Autoencoder-based reduction of harmonic balance Fourier coefficients for uncertainty analysis of multi-DOF gear systems

Uncertainty quantification (UQ) in gear dynamic simulations is often faced by the curse of dimensionality , which requires many full-order model (FOM) evaluations. This paper introduces a novel framework that sequentially integrates model order reduction (MOR) and uncertainty propagation to overcome the limitations of HBM-PCE methods. A key limitation of existing methods, such as non-intrusive HBM-PCE, is that they require separate surrogate models for each response variable (displacement, velocity, acceleration) and every frequency point, leading to high computational costs, especially for real-world, high-frequency, multi-degree-of-freedom applications. The proposed approach is demonstrated on a multi-degree-of-freedom (DOF) gear system with ten uncertain macro-geometry, micro-geometry, and torque parameters. First, component mode synthesis (CMS) reduces the system from 252 DOFs to 76. Then, the harmonic balance method (HBM) solves the reduced system for 100 training samples. Fourier coefficients are compressed via an autoencoder, and a surrogate model maps uncertain inputs to latent coordinates. A comparative study of polynomial chaos expansion (PCE), Kriging, and polynomial chaos Kriging confirms the efficiency of the surrogate models in capturing time and frequency-domain displacement, velocity, and acceleration responses. Validated against 6,000 FOM samples, the method achieves high accuracy with <0.6% error. The proposed method requires only as many surrogate models as the number of latent dimensions and allows uncertainty analysis of displacement, velocity, and acceleration to be completed in a single workflow. The approach reduces the computational cost by more than two orders of magnitude compared to traditional non-intrusive HBM-PCE methods and enables an efficient and scalable uncertainty analysis of gear transmissions. • Data-driven uncertainty analysis for frequency-domain response in gear systems. • Autoencoder compression reduces Fourier coefficients to minimal dimensions. • Kriging outperforms PCE & PC-Kriging in latent space input-output mapping. • Significant computational cost reduction for FRF uncertainty estimation.