Unscented Kalman Filter has been developed for nonlinear processes, in which the statistical properties of the estimates are computed without resorting to linearization of the nonlinear equations. This leads to improved accuracy of the estimates. In this paper, we combine the merits of the Unscented Kalman Filter and the RNDDR to obtain the Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR) technique. This technique addresses all concerns arising due to the presence of nonlinearity and constraints within a recursive estimation framework, resulting in an efficient, accurate and stable method for real-time state and parameter estimation for nonlinear dynamic processes. © 2006 Elsevier Ltd. All rights reserved.

The task of improving the quality of the data so that it is consistent with material and energy balances is called reconciliation. Since chemical processes often operate dynamically in nonlinear regimes, techniques like Extended Kalman Filter (EKF) and Nonlinear Dynamic Data Reconciliation (NDDR) have been developed. There are various issues that arise with the use of either of these techniques: EKF cannot handle inequality or equality constraints, while the NDDR has high computational cost. In this paper, first, a recursive nonlinear dynamic data reconciliation (RNDDR) formulation is discussed. The RNDDR formulation extends the capability of the EKF by allowing for incorporation of algebraic constraints and bounds during correction. The covariance calculations arising in the RNDDR are same as EKF, i.e., both, nonlinearity and constraints are neglected during covariance propagation and calculation of uncertainty in filtered estimates. The use of Unscented Transformation with the RNDDR gives the Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR) formulation, which addresses all the aspects of nonlinearity and constraints in a recursive estimation framework, thus proving to be an efficient tool for real-time estimation.

Faults lead to loss of productivity and in rare cases, loss of human lives. Therefore fault diagnosis is a critical task for increased reliability and safety. There are a variety of techniques that have been proposed in the literature for fault diagnosis. A comprehensive diagnostic problem is one which involves parametric changes in the presence of sensor failures and controller or actuator malfunction. In this paper we describe a diagnostic framework that integrates qualitative models with quantitative estimation to address the comprehensive diagnostic problem. The comprehensive diagnostic framework presented in this paper can be studied as four modules. The first module, also referred to as the diagnostic module, uses qualitative techniques to generate a hypotheses set of all possible root causes. In this paper we study a signed directed graph based qualitative model for the generation of hypotheses. The second module, called the hypothesis generator intelligently constructs and reorders the candidate hypothesis sets. The third module is the nonlinear estimation module, which estimates the relevant parameters in the candidate hypothesis. The fourth module performs statistical testing of the estimation results to either validate or invalidate the hypothesis. The efficacy of the proposed framework is demonstrated on simulation examples. © 2007 Institution of Chemical Engineers.

The task of improving the quality of the data so that it is consistent with material and energy balances is called reconciliation. Since chemical processes often operate dynamically in nonlinear regimes, techniques like Extended Kalman Filter (EKF) and Nonlinear Dynamic Data Reconciliation (NDDR) have been developed. There are various issues that arise with the use of either of these techniques: EKF cannot handle inequality or equality constraints, while the NDDR has high computational cost. In this paper, a recursive nonlinear dynamic data reconciliation (RNDDR) formulation is presented. The RNDDR formulation extends the capability of the EKF by allowing for incorporation of algebraic constraints and bounds. The RNDDR is evaluated with four case studies that have been previously studied by Haseltine and Rawlings. It has been shown that the EKF fails in constructing reliable state estimates in all the four cases due to the inability in handling algebraic constraints. Reliable state estimates are achieved by the RNDDR formulation in all the cases in presence of large initialization errors.

The study of gene regulatory networks is a significant problem in systems biology. Of particular interest is the problem of determining the unknown or hidden higher level regulatory signals by using gene expression data from DNA microarray experiments. Several studies in this area have demonstrated the critical aspect of the network structure in tackling the network modelling problem. Structural analysis of systems has proved useful in a number of contexts, viz., observability, controllability, fault diagnosis, sparse matrix computations etc. In this contribution, we formally define structural properties that are relevant to Gene Regulatory Networks. We explore the structural implications of certain quantitative methods and explain completely the connections between the identifiability conditions and structural criteria of observability and distinguishability. We illustrate these concepts in case studies using representative biologically motivated network examples. The present work bridges the quantitative modelling methods with those based on the structural analysis. © 2006 IEEE.

In any modern chemical plant or refinery, process operation and the quality of product depend on the reliability of data used for process monitoring and control. The_task_of improving the quality of data to be consistent with material and energy balances is called reconciliation. Because chemical processes often operate dynamically in nonlinear regimes, techniques such as extended-Kalman filter (EKF) and nonlinear dynamic data reconciliation (NDDR) have been developed for reconciliation. There are various issues that arise with the use of either of these techniques. EKF cannot handle inequality or equality constraints, whereas the NDDR has high computational cost. Therefore, a more efficient and robust method is required for reconciling process measurements and estimating parameters involved in nonlinear dynamic processes. Two solution techniques are presented: recursive nonlinear dynamic data reconciliation (RNDDR) and a combined predictor-corrector optimization (CPCO) method for efficient state and parameter estimation in nonlinear svstems. The proposed approaches combine the efficiency of EKF and the ability of NDDR to handle algebraic inequality and equality constraints. Moreover, the CPCO technique allows deterministic parameter variation, thus relaxing another restriction of EKF where the parameter changes are modeled through a discrete stochastic equation. The proposed techniques are compared against the EKF and the NDDR formulations through simulation studies on a continuous stirred tank reactor and a polymerization reactor. In general, the RNDDR performs as well as the two traditional approaches, whereas the CPCO formulation provides more accurate results than RNDDR at a marginal increase in computational cost. © 2005 American Institute of Chemical Engineers.

In part 2 of this two-part series, an approach for diagnosis and quantification of stiction using a simple single-parameter model is proposed. The stiction model, in conjunction with an identified process model from routine operating data, is shown to successfully facilitate stiction diagnosis. An optimization approach is used to jointly identify the process model and the stiction parameter. This approach is based on the identification of a Hammerstein model of the system comprising the sticky valve and the process. In this work, a new identification procedure for Hammerstein systems that supports stiction diagnosis is proposed. Industrial and simulation case studies are shown to demonstrate the application of the proposed approach for diagnosing stiction. © 2005 American Chemical Society.