On the performance of data-driven dynamic models for temperature compensation on bridge monitoring data

In Structural Health Monitoring, environmental and operational variables present a persistent challenge. These variables induce fluctuations in measured data, consequently reducing the system’s sensitivity to detect anomalies. Local temperature stands out as a significant external factor in bridge monitoring, which can be accounted for and effectively compensated through data-driven modelling. The literature offers numerous algorithms to model the complex, often non-linear and time-variant relationship between temperature and measured responses. This work aims to test the algorithm of Sparse Identification of Nonlinear Dynamics with Control on SHM data, with the objective of finding a more flexible, interpretable and noise-robust solution to the issue. We compare its performance against the Auto-Regressive model with exogenous inputs and the static linear regression. Our comparative analysis focuses on displacement signals from two distinct data sets, acquired from a steel Warren truss bridge and a reinforced concrete bridge equipped with a resident monitoring system. Unlike many existing studies, this research also examines the models’ robustness against noise and their accuracy for predictions that span long time horizons. The numerical results from Sparse Identification of Nonlinear Dynamics with Control are promising, showcasing accurate predictions and robustness against noisy state variable data. In contrast, the Auto-Regressive model with exogenous inputs model and linear regression exhibit difficulties in noise rejection, one for noise in the initialization phase and the other for noisy exogenous inputs. This may significantly impact their performance if used in Structural Health Monitoring applications.