Back-propagation neural network modeling for a pulse tube refrigerator with passive displacer

The pulse tube refrigerator (PTR) with passive displacer is a potential alternative for high-efficiency PTR. One of the main problems is that massive experiments are expensive and time-consuming. A back-propagation neural network (BPNN) model is proposed to overcome this challenge. The cooling capacity and relative Carnot efficiency of the PTR with passive displacer can be predicted instead of experiments when the charging pressure, operating frequency, input electrical power, and cooling temperature are determined. The optimal BPNN with the least mean square error is obtained by optimizing the network structure, transfer function, and training function. As a result, the coefficient of determination (R2) values for the training and testing data are 0.9995 and 0.9992, respectively. The predicted values are achieved within eight milliseconds, agreeing with the experimental values. The maximum relative Carnot efficiency of 23.2% occurs at 140 K with a cooling capacity of 15 W. It is concluded that the BPNN is an effective model for simulating the performance of the PTR with passive displacer quickly. Furthermore, the mathematical formulas and the capability to predict the effects of the operating parameters are demonstrated, which is scarce in the literature on the PTR. The BPNN model can be applied to accelerate the development of the PTR with passive displacer.