Residual-Based Identification of the Input Forces Using Gaussian Process Discrepancy Model

This chapter presents a novel approach for system identification in the presence of incomplete output information available and with limited knowledge of the input forces. The correct identification of the dynamic system is a challenging task, and it becomes more problematic when the input information is unavailable. To overcome this limitation, this work integrates a set of system measurements with computational model responses, enabling recovery of dynamic system states and subsequent analysis of the model through an inverse problem formulation based on Bayesian model updating. The difference between the computational model response and the measurements is described with Gaussian Process discrepancy model that uses time-based kernel covariance function for the inference on model parameters. Such an assumption mitigates the effect of the measurement noise on parameter estimation, leading to improved fidelity in parameter estimation and uncertainty quantification. To find the forces applied to the system, an optimization strategy is used that aims to minimize the residuals of the input forces at the locations where the knowledge of forces is available. The inputs are identified using a combination of the known system measurement with pseudo-measurements, followed by an inference on the structural model parameters. The proposed technique shows promising results, offering a methodology for input and parameter estimation. The practical implications of the work include its potential application in real-world scenarios requiring consistent system identification and force estimation.