Multi-metric strain estimation at unmeasured locations of plate structures using augmented Kalman filter

Abstract

A gusset plate is a structural element that is commonly used to provide moment connections between steel members. Despite their importance, the performance of gusset plates in field structures can be poorly understood making them susceptible to failure. A well-known example is the catastrophic collapse of the I-35W Bridge in Minneapolis, MN on August 1, 2007 caused by a gusset plate failure. To prevent this type of failure, it is necessary to better predict and understand the stress and strain distribution in a plate element during field conditions. This work approaches the problem by using a numerical model combined with a linear recursive state estimation algorithm, known as the Kalman Filter, to update the model-based prediction with real time measurements taken on the structure. The finite element model was developed using the Mindlin plate theory which incorporates bending and shear deformations of the plate in the out-of-plane direction. The strain responses at arbitrary locations are estimated throughout the plate, including unmeasured locations, using limited sensor information and in the presence of noise and model errors. The results show how the different combinations of sensor data impact strain estimation accuracy under various loading conditions. The different combinations considered are: strain only, acceleration only, and acceleration and strain. The numerical studies demonstrate that the most accurate estimations are provided with the multi-metric combination of acceleration and strain. This opens future paths of development for force estimation, finding stress concentrations and buckling prediction in plate elements and potential expansion to shell elements.