Performance of equilibrium-based system identification algorithms with incomplete state data

Time-domain parametric system identification algorithms are a main staple of structural health-monitoring applications. In this study, we consider a class of such algorithms whereby a time-invariant system is parameterized through the use of a spatially discretized model, and the optimal values of the system parameters are obtained by minimizing the norm of an equilibrium-error function. The general form of these error functions is the difference between the known external forces and the internal forces of the discrete model predicted through the use of an iterative set of system parameters and the state data measured in the time-domain. The complete set of state data consists of displacement, velocity and acceleration time-histories. For the aforementioned class of time-domain system identification algorithms in existing literature, this complete set of state data is required as input. Therefore, the displacement and velocity time-histories need to be obtained, either by numerical integration of measured acceleration data, or by their direct and independent measurements with appropriate sensors. Integration of acceleration data introduces baseline drifts and numerical errors due to convolution of noise in measurements; whereas, the use of independently measured displacements and velocities are plagued by imperfect time-synchronization of state data as well as the mismatch of the optimal frequency and amplitude ranges of their respective sensors. The aforementioned class of system identification algorithms, which require complete state data, are highly sensitive to such errors, and as a result, their use in practical applications are severely limited. In this study, we present a rational variant of the aforementioned class of algorithms that requires only acceleration data. We investigate the accuracy and the robustness of this novel algorithm, and compare its performance to the complete-state algorithm through numerical simulations.