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 μh and standard deviation σh. 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 μs and the population mean μh is tested. The results of the test can determine that the hypothesis is rejected (μh ≠ μc 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.

A methodology based on Principal Component Analysis (PCA) and clustering is evaluated for process monitoring and process analysis of a pilot-scale SBR removing nitrogen and phosphorus. The first step of this method is to build a multi-way PCA (MPCA) model using the historical process data. In the second step, the principal scores and the Q-statistics resulting from the MPCA model are fed to the LAMDA clustering algorithm. This procedure is iterated twice. The first iteration provides an efficient and effective discrimination between normal and abnormal operational conditions. The second iteration of the procedure allowed a clear-cut discrimination of applied operational changes in the SBR history. Important to add is that this procedure helped identifying some changes in the process behaviour, which would not have been possible, had we only relied on visually inspecting this online data set of the SBR (which is traditionally the case in practice). Hence the PCA based clustering methodology is a promising tool to efficiently interpret and analyse the SBR process behaviour using large historical online data sets.