Distributed Dynamic Load Identification of Beam Structures Using a Bayesian Method

The distributed dynamic load is difficult to obtain due to the complexity of loads in practical engineering, such as the aerodynamic loads of aircraft and the distributed dynamic loads of sea-crossing bridges. Thus, distributed dynamic load identification is important to deal with these difficulties, which is generally an ill-posed problem considering the inversion of the infinite dynamic loads. The traditional Tikhonov regularization technique is limited on the optimal regularization parameters selection. Consequently, in this paper, we develop a novel distributed dynamic load identification algorithm in combination with the orthogonal polynomials and the Bayesian framework. Thus, the orthogonal polynomial coefficients in the load identification model are regarded as the prior probability distribution of unknown variables in the Bayesian inference. Simultaneously, the posterior probability distribution of the orthogonal polynomial coefficients is derived based on the Bayesian formula and the likelihood function. The regularization parameters and the standard deviation of the response error are also treated as random variables to obtain the corresponding prior distribution in the multi-level Bayesian model. Moreover, the maximum posterior estimate is applied aiming at determining the regularization parameters, as well as the orthogonal polynomial coefficients to reconstruct the distributed dynamic loads. Compared with the Tikhonov regularization, a series of numerical simulations are studied to verify the effectiveness and high accuracy, as well as the noise resistance, and the results illustrate that this approach is effective to reconstruct the distributed dynamic loads.