Study on Ill-Conditioned Total Least Squares Load Identification Method Based on the IGG Weight Function

To address the ill-conditioned problem and unknown noise interference in ship load identification, this study proposes the ill-conditioned Total Least Squares (TLS) load identification method using the anti-error principle of the IGG weight function (IGG-TLS). First, the weight factor is iteratively updated through the IGG weight function. The weight matrix is constructed adaptively by multiplying the weight factor with the initial unit weight matrix. Then, the regularization criterion for the ill-conditioned IGG-TLS model is established based on the Tikhonov regularization principle. And the Lagrange multiplier is employed to solve the IGG-TLS method. Finally, the load identification accuracies of the IGG-TLS method are investigated through the simulation analysis and experimental verification of the rectangular plate under different noise and SNR conditions. The results demonstrate that the IGG-TLS method can achieve high accuracy in load identification without the need to pre-construct the weight matrix, even when the SNR is unknown. Additionally, the IGG-TLS method can effectively correct the identification errors in the TLS method, demonstrating high accuracy and noise immunity under conditions of equal-weight and unequal-weight noise.