An improved spectral decomposition flexibility perturbation method for finite element model updating

Finite element analysis is the most powerful tool to predict the behavior of a structure in engineering practice. Generally, the initial finite element model must be corrected with experimental data due to its complexity. Thus, it is very necessary to study a finite element model updating method with high precision and high efficiency. To this end, this article presented an improved spectral decomposition flexibility perturbation method for structural finite element model updating. The improvements of the proposed method lie in two aspects. First, using the uniform correction model, the proposed method is more economical in computation than the initial method because the spectral decomposition and reorganization of elemental stiffness matrices can be avoided. Second, using the twice singular-value-truncation method, the proposed method has better performance than the initial method in combating data noise. A beam structure is employed to demonstrate the proposed method for model updating in a noisy environment. It was found that the result obtained by least squares estimate is seriously distorted and the result obtained by the first singular value truncation is also not entirely satisfactory. Only the result obtained by the second singular value truncation is the most stable and accurate. Overall, the improved spectral decomposition flexibility perturbation method is robust and effective in small modification case, large modification case, adjacent modification case, and multiple modifications case. The proposed method may be very useful for structural finite element model updating in the noisy environment