(433a) Grey-Box Modeling and Estimation for Health Monitoring of High Temperature Boiler Components

Due to increased penetration of intermittent renewables to the energy grid, most power plants are forced to cycle their loads frequently and rapidly, operate at low load conditions for a sustained period, and start-up and shut down several hundred times in a year. These severe operations are causing substantial damage to the boiler components, compromising these plants' reliability and driving up costs. To mitigate these issues, developing advanced condition monitoring tools can be instrumental in understanding the impacts of load-following. These tools can eventually help these plants to make efficient plans for preventive maintenance, avoid undesired forced outages and develop advanced process control strategies for improved flexibility without compromising safety and reliability. Although condition monitoring using measurement data is widely used for operating plants, these monitoring techniques have been mainly developed for rotary equipment items. Condition monitoring of static equipment items such as the boiler components is challenging due to difficulty in estimating equipment health by simply using the measurement data. Furthermore, due to harsh operating conditions in high temperature regions that are most vulnerable to failure especially in the coal-fired boilers, there can be no or limited number of sensors. In addition, it is impractical to measure certain variables of interest. For example, even though the through-wall temperature profile of a tube in the high temperature superheater section of a boiler can provide important indication of scale formation or fouling, it is impractical to estimate the through-wall temperature profile. Hence, in this work we have developed a grey-box modeling and estimation approach for monitoring the health of critical boiler components. The grey-box model synergistically combines dynamic first-principles physics-based models with black-box models that are developed using the measurement data from operating plants.

Various grey-box modeling approaches for superheater systems in steam boilers have been proposed using linear state space and detailed dynamic model of the physical system along with closed-loop data for parameter estimation using the prediction error method ^{[1], [2]}. A model-based approach was implemented to characterize the performance of the steam boiler system and an electric boiler for a hot water system. using nonlinear differential and algebraic equations model of mass and energy balances ^{[3], [4]}. Model parameters are adjusted using plant data using a nonlinear least-square optimization formulation. Detailed parametric models for various sections of a boiler system utilizing a genetic algorithm for parameter estimation have also been proposed ^[5].

Application of grey-box modeling approach for health monitoring of boiler systems is not well developed and lacks validation with operational data. Some studies have been conducted to determine the amount of oxide scale growth formation using damaged tubes from operating systems and doing lab scale characterization on them^[6]. Empiricial methods for estimating remaining life using creep data analysis based on parabolic growth law for oxide evolution under the assumption of constant tube temperature have also been proposed^[7]. However, experimental analysis of oxide growth in tubes and using empirical growth laws based on lab scale data is beneficial for offline assessment only, and detailed models are required to utilize for online monitoring providing actual time prediction. Using multisource data for damage prediction and health monitoring of boiler tubes utilizing large amount of historical operational data for training deep learning models based on long short-term memory (LSTM) and backpropagation through time (BPTT) networks has also been investigated^[8]. However, using data-driven black-box models alone can lead to errors despite using extensive operational data because of the unforeseen scenarios not captured in the training data used in these models. Furthermore, work on estimators for grey-box systems is not well developed in the existing literature. A generic parameter estimation framework using stochastic grey-box models has been studied using extended Kalman filtering based on maximum likelihood and maximum a posteriori estimation for estimation^[9]. A moving horizon estimation (MHE) scheme for parameter estimation in grey-box models based on a synthetic example using Monte Carlo simulation has also been proposed^[10]. Grey box state estimators using an unscented Kalman filter have been proposed for systems with correlated and unmeasured disturbances combining mechanistic models with a discrete disturbance model^[11]. One of the key issues in estimators for grey-box systems is the computation of error covariance matrix as the state transition matrix for the black-box model is not available explicitly. Furthermore, process noise covariance for the black-box model is difficult to estimate or assume.

