Semi-supervised graph convolutional network to predict position- and speed-dependent tool tip dynamics with limited labeled data

Abstract

The tool tip frequency response function (FRF), as one of the essential inputs to calculate the stability lobe diagram (SLD), varies with the position and speed of changes in the moving components within the machine tool work volume. How to predict the position- and speed-dependent tool tip dynamics accurately has become one of the most challenging tasks in obtaining SLDs while avoiding chatter. However, traditional finite element analyses or kinematic modelling-based methods are costly and time consuming. Data-driven machine learning methods require large amounts of labeled data to train a model, but labeled industrial data are limited and extremely valuable in real manufacturing industries.To minimize experimentation, an improved semi-supervised graph convolutional network (GCN) is proposed to predict position- and speed- dependent tool tip dynamics with limited labeled data. First, the inverse stability solution is applied to identify dominant modal parameters under cutting conditions to obtain labeled samples. Subsequently, both the limited labeled samples and large amounts of unlabeled samples are converted into graph data to train a GCN regression model integrated with a multilayer perceptron. To avoid overfitting under limited data conditions, the conventional GCN is extended by stacking a transposed GCN, which is utilized to reconstruct the initial node features. The results demonstrate an improved prediction performance by adding the unsupervised reconstruction error into the loss function. Compared with other machine learning methods, our proposed method has superior performance in predicting tool tip dynamics with only 20% of the labeled samples. Finally, the SLDs were reconstructed with predicted FRFs, and the accuracy of the SLDs was validated through chatter tests.