Assessment of regression variabilities and biases: a demonstration in the context of structural health monitoring

The challenge that is at the forefront of data-driven vibration-based structural health monitoring (VSHM) is the detrimental effect caused by environmental and operational variations (EOVs). Therefore, action must be taken in order to mitigate the effects of the EOVs without affecting the influence of damage. A number of regression-based approaches have been applied in VSHM, using measured environmental and operational parameters to model damage sensitive features (DSFs). In this work, a forward stepwise method is compared with Lasso regression for the purpose of regression model optimisation. The Akaike information criterion (AIC) and the variance of the covariance of the input variables are used to quantitatively assess the quality of the regression models. Additionally, the F-statistic is used to determine which DSFs should or should not be regressed. The results of the analysis showed that the reduced order forward stepwise regression had the lowest AIC and was the most appropriate model despite not having the most stable coefficient matrices. Ultimately, the choice of optimisation method has a significant impact on the quality of future predictions.