A novel dynamic load identification method based on improved basis functions and implicit Newmark-[formula omitted] for continuous system with unknown initial conditions

Abstract

For structural design and optimization, precise knowledge of dynamic load on structures is essential. However, load identification can be sensitive to the initial conditions, and even small variations can lead to inaccurate results. The existing load identification methods always assume that the structure’s initial condition is zero, which is not the case in real engineering problems where structures are already in a state of vibration before load identification implementation. In this work, we propose a novel dynamic load identification method that takes into account unknown initial conditions of structures which is based on the improved basis functions and implicit Newmark-β method. The real vibration response is decomposed into forced vibration caused by dynamic load and free vibration caused by initial condition, which are characterized by the coefficients of undetermined orthogonal polynomials. Moreover, to overcome the ill-posedness problem arising from factors such as response noise and model error, we introduce the L1 regularization method. To validate the performance of the proposed method, numerical simulations and tests of load identification are conducted on simply supported beam. The effects of noise and model error on the load identification results are analyzed. Finally, we discuss the impact of modal truncation order and the effect of measurement points on load identification.