A seasonal ARIMAX time series model for strain-temperature relationship in an instrumented bridge

Data gathered by continuously operating instrumented structural health monitoring (SHM) systems installed on full-scale civil infrastructures are inherently influenced by environmental and operational conditions, including temperature, humidity, wind, solar radiation, live loads, and others. In order to interpret the SHM data correctly, the environmental and operational effects need to be separated from changes due to damages sustained by the structure. This study examines the dependence between time histories of static, hourly sampled strains and temperatures recorded by a multi-sensor SHM system installed in a major post-tensioned bridge and operating continuously for a long time. The strain-temperature relationship is modeled using a seasonal autoregressive integrated moving average model with exogenous inputs (SARIMAX), also referred to as a transfer function (TF). By studying the SARIMAX model, using an outlier detection and intervention analysis technique, various unusual events as well as structural change or damage can be revealed. Such events or structural changes may result, among other causes, from a sudden settlement of foundation, excessive traffic load or failure of post-tensioning cables; but they may also be caused by unusual temperature variations. The SARIMAX approach helps to differentiate the genuine structural changes from those due to environmental factors.