Output-only complete mode shape identification of bridges using a limited number of sensors

Abstract

Mode shape is an important structural property that needs be identified in structural condition monitoring and analysis. The conventional modal identification methods usually can only provide sparse and low-spatial resolution mode shape measurements because of the limited number of sensors, which could seriously affect the effectiveness and accuracy of the mode shape-based structural damage detection methods. In this paper, a new output-only method is proposed for identifying the complete mode shapes for beam-like bridge structures under a moving load using a limited number of sensors based on proper orthogonal decomposition (POD). Firstly, the physical interpretation of the POD of the responses of a beam-like bridge under a moving load is derived. It is proved that each component of the POD consists of a mode shape of the bridge and a dynamic component with the frequency corresponding to this mode. The contribution ratio of the component in the POD gives an excellent estimation of the modal contribution ratio (CR) in terms of the vibration energy. The mode shape can be identified by filtering out the dynamic information in each component of the POD. The identified mode shapes have a high spatial resolution that they can be regarded as the complete mode shapes of the bridge. To demonstrate the proposed method, a beam bridge with different boundary conditions is numerically modelled and a simply supported beam bridge model is tested in the lab. Both the numerical and experimental results demonstrate that this method can successfully identify the complete mode shapes with high resolution and modal contribution ratios with a limited number of sensors. This method breaks through the challenge on the requirement of a large number of sensors in vibration tests for full mode shape identifications in traditional methods.