Machine learning techniques based multi-parameter analysis and design of nonlinear helical structures considering internal structure collisions

Helical structures are widely used in various engineering disciplines due to their energy storage and vibration damping characteristics. Existing studies have investigated the dynamic responses of various helical structures under static, low-speed dynamic and high-speed dynamic loadings. However, systematic understandings on the relationship between the complicated multi-parameters of helical structures and significant spike forces remain challenging. The present work develops a transient finite element model for a beehive helical structure sample, of which results are validated by a real engine test at 7800 rpm engine speed. The simulation results are in excellent agreement with the testing results and reveal that the dynamic spike forces are caused by collision effects between narrow coils. Next, 2 types of machine learning models, namely a deep neural networks (DNN) model and a genetic programming (GP) model, are developed and compared using simulation results. It is noted that the deep neural networks model has better prediction accuracy with the R² value of the testing set reaches 0.939. Finally, the relationships between multiple geometric parameters of the helical structure and the peak dynamic forces are plotted based on the developed machine learning model. In addition, design spaces that balance lower peak forces and vibration damping performance are proposed. These findings would be beneficial for systematic multi-parameter analysis and better designs of helical structures with superior mechanical performance.