Structural dynamic response reconstruction with multi-type sensors, unknown input, and rank deficient feedthrough matrix

This paper presents a novel algorithm that reconstructs structural responses under unknown inputs and rank-deficient feedthrough matrix conditions. The algorithm eliminates one of the major constraints of existing filters (i.e., the requirement of a full-rank matrix), allowing the number of accelerometers required in real applications to be reduced. A unified linear input and state estimator (ULISE) is introduced into structural response reconstruction for the first time. The ULISE requires no prior assumptions on the time histories of unknown inputs. The direct feedthrough matrix can either be rank-deficient or full-column-rank. Moreover, the ULISE eliminates the time delay problem in the input reconstruction based on displacement measurement. The effectiveness of the proposed ULISE-based structural response reconstruction algorithm is evaluated and validated through numerical simulations and laboratory tests. The proposed algorithm achieves reasonable joint input–state estimation even under rank-deficient feedthrough matrix conditions and can be regarded as a generalized and improved version of the existing response reconstruction filters.