Shape function method of Tikhonov regularization for vertical bending moment identification based on parameter updating

•An improved shape function construction method is proposed.•A shape function method-based simultaneous identification method is established.•A simultaneous identification method including shape function method is established. To accurate identifying vertical bending moment and structural parameters for hull structure, a simultaneous identification technique combined with shape function method (SFM) and sensitivity method was developed. The shape function construction incorporated Tikhonov regularization to enhance the stability of SFM (SFM_Tikhonov). Numerical and experimental studies were conducted. Numerical results showed the effectiveness of SFM_Tikhonov. It achieved a reduction of over 30% in both root mean square error (RMSE) and mean absolute error (MAE) compared to SFM of moving least square fitting (SFM_MLSF). The simultaneous identification method effectively improves the accuracy of moment identification in scenarios of wrong initial parameter estimates. Experimental results show that under constant load condition, the performance of the load identification module based on SFM_Tikhonov lags behind numerical examples, although its parameter update module is unaffected. However, the proposed method remains showing its potential for advancing load identification in structural health monitoring systems.