Harigopal Raghavan

Subspace identification of continuous time models for process fault detection and isolation

This paper proposes a novel subspace approach towards identification of optimal residual models for process fault detection and isolation (PFDI) in a multivariate continuous-time system. We formulate the problem in terms of the state space model of the continuous-time system. The motivation for such a formulation is that the fault gain matrix, which links the process faults to the state variables of the system under consideration, is always available no matter how the faults vary with time. However, in the discrete-time state space model, the fault gain matrix is only available when the faults follow some known function of time within each sampling interval. To isolate faults, the fault gain matrix is essential. We develop subspace algorithms in the continuous-time domain to directly identify the residual models from sampled noisy data without separate identification of the system matrices. Furthermore, the proposed approach can also be extended towards the identification of the system matrices if they are needed. The newly proposed approach is applied to a simulated four-tank system, where a small leak from any tank is successfully detected and isolated. To make a comparison, we also apply the discrete time residual models to the tank system for detection and isolation of leaks. It is demonstrated that the continuous-time PFDI approach is practical and has better performance than the discrete-time PFDI approach. # 2003 Elsevier Science Ltd. All rights reserved.

Comparison of Expectation-Maximization Based Parameter Estimation Using Particle Filter, Unscented and Extended Kalman Filtering Techniques

Abstract The primary requirement of filtering algorithms such as Particle Filter (PF), Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF) is the availability of an accurate nonlinear state space model. In the absence of good parameter values, one has to estimate both the hidden states and the unknown parameters in a joint framework using measurements available from the process. This problem of joint state and parameter estimation for nonlinear systems can be solved recursively through the combination of a nonlinear smoother and a maximum likelihood parameter estimation scheme. Expectation Maximization (EM) is an efficient optimization algorithm which can provide the maximum likelihood estimate of the model parameters even in the presence of missing data. The algorithm can generate parameter estimates that maximize the likelihood of all the data including those with missing output measurements. This paper presents an approach which combines the EM algorithm with a suitable nonlinear smoother, such as PF, UKF or EKF based smoother. An application of this method to a simulated Continuous Fermentor process with unknown model parameters is presented. A comparative study of the results, when the different smoothing schemes were used in this approach, is presented. The results show that the UKS based technique was able to generate unbiased parameter estimates. The Particle Smoother based parameter estimates converged in the neighbouhood of their true values, but the technique was found to be computationally intensive compared to the UKS and EKS based techniques.

Fault Diagnosis-Relevant Subspace Identification of Continuous Time Systems

Abstract Since most physical processes are continuous-time by nature, knowledge of system models in continuous-time domain is indispensable for diagnosis of process faults. This paper proposes a novel subspace-based approach towards identification of fault diagnosis-relevant models in multivariate dynamic continuous-time systems from sampled noisy data. A numerical example is given to demonstrate the validity of the theory.

Application of Inductive Monitoring System for equipment condition monitoring

Abstract In most industries model based reasoning techniques are used as the monitoring and diagnosis scheme for process faults. But even though model-based reasoning is an excellent tool for performing system monitoring, it is often difficult and time consuming to build the right model for the system. Inductive Monitoring System (IMS) is a technique that automatically produces health monitoring knowledge bases for systems that are either difficult to model or which require models that are too complex to use for real time monitoring. The technique automatically defines groups of consistent system parameter data by examining nominal system data and generates a normal operation baseline. It uses a clustering algorithm to form groups of nominal values for sets of related parameters. The nominal values generate constraints on those parameter values that should hold during nominal operation. During abnormal operation, the constraints set on the parameter values are broken and IMS automatically identifies the anomalous behavior of the system. IMS can also provide a statistically weighted measure of the deviation of current system behavior from the normal operation baseline. The advantage of using IMS is that it is fast and simple yet very effective. Each of the clusters generated by IMS represents a different mode of operation of the plant. Abnormal behavior can also be grouped into clusters and identified as specific failure mode. This paper explains the application of IMS for monitoring industrial processes with specific case studies concerned with monitoring of rotating equipment.

IDENTIFICATION OF STATE-SPACE MODELS FOR PROCESSES WITH IRREGULARLY SAMPLED OUTPUTS

Abstract In many processes, variables which indicate product quality are irregularly sampled. Often, the inter-sample behavior of these quality variables can be inferred from manipulated variables (MV) and other process variables which are measured frequently. When the quality variables are irregularly sampled, Maximum Likelihood Estimation (MLE) can be performed using the Expectation Maximization (EM) approach. The initial model required for the EM algorithm can be obtained using a realization-based subspace identification technique. We describe such a model identification method and present its application on simulation and industrial case studies.

Application of PLS-Based Regression for Monitoring Bitumen Recovery in a Separation Cell

Abstract Partial Least Squares (PLS) is a technique used to perform regression between blocks of explanatory variables and dependent variables. PLS uses projections of original variables along directions which maximize the covariance between these blocks. It has been popular due to its data-reduction property and its ability to handle collinearity within the data blocks. In this paper some issues which arise in the the development of multivariate static models of industrial processes using PLS regression are studied. An industrial example of the application of PLS regression for the development of inferential sensors to predict the Bitumen Recovery in a separation cell is shown. Some of the challenges encountered in the development and online implementation of the inferential sensors and the proposed solutions are presented.