Objectives To address the issues of low computational efficiency and scarce experimental samples in hull surface vibration prediction, a multi-fidelity method with self-updating capability for high-dimensional frequency response fields is investigated.
Methods Principal component analysis (PCA) is first employed to compress the original high-dimensional frequency response data. Each raw frequency response function vector contains thousands of frequency points, introducing the curse of dimensionality while suffering from strong inter-frequency correlations and sensitivity to local peak shifts. PCA transforms these vectors into a low-dimensional principal component score space, retaining only the first four principal components that capture the dominant spectral variation patterns while filtering out numerical noise. This compression drastically reduces the output dimension while preserving the underlying physical characteristics of structural modal coupling, thus providing a compact yet information-rich representation for subsequent surrogate modeling. A two-layer Co-Kriging surrogate model is then constructed within the excitation-response coordinate space to fuse multi-fidelity data from both simulations and experiments. The first layer, built upon 16 simulation points generated by Latin hypercube sampling, employs a product kernel that decouples the correlations of excitation and response coordinates to accurately capture the spatial propagation of vibration transmission. The second layer uses an auto-regressive Co-Kriging structure, in which the high-fidelity experimental principal component scores are expressed as a linear scaling and a global bias of the low-fidelity predictions, supplemented by an independent Gaussian process residual. This hierarchical architecture exploits the broad coverage of low-fidelity simulations while precisely correcting systematic deviations using only nine high-fidelity experimental samples, effectively reconciling the trade-off between accuracy and data acquisition cost. Furthermore, an active learning strategy based on posterior variance maximization is introduced to implement sequential sample infilling and model updating. By scanning the geometric domain and identifying points with maximum posterior variance, the strategy guides the selection of the most informative locations for additional measurements.
Results Cross-validation results demonstrate that the mean absolute error (MAE) of the proposed method is approximately 2.55 dB, the coefficient of determination reaches 0.92, and the overall vibration level error is 1.78 dB on average over the 0–3 000 Hz frequency range. With only three supplementary experimental samples through the active learning strategy, the global root mean square error (RMSE) is reduced by 7.7%, demonstrating the efficiency and robustness of the variance-based infilling criterion. This method achieves accurate characterization of frequency-spatial high-dimensional response fields and is applicable to surrogate modeling under small-sample constraints. Once trained, the model reduces prediction time from hours to seconds for any new excitation-response channel.
Conclusions The self-updating mechanism further equips the model to continuously assimilate newly acquired measurement data during in-service operation, progressively refining predictions without full-scale re-simulation or re-testing. This work thus provides a valuable reference for model updating and online vibration assessment in ship digital twin systems.
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