The modal distribution method: a new statistical algorithm for analyzing measured acceleration data

Abstract

A new statistical method is proposed to quantify the significance of changes in mean frequencies of individual modal vibrations of measured structural response data. In this new method, called the modal distribution method, a power spectrum of measured structural response resulting from a Fourier transform is interpreted as being a series of independent modal responses. Each modal response is isolated over a frequency range and treated as a statistical distribution. The first two spectral moments are calculated directly from each of these distributions. A combined statistical comparison of the means of modal frequencies in separate data windows is used to produce a quantitative significance level of the observed differences between power spectra. Significant changes between these spectra indicate a change in the underlying process, such as damage detection in a structural health monitoring application. The method is general and may find a broad variety of applications, but it seems particularly well suited for structural health monitoring applications because the excitation is not required as input. An example is presented based on measured full-scale acceleration data from a drilling riser. To validate the new method, a power spectrum resulting from the field data is idealized to a target spectrum with known mean and variance of each mode. The idealized spectrum is subtly changed and new acceleration time-histories are simulated from these modified spectra to asses the effectiveness of the new method. The modal distribution method is found to be very effective at detecting subtle changes of mean modal frequencies.