A direct approach for full-field state-parameter estimation from fusion of noncollocated multi-rate sensor data using UKF-based algorithms

Heterogeneous sensor setups may entail measurements recorded at varying sampling frequencies, commonly known as multi-rate data. For system identification and state estimation with such data, existing studies mostly focus on data fusion algorithms that utilize acceleration measurements, with collocated measurements of other types at lower sampling frequencies, to estimate the displacement at the collocated location with the sampling frequency of the acceleration measurements. The obtained displacements, along with the available acceleration measurements, are then utilized for system identification. This paper introduces a direct and straightforward methodology aimed at estimating the states (i.e., displacements and velocities) along with the unknown structural parameters from fused multi-rate data through Unscented Kalman Filter (UKF) based algorithms with a modification during measurement update. By utilizing all available measurements at any time instant, which can differ due to the multi-rate nature, and by modifying the non-linear measurement equation of the system accordingly at the considered time instant, the UKF framework is suitably tailored for direct applications with multi-rate measurements. The approach is demonstrated with a variety of numerical and laboratory-scale experiments, including fusion of higher sampling frequency acceleration data with lower sampling frequency displacement, axial strain, or bending strain data. The results show that the approach is successful in accurately estimating full-field states and parameters. The state estimates compare well with those obtained using existing data fusion algorithms. The advantages of the approach lie in not requiring collocated sensing, in its generalizability for different types of measurements, in its simplicity and ease of implementation, and in achieving both the state and parameter estimates simultaneously.