A recursive nonlinear virtual sensing method for joint input-state-parameter estimation of partially measured structures

This paper proposes a novel nonlinear filter for system identification, enabling online joint input-state parameter estimation in time-varying structural systems. The filter can be universally applied to systems with and without direct feedthrough, as well as systems with a rank-deficient feedforward. Unlike Kalman-type methods, the proposed method does not rely on prior statistical information or fictitious evolution models for inputs. As opposed to the existing nonlinear Minimum-Variance Unbiased (MVU) methods, this filter handles a different system inversion problem, leading to a distinct mathematical formulation and rank condition requirement for the feedforward matrix. As such, the proposed method not only enables universal applicability for various systems concerning the rank condition constraints but also achieves higher estimation quality compared to existing nonlinear MVU filters due to a well-conditioned system inversion. A comparative study is carried out to assess the universal applicability of the proposed method dealing with different sensor networks and different time-varying damage scenarios. The proposed method is also shown to be capable of tackling a rank-deficient example to which other nonlinear MVU methods are not applicable. Moreover, experimental assessment is conducted to evaluate the robustness in real conditions. The numerical and experimental studies show that the proposed method achieves higher estimation quality and enhanced numerical stability compared to other nonlinear MVU methods.