A new regularization method for the dynamic load identification of stochastic structures

For the dynamic load identification for stochastic structures, ill-posedness and randomness are main causes that lead to instability and low accuracy. Monte-Carlo simulation (MCS) method is a robust and effective random simulation technique for the dynamic load identification problems of stochastic structures. However, it needs large computational cost and is also inefficient for practical engineering applications because of the requirement of a large quantity of samples. In order to improve its computational efficiency, this paper proposes a novel computational algorithm for the dynamic load identification of stochastic structures. First, the newly developed algorithm transforms dynamic load identification problems for stochastic structures into equivalent deterministic dynamic load identification problems. Second, a new regularization method is proposed to realize the deterministic dynamic load identification. Third, the assessments of the statistics of identified loads are obtained based on statistical theory. Finally, the stability and robustness of the proposed algorithm are well validated by two engineering examples. It is demonstrated that the newly developed regularization method outperforms the traditional Tikhonov regularization method in computational accuracy. Moreover, the newly proposed algorithm can significantly improve the computational efficiency of MCS and is very stable and effective in solving the dynamic load identification for stochastic structures.