Multi-fidelity harmonic balance method: A non-intrusive approach

This paper presents a novel non-intrusive hierarchical multi-fidelity harmonic balance method (HBM) framework for efficient uncertainty quantification (UQ) of nonlinear frequency response functions (FRFs) with application to gear transmission dynamics. The framework uniquely combines proper orthogonal decomposition (POD) to reduce the dimensionality of HBM-derived Fourier coefficients, enable efficient surrogate modeling in latent space, and retain access to both time- and frequency-domain responses. A key innovation is aligning low- and high-fidelity Fourier coefficient latent spaces via Procrustes analysis to improve the construction of a multi-fidelity surrogate using hierarchical Kriging with polynomial chaos Kriging (PCK) as the trend function. Further, computational efficiency in low-fidelity evaluations is achieved by integrating POD with linear regression for rapid compliance matrix estimation in loaded tooth contact analysis (LTCA). Numerical results demonstrate significant computational savings for uncertain FRF predictions of 5000 Monte Carlo (MC) samples. The proposed novelties represent the first application of hierarchical Kriging across aligned Fourier latent spaces and accelerated LTCA within a scalable framework for moderate-dimensional, vector-valued FRF uncertainty analysis, supporting broad applicability to nonlinear dynamical systems modeled with Frequency domain solvers.