A Neural Network Approach to 3D Printed Surrogate Systems

摘要

The geometry of a Stradivarius violin was recently replicated through additive manufacturing, but nevertheless failed to produce a tone of professional quality. Due to the material limits of additive manufacturing, it is clear that purely geometric replicas are unlikely to create violins of comparable sound. We propose a "surrogate" system approach, which tailors some combination of a structure's material and geometric properties to mimic the performance of a target system. Finite element (FE) methods can approximate the vibrational performance of a violin or similar structure with high precision, given its specific physical properties and geometry. Surrogate systems, however, require the solution of the inverse problem. This can be achieved through artificial neural networks (ANN), a powerful tool for non-linear function estimation. As a stepping-stone to the violin problem, we first developed a surrogate method for simple beam structures. A neural network was trained on 7500 randomized beams to predict a thickness profile for a set of desired mode shapes and frequencies. Numerical simulation shows surrogates with good performance (<8 % modal error, <18 % frequency error) for target structures with a similar degree of thickness variation to that used in training the neural network. Performance improves dramatically (<2 % modal error, <7 % frequency error) for slightly less complex target structures.