A structural damage detection indicator based on principal component analysis and statistical hypothesis testing

A comprehensive statistical analysis is performed for structural health monitoring (SHM). The analysis starts by obtaining the baseline principal component analysis (PCA) model and projections using measurements from the healthy or undamaged structure. PCA is used in this framework as a way to compress and extract information from the sensor-data stored for the structure which summarizes most of the variance in a few (new) variables into the baseline model space. When the structure needs to be inspected, new experiments are performed and they are projected into the baseline PCA model. Each experiment is considered as a random process and, consequently, each projection into the PCA model is treated as a random variable. Then, using a random sample of a limited number of experiments on the healthy structure, it can be inferred using the χ² test that the population or baseline projection is normally distributed with mean μ_h and standard deviation σ_h. The objective is then to analyse whether the distribution of samples that come from the current structure (healthy or not) is related to the healthy one. More precisely, a test for the equality of population means is performed with a random sample, that is, the equality of the sample mean μ_s and the population mean μ_h is tested. The results of the test can determine that the hypothesis is rejected (μ_h ≠ μ_c and the structure is damaged) or that there is no evidence to suggest that the two means are different, so the structure can be considered as healthy. The results indicate that the test is able to accurately classify random samples as healthy or not. (paper)