Nonlinear Response Characterization of Post-Tensioned R.C. Bridges through Hilbert–Huang Transform Analysis

A novel methodology for the characterisation of the nonlinear behaviour of post-tensioned r.c. bridges, which exploits the response to heavy traffic travelling during operational conditions, is presented. This type of bridges shows a nonlinear elastic behaviour due to the partial opening of cracks under heavy loads whose entity is related to the intensity of the prestressing force. The properties of this response vary because of material relaxation or damage of the prestressing system. The study exploits the abilities of the Hilbert–Huang transform (HHT) to extract the instantaneous properties of the dynamic response, and a novel procedure to characterise the nonlinear elastic response is presented and investigated through theoretical applications on simplified dynamic systems. A frequency-amplitude correlation chart is proposed as a visual tool to retrieve useful information on the nonlinear response related to the instantaneous variation of the natural frequency with the response amplitude. With the aim of denoising and eliminating spurious contributions introduced by the local nature of the information extracted through the Hilbert spectral analysis, a probabilistic model is proposed for the result interpretation, through which the probability distribution of the instantaneous natural frequencies conditional to different levels of the response amplitude is provided and potential bridge’s response modifications and anomalous behaviours of the prestressing system can be detected. An extensive parametric analysis is performed to assess the influence of the most relevant parameters governing the problem and verify the effectiveness of the proposed strategy.