Co-rotational Reduced Order Kalman Filter Finite Element Method for the Real-time Implementation of Large-scale Structural Models

Abstract

The real-time implementation of large-scale structural models without sacrificing their physical realism is challenging. This paper introduces a conceptual framework named the Co-rotational Reduced Order Kalman Filter Finite Element Method (CROKF-FEM) for the realistic linear elastic analysis of large-scale structures in real-time. The standard linear finite element method (FEM) is employed for high-precision deformation modeling, and element matrices are pre-computed in the space domain. To avoid the inflated elements of standard linear FEM due to large rotation, a co-rotational formulation is devised. Then, the system is discretized in the time domain using the Wilson- θ implicit integration scheme and a further state-space model is developed. Subsequently, a reduced-order model is constructed using the balanced truncation method. Finally, a Kalman filter algorithm is created on the reduced model for online estimation. This approach preserves all the benefits of traditional linear FEM with a similar deformation accuracy while achieving significant real-time performance.