ARX and open loop residuals in damage detection

The paper examines the autoregressive with exogenous input (ARX) structure as a residual generator for damage detection. It is shown that ARX residuals are given by the discrete time convolution of the open loop (OL) residuals with a kernel defined by the AR coefficient matrices of the model. Examination of the transfer matrix from OL to ARX residuals shows that the poles of the physical system appear as transmission zeros and that the null space span is given by the eigenvector corresponding to the pole. These results, together with the fact that the OL residuals tend to have a spatial distribution that, in the vicinity of each pole, is dominated by the associated mode shape, show that the ARX structure annihilates the OL residuals near the resonant frequencies. Given that the contribution of damage to the OL residuals tends to be concentrated near the natural frequencies the ARX structure is not an effective residual generator. Results from a Monte Carlo simulation study support the contention that OL residuals have a better damage classification capacity than the ARX ones.