Structural load identification and response reconstruction based on improved multiplicative regularization

ObjectiveTo improve the accuracy of loads identification and responses reconstruction for the traditional multiplicative regularization method, an improved multiplicative regularization method considering the influence of measurement noise was proposed to identify the loads, and the responses were reconstructed using the identified loads.MethodsFirstly, the load identification and response reconstruction equations were constructed based on the state space model. Secondly, the singular entropy increment denoising of the measurement responses was carried out, the objective function was constructed to identify the external loads of the structure, the global weighting matrix was redefined, and the global smoothing operator that can be selectively modified according to the magnitude of the singular value was introduced to improve the degree to which the load satisfies the constraints. Thirdly, the iterative weighted least squares method was adopted to solve the objective function based on the denoised measurement responses and the transfer matrix, the stable solution of the load was obtained and the responses of the unmeasured positions were reconstructed. Finally, the numerical simulation and the test analysis for the simply supported beam model were carried out to verify the effectiveness of the proposed method.ResultsThe results show that the proposed method can improve the ill-posedness of the reconstruction equations, identify the loads accurately and reconstruct the dynamic responses of the unmeasured positions.