Effects of noise and measurement error on load reconstruction of dynamic loads in the frequency domain

Abstract

Load reconstruction involves solving the inverse problem by using measured structural responses to determine the forces acting on a structure. The inverse problem is almost always ill-conditioned making solving the inverse problem more difficult compared to the forward problem. Response measurements will always contain a level of noise even under the best of conditions. Various methods of performing load reconstruction have been developed in the time and frequency domains. A common problem encountered by all load reconstruction methods are their sensitivity to noise, because of the ill-conditioned nature of the inverse problem. The frequency domain methods have the benefit of limiting the band in which load reconstruction is performed which can eliminate some of the effects of noise. However, frequency domain methods remain sensitive to noise and in certain practical applications noise is present in the same frequency band in which the loads are to be reconstructed. From the literature reviewed, frequency domain methods are less sensitive to noise and have the benefit that they can be performed with very little prior knowledge of the system. The aim of this research was to establish the sensitivity of several commonly used load reconstruction methods used in engineering applications. In order to accomplish this, literature was reviewed to gain insights into the field of load reconstruction. Mathematical models were created to test the sensitivity of selected load reconstruction methods. These models consisted of a lumped mass analytical model, a rigid body simulation model and an elastic beam model which was replicated experimentally. The feasibility of using finite element modelling in conjunction with experimental data to perform load reconstruction was also briefly evaluated. It was found that systematic errors posed the greatest risk as in many of the test cases, no clear indications of any error were noticeable. Meaning that there is a great risk of drawing inaccurate conclusions when systematic errors are present in measured data. In terms of stochastic noise, it was found that the Tikhonov methods were the best performing methods. These methods were able to maintain accuracy up to high noise levels. It was also found that it is feasible to make use of finite element analysis in conjunction with experimental data to perform load reconstruction. However, the accuracy of the finite element modelling plays a major role in the accuracy of the load reconstruction.