Shape function method based on truncated singular value decomposition regularization for hull longitudinal bending moment identification

The longitudinal bending moment plays a crucial role in hull structural health monitoring. To enhance its identification accuracy, a refined method based on shape function method was developed. It incorporated truncated singular value decomposition (TSVD) regularization within shape function method of moving least square fitting(SFM_MLSF) and was combined with the influence coefficient matrix method (ICM). Numerical and experimental studies were conducted for validation. Numerical results showed that ICM-based SFM_MLSF significantly improved the identification accuracy. It achieved a reduction of over 40% in both root mean square error (RMSE) and mean absolute error (MAE) compared to ICM at different sampling frequencies. SFM_TSVD outperformed SFM_MLSF, with a maximum reduction of 57% in RMSE and MAE for various neighborhood lengths and base function scales. Experimental investigations corroborated the viewpoints that SFM_TSVD manifesting superior performance in comparison to SFM_MLSF. It demonstrates the potential of SFM_TSVD for advancing load identification within structural health monitoring.