Experimental study of the time domain damage identification

Abstract

A theoretical and experimental study was undertaken to validate the use of a novel time-domain system identification (SI) method for detecting changes in stiffnesses of uniform cross section fixed-fixed and simply supported beams. By quantifying the reduction of beam's elemental stiffnesses, the location of damage can be detected. The Iterative Least Squares (ILS-UI) algorithm, a novel, time-domain SI algorithm, being developed at the University of Arizona for nondestructive evaluation of structures, is used for this purpose. The ILS-UI algorithm requires the use of nodal response time histories to develop an equivalent multi-degree-of-freedom model in which the number of node points is equal to the number of sensors used in the experiment. To optimize the number of sensors, a finite element model was developed in which the beam was discretized into an optimum number of node points, such that nodal responses at these node points are equivalent to that of the continuous beam. As a prelude to the experimental validation, a simulation was performed to study errors in the numerical integration of a digitized signal for three different rules: trapezoidal, Simpson's and Boole's. It was shown that Simpson's rule and Boole's rule yield smaller errors than the trapezoidal rule, especially when lower sampling rates are used. Several post processing techniques to remove noise, to filter out high frequencies and remove slope and offset from a data set were also demonstrated. In the first phase of the validation experiments, the optimum number of node points was determined for the fixed beam. Also, a method was developed to scale angular response based on the measured transverse response. The ILS-UI algorithm was then used to predict element stiffnesses for the fixed beam. The stiffness predictions did not converge. This prompted an investigation to determine the root cause of the failure. It was found that amplitude and phase errors in the accelerometer's measurements were the root cause of the failure. After this was determined, an alternative approach was developed to mitigate the amplitude and phase shift errors. To validate the alternative approach, nodal responses were measured for the beam with and without damage. The ILS-UI algorithm was demonstrated to successfully quantify reduction in the beam's element stiffnesses and the location of damage was identified.