An examination of the ARX as a residual generator for damage detection

Residuals that capture the difference between anticipated behavior and actual observations are often used to identify damage. Wanting to control the influence of unmeasured disturbances and noise in residuals, it is common to generate reference signals using feedback from measured outputs. Since there is much flexibility in the gains a wide range of models that react differently to changes are possible. This paper examines two questions: 1) how damage residuals generated by different closed loop models relate to each other and 2) how to rank the expected efficiency of alternative models. On the first question examination shows that the residuals from any model can be viewed as sums of filtered open loop residuals where the filter coefficients depend on the model structure but not on the damage. On the second item a general procedure based on Bayesian decision-making is proposed to quantify the economical benefit in adopting a specific autoregressive model.