Advancing the energy consumption prediction of the milling machine with small sample sets: a virtual sample generation approach with MC-PSO

Energy forecasting models are essential for energy monitoring and optimization in industrial production. However, the training and testing of predictive models often require a large amount of data, but the experimental data collected not only contains noise but also is time-consuming and costly. In this article, a deep neural network model and a virtual sample generation method based on Monte Carlo-Particle Swarm Optimization are developed. A novel deep neural network architecture is designed to extract machine tool energy consumption characteristics from sample sets. The output of virtual samples generated based on probability distribution is sampled via Monte Carlo, whereas the input of virtual samples is determined using the particle swarm optimization, and the virtual samples are ultimately generated. The proposed method effectively bridges the information gap in limited-sample datasets, thereby enhancing the performance of the model. To verify the effectiveness of the method, the impacts of normal, uniform and exponential distributions on the quality of virtual samples were analyzed. Four unbalanced experimental datasets were designed for comparative analysis. The findings demonstrate that the proposed method is well-suited for small sample datasets and can enhance the prediction accuracy of trained models by over 20% with the inclusion of 100 virtual samples.