The artificial neural networks (ANNs) are commonly used in prediction of different systems behavior. In the ANN network hyper parameters similar to number of hidden layers and learning rate, when required, are commonly chosen manually. In the present study, an ANN is designed for investigating stability analysis of a spinning micro-scale cylindrical structure. In this regard, the weights and biases in the network are optimized using particle swarm algorithm (PSO). A second concurrent optimization using firefly algorithm is engaged for the purpose of optimizing the number of perceptrons in two hidden layers. The ANN is trained using data obtained from numerical solution of modified strain gradient theory (MSGT) equations for dynamic behavior of the spinning cylinder equipped with piezo electric layer. The numerical procedure comprises differential quadrature method. At the next stage of the optimization, the input parameters including thickness, radius and length of different layers of cylinder, elasticity constants and model parameters are optimized using another round of PSO to obtain the optimum stability condition of the cylinder. The results show that ANN could predict the dynamic behavior and phase-plane diagram of the structure in an accurate way comparing to the numerical results. On the other hand, having a trained ANN, the optimization of the parameters are performed in a simple way.

中文翻译：

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使用 PSO-ANN 和萤火虫优化算法改进旋转 FG 压电圆柱结构的动态稳定性

人工神经网络（ANN）通常用于预测不同系统的行为。在 ANN 网络中，当需要时，类似于隐藏层数量和学习率的超参数通常是手动选择的。在本研究中，人工神经网络被设计用于研究旋转微尺度圆柱形结构的稳定性分析。在这方面，网络中的权重和偏差使用粒子群算法（PSO）进行优化。使用萤火虫算法进行第二次并发优化，目的是优化两个隐藏层中感知器的数量。使用从修正应变梯度理论 (MSGT) 方程的数值解获得的数据来训练 ANN，以了解配备压电层的旋转圆柱体的动态行为。数值过程包括微分求积法。在优化的下一阶段，使用另一轮PSO对输入参数包括圆柱体不同层的厚度、半径和长度、弹性常数和模型参数进行优化，以获得圆柱体的最佳稳定性条件。结果表明，与数值结果相比，人工神经网络能够准确地预测结构的动态行为和相平面图。另一方面，有了经过训练的人工神经网络，参数的优化就可以以简单的方式进行。