Nonlinear state estimation of differential algebraic systems
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.
Fault diagnosis and fault tolerant control using reduced order models
In this work, we have developed a reduced order model relevant for fault diagnosis and control. This model is combined with a generalized likelihood ratio (GLR) method and integrated with fault tolerant control schemes developed earlier. Simulation studies of an ideal binary distillation column show that the use of reduced order model improves the diagnostic performance thereby leading to improved fault tolerance. Furthermore, the proposed strategy is also computational more efficient. In inferential control, such as the use of temperature measurements to infer product compositions, the proposed fault tolerant control scheme performs better than the conventional control scheme when various soft faults occur. © 2008 Canadian Society for Chemical Engineering.
Integrating principal component analysis and vector quantization with support vector regression for sulfur content prediction in hydrodesulfurization process
An accurate prediction of sulfur content is very important for the proper operation and product quality control in hydrodesulfurization (HDS) process. For this purpose, a reliable data-driven soft sensor utilizing Support Vector Regression (SVR) was developed and the effects of integrating Vector Quantization (VQ) with Principle Component Analysis (PCA) were studied in the assessment of this soft sensor. First, in the pre-processing step the PCA and VQ techniques were used to reduce dimensions of the original input datasets. Then, the compressed datasets were used as input variables for the SVR model. Experimental data from the HDS setup were employed to validate the proposed integrated model. The integration of VQ/PCA techniques with SVR model was able to increase the prediction accuracy of SVR. The obtained results show that integrated technique (VQ-SVR) was better than (PCA-SVR) in prediction accuracy. Also, VQ decreased the sum of the training and test time of SVR model in comparison with PCA. For further evaluation, the performance of VQ-SVR model was also compared to that of SVR. The obtained results indicated that VQ-SVR model delivered the best satisfactory predicting performance (AARE = 0.0668 and R2 = 0.995) in comparison with investigated models.
A graph partitioning algorithm for leak detection in water distribution networks
Urban water distribution networks (WDNs) are large scale complex systems with limited instrumentation. Due to aging and poor maintenance, significant loss of water can occur through leaks. We present a method for leak detection in WDNs using repeated water balance and minimal use of additional off-line flow measurements. A multi-stage graph partitioning approach is used to determine where the off-line flow measurements are to be made, with the objective of minimizing the measurement cost. The graph partitioning problem is formulated and solved as a multi-objective mixed integer linear program (MILP). We further derive an approximate method inspired by spectral graph bisection to solve the MILP, which is suitable for very large scale networks. The proposed methods are tested on large scale benchmark networks, and the results indicate that on average, flows in less than 3% of the pipes need to be measured to identify the leaky pipe or joint.
Data reconciliation for chemical reaction systems using vessel extents and shape constraints
Concentrations measurements are typically corrupted by noise. Data reconciliation techniques improve the accuracy of measurements by using redundancies in the material and energy balances expressed as relationships between measurements. Since in the absence of kinetic models these relationships cannot integrate information regarding past measurements, they are expressed in the form of algebraic constraints. This paper shows that, even in the absence of a kinetic model, one can use shape constraints to relate measurements at different time instants, thereby improving the accuracy of reconciled estimates. The construction of shape constraints depends on the operating mode of the reactor. Moreover, it is shown that the representation of the reaction system in terms of vessel extents helps identify additional shape constraints. A procedure for deriving shape constraints from measurements is also described. Data reconciliation using both numbers of moles and extents is illustrated via a simulated case study.
