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<p>The coupled characteristics of the cooling powers and temperatures of the two cold heads of the two-stage pulse tube refrigerators (PTRs) increase the difficulties of modeling and application. This study proposes an artificial neural network (ANN) for predicting the power performance of a two-stage PTR. The experiment results show that the temperatures and cooling powers of the cold heads exhibit strong nonlinear characteristics so as to bring extreme difficulty for the performance modeling analytically. The ANN includes four-layer to predict the two cooling powers of the cold heads while the two temperatures of cold heads are the inputs. After the hyperparameter tuning, the number of the neural of two hidden layers is 8 and 6, respectively. Compared with the modelling methods of Decision Trees, Random Forests, multivariate polynomial fitting and Support Vector Regression, the ANN model can achieve the highest coefficient of determination <i>R</i><sup>2</sup> of 0.998 and the maximum relative errors of 1.6% as well as less than 5 milliseconds prediction time. Through SHapley Additive exPlanations (SHAP) analysis, the contributions of the 1<sup>st</sup> and 2<sup>nd</sup> temperatures to the cooling powers are quantified. By removing low-contribution data points identified through SHAP analysis selectively, the training dataset reduces by 34% and the maximum relative error of the model is still no more than 5%. It provides powerful guidance for selecting the appropriate training dataset and powerful tools for coupling with the other refrigerator models and systems.</p>

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Artificial Neural Network-Based Performance Prediction of a Two-Stage Pulse Tube Refrigerator

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Qibiao Hong,
  • Wendi Bao,
  • Xuebin Tang,
  • Zheng Cui,
  • You Wu,
  • Wei Sun,
  • Xu Cheng,
  • Wei Shao

摘要

The coupled characteristics of the cooling powers and temperatures of the two cold heads of the two-stage pulse tube refrigerators (PTRs) increase the difficulties of modeling and application. This study proposes an artificial neural network (ANN) for predicting the power performance of a two-stage PTR. The experiment results show that the temperatures and cooling powers of the cold heads exhibit strong nonlinear characteristics so as to bring extreme difficulty for the performance modeling analytically. The ANN includes four-layer to predict the two cooling powers of the cold heads while the two temperatures of cold heads are the inputs. After the hyperparameter tuning, the number of the neural of two hidden layers is 8 and 6, respectively. Compared with the modelling methods of Decision Trees, Random Forests, multivariate polynomial fitting and Support Vector Regression, the ANN model can achieve the highest coefficient of determination R2 of 0.998 and the maximum relative errors of 1.6% as well as less than 5 milliseconds prediction time. Through SHapley Additive exPlanations (SHAP) analysis, the contributions of the 1st and 2nd temperatures to the cooling powers are quantified. By removing low-contribution data points identified through SHAP analysis selectively, the training dataset reduces by 34% and the maximum relative error of the model is still no more than 5%. It provides powerful guidance for selecting the appropriate training dataset and powerful tools for coupling with the other refrigerator models and systems.