Researchers from the French technological university IMT Atlantique have developed a novel neural-accelerated dynamic (NAD) model for heat pumps’ heat exchangers. This model integrates both the strengths of numerical modeling and machine learning to achieve a computationally efficient model with high precision.
“Among the heat pump’s components, heat exchangers involve complex heat transfer phenomena and contribute to the majority of the dynamics of the heat pump. Among the common numerical approaches used in the dynamic modeling of heat exchangers, the finite-volume (FV) method is well-recognized for its robustness and high accuracy,” explained the researchers. “However, it is often outpaced in terms of computational efficiency compared to other methods.”
The novel NAD method is based on a simplified model, meaning that instead of splitting the heat exchanger into many small parts, it treats it as one. However, simplified models can only approximate outlet values, and the novel model tries to increase that accuracy by introducing a neural network.
“A simple deep neural network (DNN) is used in the NAD model. For the condenser and evaporator NAD model, separate DNNs are used,” the academics explained. “For both, a similar neural network architecture was used in this study, which comprises an input layer, two hidden layers with 30 neurons each, and an output layer. Rectified Linear Unit (ReLU) activation functions were applied after each layer except the input and output layers to introduce non-linearity.”
This neural network is therefore able to predict the outlet values, which the simplified model cannot. However, together they form a universal differential equation (UDE). “The main idea of UDE is to use neural networks as universal approximators within differential equations. It allows the portion of physics contributing to the system’s main dynamics to be approximated by incorporating the neural network into the differential equations,” they explained.
To validate the novel NAD model, the group has tested it against a regular FV model. Five different sets of heat pump performance spans were tested, namely 5,000 seconds, 10,000 seconds, 15,000 seconds, 20,000 seconds, and 30,000 seconds. In the simulation of 5,000 seconds, NAD was 194 times faster than the FV model. In the other cases, it was 233, 343, 319, and 267 times faster, respectively.
In the validation process, the NAD model achieved an average acceleration of 271 times, compared to the FV model and also demonstrated excellent accuracy compared to the FV model, with errors of approximately less than 0.4%, and an R2 score of around 0.95, underscoring their high level of accuracy and reliability, according to the research team. Furthermore, the combination of the simplified physical model and machine learning showed the NAD model is “more robust and interpretable.”
The proposed technique was presented in “Neural-Accelerated Dynamic modeling of heat pumps,” published in Applied Thermal Engineering.
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