Recursive Nonlinear Dynamic Data Reconciliation Research Articles

An improved recursive non-linear dynamic data reconciliation for non-linear state estimation subject to bound constraints

An improved recursive non-linear dynamic data reconciliation for non-linear state estimation subject to bound constraints

Reactivity and Delayed Neutron Precursors’ Concentration Estimation Based on Recursive Nonlinear Dynamic Data Reconciliation Technique

Reactivity is widely used as the paramount means for defining nuclear reactor status, but there is no physical sensor available to measure this parameter directly. Similarly delayed neutron precursors’ concentrations, the source of the delayed neutrons which play important role in reactor control cannot be measured directly. Hence, these quantities must be calculated or estimated from observed neutron flux transients. Recently, Kalman filter (KF) and its variants have been used for the reactivity estimation. A key limitation of KF and all of its variants is that they cannot account for the constraints on state variables systematically, which may cause the filter’s instability. In this paper, a constrained estimator based on the recursive nonlinear dynamic data reconciliation technique is proposed for the estimation of reactivity and delayed neutron precursors’ concentrations in the nuclear reactor. The effectiveness of the proposed technique has been evaluated through the step test signal in the presence of measurement noise and experimental power variation data sets collected from one of the Indian reactors.

Robust and reliable estimation via recursive nonlinear dynamic data reconciliation based on cubature Kalman filter

Since measurements of process variables are subject to measurements errors as well as process variability, data reconciliation is the procedure of optimally adjusting measured date so that the adjusted values obey the conservation laws and constraints. Thus, data reconciliation for dynamic systems is fundamental and important for control, fault detection, and system optimization. Attempts to successfully implement estimators are often hindered by serve process nonlinearities, complicated state constraints, and un-measurable perturbations. As a constrained minimization problem, the dynamic data reconciliation is dynamically carried out to product smoothed estimates with variances from the original data. Many algorithms are proposed to solve such state estimation such as the extended Kalman filter (EKF), the unscented Kalman filter, and the cubature Kalman filter (CKF). In this paper, we investigate the use of CKF algorithm in comparative with the EKF to solve the nonlinear dynamic data reconciliation problem. First we give a broad overview of the recursive nonlinear data dynamic reconciliation (RNDDR) scheme, then present an extension to the CKF algorithm, and finally address the issue of how to solve the constraints in the CKF approach. The CCRNDDR method is proposed by applying the RNDDR in the CKF algorithm to handle nonlinearity and algebraic constraints and bounds. As the sampling idea is incorporated into the RNDDR framework, more accurate estimates can obtained via the recursive nature of the estimation procedure. The performance of the CKF approach is compared with EKF and RNDDR on nonlinear process systems with constraints. The conclusion is that with an error optimization solution of the correction step, the reformulated CKF shows high performance on the selection of nonlinear constrained process systems. Simulation results show the CCRNDDR is an efficient, accurate and stable method for real-time state estimation for nonlinear dynamic processes.

Constrained Unscented Gaussian Sum Filter for state estimation of nonlinear dynamical systems

Abstract This work presents a novel constrained Bayesian state estimation approach for nonlinear dynamical systems. The proposed approach uses the recently proposed Unscented Gaussian Sum Filter to represent the underlying non-Gaussian densities as sum of Gaussians, and explicitly incorporates constraints on states during the measurement update step. This approach, labeled Constrained-Unscented Gaussian Sum Filter (C-UGSF), can thus model non-Gaussianity in constrained, nonlinear state estimation problems. Its applicability is demonstrated using three nonlinear, constrained state estimation case studies taken from literature, namely, (i) a gas phase batch reactor, (ii) an isothermal batch process, and (iii) a continuous polymerization process. Results demonstrate superior estimation performance along with a significant improvement in computational time when compared to Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR), which is a popular nonlinear, constrained state estimation approach available in literature.

Optimization Based Constrained Gaussian Sum Unscented Kalman Filter∗∗The authors thank the Department of Science and Technology, India, for partial financial assistance under grant 13DST057.

Abstract This work presents a novel constrained nonlinear state estimation approach for nonlinear dynamical systems. The proposed approach combines two key elements from well know Gaussian Sum Unscented Kalman Filter (GS-UKF) and Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR) approaches. The proposed approach uses sum of Gaussians representation in GS-UKF and explicit constrained update in URNDDR to obtain feasible state estimates. The benefits of the proposed approach are demonstrated over the available constrained GS-UKF variants using a three state isothermal batch process case study available in literature.

