A Learnable Radial Basis Function Network–Based Method for Decomposing Shock-Induced Vibration Signals

Structural shock responses caused by underwater explosions contain transient components with overlapping frequency contents, which makes modal decomposition difficult. This paper proposes an adaptive decomposition and reconstruction method based on a learnable radial basis function network (RBFN). The response spectrum is represented by a compact set of Gaussian kernels, whose centers, bandwidths, and amplitudes are learned in the frequency domain. Sequential parameter updates, bandwidth penalization, and pruning based on kernel overlap are used to obtain modal components with limited spectral leakage and interpretable spectral features. The method is evaluated using acceleration responses from 50 points in a stiffened plate frame underwater explosion simulation and is compared with empirical mode decomposition (EMD), variational mode decomposition (VMD), empirical wavelet transform (EWT), Hilbert vibration decomposition (HVD), and local mean decomposition (LMD). The assessment considers reconstruction fidelity, phase portrait consistency, modal correlation, spectral overlap, computational cost, and parameter stability. The results show that RBFN preserves reconstruction consistency while reducing spectral overlap under the tested conditions. The near-zero reconstruction error of EMD is discussed as a consequence of its additive completeness rather than direct evidence of modal separation quality. Measured shock responses from unstiffened and stiffened plate frame structures are further analyzed to examine the applicability of the learned spectral partition to experimental signals with broadband spectral contents and multiple peaks.