Extrapolation of AR models using cubic splines for damage progression evaluation in composite structures

This paper presents the potentiality of the use of extrapolation of a set of Auto-Regressive (AR) models to inspect a future damage sensitive indices based on changes in one-step-ahead prediction errors. The key idea is to use multiple AR models to assess a data-driven model to represent and predict the time-series outputs of the PZT sensors receiving Lamb waves in a composite coupon. Based on some simplified assumptions, after detecting initial damage using some previous classifier, its progression evaluation by interpolating the AR parameters is proposed and examined based on cubic spline functions. After, an extrapolated AR model using this information may verify the future state and to inspect how the damage could progress. An aeronautical composite panel with bonded piezoelectric elements that act both as sensors and actuators is utilized to examine the relationship between the variation of the identified model parameters with various levels of simulated damage. The results have shown a smooth and adequate correlation between the estimates obtained by the extrapolated model and the actual progress of the damage observed. The significant advantage of the proposed procedure is implementing this task without adopting a complicated and costly mathematical-physical model.