Constrained unscented recursive estimator for nonlinear dynamic systems

Nonlinear constrained state estimation is an important task in performance monitoring, online optimization and control. There has been recent interest in developing estimators based on the idea of unscented transformation for constrained nonlinear systems. One of these approaches is the unscented recursive nonlinear dynamic data reconciliation (URNDDR) method. The URNDDR approach follows the traditional predictor-corrector framework. Constraints are handled in the prediction step through a projection algorithm and in the correction step through an optimization formulation. It has been shown that URNDDR produces very accurate estimates at the cost of computational expense. However, there are two issues that need to be addressed in the URNDDR framework: (i) URNDDR approach was primarily developed to handle bound constraints and needs to be enhanced to handle general nonlinear equality and inequality constraints, and (ii) computational concerns in the application of the URNDDR approach needs to be addressed. In this paper, a new estimation technique named constrained unscented recursive estimator (CURE) is proposed, which eliminates these disadvantages of URNDDR, while providing estimates with almost the same accuracy.

Unscented Transformation‐Based Filters: Performance Comparison Analysis for the State Estimation in Polymerization Processes with Delayed Measurements

AbstractState estimation with delayed measurements is essential to the operation of polymer processes due to the limited availability of reliable online sensors and the unavoidable hold‐up time in the acquisition of critical variables data. In this work, a two‐timescale approach is applied to three filters based on the Unscented Transformation, the Unscented Kalman Filter, the Unscented Recursive Nonlinear Dynamic Data Reconciliation and the Reformulated Constrained Unscented Kalman Filter, in order to incorporate delayed measurements into their estimation scheme. A comprehensive comparative analysis is performed, which shows that the three of them have very good accuracy and convergence properties. However, the Unscented Kalman Filter performs better in terms of computational time. magnified image

Modified unscented recursive nonlinear dynamic data reconciliation for constrained state estimation

In state estimation problems, often, the true states satisfy certain constraints resulting from the physics of the problem, that need to be incorporated and satisfied during the estimation procedure. Amongst various constrained nonlinear state estimation algorithms proposed in the literature, the unscented recursive nonlinear dynamic data reconciliation (URNDDR) presented in [1] seems to be promising since it is able to incorporate constraints while maintaining the recursive nature of estimation. In this article, we propose a modified URNDDR algorithm that gives superior performance when compared with the basic URNDDR. The improvements are obtained via better constraint handling and are demonstrated on representative case studies [2,3]. In addition to this modification, an efficient strategy combining basic unscented Kalman filter (UKF), URNDDR and modified URNDDR is also proposed in this article for solving large scale state estimation problems at relatively low computational cost. The utility of the proposed strategy is demonstrated by applying it to the Tennessee Eastman challenge process [4].

A Support Vector Regression Approach for Recursive Simultaneous Data Reconciliation and Gross Error Detection in Nonlinear Dynamical Systems

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 show nonlinear dynamics, techniques like extended Kalman filter (EKF) and nonlinear dynamic data reconciliation (NDDR) have been developed to improve the data quality. Recently, the recursive nonlinear dynamic data reconciliation (RNDDR) technique has been proposed, which combines the merits of EKF and NDDR techniques. However, the RNDDR technique cannot handle measurements with gross errors. In this paper, a support vector (SV) regression approach for recursive simultaneous data reconciliation and gross error detection in nonlinear dynamical systems is proposed. SV regression is a compromise between the empirical risk and the model complexity, and for data reconciliation it is robust to random and gross errors. By minimizing the regularized risk instead of the maximum likelihood in the RNDDR, our approach could achieve not only recursive nonlinear dynamic data reconciliation but also gross error detection simultaneously. The nonlinear dynamic system simulation results in this paper show that the proposed approach is robust, efficient, stable, and accurate for simultaneous data reconciliation and gross error detection in nonlinear dynamic systems within a recursive real-time estimation framework. It can also give better performance of control.

Robust and reliable estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation

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.

Recursive estimation in constrained nonlinear dynamical systems

AbstractIn 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 systems. 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 AIChE J, 51: 946–959, 2005

Robust Constrained Estimation via Unscented Transformation

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