Statistical Damage Classification Using Sequential Probability Ratio Tests

The primary objective of damage detection is to ascertain with confidence if damage is present or not within a structure of interest. In this study, a damage classification problem is cast in the context of the statistical pattern recognition paradigm. First, a time prediction model, called an autoregressive and autoregressive with exogenous inputs (AR-ARX) model, is fit to a vibration signal measured during a normal operating condition of the structure. When a new time signal is recorded from an unknown state of the system, the prediction errors are computed for the new data set using the time prediction model. When the structure undergoes structural degradation, it is expected that the prediction errors will increase for the damage case. Based on this premise, a damage classifier is constructed using a sequential hypothesis testing technique called the sequential probability ratio test (SPRT). The SPRT is one form of parametric statistical inference tests, and the adoption of the SPRT to damage detection problems can improve the early identification of conditions that could lead to performance degradation and safety concerns. The sequential test assumes a probability distribution of the sample data sets, and a Gaussian distribution of the sample data sets is often used. This assumption, however, might impose potentially misleading behavior on the extreme values of the data, i.e. those points in the tails of the distribution. As the problem of damage detection specifically focuses attention on the tails, the assumption of normality is likely to lead the analysis astray. To overcome this difficulty, the performance of the SPRT is improved by integrating extreme values statistics, which specifically models behavior in the tails of the distribution of interest into the SPRT.