On the investigation of Statistical Alignment performance for enhancing damage identification across a population of heterogeneous shear structures

The development of machine learning algorithms for Structural Health Monitoring (SHM) is rapidly advancing. However, their application for real-world structures finds a high number of complications. One is the need for comprehensive data for training the proper algorithms. Thus, Population-Based Health Monitoring (PBSHM) overcomes these challenges by sharing information between different structures. In this framework, it is necessary to understand to what extent knowledge can be shared, especially for heterogeneous datasets. Therefore, this study implements a simple domain adaptation technique based on Statistical Alignment (SA) on a population of heterogeneous shear structures to investigate how the performance changes due to the variations within the population. The scenarios proposed are solved with normal-condition alignment (NCA) and normal-correlation alignment (NCORAL). Two case studies are analyzed. The first is related to numerical structures. It is created by simulating multiple source and target datasets, containing the features and labels of each data point. The features consist of the natural frequencies of each structure, and the label is a binary vector indicating if the data point corresponds to a damage condition or not. To calculate the natural frequencies, the structure is modelled as a shear-type with chain-like models, and the mass and stiffness matrices are calculated considering the equation of motion. The damage is then introduced with a reduction of the stiffness of a column, leading to reduced values of the related frequencies. It is important to highlight that, in each sample, a variation of the material properties is introduced, trying to simulate the actual variability on measured data. The second case study extends the implementation to an experimental case study of a three-story frame structure to test this methodology for sharing knowledge between real and simulated data.