Scaled Spherical Simplex Filter and State-Space Damage-Plasticity Finite-Element Model for Computationally Efficient System Identification

Abstract

This work presents an efficient online system identification approach by integrating a reduced sigma points–based filter with a high-fidelity mechanics-based state-space hysteretic finite-element modeling framework. The efficacy and computational efficiency of any sampling/sigma points–based nonlinear filtering process are conditional on the number of sigma/sample points required by the filter at each time step to quantify statistical properties of the involved quantities, as well as on the accuracy and computational cost of the underlying system model. A scaled spherical simplex filter (S3F) with a significantly decreased n+2 sigma points set size is thus presented that is able to achieve similar robustness and accuracy as the state-of-the-art 2n+1 sigma points unscented Kalman filter (UKF) for an n-dimensional state-space, yet with approximately 50% less computational requirements. The filtering framework is integrated with a recently developed fully parametrized damage plasticity–consistent hysteretic finite-element modeling approach that is able to account for distributed plasticity, axial-moment–shear interactions, and degradations in one unified formulation by employing the concepts of continuum damage mechanics and classical multiaxial plasticity. In the presented hysteretic model, the system matrices are constant and do not require updating throughout the analysis, whereas the degradations and inelasticity are updated through element-level hysteretic evolution equations in the form of resultant stress–strain laws. Overall, the system can be presented in a state-space form and can be solved with any first-order ordinary differential equation solver, without any linearization or gradient requirements, rendering the high-fidelity formulation robust and computationally efficient and enabling ideal compatibility in terms of computational implementation with the filtering methodology for online joint state-parameter identification.