Compensation of Temperature Shift in Strain Monitoring Data via Auto-Regressive Models

Structural health monitoring (SHM) data are generally affected by environmental and operational variabilities (EOVs). Amongst the various, temperature is acknowledged to play a major role, especially for outdoor monitoring systems. In structures such as bridges, which are entirely exposed, thermal inertia might cause a time delay between the response of the structure and the recorded ambient temperature. Thus, it is essential to determine this time delay to properly interpret and exploit the SHM data in tasks like model updating, anomaly detection, damage classification, and structural prognosis. In this work, we analyze how auto-regressive with exogenous input (ARX), nonlinear auto-regressive with exogenous input (NL-ARX), and auto-regressive moving average with exogenous input (ARMAX) models can be used to tackle this problem. To this purpose, we consider pseudo-data generated from a numerical model of a steel truss bridge where the temperature effect on some structural elements is introduced by considering non-linear temperature-dependent material properties. Thermal inertia is modeled by imposing a step-wise time delay from 0 to 12 h. Using this data set we conduct a parametric study to compute ARX, NL-ARX, and ARMAX parameters having the optimal combination of the final prediction error (FPE). The results show that NL-ARX outperforms ARX and ARMAX by accurately predicting the time-delay in all but one simulated scenarios.