Robust mitigation of EOVs using multivariate nonlinear regression within a vibration-based SHM methodology

A significant issue that has plagued data-driven Vibration-based Structural Health Monitoring (VSHM) is the mitigation of Environmental and Operational Variations (EOVs). The Damage Sensitive Features (DSFs) that are obtained from the vibration response of the structure are influenced by EOVs. Regression analysis, such as multivariate nonlinear regression, can be used to create relationships between Environmental and Operational Parameters (EOPs) and the DSFs, with EOV-insensitive DSFs created by taking the regression residuals. Inherent issues, originating from nuances in their design, exist within the design of the regression models, following from the overall uncertainty and redundancy in predictors and explained variables, leading to poor performance. To overcome this, a comprehensive nonlinear stepwise regression methodology has been developed to scour the regression models of as much uncertainty as possible. The proposed methodology addresses a number of crucial ideas: removing co-nonlinear variables, identifying the most influential EOPs, facilitating the selection of compact regression bases and determining which DSFs should be regressed. Robust DSFs are created by combining non-regressed DSFs with critically thought-out regressed DSFs. Ultimately, reducing the uncertainty within the models will lead to more confidence in the decision making within a VSHM methodology.