Detecting sudden changes in stiffness using high-pass filters

It is often of interest to detect the time of occurrence of sudden change in structural parameters, particularly the changes in structural stiffness for health monitoring purposes as a change in stiffness also implies some damage in one or more structural elements. Although well known, it is formally shown here that a sudden change in stiffness induces a sudden change in the acceleration response. Several methods have been used in the literature to detect such sudden changes. The wavelet transform, in particular the discrete wavelets transform, is one of the popular approaches. In this approach, the sudden changes have been shown to manifest themselves as spikes in the plots of the details of the discrete wavelet transform of the acceleration response. In this paper, we provide an analytical rationale to explain what constitutes these spikes and their relationship to the discontinuity being detected. In particular, it is shown that a spike corresponds to the scaled step-response of a high-pass filter and that a step discontinuity can be detected using a high-pass filter with properly chosen cut-off frequency where the discontinuity manifests as a clear spike in the filtered output. How the measurement error and sampling frequency affect the detection is discussed. An example of a multi-degree-of-freedom system subjected to the base excitation, with sudden changes in its structural elements, is presented to illustrate the approach. Copyright (c) 2011 John Wiley & Sons, Ltd.