In-service Bridge State Analysis Based On Non-linear Chaotic Dynamics Theory

The estimation of a bridge safety state using bridge health monitoring information is of great concern both to the domestic and foreign researchers. This paper, by theoretical analysis, model simulation and project application, presents a novel theoretical and technological bridge state analysis system based on non-linear chaotic dynamics.(1) Firstly, a bridge in service is deemed as a higher-dimension non-linear dynamic system. Accordingly, the critical stable conditions for the coupled vehicle-bridge model are obtained. The results indicate that the coupled vehicle-bridge model tends to achieve stability under some conditions while become unstable under the others. Combined with the previous results from the researches on global bifurcation critical conditions of cantilever beams, bridge cables, it is concluded that higher-dimension non-linear dynamics is feasible and valid to estimate a bridge state.(2) A finite element ASCE Benchmark model and Benchmark experiment model are established and the maximum Lyapunov exponents are drawn from the acceleration time series of both models. The results indicate that with the―damage‖degrees added under conditions 7, 8, and 9, the maximum Lyapunov exponents at each monitoring station on the bridge demonstrate the same evolution tendency. Therefore, it is concluded that ASCE Benchmark finite element model and test model are in chaos, and their maximum Lyapunov exponents are not only sensitive to but also able to estimate the bridge state. For more accurate estimation of bridge safety state, this paper adopts a couple of indicators based on the maximum Lyapunov exponent entropy. The test results show that maximum Lyapunov exponent entropy contributes to a better estimation of the bridge state without the unsteadiness caused by the different directions of chaos.(3) Due to the lack of―negative samples‖in analyzing bridge state, a bridge state recognition model based on support vector machine is proposed in this paper. This model, by making use of the chaotic indicators, will provide technical support for the long-term prediction of the safety state of bridges in service.(4) A bridge state prediction model is set up by using multi-layer recursive BP neural network. The optimum embeds dimensions, as the steps of multi-layer recursive BP neural network, are taken from the time series of the bridge monitoring information by using chaotic time series and reconstructed phase space theory., Using chaotic time series to reconstruct phase space and applying multi-layer recursive BP neural network to predict bridge health facilitates further estimation and prediction of bridge safety condition.(5) A new method for bridge state estimation is put forward by using time-delayed transfer entropy and mutual information. An analysis of the monitoring information from Mashangxi Bridge in Chongqing shows that, the mechanical correlation between different monitoring stations on the bridge agrees well with those from the monitoring information. Therefore, the bridge state can be estimated by using time-delayed transfer entropy and mutual information.(6) The chaotic time series analysis of the information from different monitoring stations at different times from Mashangxi Bridge indicates that, all the maximum Lyapunov exponents exceed 0 and the number of correlation dimension is almost 3.8(non-integer). Therefore, Mashangxi Bridge is in chaos, and the chaotic indicators develop in a uniform and steady way.This research on the bridge state estimation using non-linear chaotic dynamics is a new way of estimating bridge state, and the results will provide a reference for the like researches in the future.