Load identification approach based on basis pursuit denoising algorithm

Abstract

The information of the external loads is of great interest in many fields of structural analysis, such as structural health monitoring (SHM) systems or assessment of damage after extreme events. However, in most cases it is not possible to measure the external forces directly, so they need to be reconstructed. Load reconstruction refers to the problem of estimating an input to a dynamic system when the system output and the impulse response functions are usually the knowns. Generally, this leads to a so called ill-posed inverse problem, which involves solving an underdetermined linear system of equations. For most practical applications it can be assumed that the applied loads are not arbitrarily distributed in time and space, at least some specific characteristics about the external excitation are known a priori. In this contribution this knowledge was used to develop a more suitable force reconstruction method, which allows identifying the time history and the force location simultaneously by employing significantly fewer sensors compared to other reconstruction approaches. The properties of the external force are used to transform the ill-posed problem into a sparse recovery task. The sparse solution is acquired by solving a minimization problem known as basis pursuit denoising (BPDN). The possibility of reconstructing loads based on noisy structural measurement signals will be demonstrated by considering two frequently occurring loading conditions: harmonic excitation and impact events, separately and combined. First a simulation study of a simple plate structure is carried out and thereafter an experimental investigation of a real beam is performed.