Multisource uncertain dynamic load identification fitted by Legendre polynomial based on precise integration and the Savitzky–Golay filters

Abstract

AbstractIn this article, a precise integral method (PIM) for the load identification of continuous structures based on the polynomial nonlinear hypothesis is presented. Essentially, load identification can be regarded as solving a dynamic equation in an inverse process. PIM is famous for its high precision in positive engineering problems. It has been already used in load reconstruction, but most cases are with discrete structures. In each time step, the dynamic responses of the measured points are used to identify the load without establishing a recursive chain, so PIM is not sensitive to the initial value and has no accumulated error. Legendrepolynomials (LPIM) is a computational scheme. The dynamic load is assumed to be a polynomial fitting nonlinear function in each integral time step with LPIM. Just with the first modal, LPIM can reliably identify the concentrated load. In addition, as uncertainty is getting more and more attention in engineer, it is also needed to be considered in load identification. In linear systems, interval vertex is a reliable method to obtain the load bounds in the virtue of multisource uncertainties. The results of identified load are too lumpy because of the polynomial fitting. To improve the precision, Savitsky–Golay (S–G) filters which fit the curves by polynomials in a frame length is introduced to smooth down the load in high fidelity. Eight numerical examples are investigated to demonstrated the efficiency and precision of the developed method.