Chaos theory analysis of a cable-stayed bridge: Part II. Analysis of monitoring data for base-line conditions

Long term structural health monitoring has become recognized as an important tool for ensuring the structural performance of our nation's cable-stayed bridges. However, this depends upon the establishment of a reliable base-line of structural condition at the early stage of the bridge's service life. The recent completion of the Bill Emerson Memorial Bridge at Cape Girardeau, MO, which included the installation of a network of seismic motion sensors, provides an opportunity to investigate the issues of creating such a base-line. Moreover, the availability of such a monitoring data set enables the evaluation of the possibility of inherent chaotic behavior in cable-stayed structures. This study analyzed the time series data sets collected from various locations along the bridge deck and tower of the Bill Emerson Bridge using CTBR, a Windows-based software application developed by Turner-Fairbank Highway Research Center of FHWA. This software automates the process of extracting the Lyapunov exponents, which are used to characterize the nonlinear dynamics of a structure. The analysis found one or more positive Lyapunov exponents, the signature of chaotic behavior, at various locations on the bridge deck. This phenomenon, resulting from ambient traffic loading rather than from wind and rain loading on the stays themselves, illustrates a mechanism that has been implicated in chaotic behavior of other cable stayed bridges. The analysis has thus revealed a previously unknown effect of chaotic deck motions that could couple into the stay cables. This research demonstrates that once the base-line chaotic systems have been identified it will be possible to track the values of the Lyapunov exponents over time to monitor the structural health of the bridge.