Statistical Damage Classification Using Sequential Probability Ratio Tests.

Abstract

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 Auto Regressive-Auto Regressive model 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. LA-UR-02-998: will be submitted for publication of International Journal of Structural Health Monitoring 2Based on this premise, a damage classifier is constructed using a sequential hypothesis testing technique called a 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 the probability distribution of the sample data sets, and a Gaussian distribution of the sample data sets is often assumed. 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 sequential hypothesis test is improved by integrating extreme values statistics, which specifically model behavior in the tails of the distribution of interest, into the sequential probability ratio test.

Cognitive sensor networks for structure defect monitoring and classification using guided wave signals

“…Sequential hypothesis test has been applied to structure health monitoring in the past. 22,23,24 Although the majority of research in sequential hypothesis testing has been restricted to two hypotheses, there are several situations, particularly in engineering applications, where it is natural to consider more than two hypotheses. 25,26 For example, in the context of multiple-resolution-element radar, we have sequential decision problems with a single null hypothesis and multiple alternative hypotheses.…”

A vibration model residual-based sequential probability ratio test framework for structural health monitoring

“…9,[11][12][13][14] On the other hand, parametric time series methods are those based on the corresponding parametric time series representations, such as the autoregressive moving average (ARMA) models 15,16 , and their principles have been used in a number of studies. 8,9,[17][18][19][20][21][22] For an extended overview of the main statistical time series methods for SHM, the interested reader is referred to Fassois and Sakellariou,5,6 while experimental assessments of various scalar and vector methods are provided in Kopsaftopoulos and Fassois. 9,23 The vast majority of statistical time series SHM methods is based on fixed sample size (FSS) hypothesis testing procedures which are used in the statistical decision making.…”

Structural health monitoring of progressive damage

“…DSFs are functions of the measurements that are designed to indicate damage. Many DSFs have been developed [10][11][12][13][14][15][16] and shown to reflect both the presence, amount, and type of damage. Typical DSFs are designed to be simple enough to be embedded into the sensing unit.…”

“…When the data consist of a mixture of data from both distributions, such as when a failure transition occurs while monitoring, these algorithms are not optimal. Sohn et al [11] applied SPRT to classify structural damage utilizing residuals from AR model as DSFs. They observe the test statistic moves away from the detection threshold when the structure is intact, and then moves toward it when damage happens when SPRT is applied to mixed data.…”