An amplitude-nested surrogate model for nonlinear response using double-layer Hilbert–Huang transform. (1st April 2023) - Cui, Jiang
Abstract: Uncertainty parameters are ubiquitous in engineering and have a significant influence on the performance of mechanical systems. When evaluating the effect of uncertainty parameters on time-dependent response, a previous method is based on building surrogate models at each time instant for the amplitude, phase, and trend of the response, which can be obtained through signal decomposition techniques such as Hilbert–Huang transform. However, for a nonlinear oscillatory response, not only the response itself but also its amplitude might contain vibration components. Therefore, when modeling nonlinear responses, the previous method encounters an approximation error due to the increasingly complicated relationship between uncertainty parameters and the amplitude over time. To reduce this error, this paper proposes an amplitude-nested surrogate model using double-layer Hilbert–Huang transform through two steps. First, the response and its amplitude are successively decomposed through Hilbert–Huang transform to obtain the first- and second-layer decomposition results, respectively. Then, the polynomial surrogate models are built for the amplitude, phase, and trend in the first- and second-layer results at each time instant. The proposed method can improve the accuracy of the previous single-layer surrogate model without increasing the number of samples. Numerical examples have verified the effectiveness of the proposed method. This method can expand uncertainty analysis methods of dynamics. Graphical abstract: