(484g) State and Parameter Estimation of Complex Dynamic Systems Using Nonlinear Grey Box Modeling: Application to an Industrial Steam Superheater System

Process systems can be modeled using first principles known as white-box models or using measurement data known as black-box models. However, modeling systems using white-box models can be time consuming and challenging for systems whose physics are complex and not well understood. On the other hand, black-box models although having faster convergence and simple structures can lead to error when used for systems with high nonlinearity and inadequate and noisy measurement data. As an example, high temperature systems such as steam superheater system have complex dynamics with limited measurements available for key state variables like metal wall and flue gas temperatures. Modeling such systems by using either the white-box or black-box models may give inaccurate results. Grey-box models can synergistically combine white box models with black box models making state and parameter estimation tractable, accurate, and computationally feasible.^[1]

The type of grey box modeling approach employed for a system depends on several factors concerning the current knowledge, operating data and the application area. In literature three broad classification have been listed - constrained black box modeling where physical information are used as constraints for the black box model, mechanistic modeling where first principles model is utilized along with parameter estimation for unknowns, and hybrid modeling where the white-box and black-box models are separated and solved in series or in parallel.^[2]This current work employs a mechanistic grey-box modeling approach for an industrial dynamic steam superheater system represented by non-linear differential-algebraic equation systems. Here we consider that the algebraic equations are uncertain. Unknown parameters associated with such systems like heat transfer coefficients or flow parameters are estimated using data with consideration of correlated and non-gaussian measurement noise.

Non-Linear neural networks models have been developed for simulating and state estimation for a superheater attemperator system based on plant data^[3].A detailed highly non-linear boiler model has been proposed in conjunction with a non-linear moving horizon estimator for state and unmeasured disturbance estimation.^[4] Stochastic grey-box models given by differential equations for system dynamics and discrete time measurement equations were used with extended Kalman filtering for parameter estimation ^[5]_. Grey box state estimators using an unscented Kalman filter have been proposed for systems with correlated and unmeasured disturbances ^[6]. However, state and parameter estimation of superheaters represented by a grey-box model is currently not available in the open literature. We also consider state and parameter estimation for systems with uncertain algebraic equations in presence of correlated noise in the measurement data.

In this work, a non-linear grey-box model is modeled for joint state and parameter estimation of the superheater system. The dynamic first-principles 3-D DAE model considers thick-walled tubes and utilizing prior knowledge of the physics of the system. ^[7][8] In addition a linear parametric model is also used to estimate heat transfer coefficients and oxide scale growth on metal tubes within the system.The estimation algorithm used in the framework utilizes a modification of the standard extended Kalman filter in order to account for exact and uncertain algebraic equations of the DAE model. Furthermore, the available measurement data for such systems is limited and inadequate. Hence, the modified EKF also accounts for measurement noise which are correlated and non-gaussian in both the DAE model and the linear parametric model. Several months of data from a coal-fired power plant boiler is used for the testing and validation of this proposed grey-box modeling and estimation framework. The result of this framework is compared with existing EKF-DAE algorithms based on white-box models with uncorrelated Gaussian noise.

References

1. Řehoř, J., & Havlena, V. (2011). A practical approach to grey-box model identification. In IFAC Proceedings Volumes (IFAC-PapersOnline) (Vol. 44, Issue 1 PART 1, pp. 10776–10781).
2. Sohlberg, B., & Jacobsen, E. (2008). Grey box modeling branches and experiences. In IFAC Proceedings Volumes (IFAC-PapersOnline) (Vol. 17, Issue 1 PART 1).
3. Bendtsen, J. D., & Sorensen, O. (2000). Simulation, state estimation and control of nonlinear superheater attemporator using neural networks. Proceedings of the American Control Conference, 2, 1430–1434.
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