Incorporating delayed and infrequent measurements in Extended Kalman Filter based nonlinear state estimation
This work deals with state estimation in the presence of delayed and infrequent measurements. While most measurements (referred to as secondary measurements) are available frequently and instantaneously, there might be a delay associated with acquiring other measurements (primary measurements) due to long analysis times involved. The primary measurements are usually sampled at irregular intervals and the exact delay is also unknown. The traditional fixed-lag smoothing algorithm, which has been applied for a variety of chemical processes systems, can be computationally inefficient for such situations and alternate methods to handle delays are necessary. In this paper, we analyze several existing methods to incorporate measurement delays and reinterpret their results under a common unified framework (for Extended Kalman Filter). Extensions to handle time-varying and uncertain delays, as well as out of sequence measurement arrival are also presented. Simulation studies on a linear distillation column and a nonlinear polymerization reactor are used to compare the performance of these methods based on RMSE values and computation times. A large scale nonlinear reactive distillation column example is also used to illustrate the practicality of the suggested method. © 2010 Elsevier Ltd. All rights reserved.
Leak detection in gas pipeline networks using an efficient state estimator. Part-I: Theory and simulations
Dynamic simulation models can be used along with flow and pressure measurements, for on-line leak detection and identification in gas pipeline networks. In this two part paper, a methodology is proposed for detecting and localizing leaks occurring in gas pipelines. The main features of the proposed methodology are: (i) it is applicable to both single pipelines and pipeline networks and (ii) it considers non-ideal gas mixtures. In order to achieve the desired computational efficiency for on-line deployment, an efficient state estimation technique based on a transfer function model, previously developed by the authors, is embedded in a hypothesis testing framework. In Part-I of this paper, a detailed description of the methodology is presented, and its performance is evaluated using simulations on two illustrative pipeline systems. The proposed method is shown to perform satisfactorily even with noisy measurements and during transient conditions, provided there is sufficient redundancy in the measurements. © 2010 Elsevier Ltd.
From data to diagnosis and control using generalized orthonormal basis filters. Part II: Model predictive and fault tolerant control
Given a state space model together with the state noise and measurement noise characteristics, there are well established procedures to design a Kalman filter based model predictive control (MPC) and fault diagnosis scheme. In practice, however, such disturbance models relating the true root cause of the unmeasured disturbances with the states/outputs are difficult to develop. To alleviate this difficulty, we reformulate the MPC scheme proposed by K.R. Muske and J.B. Rawlings [Model predictive control with linear models, AIChE J. 39 (1993) 262-287] and the fault tolerant control scheme (FTCS) proposed by J. Prakash, S.C. Patwardhan, and S. Narasimhan [A supervisory approach to fault tolerant control of linear multivariable systems, Ind. Eng. Chem. Res. 41 (2002) 2270-2281] starting from the innovations form of state space model identified using generalized orthonormal basis function (GOBF) parameterization. The efficacy of the proposed MPC scheme and the on-line FTCS is demonstrated by conducting simulation studies on the benchmark shell control problem (SCP) and experimental studies on a laboratory scale continuous stirred tank heater (CSTH) system. The analysis of the simulation and experimental results reveals that the MPC scheme formulated using the identified observers produces superior regulatory performance when compared to the regulatory performance of conventional MPC controller even in the presence of significant plant model mismatch. The FTCS reformulated using the innovations form of state space model is able to isolate sensor as well as actuator faults occurring sequentially in time. In particular, the proposed FTCS is able to eliminate offset between the true value of the measured variable and the setpoint in the presence of sensor biases. Thus, the simulation and experimental study clearly demonstrate the advantages of formulating MPC and generalized likelihood ratio (GLR) based fault diagnosis schemes using the innovations form of state space model identified from input output data. © 2005 Elsevier Ltd. All rights reserved.
Sensor Network Design for Maximizing Reliability of Bilinear Processes
The problem of selecting the variables to be measured in order to maximize process reliability was tackled in our previous articles (Ali and Narasimhan, 1993, 1995). In this article, this approach is extended to the optimal design of sensor networks for bilinear processes. Diverse processes, such as a mineral beneficiation plant, a separation system of a synthetic juice plant, and a crude preheat train of a refinery are used to illustrate the utility of this approach.
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. © 2006 Elsevier Ltd. All rights reserved.