Identification of moving loads using the ℓ1 norm minimization

Abstract

This contribution deals with the inverse problem of indirect identification of moving loads. The identification is performed based on the recorded response of the loaded structure and its numerical model. A specific feature of such problems is a very large number of the degrees of freedom (DOFs) that can be excited and a limited number of available sensors. As a result, unless the solution space is significantly limited, the identification problem is underdetermined: it has an infinite number of exact, observationally indistinguishable solutions. We propose an approach based on the assumption of sparsity of the excitation, which can be expressed in the form of a requirement of a bounded l 1 norm of the solution. As long as the loads are sparse, the approach allows them to be freely moving, without the usual assumption of a constant velocity. We first test the approach in a numerical example with 10% rms measurement noise. A good qualitative agreement of the numerical results allows to proceed with experimental investigations, and the moving load identification is then carried out based on the response measured experimentally on a lab test stand.

Trajectory Identification for Moving Loads by Multicriterial Optimization

“…The focus on the trajectory contrasts with the usual approaches that concentrate on identification of the time-dependent force magnitude and typically assume the load to be stationary or the trajectory to be known. Earlier attempts included sparsity-based identification of 1D trajectories of moving mass loads on a laboratory beam with transient dynamics [ 35 ], but they did not consider the geometric characteristics of the trajectory. Here, a fully two-dimensional case is considered: the unknown load is freely moving in 2D on a plate structure.…”