To address these challenges, in this work we have developed several hybrid grey-box modeling approaches combining white-box physics-based models with data-driven artificial intelligence (AI ) black-box models.The white-box model is based on a dynamic distributed first-principles 3-D DAE model considering thick-walled tubes and utilizing prior knowledge of the physics of the system. In addition, black-box models are developed using neural network and Bayesian machine learning models. Three different grey-box structures are developed - physics-based and black-box models arranges in series, physics-based and black-box models arranges in parallel, black-box model integrated within physics-based model where one or more phenomena or mechanisms or represented by a data-driven model. Formation of the oxide scale leads to higher heat transfer resistances leading to local temperature rise that can accelerate creep damage. The oxide scale growth is calculated using a parabolic growth rate law for different material specifications. Spatial and temporal variation of temperature is used for estimating creep failure using the Larson-Miller Parameter (LMP) method is used to predict damage accumulation in the system. The work on developing estimators for grey-box systems considered two cases- one where the structure and functional representation of the black-box model are known and another where this information are not available. The estimator algorithms have also been developed for three grey-box structures- series, parallel and integrated. The utility of the framework as an online health-monitoring tool is studied for a power plant boiler superheater system.

References

[1] T. T. K. Ly and H. M. Son, “Grey-Box Identification of Steam Boiler Using Linear State-Space Model and Closed-Loop Data,” vol. 101, no. I, pp. 25–29, 2014.

[2] T. T. K. Ly, “GREY-BOX LPV MODEL IDENTIFICATION OF BOILER SUPERHEATED STEAM TEMPERATURE,” 2020.

[3] J. B. T. BARSZCZ, P. CZOP, “Model-Based Evaluation of a Power Plant Steam Boiler System,” Probl. Eksploat., vol. 2, pp. 7–19, 2011, [Online]. Available: www.problemyeksploatacji.itee.radom.pl

[4] A. A. Farooq, A. Afram, N. Schulz, and F. Janabi-Sharifi, “Grey-box modeling of a low pressure electric boiler for domestic hot water system,” Appl. Therm. Eng., vol. 84, pp. 257–267, 2015, doi:

10.1016/j.applthermaleng.2015.03.050.

[5] A. Chaibakhsh, A. Ghaffari, and S. A. A. Moosavian, “A simulated model for a once-through boiler by parameter adjustment based on genetic algorithms,” Simul. Model. Pract. Theory, vol. 15, no. 9, pp. 1029– 1051, 2007, doi: 10.1016/j.simpat.2007.06.004.

[6] R. Shukla and D. Pareek, “Condition Assessment of Re-heater / Superheater Tubes using Internal Oxide Scale Thickness Measurement – The Right Way,” e-Journal Nondestruct. Test., pp. 1–8, 2019.

[7] J. D. Angelo, A. Bennecer, S. Kaczmarczyk, and P. Picton, “Modelling of thermal behaviour of iron oxide layers on boiler tubes,” J. Phys. Conf. Ser., vol. 721, no. 1, 2016, doi: 10.1088/1742-6596/721/1/012002.

[8] G. Liu et al., “Typical Damage Prediction and Reliability Analysis of Superheater Tubes in Power Station Boilers Based on Multisource Data Analysis,” Energies, vol. 15, no. 3, 2022, doi: 10.3390/en15031005.

[9] N. R. Kristensen, H. Madsen, and S. B. Jørgensen, “Parameter estimation in stochastic grey-box models,” Automatica, vol. 40, no. 2, pp. 225–237, 2004, doi: 10.1016/j.automatica.2003.10.001.

[10] A. J. Isaksson, D. Törnqvist, J. Sjöberg, and L. Ljung, “Grey-box identification based on horizon estimation and nonlinear optimization,” Proc. Isc. Int. Symp. Stoch. Syst. Theory its Appl., vol. 2010, no. 0, pp. 1–6, 2010, doi: 10.5687/sss.2010.1.

[11] V. A. Bavdekar and S. C. Patwardhan, “Development of grey box state estimators for systems subjected to time correlated unmeasured disturbances,” J. Process Control, vol. 22, no. 9, pp. 1543–1558, 2012, doi: 10.1016/j.jprocont.2012.06.004.