Equivalent force-based Kalman-type filter and reduced system function for full-field response reconstruction

Abstract In structural health monitoring, full-field response sensing and monitoring are essential to establish a digital twin model. However, directly measuring all required structural loads and responses is costly and impractical. Simultaneous estimations of structural loads and responses are consequently developed, which is, however, an ill-posed problem. This paper aims to address the ill-posed nature of the simultaneous estimation of load and response from insufficient observations, which is realized by reducing the dimension of unknown loads via principal component analysis to derive the equivalent system functions. First, a set of force basis vectors is calculated from the structural impulse responses in a single time step to replace the original load vector. Subsequently, a reduced equivalent system model is obtained with sufficient controllability on the original system model. Then, the equivalent loads and full-field responses can be simultaneously estimated by the Kalman-type joint input-state estimation filters. The proposed technique is applied to a numerical beam model and a real long-span sea-crossing bridge under operational traffic and typhoon loads. Results show that the full-field responses to arbitrarily distributed and unknown loads are correctly reconstructed from noisy data.