An efficient method to reduce ill-posedness for structural dynamic load identification

For the inverse problem of structural dynamic load identification, high system ill-posedness is a main cause leading to instability and low accuracy. In this study, an efficient interpolation-based method is proposed to reduce ill-posedness availably and identify dynamic load stably. The load history is discretized into a series of time elements, and the load profile in each time element is approximated through interpolation functions. Then, in the whole time domain, the dynamic responses under interpolation function loads are calculated through a few finite element analysis and then assembled together to form a global kernel function matrix for load identification. Using singular value decomposition (SVD), the ill-posed degree of the global kernel function matrix can be analyzed. Compared with the conventional Green kernel function method (GKFM), the ill-posedness of global kernel function matrix in the proposed method is significantly reduced. Especially, when the length of time element is selected appropriately, the global kernel function matrix is entirely well-posed and the corresponding dynamic load can be stably identified without any regularization operation. Numerical examples demonstrate the effectiveness of the proposed method and the correctness of identified load.