A neural operator for predicting vibration frequency response curves from limited data

TL;DR

This paper introduces a neural operator with an implicit numerical scheme that predicts vibration frequency response curves from limited data, demonstrating high accuracy and better generalization without relying on physics-based regularization.

Contribution

It presents a novel neural operator architecture that learns system dynamics from limited data and generalizes to untested conditions without physics-based regularization.

Findings

Achieves 99.87% accuracy in predicting Frequency Response Curves

Forecasts resonance behavior using only 7% of the bandwidth data

Demonstrates effective learning on a linear single-degree-of-freedom system

Abstract

In the design of engineered components, rigorous vibration testing is essential for performance validation and identification of resonant frequencies and amplitudes encountered during operation. Performing this evaluation numerically via machine learning has great potential to accelerate design iteration and make testing workflows more efficient. However, dynamical systems are conventionally difficult to solve via machine learning methods without using physics-based regularizing loss functions. To properly perform this forecasting task, a structure that has an inspectable physical obedience can be devised without the use of regularizing terms from first principles. The method employed in this work is a neural operator integrated with an implicit numerical scheme. This architecture enables operators to learn of the underlying state-space dynamics from limited data, allowing generalization to untested driving frequencies and initial conditions. This network can infer the system's global frequency response by training on a small set of input conditions. As a foundational proof of concept, this investigation verifies the machine learning algorithm with a linear, single-degree-of-freedom system, demonstrating implicit obedience of dynamics. This approach demonstrates 99.87% accuracy in predicting the Frequency Response Curve (FRC), forecasting the frequency and amplitude of linear resonance training on 7% of the bandwidth of the solution. By training machine learning models to internalize physics information rather than trajectory, better generalization accuracy can be realized, vastly improving the timeframe for vibration studies on engineered components.