Physics-constrained cooperative learning-based reference models for smart management of chillers considering extrapolation scenarios

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Smart management of building energy devices, including their optimal control and fault detection technology, is of great significance to building energy conservation. The core of smart management is the development of reference models for target energy device. However, existing reference models show poor extrapolation ability when the operation conditions of online data are outside the scope of training data. To tackle this problem, here we propose a novel physics-constrained cooperative learning framework to train multiple reference models in a cooperative manner in order to improve their extrapolation ability. The general idea of cooperative learning is to constrain the output of different reference models on unknown operation conditions such that the physical inconsistent loss is minimized. In this study, two novel physical inconsistent losses, including energy conservation inconsistent loss and mass conservation inconsistent loss, are designed for seven output reference variables of chiller, forming the physics-constrained cooperative neural networks (PCNNs). Comprehensive data experiments are conducted to compare the model performance of PCNNs with other machine learning models, including Support Vector Machine (SVM), Random Forest (RF), and Artificial Neural Network (ANN). The experimental results showed that the PCNNs outperformed the other models under extrapolation scenarios, showing a lager performance improvement of mean absolute error (MAE) and root mean squared error (RMSE) metrics with 26.94% and 23.49%, respectively. The proposed physics-constrained cooperative learning framework might provide a new perspective for the development of reference models in building energy system.