A new framework for data reconciliation and measurement bias identification in generalized linear dynamic systems

Abstract

This article describes a new framework for data reconciliation in generalized linear dynamic systems, in which the well-known Kalman filter (KF) is inadequate for filtering. In contrast to the classical formulation, the proposed framework is in a more concise form but still remains the same filtering accuracy. This comes from the properties of linear dynamic systems and the features of the linear equality constrained least squares solution. Meanwhile, the statistical properties of the framework offer new potentials for dynamic measurement bias detection and identification techniques. On the basis of this new framework, a filtering formula is rederived directly and the generalized likelihood ratio method is modified for generalized linear dynamic systems. Simulation studies of a material network present the effects of both the techniques and emphatically demonstrate the characteristics of the identification approach. Moreover, the new framework provides some insights about the connections between linear dynamic data reconciliation, linear steady state data reconciliation, and KF. V V C 2009 American Institute of Chemical Engineers AIChE J, 56: 1787AIChE J, 56: -1800AIChE J, 56: , 2010 Keywords: dynamic data reconciliation, linear equality constrained least squares, kalman filter, bias detection, bias identification IntroductionDynamic data reconciliation (DDR) is a process of estimating variables on the basis of measurements and dynamic material or energy balance constraints. DDR can provide more reliable information about the current state of a process. An implicit assumption in DDR is that measurement errors are independent with time and normally distributed with an expected value zero. However, the assumption is nullified when process data contain measurement biases. A measurement bias is made when a measurement of a variable deviates far from its true value due to malfunction on a device or improper use of a device. It can be described as a step function which has a large unknown magnitude.1 Measurement biases seriously distort the results of DDR. Thus before DDR is performed, the statistical properties of measurement data should be checked to detect and identify measurement biases. Both DDR and measurement bias identification exploit the same information contained in measurements and balance constraints. Many studies have been conducted on linear dynamic data reconciliation (LDDR) techniques. Some of the most widely used techniques are rooted on Kalman filter (KF). These techniques are well-developed for a class of linear dynamic systems. The deterministic part of these systems can be represented by a standard state space equation x kþ1 ¼ Ax k þ Bu k where x k is an unknown vector at time instant k and u k is a vector representing known time varying parameters. As far as we know, this system representation is restricted to two kinds of situations. One is the nominal steady state condition (i.e., variation around nominal point) for the purpose of control. The other is the quasi steady state process. In a qua...

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