Comparison of Constrained Unscented and Cubature Kalman Filters for Nonlinear System Parameter Identification

Abstract

Accurate and efficient parameter identification along with uncertainty quantification in nonlinear systems is crucial for enabling practical and reliable structural health monitoring and digital twinning. This paper presents a novel procedure for estimating parameters that combines Bayesian filters and truncated probability density functions (PDFs). To simplify the state-space equations, only model parameters are incorporated in the state equations, whereas the measurement equations are implicitly considered in the state vector of displacement and velocity. This simplification enables the unified implementation of three different types of Bayesian filters: the unscented Kalman filter, third-degree cubature Kalman filter, and fifth-degree cubature Kalman filter. Consequently, it facilitates the seamless integration of complex numerical models into the parameter identification procedure. To improve the robustness of the proposed method, the truncated PDF is employed to enforce constraints that prevent the covariance matrix from becoming singular. The applicability and accuracy of the proposed method were evaluated using a 10-story numerical example and a 12-story shake-table model. Based on the selected parameters for tuning, the estimated results are consistent with both the simulated and experimental data, demonstrating that the Bayesian filters can estimate parameters and quantify their uncertainties. Comparison of the estimation accuracy, computational cost, and efficiency index among the three types of Bayesian filters reveals that the fifth-degree cubature Kalman filter has the highest accuracy. When dealing with less complex structural models, the unscented Kalman filter demonstrates superior efficiency. These findings are useful for finite-element model updating and assessment of structural performance.