Application of Chaos Theory Analysis to Accelerometer Data in Structural Health Monitoring of Highway Bridges

摘要

Many existing structural health monitoring (SHM) systems use a network of accelerometers to collect structural vibrations for detecting possible damage to the bridges. The advanced chaos theory analysis (CTA), however, is originally developed as a nonlinear dynamics approach to analyze displacement vibrations by extracting the characteristic invariants of a general nonlinear system, known as Lyapunov exponents, in identifying changes in the structure caused by instability or damage. The question now is whether the chaos theory analysis can be applied to acceleration data since nonlinear acceleration data cannot simply be converted into displacements by conventional linear dynamics approaches due to the concerns about the integrability of the nonlinear system responses. This study implemented a geometric dynamics analytical process in chaos theory analysis to reveal the relationship between the nonlinear invariants extracted from accelerations and displacements and thus enables the extraction of these nonlinear invariants from accelerations. The discovery of the sign invariant and scaling properties for these invariants was tested using the actual field data from a cable-stayed bridge, the Bill Emerson Bridge, and the simulated responses from its nonlinear finite element bridge model. The results show a very good agreement in using the normalized Lyapunov exponents as a reliable condition index for bridge structural health monitoring.