Equivalent Identification of Distributed Random Dynamic Load by Using K–L Decomposition and Sparse Representation

Abstract

By aiming at the common distributed random dynamic loads in engineering practice, an equivalent identification method that is based on K–L decomposition and sparse representation is proposed. Considering that the establishment of a probability model of the distributed random dynamic load is usually unfeasible because of the requirement of a large number of samples, this method describes it by using an interval process model. Through K–L series expansion, the interval process model of the distributed random dynamic load is recast as the sum of the load median function and the load uncertainty. Then, the original load identification problem is transformed into two deterministic ones: the identification of the load median function and the reconstruction of the load covariance matrix, which reveals the load uncertainty characteristics. By integrating the structural modal parameters, and by adopting the Green’s kernel function method and sparse representation, the continuously distributed load median function is equivalently identified as several concentrated dynamic loads that act on the appropriate positions. On the basis of the realization of the first inverse problem, the forward model of the load covariance matrix reconstruction is derived by using K–L series expansion and spectral decomposition. The resolutions to both inverse problems are assisted by the regularization operation so as to overcome the inherent ill-posedness. At the end, a numerical example is presented to show the effectiveness of the proposed method.