(346t) Condition Monitoring of Non-Linear Differential-Algebraic Equation Systems with Colored Process and Measurement Noise

Condition monitoring of many process systems is of high importance yet challenging using existing filtering techniques due to unknown model structures, process and measurement noise characteristics, unmeasured variables, and non-linear transformation of the process and measurement noise especially for highly nonlinear models. Many process systems are difficult to be modeled accurately by using first-principles models due to poorly understood physics. While measurement data can provide valuable information, they are often inadequate and noisy^[1]. For example, monitoring of equipment items that operate under harsh conditions is of utmost importance, but it may be impractical to place sensors in certain locations and measure certain variables such as through wall temperature profile of a thick metal wall. Furthermore, many process systems are modelled by using differential-algebraic equation (DAE) systems which contain exact and uncertain algebraic equations^[2]. Process noise characteristics of many such systems can be highly correlated, yet difficult to characterize or quantify. In addition, the measurements may have outliers and are non-Gaussian making condition monitoring of these systems even more challenging^[3].

Condition monitoring for nonlinear systems in presence of non-gaussian measurement noise can be done using linear and extended Kalman filter ^[4][5].However, it is difficult in general to incorporate non-Gaussian noise. For systems with time-varying process noise, adaptive linear Kalman filters have been used ^[6]. Bayesian state estimation using particle filters has been used for nonlinear systems^[7]. Various extended Kalman Filter (EKF) algorithms based on both differential and algebraic equations along with exact algebraic equations and uncertain measurement noise characteristics have also been developed but considering white Gaussian noise ^[8][9]. This work focuses on developing condition monitoring algorithms for nonlinear DAE systems with correlated non-Gaussian process and measurement noise in presence of exact and uncertain algebraic equations.

In this work, we have developed a novel approach for incorporating colored and non-Gaussian noise in the extended Kalman filter and unscented Kalman filter algorithms. The framework can accommodate non-Gaussian and independent as well as non-Gaussian and correlated process and measurement noises. Standard Kalman filtering approaches are also suitably modified for DAE systems with exact and uncertain algebraic equations. Furthermore, it is desired that the estimated state variables do satisfy certain additional equality constraints. The develop algorithm employs reformulation of the covariance matrix calculations, partitioning of the covariance matrix, augmentation and measurement differencing.

The developed approach is validated using industrial data for an operating powerplant superheater section in a natural gas combined cycle plant. The system is highly non-linear and is modeled using a first-principles 2-D DAE model^[10].The measurements data available for such real systems is often limited with critical key state variables like flue gas and tube temperatures often missing due to high temperature and harsh operating conditions. A dynamic data reconciliation framework is also developed for satisfying mass and energy balances in the measured data, prior to using the data in the condition monitoring algorithm. Performance of the developed algorithm is compared with existing EKF-DAE algorithms based on white Gaussian noise assumption. It is observed that the developed algorithm results in significant improvement in estimation errors with reasonable increase in the computational effort.