(433h) A Training Methodology for Hybrid Building Thermal Models with Time-Varying Heat Disturbances

In 2021, the combined energy consumption of the residential and commercial building sectors accounted for about 28% of total U.S. end-use energy consumption [1]. With rising energy prices and demand [2], energy-efficient building operations are more critical than ever. Studies have shown that model predictive control (MPC) can have a positive impact on building operations (refer to the review [3] and the references therein). However, the widespread adoption of MPC in buildings is limited due to the challenges of developing and training a model [4]. This task is complex because model parameter estimation is coupled to estimating the unmeasured time-varying heat disturbance resulting from occupancy, solar radiation, and electrical equipment.

Hybrid models, which consist of physics-based and data-driven models, have been proposed for control-oriented building thermal modeling [4-6]. In our previous study [5], a physics-based thermal resistance-capacitance (RC) network model, derived from first principles, and a feedforward neural network, used to forecast the unmeasured heat disturbances, were integrated to form a parameterized hybrid model. This work proposed a method for training both model parameters simultaneously. In [6], a hybrid model was proposed that modeled the building thermal dynamics using a physics-based model and forecasted the unmeasured disturbances using a neural network. The neural network and physics-based models, however, were trained separately. The advantage of simultaneously training the hybrid model parameters is that this approach minimizes overall prediction errors and can potentially avoid compounding prediction errors resulting from training models separately. However, the model parameters obtained during training can depend on the initial parameter estimates provided to the solver due to the non-convexity of training problems.

First-order training methods (e.g., gradient descent and stochastic gradient descent) are commonly used to train neural network models, owing to the availability of large datasets. However, in the case of modeling building thermal dynamics, the amount of data available for estimating model parameters is limited owing to practical considerations (i.e., minimizing potential comfort violations to building occupants). In this context, second-order or quasi-Newton methods like the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm can be considered. To this end, a novel heuristic three-step method for training hybrid building thermal models is proposed to improve the prediction of the building thermal dynamics with a lower computational time compared to using a single solver. The proposed method combines two gradient descent steps and one BFGS step, leveraging the advantages of BFGS while addressing the need to find a good initial parameter estimate to provide to the solver. The purpose of each training step is discussed. We propose a model validation approach agnostic to whether state or output measurements are available. As demonstrated by our hybrid model training results, the hybrid model trained using the three-step method achieves higher accuracy in predicting building thermal dynamics with fewer iterations compared to the same model trained using a single solver.

References

[1] “March 2023 monthly energy review”, Technical report, U.S. Energy Information Administration, 2023.

[2] C.F. Alvarez, G. Molnar, “What is behind soaring energy prices and what happens next?”, Technical Report, International Energy Agency, 2021.

[3] A. Afram, F. Janabi-Sharifi, A. S. Fung, and K. Raahemifar, “Artificial neural network (ANN) based model predictive control (MPC) and optimization of HVAC systems: A state of the art review and case study of a residential HVAC system”, Energy and Buildings 141 (2017), pp. 96–113.

[4] M. Ellis, “Machine Learning Enhanced Grey-Box Modeling for Building Thermal Modeling,” In Proceedings of the American Control Conference, New Orleans LA USA, pp. 3927-3932, 25-28 May, 2021.

[5] P. Krishna and M.J. Ellis, "Control-Oriented Hybrid Modeling Framework for Building Thermal Modeling," in Energy Systems and Processes: Recent Advances in Design and Control, edited by M. Li (AIP Publishing, Melville, New York, 2023), Chapter 9, pp. 9-1–9-28.

[6] P. Kumar, J.B. Rawlings, M.J. Wenzel, M.J. Risbeck, “Grey-box model and neural network disturbance predictor identification for economic MPC in building energy systems”, Energy & Buildings (2023)