Abstract In this study, an artificial neural network model is built to predict the dynamic performance of a beta-type free piston Stirling engine. The influences of six input dynamic parameters on operating frequency, amplitude ratio and phase angle are analyzed. The operating frequency is significantly affected by the spring stiffness and the mass of the pistons. However, the relationships of the dynamic parameters are comprehensive, which are determined by multiple parameters. Then, a number of dynamic output parameters are used as training and testing data. The best results are obtained by 6-6-1, 6-6-1 and 6-10-6-1 network architectures for the operating frequency, amplitude ratio and phase angle respectively. For these network architectures, the back propagation algorithm, namely Levenberg-Marguardt is applied. Stirling engine’s dynamic performance predicted with the network model is compared with the actual values. After training, correlation coefficients (R2) values for training and testing data are close to 1. The mean relative errors of the operating frequency, amplitude ratio and phase angle are 0.85%, 2.78% and 3.19% for the training process. These results show that the artificial neural network model is an acceptable and powerful approach for predicting the dynamic performance of the beta-type free piston Stirling engine.

中文翻译：

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人工神经网络在自由活塞斯特林发动机动态性能预测中的应用

摘要 在这项研究中，建立了人工神经网络模型来预测β 型自由活塞斯特林发动机的动态性能。分析了六个输入动态参数对工作频率、幅值比和相位角的影响。工作频率受弹簧刚度和活塞质量的显着影响。但是，动态参数之间的关系是综合的，是由多个参数决定的。然后，使用多个动态输出参数作为训练和测试数据。6-6-1、6-6-1 和 6-10-6-1 网络架构分别获得了工作频率、幅度比和相角的最佳结果。对于这些网络架构，应用了反向传播算法，即 Levenberg-Marguardt。将网络模型预测的斯特林发动机动态性能与实际值进行比较。训练后，训练和测试数据的相关系数（R2）值接近于1。训练过程中工作频率、幅度比和相角的平均相对误差分别为0.85%、2.78%和3.19%。这些结果表明，人工神经网络模型是一种可以接受且强大的预测 β 型自由活塞斯特林发动机动态性能的方法。