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Automatic differentiation driven parameter parallel incremental harmonic balance method
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DOI：10.1016/j.ijmecsci.2026.112049.png)
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Abstract
En 中文
Automatic differentiation (AD) enables the Jacobian matrices required by incremental harmonic balance (IHB) to be constructed without manual differentiation or finite-difference perturbations. This study develops an AD-driven, parameter-parallel IHB framework, termed IHB-ADP, for simultaneously solving independent nonlinear dynamical subsystems. The complete mapping from frequency-domain coefficients to residuals is encapsulated as a differentiable computational graph, while response reconstruction, residual evaluation, Jacobian construction, and Newton correction are implemented as GPU-batched tensor operations. An identification-exit mechanism independently manages subsystem convergence and failure, whereas a perturbation–restart mechanism avoids evaluating Newton Jacobians at isolated nondifferentiable sampling states. Tests on the Van der Pol, Duffing, and Mathieu systems show minimum speedups of approximately 1.80 over other GPU-batched implementations and 7.92 over serial baselines, demonstrating contributions from both the numerical formulation and parameter-level parallelism. For the Mathieu system, a gradient-guided prediction-bias-correction strategy constructs parameter sets along prescribed stability boundaries near intersections. Dynamic tests on a quasi-zero-stiffness isolation platform show good agreement between calculated and measured responses. Finally, coordinate-dependent Fourier sets and event-localized Bernoulli enrichment are incorporated to analyze a stacked piezoelectric energy harvester with multiscale responses and unilateral contact. These results demonstrate that IHB-ADP provides an efficient and flexible framework for parameter-batched analysis of low- to moderate-dimensional nonlinear dynamic systems.
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