March 3, 2026Open Access

Intelligence-based prediction of coefficient of performance for a novel high-temperature industrial heat pump: Comparative performance of ANN and ANFIS models

Key Points

The FFBP-ANN model achieved an R squared of 0.9999, outperforming the ANFIS model's R squared of 0.9863, highlighting its higher predictive accuracy.
Experimental tests utilized input variables including temperature ratios and average source temperatures for both models in a biogas facility setting.
The FFBPNN employed the Levenberg-Marquardt training algorithm, while ANFIS utilized a hybrid optimization method for model improvements.
These findings support the adoption of ANN for accurate coefficient of performance predictions in high-temperature industrial heat pumps.

Abstract

This study presents a comparative evaluation of the artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) approaches for predicting the coefficient of performance (COP) of the HoegTemp, a high-temperature heat pump (HTHP) based on a Stirling cycle (SC) with a design heat capacity of 400 kW. Experimental tests were conducted at the IVAR biogas facility in Stavanger, Norway. This study employed a feedforward backpropagation neural network (FFBPNN) model with one and two hidden layers, with various numbers of neurons and three activation functions, as well as the ANFIS approach, to estimate the COP of the SC-HTHP. The FFBPNN model used the Levenberg-Marquardt (LM) and Bayesian regularization (BR) training algorithms, while the ANFIS model utilized a hybrid optimization method and grid partitioning. The ANN and ANFIS models were evaluated using the following input variables: temperature ratio (1.4–1.6 K/K), average source temperature (21–22 °C), average sink temperature (139–199 °C) and hot water inlet temperature (137–197 °C), with COP as the output variable. The results demonstrated that the FFBP-ANN model exhibited superior predictive accuracy compared to the ANFIS model, achieving R 2 = 0.9999, MSE = 0.00010, MAE = 0.00804, and RMSE = 0.01000, whereas the ANFIS approach resulted in R 2 = 0.9863, MSE = 0.00019, MAE = 0.01114, and RMSE = 0.01392. The optimal ANN topology was 4–23-16–1 with tansig–logsig–purelin activation functions. In contrast, the best membership functions selected for ANFIS were Gaussian for the input layer and constant for the output layer.

Intelligence-based prediction of coefficient of performance for a novel high-temperature industrial heat pump: Comparative performance of ANN and ANFIS models

Key Points

Abstract

Cite This Study