ARX residuals in damage detection

The relationship between residuals obtained from Autoregressive with Exogenous Input (ARX) predictors is examined from the perspective of resolution in damage detection. It is shown that residuals from all ARX structures are filtered versions of those obtained when only inputs are used to compute the predictions, i.e. the output error (OE) residuals. Examination shows that the transfer matrix from the OE residuals to the equation error (EE) ones has repeated poles at the origin and transmission zeros and zero directions that coincide with the poles and eigenvectors of the input-output map. This result, together with an examination of the spectral distribution of the OE residuals suggest that these are likely more informative for damage detection than the EE ones. Results of a Monte Carlo study and tests on an aluminum beam, where damage is simulated by the addition of a small mass, are shown to support this contention.