Dariouchy Abdelilah, Aassif El Houcein, Décultot Dominique, Maze Gérard
Laboratoire d'Acoustique Ultrasonore et d'Electronique Unité Mixte de Recherche Centre National de la Recherche Scientifique 6068, Université du Havre, Institut Universitaire de Technologie, Place Robert Schuman, 76610 Le Havre, France.
IEEE Trans Ultrason Ferroelectr Freq Control. 2007 May;54(5):1055-64. doi: 10.1109/tuffc.2007.351.
A neural network is developed to predict cut-off dimensionless frequencies of the antisymmetric circumferential waves (Ai) propagating around an elastic circular cylindrical shell of different radius ratio b/a (a, outer radius; b, inner radius). The useful data to train and test the performances of the model are determinated from calculated trajectories of natural modes of resonances or extracted from time-frequency representations of Wigner-Ville of the acoustic backscattered time signal obtained from a computation. In this work, the studied tubes are made of aluminum or stainless steel. The material density, the radius ratio b/a, the index i of the antisymmetric waves, and the propagation velocities in the tube, are selected like relevant entries of the model of neural network. During the development of the network, several configurations are evaluated. The optimal model selected is a network with two hidden layers. This model is able to predict the cut-off dimensionless frequencies with a mean relative error (MRE) of about 1%, a mean absolute error (MAE) of 3.10(-3) k1a, and a standard error (SE) of 10(-3) k1a (k1a is the dimensionless frequency, k is the wave number in water).
开发了一种神经网络，用于预测在不同半径比b/a（a为外半径；b为内半径）的弹性圆柱壳周围传播的反对称圆周波（Ai）的截止无量纲频率。用于训练和测试模型性能的有用数据是从共振自然模态的计算轨迹中确定的，或者是从通过计算获得的声学反向散射时间信号的维格纳-威利时频表示中提取的。在这项工作中，所研究的管道由铝或不锈钢制成。材料密度、半径比b/a、反对称波的指数i以及管道中的传播速度，被选为神经网络模型的相关输入。在网络开发过程中，对几种配置进行了评估。所选的最优模型是一个具有两个隐藏层的网络。该模型能够预测截止无量纲频率，平均相对误差（MRE）约为1%，平均绝对误差（MAE）为3.10(-3)k1a，标准误差（SE）为10(-3)k1a（k1a是无量纲频率，k是水中的波数）。
